LMFDB - Dirichlet character orbit 30345.im

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(204)) M = H._module chi = DirichletCharacter(H, M([102,51,136,132])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(137,30345)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$30345$
Conductor:	$30345$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$204$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{204})$
Fixed field:	Number field defined by a degree 204 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{30345}(137,\cdot)$	$1$	$1$	$e\left(\frac{5}{204}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{61}{102}\right)$
$\chi_{30345}(443,\cdot)$	$1$	$1$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{41}{102}\right)$
$\chi_{30345}(1208,\cdot)$	$1$	$1$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{25}{102}\right)$
$\chi_{30345}(1922,\cdot)$	$1$	$1$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{1}{102}\right)$
$\chi_{30345}(2228,\cdot)$	$1$	$1$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{83}{102}\right)$
$\chi_{30345}(2942,\cdot)$	$1$	$1$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{59}{102}\right)$
$\chi_{30345}(2993,\cdot)$	$1$	$1$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{67}{102}\right)$
$\chi_{30345}(3707,\cdot)$	$1$	$1$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{43}{102}\right)$
$\chi_{30345}(4013,\cdot)$	$1$	$1$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{23}{102}\right)$
$\chi_{30345}(4727,\cdot)$	$1$	$1$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{101}{102}\right)$
$\chi_{30345}(4778,\cdot)$	$1$	$1$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{7}{102}\right)$
$\chi_{30345}(5798,\cdot)$	$1$	$1$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{65}{102}\right)$
$\chi_{30345}(6512,\cdot)$	$1$	$1$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{41}{102}\right)$
$\chi_{30345}(6563,\cdot)$	$1$	$1$	$e\left(\frac{203}{204}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{5}{204}\right)$	$e\left(\frac{49}{102}\right)$
$\chi_{30345}(7277,\cdot)$	$1$	$1$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{25}{102}\right)$
$\chi_{30345}(7583,\cdot)$	$1$	$1$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{5}{102}\right)$
$\chi_{30345}(8297,\cdot)$	$1$	$1$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{83}{102}\right)$
$\chi_{30345}(8348,\cdot)$	$1$	$1$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{91}{102}\right)$
$\chi_{30345}(9062,\cdot)$	$1$	$1$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{67}{102}\right)$
$\chi_{30345}(9368,\cdot)$	$1$	$1$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{47}{102}\right)$
$\chi_{30345}(10082,\cdot)$	$1$	$1$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{23}{102}\right)$
$\chi_{30345}(10133,\cdot)$	$1$	$1$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{31}{102}\right)$
$\chi_{30345}(10847,\cdot)$	$1$	$1$	$e\left(\frac{29}{204}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{7}{102}\right)$
$\chi_{30345}(11153,\cdot)$	$1$	$1$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{89}{102}\right)$
$\chi_{30345}(11867,\cdot)$	$1$	$1$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{65}{102}\right)$
$\chi_{30345}(11918,\cdot)$	$1$	$1$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{73}{102}\right)$
$\chi_{30345}(12632,\cdot)$	$1$	$1$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{49}{102}\right)$
$\chi_{30345}(12938,\cdot)$	$1$	$1$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{29}{102}\right)$
$\chi_{30345}(13652,\cdot)$	$1$	$1$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{5}{102}\right)$
$\chi_{30345}(13703,\cdot)$	$1$	$1$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{13}{102}\right)$
$\chi_{30345}(14417,\cdot)$	$1$	$1$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{91}{102}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{30345}(137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{204}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)
\(\chi_{30345}(443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)
\(\chi_{30345}(1208,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{25}{102}\right)\)
\(\chi_{30345}(1922,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{1}{102}\right)\)
\(\chi_{30345}(2228,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{83}{102}\right)\)
\(\chi_{30345}(2942,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)
\(\chi_{30345}(2993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{67}{102}\right)\)
\(\chi_{30345}(3707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{43}{102}\right)\)
\(\chi_{30345}(4013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{23}{102}\right)\)
\(\chi_{30345}(4727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{101}{102}\right)\)
\(\chi_{30345}(4778,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)
\(\chi_{30345}(5798,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{65}{102}\right)\)
\(\chi_{30345}(6512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)
\(\chi_{30345}(6563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{204}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{5}{204}\right)\)	\(e\left(\frac{49}{102}\right)\)
\(\chi_{30345}(7277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{25}{102}\right)\)
\(\chi_{30345}(7583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{5}{102}\right)\)
\(\chi_{30345}(8297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{83}{102}\right)\)
\(\chi_{30345}(8348,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{91}{102}\right)\)
\(\chi_{30345}(9062,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{67}{102}\right)\)
\(\chi_{30345}(9368,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{47}{102}\right)\)
\(\chi_{30345}(10082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{23}{102}\right)\)
\(\chi_{30345}(10133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{31}{102}\right)\)
\(\chi_{30345}(10847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{204}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)
\(\chi_{30345}(11153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)
\(\chi_{30345}(11867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{65}{102}\right)\)
\(\chi_{30345}(11918,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{73}{102}\right)\)
\(\chi_{30345}(12632,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{49}{102}\right)\)
\(\chi_{30345}(12938,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{29}{102}\right)\)
\(\chi_{30345}(13652,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{5}{102}\right)\)
\(\chi_{30345}(13703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{13}{102}\right)\)
\(\chi_{30345}(14417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{91}{102}\right)\)

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First 31 of 64 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.im
Modulus	$30345$
Conductor	$30345$
Order	$204$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(30345\)
Conductor:	\(30345\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(204\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)