LMFDB - Group of Dirichlet characters of modulus 36100

Show commands: PariGP / SageMath

sage: H = DirichletGroup(36100)

pari: g = idealstar(,36100,2)

Character group

sage: G.order() pari: g.no
Order	=	13680
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{3420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{36100}(18051,\cdot)$, $\chi_{36100}(5777,\cdot)$, $\chi_{36100}(21301,\cdot)$

First 32 of 13680 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{36100}(1,\cdot)$	36100.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{36100}(3,\cdot)$	36100.fm	3420	yes	$-1$	$1$	$e\left(\frac{1519}{3420}\right)$	$e\left(\frac{49}{228}\right)$	$e\left(\frac{1519}{1710}\right)$	$e\left(\frac{317}{570}\right)$	$e\left(\frac{1253}{3420}\right)$	$e\left(\frac{1381}{3420}\right)$	$e\left(\frac{1127}{1710}\right)$	$e\left(\frac{2357}{3420}\right)$	$e\left(\frac{379}{1140}\right)$	$e\left(\frac{521}{855}\right)$
$\chi_{36100}(7,\cdot)$	36100.ea	228	no	$1$	$1$	$e\left(\frac{49}{228}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{85}{228}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{109}{114}\right)$
$\chi_{36100}(9,\cdot)$	36100.fe	1710	no	$1$	$1$	$e\left(\frac{1519}{1710}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{664}{855}\right)$	$e\left(\frac{32}{285}\right)$	$e\left(\frac{1253}{1710}\right)$	$e\left(\frac{1381}{1710}\right)$	$e\left(\frac{272}{855}\right)$	$e\left(\frac{647}{1710}\right)$	$e\left(\frac{379}{570}\right)$	$e\left(\frac{187}{855}\right)$
$\chi_{36100}(11,\cdot)$	36100.es	570	yes	$-1$	$1$	$e\left(\frac{317}{570}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{32}{285}\right)$	$e\left(\frac{137}{190}\right)$	$e\left(\frac{92}{285}\right)$	$e\left(\frac{229}{285}\right)$	$e\left(\frac{226}{285}\right)$	$e\left(\frac{481}{570}\right)$	$e\left(\frac{127}{190}\right)$	$e\left(\frac{191}{285}\right)$
$\chi_{36100}(13,\cdot)$	36100.fl	3420	no	$1$	$1$	$e\left(\frac{1253}{3420}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{1253}{1710}\right)$	$e\left(\frac{92}{285}\right)$	$e\left(\frac{1861}{3420}\right)$	$e\left(\frac{2597}{3420}\right)$	$e\left(\frac{709}{1710}\right)$	$e\left(\frac{3079}{3420}\right)$	$e\left(\frac{113}{1140}\right)$	$e\left(\frac{217}{855}\right)$
$\chi_{36100}(17,\cdot)$	36100.fk	3420	no	$-1$	$1$	$e\left(\frac{1381}{3420}\right)$	$e\left(\frac{85}{228}\right)$	$e\left(\frac{1381}{1710}\right)$	$e\left(\frac{229}{285}\right)$	$e\left(\frac{2597}{3420}\right)$	$e\left(\frac{2719}{3420}\right)$	$e\left(\frac{664}{855}\right)$	$e\left(\frac{2153}{3420}\right)$	$e\left(\frac{241}{1140}\right)$	$e\left(\frac{913}{1710}\right)$
$\chi_{36100}(21,\cdot)$	36100.fh	1710	no	$-1$	$1$	$e\left(\frac{1127}{1710}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{272}{855}\right)$	$e\left(\frac{226}{285}\right)$	$e\left(\frac{709}{1710}\right)$	$e\left(\frac{664}{855}\right)$	$e\left(\frac{707}{1710}\right)$	$e\left(\frac{833}{855}\right)$	$e\left(\frac{557}{570}\right)$	$e\left(\frac{967}{1710}\right)$
$\chi_{36100}(23,\cdot)$	36100.fn	3420	yes	$1$	$1$	$e\left(\frac{2357}{3420}\right)$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{647}{1710}\right)$	$e\left(\frac{481}{570}\right)$	$e\left(\frac{3079}{3420}\right)$	$e\left(\frac{2153}{3420}\right)$	$e\left(\frac{833}{855}\right)$	$e\left(\frac{3001}{3420}\right)$	$e\left(\frac{77}{1140}\right)$	$e\left(\frac{611}{1710}\right)$
