LMFDB - Dirichlet character orbit 30345.jz

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(408)) M = H._module chi = DirichletCharacter(H, M([0,306,68,399])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(178,30345)) 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:	$408$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 10115.ey	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:	$\Q(\zeta_{408})$
Fixed field:	Number field defined by a degree 408 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{30345}(178,\cdot)$	$1$	$1$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{65}{408}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{5}{204}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{271}{408}\right)$	$e\left(\frac{65}{204}\right)$
$\chi_{30345}(682,\cdot)$	$1$	$1$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{179}{408}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{37}{408}\right)$	$e\left(\frac{179}{204}\right)$
$\chi_{30345}(808,\cdot)$	$1$	$1$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{379}{408}\right)$	$e\left(\frac{185}{204}\right)$
$\chi_{30345}(943,\cdot)$	$1$	$1$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{265}{408}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{193}{204}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{383}{408}\right)$	$e\left(\frac{61}{204}\right)$
$\chi_{30345}(1447,\cdot)$	$1$	$1$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{163}{204}\right)$
$\chi_{30345}(1573,\cdot)$	$1$	$1$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{131}{408}\right)$	$e\left(\frac{121}{204}\right)$
$\chi_{30345}(1732,\cdot)$	$1$	$1$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{95}{408}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{145}{408}\right)$	$e\left(\frac{95}{204}\right)$
$\chi_{30345}(1963,\cdot)$	$1$	$1$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{305}{408}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{101}{204}\right)$
$\chi_{30345}(2497,\cdot)$	$1$	$1$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{247}{408}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{377}{408}\right)$	$e\left(\frac{43}{204}\right)$
$\chi_{30345}(2593,\cdot)$	$1$	$1$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{149}{408}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{149}{204}\right)$
$\chi_{30345}(2728,\cdot)$	$1$	$1$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{97}{408}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{191}{408}\right)$	$e\left(\frac{97}{204}\right)$
$\chi_{30345}(3232,\cdot)$	$1$	$1$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{307}{408}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{103}{204}\right)$
$\chi_{30345}(3517,\cdot)$	$1$	$1$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{359}{408}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{97}{408}\right)$	$e\left(\frac{155}{204}\right)$
$\chi_{30345}(3748,\cdot)$	$1$	$1$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{137}{408}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{295}{408}\right)$	$e\left(\frac{137}{204}\right)$
$\chi_{30345}(4252,\cdot)$	$1$	$1$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{133}{408}\right)$	$e\left(\frac{59}{204}\right)$
$\chi_{30345}(4282,\cdot)$	$1$	$1$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{329}{408}\right)$	$e\left(\frac{103}{204}\right)$
$\chi_{30345}(4378,\cdot)$	$1$	$1$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{317}{408}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{355}{408}\right)$	$e\left(\frac{113}{204}\right)$
$\chi_{30345}(4513,\cdot)$	$1$	$1$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{133}{204}\right)$
$\chi_{30345}(5017,\cdot)$	$1$	$1$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{43}{408}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{173}{408}\right)$	$e\left(\frac{43}{204}\right)$
$\chi_{30345}(5143,\cdot)$	$1$	$1$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{253}{408}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{107}{408}\right)$	$e\left(\frac{49}{204}\right)$
$\chi_{30345}(5302,\cdot)$	$1$	$1$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{215}{408}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{95}{204}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{49}{408}\right)$	$e\left(\frac{11}{204}\right)$
$\chi_{30345}(5533,\cdot)$	$1$	$1$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{377}{408}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{29}{204}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{173}{204}\right)$
$\chi_{30345}(6037,\cdot)$	$1$	$1$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{203}{204}\right)$
$\chi_{30345}(6067,\cdot)$	$1$	$1$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{367}{408}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{281}{408}\right)$	$e\left(\frac{163}{204}\right)$
$\chi_{30345}(6163,\cdot)$	$1$	$1$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{77}{204}\right)$
$\chi_{30345}(6298,\cdot)$	$1$	$1$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{169}{408}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{215}{408}\right)$	$e\left(\frac{169}{204}\right)$
$\chi_{30345}(6928,\cdot)$	$1$	$1$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{13}{408}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{299}{408}\right)$	$e\left(\frac{13}{204}\right)$
$\chi_{30345}(7087,\cdot)$	$1$	$1$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{71}{408}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{1}{408}\right)$	$e\left(\frac{71}{204}\right)$
$\chi_{30345}(7318,\cdot)$	$1$	$1$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{209}{408}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{319}{408}\right)$	$e\left(\frac{5}{204}\right)$
$\chi_{30345}(7822,\cdot)$	$1$	$1$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{347}{408}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{229}{408}\right)$	$e\left(\frac{143}{204}\right)$
