LMFDB - Dirichlet character orbit 40310.fd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(644)) M = H._module chi = DirichletCharacter(H, M([483,46,546])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(33,40310)) 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.ff	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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(33,\cdot)$	$1$	$1$	$e\left(\frac{237}{644}\right)$	$e\left(\frac{643}{644}\right)$	$e\left(\frac{237}{322}\right)$	$e\left(\frac{71}{322}\right)$	$e\left(\frac{513}{644}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{277}{322}\right)$	$e\left(\frac{59}{161}\right)$	$e\left(\frac{367}{644}\right)$	$e\left(\frac{67}{644}\right)$
$\chi_{40310}(187,\cdot)$	$1$	$1$	$e\left(\frac{215}{644}\right)$	$e\left(\frac{173}{644}\right)$	$e\left(\frac{215}{322}\right)$	$e\left(\frac{275}{322}\right)$	$e\left(\frac{123}{644}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{57}{322}\right)$	$e\left(\frac{97}{161}\right)$	$e\left(\frac{265}{644}\right)$	$e\left(\frac{1}{644}\right)$
$\chi_{40310}(353,\cdot)$	$1$	$1$	$e\left(\frac{297}{644}\right)$	$e\left(\frac{227}{644}\right)$	$e\left(\frac{297}{322}\right)$	$e\left(\frac{305}{322}\right)$	$e\left(\frac{113}{644}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{233}{322}\right)$	$e\left(\frac{131}{161}\right)$	$e\left(\frac{411}{644}\right)$	$e\left(\frac{247}{644}\right)$
$\chi_{40310}(383,\cdot)$	$1$	$1$	$e\left(\frac{585}{644}\right)$	$e\left(\frac{291}{644}\right)$	$e\left(\frac{263}{322}\right)$	$e\left(\frac{269}{322}\right)$	$e\left(\frac{125}{644}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{215}{322}\right)$	$e\left(\frac{58}{161}\right)$	$e\left(\frac{107}{644}\right)$	$e\left(\frac{467}{644}\right)$
$\chi_{40310}(477,\cdot)$	$1$	$1$	$e\left(\frac{187}{644}\right)$	$e\left(\frac{453}{644}\right)$	$e\left(\frac{187}{322}\right)$	$e\left(\frac{37}{322}\right)$	$e\left(\frac{95}{644}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{99}{322}\right)$	$e\left(\frac{160}{161}\right)$	$e\left(\frac{545}{644}\right)$	$e\left(\frac{561}{644}\right)$
$\chi_{40310}(643,\cdot)$	$1$	$1$	$e\left(\frac{185}{644}\right)$	$e\left(\frac{59}{644}\right)$	$e\left(\frac{185}{322}\right)$	$e\left(\frac{319}{322}\right)$	$e\left(\frac{1}{644}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{79}{322}\right)$	$e\left(\frac{61}{161}\right)$	$e\left(\frac{243}{644}\right)$	$e\left(\frac{555}{644}\right)$
$\chi_{40310}(937,\cdot)$	$1$	$1$	$e\left(\frac{639}{644}\right)$	$e\left(\frac{625}{644}\right)$	$e\left(\frac{317}{322}\right)$	$e\left(\frac{61}{322}\right)$	$e\left(\frac{87}{644}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{111}{322}\right)$	$e\left(\frac{155}{161}\right)$	$e\left(\frac{533}{644}\right)$	$e\left(\frac{629}{644}\right)$
$\chi_{40310}(1057,\cdot)$	$1$	$1$	$e\left(\frac{383}{644}\right)$	$e\left(\frac{425}{644}\right)$	$e\left(\frac{61}{322}\right)$	$e\left(\frac{93}{322}\right)$	$e\left(\frac{291}{644}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{127}{322}\right)$	$e\left(\frac{41}{161}\right)$	$e\left(\frac{517}{644}\right)$	$e\left(\frac{505}{644}\right)$
$\chi_{40310}(1327,\cdot)$	$1$	$1$	$e\left(\frac{71}{644}\right)$	$e\left(\frac{141}{644}\right)$	$e\left(\frac{71}{322}\right)$	$e\left(\frac{293}{322}\right)$	$e\left(\frac{439}{644}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{227}{322}\right)$	$e\left(\frac{53}{161}\right)$	$e\left(\frac{417}{644}\right)$	$e\left(\frac{213}{644}\right)$
