LMFDB - Dirichlet character orbit 30345.jh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(272)) M = H._module chi = DirichletCharacter(H, M([0,68,0,213])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(22,30345)) 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:	$272$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1445.bg	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:	$\Q(\zeta_{272})$
Fixed field:	Number field defined by a degree 272 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{30345}(22,\cdot)$	$1$	$1$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{3}{272}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{37}{136}\right)$
$\chi_{30345}(337,\cdot)$	$1$	$1$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{49}{272}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{129}{136}\right)$
$\chi_{30345}(547,\cdot)$	$1$	$1$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{71}{272}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{105}{136}\right)$
$\chi_{30345}(568,\cdot)$	$1$	$1$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{253}{272}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{99}{272}\right)$	$e\left(\frac{73}{272}\right)$	$e\left(\frac{83}{136}\right)$
$\chi_{30345}(673,\cdot)$	$1$	$1$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{115}{136}\right)$
$\chi_{30345}(862,\cdot)$	$1$	$1$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{271}{272}\right)$	$e\left(\frac{133}{136}\right)$
$\chi_{30345}(1303,\cdot)$	$1$	$1$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{79}{272}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{47}{136}\right)$
$\chi_{30345}(1723,\cdot)$	$1$	$1$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{71}{272}\right)$	$e\left(\frac{165}{272}\right)$	$e\left(\frac{87}{136}\right)$
$\chi_{30345}(1807,\cdot)$	$1$	$1$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{259}{272}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{7}{272}\right)$	$e\left(\frac{21}{136}\right)$
$\chi_{30345}(2122,\cdot)$	$1$	$1$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{31}{272}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{65}{136}\right)$
$\chi_{30345}(2332,\cdot)$	$1$	$1$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{33}{136}\right)$
$\chi_{30345}(2353,\cdot)$	$1$	$1$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{91}{136}\right)$
$\chi_{30345}(2458,\cdot)$	$1$	$1$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{5}{272}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{203}{272}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{107}{136}\right)$
$\chi_{30345}(2647,\cdot)$	$1$	$1$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{251}{272}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{181}{272}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{13}{136}\right)$
$\chi_{30345}(3088,\cdot)$	$1$	$1$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{49}{272}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{31}{272}\right)$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{15}{136}\right)$
$\chi_{30345}(3592,\cdot)$	$1$	$1$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{243}{272}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{237}{272}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{5}{136}\right)$
$\chi_{30345}(3907,\cdot)$	$1$	$1$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{239}{272}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{227}{272}\right)$	$e\left(\frac{1}{136}\right)$
$\chi_{30345}(4117,\cdot)$	$1$	$1$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{199}{272}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{137}{272}\right)$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{97}{136}\right)$
$\chi_{30345}(4138,\cdot)$	$1$	$1$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{269}{272}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{259}{272}\right)$	$e\left(\frac{169}{272}\right)$	$e\left(\frac{99}{136}\right)$
$\chi_{30345}(4243,\cdot)$	$1$	$1$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{133}{272}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{99}{136}\right)$
$\chi_{30345}(4432,\cdot)$	$1$	$1$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{267}{272}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{191}{272}\right)$	$e\left(\frac{29}{136}\right)$
$\chi_{30345}(5293,\cdot)$	$1$	$1$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{185}{272}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{167}{272}\right)$	$e\left(\frac{5}{272}\right)$	$e\left(\frac{15}{136}\right)$
$\chi_{30345}(5377,\cdot)$	$1$	$1$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{227}{272}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{77}{272}\right)$	$e\left(\frac{87}{272}\right)$	$e\left(\frac{125}{136}\right)$
$\chi_{30345}(5692,\cdot)$	$1$	$1$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{175}{272}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{115}{272}\right)$	$e\left(\frac{73}{136}\right)$
$\chi_{30345}(5902,\cdot)$	$1$	$1$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{233}{272}\right)$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{25}{136}\right)$
$\chi_{30345}(5923,\cdot)$	$1$	$1$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{107}{136}\right)$
$\chi_{30345}(6028,\cdot)$	$1$	$1$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{43}{272}\right)$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{91}{136}\right)$
$\chi_{30345}(6217,\cdot)$	$1$	$1$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{229}{272}\right)$	$e\left(\frac{15}{272}\right)$	$e\left(\frac{45}{136}\right)$
$\chi_{30345}(6658,\cdot)$	$1$	$1$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{87}{136}\right)$
$\chi_{30345}(7078,\cdot)$	$1$	$1$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{215}{272}\right)$	$e\left(\frac{197}{272}\right)$	$e\left(\frac{47}{136}\right)$
