LMFDB - Dirichlet character orbit 30345.gk

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(68)) M = H._module chi = DirichletCharacter(H, M([0,17,34,48])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(307,30345)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$30345$
Conductor:	$10115$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$68$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 10115.dj	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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{30345}(307,\cdot)$	$1$	$1$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{30345}(1378,\cdot)$	$1$	$1$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{30345}(2092,\cdot)$	$1$	$1$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{30345}(3163,\cdot)$	$1$	$1$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{30345}(3877,\cdot)$	$1$	$1$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{30345}(4948,\cdot)$	$1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{15}{34}\right)$
$\chi_{30345}(5662,\cdot)$	$1$	$1$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{7}{34}\right)$
$\chi_{30345}(6733,\cdot)$	$1$	$1$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{30345}(7447,\cdot)$	$1$	$1$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{30345}(8518,\cdot)$	$1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{30345}(9232,\cdot)$	$1$	$1$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{30345}(10303,\cdot)$	$1$	$1$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{23}{34}\right)$
$\chi_{30345}(11017,\cdot)$	$1$	$1$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{15}{34}\right)$
$\chi_{30345}(12088,\cdot)$	$1$	$1$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{30345}(12802,\cdot)$	$1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{30345}(14587,\cdot)$	$1$	$1$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{30345}(15658,\cdot)$	$1$	$1$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{30345}(16372,\cdot)$	$1$	$1$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{23}{34}\right)$
$\chi_{30345}(17443,\cdot)$	$1$	$1$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{30345}(18157,\cdot)$	$1$	$1$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{30345}(19228,\cdot)$	$1$	$1$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{30345}(21013,\cdot)$	$1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{5}{34}\right)$
$\chi_{30345}(21727,\cdot)$	$1$	$1$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{30345}(22798,\cdot)$	$1$	$1$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{30345}(23512,\cdot)$	$1$	$1$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{30345}(24583,\cdot)$	$1$	$1$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{30345}(25297,\cdot)$	$1$	$1$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{30345}(26368,\cdot)$	$1$	$1$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{30345}(27082,\cdot)$	$1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{5}{34}\right)$
$\chi_{30345}(28153,\cdot)$	$1$	$1$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{30345}(28867,\cdot)$	$1$	$1$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{19}{34}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{30345}(307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{30345}(1378,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{30345}(2092,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{30345}(3163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{30345}(3877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{30345}(4948,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)
\(\chi_{30345}(5662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)
\(\chi_{30345}(6733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{30345}(7447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{30345}(8518,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{30345}(9232,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{30345}(10303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{30345}(11017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)
\(\chi_{30345}(12088,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{30345}(12802,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{30345}(14587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{30345}(15658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{30345}(16372,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{30345}(17443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{30345}(18157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{30345}(19228,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{30345}(21013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)
\(\chi_{30345}(21727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{30345}(22798,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{30345}(23512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{30345}(24583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{30345}(25297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{30345}(26368,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{30345}(27082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)
\(\chi_{30345}(28153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{30345}(28867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)

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Basic properties

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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.gk
Modulus	$30345$
Conductor	$10115$
Order	$68$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(30345\)
Conductor:	\(10115\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(68\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 10115.dj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)