LMFDB - Dirichlet character orbit 40310.fv

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(1932)) M = H._module chi = DirichletCharacter(H, M([0,1725,1064])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,40310)) 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:	$1932$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4031.bv	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:	$\Q(\zeta_{1932})$
Fixed field:	Number field defined by a degree 1932 polynomial (not computed)

First 23 of 528 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(11,\cdot)$	$-1$	$1$	$e\left(\frac{85}{1932}\right)$	$e\left(\frac{121}{483}\right)$	$e\left(\frac{85}{966}\right)$	$e\left(\frac{341}{1932}\right)$	$e\left(\frac{307}{966}\right)$	$e\left(\frac{187}{276}\right)$	$e\left(\frac{1217}{1932}\right)$	$e\left(\frac{569}{1932}\right)$	$e\left(\frac{117}{161}\right)$	$e\left(\frac{85}{644}\right)$
$\chi_{40310}(31,\cdot)$	$-1$	$1$	$e\left(\frac{1577}{1932}\right)$	$e\left(\frac{347}{483}\right)$	$e\left(\frac{611}{966}\right)$	$e\left(\frac{1417}{1932}\right)$	$e\left(\frac{593}{966}\right)$	$e\left(\frac{47}{276}\right)$	$e\left(\frac{145}{1932}\right)$	$e\left(\frac{1033}{1932}\right)$	$e\left(\frac{108}{161}\right)$	$e\left(\frac{289}{644}\right)$
$\chi_{40310}(391,\cdot)$	$-1$	$1$	$e\left(\frac{257}{1932}\right)$	$e\left(\frac{59}{483}\right)$	$e\left(\frac{257}{966}\right)$	$e\left(\frac{781}{1932}\right)$	$e\left(\frac{485}{966}\right)$	$e\left(\frac{179}{276}\right)$	$e\left(\frac{793}{1932}\right)$	$e\left(\frac{493}{1932}\right)$	$e\left(\frac{81}{161}\right)$	$e\left(\frac{257}{644}\right)$
$\chi_{40310}(421,\cdot)$	$-1$	$1$	$e\left(\frac{803}{1932}\right)$	$e\left(\frac{143}{483}\right)$	$e\left(\frac{803}{966}\right)$	$e\left(\frac{403}{1932}\right)$	$e\left(\frac{275}{966}\right)$	$e\left(\frac{221}{276}\right)$	$e\left(\frac{1087}{1932}\right)$	$e\left(\frac{1375}{1932}\right)$	$e\left(\frac{109}{161}\right)$	$e\left(\frac{159}{644}\right)$
$\chi_{40310}(541,\cdot)$	$-1$	$1$	$e\left(\frac{1621}{1932}\right)$	$e\left(\frac{421}{483}\right)$	$e\left(\frac{655}{966}\right)$	$e\left(\frac{1889}{1932}\right)$	$e\left(\frac{661}{966}\right)$	$e\left(\frac{199}{276}\right)$	$e\left(\frac{1025}{1932}\right)$	$e\left(\frac{1373}{1932}\right)$	$e\left(\frac{125}{161}\right)$	$e\left(\frac{333}{644}\right)$
$\chi_{40310}(561,\cdot)$	$-1$	$1$	$e\left(\frac{1271}{1932}\right)$	$e\left(\frac{8}{483}\right)$	$e\left(\frac{305}{966}\right)$	$e\left(\frac{1735}{1932}\right)$	$e\left(\frac{647}{966}\right)$	$e\left(\frac{257}{276}\right)$	$e\left(\frac{787}{1932}\right)$	$e\left(\frac{1303}{1932}\right)$	$e\left(\frac{41}{161}\right)$	$e\left(\frac{627}{644}\right)$
$\chi_{40310}(591,\cdot)$	$-1$	$1$	$e\left(\frac{1681}{1932}\right)$	$e\left(\frac{478}{483}\right)$	$e\left(\frac{715}{966}\right)$	$e\left(\frac{425}{1932}\right)$	$e\left(\frac{139}{966}\right)$	$e\left(\frac{55}{276}\right)$	$e\left(\frac{293}{1932}\right)$	$e\left(\frac{1661}{1932}\right)$	$e\left(\frac{75}{161}\right)$	$e\left(\frac{393}{644}\right)$