$\chi_{36100}(27,\cdot)$	36100.fa	1140	yes	$-1$	$1$	$e\left(\frac{379}{1140}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{379}{570}\right)$	$e\left(\frac{127}{190}\right)$	$e\left(\frac{113}{1140}\right)$	$e\left(\frac{241}{1140}\right)$	$e\left(\frac{557}{570}\right)$	$e\left(\frac{77}{1140}\right)$	$e\left(\frac{379}{380}\right)$	$e\left(\frac{236}{285}\right)$
$\chi_{36100}(29,\cdot)$	36100.fd	1710	no	$-1$	$1$	$e\left(\frac{521}{855}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{187}{855}\right)$	$e\left(\frac{191}{285}\right)$	$e\left(\frac{217}{855}\right)$	$e\left(\frac{913}{1710}\right)$	$e\left(\frac{967}{1710}\right)$	$e\left(\frac{611}{1710}\right)$	$e\left(\frac{236}{285}\right)$	$e\left(\frac{77}{1710}\right)$
$\chi_{36100}(31,\cdot)$	36100.eo	570	yes	$1$	$1$	$e\left(\frac{128}{285}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{256}{285}\right)$	$e\left(\frac{51}{190}\right)$	$e\left(\frac{47}{570}\right)$	$e\left(\frac{122}{285}\right)$	$e\left(\frac{481}{570}\right)$	$e\left(\frac{143}{570}\right)$	$e\left(\frac{33}{95}\right)$	$e\left(\frac{491}{570}\right)$
$\chi_{36100}(33,\cdot)$	36100.fl	3420	no	$1$	$1$	$e\left(\frac{1}{3420}\right)$	$e\left(\frac{103}{228}\right)$	$e\left(\frac{1}{1710}\right)$	$e\left(\frac{79}{285}\right)$	$e\left(\frac{2357}{3420}\right)$	$e\left(\frac{709}{3420}\right)$	$e\left(\frac{773}{1710}\right)$	$e\left(\frac{1823}{3420}\right)$	$e\left(\frac{1}{1140}\right)$	$e\left(\frac{239}{855}\right)$
$\chi_{36100}(37,\cdot)$	36100.el	380	no	$1$	$1$	$e\left(\frac{167}{380}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{167}{190}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{319}{380}\right)$	$e\left(\frac{223}{380}\right)$	$e\left(\frac{81}{190}\right)$	$e\left(\frac{61}{380}\right)$	$e\left(\frac{121}{380}\right)$	$e\left(\frac{13}{95}\right)$
$\chi_{36100}(39,\cdot)$	36100.du	190	yes	$-1$	$1$	$e\left(\frac{77}{95}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{167}{190}\right)$	$e\left(\frac{173}{190}\right)$	$e\left(\frac{31}{190}\right)$	$e\left(\frac{7}{95}\right)$	$e\left(\frac{56}{95}\right)$	$e\left(\frac{41}{95}\right)$	$e\left(\frac{82}{95}\right)$
$\chi_{36100}(41,\cdot)$	36100.fh	1710	no	$-1$	$1$	$e\left(\frac{1079}{1710}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{224}{855}\right)$	$e\left(\frac{52}{285}\right)$	$e\left(\frac{433}{1710}\right)$	$e\left(\frac{748}{855}\right)$	$e\left(\frac{29}{1710}\right)$	$e\left(\frac{686}{855}\right)$	$e\left(\frac{509}{570}\right)$	$e\left(\frac{1249}{1710}\right)$
$\chi_{36100}(43,\cdot)$	36100.eu	684	no	$1$	$1$	$e\left(\frac{605}{684}\right)$	$e\left(\frac{13}{228}\right)$	$e\left(\frac{263}{342}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{187}{684}\right)$	$e\left(\frac{77}{684}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{649}{684}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{29}{342}\right)$
$\chi_{36100}(47,\cdot)$	36100.fn	3420	yes	$1$	$1$	$e\left(\frac{59}{3420}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{59}{1710}\right)$	$e\left(\frac{487}{570}\right)$	$e\left(\frac{553}{3420}\right)$	$e\left(\frac{791}{3420}\right)$	$e\left(\frac{146}{855}\right)$	$e\left(\frac{3247}{3420}\right)$	$e\left(\frac{59}{1140}\right)$	$e\left(\frac{1697}{1710}\right)$