$\chi_{40310}(1543,\cdot)$	$1$	$1$	$e\left(\frac{305}{644}\right)$	$e\left(\frac{515}{644}\right)$	$e\left(\frac{305}{322}\right)$	$e\left(\frac{143}{322}\right)$	$e\left(\frac{489}{644}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{313}{322}\right)$	$e\left(\frac{44}{161}\right)$	$e\left(\frac{331}{644}\right)$	$e\left(\frac{271}{644}\right)$
$\chi_{40310}(1773,\cdot)$	$1$	$1$	$e\left(\frac{125}{644}\right)$	$e\left(\frac{475}{644}\right)$	$e\left(\frac{125}{322}\right)$	$e\left(\frac{85}{322}\right)$	$e\left(\frac{401}{644}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{123}{322}\right)$	$e\left(\frac{150}{161}\right)$	$e\left(\frac{199}{644}\right)$	$e\left(\frac{375}{644}\right)$
$\chi_{40310}(2093,\cdot)$	$1$	$1$	$e\left(\frac{45}{644}\right)$	$e\left(\frac{171}{644}\right)$	$e\left(\frac{45}{322}\right)$	$e\left(\frac{95}{322}\right)$	$e\left(\frac{505}{644}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{289}{322}\right)$	$e\left(\frac{54}{161}\right)$	$e\left(\frac{355}{644}\right)$	$e\left(\frac{135}{644}\right)$
$\chi_{40310}(2703,\cdot)$	$1$	$1$	$e\left(\frac{165}{644}\right)$	$e\left(\frac{627}{644}\right)$	$e\left(\frac{165}{322}\right)$	$e\left(\frac{241}{322}\right)$	$e\left(\frac{349}{644}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{201}{322}\right)$	$e\left(\frac{37}{161}\right)$	$e\left(\frac{443}{644}\right)$	$e\left(\frac{495}{644}\right)$
$\chi_{40310}(2913,\cdot)$	$1$	$1$	$e\left(\frac{285}{644}\right)$	$e\left(\frac{439}{644}\right)$	$e\left(\frac{285}{322}\right)$	$e\left(\frac{65}{322}\right)$	$e\left(\frac{193}{644}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{113}{322}\right)$	$e\left(\frac{20}{161}\right)$	$e\left(\frac{531}{644}\right)$	$e\left(\frac{211}{644}\right)$
$\chi_{40310}(2933,\cdot)$	$1$	$1$	$e\left(\frac{489}{644}\right)$	$e\left(\frac{55}{644}\right)$	$e\left(\frac{167}{322}\right)$	$e\left(\frac{281}{322}\right)$	$e\left(\frac{121}{644}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{221}{322}\right)$	$e\left(\frac{136}{161}\right)$	$e\left(\frac{423}{644}\right)$	$e\left(\frac{179}{644}\right)$
$\chi_{40310}(2967,\cdot)$	$1$	$1$	$e\left(\frac{583}{644}\right)$	$e\left(\frac{541}{644}\right)$	$e\left(\frac{261}{322}\right)$	$e\left(\frac{229}{322}\right)$	$e\left(\frac{31}{644}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{195}{322}\right)$	$e\left(\frac{120}{161}\right)$	$e\left(\frac{449}{644}\right)$	$e\left(\frac{461}{644}\right)$
$\chi_{40310}(2993,\cdot)$	$1$	$1$	$e\left(\frac{249}{644}\right)$	$e\left(\frac{431}{644}\right)$	$e\left(\frac{249}{322}\right)$	$e\left(\frac{311}{322}\right)$	$e\left(\frac{433}{644}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{75}{322}\right)$	$e\left(\frac{9}{161}\right)$	$e\left(\frac{247}{644}\right)$	$e\left(\frac{103}{644}\right)$
$\chi_{40310}(3257,\cdot)$	$1$	$1$	$e\left(\frac{555}{644}\right)$	$e\left(\frac{177}{644}\right)$	$e\left(\frac{233}{322}\right)$	$e\left(\frac{313}{322}\right)$	$e\left(\frac{3}{644}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{237}{322}\right)$	$e\left(\frac{22}{161}\right)$	$e\left(\frac{85}{644}\right)$	$e\left(\frac{377}{644}\right)$
