LMFDB - Dirichlet character orbit 2183.y

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2183, base_ring=CyclotomicField(116)) M = H._module chi = DirichletCharacter(H, M([87,102])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(6,2183)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2183$
Conductor:	$2183$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$116$	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:	$\Q(\zeta_{116})$
Fixed field:	Number field defined by a degree 116 polynomial (not computed)

First 31 of 56 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{2183}(6,\cdot)$	$1$	$1$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{14}{29}\right)$
$\chi_{2183}(31,\cdot)$	$1$	$1$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{18}{29}\right)$
$\chi_{2183}(43,\cdot)$	$1$	$1$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{21}{29}\right)$
$\chi_{2183}(142,\cdot)$	$1$	$1$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{10}{29}\right)$
$\chi_{2183}(179,\cdot)$	$1$	$1$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{27}{29}\right)$
$\chi_{2183}(191,\cdot)$	$1$	$1$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{20}{29}\right)$
$\chi_{2183}(216,\cdot)$	$1$	$1$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{13}{29}\right)$
$\chi_{2183}(290,\cdot)$	$1$	$1$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{17}{29}\right)$
$\chi_{2183}(327,\cdot)$	$1$	$1$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{19}{29}\right)$
$\chi_{2183}(339,\cdot)$	$1$	$1$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{4}{29}\right)$
$\chi_{2183}(364,\cdot)$	$1$	$1$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{55}{116}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{15}{29}\right)$
$\chi_{2183}(401,\cdot)$	$1$	$1$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{12}{29}\right)$
$\chi_{2183}(450,\cdot)$	$1$	$1$	$e\left(\frac{81}{116}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{6}{29}\right)$
$\chi_{2183}(512,\cdot)$	$1$	$1$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{11}{29}\right)$
$\chi_{2183}(524,\cdot)$	$1$	$1$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{22}{29}\right)$
$\chi_{2183}(549,\cdot)$	$1$	$1$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{1}{29}\right)$
$\chi_{2183}(561,\cdot)$	$1$	$1$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{2}{29}\right)$
$\chi_{2183}(586,\cdot)$	$1$	$1$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{25}{29}\right)$
$\chi_{2183}(598,\cdot)$	$1$	$1$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{23}{29}\right)$
$\chi_{2183}(623,\cdot)$	$1$	$1$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{59}{116}\right)$	$e\left(\frac{81}{116}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{24}{29}\right)$
$\chi_{2183}(660,\cdot)$	$1$	$1$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{8}{29}\right)$
$\chi_{2183}(672,\cdot)$	$1$	$1$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{28}{29}\right)$
$\chi_{2183}(746,\cdot)$	$1$	$1$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{9}{29}\right)$
$\chi_{2183}(857,\cdot)$	$1$	$1$	$e\left(\frac{69}{116}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{18}{29}\right)$
$\chi_{2183}(882,\cdot)$	$1$	$1$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{107}{116}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{16}{29}\right)$
$\chi_{2183}(919,\cdot)$	$1$	$1$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{5}{29}\right)$
$\chi_{2183}(968,\cdot)$	$1$	$1$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{10}{29}\right)$
$\chi_{2183}(1005,\cdot)$	$1$	$1$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{27}{29}\right)$
$\chi_{2183}(1042,\cdot)$	$1$	$1$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{13}{29}\right)$
$\chi_{2183}(1104,\cdot)$	$1$	$1$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{7}{29}\right)$
$\chi_{2183}(1116,\cdot)$	$1$	$1$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{7}{116}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{17}{29}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{2183}(6,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)
\(\chi_{2183}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)
\(\chi_{2183}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)
\(\chi_{2183}(142,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)
\(\chi_{2183}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)
\(\chi_{2183}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)
\(\chi_{2183}(216,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)
\(\chi_{2183}(290,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)
\(\chi_{2183}(327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)
\(\chi_{2183}(339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)
\(\chi_{2183}(364,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{55}{116}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)
\(\chi_{2183}(401,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)
\(\chi_{2183}(450,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{116}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)
\(\chi_{2183}(512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)
\(\chi_{2183}(524,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)
\(\chi_{2183}(549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)
\(\chi_{2183}(561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)
\(\chi_{2183}(586,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)
\(\chi_{2183}(598,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)
\(\chi_{2183}(623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{59}{116}\right)\)	\(e\left(\frac{81}{116}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)
\(\chi_{2183}(660,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)
\(\chi_{2183}(672,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)
\(\chi_{2183}(746,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)
\(\chi_{2183}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)
\(\chi_{2183}(882,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{107}{116}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)
\(\chi_{2183}(919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)
\(\chi_{2183}(968,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)
\(\chi_{2183}(1005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)
\(\chi_{2183}(1042,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)
\(\chi_{2183}(1104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)
\(\chi_{2183}(1116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{7}{116}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)

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First 31 of 56 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	2183.y
Modulus	$2183$
Conductor	$2183$
Order	$116$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2183\)
Conductor:	\(2183\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(116\)	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)