$\chi_{30345}(7852,\cdot)$	$1$	$1$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{223}{408}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{233}{408}\right)$	$e\left(\frac{19}{204}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{30345}(178,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{65}{408}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{5}{204}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{271}{408}\right)\)	\(e\left(\frac{65}{204}\right)\)
\(\chi_{30345}(682,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{179}{408}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{37}{408}\right)\)	\(e\left(\frac{179}{204}\right)\)
\(\chi_{30345}(808,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{379}{408}\right)\)	\(e\left(\frac{185}{204}\right)\)
\(\chi_{30345}(943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{265}{408}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{193}{204}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{383}{408}\right)\)	\(e\left(\frac{61}{204}\right)\)
\(\chi_{30345}(1447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{163}{204}\right)\)
\(\chi_{30345}(1573,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{131}{408}\right)\)	\(e\left(\frac{121}{204}\right)\)
\(\chi_{30345}(1732,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{95}{408}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{145}{408}\right)\)	\(e\left(\frac{95}{204}\right)\)
\(\chi_{30345}(1963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{305}{408}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{101}{204}\right)\)
\(\chi_{30345}(2497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{247}{408}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{377}{408}\right)\)	\(e\left(\frac{43}{204}\right)\)
\(\chi_{30345}(2593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{149}{408}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{149}{204}\right)\)
\(\chi_{30345}(2728,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{97}{408}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{191}{408}\right)\)	\(e\left(\frac{97}{204}\right)\)
\(\chi_{30345}(3232,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{307}{408}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{103}{204}\right)\)
\(\chi_{30345}(3517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{359}{408}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{97}{408}\right)\)	\(e\left(\frac{155}{204}\right)\)
\(\chi_{30345}(3748,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{137}{408}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{295}{408}\right)\)	\(e\left(\frac{137}{204}\right)\)
\(\chi_{30345}(4252,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{133}{408}\right)\)	\(e\left(\frac{59}{204}\right)\)
\(\chi_{30345}(4282,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{329}{408}\right)\)	\(e\left(\frac{103}{204}\right)\)
\(\chi_{30345}(4378,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{317}{408}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{355}{408}\right)\)	\(e\left(\frac{113}{204}\right)\)
\(\chi_{30345}(4513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{133}{204}\right)\)
\(\chi_{30345}(5017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{43}{408}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{173}{408}\right)\)	\(e\left(\frac{43}{204}\right)\)
\(\chi_{30345}(5143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{253}{408}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{107}{408}\right)\)	\(e\left(\frac{49}{204}\right)\)
\(\chi_{30345}(5302,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{215}{408}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{95}{204}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{49}{408}\right)\)	\(e\left(\frac{11}{204}\right)\)
\(\chi_{30345}(5533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{377}{408}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{29}{204}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{173}{204}\right)\)
\(\chi_{30345}(6037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{203}{204}\right)\)
\(\chi_{30345}(6067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{367}{408}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{281}{408}\right)\)	\(e\left(\frac{163}{204}\right)\)
\(\chi_{30345}(6163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{77}{204}\right)\)
\(\chi_{30345}(6298,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{169}{408}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{215}{408}\right)\)	\(e\left(\frac{169}{204}\right)\)
\(\chi_{30345}(6928,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{13}{408}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{299}{408}\right)\)	\(e\left(\frac{13}{204}\right)\)
\(\chi_{30345}(7087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{71}{408}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{1}{408}\right)\)	\(e\left(\frac{71}{204}\right)\)
\(\chi_{30345}(7318,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{209}{408}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{319}{408}\right)\)	\(e\left(\frac{5}{204}\right)\)
\(\chi_{30345}(7822,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{347}{408}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{229}{408}\right)\)	\(e\left(\frac{143}{204}\right)\)
\(\chi_{30345}(7852,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{223}{408}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{233}{408}\right)\)	\(e\left(\frac{19}{204}\right)\)

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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.jz
Modulus	$30345$
Conductor	$10115$
Order	$408$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(30345\)
Conductor:	\(10115\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(408\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 10115.ey	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)