LMFDB - Dirichlet character orbit 40310.fp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(966)) M = H._module chi = DirichletCharacter(H, M([0,897,70])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(51,40310)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$40310$
Conductor:	$4031$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$966$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4031.bt	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:	$\Q(\zeta_{483})$
Fixed field:	Number field defined by a degree 966 polynomial (not computed)

First 31 of 264 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(51,\cdot)$	$1$	$1$	$e\left(\frac{593}{966}\right)$	$e\left(\frac{370}{483}\right)$	$e\left(\frac{110}{483}\right)$	$e\left(\frac{697}{966}\right)$	$e\left(\frac{170}{483}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{751}{966}\right)$	$e\left(\frac{367}{966}\right)$	$e\left(\frac{85}{161}\right)$	$e\left(\frac{271}{322}\right)$
$\chi_{40310}(71,\cdot)$	$1$	$1$	$e\left(\frac{95}{966}\right)$	$e\left(\frac{100}{483}\right)$	$e\left(\frac{95}{483}\right)$	$e\left(\frac{97}{966}\right)$	$e\left(\frac{59}{483}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{451}{966}\right)$	$e\left(\frac{295}{966}\right)$	$e\left(\frac{110}{161}\right)$	$e\left(\frac{95}{322}\right)$
$\chi_{40310}(121,\cdot)$	$1$	$1$	$e\left(\frac{85}{966}\right)$	$e\left(\frac{242}{483}\right)$	$e\left(\frac{85}{483}\right)$	$e\left(\frac{341}{966}\right)$	$e\left(\frac{307}{483}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{251}{966}\right)$	$e\left(\frac{569}{966}\right)$	$e\left(\frac{73}{161}\right)$	$e\left(\frac{85}{322}\right)$
$\chi_{40310}(361,\cdot)$	$1$	$1$	$e\left(\frac{445}{966}\right)$	$e\left(\frac{443}{483}\right)$	$e\left(\frac{445}{483}\right)$	$e\left(\frac{251}{966}\right)$	$e\left(\frac{73}{483}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{689}{966}\right)$	$e\left(\frac{365}{966}\right)$	$e\left(\frac{117}{161}\right)$	$e\left(\frac{123}{322}\right)$
$\chi_{40310}(441,\cdot)$	$1$	$1$	$e\left(\frac{139}{966}\right)$	$e\left(\frac{248}{483}\right)$	$e\left(\frac{139}{483}\right)$	$e\left(\frac{569}{966}\right)$	$e\left(\frac{127}{483}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{365}{966}\right)$	$e\left(\frac{635}{966}\right)$	$e\left(\frac{144}{161}\right)$	$e\left(\frac{139}{322}\right)$
$\chi_{40310}(941,\cdot)$	$1$	$1$	$e\left(\frac{193}{966}\right)$	$e\left(\frac{254}{483}\right)$	$e\left(\frac{193}{483}\right)$	$e\left(\frac{797}{966}\right)$	$e\left(\frac{430}{483}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{479}{966}\right)$	$e\left(\frac{701}{966}\right)$	$e\left(\frac{54}{161}\right)$	$e\left(\frac{193}{322}\right)$
$\chi_{40310}(961,\cdot)$	$1$	$1$	$e\left(\frac{611}{966}\right)$	$e\left(\frac{211}{483}\right)$	$e\left(\frac{128}{483}\right)$	$e\left(\frac{451}{966}\right)$	$e\left(\frac{110}{483}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{145}{966}\right)$	$e\left(\frac{67}{966}\right)$	$e\left(\frac{55}{161}\right)$	$e\left(\frac{289}{322}\right)$
$\chi_{40310}(1211,\cdot)$	$1$	$1$	$e\left(\frac{565}{966}\right)$	$e\left(\frac{188}{483}\right)$	$e\left(\frac{82}{483}\right)$	$e\left(\frac{221}{966}\right)$	$e\left(\frac{478}{483}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{191}{966}\right)$	$e\left(\frac{941}{966}\right)$	$e\left(\frac{78}{161}\right)$	$e\left(\frac{243}{322}\right)$
