LMFDB - Dirichlet character orbit 40310.fa

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(644)) M = H._module chi = DirichletCharacter(H, M([161,345,574])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(27,40310)) 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.fk	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:	$\Q(\zeta_{644})$
Fixed field:	Number field defined by a degree 644 polynomial (not computed)

First 31 of 264 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(27,\cdot)$	$-1$	$1$	$e\left(\frac{313}{322}\right)$	$e\left(\frac{157}{644}\right)$	$e\left(\frac{152}{161}\right)$	$e\left(\frac{85}{644}\right)$	$e\left(\frac{281}{644}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{445}{644}\right)$	$e\left(\frac{139}{644}\right)$	$e\left(\frac{341}{644}\right)$	$e\left(\frac{295}{322}\right)$
$\chi_{40310}(317,\cdot)$	$-1$	$1$	$e\left(\frac{201}{322}\right)$	$e\left(\frac{465}{644}\right)$	$e\left(\frac{40}{161}\right)$	$e\left(\frac{141}{644}\right)$	$e\left(\frac{57}{644}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{473}{644}\right)$	$e\left(\frac{223}{644}\right)$	$e\left(\frac{5}{644}\right)$	$e\left(\frac{281}{322}\right)$
$\chi_{40310}(337,\cdot)$	$-1$	$1$	$e\left(\frac{307}{322}\right)$	$e\left(\frac{369}{644}\right)$	$e\left(\frac{146}{161}\right)$	$e\left(\frac{249}{644}\right)$	$e\left(\frac{361}{644}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{205}{644}\right)$	$e\left(\frac{339}{644}\right)$	$e\left(\frac{461}{644}\right)$	$e\left(\frac{277}{322}\right)$
$\chi_{40310}(583,\cdot)$	$-1$	$1$	$e\left(\frac{221}{322}\right)$	$e\left(\frac{295}{644}\right)$	$e\left(\frac{60}{161}\right)$	$e\left(\frac{131}{644}\right)$	$e\left(\frac{327}{644}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{307}{644}\right)$	$e\left(\frac{93}{644}\right)$	$e\left(\frac{571}{644}\right)$	$e\left(\frac{19}{322}\right)$
$\chi_{40310}(867,\cdot)$	$-1$	$1$	$e\left(\frac{291}{322}\right)$	$e\left(\frac{505}{644}\right)$	$e\left(\frac{130}{161}\right)$	$e\left(\frac{257}{644}\right)$	$e\left(\frac{145}{644}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{209}{644}\right)$	$e\left(\frac{443}{644}\right)$	$e\left(\frac{137}{644}\right)$	$e\left(\frac{229}{322}\right)$
$\chi_{40310}(873,\cdot)$	$-1$	$1$	$e\left(\frac{109}{322}\right)$	$e\left(\frac{603}{644}\right)$	$e\left(\frac{109}{161}\right)$	$e\left(\frac{187}{644}\right)$	$e\left(\frac{103}{644}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{335}{644}\right)$	$e\left(\frac{177}{644}\right)$	$e\left(\frac{235}{644}\right)$	$e\left(\frac{5}{322}\right)$
$\chi_{40310}(967,\cdot)$	$-1$	$1$	$e\left(\frac{269}{322}\right)$	$e\left(\frac{209}{644}\right)$	$e\left(\frac{108}{161}\right)$	$e\left(\frac{429}{644}\right)$	$e\left(\frac{9}{644}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{617}{644}\right)$	$e\left(\frac{103}{644}\right)$	$e\left(\frac{577}{644}\right)$	$e\left(\frac{163}{322}\right)$
$\chi_{40310}(1187,\cdot)$	$-1$	$1$	$e\left(\frac{229}{322}\right)$	$e\left(\frac{549}{644}\right)$	$e\left(\frac{68}{161}\right)$	$e\left(\frac{449}{644}\right)$	$e\left(\frac{113}{644}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{305}{644}\right)$	$e\left(\frac{363}{644}\right)$	$e\left(\frac{89}{644}\right)$	$e\left(\frac{43}{322}\right)$