$\chi_{40310}(711,\cdot)$	$-1$	$1$	$e\left(\frac{19}{1932}\right)$	$e\left(\frac{10}{483}\right)$	$e\left(\frac{19}{966}\right)$	$e\left(\frac{599}{1932}\right)$	$e\left(\frac{205}{966}\right)$	$e\left(\frac{97}{276}\right)$	$e\left(\frac{863}{1932}\right)$	$e\left(\frac{59}{1932}\right)$	$e\left(\frac{11}{161}\right)$	$e\left(\frac{19}{644}\right)$
$\chi_{40310}(781,\cdot)$	$-1$	$1$	$e\left(\frac{275}{1932}\right)$	$e\left(\frac{221}{483}\right)$	$e\left(\frac{275}{966}\right)$	$e\left(\frac{535}{1932}\right)$	$e\left(\frac{425}{966}\right)$	$e\left(\frac{53}{276}\right)$	$e\left(\frac{187}{1932}\right)$	$e\left(\frac{1159}{1932}\right)$	$e\left(\frac{66}{161}\right)$	$e\left(\frac{275}{644}\right)$
$\chi_{40310}(831,\cdot)$	$-1$	$1$	$e\left(\frac{557}{1932}\right)$	$e\left(\frac{344}{483}\right)$	$e\left(\frac{557}{966}\right)$	$e\left(\frac{1189}{1932}\right)$	$e\left(\frac{773}{966}\right)$	$e\left(\frac{11}{276}\right)$	$e\left(\frac{997}{1932}\right)$	$e\left(\frac{1}{1932}\right)$	$e\left(\frac{153}{161}\right)$	$e\left(\frac{557}{644}\right)$
$\chi_{40310}(881,\cdot)$	$-1$	$1$	$e\left(\frac{1121}{1932}\right)$	$e\left(\frac{107}{483}\right)$	$e\left(\frac{155}{966}\right)$	$e\left(\frac{565}{1932}\right)$	$e\left(\frac{503}{966}\right)$	$e\left(\frac{203}{276}\right)$	$e\left(\frac{685}{1932}\right)$	$e\left(\frac{1549}{1932}\right)$	$e\left(\frac{5}{161}\right)$	$e\left(\frac{477}{644}\right)$
$\chi_{40310}(901,\cdot)$	$-1$	$1$	$e\left(\frac{1801}{1932}\right)$	$e\left(\frac{109}{483}\right)$	$e\left(\frac{835}{966}\right)$	$e\left(\frac{1361}{1932}\right)$	$e\left(\frac{61}{966}\right)$	$e\left(\frac{43}{276}\right)$	$e\left(\frac{761}{1932}\right)$	$e\left(\frac{305}{1932}\right)$	$e\left(\frac{136}{161}\right)$	$e\left(\frac{513}{644}\right)$
$\chi_{40310}(971,\cdot)$	$-1$	$1$	$e\left(\frac{229}{1932}\right)$	$e\left(\frac{451}{483}\right)$	$e\left(\frac{229}{966}\right)$	$e\left(\frac{305}{1932}\right)$	$e\left(\frac{793}{966}\right)$	$e\left(\frac{7}{276}\right)$	$e\left(\frac{233}{1932}\right)$	$e\left(\frac{101}{1932}\right)$	$e\left(\frac{158}{161}\right)$	$e\left(\frac{229}{644}\right)$
$\chi_{40310}(1001,\cdot)$	$-1$	$1$	$e\left(\frac{523}{1932}\right)$	$e\left(\frac{199}{483}\right)$	$e\left(\frac{523}{966}\right)$	$e\left(\frac{1439}{1932}\right)$	$e\left(\frac{457}{966}\right)$	$e\left(\frac{157}{276}\right)$	$e\left(\frac{1283}{1932}\right)$	$e\left(\frac{1319}{1932}\right)$	$e\left(\frac{74}{161}\right)$	$e\left(\frac{523}{644}\right)$
$\chi_{40310}(1091,\cdot)$	$-1$	$1$	$e\left(\frac{967}{1932}\right)$	$e\left(\frac{331}{483}\right)$	$e\left(\frac{1}{966}\right)$	$e\left(\frac{1811}{1932}\right)$	$e\left(\frac{265}{966}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{503}{1932}\right)$	$e\left(\frac{359}{1932}\right)$	$e\left(\frac{26}{161}\right)$	$e\left(\frac{323}{644}\right)$
$\chi_{40310}(1121,\cdot)$	$-1$	$1$	$e\left(\frac{1873}{1932}\right)$	$e\left(\frac{274}{483}\right)$	$e\left(\frac{907}{966}\right)$	$e\left(\frac{377}{1932}\right)$	$e\left(\frac{787}{966}\right)$	$e\left(\frac{91}{276}\right)$	$e\left(\frac{269}{1932}\right)$	$e\left(\frac{1037}{1932}\right)$	$e\left(\frac{76}{161}\right)$	$e\left(\frac{585}{644}\right)$