$\chi_{36100}(49,\cdot)$	36100.dg	114	no	$1$	$1$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{52}{57}\right)$
$\chi_{36100}(51,\cdot)$	36100.ed	342	no	$1$	$1$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{109}{342}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{49}{342}\right)$
$\chi_{36100}(53,\cdot)$	36100.fl	3420	no	$1$	$1$	$e\left(\frac{629}{3420}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{629}{1710}\right)$	$e\left(\frac{101}{285}\right)$	$e\left(\frac{1693}{3420}\right)$	$e\left(\frac{1361}{3420}\right)$	$e\left(\frac{577}{1710}\right)$	$e\left(\frac{967}{3420}\right)$	$e\left(\frac{629}{1140}\right)$	$e\left(\frac{706}{855}\right)$
$\chi_{36100}(59,\cdot)$	36100.fj	1710	yes	$1$	$1$	$e\left(\frac{1649}{1710}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{794}{855}\right)$	$e\left(\frac{389}{570}\right)$	$e\left(\frac{359}{855}\right)$	$e\left(\frac{1211}{1710}\right)$	$e\left(\frac{599}{1710}\right)$	$e\left(\frac{401}{855}\right)$	$e\left(\frac{509}{570}\right)$	$e\left(\frac{679}{1710}\right)$
$\chi_{36100}(61,\cdot)$	36100.ey	855	no	$1$	$1$	$e\left(\frac{848}{855}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{841}{855}\right)$	$e\left(\frac{68}{285}\right)$	$e\left(\frac{601}{855}\right)$	$e\left(\frac{167}{855}\right)$	$e\left(\frac{293}{855}\right)$	$e\left(\frac{64}{855}\right)$	$e\left(\frac{278}{285}\right)$	$e\left(\frac{148}{855}\right)$
$\chi_{36100}(63,\cdot)$	36100.fn	3420	yes	$1$	$1$	$e\left(\frac{353}{3420}\right)$	$e\left(\frac{221}{228}\right)$	$e\left(\frac{353}{1710}\right)$	$e\left(\frac{199}{570}\right)$	$e\left(\frac{2671}{3420}\right)$	$e\left(\frac{617}{3420}\right)$	$e\left(\frac{62}{855}\right)$	$e\left(\frac{2269}{3420}\right)$	$e\left(\frac{353}{1140}\right)$	$e\left(\frac{299}{1710}\right)$
$\chi_{36100}(67,\cdot)$	36100.fm	3420	yes	$-1$	$1$	$e\left(\frac{1301}{3420}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{1301}{1710}\right)$	$e\left(\frac{73}{570}\right)$	$e\left(\frac{427}{3420}\right)$	$e\left(\frac{719}{3420}\right)$	$e\left(\frac{193}{1710}\right)$	$e\left(\frac{1663}{3420}\right)$	$e\left(\frac{161}{1140}\right)$	$e\left(\frac{574}{855}\right)$
$\chi_{36100}(69,\cdot)$	36100.by	30	no	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$-1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{36100}(71,\cdot)$	36100.ff	1710	yes	$1$	$1$	$e\left(\frac{691}{855}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{527}{855}\right)$	$e\left(\frac{377}{570}\right)$	$e\left(\frac{679}{1710}\right)$	$e\left(\frac{4}{855}\right)$	$e\left(\frac{1637}{1710}\right)$	$e\left(\frac{1411}{1710}\right)$	$e\left(\frac{121}{285}\right)$	$e\left(\frac{217}{1710}\right)$
$\chi_{36100}(73,\cdot)$	36100.fk	3420	no	$-1$	$1$	$e\left(\frac{1267}{3420}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{1267}{1710}\right)$	$e\left(\frac{58}{285}\right)$	$e\left(\frac{659}{3420}\right)$	$e\left(\frac{553}{3420}\right)$	$e\left(\frac{208}{855}\right)$	$e\left(\frac{2951}{3420}\right)$	$e\left(\frac{127}{1140}\right)$	$e\left(\frac{1141}{1710}\right)$
