LMFDB - Dirichlet character orbit 8325.ld

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8325, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([60,171,55])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(13, 8325)) 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("8325.13"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8325$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$8325$	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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{8325}(13,\cdot)$	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{143}{180}\right)$
$\chi_{8325}(52,\cdot)$	$1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{97}{180}\right)$
$\chi_{8325}(133,\cdot)$	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{151}{180}\right)$
$\chi_{8325}(187,\cdot)$	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{13}{180}\right)$
$\chi_{8325}(313,\cdot)$	$1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{163}{180}\right)$
$\chi_{8325}(463,\cdot)$	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{23}{180}\right)$
$\chi_{8325}(1327,\cdot)$	$1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{137}{180}\right)$
$\chi_{8325}(1537,\cdot)$	$1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{73}{180}\right)$
$\chi_{8325}(1633,\cdot)$	$1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{11}{180}\right)$
$\chi_{8325}(1663,\cdot)$	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{103}{180}\right)$
$\chi_{8325}(1678,\cdot)$	$1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{179}{180}\right)$
$\chi_{8325}(1717,\cdot)$	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{61}{180}\right)$
$\chi_{8325}(1798,\cdot)$	$1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{180}\right)$
$\chi_{8325}(1852,\cdot)$	$1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{157}{180}\right)$
$\chi_{8325}(1978,\cdot)$	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{19}{180}\right)$
$\chi_{8325}(2128,\cdot)$	$1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{59}{180}\right)$
$\chi_{8325}(2497,\cdot)$	$1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{149}{180}\right)$
$\chi_{8325}(2947,\cdot)$	$1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{89}{180}\right)$
$\chi_{8325}(2992,\cdot)$	$1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{101}{180}\right)$
$\chi_{8325}(3202,\cdot)$	$1$	$1$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{37}{180}\right)$
$\chi_{8325}(3298,\cdot)$	$1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{47}{180}\right)$
$\chi_{8325}(3328,\cdot)$	$1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{139}{180}\right)$
$\chi_{8325}(3463,\cdot)$	$1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{43}{180}\right)$
$\chi_{8325}(3517,\cdot)$	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{121}{180}\right)$
$\chi_{8325}(4162,\cdot)$	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{113}{180}\right)$
$\chi_{8325}(4612,\cdot)$	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{53}{180}\right)$
$\chi_{8325}(4867,\cdot)$	$1$	$1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{180}\right)$
$\chi_{8325}(4963,\cdot)$	$1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{83}{180}\right)$
$\chi_{8325}(5008,\cdot)$	$1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{71}{180}\right)$
$\chi_{8325}(5047,\cdot)$	$1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{169}{180}\right)$
$\chi_{8325}(5128,\cdot)$	$1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{79}{180}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{8325}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{143}{180}\right)\)
\(\chi_{8325}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{97}{180}\right)\)
\(\chi_{8325}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{151}{180}\right)\)
\(\chi_{8325}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{13}{180}\right)\)
\(\chi_{8325}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{163}{180}\right)\)
\(\chi_{8325}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{23}{180}\right)\)
\(\chi_{8325}(1327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{137}{180}\right)\)
\(\chi_{8325}(1537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{73}{180}\right)\)
\(\chi_{8325}(1633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{11}{180}\right)\)
\(\chi_{8325}(1663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{103}{180}\right)\)
\(\chi_{8325}(1678,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{179}{180}\right)\)
\(\chi_{8325}(1717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{61}{180}\right)\)
\(\chi_{8325}(1798,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{180}\right)\)
\(\chi_{8325}(1852,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{157}{180}\right)\)
\(\chi_{8325}(1978,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{19}{180}\right)\)
\(\chi_{8325}(2128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{59}{180}\right)\)
\(\chi_{8325}(2497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{149}{180}\right)\)
\(\chi_{8325}(2947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{89}{180}\right)\)
\(\chi_{8325}(2992,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{101}{180}\right)\)
\(\chi_{8325}(3202,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{37}{180}\right)\)
\(\chi_{8325}(3298,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{47}{180}\right)\)
\(\chi_{8325}(3328,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{139}{180}\right)\)
\(\chi_{8325}(3463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{43}{180}\right)\)
\(\chi_{8325}(3517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{121}{180}\right)\)
\(\chi_{8325}(4162,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{113}{180}\right)\)
\(\chi_{8325}(4612,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{53}{180}\right)\)
\(\chi_{8325}(4867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{180}\right)\)
\(\chi_{8325}(4963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{83}{180}\right)\)
\(\chi_{8325}(5008,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{71}{180}\right)\)
\(\chi_{8325}(5047,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{169}{180}\right)\)
\(\chi_{8325}(5128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{79}{180}\right)\)

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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	8325.ld
Modulus	$8325$
Conductor	$8325$
Order	$180$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8325\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8325\)	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);