$\chi_{40310}(1141,\cdot)$	$-1$	$1$	$e\left(\frac{67}{1932}\right)$	$e\left(\frac{442}{483}\right)$	$e\left(\frac{67}{966}\right)$	$e\left(\frac{587}{1932}\right)$	$e\left(\frac{367}{966}\right)$	$e\left(\frac{37}{276}\right)$	$e\left(\frac{1823}{1932}\right)$	$e\left(\frac{1835}{1932}\right)$	$e\left(\frac{132}{161}\right)$	$e\left(\frac{67}{644}\right)$
$\chi_{40310}(1181,\cdot)$	$-1$	$1$	$e\left(\frac{461}{1932}\right)$	$e\left(\frac{446}{483}\right)$	$e\left(\frac{461}{966}\right)$	$e\left(\frac{1213}{1932}\right)$	$e\left(\frac{449}{966}\right)$	$e\left(\frac{131}{276}\right)$	$e\left(\frac{1009}{1932}\right)$	$e\left(\frac{313}{1932}\right)$	$e\left(\frac{72}{161}\right)$	$e\left(\frac{461}{644}\right)$
$\chi_{40310}(1371,\cdot)$	$-1$	$1$	$e\left(\frac{307}{1932}\right)$	$e\left(\frac{187}{483}\right)$	$e\left(\frac{307}{966}\right)$	$e\left(\frac{527}{1932}\right)$	$e\left(\frac{211}{966}\right)$	$e\left(\frac{13}{276}\right)$	$e\left(\frac{827}{1932}\right)$	$e\left(\frac{1055}{1932}\right)$	$e\left(\frac{93}{161}\right)$	$e\left(\frac{307}{644}\right)$
$\chi_{40310}(1431,\cdot)$	$-1$	$1$	$e\left(\frac{1187}{1932}\right)$	$e\left(\frac{218}{483}\right)$	$e\left(\frac{221}{966}\right)$	$e\left(\frac{307}{1932}\right)$	$e\left(\frac{605}{966}\right)$	$e\left(\frac{17}{276}\right)$	$e\left(\frac{1039}{1932}\right)$	$e\left(\frac{127}{1932}\right)$	$e\left(\frac{111}{161}\right)$	$e\left(\frac{543}{644}\right)$
$\chi_{40310}(1461,\cdot)$	$-1$	$1$	$e\left(\frac{673}{1932}\right)$	$e\left(\frac{100}{483}\right)$	$e\left(\frac{673}{966}\right)$	$e\left(\frac{677}{1932}\right)$	$e\left(\frac{601}{966}\right)$	$e\left(\frac{211}{276}\right)$	$e\left(\frac{1385}{1932}\right)$	$e\left(\frac{1073}{1932}\right)$	$e\left(\frac{110}{161}\right)$	$e\left(\frac{29}{644}\right)$
$\chi_{40310}(1471,\cdot)$	$-1$	$1$	$e\left(\frac{1469}{1932}\right)$	$e\left(\frac{341}{483}\right)$	$e\left(\frac{503}{966}\right)$	$e\left(\frac{961}{1932}\right)$	$e\left(\frac{953}{966}\right)$	$e\left(\frac{251}{276}\right)$	$e\left(\frac{1849}{1932}\right)$	$e\left(\frac{901}{1932}\right)$	$e\left(\frac{37}{161}\right)$	$e\left(\frac{181}{644}\right)$
$\chi_{40310}(1511,\cdot)$	$-1$	$1$	$e\left(\frac{101}{1932}\right)$	$e\left(\frac{104}{483}\right)$	$e\left(\frac{101}{966}\right)$	$e\left(\frac{337}{1932}\right)$	$e\left(\frac{683}{966}\right)$	$e\left(\frac{167}{276}\right)$	$e\left(\frac{1537}{1932}\right)$	$e\left(\frac{517}{1932}\right)$	$e\left(\frac{50}{161}\right)$	$e\left(\frac{101}{644}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{1932}\right)\)	\(e\left(\frac{121}{483}\right)\)	\(e\left(\frac{85}{966}\right)\)	\(e\left(\frac{341}{1932}\right)\)	\(e\left(\frac{307}{966}\right)\)	\(e\left(\frac{187}{276}\right)\)	\(e\left(\frac{1217}{1932}\right)\)	\(e\left(\frac{569}{1932}\right)\)	\(e\left(\frac{117}{161}\right)\)	\(e\left(\frac{85}{644}\right)\)
