LMFDB - Dirichlet character orbit 30345.kr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(816)) M = H._module chi = DirichletCharacter(H, M([0,0,136,27])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(31,30345)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$30345$
Conductor:	$2023$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$816$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bn	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:	$\Q(\zeta_{816})$
Fixed field:	Number field defined by a degree 816 polynomial (not computed)

First 31 of 256 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{30345}(31,\cdot)$	$1$	$1$	$e\left(\frac{253}{408}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{349}{816}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{121}{408}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{581}{816}\right)$	$e\left(\frac{247}{408}\right)$
$\chi_{30345}(61,\cdot)$	$1$	$1$	$e\left(\frac{239}{408}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{191}{816}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{223}{272}\right)$	$e\left(\frac{7}{816}\right)$	$e\left(\frac{293}{408}\right)$
$\chi_{30345}(241,\cdot)$	$1$	$1$	$e\left(\frac{373}{408}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{421}{816}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{1}{408}\right)$	$e\left(\frac{117}{272}\right)$	$e\left(\frac{605}{816}\right)$	$e\left(\frac{319}{408}\right)$
$\chi_{30345}(346,\cdot)$	$1$	$1$	$e\left(\frac{331}{408}\right)$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{763}{816}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{247}{408}\right)$	$e\left(\frac{203}{272}\right)$	$e\left(\frac{515}{816}\right)$	$e\left(\frac{49}{408}\right)$
$\chi_{30345}(481,\cdot)$	$1$	$1$	$e\left(\frac{281}{408}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{665}{816}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{137}{272}\right)$	$e\left(\frac{97}{816}\right)$	$e\left(\frac{155}{408}\right)$
$\chi_{30345}(556,\cdot)$	$1$	$1$	$e\left(\frac{49}{408}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{145}{816}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{377}{816}\right)$	$e\left(\frac{43}{408}\right)$
$\chi_{30345}(691,\cdot)$	$1$	$1$	$e\left(\frac{251}{408}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{35}{816}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{191}{408}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{91}{816}\right)$	$e\left(\frac{137}{408}\right)$
$\chi_{30345}(796,\cdot)$	$1$	$1$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{461}{816}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{205}{272}\right)$	$e\left(\frac{709}{816}\right)$	$e\left(\frac{359}{408}\right)$
$\chi_{30345}(976,\cdot)$	$1$	$1$	$e\left(\frac{55}{408}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{679}{816}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{115}{408}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{623}{816}\right)$	$e\left(\frac{373}{408}\right)$
$\chi_{30345}(1006,\cdot)$	$1$	$1$	$e\left(\frac{5}{408}\right)$	$e\left(\frac{5}{204}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{581}{816}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{233}{408}\right)$	$e\left(\frac{197}{272}\right)$	$e\left(\frac{205}{816}\right)$	$e\left(\frac{71}{408}\right)$
$\chi_{30345}(1111,\cdot)$	$1$	$1$	$e\left(\frac{11}{408}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{299}{816}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{107}{272}\right)$	$e\left(\frac{451}{816}\right)$	$e\left(\frac{401}{408}\right)$
$\chi_{30345}(1321,\cdot)$	$1$	$1$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{593}{816}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{73}{816}\right)$	$e\left(\frac{83}{408}\right)$
$\chi_{30345}(1501,\cdot)$	$1$	$1$	$e\left(\frac{313}{408}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{793}{816}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{61}{408}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{593}{816}\right)$	$e\left(\frac{283}{408}\right)$
$\chi_{30345}(1711,\cdot)$	$1$	$1$	$e\left(\frac{43}{408}\right)$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{19}{816}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{127}{408}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{539}{816}\right)$	$e\left(\frac{121}{408}\right)$
$\chi_{30345}(1741,\cdot)$	$1$	$1$	$e\left(\frac{383}{408}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{359}{816}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{607}{816}\right)$	$e\left(\frac{53}{408}\right)$
$\chi_{30345}(1816,\cdot)$	$1$	$1$	$e\left(\frac{205}{408}\right)$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{157}{816}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{169}{408}\right)$	$e\left(\frac{189}{272}\right)$	$e\left(\frac{245}{816}\right)$	$e\left(\frac{55}{408}\right)$
$\chi_{30345}(1846,\cdot)$	$1$	$1$	$e\left(\frac{335}{408}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{575}{816}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{107}{408}\right)$	$e\left(\frac{143}{272}\right)$	$e\left(\frac{679}{816}\right)$	$e\left(\frac{269}{408}\right)$
$\chi_{30345}(2026,\cdot)$	$1$	$1$	$e\left(\frac{13}{408}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{613}{816}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{361}{408}\right)$	$e\left(\frac{213}{272}\right)$	$e\left(\frac{125}{816}\right)$	$e\left(\frac{103}{408}\right)$
$\chi_{30345}(2131,\cdot)$	$1$	$1$	$e\left(\frac{355}{408}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{43}{816}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{223}{408}\right)$	$e\left(\frac{251}{272}\right)$	$e\left(\frac{275}{816}\right)$	$e\left(\frac{145}{408}\right)$
$\chi_{30345}(2266,\cdot)$	$1$	$1$	$e\left(\frac{65}{408}\right)$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{617}{816}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{173}{408}\right)$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{625}{816}\right)$	$e\left(\frac{107}{408}\right)$
$\chi_{30345}(2341,\cdot)$	$1$	$1$	$e\left(\frac{265}{408}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{193}{816}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{109}{408}\right)$	$e\left(\frac{241}{272}\right)$	$e\left(\frac{665}{816}\right)$	$e\left(\frac{91}{408}\right)$
