LMFDB - Dirichlet character orbit 4225.cz

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4225, base_ring=CyclotomicField(780)) M = H._module chi = DirichletCharacter(H, M([507,730])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(17,4225)) 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:	$780$	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:	$\Q(\zeta_{780})$
Fixed field:	Number field defined by a degree 780 polynomial (not computed)

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{4225}(17,\cdot)$	$-1$	$1$	$e\left(\frac{457}{780}\right)$	$e\left(\frac{469}{780}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{73}{390}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{79}{390}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{127}{130}\right)$
$\chi_{4225}(62,\cdot)$	$-1$	$1$	$e\left(\frac{461}{780}\right)$	$e\left(\frac{497}{780}\right)$	$e\left(\frac{71}{390}\right)$	$e\left(\frac{89}{390}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{107}{390}\right)$	$e\left(\frac{283}{390}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{121}{130}\right)$
$\chi_{4225}(88,\cdot)$	$-1$	$1$	$e\left(\frac{491}{780}\right)$	$e\left(\frac{707}{780}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{209}{390}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{317}{390}\right)$	$e\left(\frac{73}{390}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{11}{130}\right)$
$\chi_{4225}(108,\cdot)$	$-1$	$1$	$e\left(\frac{427}{780}\right)$	$e\left(\frac{259}{780}\right)$	$e\left(\frac{37}{390}\right)$	$e\left(\frac{343}{390}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{259}{390}\right)$	$e\left(\frac{131}{390}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{107}{130}\right)$
$\chi_{4225}(127,\cdot)$	$-1$	$1$	$e\left(\frac{29}{780}\right)$	$e\left(\frac{593}{780}\right)$	$e\left(\frac{29}{390}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{203}{390}\right)$	$e\left(\frac{187}{390}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{119}{130}\right)$
$\chi_{4225}(153,\cdot)$	$-1$	$1$	$e\left(\frac{683}{780}\right)$	$e\left(\frac{491}{780}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{197}{390}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{163}{260}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{289}{390}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{113}{130}\right)$
$\chi_{4225}(173,\cdot)$	$-1$	$1$	$e\left(\frac{439}{780}\right)$	$e\left(\frac{343}{780}\right)$	$e\left(\frac{49}{390}\right)$	$e\left(\frac{1}{390}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{343}{390}\right)$	$e\left(\frac{47}{390}\right)$	$e\left(\frac{147}{260}\right)$	$e\left(\frac{89}{130}\right)$
$\chi_{4225}(212,\cdot)$	$-1$	$1$	$e\left(\frac{181}{780}\right)$	$e\left(\frac{97}{780}\right)$	$e\left(\frac{181}{390}\right)$	$e\left(\frac{139}{390}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{21}{130}\right)$
$\chi_{4225}(238,\cdot)$	$-1$	$1$	$e\left(\frac{451}{780}\right)$	$e\left(\frac{427}{780}\right)$	$e\left(\frac{61}{390}\right)$	$e\left(\frac{49}{390}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{191}{260}\right)$	$e\left(\frac{37}{390}\right)$	$e\left(\frac{353}{390}\right)$	$e\left(\frac{183}{260}\right)$	$e\left(\frac{71}{130}\right)$
$\chi_{4225}(277,\cdot)$	$-1$	$1$	$e\left(\frac{349}{780}\right)$	$e\left(\frac{493}{780}\right)$	$e\left(\frac{349}{390}\right)$	$e\left(\frac{31}{390}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{103}{390}\right)$	$e\left(\frac{287}{390}\right)$	$e\left(\frac{137}{260}\right)$	$e\left(\frac{29}{130}\right)$
$\chi_{4225}(283,\cdot)$	$-1$	$1$	$e\left(\frac{287}{780}\right)$	$e\left(\frac{59}{780}\right)$	$e\left(\frac{287}{390}\right)$	$e\left(\frac{173}{390}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{59}{390}\right)$	$e\left(\frac{331}{390}\right)$	$e\left(\frac{211}{260}\right)$	$e\left(\frac{57}{130}\right)$
$\chi_{4225}(303,\cdot)$	$-1$	$1$	$e\left(\frac{463}{780}\right)$	$e\left(\frac{511}{780}\right)$	$e\left(\frac{73}{390}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{203}{260}\right)$	$e\left(\frac{121}{390}\right)$	$e\left(\frac{269}{390}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{53}{130}\right)$
