LMFDB - Dirichlet character orbit 3871.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3871, base_ring=CyclotomicField(546)) M = H._module chi = DirichletCharacter(H, M([286,210])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(46,3871)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3871$
Conductor:	$3871$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$273$	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:	$\Q(\zeta_{273})$
Fixed field:	Number field defined by a degree 273 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{3871}(46,\cdot)$	$1$	$1$	$e\left(\frac{43}{273}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{86}{273}\right)$	$e\left(\frac{10}{273}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{223}{273}\right)$	$e\left(\frac{53}{273}\right)$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{61}{273}\right)$
$\chi_{3871}(65,\cdot)$	$1$	$1$	$e\left(\frac{83}{273}\right)$	$e\left(\frac{193}{273}\right)$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{83}{91}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{115}{273}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{86}{273}\right)$
$\chi_{3871}(100,\cdot)$	$1$	$1$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{229}{273}\right)$	$e\left(\frac{11}{273}\right)$
$\chi_{3871}(144,\cdot)$	$1$	$1$	$e\left(\frac{148}{273}\right)$	$e\left(\frac{206}{273}\right)$	$e\left(\frac{23}{273}\right)$	$e\left(\frac{136}{273}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{57}{91}\right)$	$e\left(\frac{139}{273}\right)$	$e\left(\frac{11}{273}\right)$	$e\left(\frac{176}{273}\right)$	$e\left(\frac{229}{273}\right)$
$\chi_{3871}(179,\cdot)$	$1$	$1$	$e\left(\frac{67}{273}\right)$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{134}{273}\right)$	$e\left(\frac{187}{273}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{67}{91}\right)$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{254}{273}\right)$	$e\left(\frac{242}{273}\right)$	$e\left(\frac{76}{273}\right)$
$\chi_{3871}(247,\cdot)$	$1$	$1$	$e\left(\frac{131}{273}\right)$	$e\left(\frac{127}{273}\right)$	$e\left(\frac{262}{273}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{86}{91}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{254}{273}\right)$	$e\left(\frac{244}{273}\right)$	$e\left(\frac{82}{273}\right)$	$e\left(\frac{116}{273}\right)$
$\chi_{3871}(289,\cdot)$	$1$	$1$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{58}{273}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{4}{273}\right)$	$e\left(\frac{64}{273}\right)$	$e\left(\frac{257}{273}\right)$
$\chi_{3871}(326,\cdot)$	$1$	$1$	$e\left(\frac{235}{273}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{197}{273}\right)$	$e\left(\frac{61}{273}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{241}{273}\right)$	$e\left(\frac{23}{273}\right)$	$e\left(\frac{95}{273}\right)$	$e\left(\frac{181}{273}\right)$
$\chi_{3871}(338,\cdot)$	$1$	$1$	$e\left(\frac{176}{273}\right)$	$e\left(\frac{31}{273}\right)$	$e\left(\frac{79}{273}\right)$	$e\left(\frac{206}{273}\right)$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{85}{91}\right)$	$e\left(\frac{62}{273}\right)$	$e\left(\frac{109}{273}\right)$	$e\left(\frac{106}{273}\right)$	$e\left(\frac{110}{273}\right)$
$\chi_{3871}(354,\cdot)$	$1$	$1$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{59}{273}\right)$	$e\left(\frac{64}{273}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{226}{273}\right)$	$e\left(\frac{230}{273}\right)$	$e\left(\frac{131}{273}\right)$	$e\left(\frac{172}{273}\right)$
$\chi_{3871}(368,\cdot)$	$1$	$1$	$e\left(\frac{16}{273}\right)$	$e\left(\frac{251}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{118}{273}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{229}{273}\right)$	$e\left(\frac{134}{273}\right)$	$e\left(\frac{233}{273}\right)$	$e\left(\frac{10}{273}\right)$
$\chi_{3871}(380,\cdot)$	$1$	$1$	$e\left(\frac{11}{273}\right)$	$e\left(\frac{19}{273}\right)$	$e\left(\frac{22}{273}\right)$	$e\left(\frac{47}{273}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{38}{273}\right)$	$e\left(\frac{58}{273}\right)$	$e\left(\frac{109}{273}\right)$	$e\left(\frac{41}{273}\right)$
