LMFDB - Dirichlet character orbit 2527.cd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2527, base_ring=CyclotomicField(342)) M = H._module chi = DirichletCharacter(H, M([57,233])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(10,2527)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2527$
Conductor:	$2527$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$342$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{171})$
Fixed field:	Number field defined by a degree 342 polynomial (not computed)

First 31 of 108 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{2527}(10,\cdot)$	$1$	$1$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{2527}(33,\cdot)$	$1$	$1$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{97}{171}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{2527}(40,\cdot)$	$1$	$1$	$e\left(\frac{121}{342}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{2527}(108,\cdot)$	$1$	$1$	$e\left(\frac{191}{342}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{23}{342}\right)$	$e\left(\frac{7}{342}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{2527}(117,\cdot)$	$1$	$1$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{92}{171}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{2527}(129,\cdot)$	$1$	$1$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{136}{171}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{137}{342}\right)$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{2527}(143,\cdot)$	$1$	$1$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{71}{342}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{2527}(166,\cdot)$	$1$	$1$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{143}{171}\right)$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{7}{342}\right)$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{2527}(173,\cdot)$	$1$	$1$	$e\left(\frac{85}{342}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{2527}(241,\cdot)$	$1$	$1$	$e\left(\frac{317}{342}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{185}{342}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{2527}(250,\cdot)$	$1$	$1$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{337}{342}\right)$	$e\left(\frac{281}{342}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{2527}(276,\cdot)$	$1$	$1$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{179}{342}\right)$	$e\left(\frac{337}{342}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{2527}(306,\cdot)$	$1$	$1$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{253}{342}\right)$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{2527}(374,\cdot)$	$1$	$1$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{2527}(383,\cdot)$	$1$	$1$	$e\left(\frac{331}{342}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{13}{342}\right)$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{2527}(395,\cdot)$	$1$	$1$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{281}{342}\right)$	$e\left(\frac{145}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{2527}(409,\cdot)$	$1$	$1$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{13}{342}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{2527}(432,\cdot)$	$1$	$1$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{136}{171}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{2527}(439,\cdot)$	$1$	$1$	$e\left(\frac{13}{342}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{109}{342}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{2527}(507,\cdot)$	$1$	$1$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{2527}(516,\cdot)$	$1$	$1$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{31}{342}\right)$	$e\left(\frac{173}{342}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{2527}(528,\cdot)$	$1$	$1$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{2527}(542,\cdot)$	$1$	$1$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{31}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{2527}(565,\cdot)$	$1$	$1$	$e\left(\frac{253}{342}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{2527}(572,\cdot)$	$1$	$1$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{2527}(640,\cdot)$	$1$	$1$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{115}{342}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{104}{171}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{2527}(649,\cdot)$	$1$	$1$	$e\left(\frac{169}{342}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{2527}(661,\cdot)$	$1$	$1$	$e\left(\frac{35}{342}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{2527}(675,\cdot)$	$1$	$1$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{2527}(698,\cdot)$	$1$	$1$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{169}{342}\right)$	$e\left(\frac{215}{342}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{2527}(705,\cdot)$	$1$	$1$	$e\left(\frac{283}{342}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{16}{19}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{2527}(10,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)
\(\chi_{2527}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{342}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{97}{171}\right)\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{2527}(40,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{342}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{2527}(108,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{342}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{23}{342}\right)\)	\(e\left(\frac{7}{342}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{107}{171}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{2527}(117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{92}{171}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{2527}(129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{136}{171}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{137}{342}\right)\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{2527}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{71}{342}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{2527}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{143}{171}\right)\)	\(e\left(\frac{73}{171}\right)\)	\(e\left(\frac{7}{342}\right)\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{2527}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{342}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{73}{171}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)
\(\chi_{2527}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{317}{342}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{185}{342}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{80}{171}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{2527}(250,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{337}{342}\right)\)	\(e\left(\frac{281}{342}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{2527}(276,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{139}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{179}{342}\right)\)	\(e\left(\frac{337}{342}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{107}{171}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{2527}(306,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{253}{342}\right)\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{2527}(374,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{2527}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{342}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{13}{342}\right)\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{2527}(395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{73}{171}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{281}{342}\right)\)	\(e\left(\frac{145}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{2527}(409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{13}{342}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{2527}(432,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{136}{171}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{2527}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{342}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{109}{342}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{2527}(507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{2527}(516,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{31}{342}\right)\)	\(e\left(\frac{173}{342}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{55}{171}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{2527}(528,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{11}{342}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{2527}(542,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{31}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{2527}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{342}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{2527}(572,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{142}{171}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{2527}(640,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{342}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{115}{342}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{104}{171}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{2527}(649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{342}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{2527}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{342}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{2527}(675,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{80}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{2527}(698,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{169}{342}\right)\)	\(e\left(\frac{215}{342}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)
\(\chi_{2527}(705,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{342}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)

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First 31 of 108 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	2527.cd
Modulus	$2527$
Conductor	$2527$
Order	$342$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2527\)
Conductor:	\(2527\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(342\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)