$\chi_{4225}(322,\cdot)$	$-1$	$1$	$e\left(\frac{293}{780}\right)$	$e\left(\frac{101}{780}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{197}{390}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{289}{390}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{113}{130}\right)$
$\chi_{4225}(342,\cdot)$	$-1$	$1$	$e\left(\frac{517}{780}\right)$	$e\left(\frac{109}{780}\right)$	$e\left(\frac{127}{390}\right)$	$e\left(\frac{313}{390}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{257}{260}\right)$	$e\left(\frac{109}{390}\right)$	$e\left(\frac{281}{390}\right)$	$e\left(\frac{121}{260}\right)$	$e\left(\frac{37}{130}\right)$
$\chi_{4225}(348,\cdot)$	$-1$	$1$	$e\left(\frac{479}{780}\right)$	$e\left(\frac{623}{780}\right)$	$e\left(\frac{89}{390}\right)$	$e\left(\frac{161}{390}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{233}{390}\right)$	$e\left(\frac{157}{390}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{29}{130}\right)$
$\chi_{4225}(387,\cdot)$	$-1$	$1$	$e\left(\frac{641}{780}\right)$	$e\left(\frac{197}{780}\right)$	$e\left(\frac{251}{390}\right)$	$e\left(\frac{29}{390}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{121}{260}\right)$	$e\left(\frac{197}{390}\right)$	$e\left(\frac{193}{390}\right)$	$e\left(\frac{233}{260}\right)$	$e\left(\frac{111}{130}\right)$
$\chi_{4225}(413,\cdot)$	$-1$	$1$	$e\left(\frac{671}{780}\right)$	$e\left(\frac{407}{780}\right)$	$e\left(\frac{281}{390}\right)$	$e\left(\frac{149}{390}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{151}{260}\right)$	$e\left(\frac{17}{390}\right)$	$e\left(\frac{373}{390}\right)$	$e\left(\frac{63}{260}\right)$	$e\left(\frac{1}{130}\right)$
$\chi_{4225}(433,\cdot)$	$-1$	$1$	$e\left(\frac{487}{780}\right)$	$e\left(\frac{679}{780}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{193}{390}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{227}{260}\right)$	$e\left(\frac{289}{390}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{17}{130}\right)$
$\chi_{4225}(452,\cdot)$	$-1$	$1$	$e\left(\frac{209}{780}\right)$	$e\left(\frac{293}{780}\right)$	$e\left(\frac{209}{390}\right)$	$e\left(\frac{251}{390}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{209}{260}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{109}{130}\right)$
$\chi_{4225}(472,\cdot)$	$-1$	$1$	$e\left(\frac{73}{780}\right)$	$e\left(\frac{121}{780}\right)$	$e\left(\frac{73}{390}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{121}{390}\right)$	$e\left(\frac{269}{390}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{53}{130}\right)$
$\chi_{4225}(478,\cdot)$	$-1$	$1$	$e\left(\frac{83}{780}\right)$	$e\left(\frac{191}{780}\right)$	$e\left(\frac{83}{390}\right)$	$e\left(\frac{137}{390}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{83}{260}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{103}{130}\right)$
$\chi_{4225}(498,\cdot)$	$-1$	$1$	$e\left(\frac{499}{780}\right)$	$e\left(\frac{763}{780}\right)$	$e\left(\frac{109}{390}\right)$	$e\left(\frac{241}{390}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{373}{390}\right)$	$e\left(\frac{17}{390}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{129}{130}\right)$
$\chi_{4225}(517,\cdot)$	$-1$	$1$	$e\left(\frac{557}{780}\right)$	$e\left(\frac{389}{780}\right)$	$e\left(\frac{167}{390}\right)$	$e\left(\frac{83}{390}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{37}{260}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{1}{390}\right)$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{107}{130}\right)$
$\chi_{4225}(537,\cdot)$	$-1$	$1$	$e\left(\frac{241}{780}\right)$	$e\left(\frac{517}{780}\right)$	$e\left(\frac{241}{390}\right)$	$e\left(\frac{379}{390}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{127}{390}\right)$	$e\left(\frac{263}{390}\right)$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{61}{130}\right)$
$\chi_{4225}(563,\cdot)$	$-1$	$1$	$e\left(\frac{511}{780}\right)$	$e\left(\frac{67}{780}\right)$	$e\left(\frac{121}{390}\right)$	$e\left(\frac{289}{390}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{251}{260}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{323}{390}\right)$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{111}{130}\right)$