$\chi_{40310}(3647,\cdot)$	$1$	$1$	$e\left(\frac{99}{644}\right)$	$e\left(\frac{505}{644}\right)$	$e\left(\frac{99}{322}\right)$	$e\left(\frac{209}{322}\right)$	$e\left(\frac{467}{644}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{185}{322}\right)$	$e\left(\frac{151}{161}\right)$	$e\left(\frac{137}{644}\right)$	$e\left(\frac{297}{644}\right)$
$\chi_{40310}(3717,\cdot)$	$1$	$1$	$e\left(\frac{87}{644}\right)$	$e\left(\frac{73}{644}\right)$	$e\left(\frac{87}{322}\right)$	$e\left(\frac{291}{322}\right)$	$e\left(\frac{547}{644}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{65}{322}\right)$	$e\left(\frac{40}{161}\right)$	$e\left(\frac{257}{644}\right)$	$e\left(\frac{261}{644}\right)$
$\chi_{40310}(3747,\cdot)$	$1$	$1$	$e\left(\frac{515}{644}\right)$	$e\left(\frac{25}{644}\right)$	$e\left(\frac{193}{322}\right)$	$e\left(\frac{157}{322}\right)$	$e\left(\frac{55}{644}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{159}{322}\right)$	$e\left(\frac{135}{161}\right)$	$e\left(\frac{485}{644}\right)$	$e\left(\frac{257}{644}\right)$
$\chi_{40310}(3763,\cdot)$	$1$	$1$	$e\left(\frac{477}{644}\right)$	$e\left(\frac{267}{644}\right)$	$e\left(\frac{155}{322}\right)$	$e\left(\frac{41}{322}\right)$	$e\left(\frac{201}{644}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{101}{322}\right)$	$e\left(\frac{25}{161}\right)$	$e\left(\frac{543}{644}\right)$	$e\left(\frac{143}{644}\right)$
$\chi_{40310}(3837,\cdot)$	$1$	$1$	$e\left(\frac{107}{644}\right)$	$e\left(\frac{149}{644}\right)$	$e\left(\frac{107}{322}\right)$	$e\left(\frac{47}{322}\right)$	$e\left(\frac{199}{644}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{265}{322}\right)$	$e\left(\frac{64}{161}\right)$	$e\left(\frac{57}{644}\right)$	$e\left(\frac{321}{644}\right)$
$\chi_{40310}(4093,\cdot)$	$1$	$1$	$e\left(\frac{349}{644}\right)$	$e\left(\frac{167}{644}\right)$	$e\left(\frac{27}{322}\right)$	$e\left(\frac{57}{322}\right)$	$e\left(\frac{625}{644}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{109}{322}\right)$	$e\left(\frac{129}{161}\right)$	$e\left(\frac{535}{644}\right)$	$e\left(\frac{403}{644}\right)$
$\chi_{40310}(4383,\cdot)$	$1$	$1$	$e\left(\frac{433}{644}\right)$	$e\left(\frac{615}{644}\right)$	$e\left(\frac{111}{322}\right)$	$e\left(\frac{127}{322}\right)$	$e\left(\frac{65}{644}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{305}{322}\right)$	$e\left(\frac{101}{161}\right)$	$e\left(\frac{339}{644}\right)$	$e\left(\frac{11}{644}\right)$
$\chi_{40310}(5137,\cdot)$	$1$	$1$	$e\left(\frac{55}{644}\right)$	$e\left(\frac{209}{644}\right)$	$e\left(\frac{55}{322}\right)$	$e\left(\frac{295}{322}\right)$	$e\left(\frac{331}{644}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{67}{322}\right)$	$e\left(\frac{66}{161}\right)$	$e\left(\frac{577}{644}\right)$	$e\left(\frac{165}{644}\right)$
$\chi_{40310}(5387,\cdot)$	$1$	$1$	$e\left(\frac{631}{644}\right)$	$e\left(\frac{337}{644}\right)$	$e\left(\frac{309}{322}\right)$	$e\left(\frac{223}{322}\right)$	$e\left(\frac{355}{644}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{31}{322}\right)$	$e\left(\frac{81}{161}\right)$	$e\left(\frac{613}{644}\right)$	$e\left(\frac{605}{644}\right)$
$\chi_{40310}(5503,\cdot)$	$1$	$1$	$e\left(\frac{449}{644}\right)$	$e\left(\frac{547}{644}\right)$	$e\left(\frac{127}{322}\right)$	$e\left(\frac{125}{322}\right)$	$e\left(\frac{173}{644}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{143}{322}\right)$	$e\left(\frac{88}{161}\right)$	$e\left(\frac{179}{644}\right)$	$e\left(\frac{59}{644}\right)$
