LMFDB - Dirichlet character orbit 5766.v

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5766, base_ring=CyclotomicField(310)) M = H._module chi = DirichletCharacter(H, M([0,266])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(97,5766)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5766$
Conductor:	$961$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$155$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 961.l	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:	$\Q(\zeta_{155})$
Fixed field:	Number field defined by a degree 155 polynomial (not computed)

First 31 of 120 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$35$
$\chi_{5766}(97,\cdot)$	$1$	$1$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{94}{155}\right)$	$e\left(\frac{24}{155}\right)$	$e\left(\frac{13}{155}\right)$	$e\left(\frac{126}{155}\right)$	$e\left(\frac{97}{155}\right)$	$e\left(\frac{101}{155}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{132}{155}\right)$	$e\left(\frac{24}{155}\right)$
$\chi_{5766}(109,\cdot)$	$1$	$1$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{138}{155}\right)$	$e\left(\frac{88}{155}\right)$	$e\left(\frac{151}{155}\right)$	$e\left(\frac{152}{155}\right)$	$e\left(\frac{149}{155}\right)$	$e\left(\frac{112}{155}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{19}{155}\right)$	$e\left(\frac{88}{155}\right)$
$\chi_{5766}(157,\cdot)$	$1$	$1$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{32}{155}\right)$	$e\left(\frac{117}{155}\right)$	$e\left(\frac{44}{155}\right)$	$e\left(\frac{33}{155}\right)$	$e\left(\frac{66}{155}\right)$	$e\left(\frac{8}{155}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{101}{155}\right)$	$e\left(\frac{117}{155}\right)$
$\chi_{5766}(163,\cdot)$	$1$	$1$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{26}{155}\right)$	$e\left(\frac{66}{155}\right)$	$e\left(\frac{152}{155}\right)$	$e\left(\frac{114}{155}\right)$	$e\left(\frac{73}{155}\right)$	$e\left(\frac{84}{155}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{66}{155}\right)$
$\chi_{5766}(283,\cdot)$	$1$	$1$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{89}{155}\right)$	$e\left(\frac{3}{155}\right)$	$e\left(\frac{41}{155}\right)$	$e\left(\frac{82}{155}\right)$	$e\left(\frac{71}{155}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{102}{155}\right)$	$e\left(\frac{89}{155}\right)$
$\chi_{5766}(295,\cdot)$	$1$	$1$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{108}{155}\right)$	$e\left(\frac{143}{155}\right)$	$e\left(\frac{71}{155}\right)$	$e\left(\frac{92}{155}\right)$	$e\left(\frac{29}{155}\right)$	$e\left(\frac{27}{155}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{89}{155}\right)$	$e\left(\frac{143}{155}\right)$
$\chi_{5766}(343,\cdot)$	$1$	$1$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{102}{155}\right)$	$e\left(\frac{92}{155}\right)$	$e\left(\frac{24}{155}\right)$	$e\left(\frac{18}{155}\right)$	$e\left(\frac{36}{155}\right)$	$e\left(\frac{103}{155}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{41}{155}\right)$	$e\left(\frac{92}{155}\right)$
$\chi_{5766}(349,\cdot)$	$1$	$1$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{121}{155}\right)$	$e\left(\frac{21}{155}\right)$	$e\left(\frac{147}{155}\right)$	$e\left(\frac{149}{155}\right)$	$e\left(\frac{143}{155}\right)$	$e\left(\frac{69}{155}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{38}{155}\right)$	$e\left(\frac{21}{155}\right)$
$\chi_{5766}(469,\cdot)$	$1$	$1$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{154}{155}\right)$	$e\left(\frac{148}{155}\right)$	$e\left(\frac{111}{155}\right)$	$e\left(\frac{67}{155}\right)$	$e\left(\frac{41}{155}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{72}{155}\right)$	$e\left(\frac{154}{155}\right)$
$\chi_{5766}(481,\cdot)$	$1$	$1$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{78}{155}\right)$	$e\left(\frac{43}{155}\right)$	$e\left(\frac{146}{155}\right)$	$e\left(\frac{32}{155}\right)$	$e\left(\frac{64}{155}\right)$	$e\left(\frac{97}{155}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{4}{155}\right)$	$e\left(\frac{43}{155}\right)$
$\chi_{5766}(529,\cdot)$	$1$	$1$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{17}{155}\right)$	$e\left(\frac{67}{155}\right)$	$e\left(\frac{4}{155}\right)$	$e\left(\frac{3}{155}\right)$	$e\left(\frac{6}{155}\right)$	$e\left(\frac{43}{155}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{136}{155}\right)$	$e\left(\frac{67}{155}\right)$