$\chi_{40310}(1207,\cdot)$	$-1$	$1$	$e\left(\frac{125}{322}\right)$	$e\left(\frac{145}{644}\right)$	$e\left(\frac{125}{161}\right)$	$e\left(\frac{501}{644}\right)$	$e\left(\frac{641}{644}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{9}{644}\right)$	$e\left(\frac{395}{644}\right)$	$e\left(\frac{237}{644}\right)$	$e\left(\frac{53}{322}\right)$
$\chi_{40310}(1413,\cdot)$	$-1$	$1$	$e\left(\frac{99}{322}\right)$	$e\left(\frac{527}{644}\right)$	$e\left(\frac{99}{161}\right)$	$e\left(\frac{31}{644}\right)$	$e\left(\frac{451}{644}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{579}{644}\right)$	$e\left(\frac{81}{644}\right)$	$e\left(\frac{435}{644}\right)$	$e\left(\frac{297}{322}\right)$
$\chi_{40310}(1423,\cdot)$	$-1$	$1$	$e\left(\frac{61}{322}\right)$	$e\left(\frac{367}{644}\right)$	$e\left(\frac{61}{161}\right)$	$e\left(\frac{211}{644}\right)$	$e\left(\frac{99}{644}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{347}{644}\right)$	$e\left(\frac{489}{644}\right)$	$e\left(\frac{551}{644}\right)$	$e\left(\frac{183}{322}\right)$
$\chi_{40310}(1477,\cdot)$	$-1$	$1$	$e\left(\frac{173}{322}\right)$	$e\left(\frac{381}{644}\right)$	$e\left(\frac{12}{161}\right)$	$e\left(\frac{477}{644}\right)$	$e\left(\frac{1}{644}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{641}{644}\right)$	$e\left(\frac{83}{644}\right)$	$e\left(\frac{565}{644}\right)$	$e\left(\frac{197}{322}\right)$
$\chi_{40310}(1493,\cdot)$	$-1$	$1$	$e\left(\frac{9}{322}\right)$	$e\left(\frac{487}{644}\right)$	$e\left(\frac{9}{161}\right)$	$e\left(\frac{559}{644}\right)$	$e\left(\frac{363}{644}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{199}{644}\right)$	$e\left(\frac{505}{644}\right)$	$e\left(\frac{303}{644}\right)$	$e\left(\frac{27}{322}\right)$
$\chi_{40310}(1743,\cdot)$	$-1$	$1$	$e\left(\frac{137}{322}\right)$	$e\left(\frac{43}{644}\right)$	$e\left(\frac{137}{161}\right)$	$e\left(\frac{495}{644}\right)$	$e\left(\frac{159}{644}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{167}{644}\right)$	$e\left(\frac{317}{644}\right)$	$e\left(\frac{319}{644}\right)$	$e\left(\frac{89}{322}\right)$
$\chi_{40310}(2033,\cdot)$	$-1$	$1$	$e\left(\frac{81}{322}\right)$	$e\left(\frac{519}{644}\right)$	$e\left(\frac{81}{161}\right)$	$e\left(\frac{523}{644}\right)$	$e\left(\frac{47}{644}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{503}{644}\right)$	$e\left(\frac{37}{644}\right)$	$e\left(\frac{151}{644}\right)$	$e\left(\frac{243}{322}\right)$
$\chi_{40310}(2283,\cdot)$	$-1$	$1$	$e\left(\frac{169}{322}\right)$	$e\left(\frac{415}{644}\right)$	$e\left(\frac{8}{161}\right)$	$e\left(\frac{479}{644}\right)$	$e\left(\frac{591}{644}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{159}{644}\right)$	$e\left(\frac{109}{644}\right)$	$e\left(\frac{323}{644}\right)$	$e\left(\frac{185}{322}\right)$
$\chi_{40310}(2357,\cdot)$	$-1$	$1$	$e\left(\frac{85}{322}\right)$	$e\left(\frac{485}{644}\right)$	$e\left(\frac{85}{161}\right)$	$e\left(\frac{521}{644}\right)$	$e\left(\frac{101}{644}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{341}{644}\right)$	$e\left(\frac{11}{644}\right)$	$e\left(\frac{393}{644}\right)$	$e\left(\frac{255}{322}\right)$
$\chi_{40310}(2607,\cdot)$	$-1$	$1$	$e\left(\frac{235}{322}\right)$	$e\left(\frac{337}{644}\right)$	$e\left(\frac{74}{161}\right)$	$e\left(\frac{285}{644}\right)$	$e\left(\frac{33}{644}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{545}{644}\right)$	$e\left(\frac{163}{644}\right)$	$e\left(\frac{613}{644}\right)$	$e\left(\frac{61}{322}\right)$