$\chi_{40310}(1281,\cdot)$	$1$	$1$	$e\left(\frac{925}{966}\right)$	$e\left(\frac{389}{483}\right)$	$e\left(\frac{442}{483}\right)$	$e\left(\frac{131}{966}\right)$	$e\left(\frac{244}{483}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{629}{966}\right)$	$e\left(\frac{737}{966}\right)$	$e\left(\frac{122}{161}\right)$	$e\left(\frac{281}{322}\right)$
$\chi_{40310}(1401,\cdot)$	$1$	$1$	$e\left(\frac{353}{966}\right)$	$e\left(\frac{397}{483}\right)$	$e\left(\frac{353}{483}\right)$	$e\left(\frac{757}{966}\right)$	$e\left(\frac{326}{483}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{781}{966}\right)$	$e\left(\frac{181}{966}\right)$	$e\left(\frac{2}{161}\right)$	$e\left(\frac{31}{322}\right)$
$\chi_{40310}(1811,\cdot)$	$1$	$1$	$e\left(\frac{781}{966}\right)$	$e\left(\frac{212}{483}\right)$	$e\left(\frac{298}{483}\right)$	$e\left(\frac{167}{966}\right)$	$e\left(\frac{241}{483}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{647}{966}\right)$	$e\left(\frac{239}{966}\right)$	$e\left(\frac{40}{161}\right)$	$e\left(\frac{137}{322}\right)$
$\chi_{40310}(1831,\cdot)$	$1$	$1$	$e\left(\frac{415}{966}\right)$	$e\left(\frac{386}{483}\right)$	$e\left(\frac{415}{483}\right)$	$e\left(\frac{17}{966}\right)$	$e\left(\frac{334}{483}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{89}{966}\right)$	$e\left(\frac{221}{966}\right)$	$e\left(\frac{6}{161}\right)$	$e\left(\frac{93}{322}\right)$
$\chi_{40310}(1861,\cdot)$	$1$	$1$	$e\left(\frac{743}{966}\right)$	$e\left(\frac{172}{483}\right)$	$e\left(\frac{260}{483}\right)$	$e\left(\frac{901}{966}\right)$	$e\left(\frac{314}{483}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{853}{966}\right)$	$e\left(\frac{121}{966}\right)$	$e\left(\frac{157}{161}\right)$	$e\left(\frac{99}{322}\right)$
$\chi_{40310}(1981,\cdot)$	$1$	$1$	$e\left(\frac{185}{966}\right)$	$e\left(\frac{271}{483}\right)$	$e\left(\frac{185}{483}\right)$	$e\left(\frac{799}{966}\right)$	$e\left(\frac{242}{483}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{319}{966}\right)$	$e\left(\frac{727}{966}\right)$	$e\left(\frac{121}{161}\right)$	$e\left(\frac{185}{322}\right)$
$\chi_{40310}(2101,\cdot)$	$1$	$1$	$e\left(\frac{389}{966}\right)$	$e\left(\frac{79}{483}\right)$	$e\left(\frac{389}{483}\right)$	$e\left(\frac{265}{966}\right)$	$e\left(\frac{206}{483}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{535}{966}\right)$	$e\left(\frac{547}{966}\right)$	$e\left(\frac{103}{161}\right)$	$e\left(\frac{67}{322}\right)$
$\chi_{40310}(2151,\cdot)$	$1$	$1$	$e\left(\frac{953}{966}\right)$	$e\left(\frac{88}{483}\right)$	$e\left(\frac{470}{483}\right)$	$e\left(\frac{607}{966}\right)$	$e\left(\frac{419}{483}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{223}{966}\right)$	$e\left(\frac{163}{966}\right)$	$e\left(\frac{129}{161}\right)$	$e\left(\frac{309}{322}\right)$
$\chi_{40310}(2271,\cdot)$	$1$	$1$	$e\left(\frac{871}{966}\right)$	$e\left(\frac{383}{483}\right)$	$e\left(\frac{388}{483}\right)$	$e\left(\frac{869}{966}\right)$	$e\left(\frac{424}{483}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{515}{966}\right)$	$e\left(\frac{671}{966}\right)$	$e\left(\frac{51}{161}\right)$	$e\left(\frac{227}{322}\right)$
$\chi_{40310}(2391,\cdot)$	$1$	$1$	$e\left(\frac{641}{966}\right)$	$e\left(\frac{268}{483}\right)$	$e\left(\frac{158}{483}\right)$	$e\left(\frac{685}{966}\right)$	$e\left(\frac{332}{483}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{745}{966}\right)$	$e\left(\frac{211}{966}\right)$	$e\left(\frac{5}{161}\right)$	$e\left(\frac{319}{322}\right)$