$\chi_{40310}(5693,\cdot)$	$1$	$1$	$e\left(\frac{9}{644}\right)$	$e\left(\frac{163}{644}\right)$	$e\left(\frac{9}{322}\right)$	$e\left(\frac{19}{322}\right)$	$e\left(\frac{101}{644}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{251}{322}\right)$	$e\left(\frac{43}{161}\right)$	$e\left(\frac{71}{644}\right)$	$e\left(\frac{27}{644}\right)$
$\chi_{40310}(5747,\cdot)$	$1$	$1$	$e\left(\frac{31}{644}\right)$	$e\left(\frac{633}{644}\right)$	$e\left(\frac{31}{322}\right)$	$e\left(\frac{137}{322}\right)$	$e\left(\frac{491}{644}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{149}{322}\right)$	$e\left(\frac{5}{161}\right)$	$e\left(\frac{173}{644}\right)$	$e\left(\frac{93}{644}\right)$
$\chi_{40310}(5793,\cdot)$	$1$	$1$	$e\left(\frac{197}{644}\right)$	$e\left(\frac{491}{644}\right)$	$e\left(\frac{197}{322}\right)$	$e\left(\frac{237}{322}\right)$	$e\left(\frac{565}{644}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{199}{322}\right)$	$e\left(\frac{11}{161}\right)$	$e\left(\frac{123}{644}\right)$	$e\left(\frac{591}{644}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{237}{644}\right)\)	\(e\left(\frac{643}{644}\right)\)	\(e\left(\frac{237}{322}\right)\)	\(e\left(\frac{71}{322}\right)\)	\(e\left(\frac{513}{644}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{277}{322}\right)\)	\(e\left(\frac{59}{161}\right)\)	\(e\left(\frac{367}{644}\right)\)	\(e\left(\frac{67}{644}\right)\)
\(\chi_{40310}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{215}{644}\right)\)	\(e\left(\frac{173}{644}\right)\)	\(e\left(\frac{215}{322}\right)\)	\(e\left(\frac{275}{322}\right)\)	\(e\left(\frac{123}{644}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{57}{322}\right)\)	\(e\left(\frac{97}{161}\right)\)	\(e\left(\frac{265}{644}\right)\)	\(e\left(\frac{1}{644}\right)\)
\(\chi_{40310}(353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{297}{644}\right)\)	\(e\left(\frac{227}{644}\right)\)	\(e\left(\frac{297}{322}\right)\)	\(e\left(\frac{305}{322}\right)\)	\(e\left(\frac{113}{644}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{233}{322}\right)\)	\(e\left(\frac{131}{161}\right)\)	\(e\left(\frac{411}{644}\right)\)	\(e\left(\frac{247}{644}\right)\)
\(\chi_{40310}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{585}{644}\right)\)	\(e\left(\frac{291}{644}\right)\)	\(e\left(\frac{263}{322}\right)\)	\(e\left(\frac{269}{322}\right)\)	\(e\left(\frac{125}{644}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{215}{322}\right)\)	\(e\left(\frac{58}{161}\right)\)	\(e\left(\frac{107}{644}\right)\)	\(e\left(\frac{467}{644}\right)\)
\(\chi_{40310}(477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{644}\right)\)	\(e\left(\frac{453}{644}\right)\)	\(e\left(\frac{187}{322}\right)\)	\(e\left(\frac{37}{322}\right)\)	\(e\left(\frac{95}{644}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{99}{322}\right)\)	\(e\left(\frac{160}{161}\right)\)	\(e\left(\frac{545}{644}\right)\)	\(e\left(\frac{561}{644}\right)\)
\(\chi_{40310}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{644}\right)\)	\(e\left(\frac{59}{644}\right)\)	\(e\left(\frac{185}{322}\right)\)	\(e\left(\frac{319}{322}\right)\)	\(e\left(\frac{1}{644}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{79}{322}\right)\)	\(e\left(\frac{61}{161}\right)\)	\(e\left(\frac{243}{644}\right)\)	\(e\left(\frac{555}{644}\right)\)
