LMFDB - Dirichlet character orbit 2415.dk

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2415, base_ring=CyclotomicField(132)) M = H._module chi = DirichletCharacter(H, M([66,33,44,12])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,2415)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2415$
Conductor:	$2415$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$132$	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:	$\Q(\zeta_{132})$
Fixed field:	Number field defined by a degree 132 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$26$
$\chi_{2415}(2,\cdot)$	$1$	$1$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{35}{66}\right)$	$i$	$e\left(\frac{41}{66}\right)$
$\chi_{2415}(32,\cdot)$	$1$	$1$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{43}{66}\right)$	$i$	$e\left(\frac{7}{66}\right)$
$\chi_{2415}(128,\cdot)$	$1$	$1$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{47}{66}\right)$	$-i$	$e\left(\frac{23}{66}\right)$
$\chi_{2415}(233,\cdot)$	$1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{5}{66}\right)$	$-i$	$e\left(\frac{53}{66}\right)$
$\chi_{2415}(242,\cdot)$	$1$	$1$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{31}{66}\right)$	$i$	$e\left(\frac{25}{66}\right)$
$\chi_{2415}(317,\cdot)$	$1$	$1$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{23}{66}\right)$	$i$	$e\left(\frac{59}{66}\right)$
$\chi_{2415}(338,\cdot)$	$1$	$1$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{41}{66}\right)$	$-i$	$e\left(\frac{65}{66}\right)$
$\chi_{2415}(347,\cdot)$	$1$	$1$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{13}{66}\right)$	$i$	$e\left(\frac{19}{66}\right)$
$\chi_{2415}(422,\cdot)$	$1$	$1$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{17}{66}\right)$	$i$	$e\left(\frac{35}{66}\right)$
$\chi_{2415}(443,\cdot)$	$1$	$1$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{29}{66}\right)$	$-i$	$e\left(\frac{17}{66}\right)$
$\chi_{2415}(473,\cdot)$	$1$	$1$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{25}{66}\right)$	$-i$	$e\left(\frac{1}{66}\right)$
$\chi_{2415}(578,\cdot)$	$1$	$1$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{49}{66}\right)$	$-i$	$e\left(\frac{31}{66}\right)$
$\chi_{2415}(653,\cdot)$	$1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{65}{66}\right)$	$-i$	$e\left(\frac{29}{66}\right)$
$\chi_{2415}(662,\cdot)$	$1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{1}{66}\right)$	$i$	$e\left(\frac{37}{66}\right)$
$\chi_{2415}(683,\cdot)$	$1$	$1$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{19}{66}\right)$	$-i$	$e\left(\frac{43}{66}\right)$
$\chi_{2415}(767,\cdot)$	$1$	$1$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{61}{66}\right)$	$i$	$e\left(\frac{13}{66}\right)$
$\chi_{2415}(788,\cdot)$	$1$	$1$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{7}{66}\right)$	$-i$	$e\left(\frac{61}{66}\right)$
$\chi_{2415}(863,\cdot)$	$1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{53}{66}\right)$	$-i$	$e\left(\frac{47}{66}\right)$
$\chi_{2415}(947,\cdot)$	$1$	$1$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{59}{66}\right)$	$i$	$e\left(\frac{5}{66}\right)$
$\chi_{2415}(968,\cdot)$	$1$	$1$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{35}{66}\right)$	$-i$	$e\left(\frac{41}{66}\right)$
$\chi_{2415}(998,\cdot)$	$1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{43}{66}\right)$	$-i$	$e\left(\frac{7}{66}\right)$
$\chi_{2415}(1208,\cdot)$	$1$	$1$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{31}{66}\right)$	$-i$	$e\left(\frac{25}{66}\right)$
$\chi_{2415}(1283,\cdot)$	$1$	$1$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{23}{66}\right)$	$-i$	$e\left(\frac{59}{66}\right)$
$\chi_{2415}(1292,\cdot)$	$1$	$1$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{37}{66}\right)$	$i$	$e\left(\frac{49}{66}\right)$
$\chi_{2415}(1313,\cdot)$	$1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{13}{66}\right)$	$-i$	$e\left(\frac{19}{66}\right)$
$\chi_{2415}(1388,\cdot)$	$1$	$1$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{17}{66}\right)$	$-i$	$e\left(\frac{35}{66}\right)$
$\chi_{2415}(1577,\cdot)$	$1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{47}{66}\right)$	$i$	$e\left(\frac{23}{66}\right)$
$\chi_{2415}(1628,\cdot)$	$1$	$1$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{1}{66}\right)$	$-i$	$e\left(\frac{37}{66}\right)$
$\chi_{2415}(1682,\cdot)$	$1$	$1$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{5}{66}\right)$	$i$	$e\left(\frac{53}{66}\right)$
$\chi_{2415}(1733,\cdot)$	$1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{61}{66}\right)$	$-i$	$e\left(\frac{13}{66}\right)$
$\chi_{2415}(1787,\cdot)$	$1$	$1$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{41}{66}\right)$	$i$	$e\left(\frac{65}{66}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(26\)
\(\chi_{2415}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(i\)	\(e\left(\frac{41}{66}\right)\)
\(\chi_{2415}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(i\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{2415}(128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(-i\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{2415}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(-i\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{2415}(242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(i\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{2415}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(i\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{2415}(338,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(-i\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{2415}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(i\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{2415}(422,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(i\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{2415}(443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(-i\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{2415}(473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(-i\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{2415}(578,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(-i\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{2415}(653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(-i\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{2415}(662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(i\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{2415}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(-i\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{2415}(767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(i\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{2415}(788,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(-i\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{2415}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(-i\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{2415}(947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(i\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{2415}(968,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(-i\)	\(e\left(\frac{41}{66}\right)\)
\(\chi_{2415}(998,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(-i\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{2415}(1208,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(-i\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{2415}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(-i\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{2415}(1292,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(i\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{2415}(1313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(-i\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{2415}(1388,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(-i\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{2415}(1577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(i\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{2415}(1628,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(-i\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{2415}(1682,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(i\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{2415}(1733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(-i\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{2415}(1787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(i\)	\(e\left(\frac{65}{66}\right)\)

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First 31 of 40 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	2415.dk
Modulus	$2415$
Conductor	$2415$
Order	$132$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2415\)
Conductor:	\(2415\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(132\)	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)