LMFDB - Dirichlet character orbit 2900.ci

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2900, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([0,28,50])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(81,2900)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2900$
Conductor:	$725$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$35$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 725.be	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:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 35 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{2900}(81,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{2900}(141,\cdot)$	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{2900}(161,\cdot)$	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{2900}(181,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{2900}(281,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{2900}(661,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{2900}(721,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{2900}(741,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{2900}(761,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{2900}(861,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{2900}(981,\cdot)$	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{2900}(1241,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{2900}(1321,\cdot)$	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{2900}(1341,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{2900}(1441,\cdot)$	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{2900}(1561,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{2900}(1821,\cdot)$	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{2900}(1881,\cdot)$	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{2900}(1921,\cdot)$	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{2900}(2021,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{2900}(2141,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{2900}(2461,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{2900}(2481,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{2900}(2721,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{31}{35}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{2900}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{2900}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{2900}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{2900}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{2900}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{2900}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{2900}(721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{2900}(741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{2900}(761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{2900}(861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{2900}(981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{2900}(1241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{2900}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{2900}(1341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{2900}(1441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{2900}(1561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{2900}(1821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{2900}(1881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{2900}(1921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{2900}(2021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{2900}(2141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{2900}(2461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{2900}(2481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{2900}(2721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	2900.ci
Modulus	$2900$
Conductor	$725$
Order	$35$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2900\)
Conductor:	\(725\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(35\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 725.be	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)