$\chi_{4225}(602,\cdot)$	$-1$	$1$	$e\left(\frac{409}{780}\right)$	$e\left(\frac{133}{780}\right)$	$e\left(\frac{19}{390}\right)$	$e\left(\frac{271}{390}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{149}{260}\right)$	$e\left(\frac{133}{390}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{57}{260}\right)$	$e\left(\frac{69}{130}\right)$
$\chi_{4225}(608,\cdot)$	$-1$	$1$	$e\left(\frac{467}{780}\right)$	$e\left(\frac{539}{780}\right)$	$e\left(\frac{77}{390}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{207}{260}\right)$	$e\left(\frac{149}{390}\right)$	$e\left(\frac{241}{390}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{47}{130}\right)$
$\chi_{4225}(628,\cdot)$	$-1$	$1$	$e\left(\frac{523}{780}\right)$	$e\left(\frac{151}{780}\right)$	$e\left(\frac{133}{390}\right)$	$e\left(\frac{337}{390}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{151}{390}\right)$	$e\left(\frac{239}{390}\right)$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{93}{130}\right)$
$\chi_{4225}(647,\cdot)$	$-1$	$1$	$e\left(\frac{473}{780}\right)$	$e\left(\frac{581}{780}\right)$	$e\left(\frac{83}{390}\right)$	$e\left(\frac{137}{390}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{249}{260}\right)$	$e\left(\frac{103}{130}\right)$
$\chi_{4225}(667,\cdot)$	$-1$	$1$	$e\left(\frac{577}{780}\right)$	$e\left(\frac{529}{780}\right)$	$e\left(\frac{187}{390}\right)$	$e\left(\frac{163}{390}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{57}{260}\right)$	$e\left(\frac{139}{390}\right)$	$e\left(\frac{251}{390}\right)$	$e\left(\frac{41}{260}\right)$	$e\left(\frac{77}{130}\right)$
$\chi_{4225}(673,\cdot)$	$-1$	$1$	$e\left(\frac{659}{780}\right)$	$e\left(\frac{323}{780}\right)$	$e\left(\frac{269}{390}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{323}{390}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{19}{130}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{4225}(17,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{457}{780}\right)\)	\(e\left(\frac{469}{780}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{73}{390}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{79}{390}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{127}{130}\right)\)
\(\chi_{4225}(62,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{461}{780}\right)\)	\(e\left(\frac{497}{780}\right)\)	\(e\left(\frac{71}{390}\right)\)	\(e\left(\frac{89}{390}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{107}{390}\right)\)	\(e\left(\frac{283}{390}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{121}{130}\right)\)
\(\chi_{4225}(88,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{491}{780}\right)\)	\(e\left(\frac{707}{780}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{209}{390}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{317}{390}\right)\)	\(e\left(\frac{73}{390}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{11}{130}\right)\)
\(\chi_{4225}(108,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{427}{780}\right)\)	\(e\left(\frac{259}{780}\right)\)	\(e\left(\frac{37}{390}\right)\)	\(e\left(\frac{343}{390}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{259}{390}\right)\)	\(e\left(\frac{131}{390}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{107}{130}\right)\)
\(\chi_{4225}(127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{780}\right)\)	\(e\left(\frac{593}{780}\right)\)	\(e\left(\frac{29}{390}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{203}{390}\right)\)	\(e\left(\frac{187}{390}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{119}{130}\right)\)
\(\chi_{4225}(153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{683}{780}\right)\)	\(e\left(\frac{491}{780}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{197}{390}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{163}{260}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{289}{390}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{113}{130}\right)\)
\(\chi_{4225}(173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{439}{780}\right)\)	\(e\left(\frac{343}{780}\right)\)	\(e\left(\frac{49}{390}\right)\)	\(e\left(\frac{1}{390}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{343}{390}\right)\)	\(e\left(\frac{47}{390}\right)\)	\(e\left(\frac{147}{260}\right)\)	\(e\left(\frac{89}{130}\right)\)
\(\chi_{4225}(212,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{780}\right)\)	\(e\left(\frac{97}{780}\right)\)	\(e\left(\frac{181}{390}\right)\)	\(e\left(\frac{139}{390}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{21}{130}\right)\)
