LMFDB - Group of Dirichlet characters of modulus 675

Show commands: PariGP / SageMath

sage: H = DirichletGroup(675)

pari: g = idealstar(,675,2)

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	=	$\chi_{675}(326,\cdot)$, $\chi_{675}(352,\cdot)$

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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{675}(1,\cdot)$	675.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{675}(2,\cdot)$	675.bi	180	yes	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{675}(4,\cdot)$	675.bg	90	yes	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{675}(7,\cdot)$	675.bb	36	no	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{675}(8,\cdot)$	675.bd	60	no	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{675}(11,\cdot)$	675.bf	90	yes	$-1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{675}(13,\cdot)$	675.bj	180	yes	$-1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{675}(14,\cdot)$	675.bh	90	yes	$-1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{675}(16,\cdot)$	675.bc	45	yes	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{675}(17,\cdot)$	675.bd	60	no	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{675}(19,\cdot)$	675.y	30	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{675}(22,\cdot)$	675.bj	180	yes	$-1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{675}(23,\cdot)$	675.bi	180	yes	$1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{675}(26,\cdot)$	675.c	2	no	$-1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$-1$	$1$
$\chi_{675}(28,\cdot)$	675.v	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{675}(29,\cdot)$	675.bh	90	yes	$-1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{675}(31,\cdot)$	675.bc	45	yes	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{675}(32,\cdot)$	675.ba	36	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{675}(34,\cdot)$	675.bg	90	yes	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{675}(37,\cdot)$	675.be	60	no	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{675}(38,\cdot)$	675.bi	180	yes	$1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{675}(41,\cdot)$	675.bf	90	yes	$-1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{675}(43,\cdot)$	675.bb	36	no	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{675}(44,\cdot)$	675.z	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{675}(46,\cdot)$	675.r	15	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{675}(47,\cdot)$	675.bi	180	yes	$1$	$1$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{675}(49,\cdot)$	675.u	18	no	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{675}(52,\cdot)$	675.bj	180	yes	$-1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{675}(53,\cdot)$	675.w	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{675}(56,\cdot)$	675.bf	90	yes	$-1$	$1$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{675}(58,\cdot)$	675.bj	180	yes	$-1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{675}(59,\cdot)$	675.bh	90	yes	$-1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$

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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	$675$
Structure	\(C_{2}\times C_{180}\)
Order	$360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{675}(1,\cdot)\)	675.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{675}(2,\cdot)\)	675.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{675}(4,\cdot)\)	675.bg	90	yes	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{675}(7,\cdot)\)	675.bb	36	no	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{675}(8,\cdot)\)	675.bd	60	no	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{675}(11,\cdot)\)	675.bf	90	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{675}(13,\cdot)\)	675.bj	180	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{675}(14,\cdot)\)	675.bh	90	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{675}(16,\cdot)\)	675.bc	45	yes	\(1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{675}(17,\cdot)\)	675.bd	60	no	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{675}(19,\cdot)\)	675.y	30	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{675}(22,\cdot)\)	675.bj	180	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{675}(23,\cdot)\)	675.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{675}(26,\cdot)\)	675.c	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{675}(28,\cdot)\)	675.v	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{675}(29,\cdot)\)	675.bh	90	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{675}(31,\cdot)\)	675.bc	45	yes	\(1\)	\(1\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{675}(32,\cdot)\)	675.ba	36	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{675}(34,\cdot)\)	675.bg	90	yes	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{675}(37,\cdot)\)	675.be	60	no	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{675}(38,\cdot)\)	675.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{675}(41,\cdot)\)	675.bf	90	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{675}(43,\cdot)\)	675.bb	36	no	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{675}(44,\cdot)\)	675.z	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{675}(46,\cdot)\)	675.r	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{675}(47,\cdot)\)	675.bi	180	yes	\(1\)	\(1\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{675}(49,\cdot)\)	675.u	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{675}(52,\cdot)\)	675.bj	180	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{675}(53,\cdot)\)	675.w	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{675}(56,\cdot)\)	675.bf	90	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{675}(58,\cdot)\)	675.bj	180	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{675}(59,\cdot)\)	675.bh	90	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)

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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.