LMFDB - Dirichlet character orbit 6500.eb

Show commands: Magma / Pari/GP / SageMath

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([0,57,25])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(69, 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("6500.69"); 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:	$150$	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.cb	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 150 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{6500}(69,\cdot)$	$1$	$1$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{17}{75}\right)$
$\chi_{6500}(309,\cdot)$	$1$	$1$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{31}{75}\right)$
$\chi_{6500}(329,\cdot)$	$1$	$1$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{38}{75}\right)$
$\chi_{6500}(569,\cdot)$	$1$	$1$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{67}{75}\right)$
$\chi_{6500}(589,\cdot)$	$1$	$1$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{44}{75}\right)$
$\chi_{6500}(829,\cdot)$	$1$	$1$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{13}{75}\right)$
$\chi_{6500}(1089,\cdot)$	$1$	$1$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{19}{75}\right)$
$\chi_{6500}(1109,\cdot)$	$1$	$1$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{11}{75}\right)$
$\chi_{6500}(1369,\cdot)$	$1$	$1$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{47}{75}\right)$
$\chi_{6500}(1609,\cdot)$	$1$	$1$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{61}{75}\right)$
$\chi_{6500}(1629,\cdot)$	$1$	$1$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{68}{75}\right)$
$\chi_{6500}(1869,\cdot)$	$1$	$1$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{22}{75}\right)$
$\chi_{6500}(1889,\cdot)$	$1$	$1$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{74}{75}\right)$
$\chi_{6500}(2129,\cdot)$	$1$	$1$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{43}{75}\right)$
$\chi_{6500}(2389,\cdot)$	$1$	$1$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{49}{75}\right)$
$\chi_{6500}(2409,\cdot)$	$1$	$1$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{41}{75}\right)$
$\chi_{6500}(2669,\cdot)$	$1$	$1$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{2}{75}\right)$
$\chi_{6500}(2909,\cdot)$	$1$	$1$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{16}{75}\right)$
$\chi_{6500}(2929,\cdot)$	$1$	$1$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{23}{75}\right)$
$\chi_{6500}(3169,\cdot)$	$1$	$1$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{52}{75}\right)$
$\chi_{6500}(3189,\cdot)$	$1$	$1$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{29}{75}\right)$
$\chi_{6500}(3429,\cdot)$	$1$	$1$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{73}{75}\right)$
$\chi_{6500}(3689,\cdot)$	$1$	$1$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{4}{75}\right)$
$\chi_{6500}(3709,\cdot)$	$1$	$1$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{71}{75}\right)$
$\chi_{6500}(3969,\cdot)$	$1$	$1$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{32}{75}\right)$
$\chi_{6500}(4209,\cdot)$	$1$	$1$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{46}{75}\right)$
$\chi_{6500}(4229,\cdot)$	$1$	$1$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{53}{75}\right)$
$\chi_{6500}(4469,\cdot)$	$1$	$1$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{7}{75}\right)$
$\chi_{6500}(4489,\cdot)$	$1$	$1$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{59}{75}\right)$
$\chi_{6500}(4729,\cdot)$	$1$	$1$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{28}{75}\right)$
$\chi_{6500}(4989,\cdot)$	$1$	$1$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{34}{75}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{6500}(69,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{17}{75}\right)\)
\(\chi_{6500}(309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{31}{75}\right)\)
\(\chi_{6500}(329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{38}{75}\right)\)
\(\chi_{6500}(569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{67}{75}\right)\)
\(\chi_{6500}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{44}{75}\right)\)
\(\chi_{6500}(829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{13}{75}\right)\)
\(\chi_{6500}(1089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{19}{75}\right)\)
\(\chi_{6500}(1109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{11}{75}\right)\)
\(\chi_{6500}(1369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{47}{75}\right)\)
\(\chi_{6500}(1609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{61}{75}\right)\)
\(\chi_{6500}(1629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{68}{75}\right)\)
\(\chi_{6500}(1869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{22}{75}\right)\)
\(\chi_{6500}(1889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{74}{75}\right)\)
\(\chi_{6500}(2129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{43}{75}\right)\)
\(\chi_{6500}(2389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{49}{75}\right)\)
\(\chi_{6500}(2409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{41}{75}\right)\)
\(\chi_{6500}(2669,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{2}{75}\right)\)
\(\chi_{6500}(2909,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{16}{75}\right)\)
\(\chi_{6500}(2929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{23}{75}\right)\)
\(\chi_{6500}(3169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{52}{75}\right)\)
\(\chi_{6500}(3189,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{29}{75}\right)\)
\(\chi_{6500}(3429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{73}{75}\right)\)
\(\chi_{6500}(3689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{4}{75}\right)\)
\(\chi_{6500}(3709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{71}{75}\right)\)
\(\chi_{6500}(3969,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{32}{75}\right)\)
\(\chi_{6500}(4209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{46}{75}\right)\)
\(\chi_{6500}(4229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{53}{75}\right)\)
\(\chi_{6500}(4469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{7}{75}\right)\)
\(\chi_{6500}(4489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{59}{75}\right)\)
\(\chi_{6500}(4729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{28}{75}\right)\)
\(\chi_{6500}(4989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{34}{75}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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.eb
Modulus	$6500$
Conductor	$1625$
Order	$150$
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:	\(150\)	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.cb	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);