\(\chi_{4225}(238,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{451}{780}\right)\)	\(e\left(\frac{427}{780}\right)\)	\(e\left(\frac{61}{390}\right)\)	\(e\left(\frac{49}{390}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{191}{260}\right)\)	\(e\left(\frac{37}{390}\right)\)	\(e\left(\frac{353}{390}\right)\)	\(e\left(\frac{183}{260}\right)\)	\(e\left(\frac{71}{130}\right)\)
\(\chi_{4225}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{349}{780}\right)\)	\(e\left(\frac{493}{780}\right)\)	\(e\left(\frac{349}{390}\right)\)	\(e\left(\frac{31}{390}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{103}{390}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{137}{260}\right)\)	\(e\left(\frac{29}{130}\right)\)
\(\chi_{4225}(283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{287}{780}\right)\)	\(e\left(\frac{59}{780}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{173}{390}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{59}{390}\right)\)	\(e\left(\frac{331}{390}\right)\)	\(e\left(\frac{211}{260}\right)\)	\(e\left(\frac{57}{130}\right)\)
\(\chi_{4225}(303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{463}{780}\right)\)	\(e\left(\frac{511}{780}\right)\)	\(e\left(\frac{73}{390}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{203}{260}\right)\)	\(e\left(\frac{121}{390}\right)\)	\(e\left(\frac{269}{390}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{53}{130}\right)\)
\(\chi_{4225}(322,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{293}{780}\right)\)	\(e\left(\frac{101}{780}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{197}{390}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{289}{390}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{113}{130}\right)\)
\(\chi_{4225}(342,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{517}{780}\right)\)	\(e\left(\frac{109}{780}\right)\)	\(e\left(\frac{127}{390}\right)\)	\(e\left(\frac{313}{390}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{257}{260}\right)\)	\(e\left(\frac{109}{390}\right)\)	\(e\left(\frac{281}{390}\right)\)	\(e\left(\frac{121}{260}\right)\)	\(e\left(\frac{37}{130}\right)\)
\(\chi_{4225}(348,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{479}{780}\right)\)	\(e\left(\frac{623}{780}\right)\)	\(e\left(\frac{89}{390}\right)\)	\(e\left(\frac{161}{390}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{233}{390}\right)\)	\(e\left(\frac{157}{390}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{29}{130}\right)\)
\(\chi_{4225}(387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{641}{780}\right)\)	\(e\left(\frac{197}{780}\right)\)	\(e\left(\frac{251}{390}\right)\)	\(e\left(\frac{29}{390}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{121}{260}\right)\)	\(e\left(\frac{197}{390}\right)\)	\(e\left(\frac{193}{390}\right)\)	\(e\left(\frac{233}{260}\right)\)	\(e\left(\frac{111}{130}\right)\)
\(\chi_{4225}(413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{671}{780}\right)\)	\(e\left(\frac{407}{780}\right)\)	\(e\left(\frac{281}{390}\right)\)	\(e\left(\frac{149}{390}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{151}{260}\right)\)	\(e\left(\frac{17}{390}\right)\)	\(e\left(\frac{373}{390}\right)\)	\(e\left(\frac{63}{260}\right)\)	\(e\left(\frac{1}{130}\right)\)
\(\chi_{4225}(433,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{487}{780}\right)\)	\(e\left(\frac{679}{780}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{193}{390}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{227}{260}\right)\)	\(e\left(\frac{289}{390}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{17}{130}\right)\)
\(\chi_{4225}(452,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{780}\right)\)	\(e\left(\frac{293}{780}\right)\)	\(e\left(\frac{209}{390}\right)\)	\(e\left(\frac{251}{390}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{209}{260}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{109}{130}\right)\)
\(\chi_{4225}(472,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{780}\right)\)	\(e\left(\frac{121}{780}\right)\)	\(e\left(\frac{73}{390}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{121}{390}\right)\)	\(e\left(\frac{269}{390}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{53}{130}\right)\)