$\chi_{30345}(2476,\cdot)$	$1$	$1$	$e\left(\frac{227}{408}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{755}{816}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{215}{408}\right)$	$e\left(\frac{131}{272}\right)$	$e\left(\frac{331}{816}\right)$	$e\left(\frac{41}{408}\right)$
$\chi_{30345}(2581,\cdot)$	$1$	$1$	$e\left(\frac{29}{408}\right)$	$e\left(\frac{29}{204}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{269}{816}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{209}{408}\right)$	$e\left(\frac{109}{272}\right)$	$e\left(\frac{373}{816}\right)$	$e\left(\frac{167}{408}\right)$
$\chi_{30345}(2761,\cdot)$	$1$	$1$	$e\left(\frac{367}{408}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{295}{816}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{211}{408}\right)$	$e\left(\frac{71}{272}\right)$	$e\left(\frac{767}{816}\right)$	$e\left(\frac{397}{408}\right)$
$\chi_{30345}(2791,\cdot)$	$1$	$1$	$e\left(\frac{53}{408}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{773}{816}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{185}{408}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{541}{816}\right)$	$e\left(\frac{263}{408}\right)$
$\chi_{30345}(2866,\cdot)$	$1$	$1$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{367}{816}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{91}{408}\right)$	$e\left(\frac{175}{272}\right)$	$e\left(\frac{791}{816}\right)$	$e\left(\frac{61}{408}\right)$
$\chi_{30345}(2896,\cdot)$	$1$	$1$	$e\left(\frac{35}{408}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{395}{816}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{155}{272}\right)$	$e\left(\frac{211}{816}\right)$	$e\left(\frac{89}{408}\right)$
$\chi_{30345}(3106,\cdot)$	$1$	$1$	$e\left(\frac{377}{408}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{641}{816}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{269}{408}\right)$	$e\left(\frac{193}{272}\right)$	$e\left(\frac{361}{816}\right)$	$e\left(\frac{131}{408}\right)$
$\chi_{30345}(3286,\cdot)$	$1$	$1$	$e\left(\frac{97}{408}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{745}{816}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{277}{408}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{305}{816}\right)$	$e\left(\frac{235}{408}\right)$
$\chi_{30345}(3496,\cdot)$	$1$	$1$	$e\left(\frac{19}{408}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{739}{816}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{151}{408}\right)$	$e\left(\frac{259}{272}\right)$	$e\left(\frac{779}{816}\right)$	$e\left(\frac{25}{408}\right)$
$\chi_{30345}(3526,\cdot)$	$1$	$1$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{791}{816}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{155}{408}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{751}{816}\right)$	$e\left(\frac{77}{408}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{30345}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{408}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{349}{816}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{121}{408}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{581}{816}\right)\)	\(e\left(\frac{247}{408}\right)\)
\(\chi_{30345}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{408}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{191}{816}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{223}{272}\right)\)	\(e\left(\frac{7}{816}\right)\)	\(e\left(\frac{293}{408}\right)\)
\(\chi_{30345}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{373}{408}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{421}{816}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{1}{408}\right)\)	\(e\left(\frac{117}{272}\right)\)	\(e\left(\frac{605}{816}\right)\)	\(e\left(\frac{319}{408}\right)\)
\(\chi_{30345}(346,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{408}\right)\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{763}{816}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{247}{408}\right)\)	\(e\left(\frac{203}{272}\right)\)	\(e\left(\frac{515}{816}\right)\)	\(e\left(\frac{49}{408}\right)\)
\(\chi_{30345}(481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{408}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{665}{816}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{137}{272}\right)\)	\(e\left(\frac{97}{816}\right)\)	\(e\left(\frac{155}{408}\right)\)
\(\chi_{30345}(556,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{408}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{145}{816}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{377}{816}\right)\)	\(e\left(\frac{43}{408}\right)\)
\(\chi_{30345}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{408}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{35}{816}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{191}{408}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{91}{816}\right)\)	\(e\left(\frac{137}{408}\right)\)
\(\chi_{30345}(796,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{461}{816}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{205}{272}\right)\)	\(e\left(\frac{709}{816}\right)\)	\(e\left(\frac{359}{408}\right)\)
\(\chi_{30345}(976,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{408}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{679}{816}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{115}{408}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{623}{816}\right)\)	\(e\left(\frac{373}{408}\right)\)
\(\chi_{30345}(1006,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{408}\right)\)	\(e\left(\frac{5}{204}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{581}{816}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{233}{408}\right)\)	\(e\left(\frac{197}{272}\right)\)	\(e\left(\frac{205}{816}\right)\)	\(e\left(\frac{71}{408}\right)\)
\(\chi_{30345}(1111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{408}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{299}{816}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{107}{272}\right)\)	\(e\left(\frac{451}{816}\right)\)	\(e\left(\frac{401}{408}\right)\)
