LMFDB - Dirichlet character orbit 1045.cr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1045, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([135,144,130])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(3,1045)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1045$
Conductor:	$1045$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$180$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{1045}(3,\cdot)$	$1$	$1$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{1045}(48,\cdot)$	$1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{1045}(53,\cdot)$	$1$	$1$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{1045}(97,\cdot)$	$1$	$1$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{1045}(108,\cdot)$	$1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{1045}(147,\cdot)$	$1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{1045}(148,\cdot)$	$1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{1045}(192,\cdot)$	$1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{1045}(203,\cdot)$	$1$	$1$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{1045}(212,\cdot)$	$1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{1045}(223,\cdot)$	$1$	$1$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{1045}(257,\cdot)$	$1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{1045}(262,\cdot)$	$1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{1045}(268,\cdot)$	$1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{1045}(317,\cdot)$	$1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{1045}(333,\cdot)$	$1$	$1$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{1045}(357,\cdot)$	$1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{1045}(383,\cdot)$	$1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{1045}(412,\cdot)$	$1$	$1$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{1045}(432,\cdot)$	$1$	$1$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{1045}(433,\cdot)$	$1$	$1$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{1045}(477,\cdot)$	$1$	$1$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{1045}(478,\cdot)$	$1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{1045}(488,\cdot)$	$1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{1045}(542,\cdot)$	$1$	$1$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{1045}(553,\cdot)$	$1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{1045}(592,\cdot)$	$1$	$1$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{1045}(603,\cdot)$	$1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{1045}(642,\cdot)$	$1$	$1$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{1045}(687,\cdot)$	$1$	$1$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{1045}(697,\cdot)$	$1$	$1$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{2}{45}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{1045}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{1045}(48,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{1045}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{1045}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{1045}(108,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{1045}(147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)
\(\chi_{1045}(148,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{1045}(192,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{1045}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{1045}(212,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{1045}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{1045}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{1045}(262,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{1045}(268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{1045}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{1045}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{1045}(357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{1045}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{1045}(412,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{1045}(432,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{1045}(433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{1045}(477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{1045}(478,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{1045}(488,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{1045}(542,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{1045}(553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{1045}(592,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{1045}(603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{1045}(642,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{1045}(687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{1045}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{2}{45}\right)\)

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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	1045.cr
Modulus	$1045$
Conductor	$1045$
Order	$180$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1045\)
Conductor:	\(1045\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(180\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)