LMFDB - Dirichlet character orbit 254144.ot

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(254144, base_ring=CyclotomicField(760)) M = H._module chi = DirichletCharacter(H, M([380,95,684,280])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(39,254144)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$254144$
Conductor:	$127072$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$760$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 127072.mp	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{760})$
Fixed field:	Number field defined by a degree 760 polynomial (not computed)

First 31 of 288 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{254144}(39,\cdot)$	$1$	$1$	$e\left(\frac{217}{760}\right)$	$e\left(\frac{151}{760}\right)$	$e\left(\frac{119}{380}\right)$	$e\left(\frac{217}{380}\right)$	$e\left(\frac{749}{760}\right)$	$e\left(\frac{46}{95}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{91}{152}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{151}{380}\right)$
$\chi_{254144}(343,\cdot)$	$1$	$1$	$e\left(\frac{623}{760}\right)$	$e\left(\frac{409}{760}\right)$	$e\left(\frac{121}{380}\right)$	$e\left(\frac{243}{380}\right)$	$e\left(\frac{91}{760}\right)$	$e\left(\frac{34}{95}\right)$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{21}{152}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{29}{380}\right)$
$\chi_{254144}(1559,\cdot)$	$1$	$1$	$e\left(\frac{119}{760}\right)$	$e\left(\frac{377}{760}\right)$	$e\left(\frac{53}{380}\right)$	$e\left(\frac{119}{380}\right)$	$e\left(\frac{43}{760}\right)$	$e\left(\frac{62}{95}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{45}{152}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{377}{380}\right)$
$\chi_{254144}(2471,\cdot)$	$1$	$1$	$e\left(\frac{121}{760}\right)$	$e\left(\frac{543}{760}\right)$	$e\left(\frac{287}{380}\right)$	$e\left(\frac{121}{380}\right)$	$e\left(\frac{197}{760}\right)$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{86}{95}\right)$	$e\left(\frac{139}{152}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{163}{380}\right)$
$\chi_{254144}(3383,\cdot)$	$1$	$1$	$e\left(\frac{427}{760}\right)$	$e\left(\frac{101}{760}\right)$	$e\left(\frac{369}{380}\right)$	$e\left(\frac{47}{380}\right)$	$e\left(\frac{199}{760}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{2}{95}\right)$	$e\left(\frac{81}{152}\right)$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{101}{380}\right)$
$\chi_{254144}(3687,\cdot)$	$1$	$1$	$e\left(\frac{73}{760}\right)$	$e\left(\frac{359}{760}\right)$	$e\left(\frac{371}{380}\right)$	$e\left(\frac{73}{380}\right)$	$e\left(\frac{301}{760}\right)$	$e\left(\frac{54}{95}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{11}{152}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{359}{380}\right)$
$\chi_{254144}(4903,\cdot)$	$1$	$1$	$e\left(\frac{329}{760}\right)$	$e\left(\frac{327}{760}\right)$	$e\left(\frac{303}{380}\right)$	$e\left(\frac{329}{380}\right)$	$e\left(\frac{253}{760}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{14}{95}\right)$	$e\left(\frac{35}{152}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{327}{380}\right)$
$\chi_{254144}(5815,\cdot)$	$1$	$1$	$e\left(\frac{331}{760}\right)$	$e\left(\frac{493}{760}\right)$	$e\left(\frac{157}{380}\right)$	$e\left(\frac{331}{380}\right)$	$e\left(\frac{407}{760}\right)$	$e\left(\frac{8}{95}\right)$	$e\left(\frac{6}{95}\right)$	$e\left(\frac{129}{152}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{113}{380}\right)$
$\chi_{254144}(6727,\cdot)$	$1$	$1$	$e\left(\frac{637}{760}\right)$	$e\left(\frac{51}{760}\right)$	$e\left(\frac{239}{380}\right)$	$e\left(\frac{257}{380}\right)$	$e\left(\frac{409}{760}\right)$	$e\left(\frac{86}{95}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{71}{152}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{51}{380}\right)$