$\chi_{5766}(535,\cdot)$	$1$	$1$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{61}{155}\right)$	$e\left(\frac{131}{155}\right)$	$e\left(\frac{142}{155}\right)$	$e\left(\frac{29}{155}\right)$	$e\left(\frac{58}{155}\right)$	$e\left(\frac{54}{155}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{23}{155}\right)$	$e\left(\frac{131}{155}\right)$
$\chi_{5766}(655,\cdot)$	$1$	$1$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{44}{155}\right)$	$e\left(\frac{64}{155}\right)$	$e\left(\frac{138}{155}\right)$	$e\left(\frac{26}{155}\right)$	$e\left(\frac{52}{155}\right)$	$e\left(\frac{11}{155}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{42}{155}\right)$	$e\left(\frac{64}{155}\right)$
$\chi_{5766}(667,\cdot)$	$1$	$1$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{48}{155}\right)$	$e\left(\frac{98}{155}\right)$	$e\left(\frac{66}{155}\right)$	$e\left(\frac{127}{155}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{12}{155}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{74}{155}\right)$	$e\left(\frac{98}{155}\right)$
$\chi_{5766}(715,\cdot)$	$1$	$1$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{87}{155}\right)$	$e\left(\frac{42}{155}\right)$	$e\left(\frac{139}{155}\right)$	$e\left(\frac{143}{155}\right)$	$e\left(\frac{131}{155}\right)$	$e\left(\frac{138}{155}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{76}{155}\right)$	$e\left(\frac{42}{155}\right)$
$\chi_{5766}(721,\cdot)$	$1$	$1$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{1}{155}\right)$	$e\left(\frac{86}{155}\right)$	$e\left(\frac{137}{155}\right)$	$e\left(\frac{64}{155}\right)$	$e\left(\frac{128}{155}\right)$	$e\left(\frac{39}{155}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{8}{155}\right)$	$e\left(\frac{86}{155}\right)$
$\chi_{5766}(841,\cdot)$	$1$	$1$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{79}{155}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{128}{155}\right)$	$e\left(\frac{96}{155}\right)$	$e\left(\frac{37}{155}\right)$	$e\left(\frac{136}{155}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{12}{155}\right)$	$e\left(\frac{129}{155}\right)$
$\chi_{5766}(853,\cdot)$	$1$	$1$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{18}{155}\right)$	$e\left(\frac{153}{155}\right)$	$e\left(\frac{141}{155}\right)$	$e\left(\frac{67}{155}\right)$	$e\left(\frac{134}{155}\right)$	$e\left(\frac{82}{155}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{144}{155}\right)$	$e\left(\frac{153}{155}\right)$
$\chi_{5766}(901,\cdot)$	$1$	$1$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{2}{155}\right)$	$e\left(\frac{17}{155}\right)$	$e\left(\frac{119}{155}\right)$	$e\left(\frac{128}{155}\right)$	$e\left(\frac{101}{155}\right)$	$e\left(\frac{78}{155}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{16}{155}\right)$	$e\left(\frac{17}{155}\right)$
$\chi_{5766}(907,\cdot)$	$1$	$1$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{96}{155}\right)$	$e\left(\frac{41}{155}\right)$	$e\left(\frac{132}{155}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{43}{155}\right)$	$e\left(\frac{24}{155}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{148}{155}\right)$	$e\left(\frac{41}{155}\right)$
$\chi_{5766}(1027,\cdot)$	$1$	$1$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{114}{155}\right)$	$e\left(\frac{39}{155}\right)$	$e\left(\frac{118}{155}\right)$	$e\left(\frac{11}{155}\right)$	$e\left(\frac{22}{155}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{137}{155}\right)$	$e\left(\frac{39}{155}\right)$
$\chi_{5766}(1039,\cdot)$	$1$	$1$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{143}{155}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{61}{155}\right)$	$e\left(\frac{7}{155}\right)$	$e\left(\frac{14}{155}\right)$	$e\left(\frac{152}{155}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{53}{155}\right)$
$\chi_{5766}(1087,\cdot)$	$1$	$1$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{72}{155}\right)$	$e\left(\frac{147}{155}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{71}{155}\right)$	$e\left(\frac{18}{155}\right)$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{111}{155}\right)$	$e\left(\frac{147}{155}\right)$
$\chi_{5766}(1093,\cdot)$	$1$	$1$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{36}{155}\right)$	$e\left(\frac{151}{155}\right)$	$e\left(\frac{127}{155}\right)$	$e\left(\frac{134}{155}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{133}{155}\right)$	$e\left(\frac{151}{155}\right)$
