LMFDB - Group of Dirichlet characters of modulus 31734

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(31734)

gp:g = idealstar(,31734,2)

magma:G = FullDirichletGroup(31734);

Character group

Order	=	10080	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{6}\times C_{840}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{31734}(14105,\cdot)$, $\chi_{31734}(30961,\cdot)$, $\chi_{31734}(22879,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 10080 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{31734}(1,\cdot)$	31734.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{31734}(5,\cdot)$	31734.lo	420	no	$1$	$1$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{32}{105}\right)$
$\chi_{31734}(7,\cdot)$	31734.iq	120	no	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{31734}(11,\cdot)$	31734.lu	840	no	$1$	$1$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{689}{840}\right)$	$e\left(\frac{433}{840}\right)$	$e\left(\frac{33}{280}\right)$	$e\left(\frac{69}{280}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{821}{840}\right)$	$e\left(\frac{151}{210}\right)$
$\chi_{31734}(13,\cdot)$	31734.lt	840	no	$-1$	$1$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{433}{840}\right)$	$e\left(\frac{61}{840}\right)$	$e\left(\frac{443}{840}\right)$	$e\left(\frac{379}{840}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{279}{280}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{31734}(17,\cdot)$	31734.lx	840	no	$1$	$1$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{33}{280}\right)$	$e\left(\frac{443}{840}\right)$	$e\left(\frac{89}{840}\right)$	$e\left(\frac{517}{840}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{311}{840}\right)$	$e\left(\frac{181}{210}\right)$
$\chi_{31734}(19,\cdot)$	31734.mc	840	no	$1$	$1$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{69}{280}\right)$	$e\left(\frac{379}{840}\right)$	$e\left(\frac{517}{840}\right)$	$e\left(\frac{521}{840}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{103}{840}\right)$	$e\left(\frac{143}{210}\right)$
$\chi_{31734}(23,\cdot)$	31734.kj	210	no	$-1$	$1$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{31734}(25,\cdot)$	31734.kc	210	no	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{64}{105}\right)$
$\chi_{31734}(29,\cdot)$	31734.lw	840	no	$-1$	$1$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{821}{840}\right)$	$e\left(\frac{279}{280}\right)$	$e\left(\frac{311}{840}\right)$	$e\left(\frac{103}{840}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{349}{840}\right)$	$e\left(\frac{89}{210}\right)$
$\chi_{31734}(31,\cdot)$	31734.kc	210	no	$1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{83}{105}\right)$
$\chi_{31734}(35,\cdot)$	31734.la	280	no	$1$	$1$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{261}{280}\right)$	$e\left(\frac{277}{280}\right)$	$e\left(\frac{31}{280}\right)$	$e\left(\frac{243}{280}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{209}{280}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{31734}(37,\cdot)$	31734.em	30	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{31734}(47,\cdot)$	31734.lu	840	no	$1$	$1$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{683}{840}\right)$	$e\left(\frac{211}{840}\right)$	$e\left(\frac{51}{280}\right)$	$e\left(\frac{183}{280}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{47}{840}\right)$	$e\left(\frac{157}{210}\right)$
$\chi_{31734}(49,\cdot)$	31734.hc	60	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{31734}(53,\cdot)$	31734.lx	840	no	$1$	$1$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{187}{280}\right)$	$e\left(\frac{457}{840}\right)$	$e\left(\frac{691}{840}\right)$	$e\left(\frac{503}{840}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{829}{840}\right)$	$e\left(\frac{209}{210}\right)$
$\chi_{31734}(55,\cdot)$	31734.jl	168	no	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{31734}(59,\cdot)$	31734.ks	210	no	$-1$	$1$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{31734}(61,\cdot)$	31734.le	420	no	$-1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{121}{420}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{64}{105}\right)$
$\chi_{31734}(65,\cdot)$	31734.lz	840	no	$-1$	$1$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{719}{840}\right)$	$e\left(\frac{703}{840}\right)$	$e\left(\frac{223}{280}\right)$	$e\left(\frac{199}{280}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{71}{840}\right)$	$e\left(\frac{121}{210}\right)$
$\chi_{31734}(67,\cdot)$	31734.md	840	no	$-1$	$1$	$e\left(\frac{347}{420}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{151}{840}\right)$	$e\left(\frac{89}{280}\right)$	$e\left(\frac{181}{840}\right)$	$e\left(\frac{773}{840}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{299}{840}\right)$	$e\left(\frac{199}{210}\right)$
$\chi_{31734}(71,\cdot)$	31734.lv	840	no	$-1$	$1$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{223}{280}\right)$	$e\left(\frac{533}{840}\right)$	$e\left(\frac{839}{840}\right)$	$e\left(\frac{367}{840}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{341}{840}\right)$	$e\left(\frac{31}{210}\right)$
$\chi_{31734}(73,\cdot)$	31734.ie	84	no	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{31734}(77,\cdot)$	31734.lc	420	no	$1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{311}{420}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{31734}(79,\cdot)$	31734.dx	24	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{31734}(83,\cdot)$	31734.gq	42	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{31734}(85,\cdot)$	31734.dw	24	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{31734}(89,\cdot)$	31734.lv	840	no	$-1$	$1$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{39}{280}\right)$	$e\left(\frac{829}{840}\right)$	$e\left(\frac{487}{840}\right)$	$e\left(\frac{191}{840}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{253}{840}\right)$	$e\left(\frac{23}{210}\right)$
$\chi_{31734}(91,\cdot)$	31734.ie	84	no	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{31734}(95,\cdot)$	31734.mh	840	no	$1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{493}{840}\right)$	$e\left(\frac{181}{840}\right)$	$e\left(\frac{743}{840}\right)$	$e\left(\frac{739}{840}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{59}{280}\right)$	$e\left(\frac{69}{70}\right)$
$\chi_{31734}(97,\cdot)$	31734.ma	840	no	$-1$	$1$	$e\left(\frac{227}{420}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{731}{840}\right)$	$e\left(\frac{727}{840}\right)$	$e\left(\frac{187}{280}\right)$	$e\left(\frac{251}{280}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{359}{840}\right)$	$e\left(\frac{109}{210}\right)$
$\chi_{31734}(101,\cdot)$	31734.ly	840	no	$1$	$1$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{347}{840}\right)$	$e\left(\frac{33}{280}\right)$	$e\left(\frac{377}{840}\right)$	$e\left(\frac{661}{840}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{103}{840}\right)$	$e\left(\frac{143}{210}\right)$

