LMFDB - Dirichlet character orbit 38025.ol

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38025, base_ring=CyclotomicField(780)) M = H._module chi = DirichletCharacter(H, M([390,234,245])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(314, 38025)) 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("38025.314"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$38025$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$12675$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$780$	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 12675.fx	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:	$\Q(\zeta_{780})$	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 780 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$14$	$16$	$17$	$19$	$22$
$\chi_{38025}(314,\cdot)$	$1$	$1$	$e\left(\frac{89}{780}\right)$	$e\left(\frac{89}{390}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{509}{780}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{89}{195}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{38025}(539,\cdot)$	$1$	$1$	$e\left(\frac{649}{780}\right)$	$e\left(\frac{259}{390}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{129}{260}\right)$	$e\left(\frac{469}{780}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{64}{195}\right)$	$e\left(\frac{31}{390}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{38025}(1034,\cdot)$	$1$	$1$	$e\left(\frac{211}{780}\right)$	$e\left(\frac{211}{390}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{211}{260}\right)$	$e\left(\frac{751}{780}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{349}{390}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{38025}(1259,\cdot)$	$1$	$1$	$e\left(\frac{491}{780}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{731}{780}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{101}{195}\right)$	$e\left(\frac{119}{390}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{38025}(1484,\cdot)$	$1$	$1$	$e\left(\frac{521}{780}\right)$	$e\left(\frac{131}{390}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{1}{260}\right)$	$e\left(\frac{701}{780}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{38025}(1619,\cdot)$	$1$	$1$	$e\left(\frac{607}{780}\right)$	$e\left(\frac{217}{390}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{87}{260}\right)$	$e\left(\frac{667}{780}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{163}{390}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{38025}(1844,\cdot)$	$1$	$1$	$e\left(\frac{587}{780}\right)$	$e\left(\frac{197}{390}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{167}{780}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{2}{195}\right)$	$e\left(\frac{263}{390}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{38025}(2069,\cdot)$	$1$	$1$	$e\left(\frac{737}{780}\right)$	$e\left(\frac{347}{390}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{17}{780}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{152}{195}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{38025}(2204,\cdot)$	$1$	$1$	$e\left(\frac{223}{780}\right)$	$e\left(\frac{223}{390}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{223}{260}\right)$	$e\left(\frac{583}{780}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{28}{195}\right)$	$e\left(\frac{367}{390}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{38025}(2294,\cdot)$	$1$	$1$	$e\left(\frac{397}{780}\right)$	$e\left(\frac{7}{390}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{137}{260}\right)$	$e\left(\frac{97}{780}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{7}{195}\right)$	$e\left(\frac{43}{390}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{38025}(2429,\cdot)$	$1$	$1$	$e\left(\frac{683}{780}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{163}{260}\right)$	$e\left(\frac{383}{780}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{17}{390}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{38025}(2654,\cdot)$	$1$	$1$	$e\left(\frac{173}{780}\right)$	$e\left(\frac{173}{390}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{173}{260}\right)$	$e\left(\frac{113}{780}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{173}{195}\right)$	$e\left(\frac{227}{390}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{38025}(2789,\cdot)$	$1$	$1$	$e\left(\frac{619}{780}\right)$	$e\left(\frac{229}{390}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{499}{780}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{34}{195}\right)$	$e\left(\frac{181}{390}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{38025}(2879,\cdot)$	$1$	$1$	$e\left(\frac{313}{780}\right)$	$e\left(\frac{313}{390}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{53}{260}\right)$	$e\left(\frac{493}{780}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{307}{390}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{38025}(3014,\cdot)$	$1$	$1$	$e\left(\frac{779}{780}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{259}{260}\right)$	$e\left(\frac{599}{780}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{161}{390}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{38025}(3239,\cdot)$	$1$	$1$	$e\left(\frac{389}{780}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{129}{260}\right)$	$e\left(\frac{209}{780}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{161}{390}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{38025}(3464,\cdot)$	$1$	$1$	$e\left(\frac{229}{780}\right)$	$e\left(\frac{229}{390}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{109}{780}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{34}{195}\right)$	$e\left(\frac{181}{390}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{38025}(3959,\cdot)$	$1$	$1$	$e\left(\frac{631}{780}\right)$	$e\left(\frac{241}{390}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{331}{780}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{38025}(4184,\cdot)$	$1$	$1$	$e\left(\frac{191}{780}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{191}{260}\right)$	$e\left(\frac{251}{780}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{191}{195}\right)$	$e\left(\frac{59}{390}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{38025}(4409,\cdot)$	$1$	$1$	$e\left(\frac{41}{780}\right)$	$e\left(\frac{41}{390}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{41}{260}\right)$	$e\left(\frac{401}{780}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{29}{390}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{38025}(4634,\cdot)$	