LMFDB - Dirichlet character orbit 25050.bh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25050, base_ring=CyclotomicField(332)) M = H._module chi = DirichletCharacter(H, M([0,249,174])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(43,25050)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$25050$
Conductor:	$835$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$332$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 835.l	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:	$\Q(\zeta_{332})$
Fixed field:	Number field defined by a degree 332 polynomial (not computed)

First 31 of 164 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{25050}(43,\cdot)$	$1$	$1$	$e\left(\frac{197}{332}\right)$	$e\left(\frac{56}{83}\right)$	$e\left(\frac{77}{332}\right)$	$e\left(\frac{175}{332}\right)$	$e\left(\frac{149}{166}\right)$	$e\left(\frac{45}{332}\right)$	$e\left(\frac{19}{166}\right)$	$e\left(\frac{14}{83}\right)$	$e\left(\frac{239}{332}\right)$	$e\left(\frac{139}{166}\right)$
$\chi_{25050}(193,\cdot)$	$1$	$1$	$e\left(\frac{133}{332}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{325}{332}\right)$	$e\left(\frac{135}{332}\right)$	$e\left(\frac{77}{166}\right)$	$e\left(\frac{177}{332}\right)$	$e\left(\frac{119}{166}\right)$	$e\left(\frac{44}{83}\right)$	$e\left(\frac{99}{332}\right)$	$e\left(\frac{93}{166}\right)$
$\chi_{25050}(307,\cdot)$	$1$	$1$	$e\left(\frac{235}{332}\right)$	$e\left(\frac{47}{83}\right)$	$e\left(\frac{75}{332}\right)$	$e\left(\frac{261}{332}\right)$	$e\left(\frac{5}{166}\right)$	$e\left(\frac{143}{332}\right)$	$e\left(\frac{53}{166}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{125}{332}\right)$	$e\left(\frac{47}{166}\right)$
$\chi_{25050}(457,\cdot)$	$1$	$1$	$e\left(\frac{7}{332}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{87}{332}\right)$	$e\left(\frac{77}{332}\right)$	$e\left(\frac{39}{166}\right)$	$e\left(\frac{219}{332}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{46}{83}\right)$	$e\left(\frac{145}{332}\right)$	$e\left(\frac{101}{166}\right)$
$\chi_{25050}(493,\cdot)$	$1$	$1$	$e\left(\frac{17}{332}\right)$	$e\left(\frac{20}{83}\right)$	$e\left(\frac{69}{332}\right)$	$e\left(\frac{187}{332}\right)$	$e\left(\frac{71}{166}\right)$	$e\left(\frac{105}{332}\right)$	$e\left(\frac{155}{166}\right)$	$e\left(\frac{5}{83}\right)$	$e\left(\frac{115}{332}\right)$	$e\left(\frac{103}{166}\right)$
$\chi_{25050}(607,\cdot)$	$1$	$1$	$e\left(\frac{55}{332}\right)$	$e\left(\frac{11}{83}\right)$	$e\left(\frac{67}{332}\right)$	$e\left(\frac{273}{332}\right)$	$e\left(\frac{93}{166}\right)$	$e\left(\frac{203}{332}\right)$	$e\left(\frac{23}{166}\right)$	$e\left(\frac{65}{83}\right)$	$e\left(\frac{1}{332}\right)$	$e\left(\frac{11}{166}\right)$
$\chi_{25050}(643,\cdot)$	$1$	$1$	$e\left(\frac{57}{332}\right)$	$e\left(\frac{28}{83}\right)$	$e\left(\frac{329}{332}\right)$	$e\left(\frac{295}{332}\right)$	$e\left(\frac{33}{166}\right)$	$e\left(\frac{313}{332}\right)$	$e\left(\frac{51}{166}\right)$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{327}{332}\right)$	$e\left(\frac{111}{166}\right)$
