LMFDB - Dirichlet character orbit 4225.co

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4225, base_ring=CyclotomicField(260)) M = H._module chi = DirichletCharacter(H, M([182,245])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(34,4225)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4225$
Conductor:	$4225$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$260$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{260})$
Fixed field:	Number field defined by a degree 260 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{4225}(34,\cdot)$	$-1$	$1$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{63}{65}\right)$
$\chi_{4225}(44,\cdot)$	$-1$	$1$	$e\left(\frac{149}{260}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{87}{260}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{187}{260}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{189}{260}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{6}{65}\right)$
$\chi_{4225}(109,\cdot)$	$-1$	$1$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{71}{260}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{51}{260}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{43}{65}\right)$
$\chi_{4225}(164,\cdot)$	$-1$	$1$	$e\left(\frac{223}{260}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{149}{260}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{63}{260}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{2}{65}\right)$
$\chi_{4225}(229,\cdot)$	$-1$	$1$	$e\left(\frac{251}{260}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{253}{260}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{233}{260}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{191}{260}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{4}{65}\right)$
$\chi_{4225}(294,\cdot)$	$-1$	$1$	$e\left(\frac{19}{260}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{57}{260}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{59}{260}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{6}{65}\right)$
$\chi_{4225}(304,\cdot)$	$-1$	$1$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{23}{260}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{163}{260}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{41}{260}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{24}{65}\right)$
$\chi_{4225}(359,\cdot)$	$-1$	$1$	$e\left(\frac{47}{260}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{187}{260}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{8}{65}\right)$
$\chi_{4225}(369,\cdot)$	$-1$	$1$	$e\left(\frac{9}{260}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{61}{65}\right)$
$\chi_{4225}(434,\cdot)$	$-1$	$1$	$e\left(\frac{137}{260}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{251}{260}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{151}{260}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{33}{65}\right)$
$\chi_{4225}(489,\cdot)$	$-1$	$1$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{49}{260}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{183}{260}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{12}{65}\right)$
$\chi_{4225}(554,\cdot)$	$-1$	$1$	$e\left(\frac{131}{260}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{133}{260}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{51}{260}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{14}{65}\right)$
$\chi_{4225}(564,\cdot)$	$-1$	$1$	$e\left(\frac{133}{260}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{42}{65}\right)$
$\chi_{4225}(619,\cdot)$	$-1$	$1$	$e\left(\frac{159}{260}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{37}{260}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{16}{65}\right)$
$\chi_{4225}(629,\cdot)$	$-1$	$1$	$e\left(\frac{1}{260}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{203}{260}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{14}{65}\right)$
$\chi_{4225}(684,\cdot)$	$-1$	$1$	$e\left(\frac{187}{260}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{1}{260}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{41}{260}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{47}{260}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{18}{65}\right)$
$\chi_{4225}(694,\cdot)$	$-1$	$1$	$e\left(\frac{129}{260}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{187}{260}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{127}{260}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{209}{260}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{51}{65}\right)$
$\chi_{4225}(759,\cdot)$	$-1$	$1$	$e\left(\frac{257}{260}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{171}{260}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{251}{260}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{23}{65}\right)$
$\chi_{4225}(814,\cdot)$	$-1$	$1$	$e\left(\frac{243}{260}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{189}{260}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{209}{260}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{22}{65}\right)$
$\chi_{4225}(879,\cdot)$	$-1$	$1$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{171}{260}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{24}{65}\right)$
$\chi_{4225}(889,\cdot)$	$-1$	$1$	$e\left(\frac{253}{260}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{4225}(954,\cdot)$	$-1$	$1$	$e\left(\frac{121}{260}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{4}{65}\right)$
$\chi_{4225}(1009,\cdot)$	$-1$	$1$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{81}{260}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{28}{65}\right)$
$\chi_{4225}(1019,\cdot)$	$-1$	$1$	$e\left(\frac{249}{260}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{107}{260}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{227}{260}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{41}{65}\right)$
$\chi_{4225}(1139,\cdot)$	$-1$	$1$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{9}{260}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{163}{260}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{4225}(1204,\cdot)$	$-1$	$1$	$e\left(\frac{151}{260}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{233}{260}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{193}{260}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{34}{65}\right)$
$\chi_{4225}(1214,\cdot)$	$-1$	$1$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{59}{260}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{173}{260}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{22}{65}\right)$
$\chi_{4225}(1269,\cdot)$	$-1$	$1$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{9}{65}\right)$	$e\left(\frac{159}{260}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{36}{65}\right)$
$\chi_{4225}(1279,\cdot)$	$-1$	$1$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{203}{260}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{59}{65}\right)$
$\chi_{4225}(1334,\cdot)$	$-1$	$1$	$e\left(\frac{207}{260}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{161}{260}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{38}{65}\right)$
$\chi_{4225}(1344,\cdot)$	$-1$	$1$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{31}{65}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{4225}(34,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)
