LMFDB - Dirichlet character orbit 3700.eh

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3700, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([90,63,130])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(3, 3700)) 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("3700.3"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3700$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3700$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$180$	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:	$\Q(\zeta_{180})$	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 180 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{3700}(3,\cdot)$	$1$	$1$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{3700}(67,\cdot)$	$1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{3700}(247,\cdot)$	$1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{3700}(263,\cdot)$	$1$	$1$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{3700}(287,\cdot)$	$1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{3700}(363,\cdot)$	$1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{3700}(447,\cdot)$	$1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{3700}(583,\cdot)$	$1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{3700}(687,\cdot)$	$1$	$1$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{3700}(983,\cdot)$	$1$	$1$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{3700}(987,\cdot)$	$1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{3700}(1003,\cdot)$	$1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{3700}(1027,\cdot)$	$1$	$1$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{3700}(1103,\cdot)$	$1$	$1$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{3700}(1187,\cdot)$	$1$	$1$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{60}\right)$
$\chi_{3700}(1283,\cdot)$	$1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{3700}(1323,\cdot)$	$1$	$1$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{3700}(1427,\cdot)$	$1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{3700}(1447,\cdot)$	$1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{3700}(1483,\cdot)$	$1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{3700}(1547,\cdot)$	$1$	$1$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{3700}(1723,\cdot)$	$1$	$1$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{3700}(1727,\cdot)$	$1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{3700}(1767,\cdot)$	$1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{49}{60}\right)$
$\chi_{3700}(1927,\cdot)$	$1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{3700}(2023,\cdot)$	$1$	$1$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{3700}(2063,\cdot)$	$1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{3700}(2167,\cdot)$	$1$	$1$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{49}{60}\right)$
$\chi_{3700}(2187,\cdot)$	$1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{60}\right)$
$\chi_{3700}(2223,\cdot)$	$1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{60}\right)$
$\chi_{3700}(2287,\cdot)$	$1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{60}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{3700}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{3700}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{3700}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{3700}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{3700}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{3700}(363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{3700}(447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{3700}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{3700}(687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{3700}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{3700}(987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{3700}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{3700}(1027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{3700}(1103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{3700}(1187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{3700}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{3700}(1323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{3700}(1427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{3700}(1447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{3700}(1483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{3700}(1547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{3700}(1723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{3700}(1727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{3700}(1767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)
\(\chi_{3700}(1927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{3700}(2023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{3700}(2063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{3700}(2167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)
\(\chi_{3700}(2187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{3700}(2223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{3700}(2287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)

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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	3700.eh
Modulus	$3700$
Conductor	$3700$
Order	$180$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3700\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3700\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(180\)	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);