LMFDB - Dirichlet character orbit 8100.dk

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8100, base_ring=CyclotomicField(270)) M = H._module chi = DirichletCharacter(H, M([0,265,54])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(41, 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("8100.41"); 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:	$2025$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$270$	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 2025.bt	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{135})$	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 270 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8100}(41,\cdot)$	$-1$	$1$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{259}{270}\right)$	$e\left(\frac{88}{135}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{269}{270}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{31}{135}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{221}{270}\right)$
$\chi_{8100}(221,\cdot)$	$-1$	$1$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{127}{270}\right)$	$e\left(\frac{64}{135}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{257}{270}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{173}{270}\right)$
$\chi_{8100}(281,\cdot)$	$-1$	$1$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{53}{270}\right)$	$e\left(\frac{116}{135}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{103}{270}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{47}{135}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{187}{270}\right)$
$\chi_{8100}(461,\cdot)$	$-1$	$1$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{2}{135}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{167}{270}\right)$	$e\left(\frac{59}{135}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{229}{270}\right)$
$\chi_{8100}(581,\cdot)$	$-1$	$1$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{16}{135}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{233}{270}\right)$	$e\left(\frac{121}{270}\right)$	$e\left(\frac{67}{135}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{77}{270}\right)$
$\chi_{8100}(641,\cdot)$	$-1$	$1$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{149}{270}\right)$	$e\left(\frac{23}{135}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{259}{270}\right)$	$e\left(\frac{233}{270}\right)$	$e\left(\frac{71}{135}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{270}\right)$
$\chi_{8100}(761,\cdot)$	$-1$	$1$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{1}{270}\right)$	$e\left(\frac{127}{135}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{221}{270}\right)$	$e\left(\frac{7}{270}\right)$	$e\left(\frac{34}{135}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{29}{270}\right)$
$\chi_{8100}(821,\cdot)$	$-1$	$1$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{197}{270}\right)$	$e\left(\frac{44}{135}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{67}{270}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{83}{135}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{43}{270}\right)$
$\chi_{8100}(941,\cdot)$	$-1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{139}{270}\right)$	$e\left(\frac{103}{135}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{209}{270}\right)$	$e\left(\frac{163}{270}\right)$	$e\left(\frac{1}{135}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{251}{270}\right)$
$\chi_{8100}(1121,\cdot)$	$-1$	$1$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{7}{270}\right)$	$e\left(\frac{79}{135}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{197}{270}\right)$	$e\left(\frac{49}{270}\right)$	$e\left(\frac{103}{135}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{203}{270}\right)$
$\chi_{8100}(1181,\cdot)$	$-1$	$1$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{23}{270}\right)$	$e\left(\frac{86}{135}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{223}{270}\right)$	$e\left(\frac{161}{270}\right)$	$e\left(\frac{107}{135}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{127}{270}\right)$
$\chi_{8100}(1361,\cdot)$	$-1$	$1$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{71}{270}\right)$	$e\left(\frac{107}{135}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{227}{270}\right)$	$e\left(\frac{119}{135}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{169}{270}\right)$
$\chi_{8100}(1481,\cdot)$	$-1$	$1$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{13}{270}\right)$	$e\left(\frac{31}{135}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{173}{270}\right)$	$e\left(\frac{91}{270}\right)$	$e\left(\frac{37}{135}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{107}{270}\right)$
$\chi_{8100}(1541,\cdot)$	$-1$	$1$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{128}{135}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{109}{270}\right)$	$e\left(\frac{23}{270}\right)$	$e\left(\frac{131}{135}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{211}{270}\right)$
$\chi_{8100}(1661,\cdot)$	$-1$	$1$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{151}{270}\right)$	$e\left(\frac{7}{135}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{161}{270}\right)$	$e\left(\frac{247}{270}\right)$	$e\left(\frac{4}{135}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{59}{270}\right)$
$\chi_{8100}(1721,\cdot)$	$-1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{167}{270}\right)$	$e\left(\frac{14}{135}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{187}{270}\right)$	$e\left(\frac{89}{270}\right)$	$e\left(\frac{8}{135}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{253}{270}\right)$
$\chi_{8100}(1841,\cdot)$	$-1$	$1$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{19}{270}\right)$	$e\left(\frac{118}{135}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{149}{270}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{106}{135}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{270}\right)$
$\chi_{8100}(2021,\cdot)$	$-1$	$1$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{157}{270}\right)$	$e\left(\frac{94}{135}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{137}{270}\right)$	$e\left(\frac{19}{270}\right)$	$e\left(\frac{73}{135}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{233}{270}\right)$
$\chi_{8100}(2081,\cdot)$	$-1$	$1$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{263}{270}\right)$	$e\left(\frac{56}{135}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{73}{270}\right)$	$e\left(\frac{221}{270}\right)$	$e\left(\frac{32}{135}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{67}{270}\right)$
