LMFDB - Dirichlet character orbit 9801.bx

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9801, base_ring=CyclotomicField(594)) M = H._module chi = DirichletCharacter(H, M([374,270])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(34, 9801)) 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("9801.34"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$9801$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$9801$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$297$	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:	yes	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:	$\Q(\zeta_{297})$	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 297 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 180 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{9801}(34,\cdot)$	$1$	$1$	$e\left(\frac{25}{297}\right)$	$e\left(\frac{50}{297}\right)$	$e\left(\frac{35}{297}\right)$	$e\left(\frac{76}{297}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{281}{297}\right)$	$e\left(\frac{101}{297}\right)$	$e\left(\frac{100}{297}\right)$	$e\left(\frac{5}{99}\right)$
$\chi_{9801}(67,\cdot)$	$1$	$1$	$e\left(\frac{215}{297}\right)$	$e\left(\frac{133}{297}\right)$	$e\left(\frac{4}{297}\right)$	$e\left(\frac{119}{297}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{100}{297}\right)$	$e\left(\frac{37}{297}\right)$	$e\left(\frac{266}{297}\right)$	$e\left(\frac{43}{99}\right)$
$\chi_{9801}(133,\cdot)$	$1$	$1$	$e\left(\frac{1}{297}\right)$	$e\left(\frac{2}{297}\right)$	$e\left(\frac{239}{297}\right)$	$e\left(\frac{205}{297}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{35}{297}\right)$	$e\left(\frac{206}{297}\right)$	$e\left(\frac{4}{297}\right)$	$e\left(\frac{20}{99}\right)$
$\chi_{9801}(166,\cdot)$	$1$	$1$	$e\left(\frac{92}{297}\right)$	$e\left(\frac{184}{297}\right)$	$e\left(\frac{10}{297}\right)$	$e\left(\frac{149}{297}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{250}{297}\right)$	$e\left(\frac{241}{297}\right)$	$e\left(\frac{71}{297}\right)$	$e\left(\frac{58}{99}\right)$
$\chi_{9801}(232,\cdot)$	$1$	$1$	$e\left(\frac{274}{297}\right)$	$e\left(\frac{251}{297}\right)$	$e\left(\frac{146}{297}\right)$	$e\left(\frac{37}{297}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{86}{297}\right)$	$e\left(\frac{14}{297}\right)$	$e\left(\frac{205}{297}\right)$	$e\left(\frac{35}{99}\right)$
$\chi_{9801}(265,\cdot)$	$1$	$1$	$e\left(\frac{266}{297}\right)$	$e\left(\frac{235}{297}\right)$	$e\left(\frac{16}{297}\right)$	$e\left(\frac{179}{297}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{103}{297}\right)$	$e\left(\frac{148}{297}\right)$	$e\left(\frac{173}{297}\right)$	$e\left(\frac{73}{99}\right)$
$\chi_{9801}(331,\cdot)$	$1$	$1$	$e\left(\frac{250}{297}\right)$	$e\left(\frac{203}{297}\right)$	$e\left(\frac{53}{297}\right)$	$e\left(\frac{166}{297}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{137}{297}\right)$	$e\left(\frac{119}{297}\right)$	$e\left(\frac{109}{297}\right)$	$e\left(\frac{50}{99}\right)$
$\chi_{9801}(430,\cdot)$	$1$	$1$	$e\left(\frac{226}{297}\right)$	$e\left(\frac{155}{297}\right)$	$e\left(\frac{257}{297}\right)$	$e\left(\frac{295}{297}\right)$	$e\left(\frac{28}{99}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{188}{297}\right)$	$e\left(\frac{224}{297}\right)$	$e\left(\frac{13}{297}\right)$	$e\left(\frac{65}{99}\right)$
$\chi_{9801}(463,\cdot)$	$1$	$1$	$e\left(\frac{20}{297}\right)$	$e\left(\frac{40}{297}\right)$	$e\left(\frac{28}{297}\right)$	$e\left(\frac{239}{297}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{106}{297}\right)$	$e\left(\frac{259}{297}\right)$	$e\left(\frac{80}{297}\right)$	$e\left(\frac{4}{99}\right)$