Click here to search among the remaining 10048 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 $\F_{q}$
Belyi maps

Modulus	$31734$
Structure	\(C_{2}\times C_{6}\times C_{840}\)
Order	$10080$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{31734}(1,\cdot)\)	31734.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{31734}(5,\cdot)\)	31734.lo	420	no	\(1\)	\(1\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{32}{105}\right)\)
\(\chi_{31734}(7,\cdot)\)	31734.iq	120	no	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{31734}(11,\cdot)\)	31734.lu	840	no	\(1\)	\(1\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{689}{840}\right)\)	\(e\left(\frac{433}{840}\right)\)	\(e\left(\frac{33}{280}\right)\)	\(e\left(\frac{69}{280}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{821}{840}\right)\)	\(e\left(\frac{151}{210}\right)\)
\(\chi_{31734}(13,\cdot)\)	31734.lt	840	no	\(-1\)	\(1\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{433}{840}\right)\)	\(e\left(\frac{61}{840}\right)\)	\(e\left(\frac{443}{840}\right)\)	\(e\left(\frac{379}{840}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{279}{280}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{31734}(17,\cdot)\)	31734.lx	840	no	\(1\)	\(1\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{33}{280}\right)\)	\(e\left(\frac{443}{840}\right)\)	\(e\left(\frac{89}{840}\right)\)	\(e\left(\frac{517}{840}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{311}{840}\right)\)	\(e\left(\frac{181}{210}\right)\)
\(\chi_{31734}(19,\cdot)\)	31734.mc	840	no	\(1\)	\(1\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{69}{280}\right)\)	\(e\left(\frac{379}{840}\right)\)	\(e\left(\frac{517}{840}\right)\)	\(e\left(\frac{521}{840}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{103}{840}\right)\)	\(e\left(\frac{143}{210}\right)\)
\(\chi_{31734}(23,\cdot)\)	31734.kj	210	no	\(-1\)	\(1\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{31734}(25,\cdot)\)	31734.kc	210	no	\(1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{64}{105}\right)\)
\(\chi_{31734}(29,\cdot)\)	31734.lw	840	no	\(-1\)	\(1\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{821}{840}\right)\)	\(e\left(\frac{279}{280}\right)\)	\(e\left(\frac{311}{840}\right)\)	\(e\left(\frac{103}{840}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{349}{840}\right)\)	\(e\left(\frac{89}{210}\right)\)
\(\chi_{31734}(31,\cdot)\)	31734.kc	210	no	\(1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{83}{105}\right)\)
\(\chi_{31734}(35,\cdot)\)	31734.la	280	no	\(1\)	\(1\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{261}{280}\right)\)	\(e\left(\frac{277}{280}\right)\)	\(e\left(\frac{31}{280}\right)\)	\(e\left(\frac{243}{280}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{209}{280}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{31734}(37,\cdot)\)	31734.em	30	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{31734}(47,\cdot)\)	31734.lu	840	no	\(1\)	\(1\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{683}{840}\right)\)	\(e\left(\frac{211}{840}\right)\)	\(e\left(\frac{51}{280}\right)\)	\(e\left(\frac{183}{280}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{47}{840}\right)\)	\(e\left(\frac{157}{210}\right)\)
\(\chi_{31734}(49,\cdot)\)	31734.hc	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{31734}(53,\cdot)\)	31734.lx	840	no	\(1\)	\(1\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{187}{280}\right)\)	\(e\left(\frac{457}{840}\right)\)	\(e\left(\frac{691}{840}\right)\)	\(e\left(\frac{503}{840}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{829}{840}\right)\)	\(e\left(\frac{209}{210}\right)\)
