LMFDB - Dirichlet character orbit 4225.cx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4225, base_ring=CyclotomicField(780)) M = H._module chi = DirichletCharacter(H, M([312,625])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(6,4225)) 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{4225}(6,\cdot)$	$-1$	$1$	$e\left(\frac{157}{780}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{157}{390}\right)$	$e\left(\frac{281}{780}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{727}{780}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{61}{65}\right)$
$\chi_{4225}(11,\cdot)$	$-1$	$1$	$e\left(\frac{359}{780}\right)$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{727}{780}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{629}{780}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{7}{65}\right)$
$\chi_{4225}(41,\cdot)$	$-1$	$1$	$e\left(\frac{581}{780}\right)$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{553}{780}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{251}{780}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{3}{65}\right)$
$\chi_{4225}(46,\cdot)$	$-1$	$1$	$e\left(\frac{343}{780}\right)$	$e\left(\frac{64}{195}\right)$	$e\left(\frac{343}{390}\right)$	$e\left(\frac{599}{780}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{83}{260}\right)$	$e\left(\frac{128}{195}\right)$	$e\left(\frac{73}{780}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{19}{65}\right)$
$\chi_{4225}(71,\cdot)$	$-1$	$1$	$e\left(\frac{373}{780}\right)$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{373}{390}\right)$	$e\left(\frac{449}{780}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{43}{780}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{29}{65}\right)$
$\chi_{4225}(106,\cdot)$	$-1$	$1$	$e\left(\frac{137}{780}\right)$	$e\left(\frac{191}{195}\right)$	$e\left(\frac{137}{390}\right)$	$e\left(\frac{121}{780}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{137}{260}\right)$	$e\left(\frac{187}{195}\right)$	$e\left(\frac{227}{780}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{11}{65}\right)$
$\chi_{4225}(111,\cdot)$	$-1$	$1$	$e\left(\frac{439}{780}\right)$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{49}{390}\right)$	$e\left(\frac{587}{780}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{74}{195}\right)$	$e\left(\frac{289}{780}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{12}{65}\right)$
$\chi_{4225}(136,\cdot)$	$-1$	$1$	$e\left(\frac{589}{780}\right)$	$e\left(\frac{7}{195}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{617}{780}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{14}{195}\right)$	$e\left(\frac{139}{780}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{62}{65}\right)$
$\chi_{4225}(141,\cdot)$	$-1$	$1$	$e\left(\frac{311}{780}\right)$	$e\left(\frac{8}{195}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{343}{780}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{51}{260}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{521}{780}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{43}{65}\right)$
$\chi_{4225}(171,\cdot)$	$-1$	$1$	$e\left(\frac{473}{780}\right)$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{83}{390}\right)$	$e\left(\frac{469}{780}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{193}{195}\right)$	$e\left(\frac{203}{780}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{19}{65}\right)$
$\chi_{4225}(206,\cdot)$	$-1$	$1$	$e\left(\frac{287}{780}\right)$	$e\left(\frac{161}{195}\right)$	$e\left(\frac{287}{390}\right)$	$e\left(\frac{151}{780}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{77}{780}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{61}{65}\right)$
$\chi_{4225}(236,\cdot)$	$-1$	$1$	$e\left(\frac{29}{780}\right)$	$e\left(\frac{2}{195}\right)$	$e\left(\frac{29}{390}\right)$	$e\left(\frac{37}{780}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{4}{195}\right)$	$e\left(\frac{179}{780}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{27}{65}\right)$
$\chi_{4225}(241,\cdot)$	$-1$	$1$	$e\left(\frac{631}{780}\right)$	$e\left(\frac{178}{195}\right)$	$e\left(\frac{241}{390}\right)$	$e\left(\frac{563}{780}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{161}{195}\right)$	$e\left(\frac{721}{780}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{63}{65}\right)$
$\chi_{4225}(266,\cdot)$	$-1$	$1$	$e\left(\frac{241}{780}\right)$	$e\left(\frac{178}{195}\right)$	$e\left(\frac{241}{390}\right)$	$e\left(\frac{173}{780}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{161}{195}\right)$	$e\left(\frac{331}{780}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{63}{65}\right)$
$\chi_{4225}(271,\cdot)$	$-1$	$1$	$e\left(\frac{263}{780}\right)$	$e\left(\frac{119}{195}\right)$	$e\left(\frac{263}{390}\right)$	$e\left(\frac{739}{780}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{43}{195}\right)$	$e\left(\frac{413}{780}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{14}{65}\right)$
$\chi_{4225}(306,\cdot)$	$-1$	$1$	$e\left(\frac{727}{780}\right)$	$e\left(\frac{151}{195}\right)$	$e\left(\frac{337}{390}\right)$	$e\left(\frac{551}{780}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{207}{260}\right)$	$e\left(\frac{107}{195}\right)$	$e\left(\frac{157}{780}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{56}{65}\right)$
