LMFDB - Dirichlet character orbit 40310.fg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(644)) M = H._module chi = DirichletCharacter(H, M([483,460,126])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(23,40310)) 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:	$644$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 20155.fi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{644})$
Fixed field:	Number field defined by a degree 644 polynomial (not computed)

First 31 of 264 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(23,\cdot)$	$1$	$1$	$e\left(\frac{543}{644}\right)$	$e\left(\frac{67}{644}\right)$	$e\left(\frac{221}{322}\right)$	$e\left(\frac{117}{161}\right)$	$e\left(\frac{405}{644}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{139}{161}\right)$	$e\left(\frac{305}{322}\right)$	$e\left(\frac{527}{644}\right)$	$e\left(\frac{341}{644}\right)$
$\chi_{40310}(103,\cdot)$	$1$	$1$	$e\left(\frac{271}{644}\right)$	$e\left(\frac{579}{644}\right)$	$e\left(\frac{271}{322}\right)$	$e\left(\frac{134}{161}\right)$	$e\left(\frac{501}{644}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{67}{161}\right)$	$e\left(\frac{103}{322}\right)$	$e\left(\frac{27}{644}\right)$	$e\left(\frac{169}{644}\right)$
$\chi_{40310}(223,\cdot)$	$1$	$1$	$e\left(\frac{107}{644}\right)$	$e\left(\frac{471}{644}\right)$	$e\left(\frac{107}{322}\right)$	$e\left(\frac{104}{161}\right)$	$e\left(\frac{521}{644}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{52}{161}\right)$	$e\left(\frac{289}{322}\right)$	$e\left(\frac{379}{644}\right)$	$e\left(\frac{321}{644}\right)$
$\chi_{40310}(373,\cdot)$	$1$	$1$	$e\left(\frac{503}{644}\right)$	$e\left(\frac{559}{644}\right)$	$e\left(\frac{181}{322}\right)$	$e\left(\frac{39}{161}\right)$	$e\left(\frac{457}{644}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{100}{161}\right)$	$e\left(\frac{209}{322}\right)$	$e\left(\frac{283}{644}\right)$	$e\left(\frac{221}{644}\right)$
$\chi_{40310}(703,\cdot)$	$1$	$1$	$e\left(\frac{183}{644}\right)$	$e\left(\frac{631}{644}\right)$	$e\left(\frac{183}{322}\right)$	$e\left(\frac{59}{161}\right)$	$e\left(\frac{229}{644}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{110}{161}\right)$	$e\left(\frac{85}{322}\right)$	$e\left(\frac{263}{644}\right)$	$e\left(\frac{549}{644}\right)$
$\chi_{40310}(777,\cdot)$	$1$	$1$	$e\left(\frac{81}{644}\right)$	$e\left(\frac{501}{644}\right)$	$e\left(\frac{81}{322}\right)$	$e\left(\frac{5}{161}\right)$	$e\left(\frac{587}{644}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{83}{161}\right)$	$e\left(\frac{291}{322}\right)$	$e\left(\frac{317}{644}\right)$	$e\left(\frac{243}{644}\right)$
$\chi_{40310}(857,\cdot)$	$1$	$1$	$e\left(\frac{313}{644}\right)$	$e\left(\frac{481}{644}\right)$	$e\left(\frac{313}{322}\right)$	$e\left(\frac{71}{161}\right)$	$e\left(\frac{543}{644}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{116}{161}\right)$	$e\left(\frac{75}{322}\right)$	$e\left(\frac{573}{644}\right)$	$e\left(\frac{295}{644}\right)$
$\chi_{40310}(893,\cdot)$	$1$	$1$	$e\left(\frac{39}{644}\right)$	$e\left(\frac{599}{644}\right)$	$e\left(\frac{39}{322}\right)$	$e\left(\frac{68}{161}\right)$	$e\left(\frac{545}{644}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{34}{161}\right)$	$e\left(\frac{319}{322}\right)$	$e\left(\frac{415}{644}\right)$	$e\left(\frac{117}{644}\right)$
