LMFDB - Dirichlet character orbit 30345.gi

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(68)) M = H._module chi = DirichletCharacter(H, M([0,34,0,13])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(64,30345)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$30345$
Conductor:	$1445$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$68$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1445.w	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:	$\Q(\zeta_{68})$
Fixed field:	Number field defined by a degree 68 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{30345}(64,\cdot)$	$1$	$1$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{30345}(1534,\cdot)$	$1$	$1$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{30345}(1849,\cdot)$	$1$	$1$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{15}{34}\right)$
$\chi_{30345}(3319,\cdot)$	$1$	$1$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{7}{34}\right)$
$\chi_{30345}(3634,\cdot)$	$1$	$1$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{30345}(5104,\cdot)$	$1$	$1$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{30345}(5419,\cdot)$	$1$	$1$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{30345}(6889,\cdot)$	$1$	$1$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{30345}(7204,\cdot)$	$1$	$1$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{30345}(8674,\cdot)$	$1$	$1$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{30345}(8989,\cdot)$	$1$	$1$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{30345}(10459,\cdot)$	$1$	$1$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{30345}(10774,\cdot)$	$1$	$1$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{23}{34}\right)$
$\chi_{30345}(12244,\cdot)$	$1$	$1$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{30345}(12559,\cdot)$	$1$	$1$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{30345}(14029,\cdot)$	$1$	$1$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{30345}(14344,\cdot)$	$1$	$1$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{30345}(15814,\cdot)$	$1$	$1$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{23}{34}\right)$
$\chi_{30345}(16129,\cdot)$	$1$	$1$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{30345}(17599,\cdot)$	$1$	$1$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{30345}(17914,\cdot)$	$1$	$1$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{30345}(19384,\cdot)$	$1$	$1$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{30345}(19699,\cdot)$	$1$	$1$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{30345}(21169,\cdot)$	$1$	$1$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{30345}(21484,\cdot)$	$1$	$1$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{30345}(22954,\cdot)$	$1$	$1$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{30345}(23269,\cdot)$	$1$	$1$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{7}{34}\right)$
$\chi_{30345}(24739,\cdot)$	$1$	$1$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{15}{34}\right)$
$\chi_{30345}(25054,\cdot)$	$1$	$1$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{30345}(26524,\cdot)$	$1$	$1$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{30345}(28309,\cdot)$	$1$	$1$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{5}{34}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{30345}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{30345}(1534,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{30345}(1849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)
\(\chi_{30345}(3319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)
\(\chi_{30345}(3634,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{30345}(5104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{30345}(5419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{30345}(6889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{30345}(7204,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{30345}(8674,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{30345}(8989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{30345}(10459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{30345}(10774,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{30345}(12244,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{30345}(12559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{30345}(14029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{30345}(14344,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{30345}(15814,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{30345}(16129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{30345}(17599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{30345}(17914,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{30345}(19384,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{30345}(19699,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{30345}(21169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{30345}(21484,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{30345}(22954,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{30345}(23269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)
\(\chi_{30345}(24739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)
\(\chi_{30345}(25054,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{30345}(26524,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{30345}(28309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 32 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	30345.gi
Modulus	$30345$
Conductor	$1445$
Order	$68$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(30345\)
Conductor:	\(1445\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(68\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1445.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)