$\chi_{40310}(2803,\cdot)$	$-1$	$1$	$e\left(\frac{283}{322}\right)$	$e\left(\frac{251}{644}\right)$	$e\left(\frac{122}{161}\right)$	$e\left(\frac{583}{644}\right)$	$e\left(\frac{359}{644}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{211}{644}\right)$	$e\left(\frac{173}{644}\right)$	$e\left(\frac{619}{644}\right)$	$e\left(\frac{205}{322}\right)$
$\chi_{40310}(2927,\cdot)$	$-1$	$1$	$e\left(\frac{103}{322}\right)$	$e\left(\frac{493}{644}\right)$	$e\left(\frac{103}{161}\right)$	$e\left(\frac{29}{644}\right)$	$e\left(\frac{505}{644}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{417}{644}\right)$	$e\left(\frac{55}{644}\right)$	$e\left(\frac{33}{644}\right)$	$e\left(\frac{309}{322}\right)$
$\chi_{40310}(3153,\cdot)$	$-1$	$1$	$e\left(\frac{309}{322}\right)$	$e\left(\frac{191}{644}\right)$	$e\left(\frac{148}{161}\right)$	$e\left(\frac{87}{644}\right)$	$e\left(\frac{227}{644}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{607}{644}\right)$	$e\left(\frac{165}{644}\right)$	$e\left(\frac{99}{644}\right)$	$e\left(\frac{283}{322}\right)$
$\chi_{40310}(3163,\cdot)$	$-1$	$1$	$e\left(\frac{5}{322}\right)$	$e\left(\frac{199}{644}\right)$	$e\left(\frac{5}{161}\right)$	$e\left(\frac{239}{644}\right)$	$e\left(\frac{631}{644}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{39}{644}\right)$	$e\left(\frac{209}{644}\right)$	$e\left(\frac{383}{644}\right)$	$e\left(\frac{15}{322}\right)$
$\chi_{40310}(3483,\cdot)$	$-1$	$1$	$e\left(\frac{11}{322}\right)$	$e\left(\frac{631}{644}\right)$	$e\left(\frac{11}{161}\right)$	$e\left(\frac{75}{644}\right)$	$e\left(\frac{551}{644}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{279}{644}\right)$	$e\left(\frac{9}{644}\right)$	$e\left(\frac{263}{644}\right)$	$e\left(\frac{33}{322}\right)$
$\chi_{40310}(3523,\cdot)$	$-1$	$1$	$e\left(\frac{303}{322}\right)$	$e\left(\frac{403}{644}\right)$	$e\left(\frac{142}{161}\right)$	$e\left(\frac{251}{644}\right)$	$e\left(\frac{307}{644}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{367}{644}\right)$	$e\left(\frac{365}{644}\right)$	$e\left(\frac{219}{644}\right)$	$e\left(\frac{265}{322}\right)$
$\chi_{40310}(3673,\cdot)$	$-1$	$1$	$e\left(\frac{31}{322}\right)$	$e\left(\frac{139}{644}\right)$	$e\left(\frac{31}{161}\right)$	$e\left(\frac{387}{644}\right)$	$e\left(\frac{499}{644}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{435}{644}\right)$	$e\left(\frac{201}{644}\right)$	$e\left(\frac{507}{644}\right)$	$e\left(\frac{93}{322}\right)$
$\chi_{40310}(3767,\cdot)$	$-1$	$1$	$e\left(\frac{95}{322}\right)$	$e\left(\frac{561}{644}\right)$	$e\left(\frac{95}{161}\right)$	$e\left(\frac{33}{644}\right)$	$e\left(\frac{397}{644}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{97}{644}\right)$	$e\left(\frac{107}{644}\right)$	$e\left(\frac{193}{644}\right)$	$e\left(\frac{285}{322}\right)$
$\chi_{40310}(3813,\cdot)$	$-1$	$1$	$e\left(\frac{289}{322}\right)$	$e\left(\frac{39}{644}\right)$	$e\left(\frac{128}{161}\right)$	$e\left(\frac{419}{644}\right)$	$e\left(\frac{279}{644}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{451}{644}\right)$	$e\left(\frac{617}{644}\right)$	$e\left(\frac{499}{644}\right)$	$e\left(\frac{223}{322}\right)$
$\chi_{40310}(4107,\cdot)$	$-1$	$1$	$e\left(\frac{139}{322}\right)$	$e\left(\frac{509}{644}\right)$	$e\left(\frac{139}{161}\right)$	$e\left(\frac{333}{644}\right)$	$e\left(\frac{25}{644}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{569}{644}\right)$	$e\left(\frac{143}{644}\right)$	$e\left(\frac{601}{644}\right)$	$e\left(\frac{95}{322}\right)$