$\chi_{36100}(77,\cdot)$	36100.em	380	no	$-1$	$1$	$e\left(\frac{293}{380}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{103}{190}\right)$	$e\left(\frac{91}{95}\right)$	$e\left(\frac{141}{380}\right)$	$e\left(\frac{67}{380}\right)$	$e\left(\frac{52}{95}\right)$	$e\left(\frac{49}{380}\right)$	$e\left(\frac{119}{380}\right)$	$e\left(\frac{119}{190}\right)$
$\chi_{36100}(79,\cdot)$	36100.fj	1710	yes	$1$	$1$	$e\left(\frac{287}{1710}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{287}{855}\right)$	$e\left(\frac{347}{570}\right)$	$e\left(\frac{77}{855}\right)$	$e\left(\frac{1703}{1710}\right)$	$e\left(\frac{1667}{1710}\right)$	$e\left(\frac{398}{855}\right)$	$e\left(\frac{287}{570}\right)$	$e\left(\frac{1627}{1710}\right)$
$\chi_{36100}(81,\cdot)$	36100.ey	855	no	$1$	$1$	$e\left(\frac{664}{855}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{473}{855}\right)$	$e\left(\frac{64}{285}\right)$	$e\left(\frac{398}{855}\right)$	$e\left(\frac{526}{855}\right)$	$e\left(\frac{544}{855}\right)$	$e\left(\frac{647}{855}\right)$	$e\left(\frac{94}{285}\right)$	$e\left(\frac{374}{855}\right)$
$\chi_{36100}(83,\cdot)$	36100.ez	1140	yes	$1$	$1$	$e\left(\frac{167}{1140}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{167}{570}\right)$	$e\left(\frac{71}{190}\right)$	$e\left(\frac{889}{1140}\right)$	$e\left(\frac{983}{1140}\right)$	$e\left(\frac{278}{285}\right)$	$e\left(\frac{631}{1140}\right)$	$e\left(\frac{167}{380}\right)$	$e\left(\frac{311}{570}\right)$

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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	$36100$
Structure	\(C_{2}\times C_{2}\times C_{3420}\)
Order	$13680$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{36100}(1,\cdot)\)	36100.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{36100}(3,\cdot)\)	36100.fm	3420	yes	\(-1\)	\(1\)	\(e\left(\frac{1519}{3420}\right)\)	\(e\left(\frac{49}{228}\right)\)	\(e\left(\frac{1519}{1710}\right)\)	\(e\left(\frac{317}{570}\right)\)	\(e\left(\frac{1253}{3420}\right)\)	\(e\left(\frac{1381}{3420}\right)\)	\(e\left(\frac{1127}{1710}\right)\)	\(e\left(\frac{2357}{3420}\right)\)	\(e\left(\frac{379}{1140}\right)\)	\(e\left(\frac{521}{855}\right)\)
\(\chi_{36100}(7,\cdot)\)	36100.ea	228	no	\(1\)	\(1\)	\(e\left(\frac{49}{228}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{85}{228}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{109}{114}\right)\)
\(\chi_{36100}(9,\cdot)\)	36100.fe	1710	no	\(1\)	\(1\)	\(e\left(\frac{1519}{1710}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{664}{855}\right)\)	\(e\left(\frac{32}{285}\right)\)	\(e\left(\frac{1253}{1710}\right)\)	\(e\left(\frac{1381}{1710}\right)\)	\(e\left(\frac{272}{855}\right)\)	\(e\left(\frac{647}{1710}\right)\)	\(e\left(\frac{379}{570}\right)\)	\(e\left(\frac{187}{855}\right)\)
\(\chi_{36100}(11,\cdot)\)	36100.es	570	yes	\(-1\)	\(1\)	\(e\left(\frac{317}{570}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{32}{285}\right)\)	\(e\left(\frac{137}{190}\right)\)	\(e\left(\frac{92}{285}\right)\)	\(e\left(\frac{229}{285}\right)\)	\(e\left(\frac{226}{285}\right)\)	\(e\left(\frac{481}{570}\right)\)	\(e\left(\frac{127}{190}\right)\)	\(e\left(\frac{191}{285}\right)\)
