LMFDB - Group of Dirichlet characters of modulus 1740

sage:H = DirichletGroup(1740)

pari:g = idealstar(,1740,2)

Character group

sage:G.order() pari:g.no
Order	=	448
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{28}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1740}(871,\cdot)$, $\chi_{1740}(581,\cdot)$, $\chi_{1740}(697,\cdot)$, $\chi_{1740}(901,\cdot)$

First 32 of 448 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$31$	$37$	$41$	$43$
$\chi_{1740}(1,\cdot)$	1740.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1740}(7,\cdot)$	1740.cv	28	no	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{28}\right)$	$i$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{15}{28}\right)$	$1$	$e\left(\frac{23}{28}\right)$
$\chi_{1740}(11,\cdot)$	1740.da	28	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$i$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$	$-i$	$e\left(\frac{3}{28}\right)$
$\chi_{1740}(13,\cdot)$	1740.cu	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{28}\right)$	$i$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{17}{28}\right)$
$\chi_{1740}(17,\cdot)$	1740.y	4	no	$-1$	$1$	$i$	$i$	$i$	$-1$	$i$	$i$	$-i$	$-1$	$-i$	$-1$
$\chi_{1740}(19,\cdot)$	1740.ce	28	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{7}\right)$	$i$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{28}\right)$	$i$	$e\left(\frac{5}{28}\right)$
$\chi_{1740}(23,\cdot)$	1740.ci	28	yes	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{28}\right)$	$i$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{25}{28}\right)$	$-1$	$e\left(\frac{1}{28}\right)$
$\chi_{1740}(31,\cdot)$	1740.db	28	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$-i$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{28}\right)$	$i$	$e\left(\frac{27}{28}\right)$
$\chi_{1740}(37,\cdot)$	1740.cm	28	no	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{4}{7}\right)$	$-i$	$e\left(\frac{1}{7}\right)$
$\chi_{1740}(41,\cdot)$	1740.bk	4	no	$1$	$1$	$1$	$-i$	$-1$	$-i$	$i$	$-1$	$i$	$-i$	$i$	$i$
$\chi_{1740}(43,\cdot)$	1740.cn	28	no	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{28}\right)$	$-1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{7}\right)$	$i$	$e\left(\frac{11}{14}\right)$
$\chi_{1740}(47,\cdot)$	1740.cr	28	yes	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{23}{28}\right)$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{7}\right)$	$i$	$e\left(\frac{5}{14}\right)$
$\chi_{1740}(49,\cdot)$	1740.by	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{9}{14}\right)$
$\chi_{1740}(53,\cdot)$	1740.cw	28	no	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{28}\right)$	$i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{28}\right)$	$-1$	$e\left(\frac{27}{28}\right)$
$\chi_{1740}(59,\cdot)$	1740.n	2	no	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$1$
$\chi_{1740}(61,\cdot)$	1740.cg	28	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$-i$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{9}{28}\right)$
$\chi_{1740}(67,\cdot)$	1740.ck	28	no	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{28}\right)$	$-i$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{25}{28}\right)$
$\chi_{1740}(71,\cdot)$	1740.ca	14	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{6}{7}\right)$
$\chi_{1740}(73,\cdot)$	1740.ct	28	no	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{14}\right)$	$-i$	$e\left(\frac{11}{14}\right)$
$\chi_{1740}(77,\cdot)$	1740.cp	28	no	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{15}{28}\right)$	$-1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{14}\right)$	$-i$	$e\left(\frac{13}{14}\right)$
$\chi_{1740}(79,\cdot)$	1740.ce	28	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{7}\right)$	$i$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{28}\right)$	$i$	$e\left(\frac{25}{28}\right)$
$\chi_{1740}(83,\cdot)$	1740.ci	28	yes	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{28}\right)$	$-1$	$e\left(\frac{5}{28}\right)$
$\chi_{1740}(89,\cdot)$	1740.cy	28	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{7}\right)$	$-i$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{28}\right)$	$-i$	$e\left(\frac{27}{28}\right)$
$\chi_{1740}(91,\cdot)$	1740.bw	14	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$-1$	$e\left(\frac{3}{7}\right)$
$\chi_{1740}(97,\cdot)$	1740.cm	28	no	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{15}{28}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{7}\right)$	$-i$	$e\left(\frac{3}{7}\right)$
$\chi_{1740}(101,\cdot)$	1740.ch	28	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{14}\right)$	$i$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{28}\right)$	$-i$	$e\left(\frac{1}{28}\right)$
$\chi_{1740}(103,\cdot)$	1740.cv	28	no	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{28}\right)$	$-i$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{28}\right)$	$1$	$e\left(\frac{17}{28}\right)$
$\chi_{1740}(107,\cdot)$	1740.ci	28	yes	$-1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{28}\right)$	$-i$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{28}\right)$	$-1$	$e\left(\frac{11}{28}\right)$
$\chi_{1740}(109,\cdot)$	1740.cd	14	no	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{4}{7}\right)$