$\chi_{9801}(529,\cdot)$	$1$	$1$	$e\left(\frac{202}{297}\right)$	$e\left(\frac{107}{297}\right)$	$e\left(\frac{164}{297}\right)$	$e\left(\frac{127}{297}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{239}{297}\right)$	$e\left(\frac{32}{297}\right)$	$e\left(\frac{214}{297}\right)$	$e\left(\frac{80}{99}\right)$
$\chi_{9801}(562,\cdot)$	$1$	$1$	$e\left(\frac{194}{297}\right)$	$e\left(\frac{91}{297}\right)$	$e\left(\frac{34}{297}\right)$	$e\left(\frac{269}{297}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{256}{297}\right)$	$e\left(\frac{166}{297}\right)$	$e\left(\frac{182}{297}\right)$	$e\left(\frac{19}{99}\right)$
$\chi_{9801}(628,\cdot)$	$1$	$1$	$e\left(\frac{178}{297}\right)$	$e\left(\frac{59}{297}\right)$	$e\left(\frac{71}{297}\right)$	$e\left(\frac{256}{297}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{290}{297}\right)$	$e\left(\frac{137}{297}\right)$	$e\left(\frac{118}{297}\right)$	$e\left(\frac{95}{99}\right)$
$\chi_{9801}(661,\cdot)$	$1$	$1$	$e\left(\frac{71}{297}\right)$	$e\left(\frac{142}{297}\right)$	$e\left(\frac{40}{297}\right)$	$e\left(\frac{2}{297}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{109}{297}\right)$	$e\left(\frac{73}{297}\right)$	$e\left(\frac{284}{297}\right)$	$e\left(\frac{34}{99}\right)$
$\chi_{9801}(760,\cdot)$	$1$	$1$	$e\left(\frac{245}{297}\right)$	$e\left(\frac{193}{297}\right)$	$e\left(\frac{46}{297}\right)$	$e\left(\frac{32}{297}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{259}{297}\right)$	$e\left(\frac{277}{297}\right)$	$e\left(\frac{89}{297}\right)$	$e\left(\frac{49}{99}\right)$
$\chi_{9801}(826,\cdot)$	$1$	$1$	$e\left(\frac{130}{297}\right)$	$e\left(\frac{260}{297}\right)$	$e\left(\frac{182}{297}\right)$	$e\left(\frac{217}{297}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{95}{297}\right)$	$e\left(\frac{50}{297}\right)$	$e\left(\frac{223}{297}\right)$	$e\left(\frac{26}{99}\right)$
$\chi_{9801}(859,\cdot)$	$1$	$1$	$e\left(\frac{122}{297}\right)$	$e\left(\frac{244}{297}\right)$	$e\left(\frac{52}{297}\right)$	$e\left(\frac{62}{297}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{112}{297}\right)$	$e\left(\frac{184}{297}\right)$	$e\left(\frac{191}{297}\right)$	$e\left(\frac{64}{99}\right)$
$\chi_{9801}(925,\cdot)$	$1$	$1$	$e\left(\frac{106}{297}\right)$	$e\left(\frac{212}{297}\right)$	$e\left(\frac{89}{297}\right)$	$e\left(\frac{49}{297}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{146}{297}\right)$	$e\left(\frac{155}{297}\right)$	$e\left(\frac{127}{297}\right)$	$e\left(\frac{41}{99}\right)$
$\chi_{9801}(958,\cdot)$	$1$	$1$	$e\left(\frac{296}{297}\right)$	$e\left(\frac{295}{297}\right)$	$e\left(\frac{58}{297}\right)$	$e\left(\frac{92}{297}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{262}{297}\right)$	$e\left(\frac{91}{297}\right)$	$e\left(\frac{293}{297}\right)$	$e\left(\frac{79}{99}\right)$
$\chi_{9801}(1024,\cdot)$	$1$	$1$	$e\left(\frac{82}{297}\right)$	$e\left(\frac{164}{297}\right)$	$e\left(\frac{293}{297}\right)$	$e\left(\frac{178}{297}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{197}{297}\right)$	$e\left(\frac{260}{297}\right)$	$e\left(\frac{31}{297}\right)$	$e\left(\frac{56}{99}\right)$
$\chi_{9801}(1057,\cdot)$	$1$	$1$	$e\left(\frac{173}{297}\right)$	$e\left(\frac{49}{297}\right)$	$e\left(\frac{64}{297}\right)$	$e\left(\frac{122}{297}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{115}{297}\right)$	$e\left(\frac{295}{297}\right)$	$e\left(\frac{98}{297}\right)$	$e\left(\frac{94}{99}\right)$
$\chi_{9801}(1123,\cdot)$	$1$	$1$	$e\left(\frac{58}{297}\right)$	$e\left(\frac{116}{297}\right)$	$e\left(\frac{200}{297}\right)$	$e\left(\frac{10}{297}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{248}{297}\right)$	$e\left(\frac{68}{297}\right)$	$e\left(\frac{232}{297}\right)$	$e\left(\frac{71}{99}\right)$
