LMFDB - Dirichlet character orbit 40320.bdo

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40320, base_ring=CyclotomicField(96)) M = H._module chi = DirichletCharacter(H, M([48,57,32,24,64])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(67,40320)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$40320$
Conductor:	$40320$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$96$	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:	$\Q(\zeta_{96})$
Fixed field:	Number field defined by a degree 96 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{40320}(67,\cdot)$	$1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{77}{96}\right)$
$\chi_{40320}(4363,\cdot)$	$1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{43}{96}\right)$
$\chi_{40320}(4603,\cdot)$	$1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{95}{96}\right)$
$\chi_{40320}(4867,\cdot)$	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{61}{96}\right)$
$\chi_{40320}(5107,\cdot)$	$1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{96}\right)$
$\chi_{40320}(9403,\cdot)$	$1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{79}{96}\right)$
$\chi_{40320}(9643,\cdot)$	$1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{35}{96}\right)$
$\chi_{40320}(9907,\cdot)$	$1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{96}\right)$
$\chi_{40320}(10147,\cdot)$	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{53}{96}\right)$
$\chi_{40320}(14443,\cdot)$	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{96}\right)$
$\chi_{40320}(14683,\cdot)$	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{71}{96}\right)$
$\chi_{40320}(14947,\cdot)$	$1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{37}{96}\right)$
$\chi_{40320}(15187,\cdot)$	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{89}{96}\right)$
$\chi_{40320}(19483,\cdot)$	$1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{55}{96}\right)$
$\chi_{40320}(19723,\cdot)$	$1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{96}\right)$
$\chi_{40320}(19987,\cdot)$	$1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{73}{96}\right)$
$\chi_{40320}(20227,\cdot)$	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{29}{96}\right)$
$\chi_{40320}(24523,\cdot)$	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{91}{96}\right)$
$\chi_{40320}(24763,\cdot)$	$1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{47}{96}\right)$
$\chi_{40320}(25027,\cdot)$	$1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{96}\right)$
$\chi_{40320}(25267,\cdot)$	$1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{65}{96}\right)$
$\chi_{40320}(29563,\cdot)$	$1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{31}{96}\right)$
$\chi_{40320}(29803,\cdot)$	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{83}{96}\right)$
$\chi_{40320}(30067,\cdot)$	$1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{49}{96}\right)$
$\chi_{40320}(30307,\cdot)$	$1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{96}\right)$
$\chi_{40320}(34603,\cdot)$	$1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{67}{96}\right)$
$\chi_{40320}(34843,\cdot)$	$1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{23}{96}\right)$
$\chi_{40320}(35107,\cdot)$	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{85}{96}\right)$
$\chi_{40320}(35347,\cdot)$	$1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{41}{96}\right)$
$\chi_{40320}(39643,\cdot)$	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{96}\right)$
$\chi_{40320}(39883,\cdot)$	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{59}{96}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{40320}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{77}{96}\right)\)
\(\chi_{40320}(4363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)
\(\chi_{40320}(4603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)
\(\chi_{40320}(4867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)
\(\chi_{40320}(5107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)
\(\chi_{40320}(9403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)
\(\chi_{40320}(9643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)
\(\chi_{40320}(9907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{96}\right)\)
\(\chi_{40320}(10147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{53}{96}\right)\)
\(\chi_{40320}(14443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)
\(\chi_{40320}(14683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)
\(\chi_{40320}(14947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)
\(\chi_{40320}(15187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)
\(\chi_{40320}(19483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{55}{96}\right)\)
\(\chi_{40320}(19723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{96}\right)\)
\(\chi_{40320}(19987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{73}{96}\right)\)
\(\chi_{40320}(20227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)
\(\chi_{40320}(24523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)
\(\chi_{40320}(24763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{40320}(25027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)
\(\chi_{40320}(25267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{65}{96}\right)\)
\(\chi_{40320}(29563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)
\(\chi_{40320}(29803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{83}{96}\right)\)
\(\chi_{40320}(30067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)
\(\chi_{40320}(30307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)
\(\chi_{40320}(34603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)
\(\chi_{40320}(34843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{23}{96}\right)\)
\(\chi_{40320}(35107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)
\(\chi_{40320}(35347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)
\(\chi_{40320}(39643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)
\(\chi_{40320}(39883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{59}{96}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 32 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	40320.bdo
Modulus	$40320$
Conductor	$40320$
Order	$96$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(40320\)
Conductor:	\(40320\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(96\)	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)