$\chi_{1740}(113,\cdot)$	1740.cp	28	no	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{28}\right)$	$-1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{14}\right)$	$i$	$e\left(\frac{1}{14}\right)$
$\chi_{1740}(119,\cdot)$	1740.cf	28	yes	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{7}\right)$	$-i$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{28}\right)$	$-i$	$e\left(\frac{9}{28}\right)$
$\chi_{1740}(121,\cdot)$	1740.bt	14	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$-1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$-1$	$e\left(\frac{3}{14}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$1740$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{28}\)
Order	$448$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{1740}(1,\cdot)\)	1740.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1740}(7,\cdot)\)	1740.cv	28	no	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(i\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(1\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{1740}(11,\cdot)\)	1740.da	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(i\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-i\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{1740}(13,\cdot)\)	1740.cu	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(i\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{1740}(17,\cdot)\)	1740.y	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{1740}(19,\cdot)\)	1740.ce	28	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(i\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(i\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{1740}(23,\cdot)\)	1740.ci	28	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(i\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(-1\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{1740}(31,\cdot)\)	1740.db	28	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-i\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(i\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{1740}(37,\cdot)\)	1740.cm	28	no	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(-i\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{1740}(41,\cdot)\)	1740.bk	4	no	\(1\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(i\)
\(\chi_{1740}(43,\cdot)\)	1740.cn	28	no	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(i\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{1740}(47,\cdot)\)	1740.cr	28	yes	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{1740}(49,\cdot)\)	1740.by	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{1740}(53,\cdot)\)	1740.cw	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{1740}(59,\cdot)\)	1740.n	2	no	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{1740}(61,\cdot)\)	1740.cg	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-i\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1740}(67,\cdot)\)	1740.ck	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-i\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{1740}(71,\cdot)\)	1740.ca	14	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1740}(73,\cdot)\)	1740.ct	28	no	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-i\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{1740}(77,\cdot)\)	1740.cp	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(-1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-i\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{1740}(79,\cdot)\)	1740.ce	28	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(i\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(i\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{1740}(83,\cdot)\)	1740.ci	28	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{1740}(89,\cdot)\)	1740.cy	28	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-i\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-i\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{1740}(91,\cdot)\)	1740.bw	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1740}(97,\cdot)\)	1740.cm	28	no	\(1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-i\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1740}(101,\cdot)\)	1740.ch	28	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(i\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(-i\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{1740}(103,\cdot)\)	1740.cv	28	no	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-i\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(1\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{1740}(107,\cdot)\)	1740.ci	28	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-i\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-1\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{1740}(109,\cdot)\)	1740.cd	14	no	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{1740}(113,\cdot)\)	1740.cp	28	no	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(-1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{1740}(119,\cdot)\)	1740.cf	28	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-i\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-i\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1740}(121,\cdot)\)	1740.bt	14	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)	\(e\left(\frac{3}{14}\right)\)

Introduction

L-functions

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Character group

First 32 of 448 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.