\(\chi_{40310}(31,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1577}{1932}\right)\)	\(e\left(\frac{347}{483}\right)\)	\(e\left(\frac{611}{966}\right)\)	\(e\left(\frac{1417}{1932}\right)\)	\(e\left(\frac{593}{966}\right)\)	\(e\left(\frac{47}{276}\right)\)	\(e\left(\frac{145}{1932}\right)\)	\(e\left(\frac{1033}{1932}\right)\)	\(e\left(\frac{108}{161}\right)\)	\(e\left(\frac{289}{644}\right)\)
\(\chi_{40310}(391,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{1932}\right)\)	\(e\left(\frac{59}{483}\right)\)	\(e\left(\frac{257}{966}\right)\)	\(e\left(\frac{781}{1932}\right)\)	\(e\left(\frac{485}{966}\right)\)	\(e\left(\frac{179}{276}\right)\)	\(e\left(\frac{793}{1932}\right)\)	\(e\left(\frac{493}{1932}\right)\)	\(e\left(\frac{81}{161}\right)\)	\(e\left(\frac{257}{644}\right)\)
\(\chi_{40310}(421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{803}{1932}\right)\)	\(e\left(\frac{143}{483}\right)\)	\(e\left(\frac{803}{966}\right)\)	\(e\left(\frac{403}{1932}\right)\)	\(e\left(\frac{275}{966}\right)\)	\(e\left(\frac{221}{276}\right)\)	\(e\left(\frac{1087}{1932}\right)\)	\(e\left(\frac{1375}{1932}\right)\)	\(e\left(\frac{109}{161}\right)\)	\(e\left(\frac{159}{644}\right)\)
\(\chi_{40310}(541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1621}{1932}\right)\)	\(e\left(\frac{421}{483}\right)\)	\(e\left(\frac{655}{966}\right)\)	\(e\left(\frac{1889}{1932}\right)\)	\(e\left(\frac{661}{966}\right)\)	\(e\left(\frac{199}{276}\right)\)	\(e\left(\frac{1025}{1932}\right)\)	\(e\left(\frac{1373}{1932}\right)\)	\(e\left(\frac{125}{161}\right)\)	\(e\left(\frac{333}{644}\right)\)
\(\chi_{40310}(561,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1271}{1932}\right)\)	\(e\left(\frac{8}{483}\right)\)	\(e\left(\frac{305}{966}\right)\)	\(e\left(\frac{1735}{1932}\right)\)	\(e\left(\frac{647}{966}\right)\)	\(e\left(\frac{257}{276}\right)\)	\(e\left(\frac{787}{1932}\right)\)	\(e\left(\frac{1303}{1932}\right)\)	\(e\left(\frac{41}{161}\right)\)	\(e\left(\frac{627}{644}\right)\)
\(\chi_{40310}(591,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1681}{1932}\right)\)	\(e\left(\frac{478}{483}\right)\)	\(e\left(\frac{715}{966}\right)\)	\(e\left(\frac{425}{1932}\right)\)	\(e\left(\frac{139}{966}\right)\)	\(e\left(\frac{55}{276}\right)\)	\(e\left(\frac{293}{1932}\right)\)	\(e\left(\frac{1661}{1932}\right)\)	\(e\left(\frac{75}{161}\right)\)	\(e\left(\frac{393}{644}\right)\)
\(\chi_{40310}(711,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{1932}\right)\)	\(e\left(\frac{10}{483}\right)\)	\(e\left(\frac{19}{966}\right)\)	\(e\left(\frac{599}{1932}\right)\)	\(e\left(\frac{205}{966}\right)\)	\(e\left(\frac{97}{276}\right)\)	\(e\left(\frac{863}{1932}\right)\)	\(e\left(\frac{59}{1932}\right)\)	\(e\left(\frac{11}{161}\right)\)	\(e\left(\frac{19}{644}\right)\)
\(\chi_{40310}(781,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{275}{1932}\right)\)	\(e\left(\frac{221}{483}\right)\)	\(e\left(\frac{275}{966}\right)\)	\(e\left(\frac{535}{1932}\right)\)	\(e\left(\frac{425}{966}\right)\)	\(e\left(\frac{53}{276}\right)\)	\(e\left(\frac{187}{1932}\right)\)	\(e\left(\frac{1159}{1932}\right)\)	\(e\left(\frac{66}{161}\right)\)	\(e\left(\frac{275}{644}\right)\)
