LMFDB - Dirichlet character orbit 30345.kd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(408)) M = H._module chi = DirichletCharacter(H, M([204,0,340,171])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(26,30345)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$30345$
Conductor:	$6069$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$408$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 6069.cv	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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{30345}(26,\cdot)$	$1$	$1$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{193}{408}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{91}{204}\right)$
$\chi_{30345}(206,\cdot)$	$1$	$1$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{31}{408}\right)$	$e\left(\frac{161}{204}\right)$
$\chi_{30345}(236,\cdot)$	$1$	$1$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{307}{408}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{227}{408}\right)$	$e\left(\frac{1}{204}\right)$
$\chi_{30345}(416,\cdot)$	$1$	$1$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{29}{408}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{157}{408}\right)$	$e\left(\frac{131}{204}\right)$
$\chi_{30345}(971,\cdot)$	$1$	$1$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{247}{408}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{71}{408}\right)$	$e\left(\frac{145}{204}\right)$
$\chi_{30345}(1181,\cdot)$	$1$	$1$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{229}{408}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{269}{408}\right)$	$e\left(\frac{127}{204}\right)$
$\chi_{30345}(1256,\cdot)$	$1$	$1$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{11}{408}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{355}{408}\right)$	$e\left(\frac{113}{204}\right)$
$\chi_{30345}(1811,\cdot)$	$1$	$1$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{361}{408}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{41}{408}\right)$	$e\left(\frac{55}{204}\right)$
$\chi_{30345}(1991,\cdot)$	$1$	$1$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{101}{204}\right)$
$\chi_{30345}(2021,\cdot)$	$1$	$1$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{193}{204}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{179}{408}\right)$	$e\left(\frac{61}{204}\right)$
$\chi_{30345}(2201,\cdot)$	$1$	$1$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{269}{408}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{373}{408}\right)$	$e\left(\frac{167}{204}\right)$
$\chi_{30345}(2831,\cdot)$	$1$	$1$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{185}{408}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{73}{408}\right)$	$e\left(\frac{83}{204}\right)$
$\chi_{30345}(2966,\cdot)$	$1$	$1$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{61}{408}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{163}{204}\right)$
$\chi_{30345}(3041,\cdot)$	$1$	$1$	$e\left(\frac{5}{204}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{275}{408}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{29}{204}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{307}{408}\right)$	$e\left(\frac{173}{204}\right)$
$\chi_{30345}(3596,\cdot)$	$1$	$1$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{121}{408}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{233}{408}\right)$	$e\left(\frac{19}{204}\right)$
$\chi_{30345}(3776,\cdot)$	$1$	$1$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{143}{408}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{127}{408}\right)$	$e\left(\frac{41}{204}\right)$
$\chi_{30345}(3806,\cdot)$	$1$	$1$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{19}{408}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{131}{408}\right)$	$e\left(\frac{121}{204}\right)$
$\chi_{30345}(3986,\cdot)$	$1$	$1$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{101}{408}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{203}{204}\right)$
$\chi_{30345}(4541,\cdot)$	$1$	$1$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{127}{408}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{167}{408}\right)$	$e\left(\frac{25}{204}\right)$
$\chi_{30345}(4616,\cdot)$	$1$	$1$	$e\left(\frac{203}{204}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{353}{408}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{265}{408}\right)$	$e\left(\frac{47}{204}\right)$
$\chi_{30345}(4751,\cdot)$	$1$	$1$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{301}{408}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{293}{408}\right)$	$e\left(\frac{199}{204}\right)$
$\chi_{30345}(4826,\cdot)$	$1$	$1$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{131}{408}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{259}{408}\right)$	$e\left(\frac{29}{204}\right)$
$\chi_{30345}(5561,\cdot)$	$1$	$1$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{175}{408}\right)$	$e\left(\frac{185}{204}\right)$
$\chi_{30345}(5591,\cdot)$	$1$	$1$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{283}{408}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{83}{408}\right)$	$e\left(\frac{181}{204}\right)$
$\chi_{30345}(5771,\cdot)$	$1$	$1$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{341}{408}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{397}{408}\right)$	$e\left(\frac{35}{204}\right)$
$\chi_{30345}(6326,\cdot)$	$1$	$1$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{271}{408}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{215}{408}\right)$	$e\left(\frac{169}{204}\right)$
$\chi_{30345}(6401,\cdot)$	$1$	$1$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{113}{408}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{95}{204}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{49}{408}\right)$	$e\left(\frac{11}{204}\right)$
$\chi_{30345}(6536,\cdot)$	$1$	$1$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{133}{408}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{101}{408}\right)$	$e\left(\frac{31}{204}\right)$
$\chi_{30345}(6611,\cdot)$	$1$	$1$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{395}{408}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{211}{408}\right)$	$e\left(\frac{89}{204}\right)$
$\chi_{30345}(7166,\cdot)$	$1$	$1$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{49}{408}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{209}{408}\right)$	$e\left(\frac{151}{204}\right)$