$\chi_{40310}(1067,\cdot)$	$1$	$1$	$e\left(\frac{473}{644}\right)$	$e\left(\frac{445}{644}\right)$	$e\left(\frac{151}{322}\right)$	$e\left(\frac{61}{161}\right)$	$e\left(\frac{335}{644}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{111}{161}\right)$	$e\left(\frac{137}{322}\right)$	$e\left(\frac{261}{644}\right)$	$e\left(\frac{131}{644}\right)$
$\chi_{40310}(1417,\cdot)$	$1$	$1$	$e\left(\frac{97}{644}\right)$	$e\left(\frac{433}{644}\right)$	$e\left(\frac{97}{322}\right)$	$e\left(\frac{4}{161}\right)$	$e\left(\frac{51}{644}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{2}{161}\right)$	$e\left(\frac{265}{322}\right)$	$e\left(\frac{157}{644}\right)$	$e\left(\frac{291}{644}\right)$
$\chi_{40310}(1707,\cdot)$	$1$	$1$	$e\left(\frac{517}{644}\right)$	$e\left(\frac{97}{644}\right)$	$e\left(\frac{195}{322}\right)$	$e\left(\frac{18}{161}\right)$	$e\left(\frac{471}{644}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{9}{161}\right)$	$e\left(\frac{307}{322}\right)$	$e\left(\frac{465}{644}\right)$	$e\left(\frac{263}{644}\right)$
$\chi_{40310}(1727,\cdot)$	$1$	$1$	$e\left(\frac{453}{644}\right)$	$e\left(\frac{369}{644}\right)$	$e\left(\frac{131}{322}\right)$	$e\left(\frac{22}{161}\right)$	$e\left(\frac{39}{644}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{11}{161}\right)$	$e\left(\frac{89}{322}\right)$	$e\left(\frac{461}{644}\right)$	$e\left(\frac{71}{644}\right)$
$\chi_{40310}(1763,\cdot)$	$1$	$1$	$e\left(\frac{319}{644}\right)$	$e\left(\frac{375}{644}\right)$	$e\left(\frac{319}{322}\right)$	$e\left(\frac{131}{161}\right)$	$e\left(\frac{181}{644}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{146}{161}\right)$	$e\left(\frac{25}{322}\right)$	$e\left(\frac{191}{644}\right)$	$e\left(\frac{313}{644}\right)$
$\chi_{40310}(2133,\cdot)$	$1$	$1$	$e\left(\frac{215}{644}\right)$	$e\left(\frac{495}{644}\right)$	$e\left(\frac{215}{322}\right)$	$e\left(\frac{57}{161}\right)$	$e\left(\frac{445}{644}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{109}{161}\right)$	$e\left(\frac{33}{322}\right)$	$e\left(\frac{587}{644}\right)$	$e\left(\frac{1}{644}\right)$
$\chi_{40310}(2257,\cdot)$	$1$	$1$	$e\left(\frac{605}{644}\right)$	$e\left(\frac{45}{644}\right)$	$e\left(\frac{283}{322}\right)$	$e\left(\frac{93}{161}\right)$	$e\left(\frac{99}{644}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{127}{161}\right)$	$e\left(\frac{3}{322}\right)$	$e\left(\frac{229}{644}\right)$	$e\left(\frac{527}{644}\right)$
$\chi_{40310}(2327,\cdot)$	$1$	$1$	$e\left(\frac{225}{644}\right)$	$e\left(\frac{533}{644}\right)$	$e\left(\frac{225}{322}\right)$	$e\left(\frac{157}{161}\right)$	$e\left(\frac{271}{644}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{159}{161}\right)$	$e\left(\frac{57}{322}\right)$	$e\left(\frac{165}{644}\right)$	$e\left(\frac{31}{644}\right)$
$\chi_{40310}(2373,\cdot)$	$1$	$1$	$e\left(\frac{339}{644}\right)$	$e\left(\frac{451}{644}\right)$	$e\left(\frac{17}{322}\right)$	$e\left(\frac{9}{161}\right)$	$e\left(\frac{477}{644}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{85}{161}\right)$	$e\left(\frac{73}{322}\right)$	$e\left(\frac{635}{644}\right)$	$e\left(\frac{373}{644}\right)$
$\chi_{40310}(2423,\cdot)$	$1$	$1$	$e\left(\frac{187}{644}\right)$	$e\left(\frac{131}{644}\right)$	$e\left(\frac{187}{322}\right)$	$e\left(\frac{99}{161}\right)$	$e\left(\frac{417}{644}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{130}{161}\right)$	$e\left(\frac{159}{322}\right)$	$e\left(\frac{223}{644}\right)$	$e\left(\frac{561}{644}\right)$