\(\chi_{31734}(55,\cdot)\)	31734.jl	168	no	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{31734}(59,\cdot)\)	31734.ks	210	no	\(-1\)	\(1\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{31734}(61,\cdot)\)	31734.le	420	no	\(-1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{121}{420}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{64}{105}\right)\)
\(\chi_{31734}(65,\cdot)\)	31734.lz	840	no	\(-1\)	\(1\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{719}{840}\right)\)	\(e\left(\frac{703}{840}\right)\)	\(e\left(\frac{223}{280}\right)\)	\(e\left(\frac{199}{280}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{71}{840}\right)\)	\(e\left(\frac{121}{210}\right)\)
\(\chi_{31734}(67,\cdot)\)	31734.md	840	no	\(-1\)	\(1\)	\(e\left(\frac{347}{420}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{151}{840}\right)\)	\(e\left(\frac{89}{280}\right)\)	\(e\left(\frac{181}{840}\right)\)	\(e\left(\frac{773}{840}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{299}{840}\right)\)	\(e\left(\frac{199}{210}\right)\)
\(\chi_{31734}(71,\cdot)\)	31734.lv	840	no	\(-1\)	\(1\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{223}{280}\right)\)	\(e\left(\frac{533}{840}\right)\)	\(e\left(\frac{839}{840}\right)\)	\(e\left(\frac{367}{840}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{341}{840}\right)\)	\(e\left(\frac{31}{210}\right)\)
\(\chi_{31734}(73,\cdot)\)	31734.ie	84	no	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{31734}(77,\cdot)\)	31734.lc	420	no	\(1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{311}{420}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{31734}(79,\cdot)\)	31734.dx	24	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{31734}(83,\cdot)\)	31734.gq	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{31734}(85,\cdot)\)	31734.dw	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{31734}(89,\cdot)\)	31734.lv	840	no	\(-1\)	\(1\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{39}{280}\right)\)	\(e\left(\frac{829}{840}\right)\)	\(e\left(\frac{487}{840}\right)\)	\(e\left(\frac{191}{840}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{253}{840}\right)\)	\(e\left(\frac{23}{210}\right)\)
\(\chi_{31734}(91,\cdot)\)	31734.ie	84	no	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{31734}(95,\cdot)\)	31734.mh	840	no	\(1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{493}{840}\right)\)	\(e\left(\frac{181}{840}\right)\)	\(e\left(\frac{743}{840}\right)\)	\(e\left(\frac{739}{840}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{59}{280}\right)\)	\(e\left(\frac{69}{70}\right)\)
\(\chi_{31734}(97,\cdot)\)	31734.ma	840	no	\(-1\)	\(1\)	\(e\left(\frac{227}{420}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{731}{840}\right)\)	\(e\left(\frac{727}{840}\right)\)	\(e\left(\frac{187}{280}\right)\)	\(e\left(\frac{251}{280}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{359}{840}\right)\)	\(e\left(\frac{109}{210}\right)\)
\(\chi_{31734}(101,\cdot)\)	31734.ly	840	no	\(1\)	\(1\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{347}{840}\right)\)	\(e\left(\frac{33}{280}\right)\)	\(e\left(\frac{377}{840}\right)\)	\(e\left(\frac{661}{840}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{103}{840}\right)\)	\(e\left(\frac{143}{210}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 10080 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.