LMFDB - Dirichlet character orbit 676000.bev

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(676000, base_ring=CyclotomicField(300)) M = H._module chi = DirichletCharacter(H, M([150,225,93,250])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(23, 676000)) 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("676000.23"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$676000$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$26000$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$300$	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 26000.pc	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{300})$	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 300 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{676000}(23,\cdot)$	$1$	$1$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{241}{300}\right)$
$\chi_{676000}(823,\cdot)$	$1$	$1$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{101}{300}\right)$
$\chi_{676000}(2727,\cdot)$	$1$	$1$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{91}{300}\right)$
$\chi_{676000}(3527,\cdot)$	$1$	$1$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{131}{300}\right)$
$\chi_{676000}(27063,\cdot)$	$1$	$1$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{289}{300}\right)$
$\chi_{676000}(27863,\cdot)$	$1$	$1$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{149}{300}\right)$
$\chi_{676000}(29767,\cdot)$	$1$	$1$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{167}{300}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{103}{300}\right)$
$\chi_{676000}(30567,\cdot)$	$1$	$1$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{209}{300}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{143}{300}\right)$
$\chi_{676000}(54103,\cdot)$	$1$	$1$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{97}{300}\right)$
$\chi_{676000}(54903,\cdot)$	$1$	$1$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{73}{300}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{257}{300}\right)$
$\chi_{676000}(83847,\cdot)$	$1$	$1$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{241}{300}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{7}{300}\right)$
$\chi_{676000}(84647,\cdot)$	$1$	$1$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{47}{300}\right)$
$\chi_{676000}(108183,\cdot)$	$1$	$1$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{197}{300}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{193}{300}\right)$
$\chi_{676000}(108983,\cdot)$	$1$	$1$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{53}{300}\right)$
$\chi_{676000}(110887,\cdot)$	$1$	$1$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{199}{300}\right)$
$\chi_{676000}(111687,\cdot)$	$1$	$1$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{239}{300}\right)$
$\chi_{676000}(135223,\cdot)$	$1$	$1$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{209}{300}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{181}{300}\right)$
$\chi_{676000}(136023,\cdot)$	$1$	$1$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{41}{300}\right)$
$\chi_{676000}(137927,\cdot)$	$1$	$1$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{151}{300}\right)$
$\chi_{676000}(138727,\cdot)$	$1$	$1$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{191}{300}\right)$
$\chi_{676000}(162263,\cdot)$	$1$	$1$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{229}{300}\right)$
$\chi_{676000}(163063,\cdot)$	$1$	$1$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{197}{300}\right)$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{89}{300}\right)$
$\chi_{676000}(164967,\cdot)$	$1$	$1$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{163}{300}\right)$
$\chi_{676000}(165767,\cdot)$	$1$	$1$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{203}{300}\right)$
$\chi_{676000}(189303,\cdot)$	$1$	$1$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{37}{300}\right)$
$\chi_{676000}(190103,\cdot)$	$1$	$1$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{197}{300}\right)$
$\chi_{676000}(219047,\cdot)$	$1$	$1$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{67}{300}\right)$
$\chi_{676000}(219847,\cdot)$	$1$	$1$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{107}{300}\right)$
$\chi_{676000}(243383,\cdot)$	$1$	$1$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{79}{300}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{133}{300}\right)$
$\chi_{676000}(244183,\cdot)$	$1$	$1$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{277}{300}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{293}{300}\right)$
$\chi_{676000}(246087,\cdot)$	$1$	$1$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{251}{300}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{259}{300}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{676000}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{241}{300}\right)\)
\(\chi_{676000}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{101}{300}\right)\)
\(\chi_{676000}(2727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{91}{300}\right)\)
\(\chi_{676000}(3527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{131}{300}\right)\)
\(\chi_{676000}(27063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{289}{300}\right)\)
\(\chi_{676000}(27863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{149}{300}\right)\)
\(\chi_{676000}(29767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{167}{300}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{103}{300}\right)\)
\(\chi_{676000}(30567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{209}{300}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{143}{300}\right)\)
\(\chi_{676000}(54103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{181}{300}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{97}{300}\right)\)
\(\chi_{676000}(54903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{73}{300}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{257}{300}\right)\)
\(\chi_{676000}(83847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{241}{300}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{7}{300}\right)\)
\(\chi_{676000}(84647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{47}{300}\right)\)
\(\chi_{676000}(108183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{197}{300}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{193}{300}\right)\)
\(\chi_{676000}(108983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{53}{300}\right)\)
\(\chi_{676000}(110887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{199}{300}\right)\)
\(\chi_{676000}(111687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{239}{300}\right)\)
\(\chi_{676000}(135223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{209}{300}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{181}{300}\right)\)
\(\chi_{676000}(136023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{41}{300}\right)\)
\(\chi_{676000}(137927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{151}{300}\right)\)
\(\chi_{676000}(138727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{191}{300}\right)\)
\(\chi_{676000}(162263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{229}{300}\right)\)
\(\chi_{676000}(163063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{197}{300}\right)\)	\(e\left(\frac{181}{300}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{89}{300}\right)\)
\(\chi_{676000}(164967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{163}{300}\right)\)
\(\chi_{676000}(165767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{203}{300}\right)\)
\(\chi_{676000}(189303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{37}{300}\right)\)
\(\chi_{676000}(190103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{197}{300}\right)\)
\(\chi_{676000}(219047,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{67}{300}\right)\)
\(\chi_{676000}(219847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{107}{300}\right)\)
\(\chi_{676000}(243383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{137}{300}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{79}{300}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{133}{300}\right)\)
\(\chi_{676000}(244183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{277}{300}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{293}{300}\right)\)
\(\chi_{676000}(246087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{251}{300}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{259}{300}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 80 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	676000.bev
Modulus	$676000$
Conductor	$26000$
Order	$300$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(676000\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(26000\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(300\)	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 26000.pc	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);