$\chi_{40310}(2441,\cdot)$	$1$	$1$	$e\left(\frac{407}{966}\right)$	$e\left(\frac{403}{483}\right)$	$e\left(\frac{407}{483}\right)$	$e\left(\frac{19}{966}\right)$	$e\left(\frac{146}{483}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{895}{966}\right)$	$e\left(\frac{247}{966}\right)$	$e\left(\frac{73}{161}\right)$	$e\left(\frac{85}{322}\right)$
$\chi_{40310}(2661,\cdot)$	$1$	$1$	$e\left(\frac{761}{966}\right)$	$e\left(\frac{13}{483}\right)$	$e\left(\frac{278}{483}\right)$	$e\left(\frac{655}{966}\right)$	$e\left(\frac{254}{483}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{247}{966}\right)$	$e\left(\frac{787}{966}\right)$	$e\left(\frac{127}{161}\right)$	$e\left(\frac{117}{322}\right)$
$\chi_{40310}(2761,\cdot)$	$1$	$1$	$e\left(\frac{671}{966}\right)$	$e\left(\frac{325}{483}\right)$	$e\left(\frac{188}{483}\right)$	$e\left(\frac{919}{966}\right)$	$e\left(\frac{71}{483}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{379}{966}\right)$	$e\left(\frac{355}{966}\right)$	$e\left(\frac{116}{161}\right)$	$e\left(\frac{27}{322}\right)$
$\chi_{40310}(2851,\cdot)$	$1$	$1$	$e\left(\frac{647}{966}\right)$	$e\left(\frac{376}{483}\right)$	$e\left(\frac{164}{483}\right)$	$e\left(\frac{925}{966}\right)$	$e\left(\frac{473}{483}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{865}{966}\right)$	$e\left(\frac{433}{966}\right)$	$e\left(\frac{156}{161}\right)$	$e\left(\frac{3}{322}\right)$
$\chi_{40310}(3141,\cdot)$	$1$	$1$	$e\left(\frac{31}{966}\right)$	$e\left(\frac{236}{483}\right)$	$e\left(\frac{31}{483}\right)$	$e\left(\frac{113}{966}\right)$	$e\left(\frac{4}{483}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{137}{966}\right)$	$e\left(\frac{503}{966}\right)$	$e\left(\frac{2}{161}\right)$	$e\left(\frac{31}{322}\right)$
$\chi_{40310}(3341,\cdot)$	$1$	$1$	$e\left(\frac{601}{966}\right)$	$e\left(\frac{353}{483}\right)$	$e\left(\frac{118}{483}\right)$	$e\left(\frac{695}{966}\right)$	$e\left(\frac{358}{483}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{911}{966}\right)$	$e\left(\frac{341}{966}\right)$	$e\left(\frac{18}{161}\right)$	$e\left(\frac{279}{322}\right)$
$\chi_{40310}(3721,\cdot)$	$1$	$1$	$e\left(\frac{745}{966}\right)$	$e\left(\frac{47}{483}\right)$	$e\left(\frac{262}{483}\right)$	$e\left(\frac{659}{966}\right)$	$e\left(\frac{361}{483}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{893}{966}\right)$	$e\left(\frac{839}{966}\right)$	$e\left(\frac{100}{161}\right)$	$e\left(\frac{101}{322}\right)$
$\chi_{40310}(3921,\cdot)$	$1$	$1$	$e\left(\frac{965}{966}\right)$	$e\left(\frac{304}{483}\right)$	$e\left(\frac{482}{483}\right)$	$e\left(\frac{121}{966}\right)$	$e\left(\frac{218}{483}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{463}{966}\right)$	$e\left(\frac{607}{966}\right)$	$e\left(\frac{109}{161}\right)$	$e\left(\frac{321}{322}\right)$
$\chi_{40310}(4151,\cdot)$	$1$	$1$	$e\left(\frac{947}{966}\right)$	$e\left(\frac{463}{483}\right)$	$e\left(\frac{464}{483}\right)$	$e\left(\frac{367}{966}\right)$	$e\left(\frac{278}{483}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{103}{966}\right)$	$e\left(\frac{907}{966}\right)$	$e\left(\frac{139}{161}\right)$	$e\left(\frac{303}{322}\right)$