\(\chi_{36100}(13,\cdot)\)	36100.fl	3420	no	\(1\)	\(1\)	\(e\left(\frac{1253}{3420}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{1253}{1710}\right)\)	\(e\left(\frac{92}{285}\right)\)	\(e\left(\frac{1861}{3420}\right)\)	\(e\left(\frac{2597}{3420}\right)\)	\(e\left(\frac{709}{1710}\right)\)	\(e\left(\frac{3079}{3420}\right)\)	\(e\left(\frac{113}{1140}\right)\)	\(e\left(\frac{217}{855}\right)\)
\(\chi_{36100}(17,\cdot)\)	36100.fk	3420	no	\(-1\)	\(1\)	\(e\left(\frac{1381}{3420}\right)\)	\(e\left(\frac{85}{228}\right)\)	\(e\left(\frac{1381}{1710}\right)\)	\(e\left(\frac{229}{285}\right)\)	\(e\left(\frac{2597}{3420}\right)\)	\(e\left(\frac{2719}{3420}\right)\)	\(e\left(\frac{664}{855}\right)\)	\(e\left(\frac{2153}{3420}\right)\)	\(e\left(\frac{241}{1140}\right)\)	\(e\left(\frac{913}{1710}\right)\)
\(\chi_{36100}(21,\cdot)\)	36100.fh	1710	no	\(-1\)	\(1\)	\(e\left(\frac{1127}{1710}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{272}{855}\right)\)	\(e\left(\frac{226}{285}\right)\)	\(e\left(\frac{709}{1710}\right)\)	\(e\left(\frac{664}{855}\right)\)	\(e\left(\frac{707}{1710}\right)\)	\(e\left(\frac{833}{855}\right)\)	\(e\left(\frac{557}{570}\right)\)	\(e\left(\frac{967}{1710}\right)\)
\(\chi_{36100}(23,\cdot)\)	36100.fn	3420	yes	\(1\)	\(1\)	\(e\left(\frac{2357}{3420}\right)\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{647}{1710}\right)\)	\(e\left(\frac{481}{570}\right)\)	\(e\left(\frac{3079}{3420}\right)\)	\(e\left(\frac{2153}{3420}\right)\)	\(e\left(\frac{833}{855}\right)\)	\(e\left(\frac{3001}{3420}\right)\)	\(e\left(\frac{77}{1140}\right)\)	\(e\left(\frac{611}{1710}\right)\)
\(\chi_{36100}(27,\cdot)\)	36100.fa	1140	yes	\(-1\)	\(1\)	\(e\left(\frac{379}{1140}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{379}{570}\right)\)	\(e\left(\frac{127}{190}\right)\)	\(e\left(\frac{113}{1140}\right)\)	\(e\left(\frac{241}{1140}\right)\)	\(e\left(\frac{557}{570}\right)\)	\(e\left(\frac{77}{1140}\right)\)	\(e\left(\frac{379}{380}\right)\)	\(e\left(\frac{236}{285}\right)\)
\(\chi_{36100}(29,\cdot)\)	36100.fd	1710	no	\(-1\)	\(1\)	\(e\left(\frac{521}{855}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{187}{855}\right)\)	\(e\left(\frac{191}{285}\right)\)	\(e\left(\frac{217}{855}\right)\)	\(e\left(\frac{913}{1710}\right)\)	\(e\left(\frac{967}{1710}\right)\)	\(e\left(\frac{611}{1710}\right)\)	\(e\left(\frac{236}{285}\right)\)	\(e\left(\frac{77}{1710}\right)\)
\(\chi_{36100}(31,\cdot)\)	36100.eo	570	yes	\(1\)	\(1\)	\(e\left(\frac{128}{285}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{256}{285}\right)\)	\(e\left(\frac{51}{190}\right)\)	\(e\left(\frac{47}{570}\right)\)	\(e\left(\frac{122}{285}\right)\)	\(e\left(\frac{481}{570}\right)\)	\(e\left(\frac{143}{570}\right)\)	\(e\left(\frac{33}{95}\right)\)	\(e\left(\frac{491}{570}\right)\)
\(\chi_{36100}(33,\cdot)\)	36100.fl	3420	no	\(1\)	\(1\)	\(e\left(\frac{1}{3420}\right)\)	\(e\left(\frac{103}{228}\right)\)	\(e\left(\frac{1}{1710}\right)\)	\(e\left(\frac{79}{285}\right)\)	\(e\left(\frac{2357}{3420}\right)\)	\(e\left(\frac{709}{3420}\right)\)	\(e\left(\frac{773}{1710}\right)\)	\(e\left(\frac{1823}{3420}\right)\)	\(e\left(\frac{1}{1140}\right)\)	\(e\left(\frac{239}{855}\right)\)
\(\chi_{36100}(37,\cdot)\)	36100.el	380	no	\(1\)	\(1\)	\(e\left(\frac{167}{380}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{167}{190}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{319}{380}\right)\)	\(e\left(\frac{223}{380}\right)\)	\(e\left(\frac{81}{190}\right)\)	\(e\left(\frac{61}{380}\right)\)	\(e\left(\frac{121}{380}\right)\)	\(e\left(\frac{13}{95}\right)\)
