LMFDB - Dirichlet character orbit 8712.eu

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8712, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([165,0,55,294])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(47, 8712)) 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("8712.47"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8712$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4356$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$330$	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 4356.ck	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:	$\Q(\zeta_{165})$	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 330 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8712}(47,\cdot)$	$1$	$1$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{8712}(119,\cdot)$	$1$	$1$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{8712}(191,\cdot)$	$1$	$1$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{8712}(311,\cdot)$	$1$	$1$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{8712}(335,\cdot)$	$1$	$1$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{8712}(383,\cdot)$	$1$	$1$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{221}{330}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{8712}(455,\cdot)$	$1$	$1$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{8712}(599,\cdot)$	$1$	$1$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{8712}(839,\cdot)$	$1$	$1$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{8712}(911,\cdot)$	$1$	$1$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{8712}(983,\cdot)$	$1$	$1$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{8712}(1103,\cdot)$	$1$	$1$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{8712}(1127,\cdot)$	$1$	$1$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{8712}(1175,\cdot)$	$1$	$1$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{8712}(1247,\cdot)$	$1$	$1$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{8712}(1391,\cdot)$	$1$	$1$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{8712}(1631,\cdot)$	$1$	$1$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{8712}(1895,\cdot)$	$1$	$1$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{8712}(1919,\cdot)$	$1$	$1$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{8712}(1967,\cdot)$	$1$	$1$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{8712}(2039,\cdot)$	$1$	$1$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{8712}(2183,\cdot)$	$1$	$1$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{8712}(2495,\cdot)$	$1$	$1$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{8712}(2567,\cdot)$	$1$	$1$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{8712}(2687,\cdot)$	$1$	$1$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{289}{330}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{8712}(2711,\cdot)$	$1$	$1$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{109}{330}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{8712}(2759,\cdot)$	$1$	$1$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{8712}(2831,\cdot)$	$1$	$1$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{8712}(2975,\cdot)$	$1$	$1$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{8712}(3215,\cdot)$	$1$	$1$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{8712}(3287,\cdot)$	$1$	$1$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{53}{55}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8712}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{8712}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{8712}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{8712}(311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{8712}(335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{8712}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{221}{330}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{8712}(455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{8712}(599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{2}{55}\right)\)
\(\chi_{8712}(839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{8712}(911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{8712}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{8712}(1103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{8712}(1127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{8712}(1175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{8712}(1247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{8712}(1391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{8712}(1631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{8712}(1895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{8712}(1919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{8712}(1967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{8712}(2039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{8712}(2183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{8712}(2495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{8712}(2567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{8712}(2687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{289}{330}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{8712}(2711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{109}{330}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{8712}(2759,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{8712}(2831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{8712}(2975,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{8712}(3215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{8712}(3287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{53}{55}\right)\)

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	8712.eu
Modulus	$8712$
Conductor	$4356$
Order	$330$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(8712\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4356\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(330\)	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 4356.ck	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);