LMFDB - Dirichlet character orbit 3675.dm

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3675, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([105,84,205])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(131, 3675)) 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("3675.131"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3675$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3675$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$210$	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:	yes	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:	$\Q(\zeta_{105})$	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 210 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{3675}(131,\cdot)$	$1$	$1$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{209}{210}\right)$
$\chi_{3675}(206,\cdot)$	$1$	$1$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{139}{210}\right)$
$\chi_{3675}(236,\cdot)$	$1$	$1$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{23}{210}\right)$
$\chi_{3675}(311,\cdot)$	$1$	$1$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{193}{210}\right)$
$\chi_{3675}(341,\cdot)$	$1$	$1$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{47}{210}\right)$
$\chi_{3675}(416,\cdot)$	$1$	$1$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{37}{210}\right)$
$\chi_{3675}(446,\cdot)$	$1$	$1$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{71}{210}\right)$
$\chi_{3675}(731,\cdot)$	$1$	$1$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{199}{210}\right)$
$\chi_{3675}(761,\cdot)$	$1$	$1$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{143}{210}\right)$
$\chi_{3675}(836,\cdot)$	$1$	$1$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{43}{210}\right)$
$\chi_{3675}(866,\cdot)$	$1$	$1$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{167}{210}\right)$
$\chi_{3675}(941,\cdot)$	$1$	$1$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{97}{210}\right)$
$\chi_{3675}(971,\cdot)$	$1$	$1$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{191}{210}\right)$
$\chi_{3675}(1046,\cdot)$	$1$	$1$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{151}{210}\right)$
$\chi_{3675}(1181,\cdot)$	$1$	$1$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{29}{210}\right)$
$\chi_{3675}(1286,\cdot)$	$1$	$1$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{53}{210}\right)$
$\chi_{3675}(1361,\cdot)$	$1$	$1$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{103}{210}\right)$
$\chi_{3675}(1466,\cdot)$	$1$	$1$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{157}{210}\right)$
$\chi_{3675}(1496,\cdot)$	$1$	$1$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{101}{210}\right)$
$\chi_{3675}(1571,\cdot)$	$1$	$1$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{1}{210}\right)$
$\chi_{3675}(1706,\cdot)$	$1$	$1$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{149}{210}\right)$
$\chi_{3675}(1781,\cdot)$	$1$	$1$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{109}{210}\right)$
$\chi_{3675}(1811,\cdot)$	$1$	$1$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{173}{210}\right)$
$\chi_{3675}(1886,\cdot)$	$1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{163}{210}\right)$
$\chi_{3675}(1916,\cdot)$	$1$	$1$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{197}{210}\right)$
$\chi_{3675}(2021,\cdot)$	$1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{11}{210}\right)$
$\chi_{3675}(2096,\cdot)$	$1$	$1$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{61}{210}\right)$
$\chi_{3675}(2231,\cdot)$	$1$	$1$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{59}{210}\right)$
$\chi_{3675}(2306,\cdot)$	$1$	$1$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{169}{210}\right)$
$\chi_{3675}(2336,\cdot)$	$1$	$1$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{83}{210}\right)$
$\chi_{3675}(2411,\cdot)$	$1$	$1$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{13}{210}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\(\chi_{3675}(131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{209}{210}\right)\)
\(\chi_{3675}(206,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{139}{210}\right)\)
\(\chi_{3675}(236,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{23}{210}\right)\)
\(\chi_{3675}(311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{193}{210}\right)\)
\(\chi_{3675}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{47}{210}\right)\)
\(\chi_{3675}(416,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{37}{210}\right)\)
\(\chi_{3675}(446,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{71}{210}\right)\)
\(\chi_{3675}(731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{199}{210}\right)\)
\(\chi_{3675}(761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{143}{210}\right)\)
\(\chi_{3675}(836,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{43}{210}\right)\)
\(\chi_{3675}(866,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{167}{210}\right)\)
\(\chi_{3675}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{97}{210}\right)\)
\(\chi_{3675}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{191}{210}\right)\)
\(\chi_{3675}(1046,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{151}{210}\right)\)
\(\chi_{3675}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{29}{210}\right)\)
\(\chi_{3675}(1286,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{53}{210}\right)\)
\(\chi_{3675}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{103}{210}\right)\)
\(\chi_{3675}(1466,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{157}{210}\right)\)
\(\chi_{3675}(1496,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{101}{210}\right)\)
\(\chi_{3675}(1571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{1}{210}\right)\)
\(\chi_{3675}(1706,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{149}{210}\right)\)
\(\chi_{3675}(1781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{109}{210}\right)\)
\(\chi_{3675}(1811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{173}{210}\right)\)
\(\chi_{3675}(1886,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{163}{210}\right)\)
\(\chi_{3675}(1916,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{197}{210}\right)\)
\(\chi_{3675}(2021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{11}{210}\right)\)
\(\chi_{3675}(2096,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{61}{210}\right)\)
\(\chi_{3675}(2231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{59}{210}\right)\)
\(\chi_{3675}(2306,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{169}{210}\right)\)
\(\chi_{3675}(2336,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{83}{210}\right)\)
\(\chi_{3675}(2411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{13}{210}\right)\)

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First 31 of 48 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	3675.dm
Modulus	$3675$
Conductor	$3675$
Order	$210$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3675\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3675\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(210\)	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:	yes	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);