\(\chi_{36100}(39,\cdot)\)	36100.du	190	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{95}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{167}{190}\right)\)	\(e\left(\frac{173}{190}\right)\)	\(e\left(\frac{31}{190}\right)\)	\(e\left(\frac{7}{95}\right)\)	\(e\left(\frac{56}{95}\right)\)	\(e\left(\frac{41}{95}\right)\)	\(e\left(\frac{82}{95}\right)\)
\(\chi_{36100}(41,\cdot)\)	36100.fh	1710	no	\(-1\)	\(1\)	\(e\left(\frac{1079}{1710}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{224}{855}\right)\)	\(e\left(\frac{52}{285}\right)\)	\(e\left(\frac{433}{1710}\right)\)	\(e\left(\frac{748}{855}\right)\)	\(e\left(\frac{29}{1710}\right)\)	\(e\left(\frac{686}{855}\right)\)	\(e\left(\frac{509}{570}\right)\)	\(e\left(\frac{1249}{1710}\right)\)
\(\chi_{36100}(43,\cdot)\)	36100.eu	684	no	\(1\)	\(1\)	\(e\left(\frac{605}{684}\right)\)	\(e\left(\frac{13}{228}\right)\)	\(e\left(\frac{263}{342}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{187}{684}\right)\)	\(e\left(\frac{77}{684}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{649}{684}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{29}{342}\right)\)
\(\chi_{36100}(47,\cdot)\)	36100.fn	3420	yes	\(1\)	\(1\)	\(e\left(\frac{59}{3420}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{59}{1710}\right)\)	\(e\left(\frac{487}{570}\right)\)	\(e\left(\frac{553}{3420}\right)\)	\(e\left(\frac{791}{3420}\right)\)	\(e\left(\frac{146}{855}\right)\)	\(e\left(\frac{3247}{3420}\right)\)	\(e\left(\frac{59}{1140}\right)\)	\(e\left(\frac{1697}{1710}\right)\)
\(\chi_{36100}(49,\cdot)\)	36100.dg	114	no	\(1\)	\(1\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{52}{57}\right)\)
\(\chi_{36100}(51,\cdot)\)	36100.ed	342	no	\(1\)	\(1\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{109}{342}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{49}{342}\right)\)
\(\chi_{36100}(53,\cdot)\)	36100.fl	3420	no	\(1\)	\(1\)	\(e\left(\frac{629}{3420}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{629}{1710}\right)\)	\(e\left(\frac{101}{285}\right)\)	\(e\left(\frac{1693}{3420}\right)\)	\(e\left(\frac{1361}{3420}\right)\)	\(e\left(\frac{577}{1710}\right)\)	\(e\left(\frac{967}{3420}\right)\)	\(e\left(\frac{629}{1140}\right)\)	\(e\left(\frac{706}{855}\right)\)
\(\chi_{36100}(59,\cdot)\)	36100.fj	1710	yes	\(1\)	\(1\)	\(e\left(\frac{1649}{1710}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{794}{855}\right)\)	\(e\left(\frac{389}{570}\right)\)	\(e\left(\frac{359}{855}\right)\)	\(e\left(\frac{1211}{1710}\right)\)	\(e\left(\frac{599}{1710}\right)\)	\(e\left(\frac{401}{855}\right)\)	\(e\left(\frac{509}{570}\right)\)	\(e\left(\frac{679}{1710}\right)\)
\(\chi_{36100}(61,\cdot)\)	36100.ey	855	no	\(1\)	\(1\)	\(e\left(\frac{848}{855}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{841}{855}\right)\)	\(e\left(\frac{68}{285}\right)\)	\(e\left(\frac{601}{855}\right)\)	\(e\left(\frac{167}{855}\right)\)	\(e\left(\frac{293}{855}\right)\)	\(e\left(\frac{64}{855}\right)\)	\(e\left(\frac{278}{285}\right)\)	\(e\left(\frac{148}{855}\right)\)