$\chi_{40310}(2577,\cdot)$	$1$	$1$	$e\left(\frac{573}{644}\right)$	$e\left(\frac{181}{644}\right)$	$e\left(\frac{251}{322}\right)$	$e\left(\frac{95}{161}\right)$	$e\left(\frac{527}{644}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{128}{161}\right)$	$e\left(\frac{55}{322}\right)$	$e\left(\frac{549}{644}\right)$	$e\left(\frac{431}{644}\right)$
$\chi_{40310}(2597,\cdot)$	$1$	$1$	$e\left(\frac{89}{644}\right)$	$e\left(\frac{145}{644}\right)$	$e\left(\frac{89}{322}\right)$	$e\left(\frac{85}{161}\right)$	$e\left(\frac{319}{644}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{123}{161}\right)$	$e\left(\frac{117}{322}\right)$	$e\left(\frac{237}{644}\right)$	$e\left(\frac{267}{644}\right)$
$\chi_{40310}(2717,\cdot)$	$1$	$1$	$e\left(\frac{485}{644}\right)$	$e\left(\frac{233}{644}\right)$	$e\left(\frac{163}{322}\right)$	$e\left(\frac{20}{161}\right)$	$e\left(\frac{255}{644}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{10}{161}\right)$	$e\left(\frac{37}{322}\right)$	$e\left(\frac{141}{644}\right)$	$e\left(\frac{167}{644}\right)$
$\chi_{40310}(2807,\cdot)$	$1$	$1$	$e\left(\frac{557}{644}\right)$	$e\left(\frac{249}{644}\right)$	$e\left(\frac{235}{322}\right)$	$e\left(\frac{96}{161}\right)$	$e\left(\frac{419}{644}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{48}{161}\right)$	$e\left(\frac{81}{322}\right)$	$e\left(\frac{65}{644}\right)$	$e\left(\frac{383}{644}\right)$
$\chi_{40310}(2867,\cdot)$	$1$	$1$	$e\left(\frac{461}{644}\right)$	$e\left(\frac{13}{644}\right)$	$e\left(\frac{139}{322}\right)$	$e\left(\frac{102}{161}\right)$	$e\left(\frac{415}{644}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{51}{161}\right)$	$e\left(\frac{237}{322}\right)$	$e\left(\frac{381}{644}\right)$	$e\left(\frac{95}{644}\right)$
$\chi_{40310}(3003,\cdot)$	$1$	$1$	$e\left(\frac{383}{644}\right)$	$e\left(\frac{103}{644}\right)$	$e\left(\frac{61}{322}\right)$	$e\left(\frac{127}{161}\right)$	$e\left(\frac{613}{644}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{144}{161}\right)$	$e\left(\frac{243}{322}\right)$	$e\left(\frac{195}{644}\right)$	$e\left(\frac{505}{644}\right)$
$\chi_{40310}(3097,\cdot)$	$1$	$1$	$e\left(\frac{333}{644}\right)$	$e\left(\frac{557}{644}\right)$	$e\left(\frac{11}{322}\right)$	$e\left(\frac{110}{161}\right)$	$e\left(\frac{195}{644}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{55}{161}\right)$	$e\left(\frac{123}{322}\right)$	$e\left(\frac{373}{644}\right)$	$e\left(\frac{355}{644}\right)$
$\chi_{40310}(3273,\cdot)$	$1$	$1$	$e\left(\frac{531}{644}\right)$	$e\left(\frac{279}{644}\right)$	$e\left(\frac{209}{322}\right)$	$e\left(\frac{158}{161}\right)$	$e\left(\frac{485}{644}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{79}{161}\right)$	$e\left(\frac{83}{322}\right)$	$e\left(\frac{3}{644}\right)$	$e\left(\frac{305}{644}\right)$
$\chi_{40310}(3967,\cdot)$	$1$	$1$	$e\left(\frac{389}{644}\right)$	$e\left(\frac{641}{644}\right)$	$e\left(\frac{67}{322}\right)$	$e\left(\frac{26}{161}\right)$	$e\left(\frac{251}{644}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{13}{161}\right)$	$e\left(\frac{193}{322}\right)$	$e\left(\frac{457}{644}\right)$	$e\left(\frac{523}{644}\right)$
$\chi_{40310}(3997,\cdot)$	$1$	$1$	$e\left(\frac{493}{644}\right)$	$e\left(\frac{521}{644}\right)$	$e\left(\frac{171}{322}\right)$	$e\left(\frac{100}{161}\right)$	$e\left(\frac{631}{644}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{50}{161}\right)$	$e\left(\frac{185}{322}\right)$	$e\left(\frac{61}{644}\right)$	$e\left(\frac{191}{644}\right)$