\(\chi_{40310}(937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{639}{644}\right)\)	\(e\left(\frac{625}{644}\right)\)	\(e\left(\frac{317}{322}\right)\)	\(e\left(\frac{61}{322}\right)\)	\(e\left(\frac{87}{644}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{111}{322}\right)\)	\(e\left(\frac{155}{161}\right)\)	\(e\left(\frac{533}{644}\right)\)	\(e\left(\frac{629}{644}\right)\)
\(\chi_{40310}(1057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{383}{644}\right)\)	\(e\left(\frac{425}{644}\right)\)	\(e\left(\frac{61}{322}\right)\)	\(e\left(\frac{93}{322}\right)\)	\(e\left(\frac{291}{644}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{127}{322}\right)\)	\(e\left(\frac{41}{161}\right)\)	\(e\left(\frac{517}{644}\right)\)	\(e\left(\frac{505}{644}\right)\)
\(\chi_{40310}(1327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{644}\right)\)	\(e\left(\frac{141}{644}\right)\)	\(e\left(\frac{71}{322}\right)\)	\(e\left(\frac{293}{322}\right)\)	\(e\left(\frac{439}{644}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{227}{322}\right)\)	\(e\left(\frac{53}{161}\right)\)	\(e\left(\frac{417}{644}\right)\)	\(e\left(\frac{213}{644}\right)\)
\(\chi_{40310}(1543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{305}{644}\right)\)	\(e\left(\frac{515}{644}\right)\)	\(e\left(\frac{305}{322}\right)\)	\(e\left(\frac{143}{322}\right)\)	\(e\left(\frac{489}{644}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{313}{322}\right)\)	\(e\left(\frac{44}{161}\right)\)	\(e\left(\frac{331}{644}\right)\)	\(e\left(\frac{271}{644}\right)\)
\(\chi_{40310}(1773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{644}\right)\)	\(e\left(\frac{475}{644}\right)\)	\(e\left(\frac{125}{322}\right)\)	\(e\left(\frac{85}{322}\right)\)	\(e\left(\frac{401}{644}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{123}{322}\right)\)	\(e\left(\frac{150}{161}\right)\)	\(e\left(\frac{199}{644}\right)\)	\(e\left(\frac{375}{644}\right)\)
\(\chi_{40310}(2093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{644}\right)\)	\(e\left(\frac{171}{644}\right)\)	\(e\left(\frac{45}{322}\right)\)	\(e\left(\frac{95}{322}\right)\)	\(e\left(\frac{505}{644}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{289}{322}\right)\)	\(e\left(\frac{54}{161}\right)\)	\(e\left(\frac{355}{644}\right)\)	\(e\left(\frac{135}{644}\right)\)
\(\chi_{40310}(2703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{165}{644}\right)\)	\(e\left(\frac{627}{644}\right)\)	\(e\left(\frac{165}{322}\right)\)	\(e\left(\frac{241}{322}\right)\)	\(e\left(\frac{349}{644}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{201}{322}\right)\)	\(e\left(\frac{37}{161}\right)\)	\(e\left(\frac{443}{644}\right)\)	\(e\left(\frac{495}{644}\right)\)
\(\chi_{40310}(2913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{285}{644}\right)\)	\(e\left(\frac{439}{644}\right)\)	\(e\left(\frac{285}{322}\right)\)	\(e\left(\frac{65}{322}\right)\)	\(e\left(\frac{193}{644}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{113}{322}\right)\)	\(e\left(\frac{20}{161}\right)\)	\(e\left(\frac{531}{644}\right)\)	\(e\left(\frac{211}{644}\right)\)
