LMFDB - Dirichlet character orbit 3645.w

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3645, base_ring=CyclotomicField(162)) M = H._module chi = DirichletCharacter(H, M([130,0])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(46,3645)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3645$
Conductor:	$243$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$81$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 243.i	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{81})$
Fixed field:	Number field defined by a degree 81 polynomial

First 31 of 54 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{3645}(46,\cdot)$	$1$	$1$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{34}{81}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{3645}(91,\cdot)$	$1$	$1$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{3645}(181,\cdot)$	$1$	$1$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{3645}(226,\cdot)$	$1$	$1$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{3645}(316,\cdot)$	$1$	$1$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{29}{81}\right)$	$e\left(\frac{22}{81}\right)$	$e\left(\frac{13}{81}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{3645}(361,\cdot)$	$1$	$1$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{38}{81}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{4}{27}\right)$
$\chi_{3645}(451,\cdot)$	$1$	$1$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{3645}(496,\cdot)$	$1$	$1$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{35}{81}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{70}{81}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{3645}(586,\cdot)$	$1$	$1$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{47}{81}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{3645}(631,\cdot)$	$1$	$1$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{3645}(721,\cdot)$	$1$	$1$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{35}{81}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{3645}(766,\cdot)$	$1$	$1$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{13}{81}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{56}{81}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{22}{27}\right)$
$\chi_{3645}(856,\cdot)$	$1$	$1$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{3645}(901,\cdot)$	$1$	$1$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{10}{27}\right)$
$\chi_{3645}(991,\cdot)$	$1$	$1$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{3645}(1036,\cdot)$	$1$	$1$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{56}{81}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{25}{27}\right)$
$\chi_{3645}(1126,\cdot)$	$1$	$1$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{3645}(1171,\cdot)$	$1$	$1$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{38}{81}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{3645}(1261,\cdot)$	$1$	$1$	$e\left(\frac{38}{81}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{3645}(1306,\cdot)$	$1$	$1$	$e\left(\frac{13}{81}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{34}{81}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{3645}(1396,\cdot)$	$1$	$1$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{34}{81}\right)$	$e\left(\frac{56}{81}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{3645}(1441,\cdot)$	$1$	$1$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{22}{81}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{3645}(1531,\cdot)$	$1$	$1$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{3645}(1576,\cdot)$	$1$	$1$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{22}{81}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{4}{27}\right)$
$\chi_{3645}(1666,\cdot)$	$1$	$1$	$e\left(\frac{56}{81}\right)$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{3645}(1711,\cdot)$	$1$	$1$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{64}{81}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{3645}(1801,\cdot)$	$1$	$1$	$e\left(\frac{35}{81}\right)$	$e\left(\frac{70}{81}\right)$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{3645}(1846,\cdot)$	$1$	$1$	$e\left(\frac{64}{81}\right)$	$e\left(\frac{47}{81}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{13}{81}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{3645}(1936,\cdot)$	$1$	$1$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{22}{81}\right)$	$e\left(\frac{56}{81}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{3645}(1981,\cdot)$	$1$	$1$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{47}{81}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{64}{81}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{22}{27}\right)$
$\chi_{3645}(2071,\cdot)$	$1$	$1$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{70}{81}\right)$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{14}{27}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{3645}(46,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{34}{81}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{3645}(91,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{3645}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{3645}(226,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{3645}(316,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{29}{81}\right)\)	\(e\left(\frac{22}{81}\right)\)	\(e\left(\frac{13}{81}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{3645}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{38}{81}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)
\(\chi_{3645}(451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{3645}(496,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{35}{81}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{70}{81}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{3645}(586,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{47}{81}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{3645}(631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{3645}(721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{35}{81}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{3645}(766,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{13}{81}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{56}{81}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)
\(\chi_{3645}(856,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{3645}(901,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)
\(\chi_{3645}(991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{3645}(1036,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{56}{81}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{25}{27}\right)\)
\(\chi_{3645}(1126,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{3645}(1171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{38}{81}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{3645}(1261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{81}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{3645}(1306,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{81}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{34}{81}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{3645}(1396,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{34}{81}\right)\)	\(e\left(\frac{56}{81}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{3645}(1441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{22}{81}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{3645}(1531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{3645}(1576,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{22}{81}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)
\(\chi_{3645}(1666,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{81}\right)\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{53}{81}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{3645}(1711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{64}{81}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{3645}(1801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{81}\right)\)	\(e\left(\frac{70}{81}\right)\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{3645}(1846,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{81}\right)\)	\(e\left(\frac{47}{81}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{13}{81}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{3645}(1936,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{22}{81}\right)\)	\(e\left(\frac{56}{81}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{3645}(1981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{47}{81}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{64}{81}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)
\(\chi_{3645}(2071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{70}{81}\right)\)	\(e\left(\frac{53}{81}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)

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First 31 of 54 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	3645.w
Modulus	$3645$
Conductor	$243$
Order	$81$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(3645\)
Conductor:	\(243\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(81\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 243.i	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)