$\chi_{40310}(4303,\cdot)$	$-1$	$1$	$e\left(\frac{223}{322}\right)$	$e\left(\frac{439}{644}\right)$	$e\left(\frac{62}{161}\right)$	$e\left(\frac{291}{644}\right)$	$e\left(\frac{515}{644}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{387}{644}\right)$	$e\left(\frac{241}{644}\right)$	$e\left(\frac{531}{644}\right)$	$e\left(\frac{25}{322}\right)$
$\chi_{40310}(4323,\cdot)$	$-1$	$1$	$e\left(\frac{187}{322}\right)$	$e\left(\frac{423}{644}\right)$	$e\left(\frac{26}{161}\right)$	$e\left(\frac{631}{644}\right)$	$e\left(\frac{351}{644}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{235}{644}\right)$	$e\left(\frac{153}{644}\right)$	$e\left(\frac{607}{644}\right)$	$e\left(\frac{239}{322}\right)$
$\chi_{40310}(4393,\cdot)$	$-1$	$1$	$e\left(\frac{65}{322}\right)$	$e\left(\frac{11}{644}\right)$	$e\left(\frac{65}{161}\right)$	$e\left(\frac{531}{644}\right)$	$e\left(\frac{475}{644}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{507}{644}\right)$	$e\left(\frac{141}{644}\right)$	$e\left(\frac{471}{644}\right)$	$e\left(\frac{195}{322}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(27,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{313}{322}\right)\)	\(e\left(\frac{157}{644}\right)\)	\(e\left(\frac{152}{161}\right)\)	\(e\left(\frac{85}{644}\right)\)	\(e\left(\frac{281}{644}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{445}{644}\right)\)	\(e\left(\frac{139}{644}\right)\)	\(e\left(\frac{341}{644}\right)\)	\(e\left(\frac{295}{322}\right)\)
\(\chi_{40310}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{201}{322}\right)\)	\(e\left(\frac{465}{644}\right)\)	\(e\left(\frac{40}{161}\right)\)	\(e\left(\frac{141}{644}\right)\)	\(e\left(\frac{57}{644}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{473}{644}\right)\)	\(e\left(\frac{223}{644}\right)\)	\(e\left(\frac{5}{644}\right)\)	\(e\left(\frac{281}{322}\right)\)
\(\chi_{40310}(337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{322}\right)\)	\(e\left(\frac{369}{644}\right)\)	\(e\left(\frac{146}{161}\right)\)	\(e\left(\frac{249}{644}\right)\)	\(e\left(\frac{361}{644}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{205}{644}\right)\)	\(e\left(\frac{339}{644}\right)\)	\(e\left(\frac{461}{644}\right)\)	\(e\left(\frac{277}{322}\right)\)
\(\chi_{40310}(583,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{322}\right)\)	\(e\left(\frac{295}{644}\right)\)	\(e\left(\frac{60}{161}\right)\)	\(e\left(\frac{131}{644}\right)\)	\(e\left(\frac{327}{644}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{307}{644}\right)\)	\(e\left(\frac{93}{644}\right)\)	\(e\left(\frac{571}{644}\right)\)	\(e\left(\frac{19}{322}\right)\)
\(\chi_{40310}(867,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{291}{322}\right)\)	\(e\left(\frac{505}{644}\right)\)	\(e\left(\frac{130}{161}\right)\)	\(e\left(\frac{257}{644}\right)\)	\(e\left(\frac{145}{644}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{209}{644}\right)\)	\(e\left(\frac{443}{644}\right)\)	\(e\left(\frac{137}{644}\right)\)	\(e\left(\frac{229}{322}\right)\)
\(\chi_{40310}(873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{322}\right)\)	\(e\left(\frac{603}{644}\right)\)	\(e\left(\frac{109}{161}\right)\)	\(e\left(\frac{187}{644}\right)\)	\(e\left(\frac{103}{644}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{335}{644}\right)\)	\(e\left(\frac{177}{644}\right)\)	\(e\left(\frac{235}{644}\right)\)	\(e\left(\frac{5}{322}\right)\)