\(\chi_{40310}(2933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{489}{644}\right)\)	\(e\left(\frac{55}{644}\right)\)	\(e\left(\frac{167}{322}\right)\)	\(e\left(\frac{281}{322}\right)\)	\(e\left(\frac{121}{644}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{221}{322}\right)\)	\(e\left(\frac{136}{161}\right)\)	\(e\left(\frac{423}{644}\right)\)	\(e\left(\frac{179}{644}\right)\)
\(\chi_{40310}(2967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{583}{644}\right)\)	\(e\left(\frac{541}{644}\right)\)	\(e\left(\frac{261}{322}\right)\)	\(e\left(\frac{229}{322}\right)\)	\(e\left(\frac{31}{644}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{195}{322}\right)\)	\(e\left(\frac{120}{161}\right)\)	\(e\left(\frac{449}{644}\right)\)	\(e\left(\frac{461}{644}\right)\)
\(\chi_{40310}(2993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{249}{644}\right)\)	\(e\left(\frac{431}{644}\right)\)	\(e\left(\frac{249}{322}\right)\)	\(e\left(\frac{311}{322}\right)\)	\(e\left(\frac{433}{644}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{75}{322}\right)\)	\(e\left(\frac{9}{161}\right)\)	\(e\left(\frac{247}{644}\right)\)	\(e\left(\frac{103}{644}\right)\)
\(\chi_{40310}(3257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{555}{644}\right)\)	\(e\left(\frac{177}{644}\right)\)	\(e\left(\frac{233}{322}\right)\)	\(e\left(\frac{313}{322}\right)\)	\(e\left(\frac{3}{644}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{237}{322}\right)\)	\(e\left(\frac{22}{161}\right)\)	\(e\left(\frac{85}{644}\right)\)	\(e\left(\frac{377}{644}\right)\)
\(\chi_{40310}(3647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{644}\right)\)	\(e\left(\frac{505}{644}\right)\)	\(e\left(\frac{99}{322}\right)\)	\(e\left(\frac{209}{322}\right)\)	\(e\left(\frac{467}{644}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{185}{322}\right)\)	\(e\left(\frac{151}{161}\right)\)	\(e\left(\frac{137}{644}\right)\)	\(e\left(\frac{297}{644}\right)\)
\(\chi_{40310}(3717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{644}\right)\)	\(e\left(\frac{73}{644}\right)\)	\(e\left(\frac{87}{322}\right)\)	\(e\left(\frac{291}{322}\right)\)	\(e\left(\frac{547}{644}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{65}{322}\right)\)	\(e\left(\frac{40}{161}\right)\)	\(e\left(\frac{257}{644}\right)\)	\(e\left(\frac{261}{644}\right)\)
\(\chi_{40310}(3747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{515}{644}\right)\)	\(e\left(\frac{25}{644}\right)\)	\(e\left(\frac{193}{322}\right)\)	\(e\left(\frac{157}{322}\right)\)	\(e\left(\frac{55}{644}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{159}{322}\right)\)	\(e\left(\frac{135}{161}\right)\)	\(e\left(\frac{485}{644}\right)\)	\(e\left(\frac{257}{644}\right)\)
\(\chi_{40310}(3763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{477}{644}\right)\)	\(e\left(\frac{267}{644}\right)\)	\(e\left(\frac{155}{322}\right)\)	\(e\left(\frac{41}{322}\right)\)	\(e\left(\frac{201}{644}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{101}{322}\right)\)	\(e\left(\frac{25}{161}\right)\)	\(e\left(\frac{543}{644}\right)\)	\(e\left(\frac{143}{644}\right)\)
\(\chi_{40310}(3837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{644}\right)\)	\(e\left(\frac{149}{644}\right)\)	\(e\left(\frac{107}{322}\right)\)	\(e\left(\frac{47}{322}\right)\)	\(e\left(\frac{199}{644}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{265}{322}\right)\)	\(e\left(\frac{64}{161}\right)\)	\(e\left(\frac{57}{644}\right)\)	\(e\left(\frac{321}{644}\right)\)
