LMFDB - Group of Dirichlet characters of modulus 8507

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8507)

pari: g = idealstar(,8507,2)

Character group

sage: G.order() pari: g.no
Order	=	8280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4140}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8507}(5974,\cdot)$, $\chi_{8507}(4889,\cdot)$

First 32 of 8280 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{8507}(1,\cdot)$	8507.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8507}(2,\cdot)$	8507.cs	4140	yes	$-1$	$1$	$e\left(\frac{203}{4140}\right)$	$e\left(\frac{142}{1035}\right)$	$e\left(\frac{203}{2070}\right)$	$e\left(\frac{89}{345}\right)$	$e\left(\frac{257}{1380}\right)$	$e\left(\frac{167}{276}\right)$	$e\left(\frac{203}{1380}\right)$	$e\left(\frac{284}{1035}\right)$	$e\left(\frac{1271}{4140}\right)$	$e\left(\frac{173}{2070}\right)$
$\chi_{8507}(3,\cdot)$	8507.cm	1035	yes	$1$	$1$	$e\left(\frac{142}{1035}\right)$	$e\left(\frac{122}{1035}\right)$	$e\left(\frac{284}{1035}\right)$	$e\left(\frac{334}{345}\right)$	$e\left(\frac{88}{345}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{142}{345}\right)$	$e\left(\frac{244}{1035}\right)$	$e\left(\frac{109}{1035}\right)$	$e\left(\frac{344}{1035}\right)$
$\chi_{8507}(4,\cdot)$	8507.cp	2070	yes	$1$	$1$	$e\left(\frac{203}{2070}\right)$	$e\left(\frac{284}{1035}\right)$	$e\left(\frac{203}{1035}\right)$	$e\left(\frac{178}{345}\right)$	$e\left(\frac{257}{690}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{203}{690}\right)$	$e\left(\frac{568}{1035}\right)$	$e\left(\frac{1271}{2070}\right)$	$e\left(\frac{173}{1035}\right)$
$\chi_{8507}(5,\cdot)$	8507.ch	690	yes	$-1$	$1$	$e\left(\frac{89}{345}\right)$	$e\left(\frac{334}{345}\right)$	$e\left(\frac{178}{345}\right)$	$e\left(\frac{51}{230}\right)$	$e\left(\frac{26}{115}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{89}{115}\right)$	$e\left(\frac{323}{345}\right)$	$e\left(\frac{331}{690}\right)$	$e\left(\frac{611}{690}\right)$
$\chi_{8507}(6,\cdot)$	8507.co	1380	yes	$-1$	$1$	$e\left(\frac{257}{1380}\right)$	$e\left(\frac{88}{345}\right)$	$e\left(\frac{257}{690}\right)$	$e\left(\frac{26}{115}\right)$	$e\left(\frac{203}{460}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{257}{460}\right)$	$e\left(\frac{176}{345}\right)$	$e\left(\frac{569}{1380}\right)$	$e\left(\frac{287}{690}\right)$
$\chi_{8507}(7,\cdot)$	8507.bz	276	yes	$-1$	$1$	$e\left(\frac{167}{276}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{83}{276}\right)$	$e\left(\frac{5}{138}\right)$
$\chi_{8507}(8,\cdot)$	8507.co	1380	yes	$-1$	$1$	$e\left(\frac{203}{1380}\right)$	$e\left(\frac{142}{345}\right)$	$e\left(\frac{203}{690}\right)$	$e\left(\frac{89}{115}\right)$	$e\left(\frac{257}{460}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{203}{460}\right)$	$e\left(\frac{284}{345}\right)$	$e\left(\frac{1271}{1380}\right)$	$e\left(\frac{173}{690}\right)$