$\chi_{3871}(403,\cdot)$	$1$	$1$	$e\left(\frac{103}{273}\right)$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{206}{273}\right)$	$e\left(\frac{43}{273}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{12}{91}\right)$	$e\left(\frac{58}{273}\right)$	$e\left(\frac{146}{273}\right)$	$e\left(\frac{152}{273}\right)$	$e\left(\frac{235}{273}\right)$
$\chi_{3871}(417,\cdot)$	$1$	$1$	$e\left(\frac{163}{273}\right)$	$e\left(\frac{83}{273}\right)$	$e\left(\frac{53}{273}\right)$	$e\left(\frac{76}{273}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{136}{273}\right)$
$\chi_{3871}(457,\cdot)$	$1$	$1$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{67}{273}\right)$	$e\left(\frac{250}{273}\right)$	$e\left(\frac{137}{273}\right)$	$e\left(\frac{64}{91}\right)$	$e\left(\frac{34}{91}\right)$	$e\left(\frac{134}{273}\right)$	$e\left(\frac{262}{273}\right)$	$e\left(\frac{97}{273}\right)$	$e\left(\frac{44}{273}\right)$
$\chi_{3871}(492,\cdot)$	$1$	$1$	$e\left(\frac{110}{273}\right)$	$e\left(\frac{190}{273}\right)$	$e\left(\frac{220}{273}\right)$	$e\left(\frac{197}{273}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{19}{91}\right)$	$e\left(\frac{107}{273}\right)$	$e\left(\frac{34}{273}\right)$	$e\left(\frac{271}{273}\right)$	$e\left(\frac{137}{273}\right)$
$\chi_{3871}(536,\cdot)$	$1$	$1$	$e\left(\frac{190}{273}\right)$	$e\left(\frac{80}{273}\right)$	$e\left(\frac{107}{273}\right)$	$e\left(\frac{241}{273}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{160}{273}\right)$	$e\left(\frac{158}{273}\right)$	$e\left(\frac{71}{273}\right)$	$e\left(\frac{187}{273}\right)$
$\chi_{3871}(541,\cdot)$	$1$	$1$	$e\left(\frac{152}{273}\right)$	$e\left(\frac{64}{273}\right)$	$e\left(\frac{31}{273}\right)$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{128}{273}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{95}{273}\right)$
$\chi_{3871}(571,\cdot)$	$1$	$1$	$e\left(\frac{214}{273}\right)$	$e\left(\frac{47}{273}\right)$	$e\left(\frac{155}{273}\right)$	$e\left(\frac{145}{273}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{94}{273}\right)$	$e\left(\frac{86}{273}\right)$	$e\left(\frac{11}{273}\right)$	$e\left(\frac{202}{273}\right)$
$\chi_{3871}(599,\cdot)$	$1$	$1$	$e\left(\frac{82}{273}\right)$	$e\left(\frac{92}{273}\right)$	$e\left(\frac{164}{273}\right)$	$e\left(\frac{127}{273}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{184}{273}\right)$	$e\left(\frac{209}{273}\right)$	$e\left(\frac{68}{273}\right)$	$e\left(\frac{256}{273}\right)$
$\chi_{3871}(620,\cdot)$	$1$	$1$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{194}{273}\right)$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{250}{273}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{115}{273}\right)$	$e\left(\frac{233}{273}\right)$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{160}{273}\right)$
$\chi_{3871}(653,\cdot)$	$1$	$1$	$e\left(\frac{41}{273}\right)$	$e\left(\frac{46}{273}\right)$	$e\left(\frac{82}{273}\right)$	$e\left(\frac{200}{273}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{92}{273}\right)$	$e\left(\frac{241}{273}\right)$	$e\left(\frac{34}{273}\right)$	$e\left(\frac{128}{273}\right)$
$\chi_{3871}(697,\cdot)$	$1$	$1$	$e\left(\frac{187}{273}\right)$	$e\left(\frac{50}{273}\right)$	$e\left(\frac{101}{273}\right)$	$e\left(\frac{253}{273}\right)$	$e\left(\frac{79}{91}\right)$	$e\left(\frac{5}{91}\right)$	$e\left(\frac{100}{273}\right)$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{151}{273}\right)$
$\chi_{3871}(732,\cdot)$	$1$	$1$	$e\left(\frac{106}{273}\right)$	$e\left(\frac{59}{273}\right)$	$e\left(\frac{212}{273}\right)$	$e\left(\frac{31}{273}\right)$	$e\left(\frac{55}{91}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{118}{273}\right)$	$e\left(\frac{137}{273}\right)$	$e\left(\frac{8}{273}\right)$	$e\left(\frac{271}{273}\right)$
$\chi_{3871}(800,\cdot)$	$1$	$1$	$e\left(\frac{209}{273}\right)$	$e\left(\frac{88}{273}\right)$	$e\left(\frac{145}{273}\right)$	$e\left(\frac{74}{273}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{176}{273}\right)$	$e\left(\frac{10}{273}\right)$	$e\left(\frac{160}{273}\right)$	$e\left(\frac{233}{273}\right)$
