LMFDB - Dirichlet character orbit 3905.ga

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3905, base_ring=CyclotomicField(140)) M = H._module chi = DirichletCharacter(H, M([35,84,90])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(97, 3905)) 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("3905.97"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3905$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3905$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$140$	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:	yes	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:	$\Q(\zeta_{140})$
Fixed field:	Number field defined by a degree 140 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{3905}(97,\cdot)$	$1$	$1$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3905}(168,\cdot)$	$1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3905}(247,\cdot)$	$1$	$1$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(323,\cdot)$	$1$	$1$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3905}(378,\cdot)$	$1$	$1$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3905}(467,\cdot)$	$1$	$1$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(477,\cdot)$	$1$	$1$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3905}(548,\cdot)$	$1$	$1$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3905}(807,\cdot)$	$1$	$1$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3905}(878,\cdot)$	$1$	$1$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3905}(962,\cdot)$	$1$	$1$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(1017,\cdot)$	$1$	$1$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(1028,\cdot)$	$1$	$1$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(1248,\cdot)$	$1$	$1$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(1258,\cdot)$	$1$	$1$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3905}(1312,\cdot)$	$1$	$1$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3905}(1532,\cdot)$	$1$	$1$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3905}(1588,\cdot)$	$1$	$1$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3905}(1743,\cdot)$	$1$	$1$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(1798,\cdot)$	$1$	$1$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(1897,\cdot)$	$1$	$1$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(2022,\cdot)$	$1$	$1$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3905}(2027,\cdot)$	$1$	$1$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3905}(2082,\cdot)$	$1$	$1$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3905}(2093,\cdot)$	$1$	$1$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3905}(2227,\cdot)$	$1$	$1$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(2242,\cdot)$	$1$	$1$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3905}(2313,\cdot)$	$1$	$1$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3905}(2678,\cdot)$	$1$	$1$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3905}(2732,\cdot)$	$1$	$1$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3905}(2737,\cdot)$	$1$	$1$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{4}{5}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{3905}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3905}(168,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3905}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3905}(378,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3905}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3905}(548,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3905}(807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3905}(878,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3905}(962,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(1017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(1028,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(1248,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(1258,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3905}(1312,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3905}(1532,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3905}(1588,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3905}(1743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(1798,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(1897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(2022,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3905}(2027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3905}(2082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3905}(2093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3905}(2227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(2242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3905}(2313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3905}(2678,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3905}(2732,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3905}(2737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)

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First 31 of 48 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	3905.ga
Modulus	$3905$
Conductor	$3905$
Order	$140$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3905\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3905\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(140\)	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:	yes	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);