\(\chi_{40310}(967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{269}{322}\right)\)	\(e\left(\frac{209}{644}\right)\)	\(e\left(\frac{108}{161}\right)\)	\(e\left(\frac{429}{644}\right)\)	\(e\left(\frac{9}{644}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{617}{644}\right)\)	\(e\left(\frac{103}{644}\right)\)	\(e\left(\frac{577}{644}\right)\)	\(e\left(\frac{163}{322}\right)\)
\(\chi_{40310}(1187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{322}\right)\)	\(e\left(\frac{549}{644}\right)\)	\(e\left(\frac{68}{161}\right)\)	\(e\left(\frac{449}{644}\right)\)	\(e\left(\frac{113}{644}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{305}{644}\right)\)	\(e\left(\frac{363}{644}\right)\)	\(e\left(\frac{89}{644}\right)\)	\(e\left(\frac{43}{322}\right)\)
\(\chi_{40310}(1207,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{322}\right)\)	\(e\left(\frac{145}{644}\right)\)	\(e\left(\frac{125}{161}\right)\)	\(e\left(\frac{501}{644}\right)\)	\(e\left(\frac{641}{644}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{9}{644}\right)\)	\(e\left(\frac{395}{644}\right)\)	\(e\left(\frac{237}{644}\right)\)	\(e\left(\frac{53}{322}\right)\)
\(\chi_{40310}(1413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{99}{322}\right)\)	\(e\left(\frac{527}{644}\right)\)	\(e\left(\frac{99}{161}\right)\)	\(e\left(\frac{31}{644}\right)\)	\(e\left(\frac{451}{644}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{579}{644}\right)\)	\(e\left(\frac{81}{644}\right)\)	\(e\left(\frac{435}{644}\right)\)	\(e\left(\frac{297}{322}\right)\)
\(\chi_{40310}(1423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{322}\right)\)	\(e\left(\frac{367}{644}\right)\)	\(e\left(\frac{61}{161}\right)\)	\(e\left(\frac{211}{644}\right)\)	\(e\left(\frac{99}{644}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{347}{644}\right)\)	\(e\left(\frac{489}{644}\right)\)	\(e\left(\frac{551}{644}\right)\)	\(e\left(\frac{183}{322}\right)\)
\(\chi_{40310}(1477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{322}\right)\)	\(e\left(\frac{381}{644}\right)\)	\(e\left(\frac{12}{161}\right)\)	\(e\left(\frac{477}{644}\right)\)	\(e\left(\frac{1}{644}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{641}{644}\right)\)	\(e\left(\frac{83}{644}\right)\)	\(e\left(\frac{565}{644}\right)\)	\(e\left(\frac{197}{322}\right)\)
\(\chi_{40310}(1493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{322}\right)\)	\(e\left(\frac{487}{644}\right)\)	\(e\left(\frac{9}{161}\right)\)	\(e\left(\frac{559}{644}\right)\)	\(e\left(\frac{363}{644}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{199}{644}\right)\)	\(e\left(\frac{505}{644}\right)\)	\(e\left(\frac{303}{644}\right)\)	\(e\left(\frac{27}{322}\right)\)
\(\chi_{40310}(1743,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{322}\right)\)	\(e\left(\frac{43}{644}\right)\)	\(e\left(\frac{137}{161}\right)\)	\(e\left(\frac{495}{644}\right)\)	\(e\left(\frac{159}{644}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{167}{644}\right)\)	\(e\left(\frac{317}{644}\right)\)	\(e\left(\frac{319}{644}\right)\)	\(e\left(\frac{89}{322}\right)\)
