LMFDB - Dirichlet character orbit 45738.iy

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45738, base_ring=CyclotomicField(990)) M = H._module chi = DirichletCharacter(H, M([880,0,828])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(169, 45738)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45738.169"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$45738$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3267$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$495$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 3267.bs	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{495})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 495 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 240 characters in Galois orbit

Character	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{45738}(169,\cdot)$	$1$	$1$	$e\left(\frac{166}{495}\right)$	$e\left(\frac{289}{495}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{332}{495}\right)$	$e\left(\frac{53}{495}\right)$	$e\left(\frac{349}{495}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{172}{495}\right)$
$\chi_{45738}(295,\cdot)$	$1$	$1$	$e\left(\frac{43}{495}\right)$	$e\left(\frac{382}{495}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{86}{495}\right)$	$e\left(\frac{464}{495}\right)$	$e\left(\frac{487}{495}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{301}{495}\right)$
$\chi_{45738}(421,\cdot)$	$1$	$1$	$e\left(\frac{109}{495}\right)$	$e\left(\frac{151}{495}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{218}{495}\right)$	$e\left(\frac{2}{495}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{268}{495}\right)$
$\chi_{45738}(841,\cdot)$	$1$	$1$	$e\left(\frac{212}{495}\right)$	$e\left(\frac{53}{495}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{424}{495}\right)$	$e\left(\frac{181}{495}\right)$	$e\left(\frac{398}{495}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{494}{495}\right)$
$\chi_{45738}(1093,\cdot)$	$1$	$1$	$e\left(\frac{281}{495}\right)$	$e\left(\frac{194}{495}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{67}{495}\right)$	$e\left(\frac{373}{495}\right)$	$e\left(\frac{224}{495}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{482}{495}\right)$
$\chi_{45738}(1303,\cdot)$	$1$	$1$	$e\left(\frac{247}{495}\right)$	$e\left(\frac{433}{495}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{494}{495}\right)$	$e\left(\frac{386}{495}\right)$	$e\left(\frac{403}{495}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{244}{495}\right)$
$\chi_{45738}(1345,\cdot)$	$1$	$1$	$e\left(\frac{134}{495}\right)$	$e\left(\frac{281}{495}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{268}{495}\right)$	$e\left(\frac{7}{495}\right)$	$e\left(\frac{401}{495}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{443}{495}\right)$
$\chi_{45738}(1555,\cdot)$	$1$	$1$	$e\left(\frac{91}{495}\right)$	$e\left(\frac{394}{495}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{182}{495}\right)$	$e\left(\frac{38}{495}\right)$	$e\left(\frac{409}{495}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{142}{495}\right)$
$\chi_{45738}(1681,\cdot)$	$1$	$1$	$e\left(\frac{193}{495}\right)$	$e\left(\frac{172}{495}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{386}{495}\right)$	$e\left(\frac{494}{495}\right)$	$e\left(\frac{367}{495}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{361}{495}\right)$
$\chi_{45738}(1807,\cdot)$	$1$	$1$	$e\left(\frac{394}{495}\right)$	$e\left(\frac{346}{495}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{293}{495}\right)$	$e\left(\frac{257}{495}\right)$	$e\left(\frac{226}{495}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{283}{495}\right)$
$\chi_{45738}(2227,\cdot)$	$1$	$1$	$e\left(\frac{317}{495}\right)$	$e\left(\frac{203}{495}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{139}{495}\right)$	$e\left(\frac{301}{495}\right)$	$e\left(\frac{413}{495}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{239}{495}\right)$
$\chi_{45738}(2479,\cdot)$	$1$	$1$	$e\left(\frac{206}{495}\right)$	$e\left(\frac{299}{495}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{412}{495}\right)$	$e\left(\frac{358}{495}\right)$	$e\left(\frac{284}{495}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{452}{495}\right)$
$\chi_{45738}(2605,\cdot)$	$1$	$1$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{32}{495}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{184}{495}\right)$	$e\left(\frac{287}{495}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{401}{495}\right)$
$\chi_{45738}(2731,\cdot)$	$1$	$1$	$e\left(\frac{419}{495}\right)$	$e\left(\frac{476}{495}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{343}{495}\right)$	$e\left(\frac{262}{495}\right)$	$e\left(\frac{371}{495}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{458}{495}\right)$
$\chi_{45738}(2941,\cdot)$	$1$	$1$	$e\left(\frac{16}{495}\right)$	$e\left(\frac{4}{495}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{32}{495}\right)$	$e\left(\frac{23}{495}\right)$	$e\left(\frac{469}{495}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{112}{495}\right)$