$\chi_{25050}(793,\cdot)$	$1$	$1$	$e\left(\frac{293}{332}\right)$	$e\left(\frac{42}{83}\right)$	$e\left(\frac{37}{332}\right)$	$e\left(\frac{235}{332}\right)$	$e\left(\frac{91}{166}\right)$	$e\left(\frac{13}{332}\right)$	$e\left(\frac{35}{166}\right)$	$e\left(\frac{52}{83}\right)$	$e\left(\frac{283}{332}\right)$	$e\left(\frac{125}{166}\right)$
$\chi_{25050}(1057,\cdot)$	$1$	$1$	$e\left(\frac{287}{332}\right)$	$e\left(\frac{74}{83}\right)$	$e\left(\frac{247}{332}\right)$	$e\left(\frac{169}{332}\right)$	$e\left(\frac{105}{166}\right)$	$e\left(\frac{15}{332}\right)$	$e\left(\frac{117}{166}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{301}{332}\right)$	$e\left(\frac{157}{166}\right)$
$\chi_{25050}(1093,\cdot)$	$1$	$1$	$e\left(\frac{281}{332}\right)$	$e\left(\frac{23}{83}\right)$	$e\left(\frac{125}{332}\right)$	$e\left(\frac{103}{332}\right)$	$e\left(\frac{119}{166}\right)$	$e\left(\frac{17}{332}\right)$	$e\left(\frac{33}{166}\right)$	$e\left(\frac{68}{83}\right)$	$e\left(\frac{319}{332}\right)$	$e\left(\frac{23}{166}\right)$
$\chi_{25050}(1243,\cdot)$	$1$	$1$	$e\left(\frac{181}{332}\right)$	$e\left(\frac{3}{83}\right)$	$e\left(\frac{305}{332}\right)$	$e\left(\frac{331}{332}\right)$	$e\left(\frac{131}{166}\right)$	$e\left(\frac{161}{332}\right)$	$e\left(\frac{127}{166}\right)$	$e\left(\frac{63}{83}\right)$	$e\left(\frac{287}{332}\right)$	$e\left(\frac{3}{166}\right)$
$\chi_{25050}(1543,\cdot)$	$1$	$1$	$e\left(\frac{253}{332}\right)$	$e\left(\frac{34}{83}\right)$	$e\left(\frac{109}{332}\right)$	$e\left(\frac{127}{332}\right)$	$e\left(\frac{129}{166}\right)$	$e\left(\frac{137}{332}\right)$	$e\left(\frac{139}{166}\right)$	$e\left(\frac{50}{83}\right)$	$e\left(\frac{71}{332}\right)$	$e\left(\frac{117}{166}\right)$
$\chi_{25050}(1693,\cdot)$	$1$	$1$	$e\left(\frac{41}{332}\right)$	$e\left(\frac{58}{83}\right)$	$e\left(\frac{225}{332}\right)$	$e\left(\frac{119}{332}\right)$	$e\left(\frac{15}{166}\right)$	$e\left(\frac{97}{332}\right)$	$e\left(\frac{159}{166}\right)$	$e\left(\frac{56}{83}\right)$	$e\left(\frac{43}{332}\right)$	$e\left(\frac{141}{166}\right)$
$\chi_{25050}(1957,\cdot)$	$1$	$1$	$e\left(\frac{27}{332}\right)$	$e\left(\frac{22}{83}\right)$	$e\left(\frac{51}{332}\right)$	$e\left(\frac{297}{332}\right)$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{323}{332}\right)$	$e\left(\frac{129}{166}\right)$	$e\left(\frac{47}{83}\right)$	$e\left(\frac{85}{332}\right)$	$e\left(\frac{105}{166}\right)$
$\chi_{25050}(1993,\cdot)$	$1$	$1$	$e\left(\frac{217}{332}\right)$	$e\left(\frac{60}{83}\right)$	$e\left(\frac{41}{332}\right)$	$e\left(\frac{63}{332}\right)$	$e\left(\frac{47}{166}\right)$	$e\left(\frac{149}{332}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{15}{83}\right)$	$e\left(\frac{179}{332}\right)$	$e\left(\frac{143}{166}\right)$