$\chi_{8100}(2261,\cdot)$	$-1$	$1$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{41}{270}\right)$	$e\left(\frac{77}{135}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{151}{270}\right)$	$e\left(\frac{17}{270}\right)$	$e\left(\frac{44}{135}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{109}{270}\right)$
$\chi_{8100}(2381,\cdot)$	$-1$	$1$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{163}{270}\right)$	$e\left(\frac{46}{135}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{113}{270}\right)$	$e\left(\frac{61}{270}\right)$	$e\left(\frac{7}{135}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{137}{270}\right)$
$\chi_{8100}(2441,\cdot)$	$-1$	$1$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{89}{270}\right)$	$e\left(\frac{98}{135}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{229}{270}\right)$	$e\left(\frac{83}{270}\right)$	$e\left(\frac{56}{135}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{151}{270}\right)$
$\chi_{8100}(2561,\cdot)$	$-1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{22}{135}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{217}{270}\right)$	$e\left(\frac{109}{135}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{89}{270}\right)$
$\chi_{8100}(2621,\cdot)$	$-1$	$1$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{137}{270}\right)$	$e\left(\frac{119}{135}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{37}{270}\right)$	$e\left(\frac{149}{270}\right)$	$e\left(\frac{68}{135}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{193}{270}\right)$
$\chi_{8100}(2741,\cdot)$	$-1$	$1$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{169}{270}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{89}{270}\right)$	$e\left(\frac{103}{270}\right)$	$e\left(\frac{76}{135}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{41}{270}\right)$
$\chi_{8100}(2921,\cdot)$	$-1$	$1$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{37}{270}\right)$	$e\left(\frac{109}{135}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{77}{270}\right)$	$e\left(\frac{259}{270}\right)$	$e\left(\frac{43}{135}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{263}{270}\right)$
$\chi_{8100}(2981,\cdot)$	$-1$	$1$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{233}{270}\right)$	$e\left(\frac{26}{135}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{11}{270}\right)$	$e\left(\frac{92}{135}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{7}{270}\right)$
$\chi_{8100}(3161,\cdot)$	$-1$	$1$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{11}{270}\right)$	$e\left(\frac{47}{135}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{270}\right)$	$e\left(\frac{77}{270}\right)$	$e\left(\frac{104}{135}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{49}{270}\right)$
$\chi_{8100}(3281,\cdot)$	$-1$	$1$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{43}{270}\right)$	$e\left(\frac{61}{135}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{53}{270}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{112}{135}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{167}{270}\right)$
$\chi_{8100}(3341,\cdot)$	$-1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{59}{270}\right)$	$e\left(\frac{68}{135}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{143}{270}\right)$	$e\left(\frac{116}{135}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{91}{270}\right)$
$\chi_{8100}(3461,\cdot)$	$-1$	$1$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{37}{135}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{41}{270}\right)$	$e\left(\frac{187}{270}\right)$	$e\left(\frac{79}{135}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{119}{270}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8100}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{259}{270}\right)\)	\(e\left(\frac{88}{135}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{269}{270}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{31}{135}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{221}{270}\right)\)
\(\chi_{8100}(221,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{127}{270}\right)\)	\(e\left(\frac{64}{135}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{257}{270}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{173}{270}\right)\)
\(\chi_{8100}(281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{53}{270}\right)\)	\(e\left(\frac{116}{135}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{103}{270}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{47}{135}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{187}{270}\right)\)
\(\chi_{8100}(461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{2}{135}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{167}{270}\right)\)	\(e\left(\frac{59}{135}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{229}{270}\right)\)
\(\chi_{8100}(581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{16}{135}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{233}{270}\right)\)	\(e\left(\frac{121}{270}\right)\)	\(e\left(\frac{67}{135}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{77}{270}\right)\)
\(\chi_{8100}(641,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{149}{270}\right)\)	\(e\left(\frac{23}{135}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{259}{270}\right)\)	\(e\left(\frac{233}{270}\right)\)	\(e\left(\frac{71}{135}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{270}\right)\)
\(\chi_{8100}(761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{1}{270}\right)\)	\(e\left(\frac{127}{135}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{221}{270}\right)\)	\(e\left(\frac{7}{270}\right)\)	\(e\left(\frac{34}{135}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{29}{270}\right)\)
\(\chi_{8100}(821,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{197}{270}\right)\)	\(e\left(\frac{44}{135}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{67}{270}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{83}{135}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{43}{270}\right)\)
\(\chi_{8100}(941,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{139}{270}\right)\)	\(e\left(\frac{103}{135}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{209}{270}\right)\)	\(e\left(\frac{163}{270}\right)\)	\(e\left(\frac{1}{135}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{251}{270}\right)\)
\(\chi_{8100}(1121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{7}{270}\right)\)	\(e\left(\frac{79}{135}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{197}{270}\right)\)	\(e\left(\frac{49}{270}\right)\)	\(e\left(\frac{103}{135}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{203}{270}\right)\)