$\chi_{9801}(1156,\cdot)$	$1$	$1$	$e\left(\frac{50}{297}\right)$	$e\left(\frac{100}{297}\right)$	$e\left(\frac{70}{297}\right)$	$e\left(\frac{152}{297}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{265}{297}\right)$	$e\left(\frac{202}{297}\right)$	$e\left(\frac{200}{297}\right)$	$e\left(\frac{10}{99}\right)$
$\chi_{9801}(1222,\cdot)$	$1$	$1$	$e\left(\frac{34}{297}\right)$	$e\left(\frac{68}{297}\right)$	$e\left(\frac{107}{297}\right)$	$e\left(\frac{139}{297}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{2}{297}\right)$	$e\left(\frac{173}{297}\right)$	$e\left(\frac{136}{297}\right)$	$e\left(\frac{86}{99}\right)$
$\chi_{9801}(1255,\cdot)$	$1$	$1$	$e\left(\frac{224}{297}\right)$	$e\left(\frac{151}{297}\right)$	$e\left(\frac{76}{297}\right)$	$e\left(\frac{182}{297}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{118}{297}\right)$	$e\left(\frac{109}{297}\right)$	$e\left(\frac{5}{297}\right)$	$e\left(\frac{25}{99}\right)$
$\chi_{9801}(1321,\cdot)$	$1$	$1$	$e\left(\frac{10}{297}\right)$	$e\left(\frac{20}{297}\right)$	$e\left(\frac{14}{297}\right)$	$e\left(\frac{268}{297}\right)$	$e\left(\frac{10}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{53}{297}\right)$	$e\left(\frac{278}{297}\right)$	$e\left(\frac{40}{297}\right)$	$e\left(\frac{2}{99}\right)$
$\chi_{9801}(1354,\cdot)$	$1$	$1$	$e\left(\frac{101}{297}\right)$	$e\left(\frac{202}{297}\right)$	$e\left(\frac{82}{297}\right)$	$e\left(\frac{212}{297}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{268}{297}\right)$	$e\left(\frac{16}{297}\right)$	$e\left(\frac{107}{297}\right)$	$e\left(\frac{40}{99}\right)$
$\chi_{9801}(1420,\cdot)$	$1$	$1$	$e\left(\frac{283}{297}\right)$	$e\left(\frac{269}{297}\right)$	$e\left(\frac{218}{297}\right)$	$e\left(\frac{100}{297}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{104}{297}\right)$	$e\left(\frac{86}{297}\right)$	$e\left(\frac{241}{297}\right)$	$e\left(\frac{17}{99}\right)$
$\chi_{9801}(1519,\cdot)$	$1$	$1$	$e\left(\frac{259}{297}\right)$	$e\left(\frac{221}{297}\right)$	$e\left(\frac{125}{297}\right)$	$e\left(\frac{229}{297}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{155}{297}\right)$	$e\left(\frac{191}{297}\right)$	$e\left(\frac{145}{297}\right)$	$e\left(\frac{32}{99}\right)$
$\chi_{9801}(1552,\cdot)$	$1$	$1$	$e\left(\frac{152}{297}\right)$	$e\left(\frac{7}{297}\right)$	$e\left(\frac{94}{297}\right)$	$e\left(\frac{272}{297}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{271}{297}\right)$	$e\left(\frac{127}{297}\right)$	$e\left(\frac{14}{297}\right)$	$e\left(\frac{70}{99}\right)$
$\chi_{9801}(1618,\cdot)$	$1$	$1$	$e\left(\frac{235}{297}\right)$	$e\left(\frac{173}{297}\right)$	$e\left(\frac{32}{297}\right)$	$e\left(\frac{61}{297}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{206}{297}\right)$	$e\left(\frac{296}{297}\right)$	$e\left(\frac{49}{297}\right)$	$e\left(\frac{47}{99}\right)$
$\chi_{9801}(1651,\cdot)$	$1$	$1$	$e\left(\frac{29}{297}\right)$	$e\left(\frac{58}{297}\right)$	$e\left(\frac{100}{297}\right)$	$e\left(\frac{5}{297}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{124}{297}\right)$	$e\left(\frac{34}{297}\right)$	$e\left(\frac{116}{297}\right)$	$e\left(\frac{85}{99}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{9801}(34,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{297}\right)\)	\(e\left(\frac{50}{297}\right)\)	\(e\left(\frac{35}{297}\right)\)	\(e\left(\frac{76}{297}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{281}{297}\right)\)	\(e\left(\frac{101}{297}\right)\)	\(e\left(\frac{100}{297}\right)\)	\(e\left(\frac{5}{99}\right)\)