$\chi_{5766}(1213,\cdot)$	$1$	$1$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{149}{155}\right)$	$e\left(\frac{104}{155}\right)$	$e\left(\frac{108}{155}\right)$	$e\left(\frac{81}{155}\right)$	$e\left(\frac{7}{155}\right)$	$e\left(\frac{76}{155}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{104}{155}\right)$
$\chi_{5766}(1225,\cdot)$	$1$	$1$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{108}{155}\right)$	$e\left(\frac{136}{155}\right)$	$e\left(\frac{102}{155}\right)$	$e\left(\frac{49}{155}\right)$	$e\left(\frac{67}{155}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{108}{155}\right)$
$\chi_{5766}(1273,\cdot)$	$1$	$1$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{142}{155}\right)$	$e\left(\frac{122}{155}\right)$	$e\left(\frac{79}{155}\right)$	$e\left(\frac{98}{155}\right)$	$e\left(\frac{41}{155}\right)$	$e\left(\frac{113}{155}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{51}{155}\right)$	$e\left(\frac{122}{155}\right)$
$\chi_{5766}(1279,\cdot)$	$1$	$1$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{131}{155}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{122}{155}\right)$	$e\left(\frac{14}{155}\right)$	$e\left(\frac{28}{155}\right)$	$e\left(\frac{149}{155}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{118}{155}\right)$	$e\left(\frac{106}{155}\right)$
$\chi_{5766}(1399,\cdot)$	$1$	$1$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{29}{155}\right)$	$e\left(\frac{14}{155}\right)$	$e\left(\frac{98}{155}\right)$	$e\left(\frac{151}{155}\right)$	$e\left(\frac{147}{155}\right)$	$e\left(\frac{46}{155}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{77}{155}\right)$	$e\left(\frac{14}{155}\right)$
$\chi_{5766}(1411,\cdot)$	$1$	$1$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{83}{155}\right)$	$e\left(\frac{8}{155}\right)$	$e\left(\frac{56}{155}\right)$	$e\left(\frac{42}{155}\right)$	$e\left(\frac{84}{155}\right)$	$e\left(\frac{137}{155}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{44}{155}\right)$	$e\left(\frac{8}{155}\right)$
$\chi_{5766}(1459,\cdot)$	$1$	$1$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{57}{155}\right)$	$e\left(\frac{97}{155}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{83}{155}\right)$	$e\left(\frac{11}{155}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{146}{155}\right)$	$e\left(\frac{97}{155}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(35\)
\(\chi_{5766}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{94}{155}\right)\)	\(e\left(\frac{24}{155}\right)\)	\(e\left(\frac{13}{155}\right)\)	\(e\left(\frac{126}{155}\right)\)	\(e\left(\frac{97}{155}\right)\)	\(e\left(\frac{101}{155}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{132}{155}\right)\)	\(e\left(\frac{24}{155}\right)\)
\(\chi_{5766}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{138}{155}\right)\)	\(e\left(\frac{88}{155}\right)\)	\(e\left(\frac{151}{155}\right)\)	\(e\left(\frac{152}{155}\right)\)	\(e\left(\frac{149}{155}\right)\)	\(e\left(\frac{112}{155}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{19}{155}\right)\)	\(e\left(\frac{88}{155}\right)\)
\(\chi_{5766}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{32}{155}\right)\)	\(e\left(\frac{117}{155}\right)\)	\(e\left(\frac{44}{155}\right)\)	\(e\left(\frac{33}{155}\right)\)	\(e\left(\frac{66}{155}\right)\)	\(e\left(\frac{8}{155}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{101}{155}\right)\)	\(e\left(\frac{117}{155}\right)\)
\(\chi_{5766}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{26}{155}\right)\)	\(e\left(\frac{66}{155}\right)\)	\(e\left(\frac{152}{155}\right)\)	\(e\left(\frac{114}{155}\right)\)	\(e\left(\frac{73}{155}\right)\)	\(e\left(\frac{84}{155}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{66}{155}\right)\)
\(\chi_{5766}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{89}{155}\right)\)	\(e\left(\frac{3}{155}\right)\)	\(e\left(\frac{41}{155}\right)\)	\(e\left(\frac{82}{155}\right)\)	\(e\left(\frac{71}{155}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{102}{155}\right)\)	\(e\left(\frac{89}{155}\right)\)
\(\chi_{5766}(295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{108}{155}\right)\)	\(e\left(\frac{143}{155}\right)\)	\(e\left(\frac{71}{155}\right)\)	\(e\left(\frac{92}{155}\right)\)	\(e\left(\frac{29}{155}\right)\)	\(e\left(\frac{27}{155}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{89}{155}\right)\)	\(e\left(\frac{143}{155}\right)\)