$\chi_{45738}(3067,\cdot)$	$1$	$1$	$e\left(\frac{343}{495}\right)$	$e\left(\frac{457}{495}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{191}{495}\right)$	$e\left(\frac{29}{495}\right)$	$e\left(\frac{247}{495}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{421}{495}\right)$
$\chi_{45738}(3193,\cdot)$	$1$	$1$	$e\left(\frac{184}{495}\right)$	$e\left(\frac{46}{495}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{368}{495}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{196}{495}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{298}{495}\right)$
$\chi_{45738}(3613,\cdot)$	$1$	$1$	$e\left(\frac{422}{495}\right)$	$e\left(\frac{353}{495}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{349}{495}\right)$	$e\left(\frac{421}{495}\right)$	$e\left(\frac{428}{495}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{479}{495}\right)$
$\chi_{45738}(3865,\cdot)$	$1$	$1$	$e\left(\frac{131}{495}\right)$	$e\left(\frac{404}{495}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{262}{495}\right)$	$e\left(\frac{343}{495}\right)$	$e\left(\frac{344}{495}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{422}{495}\right)$
$\chi_{45738}(3991,\cdot)$	$1$	$1$	$e\left(\frac{278}{495}\right)$	$e\left(\frac{317}{495}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{61}{495}\right)$	$e\left(\frac{214}{495}\right)$	$e\left(\frac{167}{495}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{461}{495}\right)$
$\chi_{45738}(4075,\cdot)$	$1$	$1$	$e\left(\frac{457}{495}\right)$	$e\left(\frac{238}{495}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{38}{99}\right)$	$e\left(\frac{419}{495}\right)$	$e\left(\frac{131}{495}\right)$	$e\left(\frac{433}{495}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{229}{495}\right)$
$\chi_{45738}(4327,\cdot)$	$1$	$1$	$e\left(\frac{436}{495}\right)$	$e\left(\frac{109}{495}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{377}{495}\right)$	$e\left(\frac{8}{495}\right)$	$e\left(\frac{34}{495}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{82}{495}\right)$
$\chi_{45738}(4453,\cdot)$	$1$	$1$	$e\left(\frac{493}{495}\right)$	$e\left(\frac{247}{495}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{491}{495}\right)$	$e\left(\frac{59}{495}\right)$	$e\left(\frac{127}{495}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{481}{495}\right)$
$\chi_{45738}(4579,\cdot)$	$1$	$1$	$e\left(\frac{469}{495}\right)$	$e\left(\frac{241}{495}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{443}{495}\right)$	$e\left(\frac{272}{495}\right)$	$e\left(\frac{166}{495}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{313}{495}\right)$
$\chi_{45738}(4999,\cdot)$	$1$	$1$	$e\left(\frac{32}{495}\right)$	$e\left(\frac{8}{495}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{64}{495}\right)$	$e\left(\frac{46}{495}\right)$	$e\left(\frac{443}{495}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{224}{495}\right)$
$\chi_{45738}(5251,\cdot)$	$1$	$1$	$e\left(\frac{56}{495}\right)$	$e\left(\frac{14}{495}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{112}{495}\right)$	$e\left(\frac{328}{495}\right)$	$e\left(\frac{404}{495}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{392}{495}\right)$
$\chi_{45738}(5377,\cdot)$	$1$	$1$	$e\left(\frac{428}{495}\right)$	$e\left(\frac{107}{495}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{361}{495}\right)$	$e\left(\frac{244}{495}\right)$	$e\left(\frac{47}{495}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{26}{495}\right)$
$\chi_{45738}(5461,\cdot)$	$1$	$1$	$e\left(\frac{67}{495}\right)$	$e\left(\frac{388}{495}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{134}{495}\right)$	$e\left(\frac{251}{495}\right)$	$e\left(\frac{448}{495}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{469}{495}\right)$
$\chi_{45738}(5503,\cdot)$	$1$	$1$	$e\left(\frac{494}{495}\right)$	$e\left(\frac{371}{495}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{493}{495}\right)$	$e\left(\frac{277}{495}\right)$	$e\left(\frac{311}{495}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{488}{495}\right)$
$\chi_{45738}(5713,\cdot)$	$1$	$1$	$e\left(\frac{361}{495}\right)$	$e\left(\frac{214}{495}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{227}{495}\right)$	$e\left(\frac{488}{495}\right)$	$e\left(\frac{94}{495}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{52}{495}\right)$
$\chi_{45738}(5839,\cdot)$	$1$	$1$	$e\left(\frac{148}{495}\right)$	$e\left(\frac{37}{495}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{296}{495}\right)$	$e\left(\frac{89}{495}\right)$	$e\left(\frac{7}{495}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{46}{495}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{45738}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{166}{495}\right)\)	\(e\left(\frac{289}{495}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{332}{495}\right)\)	\(e\left(\frac{53}{495}\right)\)	\(e\left(\frac{349}{495}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{172}{495}\right)\)
