LMFDB - Dirichlet character orbit 608.bt

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(72)) M = H._module chi = DirichletCharacter(H, M([36,27,52])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(3,608)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$608$
Conductor:	$608$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$72$	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:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{608}(3,\cdot)$	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{608}(51,\cdot)$	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{608}(59,\cdot)$	$1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{608}(67,\cdot)$	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{608}(91,\cdot)$	$1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{608}(147,\cdot)$	$1$	$1$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{608}(155,\cdot)$	$1$	$1$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{608}(203,\cdot)$	$1$	$1$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{608}(211,\cdot)$	$1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{608}(219,\cdot)$	$1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{608}(243,\cdot)$	$1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{608}(299,\cdot)$	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{608}(307,\cdot)$	$1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{608}(355,\cdot)$	$1$	$1$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{608}(363,\cdot)$	$1$	$1$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{608}(371,\cdot)$	$1$	$1$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{608}(395,\cdot)$	$1$	$1$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{608}(451,\cdot)$	$1$	$1$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{608}(459,\cdot)$	$1$	$1$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{608}(507,\cdot)$	$1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{608}(515,\cdot)$	$1$	$1$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{608}(523,\cdot)$	$1$	$1$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{608}(547,\cdot)$	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{608}(603,\cdot)$	$1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{36}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{608}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{608}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{608}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{608}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{608}(91,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{608}(147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{608}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{608}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{608}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{608}(219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{608}(243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{608}(299,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{608}(307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{608}(355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{608}(363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{608}(371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{608}(395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{608}(451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{608}(459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{608}(507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{608}(515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{608}(523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{608}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{608}(603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

Related number fields

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	608.bt
Modulus	$608$
Conductor	$608$
Order	$72$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(608\)
Conductor:	\(608\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(72\)	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)