\(\chi_{5766}(343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{102}{155}\right)\)	\(e\left(\frac{92}{155}\right)\)	\(e\left(\frac{24}{155}\right)\)	\(e\left(\frac{18}{155}\right)\)	\(e\left(\frac{36}{155}\right)\)	\(e\left(\frac{103}{155}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{41}{155}\right)\)	\(e\left(\frac{92}{155}\right)\)
\(\chi_{5766}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{121}{155}\right)\)	\(e\left(\frac{21}{155}\right)\)	\(e\left(\frac{147}{155}\right)\)	\(e\left(\frac{149}{155}\right)\)	\(e\left(\frac{143}{155}\right)\)	\(e\left(\frac{69}{155}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{38}{155}\right)\)	\(e\left(\frac{21}{155}\right)\)
\(\chi_{5766}(469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{154}{155}\right)\)	\(e\left(\frac{148}{155}\right)\)	\(e\left(\frac{111}{155}\right)\)	\(e\left(\frac{67}{155}\right)\)	\(e\left(\frac{41}{155}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{72}{155}\right)\)	\(e\left(\frac{154}{155}\right)\)
\(\chi_{5766}(481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{78}{155}\right)\)	\(e\left(\frac{43}{155}\right)\)	\(e\left(\frac{146}{155}\right)\)	\(e\left(\frac{32}{155}\right)\)	\(e\left(\frac{64}{155}\right)\)	\(e\left(\frac{97}{155}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{4}{155}\right)\)	\(e\left(\frac{43}{155}\right)\)
\(\chi_{5766}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{17}{155}\right)\)	\(e\left(\frac{67}{155}\right)\)	\(e\left(\frac{4}{155}\right)\)	\(e\left(\frac{3}{155}\right)\)	\(e\left(\frac{6}{155}\right)\)	\(e\left(\frac{43}{155}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{136}{155}\right)\)	\(e\left(\frac{67}{155}\right)\)
\(\chi_{5766}(535,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{61}{155}\right)\)	\(e\left(\frac{131}{155}\right)\)	\(e\left(\frac{142}{155}\right)\)	\(e\left(\frac{29}{155}\right)\)	\(e\left(\frac{58}{155}\right)\)	\(e\left(\frac{54}{155}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{23}{155}\right)\)	\(e\left(\frac{131}{155}\right)\)
\(\chi_{5766}(655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{44}{155}\right)\)	\(e\left(\frac{64}{155}\right)\)	\(e\left(\frac{138}{155}\right)\)	\(e\left(\frac{26}{155}\right)\)	\(e\left(\frac{52}{155}\right)\)	\(e\left(\frac{11}{155}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{42}{155}\right)\)	\(e\left(\frac{64}{155}\right)\)
\(\chi_{5766}(667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{48}{155}\right)\)	\(e\left(\frac{98}{155}\right)\)	\(e\left(\frac{66}{155}\right)\)	\(e\left(\frac{127}{155}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{12}{155}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{74}{155}\right)\)	\(e\left(\frac{98}{155}\right)\)
\(\chi_{5766}(715,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{87}{155}\right)\)	\(e\left(\frac{42}{155}\right)\)	\(e\left(\frac{139}{155}\right)\)	\(e\left(\frac{143}{155}\right)\)	\(e\left(\frac{131}{155}\right)\)	\(e\left(\frac{138}{155}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{76}{155}\right)\)	\(e\left(\frac{42}{155}\right)\)
\(\chi_{5766}(721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{1}{155}\right)\)	\(e\left(\frac{86}{155}\right)\)	\(e\left(\frac{137}{155}\right)\)	\(e\left(\frac{64}{155}\right)\)	\(e\left(\frac{128}{155}\right)\)	\(e\left(\frac{39}{155}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{8}{155}\right)\)	\(e\left(\frac{86}{155}\right)\)
\(\chi_{5766}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{79}{155}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{128}{155}\right)\)	\(e\left(\frac{96}{155}\right)\)	\(e\left(\frac{37}{155}\right)\)	\(e\left(\frac{136}{155}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{12}{155}\right)\)	\(e\left(\frac{129}{155}\right)\)
\(\chi_{5766}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{18}{155}\right)\)	\(e\left(\frac{153}{155}\right)\)	\(e\left(\frac{141}{155}\right)\)	\(e\left(\frac{67}{155}\right)\)	\(e\left(\frac{134}{155}\right)\)	\(e\left(\frac{82}{155}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{144}{155}\right)\)	\(e\left(\frac{153}{155}\right)\)
\(\chi_{5766}(901,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{2}{155}\right)\)	\(e\left(\frac{17}{155}\right)\)	\(e\left(\frac{119}{155}\right)\)	\(e\left(\frac{128}{155}\right)\)	\(e\left(\frac{101}{155}\right)\)	\(e\left(\frac{78}{155}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{16}{155}\right)\)	\(e\left(\frac{17}{155}\right)\)