\(\chi_{36100}(63,\cdot)\)	36100.fn	3420	yes	\(1\)	\(1\)	\(e\left(\frac{353}{3420}\right)\)	\(e\left(\frac{221}{228}\right)\)	\(e\left(\frac{353}{1710}\right)\)	\(e\left(\frac{199}{570}\right)\)	\(e\left(\frac{2671}{3420}\right)\)	\(e\left(\frac{617}{3420}\right)\)	\(e\left(\frac{62}{855}\right)\)	\(e\left(\frac{2269}{3420}\right)\)	\(e\left(\frac{353}{1140}\right)\)	\(e\left(\frac{299}{1710}\right)\)
\(\chi_{36100}(67,\cdot)\)	36100.fm	3420	yes	\(-1\)	\(1\)	\(e\left(\frac{1301}{3420}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{1301}{1710}\right)\)	\(e\left(\frac{73}{570}\right)\)	\(e\left(\frac{427}{3420}\right)\)	\(e\left(\frac{719}{3420}\right)\)	\(e\left(\frac{193}{1710}\right)\)	\(e\left(\frac{1663}{3420}\right)\)	\(e\left(\frac{161}{1140}\right)\)	\(e\left(\frac{574}{855}\right)\)
\(\chi_{36100}(69,\cdot)\)	36100.by	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(-1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{36100}(71,\cdot)\)	36100.ff	1710	yes	\(1\)	\(1\)	\(e\left(\frac{691}{855}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{527}{855}\right)\)	\(e\left(\frac{377}{570}\right)\)	\(e\left(\frac{679}{1710}\right)\)	\(e\left(\frac{4}{855}\right)\)	\(e\left(\frac{1637}{1710}\right)\)	\(e\left(\frac{1411}{1710}\right)\)	\(e\left(\frac{121}{285}\right)\)	\(e\left(\frac{217}{1710}\right)\)
\(\chi_{36100}(73,\cdot)\)	36100.fk	3420	no	\(-1\)	\(1\)	\(e\left(\frac{1267}{3420}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{1267}{1710}\right)\)	\(e\left(\frac{58}{285}\right)\)	\(e\left(\frac{659}{3420}\right)\)	\(e\left(\frac{553}{3420}\right)\)	\(e\left(\frac{208}{855}\right)\)	\(e\left(\frac{2951}{3420}\right)\)	\(e\left(\frac{127}{1140}\right)\)	\(e\left(\frac{1141}{1710}\right)\)
\(\chi_{36100}(77,\cdot)\)	36100.em	380	no	\(-1\)	\(1\)	\(e\left(\frac{293}{380}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{103}{190}\right)\)	\(e\left(\frac{91}{95}\right)\)	\(e\left(\frac{141}{380}\right)\)	\(e\left(\frac{67}{380}\right)\)	\(e\left(\frac{52}{95}\right)\)	\(e\left(\frac{49}{380}\right)\)	\(e\left(\frac{119}{380}\right)\)	\(e\left(\frac{119}{190}\right)\)
\(\chi_{36100}(79,\cdot)\)	36100.fj	1710	yes	\(1\)	\(1\)	\(e\left(\frac{287}{1710}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{287}{855}\right)\)	\(e\left(\frac{347}{570}\right)\)	\(e\left(\frac{77}{855}\right)\)	\(e\left(\frac{1703}{1710}\right)\)	\(e\left(\frac{1667}{1710}\right)\)	\(e\left(\frac{398}{855}\right)\)	\(e\left(\frac{287}{570}\right)\)	\(e\left(\frac{1627}{1710}\right)\)
\(\chi_{36100}(81,\cdot)\)	36100.ey	855	no	\(1\)	\(1\)	\(e\left(\frac{664}{855}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{473}{855}\right)\)	\(e\left(\frac{64}{285}\right)\)	\(e\left(\frac{398}{855}\right)\)	\(e\left(\frac{526}{855}\right)\)	\(e\left(\frac{544}{855}\right)\)	\(e\left(\frac{647}{855}\right)\)	\(e\left(\frac{94}{285}\right)\)	\(e\left(\frac{374}{855}\right)\)
\(\chi_{36100}(83,\cdot)\)	36100.ez	1140	yes	\(1\)	\(1\)	\(e\left(\frac{167}{1140}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{167}{570}\right)\)	\(e\left(\frac{71}{190}\right)\)	\(e\left(\frac{889}{1140}\right)\)	\(e\left(\frac{983}{1140}\right)\)	\(e\left(\frac{278}{285}\right)\)	\(e\left(\frac{631}{1140}\right)\)	\(e\left(\frac{167}{380}\right)\)	\(e\left(\frac{311}{570}\right)\)

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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.