$\chi_{40310}(4181,\cdot)$	$1$	$1$	$e\left(\frac{491}{966}\right)$	$e\left(\frac{466}{483}\right)$	$e\left(\frac{8}{483}\right)$	$e\left(\frac{481}{966}\right)$	$e\left(\frac{188}{483}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{643}{966}\right)$	$e\left(\frac{457}{966}\right)$	$e\left(\frac{94}{161}\right)$	$e\left(\frac{169}{322}\right)$
$\chi_{40310}(4211,\cdot)$	$1$	$1$	$e\left(\frac{559}{966}\right)$	$e\left(\frac{80}{483}\right)$	$e\left(\frac{76}{483}\right)$	$e\left(\frac{947}{966}\right)$	$e\left(\frac{337}{483}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{71}{966}\right)$	$e\left(\frac{719}{966}\right)$	$e\left(\frac{88}{161}\right)$	$e\left(\frac{237}{322}\right)$
$\chi_{40310}(4591,\cdot)$	$1$	$1$	$e\left(\frac{367}{966}\right)$	$e\left(\frac{5}{483}\right)$	$e\left(\frac{367}{483}\right)$	$e\left(\frac{29}{966}\right)$	$e\left(\frac{172}{483}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{95}{966}\right)$	$e\left(\frac{377}{966}\right)$	$e\left(\frac{86}{161}\right)$	$e\left(\frac{45}{322}\right)$
$\chi_{40310}(4711,\cdot)$	$1$	$1$	$e\left(\frac{431}{966}\right)$	$e\left(\frac{352}{483}\right)$	$e\left(\frac{431}{483}\right)$	$e\left(\frac{13}{966}\right)$	$e\left(\frac{227}{483}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{409}{966}\right)$	$e\left(\frac{169}{966}\right)$	$e\left(\frac{33}{161}\right)$	$e\left(\frac{109}{322}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{593}{966}\right)\)	\(e\left(\frac{370}{483}\right)\)	\(e\left(\frac{110}{483}\right)\)	\(e\left(\frac{697}{966}\right)\)	\(e\left(\frac{170}{483}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{751}{966}\right)\)	\(e\left(\frac{367}{966}\right)\)	\(e\left(\frac{85}{161}\right)\)	\(e\left(\frac{271}{322}\right)\)
\(\chi_{40310}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{966}\right)\)	\(e\left(\frac{100}{483}\right)\)	\(e\left(\frac{95}{483}\right)\)	\(e\left(\frac{97}{966}\right)\)	\(e\left(\frac{59}{483}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{451}{966}\right)\)	\(e\left(\frac{295}{966}\right)\)	\(e\left(\frac{110}{161}\right)\)	\(e\left(\frac{95}{322}\right)\)
\(\chi_{40310}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{966}\right)\)	\(e\left(\frac{242}{483}\right)\)	\(e\left(\frac{85}{483}\right)\)	\(e\left(\frac{341}{966}\right)\)	\(e\left(\frac{307}{483}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{251}{966}\right)\)	\(e\left(\frac{569}{966}\right)\)	\(e\left(\frac{73}{161}\right)\)	\(e\left(\frac{85}{322}\right)\)
\(\chi_{40310}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{445}{966}\right)\)	\(e\left(\frac{443}{483}\right)\)	\(e\left(\frac{445}{483}\right)\)	\(e\left(\frac{251}{966}\right)\)	\(e\left(\frac{73}{483}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{689}{966}\right)\)	\(e\left(\frac{365}{966}\right)\)	\(e\left(\frac{117}{161}\right)\)	\(e\left(\frac{123}{322}\right)\)
\(\chi_{40310}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{966}\right)\)	\(e\left(\frac{248}{483}\right)\)	\(e\left(\frac{139}{483}\right)\)	\(e\left(\frac{569}{966}\right)\)	\(e\left(\frac{127}{483}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{365}{966}\right)\)	\(e\left(\frac{635}{966}\right)\)	\(e\left(\frac{144}{161}\right)\)	\(e\left(\frac{139}{322}\right)\)
\(\chi_{40310}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{966}\right)\)	\(e\left(\frac{254}{483}\right)\)	\(e\left(\frac{193}{483}\right)\)	\(e\left(\frac{797}{966}\right)\)	\(e\left(\frac{430}{483}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{479}{966}\right)\)	\(e\left(\frac{701}{966}\right)\)	\(e\left(\frac{54}{161}\right)\)	\(e\left(\frac{193}{322}\right)\)
