LMFDB - Dirichlet character orbit 10470.cd

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10470, base_ring=CyclotomicField(116)) M = H._module chi = DirichletCharacter(H, M([58,58,17])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(179, 10470)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("10470.179"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$10470$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$5235$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$116$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 5235.ce	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{116})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 116 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 56 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{10470}(179,\cdot)$	$1$	$1$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{11}{58}\right)$
$\chi_{10470}(359,\cdot)$	$1$	$1$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{59}{116}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{27}{58}\right)$
$\chi_{10470}(659,\cdot)$	$1$	$1$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{107}{116}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{47}{58}\right)$
$\chi_{10470}(719,\cdot)$	$1$	$1$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{107}{116}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{3}{58}\right)$
$\chi_{10470}(989,\cdot)$	$1$	$1$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{55}{116}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{1}{58}\right)$
$\chi_{10470}(1019,\cdot)$	$1$	$1$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{49}{58}\right)$
$\chi_{10470}(1229,\cdot)$	$1$	$1$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{39}{58}\right)$
$\chi_{10470}(1349,\cdot)$	$1$	$1$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{23}{58}\right)$
$\chi_{10470}(1499,\cdot)$	$1$	$1$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{15}{58}\right)$
$\chi_{10470}(1529,\cdot)$	$1$	$1$	$e\left(\frac{69}{116}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{55}{58}\right)$
$\chi_{10470}(1559,\cdot)$	$1$	$1$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{59}{116}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{19}{58}\right)$
$\chi_{10470}(1739,\cdot)$	$1$	$1$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{57}{58}\right)$
$\chi_{10470}(2129,\cdot)$	$1$	$1$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{31}{58}\right)$
$\chi_{10470}(2159,\cdot)$	$1$	$1$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{7}{116}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{17}{58}\right)$
$\chi_{10470}(3089,\cdot)$	$1$	$1$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{55}{116}\right)$	$e\left(\frac{69}{116}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{35}{58}\right)$
$\chi_{10470}(3149,\cdot)$	$1$	$1$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{45}{58}\right)$
$\chi_{10470}(3179,\cdot)$	$1$	$1$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{51}{58}\right)$
$\chi_{10470}(3239,\cdot)$	$1$	$1$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{53}{58}\right)$
$\chi_{10470}(3359,\cdot)$	$1$	$1$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{13}{58}\right)$
$\chi_{10470}(3389,\cdot)$	$1$	$1$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{7}{58}\right)$
$\chi_{10470}(3479,\cdot)$	$1$	$1$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{25}{58}\right)$
$\chi_{10470}(3569,\cdot)$	$1$	$1$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{37}{58}\right)$
$\chi_{10470}(4109,\cdot)$	$1$	$1$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{37}{58}\right)$
$\chi_{10470}(4199,\cdot)$	$1$	$1$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{25}{58}\right)$
$\chi_{10470}(4289,\cdot)$	$1$	$1$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{69}{116}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{7}{58}\right)$
$\chi_{10470}(4319,\cdot)$	$1$	$1$	$e\left(\frac{107}{116}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{13}{58}\right)$
$\chi_{10470}(4439,\cdot)$	$1$	$1$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{53}{58}\right)$
$\chi_{10470}(4499,\cdot)$	$1$	$1$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{51}{58}\right)$
$\chi_{10470}(4529,\cdot)$	$1$	$1$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{45}{58}\right)$
$\chi_{10470}(4589,\cdot)$	$1$	$1$	$e\left(\frac{7}{116}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{35}{58}\right)$
$\chi_{10470}(5519,\cdot)$	$1$	$1$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{17}{58}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{10470}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)
\(\chi_{10470}(359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{59}{116}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)
\(\chi_{10470}(659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{107}{116}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)
\(\chi_{10470}(719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{107}{116}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)
\(\chi_{10470}(989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{55}{116}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)
\(\chi_{10470}(1019,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)
\(\chi_{10470}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)
\(\chi_{10470}(1349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)
\(\chi_{10470}(1499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)
\(\chi_{10470}(1529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{116}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)
\(\chi_{10470}(1559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{59}{116}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)
\(\chi_{10470}(1739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)
\(\chi_{10470}(2129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)
\(\chi_{10470}(2159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{7}{116}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)
\(\chi_{10470}(3089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{55}{116}\right)\)	\(e\left(\frac{69}{116}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)
\(\chi_{10470}(3149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)
\(\chi_{10470}(3179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)
\(\chi_{10470}(3239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)
\(\chi_{10470}(3359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)
\(\chi_{10470}(3389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)
\(\chi_{10470}(3479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)
\(\chi_{10470}(3569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)
\(\chi_{10470}(4109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)
\(\chi_{10470}(4199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)
\(\chi_{10470}(4289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{69}{116}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)
\(\chi_{10470}(4319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{116}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)
\(\chi_{10470}(4439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)
\(\chi_{10470}(4499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)
\(\chi_{10470}(4529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)
\(\chi_{10470}(4589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{116}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)
\(\chi_{10470}(5519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)

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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	10470.cd
Modulus	$10470$
Conductor	$5235$
Order	$116$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(10470\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(5235\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(116\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 5235.ce	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);