$\chi_{254144}(7031,\cdot)$	$1$	$1$	$e\left(\frac{283}{760}\right)$	$e\left(\frac{309}{760}\right)$	$e\left(\frac{241}{380}\right)$	$e\left(\frac{283}{380}\right)$	$e\left(\frac{511}{760}\right)$	$e\left(\frac{74}{95}\right)$	$e\left(\frac{8}{95}\right)$	$e\left(\frac{1}{152}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{309}{380}\right)$
$\chi_{254144}(8247,\cdot)$	$1$	$1$	$e\left(\frac{539}{760}\right)$	$e\left(\frac{277}{760}\right)$	$e\left(\frac{173}{380}\right)$	$e\left(\frac{159}{380}\right)$	$e\left(\frac{463}{760}\right)$	$e\left(\frac{7}{95}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{25}{152}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{277}{380}\right)$
$\chi_{254144}(9159,\cdot)$	$1$	$1$	$e\left(\frac{541}{760}\right)$	$e\left(\frac{443}{760}\right)$	$e\left(\frac{27}{380}\right)$	$e\left(\frac{161}{380}\right)$	$e\left(\frac{617}{760}\right)$	$e\left(\frac{28}{95}\right)$	$e\left(\frac{21}{95}\right)$	$e\left(\frac{119}{152}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{63}{380}\right)$
$\chi_{254144}(10071,\cdot)$	$1$	$1$	$e\left(\frac{87}{760}\right)$	$e\left(\frac{1}{760}\right)$	$e\left(\frac{109}{380}\right)$	$e\left(\frac{87}{380}\right)$	$e\left(\frac{619}{760}\right)$	$e\left(\frac{11}{95}\right)$	$e\left(\frac{32}{95}\right)$	$e\left(\frac{61}{152}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{1}{380}\right)$
$\chi_{254144}(10375,\cdot)$	$1$	$1$	$e\left(\frac{493}{760}\right)$	$e\left(\frac{259}{760}\right)$	$e\left(\frac{111}{380}\right)$	$e\left(\frac{113}{380}\right)$	$e\left(\frac{721}{760}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{23}{95}\right)$	$e\left(\frac{143}{152}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{259}{380}\right)$
$\chi_{254144}(11591,\cdot)$	$1$	$1$	$e\left(\frac{749}{760}\right)$	$e\left(\frac{227}{760}\right)$	$e\left(\frac{43}{380}\right)$	$e\left(\frac{369}{380}\right)$	$e\left(\frac{673}{760}\right)$	$e\left(\frac{27}{95}\right)$	$e\left(\frac{44}{95}\right)$	$e\left(\frac{15}{152}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{227}{380}\right)$
$\chi_{254144}(12503,\cdot)$	$1$	$1$	$e\left(\frac{751}{760}\right)$	$e\left(\frac{393}{760}\right)$	$e\left(\frac{277}{380}\right)$	$e\left(\frac{371}{380}\right)$	$e\left(\frac{67}{760}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{109}{152}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{13}{380}\right)$
$\chi_{254144}(13415,\cdot)$	$1$	$1$	$e\left(\frac{297}{760}\right)$	$e\left(\frac{711}{760}\right)$	$e\left(\frac{359}{380}\right)$	$e\left(\frac{297}{380}\right)$	$e\left(\frac{69}{760}\right)$	$e\left(\frac{31}{95}\right)$	$e\left(\frac{47}{95}\right)$	$e\left(\frac{51}{152}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{331}{380}\right)$
$\chi_{254144}(14935,\cdot)$	$1$	$1$	$e\left(\frac{199}{760}\right)$	$e\left(\frac{177}{760}\right)$	$e\left(\frac{293}{380}\right)$	$e\left(\frac{199}{380}\right)$	$e\left(\frac{123}{760}\right)$	$e\left(\frac{47}{95}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{5}{152}\right)$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{177}{380}\right)$
$\chi_{254144}(15847,\cdot)$	$1$	$1$	$e\left(\frac{201}{760}\right)$	$e\left(\frac{343}{760}\right)$	$e\left(\frac{147}{380}\right)$	$e\left(\frac{201}{380}\right)$	$e\left(\frac{277}{760}\right)$	$e\left(\frac{68}{95}\right)$	$e\left(\frac{51}{95}\right)$	$e\left(\frac{99}{152}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{343}{380}\right)$
$\chi_{254144}(16759,\cdot)$	$1$	$1$	$e\left(\frac{507}{760}\right)$	$e\left(\frac{661}{760}\right)$	$e\left(\frac{229}{380}\right)$	$e\left(\frac{127}{380}\right)$	$e\left(\frac{279}{760}\right)$	$e\left(\frac{51}{95}\right)$	$e\left(\frac{62}{95}\right)$	$e\left(\frac{41}{152}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{281}{380}\right)$
$\chi_{254144}(17063,\cdot)$	$1$	$1$	$e\left(\frac{153}{760}\right)$	$e\left(\frac{159}{760}\right)$	$e\left(\frac{231}{380}\right)$	$e\left(\frac{153}{380}\right)$	$e\left(\frac{381}{760}\right)$	$e\left(\frac{39}{95}\right)$	$e\left(\frac{53}{95}\right)$	$e\left(\frac{123}{152}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{159}{380}\right)$