\(\chi_{4225}(44,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{260}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{87}{260}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{187}{260}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{189}{260}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{6}{65}\right)\)
\(\chi_{4225}(109,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{71}{260}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{51}{260}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{43}{65}\right)\)
\(\chi_{4225}(164,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{223}{260}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{149}{260}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{63}{260}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{2}{65}\right)\)
\(\chi_{4225}(229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{251}{260}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{253}{260}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{233}{260}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{191}{260}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{4}{65}\right)\)
\(\chi_{4225}(294,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{260}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{57}{260}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{59}{260}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{6}{65}\right)\)
\(\chi_{4225}(304,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{23}{260}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{163}{260}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{41}{260}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{24}{65}\right)\)
\(\chi_{4225}(359,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{260}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{187}{260}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)
\(\chi_{4225}(369,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{260}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)
\(\chi_{4225}(434,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{260}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{251}{260}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{151}{260}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)
\(\chi_{4225}(489,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{49}{260}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{183}{260}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{12}{65}\right)\)
\(\chi_{4225}(554,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{260}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{133}{260}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{51}{260}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{14}{65}\right)\)
\(\chi_{4225}(564,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{260}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{42}{65}\right)\)
\(\chi_{4225}(619,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{159}{260}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{37}{260}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{16}{65}\right)\)
\(\chi_{4225}(629,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{260}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{203}{260}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{14}{65}\right)\)
\(\chi_{4225}(684,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{260}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{1}{260}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{41}{260}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{47}{260}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{18}{65}\right)\)
\(\chi_{4225}(694,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{129}{260}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{187}{260}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{127}{260}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{209}{260}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{51}{65}\right)\)
\(\chi_{4225}(759,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{260}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{171}{260}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{251}{260}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{23}{65}\right)\)
\(\chi_{4225}(814,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{243}{260}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{189}{260}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{209}{260}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{22}{65}\right)\)
\(\chi_{4225}(879,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{171}{260}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{24}{65}\right)\)
\(\chi_{4225}(889,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{260}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{4225}(954,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{260}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{4}{65}\right)\)
\(\chi_{4225}(1009,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{81}{260}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{28}{65}\right)\)
\(\chi_{4225}(1019,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{249}{260}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{107}{260}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{227}{260}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{41}{65}\right)\)
\(\chi_{4225}(1139,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{9}{260}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{163}{260}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{4225}(1204,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{260}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{233}{260}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{193}{260}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{34}{65}\right)\)
\(\chi_{4225}(1214,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{59}{260}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{173}{260}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{22}{65}\right)\)
\(\chi_{4225}(1269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{9}{65}\right)\)	\(e\left(\frac{159}{260}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{36}{65}\right)\)
\(\chi_{4225}(1279,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{203}{260}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{59}{65}\right)\)
\(\chi_{4225}(1334,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{207}{260}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{161}{260}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{38}{65}\right)\)
\(\chi_{4225}(1344,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{31}{65}\right)\)

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First 31 of 96 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	4225.co
Modulus	$4225$
Conductor	$4225$
Order	$260$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(4225\)
Conductor:	\(4225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(260\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)