\(\chi_{45738}(295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{495}\right)\)	\(e\left(\frac{382}{495}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{86}{495}\right)\)	\(e\left(\frac{464}{495}\right)\)	\(e\left(\frac{487}{495}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{301}{495}\right)\)
\(\chi_{45738}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{495}\right)\)	\(e\left(\frac{151}{495}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{218}{495}\right)\)	\(e\left(\frac{2}{495}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{268}{495}\right)\)
\(\chi_{45738}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{212}{495}\right)\)	\(e\left(\frac{53}{495}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{424}{495}\right)\)	\(e\left(\frac{181}{495}\right)\)	\(e\left(\frac{398}{495}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{494}{495}\right)\)
\(\chi_{45738}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{495}\right)\)	\(e\left(\frac{194}{495}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{67}{495}\right)\)	\(e\left(\frac{373}{495}\right)\)	\(e\left(\frac{224}{495}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{482}{495}\right)\)
\(\chi_{45738}(1303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{495}\right)\)	\(e\left(\frac{433}{495}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{494}{495}\right)\)	\(e\left(\frac{386}{495}\right)\)	\(e\left(\frac{403}{495}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{244}{495}\right)\)
\(\chi_{45738}(1345,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{134}{495}\right)\)	\(e\left(\frac{281}{495}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{268}{495}\right)\)	\(e\left(\frac{7}{495}\right)\)	\(e\left(\frac{401}{495}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{443}{495}\right)\)
\(\chi_{45738}(1555,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{495}\right)\)	\(e\left(\frac{394}{495}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{182}{495}\right)\)	\(e\left(\frac{38}{495}\right)\)	\(e\left(\frac{409}{495}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{142}{495}\right)\)
\(\chi_{45738}(1681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{495}\right)\)	\(e\left(\frac{172}{495}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{386}{495}\right)\)	\(e\left(\frac{494}{495}\right)\)	\(e\left(\frac{367}{495}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{361}{495}\right)\)
\(\chi_{45738}(1807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{394}{495}\right)\)	\(e\left(\frac{346}{495}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{293}{495}\right)\)	\(e\left(\frac{257}{495}\right)\)	\(e\left(\frac{226}{495}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{283}{495}\right)\)
\(\chi_{45738}(2227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{317}{495}\right)\)	\(e\left(\frac{203}{495}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{139}{495}\right)\)	\(e\left(\frac{301}{495}\right)\)	\(e\left(\frac{413}{495}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{239}{495}\right)\)
\(\chi_{45738}(2479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{206}{495}\right)\)	\(e\left(\frac{299}{495}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{412}{495}\right)\)	\(e\left(\frac{358}{495}\right)\)	\(e\left(\frac{284}{495}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{452}{495}\right)\)
\(\chi_{45738}(2605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{32}{495}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{184}{495}\right)\)	\(e\left(\frac{287}{495}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{401}{495}\right)\)
\(\chi_{45738}(2731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{419}{495}\right)\)	\(e\left(\frac{476}{495}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{343}{495}\right)\)	\(e\left(\frac{262}{495}\right)\)	\(e\left(\frac{371}{495}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{458}{495}\right)\)
\(\chi_{45738}(2941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{495}\right)\)	\(e\left(\frac{4}{495}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{32}{495}\right)\)	\(e\left(\frac{23}{495}\right)\)	\(e\left(\frac{469}{495}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{112}{495}\right)\)
\(\chi_{45738}(3067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{495}\right)\)	\(e\left(\frac{457}{495}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{191}{495}\right)\)	\(e\left(\frac{29}{495}\right)\)	\(e\left(\frac{247}{495}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{421}{495}\right)\)
\(\chi_{45738}(3193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{184}{495}\right)\)	\(e\left(\frac{46}{495}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{368}{495}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{196}{495}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{298}{495}\right)\)
