LMFDB - Dirichlet character orbit 5415.bt

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5415, base_ring=CyclotomicField(76)) M = H._module chi = DirichletCharacter(H, M([0,19,10])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(37, 5415)) 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("5415.37"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5415$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1805$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$76$	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 1805.x	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:	$\Q(\zeta_{76})$	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 76 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{5415}(37,\cdot)$	$1$	$1$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{61}{76}\right)$
$\chi_{5415}(208,\cdot)$	$1$	$1$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{13}{76}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{3}{76}\right)$
$\chi_{5415}(322,\cdot)$	$1$	$1$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{53}{76}\right)$
$\chi_{5415}(493,\cdot)$	$1$	$1$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{71}{76}\right)$
$\chi_{5415}(607,\cdot)$	$1$	$1$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{45}{76}\right)$
$\chi_{5415}(778,\cdot)$	$1$	$1$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{63}{76}\right)$
$\chi_{5415}(892,\cdot)$	$1$	$1$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{37}{76}\right)$
$\chi_{5415}(1063,\cdot)$	$1$	$1$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{55}{76}\right)$
$\chi_{5415}(1177,\cdot)$	$1$	$1$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{29}{76}\right)$
$\chi_{5415}(1348,\cdot)$	$1$	$1$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{47}{76}\right)$
$\chi_{5415}(1462,\cdot)$	$1$	$1$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{21}{76}\right)$
$\chi_{5415}(1633,\cdot)$	$1$	$1$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{39}{76}\right)$
$\chi_{5415}(1747,\cdot)$	$1$	$1$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{13}{76}\right)$
$\chi_{5415}(1918,\cdot)$	$1$	$1$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{31}{76}\right)$
$\chi_{5415}(2032,\cdot)$	$1$	$1$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{5}{76}\right)$
$\chi_{5415}(2203,\cdot)$	$1$	$1$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{23}{76}\right)$
$\chi_{5415}(2317,\cdot)$	$1$	$1$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{73}{76}\right)$
$\chi_{5415}(2488,\cdot)$	$1$	$1$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{15}{76}\right)$
$\chi_{5415}(2602,\cdot)$	$1$	$1$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{65}{76}\right)$
$\chi_{5415}(2773,\cdot)$	$1$	$1$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{7}{76}\right)$
$\chi_{5415}(3058,\cdot)$	$1$	$1$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{75}{76}\right)$
$\chi_{5415}(3172,\cdot)$	$1$	$1$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{49}{76}\right)$
$\chi_{5415}(3343,\cdot)$	$1$	$1$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{67}{76}\right)$
$\chi_{5415}(3457,\cdot)$	$1$	$1$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{41}{76}\right)$
$\chi_{5415}(3628,\cdot)$	$1$	$1$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{59}{76}\right)$
$\chi_{5415}(3742,\cdot)$	$1$	$1$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{33}{76}\right)$
$\chi_{5415}(3913,\cdot)$	$1$	$1$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{51}{76}\right)$
$\chi_{5415}(4027,\cdot)$	$1$	$1$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{25}{76}\right)$
$\chi_{5415}(4198,\cdot)$	$1$	$1$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{13}{76}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{13}{76}\right)$	$e\left(\frac{43}{76}\right)$
$\chi_{5415}(4312,\cdot)$	$1$	$1$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{17}{76}\right)$
$\chi_{5415}(4483,\cdot)$	$1$	$1$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{35}{76}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(22\)
\(\chi_{5415}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{61}{76}\right)\)
\(\chi_{5415}(208,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{13}{76}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{3}{76}\right)\)
\(\chi_{5415}(322,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{53}{76}\right)\)
\(\chi_{5415}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{71}{76}\right)\)
\(\chi_{5415}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{45}{76}\right)\)
\(\chi_{5415}(778,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{63}{76}\right)\)
\(\chi_{5415}(892,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{37}{76}\right)\)
\(\chi_{5415}(1063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{55}{76}\right)\)
\(\chi_{5415}(1177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{29}{76}\right)\)
\(\chi_{5415}(1348,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{47}{76}\right)\)
\(\chi_{5415}(1462,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{21}{76}\right)\)
\(\chi_{5415}(1633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{39}{76}\right)\)
\(\chi_{5415}(1747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{13}{76}\right)\)
\(\chi_{5415}(1918,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{31}{76}\right)\)
\(\chi_{5415}(2032,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{5}{76}\right)\)
\(\chi_{5415}(2203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{23}{76}\right)\)
\(\chi_{5415}(2317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{73}{76}\right)\)
\(\chi_{5415}(2488,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{15}{76}\right)\)
\(\chi_{5415}(2602,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{65}{76}\right)\)
\(\chi_{5415}(2773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{7}{76}\right)\)
\(\chi_{5415}(3058,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{75}{76}\right)\)
\(\chi_{5415}(3172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{49}{76}\right)\)
\(\chi_{5415}(3343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{67}{76}\right)\)
\(\chi_{5415}(3457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{41}{76}\right)\)
\(\chi_{5415}(3628,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{59}{76}\right)\)
\(\chi_{5415}(3742,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{33}{76}\right)\)
\(\chi_{5415}(3913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{51}{76}\right)\)
\(\chi_{5415}(4027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{25}{76}\right)\)
\(\chi_{5415}(4198,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{13}{76}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{13}{76}\right)\)	\(e\left(\frac{43}{76}\right)\)
\(\chi_{5415}(4312,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{17}{76}\right)\)
\(\chi_{5415}(4483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{35}{76}\right)\)

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First 31 of 36 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	5415.bt
Modulus	$5415$
Conductor	$1805$
Order	$76$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(5415\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1805\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(76\)	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 1805.x	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);