$\chi_{25050}(2107,\cdot)$	$1$	$1$	$e\left(\frac{283}{332}\right)$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{55}{332}\right)$	$e\left(\frac{125}{332}\right)$	$e\left(\frac{59}{166}\right)$	$e\left(\frac{127}{332}\right)$	$e\left(\frac{61}{166}\right)$	$e\left(\frac{10}{83}\right)$	$e\left(\frac{313}{332}\right)$	$e\left(\frac{123}{166}\right)$
$\chi_{25050}(2143,\cdot)$	$1$	$1$	$e\left(\frac{165}{332}\right)$	$e\left(\frac{33}{83}\right)$	$e\left(\frac{201}{332}\right)$	$e\left(\frac{155}{332}\right)$	$e\left(\frac{113}{166}\right)$	$e\left(\frac{277}{332}\right)$	$e\left(\frac{69}{166}\right)$	$e\left(\frac{29}{83}\right)$	$e\left(\frac{3}{332}\right)$	$e\left(\frac{33}{166}\right)$
$\chi_{25050}(2257,\cdot)$	$1$	$1$	$e\left(\frac{175}{332}\right)$	$e\left(\frac{35}{83}\right)$	$e\left(\frac{183}{332}\right)$	$e\left(\frac{265}{332}\right)$	$e\left(\frac{145}{166}\right)$	$e\left(\frac{163}{332}\right)$	$e\left(\frac{43}{166}\right)$	$e\left(\frac{71}{83}\right)$	$e\left(\frac{305}{332}\right)$	$e\left(\frac{35}{166}\right)$
$\chi_{25050}(2407,\cdot)$	$1$	$1$	$e\left(\frac{147}{332}\right)$	$e\left(\frac{46}{83}\right)$	$e\left(\frac{167}{332}\right)$	$e\left(\frac{289}{332}\right)$	$e\left(\frac{155}{166}\right)$	$e\left(\frac{283}{332}\right)$	$e\left(\frac{149}{166}\right)$	$e\left(\frac{53}{83}\right)$	$e\left(\frac{57}{332}\right)$	$e\left(\frac{129}{166}\right)$
$\chi_{25050}(2443,\cdot)$	$1$	$1$	$e\left(\frac{53}{332}\right)$	$e\left(\frac{77}{83}\right)$	$e\left(\frac{137}{332}\right)$	$e\left(\frac{251}{332}\right)$	$e\left(\frac{153}{166}\right)$	$e\left(\frac{93}{332}\right)$	$e\left(\frac{161}{166}\right)$	$e\left(\frac{40}{83}\right)$	$e\left(\frac{7}{332}\right)$	$e\left(\frac{77}{166}\right)$
$\chi_{25050}(2557,\cdot)$	$1$	$1$	$e\left(\frac{111}{332}\right)$	$e\left(\frac{72}{83}\right)$	$e\left(\frac{99}{332}\right)$	$e\left(\frac{225}{332}\right)$	$e\left(\frac{73}{166}\right)$	$e\left(\frac{295}{332}\right)$	$e\left(\frac{143}{166}\right)$	$e\left(\frac{18}{83}\right)$	$e\left(\frac{165}{332}\right)$	$e\left(\frac{155}{166}\right)$
$\chi_{25050}(2707,\cdot)$	$1$	$1$	$e\left(\frac{279}{332}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{195}{332}\right)$	$e\left(\frac{81}{332}\right)$	$e\left(\frac{13}{166}\right)$	$e\left(\frac{239}{332}\right)$	$e\left(\frac{5}{166}\right)$	$e\left(\frac{43}{83}\right)$	$e\left(\frac{325}{332}\right)$	$e\left(\frac{89}{166}\right)$
$\chi_{25050}(2743,\cdot)$	$1$	$1$	$e\left(\frac{245}{332}\right)$	$e\left(\frac{49}{83}\right)$	$e\left(\frac{57}{332}\right)$	$e\left(\frac{39}{332}\right)$	$e\left(\frac{37}{166}\right)$	$e\left(\frac{29}{332}\right)$	$e\left(\frac{27}{166}\right)$	$e\left(\frac{33}{83}\right)$	$e\left(\frac{95}{332}\right)$	$e\left(\frac{49}{166}\right)$
$\chi_{25050}(3043,\cdot)$	$1$	$1$	$e\left(\frac{37}{332}\right)$	$e\left(\frac{24}{83}\right)$	$e\left(\frac{33}{332}\right)$	$e\left(\frac{75}{332}\right)$	$e\left(\frac{135}{166}\right)$	$e\left(\frac{209}{332}\right)$	$e\left(\frac{103}{166}\right)$	$e\left(\frac{6}{83}\right)$	$e\left(\frac{55}{332}\right)$	$e\left(\frac{107}{166}\right)$
