LMFDB - Dirichlet character orbit 8100.do

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8100, base_ring=CyclotomicField(540)) M = H._module chi = DirichletCharacter(H, M([270,440,351])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(67, 8100)) 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("8100.67"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8100$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$8100$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$540$	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:	$\Q(\zeta_{540})$	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 540 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 28 of 144 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8100}(67,\cdot)$	$1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{469}{540}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{331}{540}\right)$	$e\left(\frac{121}{270}\right)$	$e\left(\frac{269}{270}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{106}{135}\right)$
$\chi_{8100}(103,\cdot)$	$1$	$1$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{127}{270}\right)$	$e\left(\frac{391}{540}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{109}{540}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{131}{270}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{19}{135}\right)$
$\chi_{8100}(187,\cdot)$	$1$	$1$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{209}{270}\right)$	$e\left(\frac{197}{540}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{443}{540}\right)$	$e\left(\frac{113}{270}\right)$	$e\left(\frac{37}{270}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{128}{135}\right)$
$\chi_{8100}(223,\cdot)$	$1$	$1$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{221}{270}\right)$	$e\left(\frac{83}{540}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{77}{540}\right)$	$e\left(\frac{197}{270}\right)$	$e\left(\frac{43}{270}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{32}{135}\right)$
$\chi_{8100}(247,\cdot)$	$1$	$1$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{157}{270}\right)$	$e\left(\frac{241}{540}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{139}{540}\right)$	$e\left(\frac{19}{270}\right)$	$e\left(\frac{11}{270}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{49}{135}\right)$
$\chi_{8100}(283,\cdot)$	$1$	$1$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{43}{270}\right)$	$e\left(\frac{379}{540}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{241}{540}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{89}{270}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{16}{135}\right)$
$\chi_{8100}(367,\cdot)$	$1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{53}{270}\right)$	$e\left(\frac{329}{540}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{71}{540}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{229}{270}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{26}{135}\right)$
$\chi_{8100}(403,\cdot)$	$1$	$1$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{227}{270}\right)$	$e\left(\frac{431}{540}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{29}{540}\right)$	$e\left(\frac{239}{270}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{119}{135}\right)$
$\chi_{8100}(427,\cdot)$	$1$	$1$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{13}{540}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{487}{540}\right)$	$e\left(\frac{187}{270}\right)$	$e\left(\frac{23}{270}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{127}{135}\right)$
$\chi_{8100}(463,\cdot)$	$1$	$1$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{229}{270}\right)$	$e\left(\frac{367}{540}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{373}{540}\right)$	$e\left(\frac{253}{270}\right)$	$e\left(\frac{47}{270}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{13}{135}\right)$
$\chi_{8100}(547,\cdot)$	$1$	$1$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{167}{270}\right)$	$e\left(\frac{461}{540}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{239}{540}\right)$	$e\left(\frac{89}{270}\right)$	$e\left(\frac{151}{270}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{59}{135}\right)$
$\chi_{8100}(583,\cdot)$	$1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{233}{270}\right)$	$e\left(\frac{239}{540}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{521}{540}\right)$	$e\left(\frac{11}{270}\right)$	$e\left(\frac{49}{270}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{71}{135}\right)$
$\chi_{8100}(727,\cdot)$	$1$	$1$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{11}{270}\right)$	$e\left(\frac{53}{540}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{407}{540}\right)$	$e\left(\frac{77}{270}\right)$	$e\left(\frac{73}{270}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{92}{135}\right)$
$\chi_{8100}(763,\cdot)$	$1$	$1$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{239}{270}\right)$	$e\left(\frac{47}{540}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{473}{540}\right)$	$e\left(\frac{53}{270}\right)$	$e\left(\frac{187}{270}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{23}{135}\right)$
$\chi_{8100}(787,\cdot)$	$1$	$1$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{229}{270}\right)$	$e\left(\frac{97}{540}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{103}{540}\right)$	$e\left(\frac{253}{270}\right)$	$e\left(\frac{47}{270}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{13}{135}\right)$
$\chi_{8100}(823,\cdot)$	$1$	$1$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{61}{270}\right)$	$e\left(\frac{343}{540}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{97}{540}\right)$	$e\left(\frac{157}{270}\right)$	$e\left(\frac{233}{270}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{7}{135}\right)$
$\chi_{8100}(967,\cdot)$	$1$	$1$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{253}{270}\right)$	$e\left(\frac{409}{540}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{451}{540}\right)$	$e\left(\frac{151}{270}\right)$	$e\left(\frac{59}{270}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{91}{135}\right)$
