LMFDB - Dirichlet character orbit 40310.ep

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(276)) M = H._module chi = DirichletCharacter(H, M([69,207,214])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(17,40310)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$40310$
Conductor:	$20155$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$276$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 20155.ef	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{276})$
Fixed field:	Number field defined by a degree 276 polynomial (not computed)

First 31 of 88 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(17,\cdot)$	$-1$	$1$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{5}{276}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{187}{276}\right)$	$e\left(\frac{241}{276}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{151}{276}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{20}{23}\right)$
$\chi_{40310}(273,\cdot)$	$-1$	$1$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{251}{276}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{169}{276}\right)$	$e\left(\frac{175}{276}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{73}{276}\right)$	$e\left(\frac{127}{276}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{40310}(853,\cdot)$	$-1$	$1$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{235}{276}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{233}{276}\right)$	$e\left(\frac{11}{276}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{197}{276}\right)$	$e\left(\frac{131}{276}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{20}{23}\right)$
$\chi_{40310}(887,\cdot)$	$-1$	$1$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{77}{276}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{175}{276}\right)$	$e\left(\frac{13}{276}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{7}{276}\right)$	$e\left(\frac{205}{276}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{9}{23}\right)$
$\chi_{40310}(2047,\cdot)$	$-1$	$1$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{197}{276}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{247}{276}\right)$	$e\left(\frac{1}{276}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{43}{276}\right)$	$e\left(\frac{37}{276}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{40310}(3173,\cdot)$	$-1$	$1$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{191}{276}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{133}{276}\right)$	$e\left(\frac{43}{276}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{211}{276}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{40310}(3497,\cdot)$	$-1$	$1$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{41}{276}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{43}{276}\right)$	$e\left(\frac{265}{276}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{79}{276}\right)$	$e\left(\frac{145}{276}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{40310}(4043,\cdot)$	$-1$	$1$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{91}{276}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{257}{276}\right)$	$e\left(\frac{191}{276}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{209}{276}\right)$	$e\left(\frac{167}{276}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{19}{23}\right)$
$\chi_{40310}(4367,\cdot)$	$-1$	$1$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{185}{276}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{19}{276}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{67}{276}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{4}{23}\right)$
$\chi_{40310}(4657,\cdot)$	$-1$	$1$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{245}{276}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{55}{276}\right)$	$e\left(\frac{217}{276}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{223}{276}\right)$	$e\left(\frac{25}{276}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{14}{23}\right)$
$\chi_{40310}(5493,\cdot)$	$-1$	$1$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{151}{276}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{17}{276}\right)$	$e\left(\frac{47}{276}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{89}{276}\right)$	$e\left(\frac{83}{276}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{40310}(6107,\cdot)$	$-1$	$1$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{265}{276}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{251}{276}\right)$	$e\left(\frac{77}{276}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{275}{276}\right)$	$e\left(\frac{89}{276}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{2}{23}\right)$
$\chi_{40310}(6363,\cdot)$	$-1$	$1$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{11}{276}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{25}{276}\right)$	$e\left(\frac{199}{276}\right)$	$e\left(\frac{127}{138}\right)$	$e\left(\frac{1}{276}\right)$	$e\left(\frac{187}{276}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{21}{23}\right)$
$\chi_{40310}(6397,\cdot)$	$-1$	$1$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{29}{276}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{91}{276}\right)$	$e\left(\frac{73}{276}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{103}{276}\right)$	$e\left(\frac{217}{276}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{1}{23}\right)$