$\chi_{25050}(3157,\cdot)$	$1$	$1$	$e\left(\frac{327}{332}\right)$	$e\left(\frac{82}{83}\right)$	$e\left(\frac{175}{332}\right)$	$e\left(\frac{277}{332}\right)$	$e\left(\frac{67}{166}\right)$	$e\left(\frac{223}{332}\right)$	$e\left(\frac{13}{166}\right)$	$e\left(\frac{62}{83}\right)$	$e\left(\frac{181}{332}\right)$	$e\left(\frac{165}{166}\right)$
$\chi_{25050}(3193,\cdot)$	$1$	$1$	$e\left(\frac{109}{332}\right)$	$e\left(\frac{55}{83}\right)$	$e\left(\frac{169}{332}\right)$	$e\left(\frac{203}{332}\right)$	$e\left(\frac{133}{166}\right)$	$e\left(\frac{185}{332}\right)$	$e\left(\frac{115}{166}\right)$	$e\left(\frac{76}{83}\right)$	$e\left(\frac{171}{332}\right)$	$e\left(\frac{55}{166}\right)$
$\chi_{25050}(3307,\cdot)$	$1$	$1$	$e\left(\frac{323}{332}\right)$	$e\left(\frac{48}{83}\right)$	$e\left(\frac{315}{332}\right)$	$e\left(\frac{233}{332}\right)$	$e\left(\frac{21}{166}\right)$	$e\left(\frac{3}{332}\right)$	$e\left(\frac{123}{166}\right)$	$e\left(\frac{12}{83}\right)$	$e\left(\frac{193}{332}\right)$	$e\left(\frac{131}{166}\right)$
$\chi_{25050}(3457,\cdot)$	$1$	$1$	$e\left(\frac{35}{332}\right)$	$e\left(\frac{7}{83}\right)$	$e\left(\frac{103}{332}\right)$	$e\left(\frac{53}{332}\right)$	$e\left(\frac{29}{166}\right)$	$e\left(\frac{99}{332}\right)$	$e\left(\frac{75}{166}\right)$	$e\left(\frac{64}{83}\right)$	$e\left(\frac{61}{332}\right)$	$e\left(\frac{7}{166}\right)$
$\chi_{25050}(3493,\cdot)$	$1$	$1$	$e\left(\frac{21}{332}\right)$	$e\left(\frac{54}{83}\right)$	$e\left(\frac{261}{332}\right)$	$e\left(\frac{231}{332}\right)$	$e\left(\frac{117}{166}\right)$	$e\left(\frac{325}{332}\right)$	$e\left(\frac{45}{166}\right)$	$e\left(\frac{55}{83}\right)$	$e\left(\frac{103}{332}\right)$	$e\left(\frac{137}{166}\right)$
$\chi_{25050}(3643,\cdot)$	$1$	$1$	$e\left(\frac{241}{332}\right)$	$e\left(\frac{15}{83}\right)$	$e\left(\frac{197}{332}\right)$	$e\left(\frac{327}{332}\right)$	$e\left(\frac{157}{166}\right)$	$e\left(\frac{141}{332}\right)$	$e\left(\frac{137}{166}\right)$	$e\left(\frac{66}{83}\right)$	$e\left(\frac{107}{332}\right)$	$e\left(\frac{15}{166}\right)$
$\chi_{25050}(3757,\cdot)$	$1$	$1$	$e\left(\frac{271}{332}\right)$	$e\left(\frac{21}{83}\right)$	$e\left(\frac{143}{332}\right)$	$e\left(\frac{325}{332}\right)$	$e\left(\frac{87}{166}\right)$	$e\left(\frac{131}{332}\right)$	$e\left(\frac{59}{166}\right)$	$e\left(\frac{26}{83}\right)$	$e\left(\frac{17}{332}\right)$	$e\left(\frac{21}{166}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{25050}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{332}\right)\)	\(e\left(\frac{56}{83}\right)\)	\(e\left(\frac{77}{332}\right)\)	\(e\left(\frac{175}{332}\right)\)	\(e\left(\frac{149}{166}\right)\)	\(e\left(\frac{45}{332}\right)\)	\(e\left(\frac{19}{166}\right)\)	\(e\left(\frac{14}{83}\right)\)	\(e\left(\frac{239}{332}\right)\)	\(e\left(\frac{139}{166}\right)\)