\(\chi_{4225}(478,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{780}\right)\)	\(e\left(\frac{191}{780}\right)\)	\(e\left(\frac{83}{390}\right)\)	\(e\left(\frac{137}{390}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{83}{260}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{103}{130}\right)\)
\(\chi_{4225}(498,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{499}{780}\right)\)	\(e\left(\frac{763}{780}\right)\)	\(e\left(\frac{109}{390}\right)\)	\(e\left(\frac{241}{390}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{373}{390}\right)\)	\(e\left(\frac{17}{390}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{129}{130}\right)\)
\(\chi_{4225}(517,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{557}{780}\right)\)	\(e\left(\frac{389}{780}\right)\)	\(e\left(\frac{167}{390}\right)\)	\(e\left(\frac{83}{390}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{37}{260}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{1}{390}\right)\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{107}{130}\right)\)
\(\chi_{4225}(537,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{780}\right)\)	\(e\left(\frac{517}{780}\right)\)	\(e\left(\frac{241}{390}\right)\)	\(e\left(\frac{379}{390}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{127}{390}\right)\)	\(e\left(\frac{263}{390}\right)\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{61}{130}\right)\)
\(\chi_{4225}(563,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{511}{780}\right)\)	\(e\left(\frac{67}{780}\right)\)	\(e\left(\frac{121}{390}\right)\)	\(e\left(\frac{289}{390}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{251}{260}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{323}{390}\right)\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{111}{130}\right)\)
\(\chi_{4225}(602,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{409}{780}\right)\)	\(e\left(\frac{133}{780}\right)\)	\(e\left(\frac{19}{390}\right)\)	\(e\left(\frac{271}{390}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{149}{260}\right)\)	\(e\left(\frac{133}{390}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{57}{260}\right)\)	\(e\left(\frac{69}{130}\right)\)
\(\chi_{4225}(608,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{467}{780}\right)\)	\(e\left(\frac{539}{780}\right)\)	\(e\left(\frac{77}{390}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{207}{260}\right)\)	\(e\left(\frac{149}{390}\right)\)	\(e\left(\frac{241}{390}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{47}{130}\right)\)
\(\chi_{4225}(628,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{523}{780}\right)\)	\(e\left(\frac{151}{780}\right)\)	\(e\left(\frac{133}{390}\right)\)	\(e\left(\frac{337}{390}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{151}{390}\right)\)	\(e\left(\frac{239}{390}\right)\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{93}{130}\right)\)
\(\chi_{4225}(647,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{473}{780}\right)\)	\(e\left(\frac{581}{780}\right)\)	\(e\left(\frac{83}{390}\right)\)	\(e\left(\frac{137}{390}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{249}{260}\right)\)	\(e\left(\frac{103}{130}\right)\)
\(\chi_{4225}(667,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{577}{780}\right)\)	\(e\left(\frac{529}{780}\right)\)	\(e\left(\frac{187}{390}\right)\)	\(e\left(\frac{163}{390}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{57}{260}\right)\)	\(e\left(\frac{139}{390}\right)\)	\(e\left(\frac{251}{390}\right)\)	\(e\left(\frac{41}{260}\right)\)	\(e\left(\frac{77}{130}\right)\)
\(\chi_{4225}(673,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{659}{780}\right)\)	\(e\left(\frac{323}{780}\right)\)	\(e\left(\frac{269}{390}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{323}{390}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{19}{130}\right)\)

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First 31 of 192 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.cz
Modulus	$4225$
Conductor	$4225$
Order	$780$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(4225\)
Conductor:	\(4225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(780\)	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)