$\chi_{254144}(18279,\cdot)$	$1$	$1$	$e\left(\frac{409}{760}\right)$	$e\left(\frac{127}{760}\right)$	$e\left(\frac{163}{380}\right)$	$e\left(\frac{29}{380}\right)$	$e\left(\frac{333}{760}\right)$	$e\left(\frac{67}{95}\right)$	$e\left(\frac{74}{95}\right)$	$e\left(\frac{147}{152}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{127}{380}\right)$
$\chi_{254144}(19191,\cdot)$	$1$	$1$	$e\left(\frac{411}{760}\right)$	$e\left(\frac{293}{760}\right)$	$e\left(\frac{17}{380}\right)$	$e\left(\frac{31}{380}\right)$	$e\left(\frac{487}{760}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{89}{152}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{293}{380}\right)$
$\chi_{254144}(20103,\cdot)$	$1$	$1$	$e\left(\frac{717}{760}\right)$	$e\left(\frac{611}{760}\right)$	$e\left(\frac{99}{380}\right)$	$e\left(\frac{337}{380}\right)$	$e\left(\frac{489}{760}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{77}{95}\right)$	$e\left(\frac{31}{152}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{231}{380}\right)$
$\chi_{254144}(20407,\cdot)$	$1$	$1$	$e\left(\frac{363}{760}\right)$	$e\left(\frac{109}{760}\right)$	$e\left(\frac{101}{380}\right)$	$e\left(\frac{363}{380}\right)$	$e\left(\frac{591}{760}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{68}{95}\right)$	$e\left(\frac{113}{152}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{109}{380}\right)$
$\chi_{254144}(21623,\cdot)$	$1$	$1$	$e\left(\frac{619}{760}\right)$	$e\left(\frac{77}{760}\right)$	$e\left(\frac{33}{380}\right)$	$e\left(\frac{239}{380}\right)$	$e\left(\frac{543}{760}\right)$	$e\left(\frac{87}{95}\right)$	$e\left(\frac{89}{95}\right)$	$e\left(\frac{137}{152}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{77}{380}\right)$
$\chi_{254144}(22535,\cdot)$	$1$	$1$	$e\left(\frac{621}{760}\right)$	$e\left(\frac{243}{760}\right)$	$e\left(\frac{267}{380}\right)$	$e\left(\frac{241}{380}\right)$	$e\left(\frac{697}{760}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{81}{95}\right)$	$e\left(\frac{79}{152}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{243}{380}\right)$
$\chi_{254144}(23447,\cdot)$	$1$	$1$	$e\left(\frac{167}{760}\right)$	$e\left(\frac{561}{760}\right)$	$e\left(\frac{349}{380}\right)$	$e\left(\frac{167}{380}\right)$	$e\left(\frac{699}{760}\right)$	$e\left(\frac{91}{95}\right)$	$e\left(\frac{92}{95}\right)$	$e\left(\frac{21}{152}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{181}{380}\right)$
$\chi_{254144}(23751,\cdot)$	$1$	$1$	$e\left(\frac{573}{760}\right)$	$e\left(\frac{59}{760}\right)$	$e\left(\frac{351}{380}\right)$	$e\left(\frac{193}{380}\right)$	$e\left(\frac{41}{760}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{103}{152}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{59}{380}\right)$
$\chi_{254144}(24967,\cdot)$	$1$	$1$	$e\left(\frac{69}{760}\right)$	$e\left(\frac{27}{760}\right)$	$e\left(\frac{283}{380}\right)$	$e\left(\frac{69}{380}\right)$	$e\left(\frac{753}{760}\right)$	$e\left(\frac{12}{95}\right)$	$e\left(\frac{9}{95}\right)$	$e\left(\frac{127}{152}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{27}{380}\right)$
$\chi_{254144}(25879,\cdot)$	$1$	$1$	$e\left(\frac{71}{760}\right)$	$e\left(\frac{193}{760}\right)$	$e\left(\frac{137}{380}\right)$	$e\left(\frac{71}{380}\right)$	$e\left(\frac{147}{760}\right)$	$e\left(\frac{33}{95}\right)$	$e\left(\frac{1}{95}\right)$	$e\left(\frac{69}{152}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{193}{380}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{254144}(39,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{760}\right)\)	\(e\left(\frac{151}{760}\right)\)	\(e\left(\frac{119}{380}\right)\)	\(e\left(\frac{217}{380}\right)\)	\(e\left(\frac{749}{760}\right)\)	\(e\left(\frac{46}{95}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{91}{152}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{151}{380}\right)\)
