LMFDB - Group of Dirichlet characters of modulus 1350

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1350)

pari: g = idealstar(,1350,2)

Character group

sage: G.order() pari: g.no
Order	=	360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1350}(1001,\cdot)$, $\chi_{1350}(1027,\cdot)$

First 32 of 360 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{1350}(1,\cdot)$	1350.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1350}(7,\cdot)$	1350.ba	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1350}(11,\cdot)$	1350.bg	90	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{1350}(13,\cdot)$	1350.bj	180	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{1350}(17,\cdot)$	1350.bd	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{1350}(19,\cdot)$	1350.z	30	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1350}(23,\cdot)$	1350.bi	180	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{1350}(29,\cdot)$	1350.bh	90	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{1350}(31,\cdot)$	1350.bc	45	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{1350}(37,\cdot)$	1350.be	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1350}(41,\cdot)$	1350.bg	90	no	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{1350}(43,\cdot)$	1350.ba	36	no	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1350}(47,\cdot)$	1350.bi	180	no	$1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{1350}(49,\cdot)$	1350.u	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1350}(53,\cdot)$	1350.w	20	no	$1$	$1$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1350}(59,\cdot)$	1350.bh	90	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{1350}(61,\cdot)$	1350.bc	45	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{1350}(67,\cdot)$	1350.bj	180	no	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{1350}(71,\cdot)$	1350.x	30	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{1350}(73,\cdot)$	1350.be	60	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1350}(77,\cdot)$	1350.bi	180	no	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{1350}(79,\cdot)$	1350.bf	90	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{1350}(83,\cdot)$	1350.bi	180	no	$1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{1350}(89,\cdot)$	1350.y	30	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{1350}(91,\cdot)$	1350.r	15	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1350}(97,\cdot)$	1350.bj	180	no	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{1350}(101,\cdot)$	1350.t	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{1350}(103,\cdot)$	1350.bj	180	no	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{1350}(107,\cdot)$	1350.f	4	no	$1$	$1$	$i$	$-1$	$-i$	$-i$	$-1$	$i$	$1$	$1$	$i$	$-1$
$\chi_{1350}(109,\cdot)$	1350.m	10	no	$1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1350}(113,\cdot)$	1350.bi	180	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{1350}(119,\cdot)$	1350.bh	90	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{79}{90}\right)$

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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	$1350$
Structure	\(C_{2}\times C_{180}\)
Order	$360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{1350}(1,\cdot)\)	1350.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1350}(7,\cdot)\)	1350.ba	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1350}(11,\cdot)\)	1350.bg	90	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{1350}(13,\cdot)\)	1350.bj	180	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{1350}(17,\cdot)\)	1350.bd	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{1350}(19,\cdot)\)	1350.z	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1350}(23,\cdot)\)	1350.bi	180	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{1350}(29,\cdot)\)	1350.bh	90	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{1350}(31,\cdot)\)	1350.bc	45	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{1350}(37,\cdot)\)	1350.be	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1350}(41,\cdot)\)	1350.bg	90	no	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{1350}(43,\cdot)\)	1350.ba	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1350}(47,\cdot)\)	1350.bi	180	no	\(1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)
\(\chi_{1350}(49,\cdot)\)	1350.u	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1350}(53,\cdot)\)	1350.w	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1350}(59,\cdot)\)	1350.bh	90	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{1350}(61,\cdot)\)	1350.bc	45	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{1350}(67,\cdot)\)	1350.bj	180	no	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{1350}(71,\cdot)\)	1350.x	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{1350}(73,\cdot)\)	1350.be	60	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1350}(77,\cdot)\)	1350.bi	180	no	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{1350}(79,\cdot)\)	1350.bf	90	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{1350}(83,\cdot)\)	1350.bi	180	no	\(1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{49}{90}\right)\)
\(\chi_{1350}(89,\cdot)\)	1350.y	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{1350}(91,\cdot)\)	1350.r	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1350}(97,\cdot)\)	1350.bj	180	no	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{1350}(101,\cdot)\)	1350.t	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{1350}(103,\cdot)\)	1350.bj	180	no	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{1350}(107,\cdot)\)	1350.f	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{1350}(109,\cdot)\)	1350.m	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1350}(113,\cdot)\)	1350.bi	180	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{1350}(119,\cdot)\)	1350.bh	90	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{79}{90}\right)\)

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L-functions

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