\(\chi_{9801}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{215}{297}\right)\)	\(e\left(\frac{133}{297}\right)\)	\(e\left(\frac{4}{297}\right)\)	\(e\left(\frac{119}{297}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{100}{297}\right)\)	\(e\left(\frac{37}{297}\right)\)	\(e\left(\frac{266}{297}\right)\)	\(e\left(\frac{43}{99}\right)\)
\(\chi_{9801}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{297}\right)\)	\(e\left(\frac{2}{297}\right)\)	\(e\left(\frac{239}{297}\right)\)	\(e\left(\frac{205}{297}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{35}{297}\right)\)	\(e\left(\frac{206}{297}\right)\)	\(e\left(\frac{4}{297}\right)\)	\(e\left(\frac{20}{99}\right)\)
\(\chi_{9801}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{297}\right)\)	\(e\left(\frac{184}{297}\right)\)	\(e\left(\frac{10}{297}\right)\)	\(e\left(\frac{149}{297}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{250}{297}\right)\)	\(e\left(\frac{241}{297}\right)\)	\(e\left(\frac{71}{297}\right)\)	\(e\left(\frac{58}{99}\right)\)
\(\chi_{9801}(232,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{274}{297}\right)\)	\(e\left(\frac{251}{297}\right)\)	\(e\left(\frac{146}{297}\right)\)	\(e\left(\frac{37}{297}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{86}{297}\right)\)	\(e\left(\frac{14}{297}\right)\)	\(e\left(\frac{205}{297}\right)\)	\(e\left(\frac{35}{99}\right)\)
\(\chi_{9801}(265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{266}{297}\right)\)	\(e\left(\frac{235}{297}\right)\)	\(e\left(\frac{16}{297}\right)\)	\(e\left(\frac{179}{297}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{103}{297}\right)\)	\(e\left(\frac{148}{297}\right)\)	\(e\left(\frac{173}{297}\right)\)	\(e\left(\frac{73}{99}\right)\)
\(\chi_{9801}(331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{250}{297}\right)\)	\(e\left(\frac{203}{297}\right)\)	\(e\left(\frac{53}{297}\right)\)	\(e\left(\frac{166}{297}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{137}{297}\right)\)	\(e\left(\frac{119}{297}\right)\)	\(e\left(\frac{109}{297}\right)\)	\(e\left(\frac{50}{99}\right)\)
\(\chi_{9801}(430,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{226}{297}\right)\)	\(e\left(\frac{155}{297}\right)\)	\(e\left(\frac{257}{297}\right)\)	\(e\left(\frac{295}{297}\right)\)	\(e\left(\frac{28}{99}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{188}{297}\right)\)	\(e\left(\frac{224}{297}\right)\)	\(e\left(\frac{13}{297}\right)\)	\(e\left(\frac{65}{99}\right)\)
\(\chi_{9801}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{297}\right)\)	\(e\left(\frac{40}{297}\right)\)	\(e\left(\frac{28}{297}\right)\)	\(e\left(\frac{239}{297}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{106}{297}\right)\)	\(e\left(\frac{259}{297}\right)\)	\(e\left(\frac{80}{297}\right)\)	\(e\left(\frac{4}{99}\right)\)
\(\chi_{9801}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{202}{297}\right)\)	\(e\left(\frac{107}{297}\right)\)	\(e\left(\frac{164}{297}\right)\)	\(e\left(\frac{127}{297}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{239}{297}\right)\)	\(e\left(\frac{32}{297}\right)\)	\(e\left(\frac{214}{297}\right)\)	\(e\left(\frac{80}{99}\right)\)
\(\chi_{9801}(562,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{194}{297}\right)\)	\(e\left(\frac{91}{297}\right)\)	\(e\left(\frac{34}{297}\right)\)	\(e\left(\frac{269}{297}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{256}{297}\right)\)	\(e\left(\frac{166}{297}\right)\)	\(e\left(\frac{182}{297}\right)\)	\(e\left(\frac{19}{99}\right)\)