\(\chi_{254144}(343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{623}{760}\right)\)	\(e\left(\frac{409}{760}\right)\)	\(e\left(\frac{121}{380}\right)\)	\(e\left(\frac{243}{380}\right)\)	\(e\left(\frac{91}{760}\right)\)	\(e\left(\frac{34}{95}\right)\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{21}{152}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{29}{380}\right)\)
\(\chi_{254144}(1559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{760}\right)\)	\(e\left(\frac{377}{760}\right)\)	\(e\left(\frac{53}{380}\right)\)	\(e\left(\frac{119}{380}\right)\)	\(e\left(\frac{43}{760}\right)\)	\(e\left(\frac{62}{95}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{45}{152}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{377}{380}\right)\)
\(\chi_{254144}(2471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{760}\right)\)	\(e\left(\frac{543}{760}\right)\)	\(e\left(\frac{287}{380}\right)\)	\(e\left(\frac{121}{380}\right)\)	\(e\left(\frac{197}{760}\right)\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{86}{95}\right)\)	\(e\left(\frac{139}{152}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{163}{380}\right)\)
\(\chi_{254144}(3383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{427}{760}\right)\)	\(e\left(\frac{101}{760}\right)\)	\(e\left(\frac{369}{380}\right)\)	\(e\left(\frac{47}{380}\right)\)	\(e\left(\frac{199}{760}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{2}{95}\right)\)	\(e\left(\frac{81}{152}\right)\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{101}{380}\right)\)
\(\chi_{254144}(3687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{760}\right)\)	\(e\left(\frac{359}{760}\right)\)	\(e\left(\frac{371}{380}\right)\)	\(e\left(\frac{73}{380}\right)\)	\(e\left(\frac{301}{760}\right)\)	\(e\left(\frac{54}{95}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{11}{152}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{359}{380}\right)\)
\(\chi_{254144}(4903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{760}\right)\)	\(e\left(\frac{327}{760}\right)\)	\(e\left(\frac{303}{380}\right)\)	\(e\left(\frac{329}{380}\right)\)	\(e\left(\frac{253}{760}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{14}{95}\right)\)	\(e\left(\frac{35}{152}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{327}{380}\right)\)
\(\chi_{254144}(5815,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{760}\right)\)	\(e\left(\frac{493}{760}\right)\)	\(e\left(\frac{157}{380}\right)\)	\(e\left(\frac{331}{380}\right)\)	\(e\left(\frac{407}{760}\right)\)	\(e\left(\frac{8}{95}\right)\)	\(e\left(\frac{6}{95}\right)\)	\(e\left(\frac{129}{152}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{113}{380}\right)\)
\(\chi_{254144}(6727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{637}{760}\right)\)	\(e\left(\frac{51}{760}\right)\)	\(e\left(\frac{239}{380}\right)\)	\(e\left(\frac{257}{380}\right)\)	\(e\left(\frac{409}{760}\right)\)	\(e\left(\frac{86}{95}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{71}{152}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{51}{380}\right)\)
\(\chi_{254144}(7031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{760}\right)\)	\(e\left(\frac{309}{760}\right)\)	\(e\left(\frac{241}{380}\right)\)	\(e\left(\frac{283}{380}\right)\)	\(e\left(\frac{511}{760}\right)\)	\(e\left(\frac{74}{95}\right)\)	\(e\left(\frac{8}{95}\right)\)	\(e\left(\frac{1}{152}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{309}{380}\right)\)
\(\chi_{254144}(8247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{539}{760}\right)\)	\(e\left(\frac{277}{760}\right)\)	\(e\left(\frac{173}{380}\right)\)	\(e\left(\frac{159}{380}\right)\)	\(e\left(\frac{463}{760}\right)\)	\(e\left(\frac{7}{95}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{25}{152}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{277}{380}\right)\)