$\chi_{8507}(9,\cdot)$	8507.cm	1035	yes	$1$	$1$	$e\left(\frac{284}{1035}\right)$	$e\left(\frac{244}{1035}\right)$	$e\left(\frac{568}{1035}\right)$	$e\left(\frac{323}{345}\right)$	$e\left(\frac{176}{345}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{284}{345}\right)$	$e\left(\frac{488}{1035}\right)$	$e\left(\frac{218}{1035}\right)$	$e\left(\frac{688}{1035}\right)$
$\chi_{8507}(10,\cdot)$	8507.ct	4140	yes	$1$	$1$	$e\left(\frac{1271}{4140}\right)$	$e\left(\frac{109}{1035}\right)$	$e\left(\frac{1271}{2070}\right)$	$e\left(\frac{331}{690}\right)$	$e\left(\frac{569}{1380}\right)$	$e\left(\frac{83}{276}\right)$	$e\left(\frac{1271}{1380}\right)$	$e\left(\frac{218}{1035}\right)$	$e\left(\frac{3257}{4140}\right)$	$e\left(\frac{1003}{1035}\right)$
$\chi_{8507}(11,\cdot)$	8507.cr	2070	yes	$-1$	$1$	$e\left(\frac{173}{2070}\right)$	$e\left(\frac{344}{1035}\right)$	$e\left(\frac{173}{1035}\right)$	$e\left(\frac{611}{690}\right)$	$e\left(\frac{287}{690}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{173}{690}\right)$	$e\left(\frac{688}{1035}\right)$	$e\left(\frac{1003}{1035}\right)$	$e\left(\frac{871}{2070}\right)$
$\chi_{8507}(12,\cdot)$	8507.cp	2070	yes	$1$	$1$	$e\left(\frac{487}{2070}\right)$	$e\left(\frac{406}{1035}\right)$	$e\left(\frac{487}{1035}\right)$	$e\left(\frac{167}{345}\right)$	$e\left(\frac{433}{690}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{487}{690}\right)$	$e\left(\frac{812}{1035}\right)$	$e\left(\frac{1489}{2070}\right)$	$e\left(\frac{517}{1035}\right)$
$\chi_{8507}(13,\cdot)$	8507.cq	2070	yes	$-1$	$1$	$e\left(\frac{223}{1035}\right)$	$e\left(\frac{833}{1035}\right)$	$e\left(\frac{446}{1035}\right)$	$e\left(\frac{257}{690}\right)$	$e\left(\frac{7}{345}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{223}{345}\right)$	$e\left(\frac{631}{1035}\right)$	$e\left(\frac{1217}{2070}\right)$	$e\left(\frac{337}{2070}\right)$
$\chi_{8507}(14,\cdot)$	8507.cm	1035	yes	$1$	$1$	$e\left(\frac{677}{1035}\right)$	$e\left(\frac{742}{1035}\right)$	$e\left(\frac{319}{1035}\right)$	$e\left(\frac{329}{345}\right)$	$e\left(\frac{128}{345}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{332}{345}\right)$	$e\left(\frac{449}{1035}\right)$	$e\left(\frac{629}{1035}\right)$	$e\left(\frac{124}{1035}\right)$
$\chi_{8507}(15,\cdot)$	8507.cq	2070	yes	$-1$	$1$	$e\left(\frac{409}{1035}\right)$	$e\left(\frac{89}{1035}\right)$	$e\left(\frac{818}{1035}\right)$	$e\left(\frac{131}{690}\right)$	$e\left(\frac{166}{345}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{64}{345}\right)$	$e\left(\frac{178}{1035}\right)$	$e\left(\frac{1211}{2070}\right)$	$e\left(\frac{451}{2070}\right)$
$\chi_{8507}(16,\cdot)$	8507.cm	1035	yes	$1$	$1$	$e\left(\frac{203}{1035}\right)$	$e\left(\frac{568}{1035}\right)$	$e\left(\frac{406}{1035}\right)$	$e\left(\frac{11}{345}\right)$	$e\left(\frac{257}{345}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{203}{345}\right)$	$e\left(\frac{101}{1035}\right)$	$e\left(\frac{236}{1035}\right)$	$e\left(\frac{346}{1035}\right)$
$\chi_{8507}(17,\cdot)$	8507.cl	828	yes	$-1$	$1$	$e\left(\frac{193}{828}\right)$	$e\left(\frac{83}{207}\right)$	$e\left(\frac{193}{414}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{175}{276}\right)$	$e\left(\frac{197}{276}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{166}{207}\right)$	$e\left(\frac{205}{828}\right)$	$e\left(\frac{295}{414}\right)$
$\chi_{8507}(18,\cdot)$	8507.cs	4140	yes	$-1$	$1$	$e\left(\frac{1339}{4140}\right)$	$e\left(\frac{386}{1035}\right)$	$e\left(\frac{1339}{2070}\right)$	$e\left(\frac{67}{345}\right)$	$e\left(\frac{961}{1380}\right)$	$e\left(\frac{211}{276}\right)$	$e\left(\frac{1339}{1380}\right)$	$e\left(\frac{772}{1035}\right)$	$e\left(\frac{2143}{4140}\right)$	$e\left(\frac{1549}{2070}\right)$
$\chi_{8507}(19,\cdot)$	8507.bo	92	yes	$1$	$1$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{8507}(20,\cdot)$	8507.cr	2070	yes	$-1$	$1$	$e\left(\frac{737}{2070}\right)$	$e\left(\frac{251}{1035}\right)$	$e\left(\frac{737}{1035}\right)$	$e\left(\frac{509}{690}\right)$	$e\left(\frac{413}{690}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{47}{690}\right)$	$e\left(\frac{502}{1035}\right)$	$e\left(\frac{97}{1035}\right)$	$e\left(\frac{109}{2070}\right)$
$\chi_{8507}(21,\cdot)$	8507.cs	4140	yes	$-1$	$1$	$e\left(\frac{3073}{4140}\right)$	$e\left(\frac{722}{1035}\right)$	$e\left(\frac{1003}{2070}\right)$	$e\left(\frac{229}{345}\right)$	$e\left(\frac{607}{1380}\right)$	$e\left(\frac{25}{276}\right)$	$e\left(\frac{313}{1380}\right)$	$e\left(\frac{409}{1035}\right)$	$e\left(\frac{1681}{4140}\right)$	$e\left(\frac{763}{2070}\right)$
$\chi_{8507}(22,\cdot)$	8507.cf	460	yes	$1$	$1$	$e\left(\frac{61}{460}\right)$	$e\left(\frac{54}{115}\right)$	$e\left(\frac{61}{230}\right)$	$e\left(\frac{33}{230}\right)$	$e\left(\frac{277}{460}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{183}{460}\right)$	$e\left(\frac{108}{115}\right)$	$e\left(\frac{127}{460}\right)$	$e\left(\frac{58}{115}\right)$
$\chi_{8507}(23,\cdot)$	8507.ct	4140	yes	$1$	$1$	$e\left(\frac{1039}{4140}\right)$	$e\left(\frac{686}{1035}\right)$	$e\left(\frac{1039}{2070}\right)$	$e\left(\frac{29}{690}\right)$	$e\left(\frac{1261}{1380}\right)$	$e\left(\frac{247}{276}\right)$	$e\left(\frac{1039}{1380}\right)$	$e\left(\frac{337}{1035}\right)$	$e\left(\frac{1213}{4140}\right)$	$e\left(\frac{17}{1035}\right)$
$\chi_{8507}(24,\cdot)$	8507.cs	4140	yes	$-1$	$1$	$e\left(\frac{1177}{4140}\right)$	$e\left(\frac{548}{1035}\right)$	$e\left(\frac{1177}{2070}\right)$	$e\left(\frac{256}{345}\right)$	$e\left(\frac{1123}{1380}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{1177}{1380}\right)$	$e\left(\frac{61}{1035}\right)$	$e\left(\frac{109}{4140}\right)$	$e\left(\frac{1207}{2070}\right)$
$\chi_{8507}(25,\cdot)$	8507.cb	345	yes	$1$	$1$	$e\left(\frac{178}{345}\right)$	$e\left(\frac{323}{345}\right)$	$e\left(\frac{11}{345}\right)$	$e\left(\frac{51}{115}\right)$	$e\left(\frac{52}{115}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{63}{115}\right)$	$e\left(\frac{301}{345}\right)$	$e\left(\frac{331}{345}\right)$	$e\left(\frac{266}{345}\right)$
$\chi_{8507}(26,\cdot)$	8507.ca	276	yes	$1$	$1$	$e\left(\frac{73}{276}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{247}{276}\right)$	$e\left(\frac{17}{69}\right)$
$\chi_{8507}(27,\cdot)$	8507.cb	345	yes	$1$	$1$	$e\left(\frac{142}{345}\right)$	$e\left(\frac{122}{345}\right)$	$e\left(\frac{284}{345}\right)$	$e\left(\frac{104}{115}\right)$	$e\left(\frac{88}{115}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{27}{115}\right)$	$e\left(\frac{244}{345}\right)$	$e\left(\frac{109}{345}\right)$	$e\left(\frac{344}{345}\right)$
$\chi_{8507}(28,\cdot)$	8507.cs	4140	yes	$-1$	$1$	$e\left(\frac{2911}{4140}\right)$	$e\left(\frac{884}{1035}\right)$	$e\left(\frac{841}{2070}\right)$	$e\left(\frac{73}{345}\right)$	$e\left(\frac{769}{1380}\right)$	$e\left(\frac{199}{276}\right)$	$e\left(\frac{151}{1380}\right)$	$e\left(\frac{733}{1035}\right)$	$e\left(\frac{3787}{4140}\right)$	$e\left(\frac{421}{2070}\right)$
$\chi_{8507}(29,\cdot)$	8507.ch	690	yes	$-1$	$1$	$e\left(\frac{332}{345}\right)$	$e\left(\frac{52}{345}\right)$	$e\left(\frac{319}{345}\right)$	$e\left(\frac{83}{230}\right)$	$e\left(\frac{13}{115}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{102}{115}\right)$	$e\left(\frac{104}{345}\right)$	$e\left(\frac{223}{690}\right)$	$e\left(\frac{593}{690}\right)$
$\chi_{8507}(30,\cdot)$	8507.cn	1380	yes	$1$	$1$	$e\left(\frac{613}{1380}\right)$	$e\left(\frac{77}{345}\right)$	$e\left(\frac{613}{690}\right)$	$e\left(\frac{103}{230}\right)$	$e\left(\frac{307}{460}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{153}{460}\right)$	$e\left(\frac{154}{345}\right)$	$e\left(\frac{1231}{1380}\right)$	$e\left(\frac{104}{345}\right)$
$\chi_{8507}(31,\cdot)$	8507.cf	460	yes	$1$	$1$	$e\left(\frac{333}{460}\right)$	$e\left(\frac{12}{115}\right)$	$e\left(\frac{103}{230}\right)$	$e\left(\frac{199}{230}\right)$	$e\left(\frac{381}{460}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{79}{460}\right)$	$e\left(\frac{24}{115}\right)$	$e\left(\frac{271}{460}\right)$	$e\left(\frac{64}{115}\right)$
$\chi_{8507}(32,\cdot)$	8507.cl	828	yes	$-1$	$1$	$e\left(\frac{203}{828}\right)$	$e\left(\frac{142}{207}\right)$	$e\left(\frac{203}{414}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{257}{276}\right)$	$e\left(\frac{7}{276}\right)$	$e\left(\frac{203}{276}\right)$	$e\left(\frac{77}{207}\right)$	$e\left(\frac{443}{828}\right)$	$e\left(\frac{173}{414}\right)$

Click here to search among the remaining 8248 characters.

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	$8507$
Structure	\(C_{2}\times C_{4140}\)
Order	$8280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{8507}(1,\cdot)\)	8507.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8507}(2,\cdot)\)	8507.cs	4140	yes	\(-1\)	\(1\)	\(e\left(\frac{203}{4140}\right)\)	\(e\left(\frac{142}{1035}\right)\)	\(e\left(\frac{203}{2070}\right)\)	\(e\left(\frac{89}{345}\right)\)	\(e\left(\frac{257}{1380}\right)\)	\(e\left(\frac{167}{276}\right)\)	\(e\left(\frac{203}{1380}\right)\)	\(e\left(\frac{284}{1035}\right)\)	\(e\left(\frac{1271}{4140}\right)\)	\(e\left(\frac{173}{2070}\right)\)
\(\chi_{8507}(3,\cdot)\)	8507.cm	1035	yes	\(1\)	\(1\)	\(e\left(\frac{142}{1035}\right)\)	\(e\left(\frac{122}{1035}\right)\)	\(e\left(\frac{284}{1035}\right)\)	\(e\left(\frac{334}{345}\right)\)	\(e\left(\frac{88}{345}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{142}{345}\right)\)	\(e\left(\frac{244}{1035}\right)\)	\(e\left(\frac{109}{1035}\right)\)	\(e\left(\frac{344}{1035}\right)\)
\(\chi_{8507}(4,\cdot)\)	8507.cp	2070	yes	\(1\)	\(1\)	\(e\left(\frac{203}{2070}\right)\)	\(e\left(\frac{284}{1035}\right)\)	\(e\left(\frac{203}{1035}\right)\)	\(e\left(\frac{178}{345}\right)\)	\(e\left(\frac{257}{690}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{203}{690}\right)\)	\(e\left(\frac{568}{1035}\right)\)	\(e\left(\frac{1271}{2070}\right)\)	\(e\left(\frac{173}{1035}\right)\)
\(\chi_{8507}(5,\cdot)\)	8507.ch	690	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{345}\right)\)	\(e\left(\frac{334}{345}\right)\)	\(e\left(\frac{178}{345}\right)\)	\(e\left(\frac{51}{230}\right)\)	\(e\left(\frac{26}{115}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{89}{115}\right)\)	\(e\left(\frac{323}{345}\right)\)	\(e\left(\frac{331}{690}\right)\)	\(e\left(\frac{611}{690}\right)\)
\(\chi_{8507}(6,\cdot)\)	8507.co	1380	yes	\(-1\)	\(1\)	\(e\left(\frac{257}{1380}\right)\)	\(e\left(\frac{88}{345}\right)\)	\(e\left(\frac{257}{690}\right)\)	\(e\left(\frac{26}{115}\right)\)	\(e\left(\frac{203}{460}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{257}{460}\right)\)	\(e\left(\frac{176}{345}\right)\)	\(e\left(\frac{569}{1380}\right)\)	\(e\left(\frac{287}{690}\right)\)
\(\chi_{8507}(7,\cdot)\)	8507.bz	276	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{276}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{83}{276}\right)\)	\(e\left(\frac{5}{138}\right)\)
\(\chi_{8507}(8,\cdot)\)	8507.co	1380	yes	\(-1\)	\(1\)	\(e\left(\frac{203}{1380}\right)\)	\(e\left(\frac{142}{345}\right)\)	\(e\left(\frac{203}{690}\right)\)	\(e\left(\frac{89}{115}\right)\)	\(e\left(\frac{257}{460}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{203}{460}\right)\)	\(e\left(\frac{284}{345}\right)\)	\(e\left(\frac{1271}{1380}\right)\)	\(e\left(\frac{173}{690}\right)\)
\(\chi_{8507}(9,\cdot)\)	8507.cm	1035	yes	\(1\)	\(1\)	\(e\left(\frac{284}{1035}\right)\)	\(e\left(\frac{244}{1035}\right)\)	\(e\left(\frac{568}{1035}\right)\)	\(e\left(\frac{323}{345}\right)\)	\(e\left(\frac{176}{345}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{284}{345}\right)\)	\(e\left(\frac{488}{1035}\right)\)	\(e\left(\frac{218}{1035}\right)\)	\(e\left(\frac{688}{1035}\right)\)
\(\chi_{8507}(10,\cdot)\)	8507.ct	4140	yes	\(1\)	\(1\)	\(e\left(\frac{1271}{4140}\right)\)	\(e\left(\frac{109}{1035}\right)\)	\(e\left(\frac{1271}{2070}\right)\)	\(e\left(\frac{331}{690}\right)\)	\(e\left(\frac{569}{1380}\right)\)	\(e\left(\frac{83}{276}\right)\)	\(e\left(\frac{1271}{1380}\right)\)	\(e\left(\frac{218}{1035}\right)\)	\(e\left(\frac{3257}{4140}\right)\)	\(e\left(\frac{1003}{1035}\right)\)
\(\chi_{8507}(11,\cdot)\)	8507.cr	2070	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{2070}\right)\)	\(e\left(\frac{344}{1035}\right)\)	\(e\left(\frac{173}{1035}\right)\)	\(e\left(\frac{611}{690}\right)\)	\(e\left(\frac{287}{690}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{173}{690}\right)\)	\(e\left(\frac{688}{1035}\right)\)	\(e\left(\frac{1003}{1035}\right)\)	\(e\left(\frac{871}{2070}\right)\)
\(\chi_{8507}(12,\cdot)\)	8507.cp	2070	yes	\(1\)	\(1\)	\(e\left(\frac{487}{2070}\right)\)	\(e\left(\frac{406}{1035}\right)\)	\(e\left(\frac{487}{1035}\right)\)	\(e\left(\frac{167}{345}\right)\)	\(e\left(\frac{433}{690}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{487}{690}\right)\)	\(e\left(\frac{812}{1035}\right)\)	\(e\left(\frac{1489}{2070}\right)\)	\(e\left(\frac{517}{1035}\right)\)
\(\chi_{8507}(13,\cdot)\)	8507.cq	2070	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{1035}\right)\)	\(e\left(\frac{833}{1035}\right)\)	\(e\left(\frac{446}{1035}\right)\)	\(e\left(\frac{257}{690}\right)\)	\(e\left(\frac{7}{345}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{223}{345}\right)\)	\(e\left(\frac{631}{1035}\right)\)	\(e\left(\frac{1217}{2070}\right)\)	\(e\left(\frac{337}{2070}\right)\)
\(\chi_{8507}(14,\cdot)\)	8507.cm	1035	yes	\(1\)	\(1\)	\(e\left(\frac{677}{1035}\right)\)	\(e\left(\frac{742}{1035}\right)\)	\(e\left(\frac{319}{1035}\right)\)	\(e\left(\frac{329}{345}\right)\)	\(e\left(\frac{128}{345}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{332}{345}\right)\)	\(e\left(\frac{449}{1035}\right)\)	\(e\left(\frac{629}{1035}\right)\)	\(e\left(\frac{124}{1035}\right)\)
\(\chi_{8507}(15,\cdot)\)	8507.cq	2070	yes	\(-1\)	\(1\)	\(e\left(\frac{409}{1035}\right)\)	\(e\left(\frac{89}{1035}\right)\)	\(e\left(\frac{818}{1035}\right)\)	\(e\left(\frac{131}{690}\right)\)	\(e\left(\frac{166}{345}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{64}{345}\right)\)	\(e\left(\frac{178}{1035}\right)\)	\(e\left(\frac{1211}{2070}\right)\)	\(e\left(\frac{451}{2070}\right)\)
\(\chi_{8507}(16,\cdot)\)	8507.cm	1035	yes	\(1\)	\(1\)	\(e\left(\frac{203}{1035}\right)\)	\(e\left(\frac{568}{1035}\right)\)	\(e\left(\frac{406}{1035}\right)\)	\(e\left(\frac{11}{345}\right)\)	\(e\left(\frac{257}{345}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{203}{345}\right)\)	\(e\left(\frac{101}{1035}\right)\)	\(e\left(\frac{236}{1035}\right)\)	\(e\left(\frac{346}{1035}\right)\)
\(\chi_{8507}(17,\cdot)\)	8507.cl	828	yes	\(-1\)	\(1\)	\(e\left(\frac{193}{828}\right)\)	\(e\left(\frac{83}{207}\right)\)	\(e\left(\frac{193}{414}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{175}{276}\right)\)	\(e\left(\frac{197}{276}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{166}{207}\right)\)	\(e\left(\frac{205}{828}\right)\)	\(e\left(\frac{295}{414}\right)\)
\(\chi_{8507}(18,\cdot)\)	8507.cs	4140	yes	\(-1\)	\(1\)	\(e\left(\frac{1339}{4140}\right)\)	\(e\left(\frac{386}{1035}\right)\)	\(e\left(\frac{1339}{2070}\right)\)	\(e\left(\frac{67}{345}\right)\)	\(e\left(\frac{961}{1380}\right)\)	\(e\left(\frac{211}{276}\right)\)	\(e\left(\frac{1339}{1380}\right)\)	\(e\left(\frac{772}{1035}\right)\)	\(e\left(\frac{2143}{4140}\right)\)	\(e\left(\frac{1549}{2070}\right)\)
\(\chi_{8507}(19,\cdot)\)	8507.bo	92	yes	\(1\)	\(1\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{8507}(20,\cdot)\)	8507.cr	2070	yes	\(-1\)	\(1\)	\(e\left(\frac{737}{2070}\right)\)	\(e\left(\frac{251}{1035}\right)\)	\(e\left(\frac{737}{1035}\right)\)	\(e\left(\frac{509}{690}\right)\)	\(e\left(\frac{413}{690}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{47}{690}\right)\)	\(e\left(\frac{502}{1035}\right)\)	\(e\left(\frac{97}{1035}\right)\)	\(e\left(\frac{109}{2070}\right)\)
\(\chi_{8507}(21,\cdot)\)	8507.cs	4140	yes	\(-1\)	\(1\)	\(e\left(\frac{3073}{4140}\right)\)	\(e\left(\frac{722}{1035}\right)\)	\(e\left(\frac{1003}{2070}\right)\)	\(e\left(\frac{229}{345}\right)\)	\(e\left(\frac{607}{1380}\right)\)	\(e\left(\frac{25}{276}\right)\)	\(e\left(\frac{313}{1380}\right)\)	\(e\left(\frac{409}{1035}\right)\)	\(e\left(\frac{1681}{4140}\right)\)	\(e\left(\frac{763}{2070}\right)\)
\(\chi_{8507}(22,\cdot)\)	8507.cf	460	yes	\(1\)	\(1\)	\(e\left(\frac{61}{460}\right)\)	\(e\left(\frac{54}{115}\right)\)	\(e\left(\frac{61}{230}\right)\)	\(e\left(\frac{33}{230}\right)\)	\(e\left(\frac{277}{460}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{183}{460}\right)\)	\(e\left(\frac{108}{115}\right)\)	\(e\left(\frac{127}{460}\right)\)	\(e\left(\frac{58}{115}\right)\)
\(\chi_{8507}(23,\cdot)\)	8507.ct	4140	yes	\(1\)	\(1\)	\(e\left(\frac{1039}{4140}\right)\)	\(e\left(\frac{686}{1035}\right)\)	\(e\left(\frac{1039}{2070}\right)\)	\(e\left(\frac{29}{690}\right)\)	\(e\left(\frac{1261}{1380}\right)\)	\(e\left(\frac{247}{276}\right)\)	\(e\left(\frac{1039}{1380}\right)\)	\(e\left(\frac{337}{1035}\right)\)	\(e\left(\frac{1213}{4140}\right)\)	\(e\left(\frac{17}{1035}\right)\)
\(\chi_{8507}(24,\cdot)\)	8507.cs	4140	yes	\(-1\)	\(1\)	\(e\left(\frac{1177}{4140}\right)\)	\(e\left(\frac{548}{1035}\right)\)	\(e\left(\frac{1177}{2070}\right)\)	\(e\left(\frac{256}{345}\right)\)	\(e\left(\frac{1123}{1380}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{1177}{1380}\right)\)	\(e\left(\frac{61}{1035}\right)\)	\(e\left(\frac{109}{4140}\right)\)	\(e\left(\frac{1207}{2070}\right)\)
\(\chi_{8507}(25,\cdot)\)	8507.cb	345	yes	\(1\)	\(1\)	\(e\left(\frac{178}{345}\right)\)	\(e\left(\frac{323}{345}\right)\)	\(e\left(\frac{11}{345}\right)\)	\(e\left(\frac{51}{115}\right)\)	\(e\left(\frac{52}{115}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{63}{115}\right)\)	\(e\left(\frac{301}{345}\right)\)	\(e\left(\frac{331}{345}\right)\)	\(e\left(\frac{266}{345}\right)\)
\(\chi_{8507}(26,\cdot)\)	8507.ca	276	yes	\(1\)	\(1\)	\(e\left(\frac{73}{276}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{247}{276}\right)\)	\(e\left(\frac{17}{69}\right)\)
\(\chi_{8507}(27,\cdot)\)	8507.cb	345	yes	\(1\)	\(1\)	\(e\left(\frac{142}{345}\right)\)	\(e\left(\frac{122}{345}\right)\)	\(e\left(\frac{284}{345}\right)\)	\(e\left(\frac{104}{115}\right)\)	\(e\left(\frac{88}{115}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{27}{115}\right)\)	\(e\left(\frac{244}{345}\right)\)	\(e\left(\frac{109}{345}\right)\)	\(e\left(\frac{344}{345}\right)\)
\(\chi_{8507}(28,\cdot)\)	8507.cs	4140	yes	\(-1\)	\(1\)	\(e\left(\frac{2911}{4140}\right)\)	\(e\left(\frac{884}{1035}\right)\)	\(e\left(\frac{841}{2070}\right)\)	\(e\left(\frac{73}{345}\right)\)	\(e\left(\frac{769}{1380}\right)\)	\(e\left(\frac{199}{276}\right)\)	\(e\left(\frac{151}{1380}\right)\)	\(e\left(\frac{733}{1035}\right)\)	\(e\left(\frac{3787}{4140}\right)\)	\(e\left(\frac{421}{2070}\right)\)
\(\chi_{8507}(29,\cdot)\)	8507.ch	690	yes	\(-1\)	\(1\)	\(e\left(\frac{332}{345}\right)\)	\(e\left(\frac{52}{345}\right)\)	\(e\left(\frac{319}{345}\right)\)	\(e\left(\frac{83}{230}\right)\)	\(e\left(\frac{13}{115}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{102}{115}\right)\)	\(e\left(\frac{104}{345}\right)\)	\(e\left(\frac{223}{690}\right)\)	\(e\left(\frac{593}{690}\right)\)
\(\chi_{8507}(30,\cdot)\)	8507.cn	1380	yes	\(1\)	\(1\)	\(e\left(\frac{613}{1380}\right)\)	\(e\left(\frac{77}{345}\right)\)	\(e\left(\frac{613}{690}\right)\)	\(e\left(\frac{103}{230}\right)\)	\(e\left(\frac{307}{460}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{153}{460}\right)\)	\(e\left(\frac{154}{345}\right)\)	\(e\left(\frac{1231}{1380}\right)\)	\(e\left(\frac{104}{345}\right)\)
\(\chi_{8507}(31,\cdot)\)	8507.cf	460	yes	\(1\)	\(1\)	\(e\left(\frac{333}{460}\right)\)	\(e\left(\frac{12}{115}\right)\)	\(e\left(\frac{103}{230}\right)\)	\(e\left(\frac{199}{230}\right)\)	\(e\left(\frac{381}{460}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{79}{460}\right)\)	\(e\left(\frac{24}{115}\right)\)	\(e\left(\frac{271}{460}\right)\)	\(e\left(\frac{64}{115}\right)\)
\(\chi_{8507}(32,\cdot)\)	8507.cl	828	yes	\(-1\)	\(1\)	\(e\left(\frac{203}{828}\right)\)	\(e\left(\frac{142}{207}\right)\)	\(e\left(\frac{203}{414}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{257}{276}\right)\)	\(e\left(\frac{7}{276}\right)\)	\(e\left(\frac{203}{276}\right)\)	\(e\left(\frac{77}{207}\right)\)	\(e\left(\frac{443}{828}\right)\)	\(e\left(\frac{173}{414}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 8280 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.