LMFDB - Dirichlet character orbit 6500.dk

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6500, base_ring=CyclotomicField(150)) M = H._module chi = DirichletCharacter(H, M([0,84,100])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(61, 6500)) 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("6500.61"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$6500$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1625$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$75$	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 1625.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:	$\Q(\zeta_{75})$	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 75 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{6500}(61,\cdot)$	$1$	$1$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{29}{75}\right)$
$\chi_{6500}(81,\cdot)$	$1$	$1$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{52}{75}\right)$
$\chi_{6500}(321,\cdot)$	$1$	$1$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{23}{75}\right)$
$\chi_{6500}(341,\cdot)$	$1$	$1$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{16}{75}\right)$
$\chi_{6500}(581,\cdot)$	$1$	$1$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{75}\right)$
$\chi_{6500}(841,\cdot)$	$1$	$1$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{41}{75}\right)$
$\chi_{6500}(861,\cdot)$	$1$	$1$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{49}{75}\right)$
$\chi_{6500}(1121,\cdot)$	$1$	$1$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{43}{75}\right)$
$\chi_{6500}(1361,\cdot)$	$1$	$1$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{74}{75}\right)$
$\chi_{6500}(1381,\cdot)$	$1$	$1$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{75}\right)$
$\chi_{6500}(1621,\cdot)$	$1$	$1$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{68}{75}\right)$
$\chi_{6500}(1641,\cdot)$	$1$	$1$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{61}{75}\right)$
$\chi_{6500}(1881,\cdot)$	$1$	$1$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{47}{75}\right)$
$\chi_{6500}(2141,\cdot)$	$1$	$1$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{11}{75}\right)$
$\chi_{6500}(2161,\cdot)$	$1$	$1$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{19}{75}\right)$
$\chi_{6500}(2421,\cdot)$	$1$	$1$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{13}{75}\right)$
$\chi_{6500}(2661,\cdot)$	$1$	$1$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{44}{75}\right)$
$\chi_{6500}(2681,\cdot)$	$1$	$1$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{67}{75}\right)$
$\chi_{6500}(2921,\cdot)$	$1$	$1$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{38}{75}\right)$
$\chi_{6500}(2941,\cdot)$	$1$	$1$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{31}{75}\right)$
$\chi_{6500}(3181,\cdot)$	$1$	$1$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{17}{75}\right)$
$\chi_{6500}(3441,\cdot)$	$1$	$1$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{56}{75}\right)$
$\chi_{6500}(3461,\cdot)$	$1$	$1$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{64}{75}\right)$
$\chi_{6500}(3721,\cdot)$	$1$	$1$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{58}{75}\right)$
$\chi_{6500}(3961,\cdot)$	$1$	$1$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{14}{75}\right)$
$\chi_{6500}(3981,\cdot)$	$1$	$1$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{37}{75}\right)$
$\chi_{6500}(4221,\cdot)$	$1$	$1$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{8}{75}\right)$
$\chi_{6500}(4241,\cdot)$	$1$	$1$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{1}{75}\right)$
$\chi_{6500}(4481,\cdot)$	$1$	$1$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{62}{75}\right)$
$\chi_{6500}(4741,\cdot)$	$1$	$1$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{26}{75}\right)$
$\chi_{6500}(4761,\cdot)$	$1$	$1$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{34}{75}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{6500}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{29}{75}\right)\)
\(\chi_{6500}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{52}{75}\right)\)
\(\chi_{6500}(321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{23}{75}\right)\)
\(\chi_{6500}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{16}{75}\right)\)
\(\chi_{6500}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{2}{75}\right)\)
\(\chi_{6500}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{41}{75}\right)\)
\(\chi_{6500}(861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{49}{75}\right)\)
\(\chi_{6500}(1121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{43}{75}\right)\)
\(\chi_{6500}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{74}{75}\right)\)
\(\chi_{6500}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{22}{75}\right)\)
\(\chi_{6500}(1621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{68}{75}\right)\)
\(\chi_{6500}(1641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{61}{75}\right)\)
\(\chi_{6500}(1881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{47}{75}\right)\)
\(\chi_{6500}(2141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{11}{75}\right)\)
\(\chi_{6500}(2161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{19}{75}\right)\)
\(\chi_{6500}(2421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{13}{75}\right)\)
\(\chi_{6500}(2661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{44}{75}\right)\)
\(\chi_{6500}(2681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{67}{75}\right)\)
\(\chi_{6500}(2921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{38}{75}\right)\)
\(\chi_{6500}(2941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{31}{75}\right)\)
\(\chi_{6500}(3181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{17}{75}\right)\)
\(\chi_{6500}(3441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{56}{75}\right)\)
\(\chi_{6500}(3461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{64}{75}\right)\)
\(\chi_{6500}(3721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{58}{75}\right)\)
\(\chi_{6500}(3961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{14}{75}\right)\)
\(\chi_{6500}(3981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{37}{75}\right)\)
\(\chi_{6500}(4221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)
\(\chi_{6500}(4241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{1}{75}\right)\)
\(\chi_{6500}(4481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{62}{75}\right)\)
\(\chi_{6500}(4741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{26}{75}\right)\)
\(\chi_{6500}(4761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{34}{75}\right)\)

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First 31 of 40 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	6500.dk
Modulus	$6500$
Conductor	$1625$
Order	$75$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(6500\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1625\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(75\)	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 1625.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);