\(\chi_{254144}(9159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{541}{760}\right)\)	\(e\left(\frac{443}{760}\right)\)	\(e\left(\frac{27}{380}\right)\)	\(e\left(\frac{161}{380}\right)\)	\(e\left(\frac{617}{760}\right)\)	\(e\left(\frac{28}{95}\right)\)	\(e\left(\frac{21}{95}\right)\)	\(e\left(\frac{119}{152}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{63}{380}\right)\)
\(\chi_{254144}(10071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{760}\right)\)	\(e\left(\frac{1}{760}\right)\)	\(e\left(\frac{109}{380}\right)\)	\(e\left(\frac{87}{380}\right)\)	\(e\left(\frac{619}{760}\right)\)	\(e\left(\frac{11}{95}\right)\)	\(e\left(\frac{32}{95}\right)\)	\(e\left(\frac{61}{152}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{1}{380}\right)\)
\(\chi_{254144}(10375,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{493}{760}\right)\)	\(e\left(\frac{259}{760}\right)\)	\(e\left(\frac{111}{380}\right)\)	\(e\left(\frac{113}{380}\right)\)	\(e\left(\frac{721}{760}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{23}{95}\right)\)	\(e\left(\frac{143}{152}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{259}{380}\right)\)
\(\chi_{254144}(11591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{749}{760}\right)\)	\(e\left(\frac{227}{760}\right)\)	\(e\left(\frac{43}{380}\right)\)	\(e\left(\frac{369}{380}\right)\)	\(e\left(\frac{673}{760}\right)\)	\(e\left(\frac{27}{95}\right)\)	\(e\left(\frac{44}{95}\right)\)	\(e\left(\frac{15}{152}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{227}{380}\right)\)
\(\chi_{254144}(12503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{751}{760}\right)\)	\(e\left(\frac{393}{760}\right)\)	\(e\left(\frac{277}{380}\right)\)	\(e\left(\frac{371}{380}\right)\)	\(e\left(\frac{67}{760}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{109}{152}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{13}{380}\right)\)
\(\chi_{254144}(13415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{297}{760}\right)\)	\(e\left(\frac{711}{760}\right)\)	\(e\left(\frac{359}{380}\right)\)	\(e\left(\frac{297}{380}\right)\)	\(e\left(\frac{69}{760}\right)\)	\(e\left(\frac{31}{95}\right)\)	\(e\left(\frac{47}{95}\right)\)	\(e\left(\frac{51}{152}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{331}{380}\right)\)
\(\chi_{254144}(14935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{760}\right)\)	\(e\left(\frac{177}{760}\right)\)	\(e\left(\frac{293}{380}\right)\)	\(e\left(\frac{199}{380}\right)\)	\(e\left(\frac{123}{760}\right)\)	\(e\left(\frac{47}{95}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{5}{152}\right)\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{177}{380}\right)\)
\(\chi_{254144}(15847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{760}\right)\)	\(e\left(\frac{343}{760}\right)\)	\(e\left(\frac{147}{380}\right)\)	\(e\left(\frac{201}{380}\right)\)	\(e\left(\frac{277}{760}\right)\)	\(e\left(\frac{68}{95}\right)\)	\(e\left(\frac{51}{95}\right)\)	\(e\left(\frac{99}{152}\right)\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{343}{380}\right)\)
\(\chi_{254144}(16759,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{507}{760}\right)\)	\(e\left(\frac{661}{760}\right)\)	\(e\left(\frac{229}{380}\right)\)	\(e\left(\frac{127}{380}\right)\)	\(e\left(\frac{279}{760}\right)\)	\(e\left(\frac{51}{95}\right)\)	\(e\left(\frac{62}{95}\right)\)	\(e\left(\frac{41}{152}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{281}{380}\right)\)
\(\chi_{254144}(17063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{760}\right)\)	\(e\left(\frac{159}{760}\right)\)	\(e\left(\frac{231}{380}\right)\)	\(e\left(\frac{153}{380}\right)\)	\(e\left(\frac{381}{760}\right)\)	\(e\left(\frac{39}{95}\right)\)	\(e\left(\frac{53}{95}\right)\)	\(e\left(\frac{123}{152}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{159}{380}\right)\)
\(\chi_{254144}(18279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{409}{760}\right)\)	\(e\left(\frac{127}{760}\right)\)	\(e\left(\frac{163}{380}\right)\)	\(e\left(\frac{29}{380}\right)\)	\(e\left(\frac{333}{760}\right)\)	\(e\left(\frac{67}{95}\right)\)	\(e\left(\frac{74}{95}\right)\)	\(e\left(\frac{147}{152}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{127}{380}\right)\)