\(\chi_{9801}(628,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{178}{297}\right)\)	\(e\left(\frac{59}{297}\right)\)	\(e\left(\frac{71}{297}\right)\)	\(e\left(\frac{256}{297}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{290}{297}\right)\)	\(e\left(\frac{137}{297}\right)\)	\(e\left(\frac{118}{297}\right)\)	\(e\left(\frac{95}{99}\right)\)
\(\chi_{9801}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{297}\right)\)	\(e\left(\frac{142}{297}\right)\)	\(e\left(\frac{40}{297}\right)\)	\(e\left(\frac{2}{297}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{109}{297}\right)\)	\(e\left(\frac{73}{297}\right)\)	\(e\left(\frac{284}{297}\right)\)	\(e\left(\frac{34}{99}\right)\)
\(\chi_{9801}(760,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{245}{297}\right)\)	\(e\left(\frac{193}{297}\right)\)	\(e\left(\frac{46}{297}\right)\)	\(e\left(\frac{32}{297}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{259}{297}\right)\)	\(e\left(\frac{277}{297}\right)\)	\(e\left(\frac{89}{297}\right)\)	\(e\left(\frac{49}{99}\right)\)
\(\chi_{9801}(826,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{130}{297}\right)\)	\(e\left(\frac{260}{297}\right)\)	\(e\left(\frac{182}{297}\right)\)	\(e\left(\frac{217}{297}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{95}{297}\right)\)	\(e\left(\frac{50}{297}\right)\)	\(e\left(\frac{223}{297}\right)\)	\(e\left(\frac{26}{99}\right)\)
\(\chi_{9801}(859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{122}{297}\right)\)	\(e\left(\frac{244}{297}\right)\)	\(e\left(\frac{52}{297}\right)\)	\(e\left(\frac{62}{297}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{112}{297}\right)\)	\(e\left(\frac{184}{297}\right)\)	\(e\left(\frac{191}{297}\right)\)	\(e\left(\frac{64}{99}\right)\)
\(\chi_{9801}(925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{106}{297}\right)\)	\(e\left(\frac{212}{297}\right)\)	\(e\left(\frac{89}{297}\right)\)	\(e\left(\frac{49}{297}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{146}{297}\right)\)	\(e\left(\frac{155}{297}\right)\)	\(e\left(\frac{127}{297}\right)\)	\(e\left(\frac{41}{99}\right)\)
\(\chi_{9801}(958,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{296}{297}\right)\)	\(e\left(\frac{295}{297}\right)\)	\(e\left(\frac{58}{297}\right)\)	\(e\left(\frac{92}{297}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{262}{297}\right)\)	\(e\left(\frac{91}{297}\right)\)	\(e\left(\frac{293}{297}\right)\)	\(e\left(\frac{79}{99}\right)\)
\(\chi_{9801}(1024,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{297}\right)\)	\(e\left(\frac{164}{297}\right)\)	\(e\left(\frac{293}{297}\right)\)	\(e\left(\frac{178}{297}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{197}{297}\right)\)	\(e\left(\frac{260}{297}\right)\)	\(e\left(\frac{31}{297}\right)\)	\(e\left(\frac{56}{99}\right)\)
\(\chi_{9801}(1057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{297}\right)\)	\(e\left(\frac{49}{297}\right)\)	\(e\left(\frac{64}{297}\right)\)	\(e\left(\frac{122}{297}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{115}{297}\right)\)	\(e\left(\frac{295}{297}\right)\)	\(e\left(\frac{98}{297}\right)\)	\(e\left(\frac{94}{99}\right)\)
\(\chi_{9801}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{297}\right)\)	\(e\left(\frac{116}{297}\right)\)	\(e\left(\frac{200}{297}\right)\)	\(e\left(\frac{10}{297}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{248}{297}\right)\)	\(e\left(\frac{68}{297}\right)\)	\(e\left(\frac{232}{297}\right)\)	\(e\left(\frac{71}{99}\right)\)
\(\chi_{9801}(1156,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{297}\right)\)	\(e\left(\frac{100}{297}\right)\)	\(e\left(\frac{70}{297}\right)\)	\(e\left(\frac{152}{297}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{265}{297}\right)\)	\(e\left(\frac{202}{297}\right)\)	\(e\left(\frac{200}{297}\right)\)	\(e\left(\frac{10}{99}\right)\)