\(\chi_{40310}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{611}{966}\right)\)	\(e\left(\frac{211}{483}\right)\)	\(e\left(\frac{128}{483}\right)\)	\(e\left(\frac{451}{966}\right)\)	\(e\left(\frac{110}{483}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{145}{966}\right)\)	\(e\left(\frac{67}{966}\right)\)	\(e\left(\frac{55}{161}\right)\)	\(e\left(\frac{289}{322}\right)\)
\(\chi_{40310}(1211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{565}{966}\right)\)	\(e\left(\frac{188}{483}\right)\)	\(e\left(\frac{82}{483}\right)\)	\(e\left(\frac{221}{966}\right)\)	\(e\left(\frac{478}{483}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{191}{966}\right)\)	\(e\left(\frac{941}{966}\right)\)	\(e\left(\frac{78}{161}\right)\)	\(e\left(\frac{243}{322}\right)\)
\(\chi_{40310}(1281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{925}{966}\right)\)	\(e\left(\frac{389}{483}\right)\)	\(e\left(\frac{442}{483}\right)\)	\(e\left(\frac{131}{966}\right)\)	\(e\left(\frac{244}{483}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{629}{966}\right)\)	\(e\left(\frac{737}{966}\right)\)	\(e\left(\frac{122}{161}\right)\)	\(e\left(\frac{281}{322}\right)\)
\(\chi_{40310}(1401,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{966}\right)\)	\(e\left(\frac{397}{483}\right)\)	\(e\left(\frac{353}{483}\right)\)	\(e\left(\frac{757}{966}\right)\)	\(e\left(\frac{326}{483}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{781}{966}\right)\)	\(e\left(\frac{181}{966}\right)\)	\(e\left(\frac{2}{161}\right)\)	\(e\left(\frac{31}{322}\right)\)
\(\chi_{40310}(1811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{781}{966}\right)\)	\(e\left(\frac{212}{483}\right)\)	\(e\left(\frac{298}{483}\right)\)	\(e\left(\frac{167}{966}\right)\)	\(e\left(\frac{241}{483}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{647}{966}\right)\)	\(e\left(\frac{239}{966}\right)\)	\(e\left(\frac{40}{161}\right)\)	\(e\left(\frac{137}{322}\right)\)
\(\chi_{40310}(1831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{415}{966}\right)\)	\(e\left(\frac{386}{483}\right)\)	\(e\left(\frac{415}{483}\right)\)	\(e\left(\frac{17}{966}\right)\)	\(e\left(\frac{334}{483}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{89}{966}\right)\)	\(e\left(\frac{221}{966}\right)\)	\(e\left(\frac{6}{161}\right)\)	\(e\left(\frac{93}{322}\right)\)
\(\chi_{40310}(1861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{743}{966}\right)\)	\(e\left(\frac{172}{483}\right)\)	\(e\left(\frac{260}{483}\right)\)	\(e\left(\frac{901}{966}\right)\)	\(e\left(\frac{314}{483}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{853}{966}\right)\)	\(e\left(\frac{121}{966}\right)\)	\(e\left(\frac{157}{161}\right)\)	\(e\left(\frac{99}{322}\right)\)
\(\chi_{40310}(1981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{966}\right)\)	\(e\left(\frac{271}{483}\right)\)	\(e\left(\frac{185}{483}\right)\)	\(e\left(\frac{799}{966}\right)\)	\(e\left(\frac{242}{483}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{319}{966}\right)\)	\(e\left(\frac{727}{966}\right)\)	\(e\left(\frac{121}{161}\right)\)	\(e\left(\frac{185}{322}\right)\)
\(\chi_{40310}(2101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{966}\right)\)	\(e\left(\frac{79}{483}\right)\)	\(e\left(\frac{389}{483}\right)\)	\(e\left(\frac{265}{966}\right)\)	\(e\left(\frac{206}{483}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{535}{966}\right)\)	\(e\left(\frac{547}{966}\right)\)	\(e\left(\frac{103}{161}\right)\)	\(e\left(\frac{67}{322}\right)\)