\(\chi_{40310}(831,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{557}{1932}\right)\)	\(e\left(\frac{344}{483}\right)\)	\(e\left(\frac{557}{966}\right)\)	\(e\left(\frac{1189}{1932}\right)\)	\(e\left(\frac{773}{966}\right)\)	\(e\left(\frac{11}{276}\right)\)	\(e\left(\frac{997}{1932}\right)\)	\(e\left(\frac{1}{1932}\right)\)	\(e\left(\frac{153}{161}\right)\)	\(e\left(\frac{557}{644}\right)\)
\(\chi_{40310}(881,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1121}{1932}\right)\)	\(e\left(\frac{107}{483}\right)\)	\(e\left(\frac{155}{966}\right)\)	\(e\left(\frac{565}{1932}\right)\)	\(e\left(\frac{503}{966}\right)\)	\(e\left(\frac{203}{276}\right)\)	\(e\left(\frac{685}{1932}\right)\)	\(e\left(\frac{1549}{1932}\right)\)	\(e\left(\frac{5}{161}\right)\)	\(e\left(\frac{477}{644}\right)\)
\(\chi_{40310}(901,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1801}{1932}\right)\)	\(e\left(\frac{109}{483}\right)\)	\(e\left(\frac{835}{966}\right)\)	\(e\left(\frac{1361}{1932}\right)\)	\(e\left(\frac{61}{966}\right)\)	\(e\left(\frac{43}{276}\right)\)	\(e\left(\frac{761}{1932}\right)\)	\(e\left(\frac{305}{1932}\right)\)	\(e\left(\frac{136}{161}\right)\)	\(e\left(\frac{513}{644}\right)\)
\(\chi_{40310}(971,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{1932}\right)\)	\(e\left(\frac{451}{483}\right)\)	\(e\left(\frac{229}{966}\right)\)	\(e\left(\frac{305}{1932}\right)\)	\(e\left(\frac{793}{966}\right)\)	\(e\left(\frac{7}{276}\right)\)	\(e\left(\frac{233}{1932}\right)\)	\(e\left(\frac{101}{1932}\right)\)	\(e\left(\frac{158}{161}\right)\)	\(e\left(\frac{229}{644}\right)\)
\(\chi_{40310}(1001,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{523}{1932}\right)\)	\(e\left(\frac{199}{483}\right)\)	\(e\left(\frac{523}{966}\right)\)	\(e\left(\frac{1439}{1932}\right)\)	\(e\left(\frac{457}{966}\right)\)	\(e\left(\frac{157}{276}\right)\)	\(e\left(\frac{1283}{1932}\right)\)	\(e\left(\frac{1319}{1932}\right)\)	\(e\left(\frac{74}{161}\right)\)	\(e\left(\frac{523}{644}\right)\)
\(\chi_{40310}(1091,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{967}{1932}\right)\)	\(e\left(\frac{331}{483}\right)\)	\(e\left(\frac{1}{966}\right)\)	\(e\left(\frac{1811}{1932}\right)\)	\(e\left(\frac{265}{966}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{503}{1932}\right)\)	\(e\left(\frac{359}{1932}\right)\)	\(e\left(\frac{26}{161}\right)\)	\(e\left(\frac{323}{644}\right)\)
\(\chi_{40310}(1121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1873}{1932}\right)\)	\(e\left(\frac{274}{483}\right)\)	\(e\left(\frac{907}{966}\right)\)	\(e\left(\frac{377}{1932}\right)\)	\(e\left(\frac{787}{966}\right)\)	\(e\left(\frac{91}{276}\right)\)	\(e\left(\frac{269}{1932}\right)\)	\(e\left(\frac{1037}{1932}\right)\)	\(e\left(\frac{76}{161}\right)\)	\(e\left(\frac{585}{644}\right)\)