\(\chi_{25050}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{332}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{325}{332}\right)\)	\(e\left(\frac{135}{332}\right)\)	\(e\left(\frac{77}{166}\right)\)	\(e\left(\frac{177}{332}\right)\)	\(e\left(\frac{119}{166}\right)\)	\(e\left(\frac{44}{83}\right)\)	\(e\left(\frac{99}{332}\right)\)	\(e\left(\frac{93}{166}\right)\)
\(\chi_{25050}(307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{332}\right)\)	\(e\left(\frac{47}{83}\right)\)	\(e\left(\frac{75}{332}\right)\)	\(e\left(\frac{261}{332}\right)\)	\(e\left(\frac{5}{166}\right)\)	\(e\left(\frac{143}{332}\right)\)	\(e\left(\frac{53}{166}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{125}{332}\right)\)	\(e\left(\frac{47}{166}\right)\)
\(\chi_{25050}(457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{332}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{87}{332}\right)\)	\(e\left(\frac{77}{332}\right)\)	\(e\left(\frac{39}{166}\right)\)	\(e\left(\frac{219}{332}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{46}{83}\right)\)	\(e\left(\frac{145}{332}\right)\)	\(e\left(\frac{101}{166}\right)\)
\(\chi_{25050}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{332}\right)\)	\(e\left(\frac{20}{83}\right)\)	\(e\left(\frac{69}{332}\right)\)	\(e\left(\frac{187}{332}\right)\)	\(e\left(\frac{71}{166}\right)\)	\(e\left(\frac{105}{332}\right)\)	\(e\left(\frac{155}{166}\right)\)	\(e\left(\frac{5}{83}\right)\)	\(e\left(\frac{115}{332}\right)\)	\(e\left(\frac{103}{166}\right)\)
\(\chi_{25050}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{332}\right)\)	\(e\left(\frac{11}{83}\right)\)	\(e\left(\frac{67}{332}\right)\)	\(e\left(\frac{273}{332}\right)\)	\(e\left(\frac{93}{166}\right)\)	\(e\left(\frac{203}{332}\right)\)	\(e\left(\frac{23}{166}\right)\)	\(e\left(\frac{65}{83}\right)\)	\(e\left(\frac{1}{332}\right)\)	\(e\left(\frac{11}{166}\right)\)
\(\chi_{25050}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{332}\right)\)	\(e\left(\frac{28}{83}\right)\)	\(e\left(\frac{329}{332}\right)\)	\(e\left(\frac{295}{332}\right)\)	\(e\left(\frac{33}{166}\right)\)	\(e\left(\frac{313}{332}\right)\)	\(e\left(\frac{51}{166}\right)\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{327}{332}\right)\)	\(e\left(\frac{111}{166}\right)\)
\(\chi_{25050}(793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{332}\right)\)	\(e\left(\frac{42}{83}\right)\)	\(e\left(\frac{37}{332}\right)\)	\(e\left(\frac{235}{332}\right)\)	\(e\left(\frac{91}{166}\right)\)	\(e\left(\frac{13}{332}\right)\)	\(e\left(\frac{35}{166}\right)\)	\(e\left(\frac{52}{83}\right)\)	\(e\left(\frac{283}{332}\right)\)	\(e\left(\frac{125}{166}\right)\)
\(\chi_{25050}(1057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{332}\right)\)	\(e\left(\frac{74}{83}\right)\)	\(e\left(\frac{247}{332}\right)\)	\(e\left(\frac{169}{332}\right)\)	\(e\left(\frac{105}{166}\right)\)	\(e\left(\frac{15}{332}\right)\)	\(e\left(\frac{117}{166}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{301}{332}\right)\)	\(e\left(\frac{157}{166}\right)\)