\(\chi_{40310}(2151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{953}{966}\right)\)	\(e\left(\frac{88}{483}\right)\)	\(e\left(\frac{470}{483}\right)\)	\(e\left(\frac{607}{966}\right)\)	\(e\left(\frac{419}{483}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{223}{966}\right)\)	\(e\left(\frac{163}{966}\right)\)	\(e\left(\frac{129}{161}\right)\)	\(e\left(\frac{309}{322}\right)\)
\(\chi_{40310}(2271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{871}{966}\right)\)	\(e\left(\frac{383}{483}\right)\)	\(e\left(\frac{388}{483}\right)\)	\(e\left(\frac{869}{966}\right)\)	\(e\left(\frac{424}{483}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{515}{966}\right)\)	\(e\left(\frac{671}{966}\right)\)	\(e\left(\frac{51}{161}\right)\)	\(e\left(\frac{227}{322}\right)\)
\(\chi_{40310}(2391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{641}{966}\right)\)	\(e\left(\frac{268}{483}\right)\)	\(e\left(\frac{158}{483}\right)\)	\(e\left(\frac{685}{966}\right)\)	\(e\left(\frac{332}{483}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{745}{966}\right)\)	\(e\left(\frac{211}{966}\right)\)	\(e\left(\frac{5}{161}\right)\)	\(e\left(\frac{319}{322}\right)\)
\(\chi_{40310}(2441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{407}{966}\right)\)	\(e\left(\frac{403}{483}\right)\)	\(e\left(\frac{407}{483}\right)\)	\(e\left(\frac{19}{966}\right)\)	\(e\left(\frac{146}{483}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{895}{966}\right)\)	\(e\left(\frac{247}{966}\right)\)	\(e\left(\frac{73}{161}\right)\)	\(e\left(\frac{85}{322}\right)\)
\(\chi_{40310}(2661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{761}{966}\right)\)	\(e\left(\frac{13}{483}\right)\)	\(e\left(\frac{278}{483}\right)\)	\(e\left(\frac{655}{966}\right)\)	\(e\left(\frac{254}{483}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{247}{966}\right)\)	\(e\left(\frac{787}{966}\right)\)	\(e\left(\frac{127}{161}\right)\)	\(e\left(\frac{117}{322}\right)\)
\(\chi_{40310}(2761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{671}{966}\right)\)	\(e\left(\frac{325}{483}\right)\)	\(e\left(\frac{188}{483}\right)\)	\(e\left(\frac{919}{966}\right)\)	\(e\left(\frac{71}{483}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{379}{966}\right)\)	\(e\left(\frac{355}{966}\right)\)	\(e\left(\frac{116}{161}\right)\)	\(e\left(\frac{27}{322}\right)\)
\(\chi_{40310}(2851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{647}{966}\right)\)	\(e\left(\frac{376}{483}\right)\)	\(e\left(\frac{164}{483}\right)\)	\(e\left(\frac{925}{966}\right)\)	\(e\left(\frac{473}{483}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{865}{966}\right)\)	\(e\left(\frac{433}{966}\right)\)	\(e\left(\frac{156}{161}\right)\)	\(e\left(\frac{3}{322}\right)\)
\(\chi_{40310}(3141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{966}\right)\)	\(e\left(\frac{236}{483}\right)\)	\(e\left(\frac{31}{483}\right)\)	\(e\left(\frac{113}{966}\right)\)	\(e\left(\frac{4}{483}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{137}{966}\right)\)	\(e\left(\frac{503}{966}\right)\)	\(e\left(\frac{2}{161}\right)\)	\(e\left(\frac{31}{322}\right)\)