$\chi_{4225}(331,\cdot)$	$-1$	$1$	$e\left(\frac{457}{780}\right)$	$e\left(\frac{166}{195}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{341}{780}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{137}{195}\right)$	$e\left(\frac{427}{780}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{31}{65}\right)$
$\chi_{4225}(336,\cdot)$	$-1$	$1$	$e\left(\frac{239}{780}\right)$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{239}{390}\right)$	$e\left(\frac{547}{780}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{154}{195}\right)$	$e\left(\frac{749}{780}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{4225}(366,\cdot)$	$-1$	$1$	$e\left(\frac{701}{780}\right)$	$e\left(\frac{8}{195}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{733}{780}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{131}{780}\right)$	$e\left(\frac{109}{130}\right)$	$e\left(\frac{43}{65}\right)$
$\chi_{4225}(371,\cdot)$	$-1$	$1$	$e\left(\frac{43}{780}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{43}{390}\right)$	$e\left(\frac{539}{780}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{53}{195}\right)$	$e\left(\frac{373}{780}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{49}{65}\right)$
$\chi_{4225}(396,\cdot)$	$-1$	$1$	$e\left(\frac{673}{780}\right)$	$e\left(\frac{154}{195}\right)$	$e\left(\frac{283}{390}\right)$	$e\left(\frac{509}{780}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{523}{780}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{64}{65}\right)$
$\chi_{4225}(431,\cdot)$	$-1$	$1$	$e\left(\frac{257}{780}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{301}{780}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{257}{260}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{107}{780}\right)$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{51}{65}\right)$
$\chi_{4225}(436,\cdot)$	$-1$	$1$	$e\left(\frac{139}{780}\right)$	$e\left(\frac{97}{195}\right)$	$e\left(\frac{139}{390}\right)$	$e\left(\frac{527}{780}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{589}{780}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{42}{65}\right)$
$\chi_{4225}(461,\cdot)$	$-1$	$1$	$e\left(\frac{109}{780}\right)$	$e\left(\frac{142}{195}\right)$	$e\left(\frac{109}{390}\right)$	$e\left(\frac{677}{780}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{89}{195}\right)$	$e\left(\frac{619}{780}\right)$	$e\left(\frac{1}{130}\right)$	$e\left(\frac{32}{65}\right)$
$\chi_{4225}(466,\cdot)$	$-1$	$1$	$e\left(\frac{191}{780}\right)$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{163}{780}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{191}{260}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{641}{780}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{3}{65}\right)$
$\chi_{4225}(496,\cdot)$	$-1$	$1$	$e\left(\frac{593}{780}\right)$	$e\left(\frac{14}{195}\right)$	$e\left(\frac{203}{390}\right)$	$e\left(\frac{649}{780}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{73}{260}\right)$	$e\left(\frac{28}{195}\right)$	$e\left(\frac{83}{780}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{59}{65}\right)$
$\chi_{4225}(531,\cdot)$	$-1$	$1$	$e\left(\frac{167}{780}\right)$	$e\left(\frac{146}{195}\right)$	$e\left(\frac{167}{390}\right)$	$e\left(\frac{751}{780}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{97}{195}\right)$	$e\left(\frac{197}{780}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{21}{65}\right)$
$\chi_{4225}(561,\cdot)$	$-1$	$1$	$e\left(\frac{149}{780}\right)$	$e\left(\frac{17}{195}\right)$	$e\left(\frac{149}{390}\right)$	$e\left(\frac{217}{780}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{149}{260}\right)$	$e\left(\frac{34}{195}\right)$	$e\left(\frac{59}{780}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{2}{65}\right)$
$\chi_{4225}(566,\cdot)$	$-1$	$1$	$e\left(\frac{331}{780}\right)$	$e\left(\frac{43}{195}\right)$	$e\left(\frac{331}{390}\right)$	$e\left(\frac{503}{780}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{71}{260}\right)$	$e\left(\frac{86}{195}\right)$	$e\left(\frac{241}{780}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{28}{65}\right)$
$\chi_{4225}(591,\cdot)$	$-1$	$1$	$e\left(\frac{541}{780}\right)$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{151}{390}\right)$	$e\left(\frac{233}{780}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{21}{260}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{31}{780}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{33}{65}\right)$
$\chi_{4225}(631,\cdot)$	$-1$	$1$	$e\left(\frac{427}{780}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{37}{390}\right)$	$e\left(\frac{491}{780}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{457}{780}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{21}{65}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{4225}(6,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{780}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{157}{390}\right)\)	\(e\left(\frac{281}{780}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{727}{780}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{61}{65}\right)\)