\(\chi_{25050}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{332}\right)\)	\(e\left(\frac{23}{83}\right)\)	\(e\left(\frac{125}{332}\right)\)	\(e\left(\frac{103}{332}\right)\)	\(e\left(\frac{119}{166}\right)\)	\(e\left(\frac{17}{332}\right)\)	\(e\left(\frac{33}{166}\right)\)	\(e\left(\frac{68}{83}\right)\)	\(e\left(\frac{319}{332}\right)\)	\(e\left(\frac{23}{166}\right)\)
\(\chi_{25050}(1243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{332}\right)\)	\(e\left(\frac{3}{83}\right)\)	\(e\left(\frac{305}{332}\right)\)	\(e\left(\frac{331}{332}\right)\)	\(e\left(\frac{131}{166}\right)\)	\(e\left(\frac{161}{332}\right)\)	\(e\left(\frac{127}{166}\right)\)	\(e\left(\frac{63}{83}\right)\)	\(e\left(\frac{287}{332}\right)\)	\(e\left(\frac{3}{166}\right)\)
\(\chi_{25050}(1543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{332}\right)\)	\(e\left(\frac{34}{83}\right)\)	\(e\left(\frac{109}{332}\right)\)	\(e\left(\frac{127}{332}\right)\)	\(e\left(\frac{129}{166}\right)\)	\(e\left(\frac{137}{332}\right)\)	\(e\left(\frac{139}{166}\right)\)	\(e\left(\frac{50}{83}\right)\)	\(e\left(\frac{71}{332}\right)\)	\(e\left(\frac{117}{166}\right)\)
\(\chi_{25050}(1693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{332}\right)\)	\(e\left(\frac{58}{83}\right)\)	\(e\left(\frac{225}{332}\right)\)	\(e\left(\frac{119}{332}\right)\)	\(e\left(\frac{15}{166}\right)\)	\(e\left(\frac{97}{332}\right)\)	\(e\left(\frac{159}{166}\right)\)	\(e\left(\frac{56}{83}\right)\)	\(e\left(\frac{43}{332}\right)\)	\(e\left(\frac{141}{166}\right)\)
\(\chi_{25050}(1957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{332}\right)\)	\(e\left(\frac{22}{83}\right)\)	\(e\left(\frac{51}{332}\right)\)	\(e\left(\frac{297}{332}\right)\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{323}{332}\right)\)	\(e\left(\frac{129}{166}\right)\)	\(e\left(\frac{47}{83}\right)\)	\(e\left(\frac{85}{332}\right)\)	\(e\left(\frac{105}{166}\right)\)
\(\chi_{25050}(1993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{332}\right)\)	\(e\left(\frac{60}{83}\right)\)	\(e\left(\frac{41}{332}\right)\)	\(e\left(\frac{63}{332}\right)\)	\(e\left(\frac{47}{166}\right)\)	\(e\left(\frac{149}{332}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{15}{83}\right)\)	\(e\left(\frac{179}{332}\right)\)	\(e\left(\frac{143}{166}\right)\)
\(\chi_{25050}(2107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{332}\right)\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{55}{332}\right)\)	\(e\left(\frac{125}{332}\right)\)	\(e\left(\frac{59}{166}\right)\)	\(e\left(\frac{127}{332}\right)\)	\(e\left(\frac{61}{166}\right)\)	\(e\left(\frac{10}{83}\right)\)	\(e\left(\frac{313}{332}\right)\)	\(e\left(\frac{123}{166}\right)\)
\(\chi_{25050}(2143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{165}{332}\right)\)	\(e\left(\frac{33}{83}\right)\)	\(e\left(\frac{201}{332}\right)\)	\(e\left(\frac{155}{332}\right)\)	\(e\left(\frac{113}{166}\right)\)	\(e\left(\frac{277}{332}\right)\)	\(e\left(\frac{69}{166}\right)\)	\(e\left(\frac{29}{83}\right)\)	\(e\left(\frac{3}{332}\right)\)	\(e\left(\frac{33}{166}\right)\)