\(\chi_{40310}(3341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{601}{966}\right)\)	\(e\left(\frac{353}{483}\right)\)	\(e\left(\frac{118}{483}\right)\)	\(e\left(\frac{695}{966}\right)\)	\(e\left(\frac{358}{483}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{911}{966}\right)\)	\(e\left(\frac{341}{966}\right)\)	\(e\left(\frac{18}{161}\right)\)	\(e\left(\frac{279}{322}\right)\)
\(\chi_{40310}(3721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{745}{966}\right)\)	\(e\left(\frac{47}{483}\right)\)	\(e\left(\frac{262}{483}\right)\)	\(e\left(\frac{659}{966}\right)\)	\(e\left(\frac{361}{483}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{893}{966}\right)\)	\(e\left(\frac{839}{966}\right)\)	\(e\left(\frac{100}{161}\right)\)	\(e\left(\frac{101}{322}\right)\)
\(\chi_{40310}(3921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{965}{966}\right)\)	\(e\left(\frac{304}{483}\right)\)	\(e\left(\frac{482}{483}\right)\)	\(e\left(\frac{121}{966}\right)\)	\(e\left(\frac{218}{483}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{463}{966}\right)\)	\(e\left(\frac{607}{966}\right)\)	\(e\left(\frac{109}{161}\right)\)	\(e\left(\frac{321}{322}\right)\)
\(\chi_{40310}(4151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{947}{966}\right)\)	\(e\left(\frac{463}{483}\right)\)	\(e\left(\frac{464}{483}\right)\)	\(e\left(\frac{367}{966}\right)\)	\(e\left(\frac{278}{483}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{103}{966}\right)\)	\(e\left(\frac{907}{966}\right)\)	\(e\left(\frac{139}{161}\right)\)	\(e\left(\frac{303}{322}\right)\)
\(\chi_{40310}(4181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{491}{966}\right)\)	\(e\left(\frac{466}{483}\right)\)	\(e\left(\frac{8}{483}\right)\)	\(e\left(\frac{481}{966}\right)\)	\(e\left(\frac{188}{483}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{643}{966}\right)\)	\(e\left(\frac{457}{966}\right)\)	\(e\left(\frac{94}{161}\right)\)	\(e\left(\frac{169}{322}\right)\)
\(\chi_{40310}(4211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{559}{966}\right)\)	\(e\left(\frac{80}{483}\right)\)	\(e\left(\frac{76}{483}\right)\)	\(e\left(\frac{947}{966}\right)\)	\(e\left(\frac{337}{483}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{71}{966}\right)\)	\(e\left(\frac{719}{966}\right)\)	\(e\left(\frac{88}{161}\right)\)	\(e\left(\frac{237}{322}\right)\)
\(\chi_{40310}(4591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{966}\right)\)	\(e\left(\frac{5}{483}\right)\)	\(e\left(\frac{367}{483}\right)\)	\(e\left(\frac{29}{966}\right)\)	\(e\left(\frac{172}{483}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{95}{966}\right)\)	\(e\left(\frac{377}{966}\right)\)	\(e\left(\frac{86}{161}\right)\)	\(e\left(\frac{45}{322}\right)\)
\(\chi_{40310}(4711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{431}{966}\right)\)	\(e\left(\frac{352}{483}\right)\)	\(e\left(\frac{431}{483}\right)\)	\(e\left(\frac{13}{966}\right)\)	\(e\left(\frac{227}{483}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{409}{966}\right)\)	\(e\left(\frac{169}{966}\right)\)	\(e\left(\frac{33}{161}\right)\)	\(e\left(\frac{109}{322}\right)\)

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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.fp
Modulus	$40310$
Conductor	$4031$
Order	$966$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(40310\)
Conductor:	\(4031\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(966\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4031.bt	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)