\(\chi_{8100}(1181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{23}{270}\right)\)	\(e\left(\frac{86}{135}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{223}{270}\right)\)	\(e\left(\frac{161}{270}\right)\)	\(e\left(\frac{107}{135}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{127}{270}\right)\)
\(\chi_{8100}(1361,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{71}{270}\right)\)	\(e\left(\frac{107}{135}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{227}{270}\right)\)	\(e\left(\frac{119}{135}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{169}{270}\right)\)
\(\chi_{8100}(1481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{13}{270}\right)\)	\(e\left(\frac{31}{135}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{173}{270}\right)\)	\(e\left(\frac{91}{270}\right)\)	\(e\left(\frac{37}{135}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{107}{270}\right)\)
\(\chi_{8100}(1541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{128}{135}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{109}{270}\right)\)	\(e\left(\frac{23}{270}\right)\)	\(e\left(\frac{131}{135}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{211}{270}\right)\)
\(\chi_{8100}(1661,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{151}{270}\right)\)	\(e\left(\frac{7}{135}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{161}{270}\right)\)	\(e\left(\frac{247}{270}\right)\)	\(e\left(\frac{4}{135}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{59}{270}\right)\)
\(\chi_{8100}(1721,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{167}{270}\right)\)	\(e\left(\frac{14}{135}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{187}{270}\right)\)	\(e\left(\frac{89}{270}\right)\)	\(e\left(\frac{8}{135}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{253}{270}\right)\)
\(\chi_{8100}(1841,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{19}{270}\right)\)	\(e\left(\frac{118}{135}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{149}{270}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{106}{135}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{270}\right)\)
\(\chi_{8100}(2021,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{157}{270}\right)\)	\(e\left(\frac{94}{135}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{137}{270}\right)\)	\(e\left(\frac{19}{270}\right)\)	\(e\left(\frac{73}{135}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{233}{270}\right)\)
\(\chi_{8100}(2081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{263}{270}\right)\)	\(e\left(\frac{56}{135}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{73}{270}\right)\)	\(e\left(\frac{221}{270}\right)\)	\(e\left(\frac{32}{135}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{67}{270}\right)\)
\(\chi_{8100}(2261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{41}{270}\right)\)	\(e\left(\frac{77}{135}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{151}{270}\right)\)	\(e\left(\frac{17}{270}\right)\)	\(e\left(\frac{44}{135}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{109}{270}\right)\)
\(\chi_{8100}(2381,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{163}{270}\right)\)	\(e\left(\frac{46}{135}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{113}{270}\right)\)	\(e\left(\frac{61}{270}\right)\)	\(e\left(\frac{7}{135}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{137}{270}\right)\)
\(\chi_{8100}(2441,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{89}{270}\right)\)	\(e\left(\frac{98}{135}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{229}{270}\right)\)	\(e\left(\frac{83}{270}\right)\)	\(e\left(\frac{56}{135}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{151}{270}\right)\)
\(\chi_{8100}(2561,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{22}{135}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{217}{270}\right)\)	\(e\left(\frac{109}{135}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{89}{270}\right)\)
\(\chi_{8100}(2621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{137}{270}\right)\)	\(e\left(\frac{119}{135}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{37}{270}\right)\)	\(e\left(\frac{149}{270}\right)\)	\(e\left(\frac{68}{135}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{193}{270}\right)\)
\(\chi_{8100}(2741,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{169}{270}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{89}{270}\right)\)	\(e\left(\frac{103}{270}\right)\)	\(e\left(\frac{76}{135}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{41}{270}\right)\)
\(\chi_{8100}(2921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{37}{270}\right)\)	\(e\left(\frac{109}{135}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{77}{270}\right)\)	\(e\left(\frac{259}{270}\right)\)	\(e\left(\frac{43}{135}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{263}{270}\right)\)
\(\chi_{8100}(2981,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{233}{270}\right)\)	\(e\left(\frac{26}{135}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{11}{270}\right)\)	\(e\left(\frac{92}{135}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{7}{270}\right)\)
\(\chi_{8100}(3161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{11}{270}\right)\)	\(e\left(\frac{47}{135}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{270}\right)\)	\(e\left(\frac{77}{270}\right)\)	\(e\left(\frac{104}{135}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{49}{270}\right)\)
\(\chi_{8100}(3281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{43}{270}\right)\)	\(e\left(\frac{61}{135}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{53}{270}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{112}{135}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{167}{270}\right)\)
\(\chi_{8100}(3341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{59}{270}\right)\)	\(e\left(\frac{68}{135}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{143}{270}\right)\)	\(e\left(\frac{116}{135}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{91}{270}\right)\)
\(\chi_{8100}(3461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{37}{135}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{41}{270}\right)\)	\(e\left(\frac{187}{270}\right)\)	\(e\left(\frac{79}{135}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{119}{270}\right)\)

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First 31 of 72 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.dk
Modulus	$8100$
Conductor	$2025$
Order	$270$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(8100\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(2025\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(270\)	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 2025.bt	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);