\(\chi_{40310}(1141,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{1932}\right)\)	\(e\left(\frac{442}{483}\right)\)	\(e\left(\frac{67}{966}\right)\)	\(e\left(\frac{587}{1932}\right)\)	\(e\left(\frac{367}{966}\right)\)	\(e\left(\frac{37}{276}\right)\)	\(e\left(\frac{1823}{1932}\right)\)	\(e\left(\frac{1835}{1932}\right)\)	\(e\left(\frac{132}{161}\right)\)	\(e\left(\frac{67}{644}\right)\)
\(\chi_{40310}(1181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{461}{1932}\right)\)	\(e\left(\frac{446}{483}\right)\)	\(e\left(\frac{461}{966}\right)\)	\(e\left(\frac{1213}{1932}\right)\)	\(e\left(\frac{449}{966}\right)\)	\(e\left(\frac{131}{276}\right)\)	\(e\left(\frac{1009}{1932}\right)\)	\(e\left(\frac{313}{1932}\right)\)	\(e\left(\frac{72}{161}\right)\)	\(e\left(\frac{461}{644}\right)\)
\(\chi_{40310}(1371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{1932}\right)\)	\(e\left(\frac{187}{483}\right)\)	\(e\left(\frac{307}{966}\right)\)	\(e\left(\frac{527}{1932}\right)\)	\(e\left(\frac{211}{966}\right)\)	\(e\left(\frac{13}{276}\right)\)	\(e\left(\frac{827}{1932}\right)\)	\(e\left(\frac{1055}{1932}\right)\)	\(e\left(\frac{93}{161}\right)\)	\(e\left(\frac{307}{644}\right)\)
\(\chi_{40310}(1431,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1187}{1932}\right)\)	\(e\left(\frac{218}{483}\right)\)	\(e\left(\frac{221}{966}\right)\)	\(e\left(\frac{307}{1932}\right)\)	\(e\left(\frac{605}{966}\right)\)	\(e\left(\frac{17}{276}\right)\)	\(e\left(\frac{1039}{1932}\right)\)	\(e\left(\frac{127}{1932}\right)\)	\(e\left(\frac{111}{161}\right)\)	\(e\left(\frac{543}{644}\right)\)
\(\chi_{40310}(1461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{673}{1932}\right)\)	\(e\left(\frac{100}{483}\right)\)	\(e\left(\frac{673}{966}\right)\)	\(e\left(\frac{677}{1932}\right)\)	\(e\left(\frac{601}{966}\right)\)	\(e\left(\frac{211}{276}\right)\)	\(e\left(\frac{1385}{1932}\right)\)	\(e\left(\frac{1073}{1932}\right)\)	\(e\left(\frac{110}{161}\right)\)	\(e\left(\frac{29}{644}\right)\)
\(\chi_{40310}(1471,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1469}{1932}\right)\)	\(e\left(\frac{341}{483}\right)\)	\(e\left(\frac{503}{966}\right)\)	\(e\left(\frac{961}{1932}\right)\)	\(e\left(\frac{953}{966}\right)\)	\(e\left(\frac{251}{276}\right)\)	\(e\left(\frac{1849}{1932}\right)\)	\(e\left(\frac{901}{1932}\right)\)	\(e\left(\frac{37}{161}\right)\)	\(e\left(\frac{181}{644}\right)\)
\(\chi_{40310}(1511,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{1932}\right)\)	\(e\left(\frac{104}{483}\right)\)	\(e\left(\frac{101}{966}\right)\)	\(e\left(\frac{337}{1932}\right)\)	\(e\left(\frac{683}{966}\right)\)	\(e\left(\frac{167}{276}\right)\)	\(e\left(\frac{1537}{1932}\right)\)	\(e\left(\frac{517}{1932}\right)\)	\(e\left(\frac{50}{161}\right)\)	\(e\left(\frac{101}{644}\right)\)

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First 23 of 528 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.fv
Modulus	$40310$
Conductor	$4031$
Order	$1932$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(40310\)
Conductor:	\(4031\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1932\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4031.bv	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)