$\chi_{3871}(828,\cdot)$	$1$	$1$	$e\left(\frac{218}{273}\right)$	$e\left(\frac{178}{273}\right)$	$e\left(\frac{163}{273}\right)$	$e\left(\frac{38}{273}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{36}{91}\right)$	$e\left(\frac{83}{273}\right)$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{1}{273}\right)$	$e\left(\frac{68}{273}\right)$
$\chi_{3871}(842,\cdot)$	$1$	$1$	$e\left(\frac{107}{273}\right)$	$e\left(\frac{160}{273}\right)$	$e\left(\frac{214}{273}\right)$	$e\left(\frac{209}{273}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{47}{273}\right)$	$e\left(\frac{43}{273}\right)$	$e\left(\frac{142}{273}\right)$	$e\left(\frac{101}{273}\right)$
$\chi_{3871}(877,\cdot)$	$1$	$1$	$e\left(\frac{155}{273}\right)$	$e\left(\frac{94}{273}\right)$	$e\left(\frac{37}{273}\right)$	$e\left(\frac{17}{273}\right)$	$e\left(\frac{83}{91}\right)$	$e\left(\frac{64}{91}\right)$	$e\left(\frac{188}{273}\right)$	$e\left(\frac{172}{273}\right)$	$e\left(\frac{22}{273}\right)$	$e\left(\frac{131}{273}\right)$
$\chi_{3871}(879,\cdot)$	$1$	$1$	$e\left(\frac{1}{273}\right)$	$e\left(\frac{101}{273}\right)$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{178}{273}\right)$	$e\left(\frac{34}{91}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{134}{273}\right)$	$e\left(\frac{103}{273}\right)$
$\chi_{3871}(891,\cdot)$	$1$	$1$	$e\left(\frac{254}{273}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{235}{273}\right)$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{148}{273}\right)$	$e\left(\frac{184}{273}\right)$	$e\left(\frac{227}{273}\right)$
$\chi_{3871}(907,\cdot)$	$1$	$1$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{230}{273}\right)$	$e\left(\frac{137}{273}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{187}{273}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{94}{273}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{3871}(46,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{273}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{86}{273}\right)\)	\(e\left(\frac{10}{273}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{223}{273}\right)\)	\(e\left(\frac{53}{273}\right)\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{61}{273}\right)\)
\(\chi_{3871}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{273}\right)\)	\(e\left(\frac{193}{273}\right)\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{83}{91}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{115}{273}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{86}{273}\right)\)
\(\chi_{3871}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{170}{273}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{229}{273}\right)\)	\(e\left(\frac{11}{273}\right)\)
\(\chi_{3871}(144,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{273}\right)\)	\(e\left(\frac{206}{273}\right)\)	\(e\left(\frac{23}{273}\right)\)	\(e\left(\frac{136}{273}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{57}{91}\right)\)	\(e\left(\frac{139}{273}\right)\)	\(e\left(\frac{11}{273}\right)\)	\(e\left(\frac{176}{273}\right)\)	\(e\left(\frac{229}{273}\right)\)
\(\chi_{3871}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{273}\right)\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{134}{273}\right)\)	\(e\left(\frac{187}{273}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{67}{91}\right)\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{254}{273}\right)\)	\(e\left(\frac{242}{273}\right)\)	\(e\left(\frac{76}{273}\right)\)
\(\chi_{3871}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{273}\right)\)	\(e\left(\frac{127}{273}\right)\)	\(e\left(\frac{262}{273}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{86}{91}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{254}{273}\right)\)	\(e\left(\frac{244}{273}\right)\)	\(e\left(\frac{82}{273}\right)\)	\(e\left(\frac{116}{273}\right)\)
\(\chi_{3871}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{58}{273}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{4}{273}\right)\)	\(e\left(\frac{64}{273}\right)\)	\(e\left(\frac{257}{273}\right)\)
\(\chi_{3871}(326,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{273}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{197}{273}\right)\)	\(e\left(\frac{61}{273}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{241}{273}\right)\)	\(e\left(\frac{23}{273}\right)\)	\(e\left(\frac{95}{273}\right)\)	\(e\left(\frac{181}{273}\right)\)