\(\chi_{4225}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{359}{780}\right)\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{727}{780}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{629}{780}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{7}{65}\right)\)
\(\chi_{4225}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{581}{780}\right)\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{553}{780}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{251}{780}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{3}{65}\right)\)
\(\chi_{4225}(46,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{343}{780}\right)\)	\(e\left(\frac{64}{195}\right)\)	\(e\left(\frac{343}{390}\right)\)	\(e\left(\frac{599}{780}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{83}{260}\right)\)	\(e\left(\frac{128}{195}\right)\)	\(e\left(\frac{73}{780}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{19}{65}\right)\)
\(\chi_{4225}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{373}{780}\right)\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{373}{390}\right)\)	\(e\left(\frac{449}{780}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{43}{780}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{29}{65}\right)\)
\(\chi_{4225}(106,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{780}\right)\)	\(e\left(\frac{191}{195}\right)\)	\(e\left(\frac{137}{390}\right)\)	\(e\left(\frac{121}{780}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{137}{260}\right)\)	\(e\left(\frac{187}{195}\right)\)	\(e\left(\frac{227}{780}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{11}{65}\right)\)
\(\chi_{4225}(111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{439}{780}\right)\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{49}{390}\right)\)	\(e\left(\frac{587}{780}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{74}{195}\right)\)	\(e\left(\frac{289}{780}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{12}{65}\right)\)
\(\chi_{4225}(136,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{589}{780}\right)\)	\(e\left(\frac{7}{195}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{617}{780}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{14}{195}\right)\)	\(e\left(\frac{139}{780}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{62}{65}\right)\)
\(\chi_{4225}(141,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{311}{780}\right)\)	\(e\left(\frac{8}{195}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{343}{780}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{51}{260}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{521}{780}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{43}{65}\right)\)
\(\chi_{4225}(171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{473}{780}\right)\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{83}{390}\right)\)	\(e\left(\frac{469}{780}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{193}{195}\right)\)	\(e\left(\frac{203}{780}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{19}{65}\right)\)
\(\chi_{4225}(206,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{287}{780}\right)\)	\(e\left(\frac{161}{195}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{151}{780}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{77}{780}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{61}{65}\right)\)
\(\chi_{4225}(236,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{780}\right)\)	\(e\left(\frac{2}{195}\right)\)	\(e\left(\frac{29}{390}\right)\)	\(e\left(\frac{37}{780}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{4}{195}\right)\)	\(e\left(\frac{179}{780}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{27}{65}\right)\)
\(\chi_{4225}(241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{631}{780}\right)\)	\(e\left(\frac{178}{195}\right)\)	\(e\left(\frac{241}{390}\right)\)	\(e\left(\frac{563}{780}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{161}{195}\right)\)	\(e\left(\frac{721}{780}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{63}{65}\right)\)
\(\chi_{4225}(266,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{780}\right)\)	\(e\left(\frac{178}{195}\right)\)	\(e\left(\frac{241}{390}\right)\)	\(e\left(\frac{173}{780}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{161}{195}\right)\)	\(e\left(\frac{331}{780}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{63}{65}\right)\)
\(\chi_{4225}(271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{780}\right)\)	\(e\left(\frac{119}{195}\right)\)	\(e\left(\frac{263}{390}\right)\)	\(e\left(\frac{739}{780}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{43}{195}\right)\)	\(e\left(\frac{413}{780}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{14}{65}\right)\)
\(\chi_{4225}(306,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{727}{780}\right)\)	\(e\left(\frac{151}{195}\right)\)	\(e\left(\frac{337}{390}\right)\)	\(e\left(\frac{551}{780}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{207}{260}\right)\)	\(e\left(\frac{107}{195}\right)\)	\(e\left(\frac{157}{780}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{56}{65}\right)\)
