LMFDB - Group of Dirichlet characters of modulus 8370

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8370)

pari: g = idealstar(,8370,2)

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	=	$\chi_{8370}(7751,\cdot)$, $\chi_{8370}(6697,\cdot)$, $\chi_{8370}(4591,\cdot)$

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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$37$	$41$	$43$
$\chi_{8370}(1,\cdot)$	8370.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8370}(7,\cdot)$	8370.hg	180	no	$-1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{180}\right)$
$\chi_{8370}(11,\cdot)$	8370.ge	90	no	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{28}{45}\right)$	$-1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{41}{90}\right)$
$\chi_{8370}(13,\cdot)$	8370.hh	180	no	$1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{179}{180}\right)$
$\chi_{8370}(17,\cdot)$	8370.fn	60	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{60}\right)$
$\chi_{8370}(19,\cdot)$	8370.ex	30	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{8370}(23,\cdot)$	8370.gz	180	no	$-1$	$1$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{143}{180}\right)$
$\chi_{8370}(29,\cdot)$	8370.gl	90	no	$1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{8370}(37,\cdot)$	8370.cd	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8370}(41,\cdot)$	8370.gg	90	no	$-1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{8370}(43,\cdot)$	8370.hh	180	no	$1$	$1$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{31}{180}\right)$
$\chi_{8370}(47,\cdot)$	8370.ha	180	no	$1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{19}{180}\right)$
$\chi_{8370}(49,\cdot)$	8370.gj	90	no	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{8370}(53,\cdot)$	8370.fx	60	no	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{8370}(59,\cdot)$	8370.gd	90	no	$-1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{7}{90}\right)$	$-1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{8370}(61,\cdot)$	8370.dk	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{8370}(67,\cdot)$	8370.fb	36	no	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8370}(71,\cdot)$	8370.dw	30	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{8370}(73,\cdot)$	8370.gc	60	no	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{8370}(77,\cdot)$	8370.gz	180	no	$-1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{89}{180}\right)$
$\chi_{8370}(79,\cdot)$	8370.go	90	no	$-1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{8370}(83,\cdot)$	8370.gy	180	no	$-1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{23}{90}\right)$	$i$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{151}{180}\right)$
$\chi_{8370}(89,\cdot)$	8370.ei	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{8370}(91,\cdot)$	8370.en	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{30}\right)$	$-1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{8370}(97,\cdot)$	8370.hd	180	no	$-1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{180}\right)$
$\chi_{8370}(101,\cdot)$	8370.gk	90	no	$-1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{8370}(103,\cdot)$	8370.hg	180	no	$-1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{41}{180}\right)$
$\chi_{8370}(107,\cdot)$	8370.fp	60	no	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{8370}(109,\cdot)$	8370.ca	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{8370}(113,\cdot)$	8370.hj	180	no	$1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{77}{180}\right)$
$\chi_{8370}(119,\cdot)$	8370.cz	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{8370}(121,\cdot)$	8370.fk	45	no	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{11}{45}\right)$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{41}{45}\right)$

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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	$8370$
Structure	\(C_{2}\times C_{6}\times C_{180}\)
Order	$2160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(37\)	\(41\)	\(43\)
\(\chi_{8370}(1,\cdot)\)	8370.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8370}(7,\cdot)\)	8370.hg	180	no	\(-1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{180}\right)\)
\(\chi_{8370}(11,\cdot)\)	8370.ge	90	no	\(1\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(-1\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)
\(\chi_{8370}(13,\cdot)\)	8370.hh	180	no	\(1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{179}{180}\right)\)
\(\chi_{8370}(17,\cdot)\)	8370.fn	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{8370}(19,\cdot)\)	8370.ex	30	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{8370}(23,\cdot)\)	8370.gz	180	no	\(-1\)	\(1\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{143}{180}\right)\)
\(\chi_{8370}(29,\cdot)\)	8370.gl	90	no	\(1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{8370}(37,\cdot)\)	8370.cd	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8370}(41,\cdot)\)	8370.gg	90	no	\(-1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{8370}(43,\cdot)\)	8370.hh	180	no	\(1\)	\(1\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{31}{180}\right)\)
\(\chi_{8370}(47,\cdot)\)	8370.ha	180	no	\(1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{19}{180}\right)\)
\(\chi_{8370}(49,\cdot)\)	8370.gj	90	no	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)
\(\chi_{8370}(53,\cdot)\)	8370.fx	60	no	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{8370}(59,\cdot)\)	8370.gd	90	no	\(-1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(-1\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)
\(\chi_{8370}(61,\cdot)\)	8370.dk	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{8370}(67,\cdot)\)	8370.fb	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8370}(71,\cdot)\)	8370.dw	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{8370}(73,\cdot)\)	8370.gc	60	no	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{8370}(77,\cdot)\)	8370.gz	180	no	\(-1\)	\(1\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{89}{180}\right)\)
\(\chi_{8370}(79,\cdot)\)	8370.go	90	no	\(-1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{8370}(83,\cdot)\)	8370.gy	180	no	\(-1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(i\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{151}{180}\right)\)
\(\chi_{8370}(89,\cdot)\)	8370.ei	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{8370}(91,\cdot)\)	8370.en	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(-1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{8370}(97,\cdot)\)	8370.hd	180	no	\(-1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{180}\right)\)
\(\chi_{8370}(101,\cdot)\)	8370.gk	90	no	\(-1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{8370}(103,\cdot)\)	8370.hg	180	no	\(-1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{41}{180}\right)\)
\(\chi_{8370}(107,\cdot)\)	8370.fp	60	no	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{8370}(109,\cdot)\)	8370.ca	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{8370}(113,\cdot)\)	8370.hj	180	no	\(1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{77}{180}\right)\)
\(\chi_{8370}(119,\cdot)\)	8370.cz	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{8370}(121,\cdot)\)	8370.fk	45	no	\(1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)

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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.