\(\chi_{9801}(1222,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{297}\right)\)	\(e\left(\frac{68}{297}\right)\)	\(e\left(\frac{107}{297}\right)\)	\(e\left(\frac{139}{297}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{2}{297}\right)\)	\(e\left(\frac{173}{297}\right)\)	\(e\left(\frac{136}{297}\right)\)	\(e\left(\frac{86}{99}\right)\)
\(\chi_{9801}(1255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{224}{297}\right)\)	\(e\left(\frac{151}{297}\right)\)	\(e\left(\frac{76}{297}\right)\)	\(e\left(\frac{182}{297}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{118}{297}\right)\)	\(e\left(\frac{109}{297}\right)\)	\(e\left(\frac{5}{297}\right)\)	\(e\left(\frac{25}{99}\right)\)
\(\chi_{9801}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{297}\right)\)	\(e\left(\frac{20}{297}\right)\)	\(e\left(\frac{14}{297}\right)\)	\(e\left(\frac{268}{297}\right)\)	\(e\left(\frac{10}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{53}{297}\right)\)	\(e\left(\frac{278}{297}\right)\)	\(e\left(\frac{40}{297}\right)\)	\(e\left(\frac{2}{99}\right)\)
\(\chi_{9801}(1354,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{297}\right)\)	\(e\left(\frac{202}{297}\right)\)	\(e\left(\frac{82}{297}\right)\)	\(e\left(\frac{212}{297}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{268}{297}\right)\)	\(e\left(\frac{16}{297}\right)\)	\(e\left(\frac{107}{297}\right)\)	\(e\left(\frac{40}{99}\right)\)
\(\chi_{9801}(1420,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{297}\right)\)	\(e\left(\frac{269}{297}\right)\)	\(e\left(\frac{218}{297}\right)\)	\(e\left(\frac{100}{297}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{104}{297}\right)\)	\(e\left(\frac{86}{297}\right)\)	\(e\left(\frac{241}{297}\right)\)	\(e\left(\frac{17}{99}\right)\)
\(\chi_{9801}(1519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{297}\right)\)	\(e\left(\frac{221}{297}\right)\)	\(e\left(\frac{125}{297}\right)\)	\(e\left(\frac{229}{297}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{155}{297}\right)\)	\(e\left(\frac{191}{297}\right)\)	\(e\left(\frac{145}{297}\right)\)	\(e\left(\frac{32}{99}\right)\)
\(\chi_{9801}(1552,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{297}\right)\)	\(e\left(\frac{7}{297}\right)\)	\(e\left(\frac{94}{297}\right)\)	\(e\left(\frac{272}{297}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{271}{297}\right)\)	\(e\left(\frac{127}{297}\right)\)	\(e\left(\frac{14}{297}\right)\)	\(e\left(\frac{70}{99}\right)\)
\(\chi_{9801}(1618,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{297}\right)\)	\(e\left(\frac{173}{297}\right)\)	\(e\left(\frac{32}{297}\right)\)	\(e\left(\frac{61}{297}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{206}{297}\right)\)	\(e\left(\frac{296}{297}\right)\)	\(e\left(\frac{49}{297}\right)\)	\(e\left(\frac{47}{99}\right)\)
\(\chi_{9801}(1651,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{297}\right)\)	\(e\left(\frac{58}{297}\right)\)	\(e\left(\frac{100}{297}\right)\)	\(e\left(\frac{5}{297}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{124}{297}\right)\)	\(e\left(\frac{34}{297}\right)\)	\(e\left(\frac{116}{297}\right)\)	\(e\left(\frac{85}{99}\right)\)

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First 31 of 180 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	9801.bx
Modulus	$9801$
Conductor	$9801$
Order	$297$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(9801\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(9801\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(297\)	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:	yes	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);