$\chi_{8100}(1003,\cdot)$	$1$	$1$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{247}{270}\right)$	$e\left(\frac{331}{540}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{229}{540}\right)$	$e\left(\frac{109}{270}\right)$	$e\left(\frac{191}{270}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{4}{135}\right)$
$\chi_{8100}(1087,\cdot)$	$1$	$1$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{239}{270}\right)$	$e\left(\frac{317}{540}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{203}{540}\right)$	$e\left(\frac{53}{270}\right)$	$e\left(\frac{187}{270}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{23}{135}\right)$
$\chi_{8100}(1123,\cdot)$	$1$	$1$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{251}{270}\right)$	$e\left(\frac{203}{540}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{377}{540}\right)$	$e\left(\frac{137}{270}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{62}{135}\right)$
$\chi_{8100}(1147,\cdot)$	$1$	$1$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{7}{270}\right)$	$e\left(\frac{181}{540}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{259}{540}\right)$	$e\left(\frac{49}{270}\right)$	$e\left(\frac{71}{270}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{34}{135}\right)$
$\chi_{8100}(1183,\cdot)$	$1$	$1$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{163}{270}\right)$	$e\left(\frac{319}{540}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{361}{540}\right)$	$e\left(\frac{61}{270}\right)$	$e\left(\frac{149}{270}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{1}{135}\right)$
$\chi_{8100}(1267,\cdot)$	$1$	$1$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{83}{270}\right)$	$e\left(\frac{449}{540}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{371}{540}\right)$	$e\left(\frac{41}{270}\right)$	$e\left(\frac{109}{270}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{56}{135}\right)$
$\chi_{8100}(1303,\cdot)$	$1$	$1$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{257}{270}\right)$	$e\left(\frac{11}{540}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{329}{540}\right)$	$e\left(\frac{179}{270}\right)$	$e\left(\frac{61}{270}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{14}{135}\right)$
$\chi_{8100}(1327,\cdot)$	$1$	$1$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{493}{540}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{67}{540}\right)$	$e\left(\frac{217}{270}\right)$	$e\left(\frac{83}{270}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{112}{135}\right)$
$\chi_{8100}(1363,\cdot)$	$1$	$1$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{307}{540}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{493}{540}\right)$	$e\left(\frac{13}{270}\right)$	$e\left(\frac{107}{270}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{133}{135}\right)$
$\chi_{8100}(1447,\cdot)$	$1$	$1$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{197}{270}\right)$	$e\left(\frac{41}{540}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{539}{540}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{89}{135}\right)$
$\chi_{8100}(1483,\cdot)$	$1$	$1$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{263}{270}\right)$	$e\left(\frac{359}{540}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{281}{540}\right)$	$e\left(\frac{221}{270}\right)$	$e\left(\frac{199}{270}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{101}{135}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8100}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{469}{540}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{331}{540}\right)\)	\(e\left(\frac{121}{270}\right)\)	\(e\left(\frac{269}{270}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{106}{135}\right)\)
\(\chi_{8100}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{127}{270}\right)\)	\(e\left(\frac{391}{540}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{109}{540}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{131}{270}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{19}{135}\right)\)
\(\chi_{8100}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{209}{270}\right)\)	\(e\left(\frac{197}{540}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{443}{540}\right)\)	\(e\left(\frac{113}{270}\right)\)	\(e\left(\frac{37}{270}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{128}{135}\right)\)
\(\chi_{8100}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{221}{270}\right)\)	\(e\left(\frac{83}{540}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{77}{540}\right)\)	\(e\left(\frac{197}{270}\right)\)	\(e\left(\frac{43}{270}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{32}{135}\right)\)
\(\chi_{8100}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{157}{270}\right)\)	\(e\left(\frac{241}{540}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{139}{540}\right)\)	\(e\left(\frac{19}{270}\right)\)	\(e\left(\frac{11}{270}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{49}{135}\right)\)
\(\chi_{8100}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{43}{270}\right)\)	\(e\left(\frac{379}{540}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{241}{540}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{89}{270}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{16}{135}\right)\)
\(\chi_{8100}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{53}{270}\right)\)	\(e\left(\frac{329}{540}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{71}{540}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{229}{270}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{26}{135}\right)\)
\(\chi_{8100}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{227}{270}\right)\)	\(e\left(\frac{431}{540}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{29}{540}\right)\)	\(e\left(\frac{239}{270}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{119}{135}\right)\)
\(\chi_{8100}(427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{13}{540}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{487}{540}\right)\)	\(e\left(\frac{187}{270}\right)\)	\(e\left(\frac{23}{270}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{127}{135}\right)\)