$\chi_{40310}(4113,\cdot)$	$1$	$1$	$e\left(\frac{311}{644}\right)$	$e\left(\frac{87}{644}\right)$	$e\left(\frac{311}{322}\right)$	$e\left(\frac{51}{161}\right)$	$e\left(\frac{449}{644}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{106}{161}\right)$	$e\left(\frac{199}{322}\right)$	$e\left(\frac{271}{644}\right)$	$e\left(\frac{289}{644}\right)$
$\chi_{40310}(4257,\cdot)$	$1$	$1$	$e\left(\frac{277}{644}\right)$	$e\left(\frac{473}{644}\right)$	$e\left(\frac{277}{322}\right)$	$e\left(\frac{33}{161}\right)$	$e\left(\frac{139}{644}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{97}{161}\right)$	$e\left(\frac{53}{322}\right)$	$e\left(\frac{289}{644}\right)$	$e\left(\frac{187}{644}\right)$
$\chi_{40310}(4317,\cdot)$	$1$	$1$	$e\left(\frac{321}{644}\right)$	$e\left(\frac{125}{644}\right)$	$e\left(\frac{321}{322}\right)$	$e\left(\frac{151}{161}\right)$	$e\left(\frac{275}{644}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{156}{161}\right)$	$e\left(\frac{223}{322}\right)$	$e\left(\frac{493}{644}\right)$	$e\left(\frac{319}{644}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{543}{644}\right)\)	\(e\left(\frac{67}{644}\right)\)	\(e\left(\frac{221}{322}\right)\)	\(e\left(\frac{117}{161}\right)\)	\(e\left(\frac{405}{644}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{139}{161}\right)\)	\(e\left(\frac{305}{322}\right)\)	\(e\left(\frac{527}{644}\right)\)	\(e\left(\frac{341}{644}\right)\)
\(\chi_{40310}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{271}{644}\right)\)	\(e\left(\frac{579}{644}\right)\)	\(e\left(\frac{271}{322}\right)\)	\(e\left(\frac{134}{161}\right)\)	\(e\left(\frac{501}{644}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{67}{161}\right)\)	\(e\left(\frac{103}{322}\right)\)	\(e\left(\frac{27}{644}\right)\)	\(e\left(\frac{169}{644}\right)\)
\(\chi_{40310}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{644}\right)\)	\(e\left(\frac{471}{644}\right)\)	\(e\left(\frac{107}{322}\right)\)	\(e\left(\frac{104}{161}\right)\)	\(e\left(\frac{521}{644}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{52}{161}\right)\)	\(e\left(\frac{289}{322}\right)\)	\(e\left(\frac{379}{644}\right)\)	\(e\left(\frac{321}{644}\right)\)
\(\chi_{40310}(373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{503}{644}\right)\)	\(e\left(\frac{559}{644}\right)\)	\(e\left(\frac{181}{322}\right)\)	\(e\left(\frac{39}{161}\right)\)	\(e\left(\frac{457}{644}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{100}{161}\right)\)	\(e\left(\frac{209}{322}\right)\)	\(e\left(\frac{283}{644}\right)\)	\(e\left(\frac{221}{644}\right)\)
\(\chi_{40310}(703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{183}{644}\right)\)	\(e\left(\frac{631}{644}\right)\)	\(e\left(\frac{183}{322}\right)\)	\(e\left(\frac{59}{161}\right)\)	\(e\left(\frac{229}{644}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{110}{161}\right)\)	\(e\left(\frac{85}{322}\right)\)	\(e\left(\frac{263}{644}\right)\)	\(e\left(\frac{549}{644}\right)\)
\(\chi_{40310}(777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{644}\right)\)	\(e\left(\frac{501}{644}\right)\)	\(e\left(\frac{81}{322}\right)\)	\(e\left(\frac{5}{161}\right)\)	\(e\left(\frac{587}{644}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{83}{161}\right)\)	\(e\left(\frac{291}{322}\right)\)	\(e\left(\frac{317}{644}\right)\)	\(e\left(\frac{243}{644}\right)\)