\(\chi_{25050}(2257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{332}\right)\)	\(e\left(\frac{35}{83}\right)\)	\(e\left(\frac{183}{332}\right)\)	\(e\left(\frac{265}{332}\right)\)	\(e\left(\frac{145}{166}\right)\)	\(e\left(\frac{163}{332}\right)\)	\(e\left(\frac{43}{166}\right)\)	\(e\left(\frac{71}{83}\right)\)	\(e\left(\frac{305}{332}\right)\)	\(e\left(\frac{35}{166}\right)\)
\(\chi_{25050}(2407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{147}{332}\right)\)	\(e\left(\frac{46}{83}\right)\)	\(e\left(\frac{167}{332}\right)\)	\(e\left(\frac{289}{332}\right)\)	\(e\left(\frac{155}{166}\right)\)	\(e\left(\frac{283}{332}\right)\)	\(e\left(\frac{149}{166}\right)\)	\(e\left(\frac{53}{83}\right)\)	\(e\left(\frac{57}{332}\right)\)	\(e\left(\frac{129}{166}\right)\)
\(\chi_{25050}(2443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{332}\right)\)	\(e\left(\frac{77}{83}\right)\)	\(e\left(\frac{137}{332}\right)\)	\(e\left(\frac{251}{332}\right)\)	\(e\left(\frac{153}{166}\right)\)	\(e\left(\frac{93}{332}\right)\)	\(e\left(\frac{161}{166}\right)\)	\(e\left(\frac{40}{83}\right)\)	\(e\left(\frac{7}{332}\right)\)	\(e\left(\frac{77}{166}\right)\)
\(\chi_{25050}(2557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{332}\right)\)	\(e\left(\frac{72}{83}\right)\)	\(e\left(\frac{99}{332}\right)\)	\(e\left(\frac{225}{332}\right)\)	\(e\left(\frac{73}{166}\right)\)	\(e\left(\frac{295}{332}\right)\)	\(e\left(\frac{143}{166}\right)\)	\(e\left(\frac{18}{83}\right)\)	\(e\left(\frac{165}{332}\right)\)	\(e\left(\frac{155}{166}\right)\)
\(\chi_{25050}(2707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{279}{332}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{195}{332}\right)\)	\(e\left(\frac{81}{332}\right)\)	\(e\left(\frac{13}{166}\right)\)	\(e\left(\frac{239}{332}\right)\)	\(e\left(\frac{5}{166}\right)\)	\(e\left(\frac{43}{83}\right)\)	\(e\left(\frac{325}{332}\right)\)	\(e\left(\frac{89}{166}\right)\)
\(\chi_{25050}(2743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{245}{332}\right)\)	\(e\left(\frac{49}{83}\right)\)	\(e\left(\frac{57}{332}\right)\)	\(e\left(\frac{39}{332}\right)\)	\(e\left(\frac{37}{166}\right)\)	\(e\left(\frac{29}{332}\right)\)	\(e\left(\frac{27}{166}\right)\)	\(e\left(\frac{33}{83}\right)\)	\(e\left(\frac{95}{332}\right)\)	\(e\left(\frac{49}{166}\right)\)
\(\chi_{25050}(3043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{332}\right)\)	\(e\left(\frac{24}{83}\right)\)	\(e\left(\frac{33}{332}\right)\)	\(e\left(\frac{75}{332}\right)\)	\(e\left(\frac{135}{166}\right)\)	\(e\left(\frac{209}{332}\right)\)	\(e\left(\frac{103}{166}\right)\)	\(e\left(\frac{6}{83}\right)\)	\(e\left(\frac{55}{332}\right)\)	\(e\left(\frac{107}{166}\right)\)