\(\chi_{4225}(331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{457}{780}\right)\)	\(e\left(\frac{166}{195}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{341}{780}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{137}{195}\right)\)	\(e\left(\frac{427}{780}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{31}{65}\right)\)
\(\chi_{4225}(336,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{239}{780}\right)\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{239}{390}\right)\)	\(e\left(\frac{547}{780}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{154}{195}\right)\)	\(e\left(\frac{749}{780}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{4225}(366,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{701}{780}\right)\)	\(e\left(\frac{8}{195}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{733}{780}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{131}{780}\right)\)	\(e\left(\frac{109}{130}\right)\)	\(e\left(\frac{43}{65}\right)\)
\(\chi_{4225}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{780}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{43}{390}\right)\)	\(e\left(\frac{539}{780}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{53}{195}\right)\)	\(e\left(\frac{373}{780}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{49}{65}\right)\)
\(\chi_{4225}(396,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{673}{780}\right)\)	\(e\left(\frac{154}{195}\right)\)	\(e\left(\frac{283}{390}\right)\)	\(e\left(\frac{509}{780}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{523}{780}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{64}{65}\right)\)
\(\chi_{4225}(431,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{780}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{301}{780}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{257}{260}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{107}{780}\right)\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{51}{65}\right)\)
\(\chi_{4225}(436,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{780}\right)\)	\(e\left(\frac{97}{195}\right)\)	\(e\left(\frac{139}{390}\right)\)	\(e\left(\frac{527}{780}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{589}{780}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{42}{65}\right)\)
\(\chi_{4225}(461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{780}\right)\)	\(e\left(\frac{142}{195}\right)\)	\(e\left(\frac{109}{390}\right)\)	\(e\left(\frac{677}{780}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{89}{195}\right)\)	\(e\left(\frac{619}{780}\right)\)	\(e\left(\frac{1}{130}\right)\)	\(e\left(\frac{32}{65}\right)\)
\(\chi_{4225}(466,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{780}\right)\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{163}{780}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{191}{260}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{641}{780}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{3}{65}\right)\)
\(\chi_{4225}(496,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{593}{780}\right)\)	\(e\left(\frac{14}{195}\right)\)	\(e\left(\frac{203}{390}\right)\)	\(e\left(\frac{649}{780}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{73}{260}\right)\)	\(e\left(\frac{28}{195}\right)\)	\(e\left(\frac{83}{780}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{59}{65}\right)\)
\(\chi_{4225}(531,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{780}\right)\)	\(e\left(\frac{146}{195}\right)\)	\(e\left(\frac{167}{390}\right)\)	\(e\left(\frac{751}{780}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{97}{195}\right)\)	\(e\left(\frac{197}{780}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{21}{65}\right)\)
\(\chi_{4225}(561,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{780}\right)\)	\(e\left(\frac{17}{195}\right)\)	\(e\left(\frac{149}{390}\right)\)	\(e\left(\frac{217}{780}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{149}{260}\right)\)	\(e\left(\frac{34}{195}\right)\)	\(e\left(\frac{59}{780}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{2}{65}\right)\)
\(\chi_{4225}(566,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{331}{780}\right)\)	\(e\left(\frac{43}{195}\right)\)	\(e\left(\frac{331}{390}\right)\)	\(e\left(\frac{503}{780}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{71}{260}\right)\)	\(e\left(\frac{86}{195}\right)\)	\(e\left(\frac{241}{780}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{28}{65}\right)\)
\(\chi_{4225}(591,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{541}{780}\right)\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{151}{390}\right)\)	\(e\left(\frac{233}{780}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{21}{260}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{31}{780}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{33}{65}\right)\)
\(\chi_{4225}(631,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{427}{780}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{37}{390}\right)\)	\(e\left(\frac{491}{780}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{457}{780}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{21}{65}\right)\)

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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.cx
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)