\(\chi_{40310}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{644}\right)\)	\(e\left(\frac{481}{644}\right)\)	\(e\left(\frac{313}{322}\right)\)	\(e\left(\frac{71}{161}\right)\)	\(e\left(\frac{543}{644}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{116}{161}\right)\)	\(e\left(\frac{75}{322}\right)\)	\(e\left(\frac{573}{644}\right)\)	\(e\left(\frac{295}{644}\right)\)
\(\chi_{40310}(893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{644}\right)\)	\(e\left(\frac{599}{644}\right)\)	\(e\left(\frac{39}{322}\right)\)	\(e\left(\frac{68}{161}\right)\)	\(e\left(\frac{545}{644}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{34}{161}\right)\)	\(e\left(\frac{319}{322}\right)\)	\(e\left(\frac{415}{644}\right)\)	\(e\left(\frac{117}{644}\right)\)
\(\chi_{40310}(1067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{473}{644}\right)\)	\(e\left(\frac{445}{644}\right)\)	\(e\left(\frac{151}{322}\right)\)	\(e\left(\frac{61}{161}\right)\)	\(e\left(\frac{335}{644}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{111}{161}\right)\)	\(e\left(\frac{137}{322}\right)\)	\(e\left(\frac{261}{644}\right)\)	\(e\left(\frac{131}{644}\right)\)
\(\chi_{40310}(1417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{644}\right)\)	\(e\left(\frac{433}{644}\right)\)	\(e\left(\frac{97}{322}\right)\)	\(e\left(\frac{4}{161}\right)\)	\(e\left(\frac{51}{644}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{2}{161}\right)\)	\(e\left(\frac{265}{322}\right)\)	\(e\left(\frac{157}{644}\right)\)	\(e\left(\frac{291}{644}\right)\)
\(\chi_{40310}(1707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{517}{644}\right)\)	\(e\left(\frac{97}{644}\right)\)	\(e\left(\frac{195}{322}\right)\)	\(e\left(\frac{18}{161}\right)\)	\(e\left(\frac{471}{644}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{9}{161}\right)\)	\(e\left(\frac{307}{322}\right)\)	\(e\left(\frac{465}{644}\right)\)	\(e\left(\frac{263}{644}\right)\)
\(\chi_{40310}(1727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{453}{644}\right)\)	\(e\left(\frac{369}{644}\right)\)	\(e\left(\frac{131}{322}\right)\)	\(e\left(\frac{22}{161}\right)\)	\(e\left(\frac{39}{644}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{11}{161}\right)\)	\(e\left(\frac{89}{322}\right)\)	\(e\left(\frac{461}{644}\right)\)	\(e\left(\frac{71}{644}\right)\)
\(\chi_{40310}(1763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{644}\right)\)	\(e\left(\frac{375}{644}\right)\)	\(e\left(\frac{319}{322}\right)\)	\(e\left(\frac{131}{161}\right)\)	\(e\left(\frac{181}{644}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{146}{161}\right)\)	\(e\left(\frac{25}{322}\right)\)	\(e\left(\frac{191}{644}\right)\)	\(e\left(\frac{313}{644}\right)\)
\(\chi_{40310}(2133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{215}{644}\right)\)	\(e\left(\frac{495}{644}\right)\)	\(e\left(\frac{215}{322}\right)\)	\(e\left(\frac{57}{161}\right)\)	\(e\left(\frac{445}{644}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{109}{161}\right)\)	\(e\left(\frac{33}{322}\right)\)	\(e\left(\frac{587}{644}\right)\)	\(e\left(\frac{1}{644}\right)\)
\(\chi_{40310}(2257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{605}{644}\right)\)	\(e\left(\frac{45}{644}\right)\)	\(e\left(\frac{283}{322}\right)\)	\(e\left(\frac{93}{161}\right)\)	\(e\left(\frac{99}{644}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{127}{161}\right)\)	\(e\left(\frac{3}{322}\right)\)	\(e\left(\frac{229}{644}\right)\)	\(e\left(\frac{527}{644}\right)\)