$1$	$1$	$e\left(\frac{61}{780}\right)$	$e\left(\frac{61}{390}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{121}{780}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{61}{195}\right)$	$e\left(\frac{319}{390}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{38025}(4769,\cdot)$	$1$	$1$	$e\left(\frac{287}{780}\right)$	$e\left(\frac{287}{390}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{467}{780}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{203}{390}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{38025}(4994,\cdot)$	$1$	$1$	$e\left(\frac{257}{780}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{257}{260}\right)$	$e\left(\frac{497}{780}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{353}{390}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{38025}(5129,\cdot)$	$1$	$1$	$e\left(\frac{643}{780}\right)$	$e\left(\frac{253}{390}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{163}{780}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{58}{195}\right)$	$e\left(\frac{217}{390}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{38025}(5219,\cdot)$	$1$	$1$	$e\left(\frac{757}{780}\right)$	$e\left(\frac{367}{390}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{517}{780}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{172}{195}\right)$	$e\left(\frac{193}{390}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{38025}(5354,\cdot)$	$1$	$1$	$e\left(\frac{383}{780}\right)$	$e\left(\frac{383}{390}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{683}{780}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{347}{390}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{38025}(5579,\cdot)$	$1$	$1$	$e\left(\frac{473}{780}\right)$	$e\left(\frac{83}{390}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{593}{780}\right)$	$e\left(\frac{103}{130}\right)$	$e\left(\frac{83}{195}\right)$	$e\left(\frac{287}{390}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{38025}(5714,\cdot)$	$1$	$1$	$e\left(\frac{259}{780}\right)$	$e\left(\frac{259}{390}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{259}{260}\right)$	$e\left(\frac{79}{780}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{64}{195}\right)$	$e\left(\frac{31}{390}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{38025}(5804,\cdot)$	$1$	$1$	$e\left(\frac{673}{780}\right)$	$e\left(\frac{283}{390}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{133}{780}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{38025}(5939,\cdot)$	$1$	$1$	$e\left(\frac{479}{780}\right)$	$e\left(\frac{89}{390}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{219}{260}\right)$	$e\left(\frac{119}{780}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{89}{195}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{38025}(6389,\cdot)$	$1$	$1$	$e\left(\frac{589}{780}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{529}{780}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{4}{195}\right)$	$e\left(\frac{331}{390}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{30}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\(\chi_{38025}(314,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{780}\right)\)	\(e\left(\frac{89}{390}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{509}{780}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{89}{195}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{38025}(539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{649}{780}\right)\)	\(e\left(\frac{259}{390}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{129}{260}\right)\)	\(e\left(\frac{469}{780}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{64}{195}\right)\)	\(e\left(\frac{31}{390}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{38025}(1034,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{780}\right)\)	\(e\left(\frac{211}{390}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{211}{260}\right)\)	\(e\left(\frac{751}{780}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{349}{390}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{38025}(1259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{491}{780}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{731}{780}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{101}{195}\right)\)	\(e\left(\frac{119}{390}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{38025}(1484,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{780}\right)\)	\(e\left(\frac{131}{390}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{1}{260}\right)\)	\(e\left(\frac{701}{780}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{38025}(1619,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{607}{780}\right)\)	\(e\left(\frac{217}{390}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{87}{260}\right)\)	\(e\left(\frac{667}{780}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{163}{390}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{38025}(1844,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{587}{780}\right)\)	\(e\left(\frac{197}{390}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{167}{780}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{2}{195}\right)\)	\(e\left(\frac{263}{390}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{38025}(2069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{737}{780}\right)\)	\(e\left(\frac{347}{390}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{17}{780}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{152}{195}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{38025}(2204,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{780}\right)\)	\(e\left(\frac{223}{390}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{223}{260}\right)\)	\(e\left(\frac{583}{780}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{28}{195}\right)\)	\(e\left(\frac{367}{390}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{38025}(2294,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{397}{780}\right)\)	\(e\left(\frac{7}{390}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{137}{260}\right)\)	\(e\left(\frac{97}{780}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{7}{195}\right)\)	\(e\left(\frac{43}{390}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{38025}(2429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{683}{780}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{163}{260}\right)\)	