\(\chi_{40310}(2033,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{322}\right)\)	\(e\left(\frac{519}{644}\right)\)	\(e\left(\frac{81}{161}\right)\)	\(e\left(\frac{523}{644}\right)\)	\(e\left(\frac{47}{644}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{503}{644}\right)\)	\(e\left(\frac{37}{644}\right)\)	\(e\left(\frac{151}{644}\right)\)	\(e\left(\frac{243}{322}\right)\)
\(\chi_{40310}(2283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{322}\right)\)	\(e\left(\frac{415}{644}\right)\)	\(e\left(\frac{8}{161}\right)\)	\(e\left(\frac{479}{644}\right)\)	\(e\left(\frac{591}{644}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{159}{644}\right)\)	\(e\left(\frac{109}{644}\right)\)	\(e\left(\frac{323}{644}\right)\)	\(e\left(\frac{185}{322}\right)\)
\(\chi_{40310}(2357,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{322}\right)\)	\(e\left(\frac{485}{644}\right)\)	\(e\left(\frac{85}{161}\right)\)	\(e\left(\frac{521}{644}\right)\)	\(e\left(\frac{101}{644}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{341}{644}\right)\)	\(e\left(\frac{11}{644}\right)\)	\(e\left(\frac{393}{644}\right)\)	\(e\left(\frac{255}{322}\right)\)
\(\chi_{40310}(2607,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{235}{322}\right)\)	\(e\left(\frac{337}{644}\right)\)	\(e\left(\frac{74}{161}\right)\)	\(e\left(\frac{285}{644}\right)\)	\(e\left(\frac{33}{644}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{545}{644}\right)\)	\(e\left(\frac{163}{644}\right)\)	\(e\left(\frac{613}{644}\right)\)	\(e\left(\frac{61}{322}\right)\)
\(\chi_{40310}(2803,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{322}\right)\)	\(e\left(\frac{251}{644}\right)\)	\(e\left(\frac{122}{161}\right)\)	\(e\left(\frac{583}{644}\right)\)	\(e\left(\frac{359}{644}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{211}{644}\right)\)	\(e\left(\frac{173}{644}\right)\)	\(e\left(\frac{619}{644}\right)\)	\(e\left(\frac{205}{322}\right)\)
\(\chi_{40310}(2927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{322}\right)\)	\(e\left(\frac{493}{644}\right)\)	\(e\left(\frac{103}{161}\right)\)	\(e\left(\frac{29}{644}\right)\)	\(e\left(\frac{505}{644}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{417}{644}\right)\)	\(e\left(\frac{55}{644}\right)\)	\(e\left(\frac{33}{644}\right)\)	\(e\left(\frac{309}{322}\right)\)
\(\chi_{40310}(3153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{309}{322}\right)\)	\(e\left(\frac{191}{644}\right)\)	\(e\left(\frac{148}{161}\right)\)	\(e\left(\frac{87}{644}\right)\)	\(e\left(\frac{227}{644}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{607}{644}\right)\)	\(e\left(\frac{165}{644}\right)\)	\(e\left(\frac{99}{644}\right)\)	\(e\left(\frac{283}{322}\right)\)
\(\chi_{40310}(3163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{322}\right)\)	\(e\left(\frac{199}{644}\right)\)	\(e\left(\frac{5}{161}\right)\)	\(e\left(\frac{239}{644}\right)\)	\(e\left(\frac{631}{644}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{39}{644}\right)\)	\(e\left(\frac{209}{644}\right)\)	\(e\left(\frac{383}{644}\right)\)	\(e\left(\frac{15}{322}\right)\)
\(\chi_{40310}(3483,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{322}\right)\)	\(e\left(\frac{631}{644}\right)\)	\(e\left(\frac{11}{161}\right)\)	\(e\left(\frac{75}{644}\right)\)	\(e\left(\frac{551}{644}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{279}{644}\right)\)	\(e\left(\frac{9}{644}\right)\)	\(e\left(\frac{263}{644}\right)\)	\(e\left(\frac{33}{322}\right)\)
