LMFDB - Dirichlet character orbit 3328.dw

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3328, base_ring=CyclotomicField(192)) M = H._module chi = DirichletCharacter(H, M([0,147,32])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(69,3328)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3328$
Conductor:	$3328$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$192$	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:	$\Q(\zeta_{192})$
Fixed field:	Number field defined by a degree 192 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{3328}(69,\cdot)$	$1$	$1$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{85}{192}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{37}{96}\right)$
$\chi_{3328}(101,\cdot)$	$1$	$1$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{151}{192}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{77}{192}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{29}{96}\right)$
$\chi_{3328}(173,\cdot)$	$1$	$1$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{19}{96}\right)$
$\chi_{3328}(205,\cdot)$	$1$	$1$	$e\left(\frac{151}{192}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{97}{192}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{155}{192}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{11}{96}\right)$
$\chi_{3328}(277,\cdot)$	$1$	$1$	$e\left(\frac{53}{192}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{192}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{49}{96}\right)$
$\chi_{3328}(309,\cdot)$	$1$	$1$	$e\left(\frac{13}{192}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{41}{96}\right)$
$\chi_{3328}(381,\cdot)$	$1$	$1$	$e\left(\frac{59}{192}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{29}{192}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{31}{96}\right)$
$\chi_{3328}(413,\cdot)$	$1$	$1$	$e\left(\frac{19}{192}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{167}{192}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{23}{96}\right)$
$\chi_{3328}(485,\cdot)$	$1$	$1$	$e\left(\frac{17}{192}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{119}{192}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{109}{192}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{61}{96}\right)$
$\chi_{3328}(517,\cdot)$	$1$	$1$	$e\left(\frac{169}{192}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{53}{96}\right)$
$\chi_{3328}(589,\cdot)$	$1$	$1$	$e\left(\frac{119}{192}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{65}{192}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{187}{192}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{43}{96}\right)$
$\chi_{3328}(621,\cdot)$	$1$	$1$	$e\left(\frac{79}{192}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{169}{192}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{35}{96}\right)$
$\chi_{3328}(693,\cdot)$	$1$	$1$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{59}{192}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{73}{96}\right)$
$\chi_{3328}(725,\cdot)$	$1$	$1$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{17}{192}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{65}{96}\right)$
$\chi_{3328}(797,\cdot)$	$1$	$1$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{192}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{55}{96}\right)$
$\chi_{3328}(829,\cdot)$	$1$	$1$	$e\left(\frac{139}{192}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{13}{192}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{47}{96}\right)$
$\chi_{3328}(901,\cdot)$	$1$	$1$	$e\left(\frac{137}{192}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{85}{96}\right)$
$\chi_{3328}(933,\cdot)$	$1$	$1$	$e\left(\frac{97}{192}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{103}{192}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{125}{192}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{77}{96}\right)$
$\chi_{3328}(1005,\cdot)$	$1$	$1$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{137}{192}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{19}{192}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{67}{96}\right)$
$\chi_{3328}(1037,\cdot)$	$1$	$1$	$e\left(\frac{7}{192}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{192}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{59}{96}\right)$
$\chi_{3328}(1109,\cdot)$	$1$	$1$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{131}{192}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{1}{96}\right)$
$\chi_{3328}(1141,\cdot)$	$1$	$1$	$e\left(\frac{61}{192}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{43}{192}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{89}{96}\right)$
$\chi_{3328}(1213,\cdot)$	$1$	$1$	$e\left(\frac{107}{192}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{79}{96}\right)$
$\chi_{3328}(1245,\cdot)$	$1$	$1$	$e\left(\frac{67}{192}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{85}{192}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{71}{96}\right)$
$\chi_{3328}(1317,\cdot)$	$1$	$1$	$e\left(\frac{65}{192}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{71}{192}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{13}{96}\right)$
$\chi_{3328}(1349,\cdot)$	$1$	$1$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{5}{96}\right)$
$\chi_{3328}(1421,\cdot)$	$1$	$1$	$e\left(\frac{167}{192}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{17}{192}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{43}{192}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{91}{96}\right)$
$\chi_{3328}(1453,\cdot)$	$1$	$1$	$e\left(\frac{127}{192}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{121}{192}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{83}{96}\right)$
$\chi_{3328}(1525,\cdot)$	$1$	$1$	$e\left(\frac{29}{192}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{11}{192}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{73}{192}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{25}{96}\right)$
$\chi_{3328}(1557,\cdot)$	$1$	$1$	$e\left(\frac{181}{192}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{115}{192}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{65}{192}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{17}{96}\right)$
$\chi_{3328}(1629,\cdot)$	$1$	$1$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{53}{192}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{7}{96}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{3328}(69,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)
\(\chi_{3328}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{151}{192}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{77}{192}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{29}{96}\right)\)
\(\chi_{3328}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{19}{96}\right)\)
\(\chi_{3328}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{192}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{97}{192}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{155}{192}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{11}{96}\right)\)
\(\chi_{3328}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{192}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{192}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{49}{96}\right)\)
\(\chi_{3328}(309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{192}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{41}{96}\right)\)
\(\chi_{3328}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{29}{192}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{31}{96}\right)\)
\(\chi_{3328}(413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{192}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{167}{192}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{23}{96}\right)\)
\(\chi_{3328}(485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{192}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{119}{192}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{109}{192}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{61}{96}\right)\)
\(\chi_{3328}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{192}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{53}{96}\right)\)
\(\chi_{3328}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{192}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{65}{192}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{187}{192}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{43}{96}\right)\)
\(\chi_{3328}(621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{192}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{169}{192}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{35}{96}\right)\)
\(\chi_{3328}(693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{73}{96}\right)\)
\(\chi_{3328}(725,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{17}{192}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{65}{96}\right)\)
\(\chi_{3328}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{192}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{55}{96}\right)\)
\(\chi_{3328}(829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{192}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{13}{192}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{3328}(901,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{192}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{85}{96}\right)\)
\(\chi_{3328}(933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{192}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{103}{192}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{125}{192}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{77}{96}\right)\)
\(\chi_{3328}(1005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{137}{192}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{19}{192}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{67}{96}\right)\)
\(\chi_{3328}(1037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{192}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{192}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{59}{96}\right)\)
\(\chi_{3328}(1109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{1}{96}\right)\)
\(\chi_{3328}(1141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{192}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{43}{192}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{89}{96}\right)\)
\(\chi_{3328}(1213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{192}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{79}{96}\right)\)
\(\chi_{3328}(1245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{192}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{71}{96}\right)\)
\(\chi_{3328}(1317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{192}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{71}{192}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{13}{96}\right)\)
\(\chi_{3328}(1349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{5}{96}\right)\)
\(\chi_{3328}(1421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{192}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{17}{192}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{43}{192}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{91}{96}\right)\)
\(\chi_{3328}(1453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{192}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{121}{192}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{83}{96}\right)\)
\(\chi_{3328}(1525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{192}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{11}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{73}{192}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{25}{96}\right)\)
\(\chi_{3328}(1557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{192}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{115}{192}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{65}{192}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{17}{96}\right)\)
\(\chi_{3328}(1629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{53}{192}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{7}{96}\right)\)

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First 31 of 64 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	3328.dw
Modulus	$3328$
Conductor	$3328$
Order	$192$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3328\)
Conductor:	\(3328\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(192\)	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)