Group of Dirichlet characters of modulus 400

• Modulus: $400$
• Structure: $C_{2}\times C_{4}\times C_{20}$
• Order: $160$

Character group

Order	=	160
Structure	=	$C_{2}\times C_{4}\times C_{20}$
Generators	=	$\chi_{400}(351,\cdot)$, $\chi_{400}(101,\cdot)$, $\chi_{400}(177,\cdot)$

First 32 of 160 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{400}(1,\cdot)$	400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{400}(3,\cdot)$	400.bd	20	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{400}(7,\cdot)$	400.o	4	no	$1$	$1$	$-i$	$-i$	$-1$	$1$	$i$	$i$	$-1$	$-1$	$i$	$i$
$\chi_{400}(9,\cdot)$	400.w	10	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{400}(11,\cdot)$	400.bk	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{400}(13,\cdot)$	400.bn	20	yes	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{400}(17,\cdot)$	400.bg	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{400}(19,\cdot)$	400.bf	20	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{400}(21,\cdot)$	400.be	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{400}(23,\cdot)$	400.bh	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{400}(27,\cdot)$	400.bd	20	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{400}(29,\cdot)$	400.bl	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{400}(31,\cdot)$	400.z	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{400}(33,\cdot)$	400.bg	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{400}(37,\cdot)$	400.bn	20	yes	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{400}(39,\cdot)$	400.ba	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{400}(41,\cdot)$	400.bb	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{400}(43,\cdot)$	400.j	4	no	$1$	$1$	$-1$	$-i$	$1$	$-i$	$1$	$-i$	$-i$	$i$	$i$	$-1$
$\chi_{400}(47,\cdot)$	400.bi	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{400}(49,\cdot)$	400.c	2	no	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{400}(51,\cdot)$	400.r	4	no	$-1$	$1$	$-i$	$1$	$-1$	$i$	$i$	$1$	$-i$	$-i$	$1$	$i$
$\chi_{400}(53,\cdot)$	400.bc	20	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{400}(57,\cdot)$	400.m	4	no	$-1$	$1$	$i$	$i$	$-1$	$-1$	$i$	$i$	$1$	$-1$	$-i$	$-i$
$\chi_{400}(59,\cdot)$	400.bf	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{400}(61,\cdot)$	400.be	20	yes	$1$	$1$	$e\left(\frac{17}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{400}(63,\cdot)$	400.bi	20	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{400}(67,\cdot)$	400.bm	20	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{400}(69,\cdot)$	400.bl	20	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{400}(71,\cdot)$	400.v	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{400}(73,\cdot)$	400.bj	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{400}(77,\cdot)$	400.bc	20	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{400}(79,\cdot)$	400.x	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$

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