$\chi_{40310}(6687,\cdot)$	$-1$	$1$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{73}{276}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{191}{276}\right)$	$e\left(\frac{41}{276}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{107}{276}\right)$	$e\left(\frac{137}{276}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{16}{23}\right)$
$\chi_{40310}(6943,\cdot)$	$-1$	$1$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{239}{276}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{217}{276}\right)$	$e\left(\frac{259}{276}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{97}{276}\right)$	$e\left(\frac{199}{276}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{13}{23}\right)$
$\chi_{40310}(7523,\cdot)$	$-1$	$1$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{143}{276}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{49}{276}\right)$	$e\left(\frac{103}{276}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{13}{276}\right)$	$e\left(\frac{223}{276}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{20}{23}\right)$
$\chi_{40310}(8393,\cdot)$	$-1$	$1$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{215}{276}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{37}{276}\right)$	$e\left(\frac{151}{276}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{145}{276}\right)$	$e\left(\frac{67}{276}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{9}{23}\right)$
$\chi_{40310}(9007,\cdot)$	$-1$	$1$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{25}{276}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{107}{276}\right)$	$e\left(\frac{101}{276}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{203}{276}\right)$	$e\left(\frac{149}{276}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{40310}(9297,\cdot)$	$-1$	$1$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{263}{276}\right)$	$e\left(\frac{29}{276}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{143}{276}\right)$	$e\left(\frac{245}{276}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{13}{23}\right)$
$\chi_{40310}(9553,\cdot)$	$-1$	$1$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{59}{276}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{139}{276}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{181}{276}\right)$	$e\left(\frac{175}{276}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{40310}(9587,\cdot)$	$-1$	$1$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{269}{276}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{235}{276}\right)$	$e\left(\frac{49}{276}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{175}{276}\right)$	$e\left(\frac{157}{276}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{18}{23}\right)$
$\chi_{40310}(10457,\cdot)$	$-1$	$1$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{17}{276}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{139}{276}\right)$	$e\left(\frac{157}{276}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{127}{276}\right)$	$e\left(\frac{13}{276}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{40310}(11003,\cdot)$	$-1$	$1$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{179}{276}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{181}{276}\right)$	$e\left(\frac{127}{276}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{217}{276}\right)$	$e\left(\frac{7}{276}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{40310}(11037,\cdot)$	$-1$	$1$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{125}{276}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{259}{276}\right)$	$e\left(\frac{229}{276}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{187}{276}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{17}{23}\right)$
$\chi_{40310}(11327,\cdot)$	$-1$	$1$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{205}{276}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{215}{276}\right)$	$e\left(\frac{221}{276}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{119}{276}\right)$	$e\left(\frac{173}{276}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{40310}(11873,\cdot)$	$-1$	$1$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{47}{276}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{157}{276}\right)$	$e\left(\frac{223}{276}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{205}{276}\right)$	$e\left(\frac{247}{276}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{4}{23}\right)$
$\chi_{40310}(11907,\cdot)$	$-1$	$1$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{209}{276}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{199}{276}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{19}{276}\right)$	$e\left(\frac{241}{276}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{40310}(12163,\cdot)$	$-1$	$1$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{107}{276}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{79}{276}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{163}{276}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{14}{23}\right)$
$\chi_{40310}(12197,\cdot)$	$-1$	$1$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{145}{276}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{179}{276}\right)$	$e\left(\frac{89}{276}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{239}{276}\right)$	$e\left(\frac{257}{276}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{40310}(12777,\cdot)$	$-1$	$1$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{217}{276}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{167}{276}\right)$	$e\left(\frac{137}{276}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{95}{276}\right)$	$e\left(\frac{101}{276}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{17}{23}\right)$

