LMFDB - Group of Dirichlet characters of modulus 8550

sage:H = DirichletGroup(8550)

pari:g = idealstar(,8550,2)

Character group

sage:G.order() pari:g.no
Order	=	2160
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{180}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{8550}(1901,\cdot)$, $\chi_{8550}(1027,\cdot)$, $\chi_{8550}(1351,\cdot)$

First 32 of 2160 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	$-1$	$1$	$7$	$11$	$13$	$17$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{8550}(1,\cdot)$	8550.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8550}(7,\cdot)$	8550.ci	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$-i$
$\chi_{8550}(11,\cdot)$	8550.ed	30	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{8550}(13,\cdot)$	8550.he	180	no	$1$	$1$	$-i$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{8550}(17,\cdot)$	8550.hd	180	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{8550}(23,\cdot)$	8550.hc	180	no	$1$	$1$	$-i$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{8550}(29,\cdot)$	8550.gu	90	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{8550}(31,\cdot)$	8550.eh	30	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8550}(37,\cdot)$	8550.ds	20	no	$1$	$1$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{8550}(41,\cdot)$	8550.gm	90	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{8550}(43,\cdot)$	8550.fa	36	no	$-1$	$1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{8550}(47,\cdot)$	8550.hi	180	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{8550}(49,\cdot)$	8550.be	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{8550}(53,\cdot)$	8550.hb	180	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{8550}(59,\cdot)$	8550.gu	90	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{8550}(61,\cdot)$	8550.fk	45	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{8550}(67,\cdot)$	8550.he	180	no	$1$	$1$	$i$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8550}(71,\cdot)$	8550.gi	90	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{8550}(73,\cdot)$	8550.hh	180	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{8550}(77,\cdot)$	8550.ft	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8550}(79,\cdot)$	8550.gf	90	no	$-1$	$1$	$-1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{8550}(83,\cdot)$	8550.fs	60	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{30}\right)$	$i$
$\chi_{8550}(89,\cdot)$	8550.gp	90	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{8550}(91,\cdot)$	8550.gk	90	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{8550}(97,\cdot)$	8550.he	180	no	$1$	$1$	$i$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{8550}(101,\cdot)$	8550.dc	18	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{18}\right)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{8550}(103,\cdot)$	8550.fy	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$	$i$
$\chi_{8550}(107,\cdot)$	8550.ce	12	no	$-1$	$1$	$i$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8550}(109,\cdot)$	8550.gr	90	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{8550}(113,\cdot)$	8550.fq	60	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8550}(119,\cdot)$	8550.ge	90	no	$-1$	$1$	$-1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{8550}(121,\cdot)$	8550.cv	15	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$

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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	$8550$
Structure	\(C_{2}\times C_{6}\times C_{180}\)
Order	$2160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{8550}(1,\cdot)\)	8550.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8550}(7,\cdot)\)	8550.ci	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)
\(\chi_{8550}(11,\cdot)\)	8550.ed	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{8550}(13,\cdot)\)	8550.he	180	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{8550}(17,\cdot)\)	8550.hd	180	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{8550}(23,\cdot)\)	8550.hc	180	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{8550}(29,\cdot)\)	8550.gu	90	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{8550}(31,\cdot)\)	8550.eh	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8550}(37,\cdot)\)	8550.ds	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)
\(\chi_{8550}(41,\cdot)\)	8550.gm	90	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{8550}(43,\cdot)\)	8550.fa	36	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{8550}(47,\cdot)\)	8550.hi	180	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{8550}(49,\cdot)\)	8550.be	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{8550}(53,\cdot)\)	8550.hb	180	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{8550}(59,\cdot)\)	8550.gu	90	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{8550}(61,\cdot)\)	8550.fk	45	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{8550}(67,\cdot)\)	8550.he	180	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8550}(71,\cdot)\)	8550.gi	90	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{8550}(73,\cdot)\)	8550.hh	180	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{8550}(77,\cdot)\)	8550.ft	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8550}(79,\cdot)\)	8550.gf	90	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{8550}(83,\cdot)\)	8550.fs	60	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(i\)
\(\chi_{8550}(89,\cdot)\)	8550.gp	90	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{8550}(91,\cdot)\)	8550.gk	90	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{8550}(97,\cdot)\)	8550.he	180	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{8550}(101,\cdot)\)	8550.dc	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{8550}(103,\cdot)\)	8550.fy	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(i\)
\(\chi_{8550}(107,\cdot)\)	8550.ce	12	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8550}(109,\cdot)\)	8550.gr	90	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{8550}(113,\cdot)\)	8550.fq	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8550}(119,\cdot)\)	8550.ge	90	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{8550}(121,\cdot)\)	8550.cv	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)

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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.