\(\chi_{254144}(19191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{411}{760}\right)\)	\(e\left(\frac{293}{760}\right)\)	\(e\left(\frac{17}{380}\right)\)	\(e\left(\frac{31}{380}\right)\)	\(e\left(\frac{487}{760}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{89}{152}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{293}{380}\right)\)
\(\chi_{254144}(20103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{717}{760}\right)\)	\(e\left(\frac{611}{760}\right)\)	\(e\left(\frac{99}{380}\right)\)	\(e\left(\frac{337}{380}\right)\)	\(e\left(\frac{489}{760}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{77}{95}\right)\)	\(e\left(\frac{31}{152}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{231}{380}\right)\)
\(\chi_{254144}(20407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{363}{760}\right)\)	\(e\left(\frac{109}{760}\right)\)	\(e\left(\frac{101}{380}\right)\)	\(e\left(\frac{363}{380}\right)\)	\(e\left(\frac{591}{760}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{68}{95}\right)\)	\(e\left(\frac{113}{152}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{109}{380}\right)\)
\(\chi_{254144}(21623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{619}{760}\right)\)	\(e\left(\frac{77}{760}\right)\)	\(e\left(\frac{33}{380}\right)\)	\(e\left(\frac{239}{380}\right)\)	\(e\left(\frac{543}{760}\right)\)	\(e\left(\frac{87}{95}\right)\)	\(e\left(\frac{89}{95}\right)\)	\(e\left(\frac{137}{152}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{77}{380}\right)\)
\(\chi_{254144}(22535,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{621}{760}\right)\)	\(e\left(\frac{243}{760}\right)\)	\(e\left(\frac{267}{380}\right)\)	\(e\left(\frac{241}{380}\right)\)	\(e\left(\frac{697}{760}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{81}{95}\right)\)	\(e\left(\frac{79}{152}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{243}{380}\right)\)
\(\chi_{254144}(23447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{760}\right)\)	\(e\left(\frac{561}{760}\right)\)	\(e\left(\frac{349}{380}\right)\)	\(e\left(\frac{167}{380}\right)\)	\(e\left(\frac{699}{760}\right)\)	\(e\left(\frac{91}{95}\right)\)	\(e\left(\frac{92}{95}\right)\)	\(e\left(\frac{21}{152}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{181}{380}\right)\)
\(\chi_{254144}(23751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{573}{760}\right)\)	\(e\left(\frac{59}{760}\right)\)	\(e\left(\frac{351}{380}\right)\)	\(e\left(\frac{193}{380}\right)\)	\(e\left(\frac{41}{760}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{103}{152}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{59}{380}\right)\)
\(\chi_{254144}(24967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{760}\right)\)	\(e\left(\frac{27}{760}\right)\)	\(e\left(\frac{283}{380}\right)\)	\(e\left(\frac{69}{380}\right)\)	\(e\left(\frac{753}{760}\right)\)	\(e\left(\frac{12}{95}\right)\)	\(e\left(\frac{9}{95}\right)\)	\(e\left(\frac{127}{152}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{27}{380}\right)\)
\(\chi_{254144}(25879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{760}\right)\)	\(e\left(\frac{193}{760}\right)\)	\(e\left(\frac{137}{380}\right)\)	\(e\left(\frac{71}{380}\right)\)	\(e\left(\frac{147}{760}\right)\)	\(e\left(\frac{33}{95}\right)\)	\(e\left(\frac{1}{95}\right)\)	\(e\left(\frac{69}{152}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{193}{380}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 288 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	254144.ot
Modulus	$254144$
Conductor	$127072$
Order	$760$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(254144\)
Conductor:	\(127072\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(760\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 127072.mp	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)