\(\chi_{45738}(3613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{422}{495}\right)\)	\(e\left(\frac{353}{495}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{349}{495}\right)\)	\(e\left(\frac{421}{495}\right)\)	\(e\left(\frac{428}{495}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{479}{495}\right)\)
\(\chi_{45738}(3865,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{495}\right)\)	\(e\left(\frac{404}{495}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{262}{495}\right)\)	\(e\left(\frac{343}{495}\right)\)	\(e\left(\frac{344}{495}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{422}{495}\right)\)
\(\chi_{45738}(3991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{278}{495}\right)\)	\(e\left(\frac{317}{495}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{61}{495}\right)\)	\(e\left(\frac{214}{495}\right)\)	\(e\left(\frac{167}{495}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{461}{495}\right)\)
\(\chi_{45738}(4075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{457}{495}\right)\)	\(e\left(\frac{238}{495}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{38}{99}\right)\)	\(e\left(\frac{419}{495}\right)\)	\(e\left(\frac{131}{495}\right)\)	\(e\left(\frac{433}{495}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{229}{495}\right)\)
\(\chi_{45738}(4327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{436}{495}\right)\)	\(e\left(\frac{109}{495}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{377}{495}\right)\)	\(e\left(\frac{8}{495}\right)\)	\(e\left(\frac{34}{495}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{82}{495}\right)\)
\(\chi_{45738}(4453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{493}{495}\right)\)	\(e\left(\frac{247}{495}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{491}{495}\right)\)	\(e\left(\frac{59}{495}\right)\)	\(e\left(\frac{127}{495}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{481}{495}\right)\)
\(\chi_{45738}(4579,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{469}{495}\right)\)	\(e\left(\frac{241}{495}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{443}{495}\right)\)	\(e\left(\frac{272}{495}\right)\)	\(e\left(\frac{166}{495}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{313}{495}\right)\)
\(\chi_{45738}(4999,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{495}\right)\)	\(e\left(\frac{8}{495}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{64}{495}\right)\)	\(e\left(\frac{46}{495}\right)\)	\(e\left(\frac{443}{495}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{224}{495}\right)\)
\(\chi_{45738}(5251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{495}\right)\)	\(e\left(\frac{14}{495}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{112}{495}\right)\)	\(e\left(\frac{328}{495}\right)\)	\(e\left(\frac{404}{495}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{392}{495}\right)\)
\(\chi_{45738}(5377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{428}{495}\right)\)	\(e\left(\frac{107}{495}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{361}{495}\right)\)	\(e\left(\frac{244}{495}\right)\)	\(e\left(\frac{47}{495}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{26}{495}\right)\)
\(\chi_{45738}(5461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{495}\right)\)	\(e\left(\frac{388}{495}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{134}{495}\right)\)	\(e\left(\frac{251}{495}\right)\)	\(e\left(\frac{448}{495}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{469}{495}\right)\)
\(\chi_{45738}(5503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{494}{495}\right)\)	\(e\left(\frac{371}{495}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{493}{495}\right)\)	\(e\left(\frac{277}{495}\right)\)	\(e\left(\frac{311}{495}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{488}{495}\right)\)
\(\chi_{45738}(5713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{495}\right)\)	\(e\left(\frac{214}{495}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{227}{495}\right)\)	\(e\left(\frac{488}{495}\right)\)	\(e\left(\frac{94}{495}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{52}{495}\right)\)
\(\chi_{45738}(5839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{495}\right)\)	\(e\left(\frac{37}{495}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{296}{495}\right)\)	\(e\left(\frac{89}{495}\right)\)	\(e\left(\frac{7}{495}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{46}{495}\right)\)

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First 31 of 240 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	45738.iy
Modulus	$45738$
Conductor	$3267$
Order	$495$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(45738\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3267\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(495\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 3267.bs	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);