\(\chi_{8100}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{229}{270}\right)\)	\(e\left(\frac{367}{540}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{373}{540}\right)\)	\(e\left(\frac{253}{270}\right)\)	\(e\left(\frac{47}{270}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{13}{135}\right)\)
\(\chi_{8100}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{167}{270}\right)\)	\(e\left(\frac{461}{540}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{239}{540}\right)\)	\(e\left(\frac{89}{270}\right)\)	\(e\left(\frac{151}{270}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{59}{135}\right)\)
\(\chi_{8100}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{233}{270}\right)\)	\(e\left(\frac{239}{540}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{521}{540}\right)\)	\(e\left(\frac{11}{270}\right)\)	\(e\left(\frac{49}{270}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{71}{135}\right)\)
\(\chi_{8100}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{11}{270}\right)\)	\(e\left(\frac{53}{540}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{407}{540}\right)\)	\(e\left(\frac{77}{270}\right)\)	\(e\left(\frac{73}{270}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{92}{135}\right)\)
\(\chi_{8100}(763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{239}{270}\right)\)	\(e\left(\frac{47}{540}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{473}{540}\right)\)	\(e\left(\frac{53}{270}\right)\)	\(e\left(\frac{187}{270}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{23}{135}\right)\)
\(\chi_{8100}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{229}{270}\right)\)	\(e\left(\frac{97}{540}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{103}{540}\right)\)	\(e\left(\frac{253}{270}\right)\)	\(e\left(\frac{47}{270}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{13}{135}\right)\)
\(\chi_{8100}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{61}{270}\right)\)	\(e\left(\frac{343}{540}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{97}{540}\right)\)	\(e\left(\frac{157}{270}\right)\)	\(e\left(\frac{233}{270}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{7}{135}\right)\)
\(\chi_{8100}(967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{253}{270}\right)\)	\(e\left(\frac{409}{540}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{451}{540}\right)\)	\(e\left(\frac{151}{270}\right)\)	\(e\left(\frac{59}{270}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{91}{135}\right)\)
\(\chi_{8100}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{247}{270}\right)\)	\(e\left(\frac{331}{540}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{229}{540}\right)\)	\(e\left(\frac{109}{270}\right)\)	\(e\left(\frac{191}{270}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{4}{135}\right)\)
\(\chi_{8100}(1087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{239}{270}\right)\)	\(e\left(\frac{317}{540}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{203}{540}\right)\)	\(e\left(\frac{53}{270}\right)\)	\(e\left(\frac{187}{270}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{23}{135}\right)\)
\(\chi_{8100}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{251}{270}\right)\)	\(e\left(\frac{203}{540}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{377}{540}\right)\)	\(e\left(\frac{137}{270}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{62}{135}\right)\)
\(\chi_{8100}(1147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{7}{270}\right)\)	\(e\left(\frac{181}{540}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{259}{540}\right)\)	\(e\left(\frac{49}{270}\right)\)	\(e\left(\frac{71}{270}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{34}{135}\right)\)
\(\chi_{8100}(1183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{163}{270}\right)\)	\(e\left(\frac{319}{540}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{361}{540}\right)\)	\(e\left(\frac{61}{270}\right)\)	\(e\left(\frac{149}{270}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{1}{135}\right)\)
\(\chi_{8100}(1267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{83}{270}\right)\)	\(e\left(\frac{449}{540}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{371}{540}\right)\)	\(e\left(\frac{41}{270}\right)\)	\(e\left(\frac{109}{270}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{56}{135}\right)\)
\(\chi_{8100}(1303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{257}{270}\right)\)	\(e\left(\frac{11}{540}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{329}{540}\right)\)	\(e\left(\frac{179}{270}\right)\)	\(e\left(\frac{61}{270}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{14}{135}\right)\)
\(\chi_{8100}(1327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{493}{540}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{67}{540}\right)\)	\(e\left(\frac{217}{270}\right)\)	\(e\left(\frac{83}{270}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{112}{135}\right)\)
\(\chi_{8100}(1363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{307}{540}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{493}{540}\right)\)	\(e\left(\frac{13}{270}\right)\)	\(e\left(\frac{107}{270}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{133}{135}\right)\)
\(\chi_{8100}(1447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{197}{270}\right)\)	\(e\left(\frac{41}{540}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{539}{540}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{89}{135}\right)\)
\(\chi_{8100}(1483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{263}{270}\right)\)	\(e\left(\frac{359}{540}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{281}{540}\right)\)	\(e\left(\frac{221}{270}\right)\)	\(e\left(\frac{199}{270}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{101}{135}\right)\)

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First 28 of 144 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	8100.do
Modulus	$8100$
Conductor	$8100$
Order	$540$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8100\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8100\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(540\)	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);