\(\chi_{25050}(3157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{327}{332}\right)\)	\(e\left(\frac{82}{83}\right)\)	\(e\left(\frac{175}{332}\right)\)	\(e\left(\frac{277}{332}\right)\)	\(e\left(\frac{67}{166}\right)\)	\(e\left(\frac{223}{332}\right)\)	\(e\left(\frac{13}{166}\right)\)	\(e\left(\frac{62}{83}\right)\)	\(e\left(\frac{181}{332}\right)\)	\(e\left(\frac{165}{166}\right)\)
\(\chi_{25050}(3193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{332}\right)\)	\(e\left(\frac{55}{83}\right)\)	\(e\left(\frac{169}{332}\right)\)	\(e\left(\frac{203}{332}\right)\)	\(e\left(\frac{133}{166}\right)\)	\(e\left(\frac{185}{332}\right)\)	\(e\left(\frac{115}{166}\right)\)	\(e\left(\frac{76}{83}\right)\)	\(e\left(\frac{171}{332}\right)\)	\(e\left(\frac{55}{166}\right)\)
\(\chi_{25050}(3307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{332}\right)\)	\(e\left(\frac{48}{83}\right)\)	\(e\left(\frac{315}{332}\right)\)	\(e\left(\frac{233}{332}\right)\)	\(e\left(\frac{21}{166}\right)\)	\(e\left(\frac{3}{332}\right)\)	\(e\left(\frac{123}{166}\right)\)	\(e\left(\frac{12}{83}\right)\)	\(e\left(\frac{193}{332}\right)\)	\(e\left(\frac{131}{166}\right)\)
\(\chi_{25050}(3457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{332}\right)\)	\(e\left(\frac{7}{83}\right)\)	\(e\left(\frac{103}{332}\right)\)	\(e\left(\frac{53}{332}\right)\)	\(e\left(\frac{29}{166}\right)\)	\(e\left(\frac{99}{332}\right)\)	\(e\left(\frac{75}{166}\right)\)	\(e\left(\frac{64}{83}\right)\)	\(e\left(\frac{61}{332}\right)\)	\(e\left(\frac{7}{166}\right)\)
\(\chi_{25050}(3493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{332}\right)\)	\(e\left(\frac{54}{83}\right)\)	\(e\left(\frac{261}{332}\right)\)	\(e\left(\frac{231}{332}\right)\)	\(e\left(\frac{117}{166}\right)\)	\(e\left(\frac{325}{332}\right)\)	\(e\left(\frac{45}{166}\right)\)	\(e\left(\frac{55}{83}\right)\)	\(e\left(\frac{103}{332}\right)\)	\(e\left(\frac{137}{166}\right)\)
\(\chi_{25050}(3643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{332}\right)\)	\(e\left(\frac{15}{83}\right)\)	\(e\left(\frac{197}{332}\right)\)	\(e\left(\frac{327}{332}\right)\)	\(e\left(\frac{157}{166}\right)\)	\(e\left(\frac{141}{332}\right)\)	\(e\left(\frac{137}{166}\right)\)	\(e\left(\frac{66}{83}\right)\)	\(e\left(\frac{107}{332}\right)\)	\(e\left(\frac{15}{166}\right)\)
\(\chi_{25050}(3757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{271}{332}\right)\)	\(e\left(\frac{21}{83}\right)\)	\(e\left(\frac{143}{332}\right)\)	\(e\left(\frac{325}{332}\right)\)	\(e\left(\frac{87}{166}\right)\)	\(e\left(\frac{131}{332}\right)\)	\(e\left(\frac{59}{166}\right)\)	\(e\left(\frac{26}{83}\right)\)	\(e\left(\frac{17}{332}\right)\)	\(e\left(\frac{21}{166}\right)\)

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First 31 of 164 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	25050.bh
Modulus	$25050$
Conductor	$835$
Order	$332$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(25050\)
Conductor:	\(835\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(332\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 835.l	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)