Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let G be the group of reduced residue classes modulo 21. Hence, or otherwise, construct a table showing the values of all the real-valued, and one of the complex-valued, Dirichlet characters modulo 21. (In your table, use w for ei/3.) Solution n 1 2 4 5 8 10 11 13 16 17 x1(n) 1 X2(n) 1 −1 1 1 1 1 1 1 1 1 1 1 X5(n) 1 X6(n) 1 w2 X7(n) 1 -W w X8(n) 1 -w2 X9(n) 1 X10(n) 1 X11 (n) w2 3- 1 X12(n) 1 -w2 X3(n) 1 1 1 X4(n) 1 -1 1 ω w2 -W w2 है ६ है ६ है ६ है ६ नाकामा 1 1 + 3 3 3 3 3 3 3 3 7-77--77--7 1 - 7 7 3 × 3 × 3333 -w2 -1 -1 1 1 - 7 3 3 3 3 3 3 3 3 w2 77-7--7-77- 1 1 1 1-773 разраза 2-17-33 3 3 3 3 3 3 -W w2 w2 -W -w2 w2 w 31 ६ है ६ है ६ है ६ है 19 20 1 - - 7 7 - - 1 1 1 1 1 זזזז

Let G be the group of reduced residue classes modulo 21. Hence, or otherwise, construct a table showing the values of all the real-valued, and one of the complex-valued, Dirichlet characters modulo 21. (In your table, use w for ei/3.) Solution n 1 2 4 5 8 10 11 13 16 17 x1(n) 1 X2(n) 1 −1 1 1 1 1 1 1 1 1 1 1 X5(n) 1 X6(n) 1 w2 X7(n) 1 -W w X8(n) 1 -w2 X9(n) 1 X10(n) 1 X11 (n) w2 3- 1 X12(n) 1 -w2 X3(n) 1 1 1 X4(n) 1 -1 1 ω w2 -W w2 है ६ है ६ है ६ है ६ नाकामा 1 1 + 3 3 3 3 3 3 3 3 7-77--77--7 1 - 7 7 3 × 3 × 3333 -w2 -1 -1 1 1 - 7 3 3 3 3 3 3 3 3 w2 77-7--7-77- 1 1 1 1-773 разраза 2-17-33 3 3 3 3 3 3 -W w2 w2 -W -w2 w2 w 31 ६ है ६ है ६ है ६ है 19 20 1 - - 7 7 - - 1 1 1 1 1 זזזז

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.5: Normal Subgroups
Problem 25E
See similar textbooks
icon
Related questions
Question
how to construct the following same table?
Let G be the group of reduced residue classes modulo 21. Hence, or otherwise, construct a table showing the values of all the real-valued, and one of the complex-valued, Dirichlet characters modulo 21. (In your table, use w for ei/3.) Solution n 1 2 4 5 8 10 11 13 16 17 x1(n) 1 X2(n) 1 −1 1 1 1 1 1 1 1 1 1 1 X5(n) 1 X6(n) 1 w2 X7(n) 1 -W w X8(n) 1 -w2 X9(n) 1 X10(n) 1 X11 (n) w2 3- 1 X12(n) 1 -w2 X3(n) 1 1 1 X4(n) 1 -1 1 ω w2 -W w2 है ६ है ६ है ६ है ६ नाकामा 1 1 + 3 3 3 3 3 3 3 3 7-77--77--7 1 - 7 7 3 × 3 × 3333 -w2 -1 -1 1 1 - 7 3 3 3 3 3 3 3 3 w2 77-7--7-77- 1 1 1 1-773 разраза 2-17-33 3 3 3 3 3 3 -W w2 w2 -W -w2 w2 w 31 ६ है ६ है ६ है ६ है 19 20 1 - - 7 7 - - 1 1 1 1 1 זזזז
Transcribed Image Text:Let G be the group of reduced residue classes modulo 21. Hence, or otherwise, construct a table showing the values of all the real-valued, and one of the complex-valued, Dirichlet characters modulo 21. (In your table, use w for ei/3.) Solution n 1 2 4 5 8 10 11 13 16 17 x1(n) 1 X2(n) 1 −1 1 1 1 1 1 1 1 1 1 1 X5(n) 1 X6(n) 1 w2 X7(n) 1 -W w X8(n) 1 -w2 X9(n) 1 X10(n) 1 X11 (n) w2 3- 1 X12(n) 1 -w2 X3(n) 1 1 1 X4(n) 1 -1 1 ω w2 -W w2 है ६ है ६ है ६ है ६ नाकामा 1 1 + 3 3 3 3 3 3 3 3 7-77--77--7 1 - 7 7 3 × 3 × 3333 -w2 -1 -1 1 1 - 7 3 3 3 3 3 3 3 3 w2 77-7--7-77- 1 1 1 1-773 разраза 2-17-33 3 3 3 3 3 3 -W w2 w2 -W -w2 w2 w 31 ६ है ६ है ६ है ६ है 19 20 1 - - 7 7 - - 1 1 1 1 1 זזזז
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS