LMFDB - Group of Dirichlet characters of modulus 8036

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8036)

pari: g = idealstar(,8036,2)

Character group

sage: G.order() pari: g.no
Order	=	3360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{840}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8036}(4019,\cdot)$, $\chi_{8036}(493,\cdot)$, $\chi_{8036}(785,\cdot)$

First 32 of 3360 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{8036}(1,\cdot)$	8036.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8036}(3,\cdot)$	8036.ee	168	yes	$-1$	$1$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{8036}(5,\cdot)$	8036.eq	420	no	$-1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{26}{105}\right)$
$\chi_{8036}(9,\cdot)$	8036.dp	84	no	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{8036}(11,\cdot)$	8036.ev	840	yes	$1$	$1$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{689}{840}\right)$	$e\left(\frac{211}{280}\right)$	$e\left(\frac{237}{280}\right)$	$e\left(\frac{239}{840}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{113}{210}\right)$
$\chi_{8036}(13,\cdot)$	8036.em	280	no	$1$	$1$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{211}{280}\right)$	$e\left(\frac{267}{280}\right)$	$e\left(\frac{69}{280}\right)$	$e\left(\frac{61}{280}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{47}{70}\right)$
$\chi_{8036}(15,\cdot)$	8036.eo	280	yes	$1$	$1$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{237}{280}\right)$	$e\left(\frac{69}{280}\right)$	$e\left(\frac{43}{280}\right)$	$e\left(\frac{107}{280}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{9}{70}\right)$
$\chi_{8036}(17,\cdot)$	8036.ex	840	no	$1$	$1$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{239}{840}\right)$	$e\left(\frac{61}{280}\right)$	$e\left(\frac{107}{280}\right)$	$e\left(\frac{89}{840}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{173}{210}\right)$
$\chi_{8036}(19,\cdot)$	8036.dv	120	no	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{8036}(23,\cdot)$	8036.ej	210	yes	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{8}{105}\right)$
$\chi_{8036}(25,\cdot)$	8036.ef	210	no	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{52}{105}\right)$
$\chi_{8036}(27,\cdot)$	8036.cz	56	yes	$-1$	$1$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{8036}(29,\cdot)$	8036.en	280	no	$-1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{187}{280}\right)$	$e\left(\frac{159}{280}\right)$	$e\left(\frac{93}{280}\right)$	$e\left(\frac{137}{280}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{39}{70}\right)$
$\chi_{8036}(31,\cdot)$	8036.cj	30	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{8036}(33,\cdot)$	8036.eq	420	no	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{44}{105}\right)$
$\chi_{8036}(37,\cdot)$	8036.ds	105	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{41}{105}\right)$
$\chi_{8036}(39,\cdot)$	8036.et	420	yes	$-1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{79}{420}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{58}{105}\right)$
$\chi_{8036}(43,\cdot)$	8036.dx	140	yes	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{8036}(45,\cdot)$	8036.el	210	no	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{1}{105}\right)$
$\chi_{8036}(47,\cdot)$	8036.eu	840	yes	$-1$	$1$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{283}{840}\right)$	$e\left(\frac{197}{280}\right)$	$e\left(\frac{279}{280}\right)$	$e\left(\frac{673}{840}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{1}{210}\right)$
$\chi_{8036}(51,\cdot)$	8036.eg	210	yes	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{74}{105}\right)$
$\chi_{8036}(53,\cdot)$	8036.ew	840	no	$-1$	$1$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{461}{840}\right)$	$e\left(\frac{219}{280}\right)$	$e\left(\frac{33}{280}\right)$	$e\left(\frac{191}{840}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{107}{210}\right)$
$\chi_{8036}(55,\cdot)$	8036.cz	56	yes	$-1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{8036}(57,\cdot)$	8036.cn	35	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{8036}(59,\cdot)$	8036.ek	210	yes	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{58}{105}\right)$
$\chi_{8036}(61,\cdot)$	8036.eq	420	no	$-1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{62}{105}\right)$
$\chi_{8036}(65,\cdot)$	8036.ew	840	no	$-1$	$1$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{19}{840}\right)$	$e\left(\frac{221}{280}\right)$	$e\left(\frac{87}{280}\right)$	$e\left(\frac{529}{840}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{193}{210}\right)$
$\chi_{8036}(67,\cdot)$	8036.dw	120	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{8036}(69,\cdot)$	8036.em	280	no	$1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{271}{280}\right)$	$e\left(\frac{47}{280}\right)$	$e\left(\frac{9}{280}\right)$	$e\left(\frac{81}{280}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{67}{70}\right)$
$\chi_{8036}(71,\cdot)$	8036.eo	280	yes	$1$	$1$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{23}{280}\right)$	$e\left(\frac{191}{280}\right)$	$e\left(\frac{257}{280}\right)$	$e\left(\frac{73}{280}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{8036}(73,\cdot)$	8036.dr	84	no	$-1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{8036}(75,\cdot)$	8036.eu	840	yes	$-1$	$1$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{79}{420}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{97}{840}\right)$	$e\left(\frac{23}{280}\right)$	$e\left(\frac{61}{280}\right)$	$e\left(\frac{667}{840}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{79}{210}\right)$

Click here to search among the remaining 3328 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	$8036$
Structure	\(C_{2}\times C_{2}\times C_{840}\)
Order	$3360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{8036}(1,\cdot)\)	8036.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8036}(3,\cdot)\)	8036.ee	168	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{8036}(5,\cdot)\)	8036.eq	420	no	\(-1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)
\(\chi_{8036}(9,\cdot)\)	8036.dp	84	no	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{8036}(11,\cdot)\)	8036.ev	840	yes	\(1\)	\(1\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{689}{840}\right)\)	\(e\left(\frac{211}{280}\right)\)	\(e\left(\frac{237}{280}\right)\)	\(e\left(\frac{239}{840}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{113}{210}\right)\)
\(\chi_{8036}(13,\cdot)\)	8036.em	280	no	\(1\)	\(1\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{211}{280}\right)\)	\(e\left(\frac{267}{280}\right)\)	\(e\left(\frac{69}{280}\right)\)	\(e\left(\frac{61}{280}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)
\(\chi_{8036}(15,\cdot)\)	8036.eo	280	yes	\(1\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{237}{280}\right)\)	\(e\left(\frac{69}{280}\right)\)	\(e\left(\frac{43}{280}\right)\)	\(e\left(\frac{107}{280}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)
\(\chi_{8036}(17,\cdot)\)	8036.ex	840	no	\(1\)	\(1\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{239}{840}\right)\)	\(e\left(\frac{61}{280}\right)\)	\(e\left(\frac{107}{280}\right)\)	\(e\left(\frac{89}{840}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{173}{210}\right)\)
\(\chi_{8036}(19,\cdot)\)	8036.dv	120	no	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{8036}(23,\cdot)\)	8036.ej	210	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)
\(\chi_{8036}(25,\cdot)\)	8036.ef	210	no	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)
\(\chi_{8036}(27,\cdot)\)	8036.cz	56	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{8036}(29,\cdot)\)	8036.en	280	no	\(-1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{187}{280}\right)\)	\(e\left(\frac{159}{280}\right)\)	\(e\left(\frac{93}{280}\right)\)	\(e\left(\frac{137}{280}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)
\(\chi_{8036}(31,\cdot)\)	8036.cj	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{8036}(33,\cdot)\)	8036.eq	420	no	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)
\(\chi_{8036}(37,\cdot)\)	8036.ds	105	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)
\(\chi_{8036}(39,\cdot)\)	8036.et	420	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{79}{420}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)
\(\chi_{8036}(43,\cdot)\)	8036.dx	140	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{8036}(45,\cdot)\)	8036.el	210	no	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)
\(\chi_{8036}(47,\cdot)\)	8036.eu	840	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{283}{840}\right)\)	\(e\left(\frac{197}{280}\right)\)	\(e\left(\frac{279}{280}\right)\)	\(e\left(\frac{673}{840}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{1}{210}\right)\)
\(\chi_{8036}(51,\cdot)\)	8036.eg	210	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{74}{105}\right)\)
\(\chi_{8036}(53,\cdot)\)	8036.ew	840	no	\(-1\)	\(1\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{461}{840}\right)\)	\(e\left(\frac{219}{280}\right)\)	\(e\left(\frac{33}{280}\right)\)	\(e\left(\frac{191}{840}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{107}{210}\right)\)
\(\chi_{8036}(55,\cdot)\)	8036.cz	56	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{8036}(57,\cdot)\)	8036.cn	35	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{8036}(59,\cdot)\)	8036.ek	210	yes	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)
\(\chi_{8036}(61,\cdot)\)	8036.eq	420	no	\(-1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)
\(\chi_{8036}(65,\cdot)\)	8036.ew	840	no	\(-1\)	\(1\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{19}{840}\right)\)	\(e\left(\frac{221}{280}\right)\)	\(e\left(\frac{87}{280}\right)\)	\(e\left(\frac{529}{840}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{193}{210}\right)\)
\(\chi_{8036}(67,\cdot)\)	8036.dw	120	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{8036}(69,\cdot)\)	8036.em	280	no	\(1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{271}{280}\right)\)	\(e\left(\frac{47}{280}\right)\)	\(e\left(\frac{9}{280}\right)\)	\(e\left(\frac{81}{280}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)
\(\chi_{8036}(71,\cdot)\)	8036.eo	280	yes	\(1\)	\(1\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{23}{280}\right)\)	\(e\left(\frac{191}{280}\right)\)	\(e\left(\frac{257}{280}\right)\)	\(e\left(\frac{73}{280}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{8036}(73,\cdot)\)	8036.dr	84	no	\(-1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{8036}(75,\cdot)\)	8036.eu	840	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{79}{420}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{97}{840}\right)\)	\(e\left(\frac{23}{280}\right)\)	\(e\left(\frac{61}{280}\right)\)	\(e\left(\frac{667}{840}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{79}{210}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 3360 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.