\(\chi_{40310}(3523,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{303}{322}\right)\)	\(e\left(\frac{403}{644}\right)\)	\(e\left(\frac{142}{161}\right)\)	\(e\left(\frac{251}{644}\right)\)	\(e\left(\frac{307}{644}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{367}{644}\right)\)	\(e\left(\frac{365}{644}\right)\)	\(e\left(\frac{219}{644}\right)\)	\(e\left(\frac{265}{322}\right)\)
\(\chi_{40310}(3673,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{322}\right)\)	\(e\left(\frac{139}{644}\right)\)	\(e\left(\frac{31}{161}\right)\)	\(e\left(\frac{387}{644}\right)\)	\(e\left(\frac{499}{644}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{435}{644}\right)\)	\(e\left(\frac{201}{644}\right)\)	\(e\left(\frac{507}{644}\right)\)	\(e\left(\frac{93}{322}\right)\)
\(\chi_{40310}(3767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{322}\right)\)	\(e\left(\frac{561}{644}\right)\)	\(e\left(\frac{95}{161}\right)\)	\(e\left(\frac{33}{644}\right)\)	\(e\left(\frac{397}{644}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{97}{644}\right)\)	\(e\left(\frac{107}{644}\right)\)	\(e\left(\frac{193}{644}\right)\)	\(e\left(\frac{285}{322}\right)\)
\(\chi_{40310}(3813,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{289}{322}\right)\)	\(e\left(\frac{39}{644}\right)\)	\(e\left(\frac{128}{161}\right)\)	\(e\left(\frac{419}{644}\right)\)	\(e\left(\frac{279}{644}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{451}{644}\right)\)	\(e\left(\frac{617}{644}\right)\)	\(e\left(\frac{499}{644}\right)\)	\(e\left(\frac{223}{322}\right)\)
\(\chi_{40310}(4107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{322}\right)\)	\(e\left(\frac{509}{644}\right)\)	\(e\left(\frac{139}{161}\right)\)	\(e\left(\frac{333}{644}\right)\)	\(e\left(\frac{25}{644}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{569}{644}\right)\)	\(e\left(\frac{143}{644}\right)\)	\(e\left(\frac{601}{644}\right)\)	\(e\left(\frac{95}{322}\right)\)
\(\chi_{40310}(4303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{223}{322}\right)\)	\(e\left(\frac{439}{644}\right)\)	\(e\left(\frac{62}{161}\right)\)	\(e\left(\frac{291}{644}\right)\)	\(e\left(\frac{515}{644}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{387}{644}\right)\)	\(e\left(\frac{241}{644}\right)\)	\(e\left(\frac{531}{644}\right)\)	\(e\left(\frac{25}{322}\right)\)
\(\chi_{40310}(4323,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{322}\right)\)	\(e\left(\frac{423}{644}\right)\)	\(e\left(\frac{26}{161}\right)\)	\(e\left(\frac{631}{644}\right)\)	\(e\left(\frac{351}{644}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{235}{644}\right)\)	\(e\left(\frac{153}{644}\right)\)	\(e\left(\frac{607}{644}\right)\)	\(e\left(\frac{239}{322}\right)\)
\(\chi_{40310}(4393,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{322}\right)\)	\(e\left(\frac{11}{644}\right)\)	\(e\left(\frac{65}{161}\right)\)	\(e\left(\frac{531}{644}\right)\)	\(e\left(\frac{475}{644}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{507}{644}\right)\)	\(e\left(\frac{141}{644}\right)\)	\(e\left(\frac{471}{644}\right)\)	\(e\left(\frac{195}{322}\right)\)

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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.fa
Modulus	$40310$
Conductor	$20155$
Order	$644$
Real	no
Primitive	no
Minimal	yes
Parity	odd

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.fk	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)