\(e\left(\frac{383}{780}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{17}{390}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{38025}(2654,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{780}\right)\)	\(e\left(\frac{173}{390}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{173}{260}\right)\)	\(e\left(\frac{113}{780}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{173}{195}\right)\)	\(e\left(\frac{227}{390}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{38025}(2789,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{619}{780}\right)\)	\(e\left(\frac{229}{390}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{499}{780}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{34}{195}\right)\)	\(e\left(\frac{181}{390}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{38025}(2879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{780}\right)\)	\(e\left(\frac{313}{390}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{53}{260}\right)\)	\(e\left(\frac{493}{780}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{307}{390}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{38025}(3014,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{779}{780}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{259}{260}\right)\)	\(e\left(\frac{599}{780}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{161}{390}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{38025}(3239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{780}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{129}{260}\right)\)	\(e\left(\frac{209}{780}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{161}{390}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{38025}(3464,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{780}\right)\)	\(e\left(\frac{229}{390}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{109}{780}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{34}{195}\right)\)	\(e\left(\frac{181}{390}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{38025}(3959,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{631}{780}\right)\)	\(e\left(\frac{241}{390}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{331}{780}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{38025}(4184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{780}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{191}{260}\right)\)	\(e\left(\frac{251}{780}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{191}{195}\right)\)	\(e\left(\frac{59}{390}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{38025}(4409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{780}\right)\)	\(e\left(\frac{41}{390}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{41}{260}\right)\)	\(e\left(\frac{401}{780}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{29}{390}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{38025}(4634,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{780}\right)\)	\(e\left(\frac{61}{390}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{121}{780}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{61}{195}\right)\)	\(e\left(\frac{319}{390}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{38025}(4769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{780}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{467}{780}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{203}{390}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{38025}(4994,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{780}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{257}{260}\right)\)	\(e\left(\frac{497}{780}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{353}{390}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{38025}(5129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{643}{780}\right)\)	\(e\left(\frac{253}{390}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{163}{780}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{58}{195}\right)\)	\(e\left(\frac{217}{390}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{38025}(5219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{757}{780}\right)\)	\(e\left(\frac{367}{390}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{517}{780}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{172}{195}\right)\)	\(e\left(\frac{193}{390}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{38025}(5354,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{383}{780}\right)\)	\(e\left(\frac{383}{390}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{683}{780}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{347}{390}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{38025}(5579,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{473}{780}\right)\)	\(e\left(\frac{83}{390}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{593}{780}\right)\)	\(e\left(\frac{103}{130}\right)\)	\(e\left(\frac{83}{195}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{38025}(5714,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{780}\right)\)	\(e\left(\frac{259}{390}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{259}{260}\right)\)	\(e\left(\frac{79}{780}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{64}{195}\right)\)	\(e\left(\frac{31}{390}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{38025}(5804,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{673}{780}\right)\)	\(e\left(\frac{283}{390}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{133}{780}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{38025}(5939,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{479}{780}\right)\)	\(e\left(\frac{89}{390}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{219}{260}\right)\)	\(e\left(\frac{119}{780}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{89}{195}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{38025}(6389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{589}{780}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{529}{780}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{4}{195}\right)\)	\(e\left(\frac{331}{390}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 192 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	38025.ol
Modulus	$38025$
Conductor	$12675$
Order	$780$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(38025\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(12675\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(780\)	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 12675.fx	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);