\(\chi_{3871}(338,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{176}{273}\right)\)	\(e\left(\frac{31}{273}\right)\)	\(e\left(\frac{79}{273}\right)\)	\(e\left(\frac{206}{273}\right)\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{85}{91}\right)\)	\(e\left(\frac{62}{273}\right)\)	\(e\left(\frac{109}{273}\right)\)	\(e\left(\frac{106}{273}\right)\)	\(e\left(\frac{110}{273}\right)\)
\(\chi_{3871}(354,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{59}{273}\right)\)	\(e\left(\frac{64}{273}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{226}{273}\right)\)	\(e\left(\frac{230}{273}\right)\)	\(e\left(\frac{131}{273}\right)\)	\(e\left(\frac{172}{273}\right)\)
\(\chi_{3871}(368,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{273}\right)\)	\(e\left(\frac{251}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{118}{273}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{229}{273}\right)\)	\(e\left(\frac{134}{273}\right)\)	\(e\left(\frac{233}{273}\right)\)	\(e\left(\frac{10}{273}\right)\)
\(\chi_{3871}(380,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{273}\right)\)	\(e\left(\frac{19}{273}\right)\)	\(e\left(\frac{22}{273}\right)\)	\(e\left(\frac{47}{273}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{38}{273}\right)\)	\(e\left(\frac{58}{273}\right)\)	\(e\left(\frac{109}{273}\right)\)	\(e\left(\frac{41}{273}\right)\)
\(\chi_{3871}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{273}\right)\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{206}{273}\right)\)	\(e\left(\frac{43}{273}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{12}{91}\right)\)	\(e\left(\frac{58}{273}\right)\)	\(e\left(\frac{146}{273}\right)\)	\(e\left(\frac{152}{273}\right)\)	\(e\left(\frac{235}{273}\right)\)
\(\chi_{3871}(417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{273}\right)\)	\(e\left(\frac{83}{273}\right)\)	\(e\left(\frac{53}{273}\right)\)	\(e\left(\frac{76}{273}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{136}{273}\right)\)
\(\chi_{3871}(457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{67}{273}\right)\)	\(e\left(\frac{250}{273}\right)\)	\(e\left(\frac{137}{273}\right)\)	\(e\left(\frac{64}{91}\right)\)	\(e\left(\frac{34}{91}\right)\)	\(e\left(\frac{134}{273}\right)\)	\(e\left(\frac{262}{273}\right)\)	\(e\left(\frac{97}{273}\right)\)	\(e\left(\frac{44}{273}\right)\)
\(\chi_{3871}(492,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{110}{273}\right)\)	\(e\left(\frac{190}{273}\right)\)	\(e\left(\frac{220}{273}\right)\)	\(e\left(\frac{197}{273}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{19}{91}\right)\)	\(e\left(\frac{107}{273}\right)\)	\(e\left(\frac{34}{273}\right)\)	\(e\left(\frac{271}{273}\right)\)	\(e\left(\frac{137}{273}\right)\)
\(\chi_{3871}(536,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{190}{273}\right)\)	\(e\left(\frac{80}{273}\right)\)	\(e\left(\frac{107}{273}\right)\)	\(e\left(\frac{241}{273}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{160}{273}\right)\)	\(e\left(\frac{158}{273}\right)\)	\(e\left(\frac{71}{273}\right)\)	\(e\left(\frac{187}{273}\right)\)
\(\chi_{3871}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{273}\right)\)	\(e\left(\frac{64}{273}\right)\)	\(e\left(\frac{31}{273}\right)\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{128}{273}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{95}{273}\right)\)
\(\chi_{3871}(571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{214}{273}\right)\)	\(e\left(\frac{47}{273}\right)\)	\(e\left(\frac{155}{273}\right)\)	\(e\left(\frac{145}{273}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{94}{273}\right)\)	\(e\left(\frac{86}{273}\right)\)	\(e\left(\frac{11}{273}\right)\)	\(e\left(\frac{202}{273}\right)\)
\(\chi_{3871}(599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{273}\right)\)	\(e\left(\frac{92}{273}\right)\)	\(e\left(\frac{164}{273}\right)\)	\(e\left(\frac{127}{273}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{184}{273}\right)\)	\(e\left(\frac{209}{273}\right)\)	\(e\left(\frac{68}{273}\right)\)	\(e\left(\frac{256}{273}\right)\)
