LMFDB - Dirichlet character orbit 104000.bbj

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104000, base_ring=CyclotomicField(300)) M = H._module chi = DirichletCharacter(H, M([150,0,297,175])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(63, 104000)) 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("104000.63"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$104000$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$6500$	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 6500.eo	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{104000}(63,\cdot)$	$-1$	$1$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{107}{150}\right)$
$\chi_{104000}(1983,\cdot)$	$-1$	$1$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{139}{150}\right)$
$\chi_{104000}(2047,\cdot)$	$-1$	$1$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{121}{150}\right)$
$\chi_{104000}(3967,\cdot)$	$-1$	$1$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{119}{150}\right)$
$\chi_{104000}(4223,\cdot)$	$-1$	$1$	$e\left(\frac{241}{300}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{53}{150}\right)$
$\chi_{104000}(8127,\cdot)$	$-1$	$1$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{143}{150}\right)$
$\chi_{104000}(8383,\cdot)$	$-1$	$1$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{79}{300}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{29}{150}\right)$
$\chi_{104000}(10303,\cdot)$	$-1$	$1$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{251}{300}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{31}{150}\right)$
$\chi_{104000}(10367,\cdot)$	$-1$	$1$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{209}{300}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{79}{150}\right)$
$\chi_{104000}(12287,\cdot)$	$-1$	$1$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{47}{150}\right)$
$\chi_{104000}(14463,\cdot)$	$-1$	$1$	$e\left(\frac{209}{300}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{97}{150}\right)$
$\chi_{104000}(14527,\cdot)$	$-1$	$1$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{103}{150}\right)$
$\chi_{104000}(16447,\cdot)$	$-1$	$1$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{131}{150}\right)$
$\chi_{104000}(16703,\cdot)$	$-1$	$1$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{71}{150}\right)$
$\chi_{104000}(18623,\cdot)$	$-1$	$1$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{79}{300}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{43}{150}\right)$
$\chi_{104000}(18687,\cdot)$	$-1$	$1$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{197}{300}\right)$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{7}{150}\right)$
$\chi_{104000}(20863,\cdot)$	$-1$	$1$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{137}{150}\right)$
$\chi_{104000}(22783,\cdot)$	$-1$	$1$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{19}{150}\right)$
$\chi_{104000}(22847,\cdot)$	$-1$	$1$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{73}{300}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{91}{150}\right)$
$\chi_{104000}(24767,\cdot)$	$-1$	$1$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{17}{300}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{89}{150}\right)$
$\chi_{104000}(25023,\cdot)$	$-1$	$1$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{83}{150}\right)$
$\chi_{104000}(28927,\cdot)$	$-1$	$1$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{73}{300}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{113}{150}\right)$
$\chi_{104000}(29183,\cdot)$	$-1$	$1$	$e\left(\frac{73}{300}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{59}{150}\right)$
$\chi_{104000}(31103,\cdot)$	$-1$	$1$	$e\left(\frac{17}{300}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{61}{150}\right)$
$\chi_{104000}(31167,\cdot)$	$-1$	$1$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{49}{150}\right)$
$\chi_{104000}(33087,\cdot)$	$-1$	$1$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{17}{150}\right)$
$\chi_{104000}(35263,\cdot)$	$-1$	$1$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{167}{300}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{127}{150}\right)$
$\chi_{104000}(35327,\cdot)$	$-1$	$1$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{73}{150}\right)$
$\chi_{104000}(37247,\cdot)$	$-1$	$1$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{101}{150}\right)$
$\chi_{104000}(37503,\cdot)$	$-1$	$1$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{101}{150}\right)$
$\chi_{104000}(39423,\cdot)$	$-1$	$1$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{73}{150}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{104000}(63,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{107}{150}\right)\)
\(\chi_{104000}(1983,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{139}{150}\right)\)
\(\chi_{104000}(2047,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{121}{150}\right)\)
\(\chi_{104000}(3967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{119}{150}\right)\)
\(\chi_{104000}(4223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{300}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{53}{150}\right)\)
\(\chi_{104000}(8127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{143}{150}\right)\)
\(\chi_{104000}(8383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{79}{300}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{29}{150}\right)\)
\(\chi_{104000}(10303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{251}{300}\right)\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{31}{150}\right)\)
\(\chi_{104000}(10367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{209}{300}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{79}{150}\right)\)
\(\chi_{104000}(12287,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{47}{150}\right)\)
\(\chi_{104000}(14463,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{300}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{97}{150}\right)\)
\(\chi_{104000}(14527,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{103}{150}\right)\)
\(\chi_{104000}(16447,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{181}{300}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{131}{150}\right)\)
\(\chi_{104000}(16703,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{71}{150}\right)\)
\(\chi_{104000}(18623,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{79}{300}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{43}{150}\right)\)
\(\chi_{104000}(18687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{197}{300}\right)\)	\(e\left(\frac{181}{300}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{7}{150}\right)\)
\(\chi_{104000}(20863,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{137}{150}\right)\)
\(\chi_{104000}(22783,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{19}{150}\right)\)
\(\chi_{104000}(22847,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{73}{300}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{91}{150}\right)\)
\(\chi_{104000}(24767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{137}{300}\right)\)	\(e\left(\frac{17}{300}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{89}{150}\right)\)
\(\chi_{104000}(25023,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{83}{150}\right)\)
\(\chi_{104000}(28927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{73}{300}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{113}{150}\right)\)
\(\chi_{104000}(29183,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{300}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{59}{150}\right)\)
\(\chi_{104000}(31103,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{300}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{61}{150}\right)\)
\(\chi_{104000}(31167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{49}{150}\right)\)
\(\chi_{104000}(33087,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{17}{150}\right)\)
\(\chi_{104000}(35263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{167}{300}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{127}{150}\right)\)
\(\chi_{104000}(35327,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{73}{150}\right)\)
\(\chi_{104000}(37247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{101}{150}\right)\)
\(\chi_{104000}(37503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{101}{150}\right)\)
\(\chi_{104000}(39423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{73}{150}\right)\)

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Basic properties

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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	104000.bbj
Modulus	$104000$
Conductor	$6500$
Order	$300$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(104000\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(6500\)	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 6500.eo	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);