\(\chi_{40310}(2327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{225}{644}\right)\)	\(e\left(\frac{533}{644}\right)\)	\(e\left(\frac{225}{322}\right)\)	\(e\left(\frac{157}{161}\right)\)	\(e\left(\frac{271}{644}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{159}{161}\right)\)	\(e\left(\frac{57}{322}\right)\)	\(e\left(\frac{165}{644}\right)\)	\(e\left(\frac{31}{644}\right)\)
\(\chi_{40310}(2373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{339}{644}\right)\)	\(e\left(\frac{451}{644}\right)\)	\(e\left(\frac{17}{322}\right)\)	\(e\left(\frac{9}{161}\right)\)	\(e\left(\frac{477}{644}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{85}{161}\right)\)	\(e\left(\frac{73}{322}\right)\)	\(e\left(\frac{635}{644}\right)\)	\(e\left(\frac{373}{644}\right)\)
\(\chi_{40310}(2423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{644}\right)\)	\(e\left(\frac{131}{644}\right)\)	\(e\left(\frac{187}{322}\right)\)	\(e\left(\frac{99}{161}\right)\)	\(e\left(\frac{417}{644}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{130}{161}\right)\)	\(e\left(\frac{159}{322}\right)\)	\(e\left(\frac{223}{644}\right)\)	\(e\left(\frac{561}{644}\right)\)
\(\chi_{40310}(2577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{573}{644}\right)\)	\(e\left(\frac{181}{644}\right)\)	\(e\left(\frac{251}{322}\right)\)	\(e\left(\frac{95}{161}\right)\)	\(e\left(\frac{527}{644}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{128}{161}\right)\)	\(e\left(\frac{55}{322}\right)\)	\(e\left(\frac{549}{644}\right)\)	\(e\left(\frac{431}{644}\right)\)
\(\chi_{40310}(2597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{644}\right)\)	\(e\left(\frac{145}{644}\right)\)	\(e\left(\frac{89}{322}\right)\)	\(e\left(\frac{85}{161}\right)\)	\(e\left(\frac{319}{644}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{123}{161}\right)\)	\(e\left(\frac{117}{322}\right)\)	\(e\left(\frac{237}{644}\right)\)	\(e\left(\frac{267}{644}\right)\)
\(\chi_{40310}(2717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{485}{644}\right)\)	\(e\left(\frac{233}{644}\right)\)	\(e\left(\frac{163}{322}\right)\)	\(e\left(\frac{20}{161}\right)\)	\(e\left(\frac{255}{644}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{10}{161}\right)\)	\(e\left(\frac{37}{322}\right)\)	\(e\left(\frac{141}{644}\right)\)	\(e\left(\frac{167}{644}\right)\)
\(\chi_{40310}(2807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{557}{644}\right)\)	\(e\left(\frac{249}{644}\right)\)	\(e\left(\frac{235}{322}\right)\)	\(e\left(\frac{96}{161}\right)\)	\(e\left(\frac{419}{644}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{48}{161}\right)\)	\(e\left(\frac{81}{322}\right)\)	\(e\left(\frac{65}{644}\right)\)	\(e\left(\frac{383}{644}\right)\)
\(\chi_{40310}(2867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{461}{644}\right)\)	\(e\left(\frac{13}{644}\right)\)	\(e\left(\frac{139}{322}\right)\)	\(e\left(\frac{102}{161}\right)\)	\(e\left(\frac{415}{644}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{51}{161}\right)\)	\(e\left(\frac{237}{322}\right)\)	\(e\left(\frac{381}{644}\right)\)	\(e\left(\frac{95}{644}\right)\)