\(\chi_{40310}(4093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{349}{644}\right)\)	\(e\left(\frac{167}{644}\right)\)	\(e\left(\frac{27}{322}\right)\)	\(e\left(\frac{57}{322}\right)\)	\(e\left(\frac{625}{644}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{109}{322}\right)\)	\(e\left(\frac{129}{161}\right)\)	\(e\left(\frac{535}{644}\right)\)	\(e\left(\frac{403}{644}\right)\)
\(\chi_{40310}(4383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{433}{644}\right)\)	\(e\left(\frac{615}{644}\right)\)	\(e\left(\frac{111}{322}\right)\)	\(e\left(\frac{127}{322}\right)\)	\(e\left(\frac{65}{644}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{305}{322}\right)\)	\(e\left(\frac{101}{161}\right)\)	\(e\left(\frac{339}{644}\right)\)	\(e\left(\frac{11}{644}\right)\)
\(\chi_{40310}(5137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{644}\right)\)	\(e\left(\frac{209}{644}\right)\)	\(e\left(\frac{55}{322}\right)\)	\(e\left(\frac{295}{322}\right)\)	\(e\left(\frac{331}{644}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{67}{322}\right)\)	\(e\left(\frac{66}{161}\right)\)	\(e\left(\frac{577}{644}\right)\)	\(e\left(\frac{165}{644}\right)\)
\(\chi_{40310}(5387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{631}{644}\right)\)	\(e\left(\frac{337}{644}\right)\)	\(e\left(\frac{309}{322}\right)\)	\(e\left(\frac{223}{322}\right)\)	\(e\left(\frac{355}{644}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{31}{322}\right)\)	\(e\left(\frac{81}{161}\right)\)	\(e\left(\frac{613}{644}\right)\)	\(e\left(\frac{605}{644}\right)\)
\(\chi_{40310}(5503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{449}{644}\right)\)	\(e\left(\frac{547}{644}\right)\)	\(e\left(\frac{127}{322}\right)\)	\(e\left(\frac{125}{322}\right)\)	\(e\left(\frac{173}{644}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{143}{322}\right)\)	\(e\left(\frac{88}{161}\right)\)	\(e\left(\frac{179}{644}\right)\)	\(e\left(\frac{59}{644}\right)\)
\(\chi_{40310}(5693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{644}\right)\)	\(e\left(\frac{163}{644}\right)\)	\(e\left(\frac{9}{322}\right)\)	\(e\left(\frac{19}{322}\right)\)	\(e\left(\frac{101}{644}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{251}{322}\right)\)	\(e\left(\frac{43}{161}\right)\)	\(e\left(\frac{71}{644}\right)\)	\(e\left(\frac{27}{644}\right)\)
\(\chi_{40310}(5747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{644}\right)\)	\(e\left(\frac{633}{644}\right)\)	\(e\left(\frac{31}{322}\right)\)	\(e\left(\frac{137}{322}\right)\)	\(e\left(\frac{491}{644}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{149}{322}\right)\)	\(e\left(\frac{5}{161}\right)\)	\(e\left(\frac{173}{644}\right)\)	\(e\left(\frac{93}{644}\right)\)
\(\chi_{40310}(5793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{644}\right)\)	\(e\left(\frac{491}{644}\right)\)	\(e\left(\frac{197}{322}\right)\)	\(e\left(\frac{237}{322}\right)\)	\(e\left(\frac{565}{644}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{199}{322}\right)\)	\(e\left(\frac{11}{161}\right)\)	\(e\left(\frac{123}{644}\right)\)	\(e\left(\frac{591}{644}\right)\)

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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.fd
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.ff	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)