LMFDB - Dirichlet character orbit 6500.ef

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6500, base_ring=CyclotomicField(300)) M = H._module chi = DirichletCharacter(H, M([0,249,275])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(33, 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("6500.33"); 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:	$300$	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 1625.cc	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:	$\Q(\zeta_{300})$	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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{6500}(33,\cdot)$	$1$	$1$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{19}{150}\right)$
$\chi_{6500}(97,\cdot)$	$1$	$1$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{91}{150}\right)$
$\chi_{6500}(197,\cdot)$	$1$	$1$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{131}{150}\right)$
$\chi_{6500}(453,\cdot)$	$1$	$1$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{241}{300}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{71}{150}\right)$
$\chi_{6500}(553,\cdot)$	$1$	$1$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{31}{150}\right)$
$\chi_{6500}(617,\cdot)$	$1$	$1$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{79}{150}\right)$
$\chi_{6500}(713,\cdot)$	$1$	$1$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{251}{300}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{47}{150}\right)$
$\chi_{6500}(717,\cdot)$	$1$	$1$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{119}{150}\right)$
$\chi_{6500}(813,\cdot)$	$1$	$1$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{197}{300}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{7}{150}\right)$
$\chi_{6500}(877,\cdot)$	$1$	$1$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{79}{300}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{43}{150}\right)$
$\chi_{6500}(973,\cdot)$	$1$	$1$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{209}{300}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{53}{150}\right)$
$\chi_{6500}(977,\cdot)$	$1$	$1$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{83}{150}\right)$
$\chi_{6500}(1073,\cdot)$	$1$	$1$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{79}{300}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{13}{150}\right)$
$\chi_{6500}(1137,\cdot)$	$1$	$1$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{37}{150}\right)$
$\chi_{6500}(1233,\cdot)$	$1$	$1$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{17}{300}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{89}{150}\right)$
$\chi_{6500}(1237,\cdot)$	$1$	$1$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{77}{150}\right)$
$\chi_{6500}(1333,\cdot)$	$1$	$1$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{49}{150}\right)$
$\chi_{6500}(1397,\cdot)$	$1$	$1$	$e\left(\frac{17}{300}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{61}{150}\right)$
$\chi_{6500}(1497,\cdot)$	$1$	$1$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{101}{150}\right)$
$\chi_{6500}(1753,\cdot)$	$1$	$1$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{101}{150}\right)$
$\chi_{6500}(1853,\cdot)$	$1$	$1$	$e\left(\frac{167}{300}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{61}{150}\right)$
$\chi_{6500}(1917,\cdot)$	$1$	$1$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{49}{150}\right)$
$\chi_{6500}(2013,\cdot)$	$1$	$1$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{277}{300}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{77}{150}\right)$
$\chi_{6500}(2017,\cdot)$	$1$	$1$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{167}{300}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{89}{150}\right)$
$\chi_{6500}(2113,\cdot)$	$1$	$1$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{37}{150}\right)$
$\chi_{6500}(2177,\cdot)$	$1$	$1$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{13}{150}\right)$
$\chi_{6500}(2273,\cdot)$	$1$	$1$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{83}{150}\right)$
$\chi_{6500}(2277,\cdot)$	$1$	$1$	$e\left(\frac{241}{300}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{53}{150}\right)$
$\chi_{6500}(2373,\cdot)$	$1$	$1$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{43}{150}\right)$
$\chi_{6500}(2437,\cdot)$	$1$	$1$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{7}{150}\right)$
$\chi_{6500}(2533,\cdot)$	$1$	$1$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{119}{150}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{6500}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{19}{150}\right)\)
\(\chi_{6500}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{91}{150}\right)\)
\(\chi_{6500}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{131}{150}\right)\)
\(\chi_{6500}(453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{241}{300}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{71}{150}\right)\)
\(\chi_{6500}(553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{31}{150}\right)\)
\(\chi_{6500}(617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{79}{150}\right)\)
\(\chi_{6500}(713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{300}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{251}{300}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{47}{150}\right)\)
\(\chi_{6500}(717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{119}{150}\right)\)
\(\chi_{6500}(813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{197}{300}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{7}{150}\right)\)
\(\chi_{6500}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{79}{300}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{43}{150}\right)\)
\(\chi_{6500}(973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{209}{300}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{53}{150}\right)\)
\(\chi_{6500}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{83}{150}\right)\)
\(\chi_{6500}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{79}{300}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{13}{150}\right)\)
\(\chi_{6500}(1137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{37}{150}\right)\)
\(\chi_{6500}(1233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{17}{300}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{89}{150}\right)\)
\(\chi_{6500}(1237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{77}{150}\right)\)
\(\chi_{6500}(1333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{49}{150}\right)\)
\(\chi_{6500}(1397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{300}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{61}{150}\right)\)
\(\chi_{6500}(1497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{101}{150}\right)\)
\(\chi_{6500}(1753,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{101}{150}\right)\)
\(\chi_{6500}(1853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{300}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{61}{150}\right)\)
\(\chi_{6500}(1917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{49}{150}\right)\)
\(\chi_{6500}(2013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{277}{300}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{77}{150}\right)\)
\(\chi_{6500}(2017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{137}{300}\right)\)	\(e\left(\frac{167}{300}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{89}{150}\right)\)
\(\chi_{6500}(2113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{137}{300}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{37}{150}\right)\)
\(\chi_{6500}(2177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{13}{150}\right)\)
\(\chi_{6500}(2273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{83}{150}\right)\)
\(\chi_{6500}(2277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{300}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{53}{150}\right)\)
\(\chi_{6500}(2373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{43}{150}\right)\)
\(\chi_{6500}(2437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{181}{300}\right)\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{7}{150}\right)\)
\(\chi_{6500}(2533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{119}{150}\right)\)

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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	6500.ef
Modulus	$6500$
Conductor	$1625$
Order	$300$
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:	\(300\)	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 1625.cc	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);