$\chi_{30345}(7346,\cdot)$	$1$	$1$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{223}{408}\right)$	$e\left(\frac{125}{204}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{30345}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{193}{408}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{91}{204}\right)\)
\(\chi_{30345}(206,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{31}{408}\right)\)	\(e\left(\frac{161}{204}\right)\)
\(\chi_{30345}(236,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{307}{408}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{227}{408}\right)\)	\(e\left(\frac{1}{204}\right)\)
\(\chi_{30345}(416,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{29}{408}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{157}{408}\right)\)	\(e\left(\frac{131}{204}\right)\)
\(\chi_{30345}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{247}{408}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{71}{408}\right)\)	\(e\left(\frac{145}{204}\right)\)
\(\chi_{30345}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{229}{408}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{269}{408}\right)\)	\(e\left(\frac{127}{204}\right)\)
\(\chi_{30345}(1256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{11}{408}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{355}{408}\right)\)	\(e\left(\frac{113}{204}\right)\)
\(\chi_{30345}(1811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{361}{408}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{41}{408}\right)\)	\(e\left(\frac{55}{204}\right)\)
\(\chi_{30345}(1991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{101}{204}\right)\)
\(\chi_{30345}(2021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{193}{204}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{179}{408}\right)\)	\(e\left(\frac{61}{204}\right)\)
\(\chi_{30345}(2201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{269}{408}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{373}{408}\right)\)	\(e\left(\frac{167}{204}\right)\)
\(\chi_{30345}(2831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{185}{408}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{73}{408}\right)\)	\(e\left(\frac{83}{204}\right)\)
\(\chi_{30345}(2966,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{61}{408}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{163}{204}\right)\)
\(\chi_{30345}(3041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{204}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{275}{408}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{29}{204}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{307}{408}\right)\)	\(e\left(\frac{173}{204}\right)\)
\(\chi_{30345}(3596,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{121}{408}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{233}{408}\right)\)	\(e\left(\frac{19}{204}\right)\)
\(\chi_{30345}(3776,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{143}{408}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{127}{408}\right)\)	\(e\left(\frac{41}{204}\right)\)
\(\chi_{30345}(3806,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{19}{408}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{131}{408}\right)\)	\(e\left(\frac{121}{204}\right)\)
\(\chi_{30345}(3986,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{101}{408}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{203}{204}\right)\)
\(\chi_{30345}(4541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{127}{408}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{167}{408}\right)\)	\(e\left(\frac{25}{204}\right)\)
\(\chi_{30345}(4616,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{204}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{353}{408}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{265}{408}\right)\)	\(e\left(\frac{47}{204}\right)\)
\(\chi_{30345}(4751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{301}{408}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{293}{408}\right)\)	\(e\left(\frac{199}{204}\right)\)
\(\chi_{30345}(4826,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{131}{408}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{259}{408}\right)\)	\(e\left(\frac{29}{204}\right)\)
\(\chi_{30345}(5561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{175}{408}\right)\)	\(e\left(\frac{185}{204}\right)\)
\(\chi_{30345}(5591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{283}{408}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{83}{408}\right)\)	\(e\left(\frac{181}{204}\right)\)
\(\chi_{30345}(5771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{341}{408}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{397}{408}\right)\)	\(e\left(\frac{35}{204}\right)\)
\(\chi_{30345}(6326,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{271}{408}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{215}{408}\right)\)	\(e\left(\frac{169}{204}\right)\)
\(\chi_{30345}(6401,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{113}{408}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{95}{204}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{49}{408}\right)\)	\(e\left(\frac{11}{204}\right)\)
\(\chi_{30345}(6536,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{133}{408}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{101}{408}\right)\)	\(e\left(\frac{31}{204}\right)\)
\(\chi_{30345}(6611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{395}{408}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{211}{408}\right)\)	\(e\left(\frac{89}{204}\right)\)
\(\chi_{30345}(7166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{49}{408}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{209}{408}\right)\)	\(e\left(\frac{151}{204}\right)\)
\(\chi_{30345}(7346,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{223}{408}\right)\)	\(e\left(\frac{125}{204}\right)\)

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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.kd
Modulus	$30345$
Conductor	$6069$
Order	$408$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(30345\)
Conductor:	\(6069\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(408\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 6069.cv	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)