LMFDB - Group of Dirichlet characters of modulus 1900

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1900)

gp:g = idealstar(,1900,2)

magma:G := FullDirichletGroup(1900);

Character group

Order	=	720	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{180}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{1900}(951,\cdot)$, $\chi_{1900}(77,\cdot)$, $\chi_{1900}(401,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 720 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{1900}(1,\cdot)$	1900.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1900}(3,\cdot)$	1900.cr	180	yes	$-1$	$1$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{1900}(7,\cdot)$	1900.bd	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{1900}(9,\cdot)$	1900.co	90	no	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{1900}(11,\cdot)$	1900.bu	30	yes	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$-1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1900}(13,\cdot)$	1900.cs	180	no	$1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{1900}(17,\cdot)$	1900.ct	180	no	$-1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{1900}(21,\cdot)$	1900.cl	90	no	$-1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{1900}(23,\cdot)$	1900.cq	180	yes	$1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{1900}(27,\cdot)$	1900.ch	60	yes	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$-i$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1900}(29,\cdot)$	1900.cp	90	no	$-1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{1900}(31,\cdot)$	1900.by	30	yes	$1$	$1$	$e\left(\frac{2}{15}\right)$	$-1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1900}(33,\cdot)$	1900.cs	180	no	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{1900}(37,\cdot)$	1900.bq	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1900}(39,\cdot)$	1900.y	10	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1900}(41,\cdot)$	1900.cl	90	no	$-1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{1900}(43,\cdot)$	1900.cd	36	no	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{1900}(47,\cdot)$	1900.cq	180	yes	$1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{1900}(49,\cdot)$	1900.s	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{1900}(51,\cdot)$	1900.bn	18	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{1900}(53,\cdot)$	1900.cs	180	no	$1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{1900}(59,\cdot)$	1900.cj	90	yes	$1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{1900}(61,\cdot)$	1900.ce	45	no	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{1900}(63,\cdot)$	1900.cq	180	yes	$1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{1900}(67,\cdot)$	1900.cr	180	yes	$-1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{1900}(69,\cdot)$	1900.bx	30	no	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$-1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1900}(71,\cdot)$	1900.cn	90	yes	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{1900}(73,\cdot)$	1900.ct	180	no	$-1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{1900}(77,\cdot)$	1900.bp	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1900}(79,\cdot)$	1900.cj	90	yes	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{1900}(81,\cdot)$	1900.ce	45	no	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{1900}(83,\cdot)$	1900.ci	60	yes	$1$	$1$	$e\left(\frac{53}{60}\right)$	$i$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{30}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$1900$
Structure	\(C_{2}\times C_{2}\times C_{180}\)
Order	$720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{1900}(1,\cdot)\)	1900.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1900}(3,\cdot)\)	1900.cr	180	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{1900}(7,\cdot)\)	1900.bd	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1900}(9,\cdot)\)	1900.co	90	no	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{1900}(11,\cdot)\)	1900.bu	30	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(-1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1900}(13,\cdot)\)	1900.cs	180	no	\(1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{1900}(17,\cdot)\)	1900.ct	180	no	\(-1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)
\(\chi_{1900}(21,\cdot)\)	1900.cl	90	no	\(-1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{90}\right)\)
\(\chi_{1900}(23,\cdot)\)	1900.cq	180	yes	\(1\)	\(1\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{1900}(27,\cdot)\)	1900.ch	60	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(-i\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1900}(29,\cdot)\)	1900.cp	90	no	\(-1\)	\(1\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{1900}(31,\cdot)\)	1900.by	30	yes	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(-1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1900}(33,\cdot)\)	1900.cs	180	no	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{1900}(37,\cdot)\)	1900.bq	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1900}(39,\cdot)\)	1900.y	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1900}(41,\cdot)\)	1900.cl	90	no	\(-1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{61}{90}\right)\)
\(\chi_{1900}(43,\cdot)\)	1900.cd	36	no	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{1900}(47,\cdot)\)	1900.cq	180	yes	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{1900}(49,\cdot)\)	1900.s	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1900}(51,\cdot)\)	1900.bn	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{1900}(53,\cdot)\)	1900.cs	180	no	\(1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{1900}(59,\cdot)\)	1900.cj	90	yes	\(1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{1900}(61,\cdot)\)	1900.ce	45	no	\(1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{1900}(63,\cdot)\)	1900.cq	180	yes	\(1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)
\(\chi_{1900}(67,\cdot)\)	1900.cr	180	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{1900}(69,\cdot)\)	1900.bx	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(-1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1900}(71,\cdot)\)	1900.cn	90	yes	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{73}{90}\right)\)
\(\chi_{1900}(73,\cdot)\)	1900.ct	180	no	\(-1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)
\(\chi_{1900}(77,\cdot)\)	1900.bp	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1900}(79,\cdot)\)	1900.cj	90	yes	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{1900}(81,\cdot)\)	1900.ce	45	no	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{1900}(83,\cdot)\)	1900.ci	60	yes	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(i\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)

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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.