\(\chi_{40310}(3003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{383}{644}\right)\)	\(e\left(\frac{103}{644}\right)\)	\(e\left(\frac{61}{322}\right)\)	\(e\left(\frac{127}{161}\right)\)	\(e\left(\frac{613}{644}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{144}{161}\right)\)	\(e\left(\frac{243}{322}\right)\)	\(e\left(\frac{195}{644}\right)\)	\(e\left(\frac{505}{644}\right)\)
\(\chi_{40310}(3097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{333}{644}\right)\)	\(e\left(\frac{557}{644}\right)\)	\(e\left(\frac{11}{322}\right)\)	\(e\left(\frac{110}{161}\right)\)	\(e\left(\frac{195}{644}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{55}{161}\right)\)	\(e\left(\frac{123}{322}\right)\)	\(e\left(\frac{373}{644}\right)\)	\(e\left(\frac{355}{644}\right)\)
\(\chi_{40310}(3273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{531}{644}\right)\)	\(e\left(\frac{279}{644}\right)\)	\(e\left(\frac{209}{322}\right)\)	\(e\left(\frac{158}{161}\right)\)	\(e\left(\frac{485}{644}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{79}{161}\right)\)	\(e\left(\frac{83}{322}\right)\)	\(e\left(\frac{3}{644}\right)\)	\(e\left(\frac{305}{644}\right)\)
\(\chi_{40310}(3967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{644}\right)\)	\(e\left(\frac{641}{644}\right)\)	\(e\left(\frac{67}{322}\right)\)	\(e\left(\frac{26}{161}\right)\)	\(e\left(\frac{251}{644}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{13}{161}\right)\)	\(e\left(\frac{193}{322}\right)\)	\(e\left(\frac{457}{644}\right)\)	\(e\left(\frac{523}{644}\right)\)
\(\chi_{40310}(3997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{493}{644}\right)\)	\(e\left(\frac{521}{644}\right)\)	\(e\left(\frac{171}{322}\right)\)	\(e\left(\frac{100}{161}\right)\)	\(e\left(\frac{631}{644}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{50}{161}\right)\)	\(e\left(\frac{185}{322}\right)\)	\(e\left(\frac{61}{644}\right)\)	\(e\left(\frac{191}{644}\right)\)
\(\chi_{40310}(4113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{644}\right)\)	\(e\left(\frac{87}{644}\right)\)	\(e\left(\frac{311}{322}\right)\)	\(e\left(\frac{51}{161}\right)\)	\(e\left(\frac{449}{644}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{106}{161}\right)\)	\(e\left(\frac{199}{322}\right)\)	\(e\left(\frac{271}{644}\right)\)	\(e\left(\frac{289}{644}\right)\)
\(\chi_{40310}(4257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{644}\right)\)	\(e\left(\frac{473}{644}\right)\)	\(e\left(\frac{277}{322}\right)\)	\(e\left(\frac{33}{161}\right)\)	\(e\left(\frac{139}{644}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{97}{161}\right)\)	\(e\left(\frac{53}{322}\right)\)	\(e\left(\frac{289}{644}\right)\)	\(e\left(\frac{187}{644}\right)\)
\(\chi_{40310}(4317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{321}{644}\right)\)	\(e\left(\frac{125}{644}\right)\)	\(e\left(\frac{321}{322}\right)\)	\(e\left(\frac{151}{161}\right)\)	\(e\left(\frac{275}{644}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{156}{161}\right)\)	\(e\left(\frac{223}{322}\right)\)	\(e\left(\frac{493}{644}\right)\)	\(e\left(\frac{319}{644}\right)\)

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First 31 of 264 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.fg
Modulus	$40310$
Conductor	$20155$
Order	$644$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(40310\)
Conductor:	\(20155\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(644\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 20155.fi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)