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

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(17,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{5}{276}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{187}{276}\right)\)	\(e\left(\frac{241}{276}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{151}{276}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{20}{23}\right)\)
\(\chi_{40310}(273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{251}{276}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{169}{276}\right)\)	\(e\left(\frac{175}{276}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{73}{276}\right)\)	\(e\left(\frac{127}{276}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{40310}(853,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{235}{276}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{233}{276}\right)\)	\(e\left(\frac{11}{276}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{197}{276}\right)\)	\(e\left(\frac{131}{276}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{20}{23}\right)\)
\(\chi_{40310}(887,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{77}{276}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{175}{276}\right)\)	\(e\left(\frac{13}{276}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{7}{276}\right)\)	\(e\left(\frac{205}{276}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{9}{23}\right)\)
\(\chi_{40310}(2047,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{197}{276}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{247}{276}\right)\)	\(e\left(\frac{1}{276}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{43}{276}\right)\)	\(e\left(\frac{37}{276}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{40310}(3173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{191}{276}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{133}{276}\right)\)	\(e\left(\frac{43}{276}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{211}{276}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{40310}(3497,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{41}{276}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{43}{276}\right)\)	\(e\left(\frac{265}{276}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{79}{276}\right)\)	\(e\left(\frac{145}{276}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{40310}(4043,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{91}{276}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{257}{276}\right)\)	\(e\left(\frac{191}{276}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{209}{276}\right)\)	\(e\left(\frac{167}{276}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{19}{23}\right)\)
\(\chi_{40310}(4367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{185}{276}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{19}{276}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{67}{276}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{4}{23}\right)\)
\(\chi_{40310}(4657,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{245}{276}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{55}{276}\right)\)	\(e\left(\frac{217}{276}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{223}{276}\right)\)	\(e\left(\frac{25}{276}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{14}{23}\right)\)
\(\chi_{40310}(5493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{151}{276}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{17}{276}\right)\)	\(e\left(\frac{47}{276}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{89}{276}\right)\)	\(e\left(\frac{83}{276}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{40310}(6107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{265}{276}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{251}{276}\right)\)	\(e\left(\frac{77}{276}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{275}{276}\right)\)	\(e\left(\frac{89}{276}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{2}{23}\right)\)
\(\chi_{40310}(6363,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{11}{276}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{25}{276}\right)\)	\(e\left(\frac{199}{276}\right)\)	\(e\left(\frac{127}{138}\right)\)	\(e\left(\frac{1}{276}\right)\)	\(e\left(\frac{187}{276}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{21}{23}\right)\)
\(\chi_{40310}(6397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{29}{276}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{91}{276}\right)\)	\(e\left(\frac{73}{276}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{103}{276}\right)\)	\(e\left(\frac{217}{276}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{1}{23}\right)\)
\(\chi_{40310}(6687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{73}{276}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{191}{276}\right)\)	\(e\left(\frac{41}{276}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{107}{276}\right)\)	\(e\left(\frac{137}{276}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{16}{23}\right)\)
\(\chi_{40310}(6943,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{239}{276}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{217}{276}\right)\)	\(e\left(\frac{259}{276}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{97}{276}\right)\)	\(e\left(\frac{199}{276}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)
\(\chi_{40310}(7523,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{143}{276}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{49}{276}\right)\)	\(e\left(\frac{103}{276}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{13}{276}\right)\)	\(e\left(\frac{223}{276}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{20}{23}\right)\)
\(\chi_{40310}(8393,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{215}{276}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{37}{276}\right)\)	\(e\left(\frac{151}{276}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{145}{276}\right)\)	\(e\left(\frac{67}{276}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{9}{23}\right)\)
\(\chi_{40310}(9007,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{25}{276}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{107}{276}\right)\)	\(e\left(\frac{101}{276}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{203}{276}\right)\)	\(e\left(\frac{149}{276}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{40310}(9297,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{263}{276}\right)\)	\(e\left(\frac{29}{276}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{143}{276}\right)\)	\(e\left(\frac{245}{276}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)
\(\chi_{40310}(9553,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{59}{276}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{139}{276}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{181}{276}\right)\)	\(e\left(\frac{175}{276}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{40310}(9587,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{269}{276}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{235}{276}\right)\)	\(e\left(\frac{49}{276}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{175}{276}\right)\)	\(e\left(\frac{157}{276}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{18}{23}\right)\)
\(\chi_{40310}(10457,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{17}{276}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{139}{276}\right)\)	\(e\left(\frac{157}{276}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{127}{276}\right)\)	\(e\left(\frac{13}{276}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{40310}(11003,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{179}{276}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{181}{276}\right)\)	\(e\left(\frac{127}{276}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{217}{276}\right)\)	\(e\left(\frac{7}{276}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{40310}(11037,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{125}{276}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{259}{276}\right)\)	\(e\left(\frac{229}{276}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{187}{276}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{17}{23}\right)\)
\(\chi_{40310}(11327,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{205}{276}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{215}{276}\right)\)	\(e\left(\frac{221}{276}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{119}{276}\right)\)	\(e\left(\frac{173}{276}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{40310}(11873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{47}{276}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{157}{276}\right)\)	\(e\left(\frac{223}{276}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{205}{276}\right)\)	\(e\left(\frac{247}{276}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{4}{23}\right)\)
\(\chi_{40310}(11907,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{209}{276}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{199}{276}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{19}{276}\right)\)	\(e\left(\frac{241}{276}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{40310}(12163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{107}{276}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{79}{276}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{163}{276}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{14}{23}\right)\)
\(\chi_{40310}(12197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{145}{276}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{179}{276}\right)\)	\(e\left(\frac{89}{276}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{239}{276}\right)\)	\(e\left(\frac{257}{276}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{40310}(12777,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{217}{276}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{167}{276}\right)\)	\(e\left(\frac{137}{276}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{95}{276}\right)\)	\(e\left(\frac{101}{276}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{17}{23}\right)\)

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First 31 of 88 characters in Galois orbit

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

Label	40310.ep
Modulus	$40310$
Conductor	$20155$
Order	$276$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(40310\)
Conductor:	\(20155\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(276\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 20155.ef	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)