LMFDB - Dirichlet character orbit 6762.bw

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6762, base_ring=CyclotomicField(154)) M = H._module chi = DirichletCharacter(H, M([0,44,56])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(85, 6762)) 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("6762.85"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$6762$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1127$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$77$	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 1127.y	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:	$\Q(\zeta_{77})$	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 77 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 60 characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$37$	$41$
$\chi_{6762}(85,\cdot)$	$1$	$1$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{50}{77}\right)$
$\chi_{6762}(127,\cdot)$	$1$	$1$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{26}{77}\right)$
$\chi_{6762}(169,\cdot)$	$1$	$1$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{65}{77}\right)$
$\chi_{6762}(211,\cdot)$	$1$	$1$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{69}{77}\right)$
$\chi_{6762}(463,\cdot)$	$1$	$1$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{46}{77}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{23}{77}\right)$
$\chi_{6762}(547,\cdot)$	$1$	$1$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{31}{77}\right)$
$\chi_{6762}(673,\cdot)$	$1$	$1$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{8}{77}\right)$
$\chi_{6762}(715,\cdot)$	$1$	$1$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{40}{77}\right)$
$\chi_{6762}(841,\cdot)$	$1$	$1$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{38}{77}\right)$
$\chi_{6762}(1051,\cdot)$	$1$	$1$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{72}{77}\right)$
$\chi_{6762}(1093,\cdot)$	$1$	$1$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{48}{77}\right)$
$\chi_{6762}(1135,\cdot)$	$1$	$1$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{10}{77}\right)$
$\chi_{6762}(1429,\cdot)$	$1$	$1$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{45}{77}\right)$
$\chi_{6762}(1513,\cdot)$	$1$	$1$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{53}{77}\right)$
$\chi_{6762}(1639,\cdot)$	$1$	$1$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{30}{77}\right)$
$\chi_{6762}(1681,\cdot)$	$1$	$1$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{62}{77}\right)$
$\chi_{6762}(1807,\cdot)$	$1$	$1$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{60}{77}\right)$
$\chi_{6762}(1849,\cdot)$	$1$	$1$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{57}{77}\right)$
$\chi_{6762}(2017,\cdot)$	$1$	$1$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{17}{77}\right)$
$\chi_{6762}(2101,\cdot)$	$1$	$1$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{32}{77}\right)$
$\chi_{6762}(2143,\cdot)$	$1$	$1$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{36}{77}\right)$
$\chi_{6762}(2395,\cdot)$	$1$	$1$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{67}{77}\right)$
$\chi_{6762}(2479,\cdot)$	$1$	$1$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{75}{77}\right)$
$\chi_{6762}(2605,\cdot)$	$1$	$1$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{52}{77}\right)$
$\chi_{6762}(2773,\cdot)$	$1$	$1$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{77}\right)$	$e\left(\frac{5}{77}\right)$
$\chi_{6762}(2815,\cdot)$	$1$	$1$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{2}{77}\right)$
$\chi_{6762}(2983,\cdot)$	$1$	$1$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{39}{77}\right)$
$\chi_{6762}(3025,\cdot)$	$1$	$1$	$e\left(\frac{15}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{15}{77}\right)$
$\chi_{6762}(3067,\cdot)$	$1$	$1$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{46}{77}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{54}{77}\right)$
$\chi_{6762}(3109,\cdot)$	$1$	$1$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{58}{77}\right)$
$\chi_{6762}(3361,\cdot)$	$1$	$1$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{12}{77}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{6762}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{50}{77}\right)\)
\(\chi_{6762}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{26}{77}\right)\)
\(\chi_{6762}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{65}{77}\right)\)
\(\chi_{6762}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{69}{77}\right)\)
\(\chi_{6762}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{46}{77}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{23}{77}\right)\)
\(\chi_{6762}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)
\(\chi_{6762}(673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)
\(\chi_{6762}(715,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)
\(\chi_{6762}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)
\(\chi_{6762}(1051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{72}{77}\right)\)
\(\chi_{6762}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)
\(\chi_{6762}(1135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{10}{77}\right)\)
\(\chi_{6762}(1429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)
\(\chi_{6762}(1513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)
\(\chi_{6762}(1639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)
\(\chi_{6762}(1681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)
\(\chi_{6762}(1807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{60}{77}\right)\)
\(\chi_{6762}(1849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{57}{77}\right)\)
\(\chi_{6762}(2017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)
\(\chi_{6762}(2101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)
\(\chi_{6762}(2143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)
\(\chi_{6762}(2395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)
\(\chi_{6762}(2479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{75}{77}\right)\)
\(\chi_{6762}(2605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{52}{77}\right)\)
\(\chi_{6762}(2773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{77}\right)\)	\(e\left(\frac{5}{77}\right)\)
\(\chi_{6762}(2815,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{2}{77}\right)\)
\(\chi_{6762}(2983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{39}{77}\right)\)
\(\chi_{6762}(3025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{15}{77}\right)\)
\(\chi_{6762}(3067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{46}{77}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{54}{77}\right)\)
\(\chi_{6762}(3109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{58}{77}\right)\)
\(\chi_{6762}(3361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)

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First 31 of 60 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	6762.bw
Modulus	$6762$
Conductor	$1127$
Order	$77$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(6762\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1127\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(77\)	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 1127.y	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);