LMFDB - Group of Dirichlet characters of modulus 225

Show commands: PariGP / SageMath

sage: H = DirichletGroup(225)

pari: g = idealstar(,225,2)

Character group

sage: G.order() pari: g.no
Order	=	120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{225}(101,\cdot)$, $\chi_{225}(127,\cdot)$

First 32 of 120 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{225}(1,\cdot)$	225.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{225}(2,\cdot)$	225.w	60	yes	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{225}(4,\cdot)$	225.u	30	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{225}(7,\cdot)$	225.o	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-1$
$\chi_{225}(8,\cdot)$	225.s	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{225}(11,\cdot)$	225.t	30	yes	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{225}(13,\cdot)$	225.x	60	yes	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{225}(14,\cdot)$	225.v	30	yes	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{225}(16,\cdot)$	225.q	15	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{225}(17,\cdot)$	225.s	20	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{225}(19,\cdot)$	225.m	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{225}(22,\cdot)$	225.x	60	yes	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{225}(23,\cdot)$	225.w	60	yes	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{225}(26,\cdot)$	225.c	2	no	$-1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$-1$	$1$
$\chi_{225}(28,\cdot)$	225.r	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{225}(29,\cdot)$	225.v	30	yes	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{225}(31,\cdot)$	225.q	15	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{225}(32,\cdot)$	225.p	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$-1$
$\chi_{225}(34,\cdot)$	225.u	30	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{225}(37,\cdot)$	225.r	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{225}(38,\cdot)$	225.w	60	yes	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{225}(41,\cdot)$	225.t	30	yes	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{225}(43,\cdot)$	225.o	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$-1$
$\chi_{225}(44,\cdot)$	225.l	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{225}(46,\cdot)$	225.h	5	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{225}(47,\cdot)$	225.w	60	yes	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{225}(49,\cdot)$	225.k	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$
$\chi_{225}(52,\cdot)$	225.x	60	yes	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{225}(53,\cdot)$	225.s	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{225}(56,\cdot)$	225.t	30	yes	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{225}(58,\cdot)$	225.x	60	yes	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{225}(59,\cdot)$	225.v	30	yes	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$

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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 $\F_{q}$

Modulus	$225$
Structure	\(C_{2}\times C_{60}\)
Order	$120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{225}(1,\cdot)\)	225.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{225}(2,\cdot)\)	225.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{225}(4,\cdot)\)	225.u	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{225}(7,\cdot)\)	225.o	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-1\)
\(\chi_{225}(8,\cdot)\)	225.s	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{225}(11,\cdot)\)	225.t	30	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{225}(13,\cdot)\)	225.x	60	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{225}(14,\cdot)\)	225.v	30	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{225}(16,\cdot)\)	225.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{225}(17,\cdot)\)	225.s	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{225}(19,\cdot)\)	225.m	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{225}(22,\cdot)\)	225.x	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{225}(23,\cdot)\)	225.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{225}(26,\cdot)\)	225.c	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{225}(28,\cdot)\)	225.r	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{225}(29,\cdot)\)	225.v	30	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{225}(31,\cdot)\)	225.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{225}(32,\cdot)\)	225.p	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(-1\)
\(\chi_{225}(34,\cdot)\)	225.u	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{225}(37,\cdot)\)	225.r	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{225}(38,\cdot)\)	225.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{225}(41,\cdot)\)	225.t	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{225}(43,\cdot)\)	225.o	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(-1\)
\(\chi_{225}(44,\cdot)\)	225.l	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{225}(46,\cdot)\)	225.h	5	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{225}(47,\cdot)\)	225.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{225}(49,\cdot)\)	225.k	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{225}(52,\cdot)\)	225.x	60	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{225}(53,\cdot)\)	225.s	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{225}(56,\cdot)\)	225.t	30	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{225}(58,\cdot)\)	225.x	60	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{225}(59,\cdot)\)	225.v	30	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)

Introduction

L-functions

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First 32 of 120 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.