\(\chi_{30345}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{593}{816}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{73}{816}\right)\)	\(e\left(\frac{83}{408}\right)\)
\(\chi_{30345}(1501,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{408}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{793}{816}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{61}{408}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{593}{816}\right)\)	\(e\left(\frac{283}{408}\right)\)
\(\chi_{30345}(1711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{408}\right)\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{19}{816}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{127}{408}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{539}{816}\right)\)	\(e\left(\frac{121}{408}\right)\)
\(\chi_{30345}(1741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{383}{408}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{359}{816}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{607}{816}\right)\)	\(e\left(\frac{53}{408}\right)\)
\(\chi_{30345}(1816,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{408}\right)\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{157}{816}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{169}{408}\right)\)	\(e\left(\frac{189}{272}\right)\)	\(e\left(\frac{245}{816}\right)\)	\(e\left(\frac{55}{408}\right)\)
\(\chi_{30345}(1846,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{335}{408}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{575}{816}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{107}{408}\right)\)	\(e\left(\frac{143}{272}\right)\)	\(e\left(\frac{679}{816}\right)\)	\(e\left(\frac{269}{408}\right)\)
\(\chi_{30345}(2026,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{408}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{613}{816}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{361}{408}\right)\)	\(e\left(\frac{213}{272}\right)\)	\(e\left(\frac{125}{816}\right)\)	\(e\left(\frac{103}{408}\right)\)
\(\chi_{30345}(2131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{355}{408}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{43}{816}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{223}{408}\right)\)	\(e\left(\frac{251}{272}\right)\)	\(e\left(\frac{275}{816}\right)\)	\(e\left(\frac{145}{408}\right)\)
\(\chi_{30345}(2266,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{408}\right)\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{617}{816}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{173}{408}\right)\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{625}{816}\right)\)	\(e\left(\frac{107}{408}\right)\)
\(\chi_{30345}(2341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{408}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{193}{816}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{109}{408}\right)\)	\(e\left(\frac{241}{272}\right)\)	\(e\left(\frac{665}{816}\right)\)	\(e\left(\frac{91}{408}\right)\)
\(\chi_{30345}(2476,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{408}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{755}{816}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{215}{408}\right)\)	\(e\left(\frac{131}{272}\right)\)	\(e\left(\frac{331}{816}\right)\)	\(e\left(\frac{41}{408}\right)\)
\(\chi_{30345}(2581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{408}\right)\)	\(e\left(\frac{29}{204}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{269}{816}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{209}{408}\right)\)	\(e\left(\frac{109}{272}\right)\)	\(e\left(\frac{373}{816}\right)\)	\(e\left(\frac{167}{408}\right)\)
\(\chi_{30345}(2761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{408}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{295}{816}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{211}{408}\right)\)	\(e\left(\frac{71}{272}\right)\)	\(e\left(\frac{767}{816}\right)\)	\(e\left(\frac{397}{408}\right)\)
\(\chi_{30345}(2791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{408}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{773}{816}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{185}{408}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{541}{816}\right)\)	\(e\left(\frac{263}{408}\right)\)
\(\chi_{30345}(2866,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{367}{816}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{91}{408}\right)\)	\(e\left(\frac{175}{272}\right)\)	\(e\left(\frac{791}{816}\right)\)	\(e\left(\frac{61}{408}\right)\)
\(\chi_{30345}(2896,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{408}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{395}{816}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{155}{272}\right)\)	\(e\left(\frac{211}{816}\right)\)	\(e\left(\frac{89}{408}\right)\)
\(\chi_{30345}(3106,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{408}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{641}{816}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{269}{408}\right)\)	\(e\left(\frac{193}{272}\right)\)	\(e\left(\frac{361}{816}\right)\)	\(e\left(\frac{131}{408}\right)\)
\(\chi_{30345}(3286,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{408}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{745}{816}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{277}{408}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{305}{816}\right)\)	\(e\left(\frac{235}{408}\right)\)
\(\chi_{30345}(3496,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{408}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{739}{816}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{151}{408}\right)\)	\(e\left(\frac{259}{272}\right)\)	\(e\left(\frac{779}{816}\right)\)	\(e\left(\frac{25}{408}\right)\)
\(\chi_{30345}(3526,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{791}{816}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{155}{408}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{751}{816}\right)\)	\(e\left(\frac{77}{408}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 256 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.kr
Modulus	$30345$
Conductor	$2023$
Order	$816$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(30345\)
Conductor:	\(2023\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(816\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)