$\chi_{30345}(7162,\cdot)$	$1$	$1$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{189}{272}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{109}{136}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{30345}(22,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{3}{272}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{37}{136}\right)\)
\(\chi_{30345}(337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{49}{272}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{129}{136}\right)\)
\(\chi_{30345}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{71}{272}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{105}{136}\right)\)
\(\chi_{30345}(568,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{253}{272}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{99}{272}\right)\)	\(e\left(\frac{73}{272}\right)\)	\(e\left(\frac{83}{136}\right)\)
\(\chi_{30345}(673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{115}{136}\right)\)
\(\chi_{30345}(862,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{271}{272}\right)\)	\(e\left(\frac{133}{136}\right)\)
\(\chi_{30345}(1303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{79}{272}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{47}{136}\right)\)
\(\chi_{30345}(1723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{71}{272}\right)\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{87}{136}\right)\)
\(\chi_{30345}(1807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{259}{272}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{7}{272}\right)\)	\(e\left(\frac{21}{136}\right)\)
\(\chi_{30345}(2122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{31}{272}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{65}{136}\right)\)
\(\chi_{30345}(2332,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{33}{136}\right)\)
\(\chi_{30345}(2353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{91}{136}\right)\)
\(\chi_{30345}(2458,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{5}{272}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{203}{272}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{107}{136}\right)\)
\(\chi_{30345}(2647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{251}{272}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{181}{272}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{13}{136}\right)\)
\(\chi_{30345}(3088,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{49}{272}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{31}{272}\right)\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{15}{136}\right)\)
\(\chi_{30345}(3592,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{243}{272}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{237}{272}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{5}{136}\right)\)
\(\chi_{30345}(3907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{239}{272}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{227}{272}\right)\)	\(e\left(\frac{1}{136}\right)\)
\(\chi_{30345}(4117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{199}{272}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{137}{272}\right)\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{97}{136}\right)\)
\(\chi_{30345}(4138,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{269}{272}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{259}{272}\right)\)	\(e\left(\frac{169}{272}\right)\)	\(e\left(\frac{99}{136}\right)\)
\(\chi_{30345}(4243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{133}{272}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{99}{136}\right)\)
\(\chi_{30345}(4432,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{267}{272}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{191}{272}\right)\)	\(e\left(\frac{29}{136}\right)\)
\(\chi_{30345}(5293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{185}{272}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{167}{272}\right)\)	\(e\left(\frac{5}{272}\right)\)	\(e\left(\frac{15}{136}\right)\)
\(\chi_{30345}(5377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{227}{272}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{77}{272}\right)\)	\(e\left(\frac{87}{272}\right)\)	\(e\left(\frac{125}{136}\right)\)
\(\chi_{30345}(5692,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{175}{272}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{115}{272}\right)\)	\(e\left(\frac{73}{136}\right)\)
\(\chi_{30345}(5902,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{233}{272}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{25}{136}\right)\)
\(\chi_{30345}(5923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{107}{136}\right)\)
\(\chi_{30345}(6028,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{43}{272}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{91}{136}\right)\)
\(\chi_{30345}(6217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{229}{272}\right)\)	\(e\left(\frac{15}{272}\right)\)	\(e\left(\frac{45}{136}\right)\)
\(\chi_{30345}(6658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{87}{136}\right)\)
\(\chi_{30345}(7078,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{215}{272}\right)\)	\(e\left(\frac{197}{272}\right)\)	\(e\left(\frac{47}{136}\right)\)
\(\chi_{30345}(7162,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{189}{272}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{109}{136}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 128 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.jh
Modulus	$30345$
Conductor	$1445$
Order	$272$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(30345\)
Conductor:	\(1445\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(272\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1445.bg	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)