\(\chi_{5766}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{96}{155}\right)\)	\(e\left(\frac{41}{155}\right)\)	\(e\left(\frac{132}{155}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{43}{155}\right)\)	\(e\left(\frac{24}{155}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{148}{155}\right)\)	\(e\left(\frac{41}{155}\right)\)
\(\chi_{5766}(1027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{114}{155}\right)\)	\(e\left(\frac{39}{155}\right)\)	\(e\left(\frac{118}{155}\right)\)	\(e\left(\frac{11}{155}\right)\)	\(e\left(\frac{22}{155}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{137}{155}\right)\)	\(e\left(\frac{39}{155}\right)\)
\(\chi_{5766}(1039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{143}{155}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{61}{155}\right)\)	\(e\left(\frac{7}{155}\right)\)	\(e\left(\frac{14}{155}\right)\)	\(e\left(\frac{152}{155}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{53}{155}\right)\)
\(\chi_{5766}(1087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{72}{155}\right)\)	\(e\left(\frac{147}{155}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{71}{155}\right)\)	\(e\left(\frac{18}{155}\right)\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{111}{155}\right)\)	\(e\left(\frac{147}{155}\right)\)
\(\chi_{5766}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{36}{155}\right)\)	\(e\left(\frac{151}{155}\right)\)	\(e\left(\frac{127}{155}\right)\)	\(e\left(\frac{134}{155}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{133}{155}\right)\)	\(e\left(\frac{151}{155}\right)\)
\(\chi_{5766}(1213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{149}{155}\right)\)	\(e\left(\frac{104}{155}\right)\)	\(e\left(\frac{108}{155}\right)\)	\(e\left(\frac{81}{155}\right)\)	\(e\left(\frac{7}{155}\right)\)	\(e\left(\frac{76}{155}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{104}{155}\right)\)
\(\chi_{5766}(1225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{108}{155}\right)\)	\(e\left(\frac{136}{155}\right)\)	\(e\left(\frac{102}{155}\right)\)	\(e\left(\frac{49}{155}\right)\)	\(e\left(\frac{67}{155}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{108}{155}\right)\)
\(\chi_{5766}(1273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{142}{155}\right)\)	\(e\left(\frac{122}{155}\right)\)	\(e\left(\frac{79}{155}\right)\)	\(e\left(\frac{98}{155}\right)\)	\(e\left(\frac{41}{155}\right)\)	\(e\left(\frac{113}{155}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{51}{155}\right)\)	\(e\left(\frac{122}{155}\right)\)
\(\chi_{5766}(1279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{131}{155}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{122}{155}\right)\)	\(e\left(\frac{14}{155}\right)\)	\(e\left(\frac{28}{155}\right)\)	\(e\left(\frac{149}{155}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{118}{155}\right)\)	\(e\left(\frac{106}{155}\right)\)
\(\chi_{5766}(1399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{29}{155}\right)\)	\(e\left(\frac{14}{155}\right)\)	\(e\left(\frac{98}{155}\right)\)	\(e\left(\frac{151}{155}\right)\)	\(e\left(\frac{147}{155}\right)\)	\(e\left(\frac{46}{155}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{77}{155}\right)\)	\(e\left(\frac{14}{155}\right)\)
\(\chi_{5766}(1411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{83}{155}\right)\)	\(e\left(\frac{8}{155}\right)\)	\(e\left(\frac{56}{155}\right)\)	\(e\left(\frac{42}{155}\right)\)	\(e\left(\frac{84}{155}\right)\)	\(e\left(\frac{137}{155}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{44}{155}\right)\)	\(e\left(\frac{8}{155}\right)\)
\(\chi_{5766}(1459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{57}{155}\right)\)	\(e\left(\frac{97}{155}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{83}{155}\right)\)	\(e\left(\frac{11}{155}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{146}{155}\right)\)	\(e\left(\frac{97}{155}\right)\)

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First 31 of 120 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	5766.v
Modulus	$5766$
Conductor	$961$
Order	$155$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(5766\)
Conductor:	\(961\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(155\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 961.l	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)