\(\chi_{3871}(620,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{194}{273}\right)\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{250}{273}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{115}{273}\right)\)	\(e\left(\frac{233}{273}\right)\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{160}{273}\right)\)
\(\chi_{3871}(653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{273}\right)\)	\(e\left(\frac{46}{273}\right)\)	\(e\left(\frac{82}{273}\right)\)	\(e\left(\frac{200}{273}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{92}{273}\right)\)	\(e\left(\frac{241}{273}\right)\)	\(e\left(\frac{34}{273}\right)\)	\(e\left(\frac{128}{273}\right)\)
\(\chi_{3871}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{273}\right)\)	\(e\left(\frac{50}{273}\right)\)	\(e\left(\frac{101}{273}\right)\)	\(e\left(\frac{253}{273}\right)\)	\(e\left(\frac{79}{91}\right)\)	\(e\left(\frac{5}{91}\right)\)	\(e\left(\frac{100}{273}\right)\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{151}{273}\right)\)
\(\chi_{3871}(732,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{106}{273}\right)\)	\(e\left(\frac{59}{273}\right)\)	\(e\left(\frac{212}{273}\right)\)	\(e\left(\frac{31}{273}\right)\)	\(e\left(\frac{55}{91}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{118}{273}\right)\)	\(e\left(\frac{137}{273}\right)\)	\(e\left(\frac{8}{273}\right)\)	\(e\left(\frac{271}{273}\right)\)
\(\chi_{3871}(800,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{209}{273}\right)\)	\(e\left(\frac{88}{273}\right)\)	\(e\left(\frac{145}{273}\right)\)	\(e\left(\frac{74}{273}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{176}{273}\right)\)	\(e\left(\frac{10}{273}\right)\)	\(e\left(\frac{160}{273}\right)\)	\(e\left(\frac{233}{273}\right)\)
\(\chi_{3871}(828,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{218}{273}\right)\)	\(e\left(\frac{178}{273}\right)\)	\(e\left(\frac{163}{273}\right)\)	\(e\left(\frac{38}{273}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{36}{91}\right)\)	\(e\left(\frac{83}{273}\right)\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{1}{273}\right)\)	\(e\left(\frac{68}{273}\right)\)
\(\chi_{3871}(842,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{273}\right)\)	\(e\left(\frac{160}{273}\right)\)	\(e\left(\frac{214}{273}\right)\)	\(e\left(\frac{209}{273}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{47}{273}\right)\)	\(e\left(\frac{43}{273}\right)\)	\(e\left(\frac{142}{273}\right)\)	\(e\left(\frac{101}{273}\right)\)
\(\chi_{3871}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{273}\right)\)	\(e\left(\frac{94}{273}\right)\)	\(e\left(\frac{37}{273}\right)\)	\(e\left(\frac{17}{273}\right)\)	\(e\left(\frac{83}{91}\right)\)	\(e\left(\frac{64}{91}\right)\)	\(e\left(\frac{188}{273}\right)\)	\(e\left(\frac{172}{273}\right)\)	\(e\left(\frac{22}{273}\right)\)	\(e\left(\frac{131}{273}\right)\)
\(\chi_{3871}(879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{273}\right)\)	\(e\left(\frac{101}{273}\right)\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{178}{273}\right)\)	\(e\left(\frac{34}{91}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{134}{273}\right)\)	\(e\left(\frac{103}{273}\right)\)
\(\chi_{3871}(891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{254}{273}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{235}{273}\right)\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{148}{273}\right)\)	\(e\left(\frac{184}{273}\right)\)	\(e\left(\frac{227}{273}\right)\)
\(\chi_{3871}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{230}{273}\right)\)	\(e\left(\frac{137}{273}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{187}{273}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{170}{273}\right)\)	\(e\left(\frac{94}{273}\right)\)

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First 31 of 144 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	3871.cn
Modulus	$3871$
Conductor	$3871$
Order	$273$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3871\)
Conductor:	\(3871\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(273\)	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)