LMFDB - Dirichlet character orbit 1338.i

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(74)) M = H._module chi = DirichletCharacter(H, M([0,70])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,1338)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1338$
Conductor:	$223$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$37$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 223.e	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{37})$
Fixed field:	Number field defined by a degree 37 polynomial

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{1338}(7,\cdot)$	$1$	$1$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{21}{37}\right)$
$\chi_{1338}(49,\cdot)$	$1$	$1$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{5}{37}\right)$
$\chi_{1338}(115,\cdot)$	$1$	$1$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{3}{37}\right)$
$\chi_{1338}(169,\cdot)$	$1$	$1$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{22}{37}\right)$
$\chi_{1338}(253,\cdot)$	$1$	$1$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{27}{37}\right)$
$\chi_{1338}(283,\cdot)$	$1$	$1$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{8}{37}\right)$
$\chi_{1338}(289,\cdot)$	$1$	$1$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{14}{37}\right)$
$\chi_{1338}(343,\cdot)$	$1$	$1$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{26}{37}\right)$
$\chi_{1338}(355,\cdot)$	$1$	$1$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{32}{37}\right)$
$\chi_{1338}(433,\cdot)$	$1$	$1$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{11}{37}\right)$
$\chi_{1338}(463,\cdot)$	$1$	$1$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{7}{37}\right)$
$\chi_{1338}(487,\cdot)$	$1$	$1$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{13}{37}\right)$
$\chi_{1338}(565,\cdot)$	$1$	$1$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{28}{37}\right)$
$\chi_{1338}(643,\cdot)$	$1$	$1$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{29}{37}\right)$
$\chi_{1338}(673,\cdot)$	$1$	$1$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{36}{37}\right)$
$\chi_{1338}(685,\cdot)$	$1$	$1$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{35}{37}\right)$
$\chi_{1338}(697,\cdot)$	$1$	$1$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{20}{37}\right)$
$\chi_{1338}(703,\cdot)$	$1$	$1$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{25}{37}\right)$
$\chi_{1338}(733,\cdot)$	$1$	$1$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{34}{37}\right)$
$\chi_{1338}(751,\cdot)$	$1$	$1$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{31}{37}\right)$
$\chi_{1338}(781,\cdot)$	$1$	$1$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{19}{37}\right)$
$\chi_{1338}(805,\cdot)$	$1$	$1$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{24}{37}\right)$
$\chi_{1338}(865,\cdot)$	$1$	$1$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{4}{37}\right)$
$\chi_{1338}(907,\cdot)$	$1$	$1$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{9}{37}\right)$
$\chi_{1338}(925,\cdot)$	$1$	$1$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{33}{37}\right)$
$\chi_{1338}(997,\cdot)$	$1$	$1$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{30}{37}\right)$
$\chi_{1338}(1063,\cdot)$	$1$	$1$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{10}{37}\right)$
$\chi_{1338}(1117,\cdot)$	$1$	$1$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{18}{37}\right)$
$\chi_{1338}(1123,\cdot)$	$1$	$1$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{17}{37}\right)$
$\chi_{1338}(1129,\cdot)$	$1$	$1$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{2}{37}\right)$
$\chi_{1338}(1147,\cdot)$	$1$	$1$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{16}{37}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{1338}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)
\(\chi_{1338}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)
\(\chi_{1338}(115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)
\(\chi_{1338}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)
\(\chi_{1338}(253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)
\(\chi_{1338}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)
\(\chi_{1338}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)
\(\chi_{1338}(343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)
\(\chi_{1338}(355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)
\(\chi_{1338}(433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)
\(\chi_{1338}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)
\(\chi_{1338}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)
\(\chi_{1338}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)
\(\chi_{1338}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)
\(\chi_{1338}(673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)
\(\chi_{1338}(685,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)
\(\chi_{1338}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)
\(\chi_{1338}(703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)
\(\chi_{1338}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)
\(\chi_{1338}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)
\(\chi_{1338}(781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)
\(\chi_{1338}(805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)
\(\chi_{1338}(865,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)
\(\chi_{1338}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)
\(\chi_{1338}(925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)
\(\chi_{1338}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)
\(\chi_{1338}(1063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)
\(\chi_{1338}(1117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)
\(\chi_{1338}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)
\(\chi_{1338}(1129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)
\(\chi_{1338}(1147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)

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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	1338.i
Modulus	$1338$
Conductor	$223$
Order	$37$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(1338\)
Conductor:	\(223\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(37\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 223.e	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)