LMFDB - Dirichlet character orbit 3648.el

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3648, base_ring=CyclotomicField(144)) M = H._module chi = DirichletCharacter(H, M([0,135,0,40])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,3648)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3648$
Conductor:	$1216$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$144$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1216.cf	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{144})$
Fixed field:	Number field defined by a degree 144 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{3648}(13,\cdot)$	$-1$	$1$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{61}{144}\right)$
$\chi_{3648}(109,\cdot)$	$-1$	$1$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{144}\right)$
$\chi_{3648}(181,\cdot)$	$-1$	$1$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{144}\right)$
$\chi_{3648}(205,\cdot)$	$-1$	$1$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{109}{144}\right)$
$\chi_{3648}(325,\cdot)$	$-1$	$1$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{131}{144}\right)$
$\chi_{3648}(421,\cdot)$	$-1$	$1$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{144}\right)$
$\chi_{3648}(469,\cdot)$	$-1$	$1$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{144}\right)$
$\chi_{3648}(565,\cdot)$	$-1$	$1$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{143}{144}\right)$
$\chi_{3648}(637,\cdot)$	$-1$	$1$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{121}{144}\right)$
$\chi_{3648}(661,\cdot)$	$-1$	$1$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{55}{144}\right)$
$\chi_{3648}(781,\cdot)$	$-1$	$1$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{77}{144}\right)$
$\chi_{3648}(877,\cdot)$	$-1$	$1$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{101}{144}\right)$
$\chi_{3648}(925,\cdot)$	$-1$	$1$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{97}{144}\right)$
$\chi_{3648}(1021,\cdot)$	$-1$	$1$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{89}{144}\right)$
$\chi_{3648}(1093,\cdot)$	$-1$	$1$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{67}{144}\right)$
$\chi_{3648}(1117,\cdot)$	$-1$	$1$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{144}\right)$
$\chi_{3648}(1237,\cdot)$	$-1$	$1$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{144}\right)$
$\chi_{3648}(1333,\cdot)$	$-1$	$1$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{144}\right)$
$\chi_{3648}(1381,\cdot)$	$-1$	$1$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{144}\right)$
$\chi_{3648}(1477,\cdot)$	$-1$	$1$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{144}\right)$
$\chi_{3648}(1549,\cdot)$	$-1$	$1$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{144}\right)$
$\chi_{3648}(1573,\cdot)$	$-1$	$1$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{91}{144}\right)$
$\chi_{3648}(1693,\cdot)$	$-1$	$1$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{113}{144}\right)$
$\chi_{3648}(1789,\cdot)$	$-1$	$1$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{137}{144}\right)$
$\chi_{3648}(1837,\cdot)$	$-1$	$1$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{133}{144}\right)$
$\chi_{3648}(1933,\cdot)$	$-1$	$1$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{125}{144}\right)$
$\chi_{3648}(2005,\cdot)$	$-1$	$1$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{103}{144}\right)$
$\chi_{3648}(2029,\cdot)$	$-1$	$1$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{144}\right)$
$\chi_{3648}(2149,\cdot)$	$-1$	$1$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{144}\right)$
$\chi_{3648}(2245,\cdot)$	$-1$	$1$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{83}{144}\right)$
$\chi_{3648}(2293,\cdot)$	$-1$	$1$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{79}{144}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{3648}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{61}{144}\right)\)
\(\chi_{3648}(109,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{144}\right)\)
\(\chi_{3648}(181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{144}\right)\)
\(\chi_{3648}(205,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{109}{144}\right)\)
\(\chi_{3648}(325,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{131}{144}\right)\)
\(\chi_{3648}(421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{144}\right)\)
\(\chi_{3648}(469,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{144}\right)\)
\(\chi_{3648}(565,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{143}{144}\right)\)
\(\chi_{3648}(637,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{121}{144}\right)\)
\(\chi_{3648}(661,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{55}{144}\right)\)
\(\chi_{3648}(781,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{77}{144}\right)\)
\(\chi_{3648}(877,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{101}{144}\right)\)
\(\chi_{3648}(925,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{97}{144}\right)\)
\(\chi_{3648}(1021,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{89}{144}\right)\)
\(\chi_{3648}(1093,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{67}{144}\right)\)
\(\chi_{3648}(1117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{144}\right)\)
\(\chi_{3648}(1237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{144}\right)\)
\(\chi_{3648}(1333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{144}\right)\)
\(\chi_{3648}(1381,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{144}\right)\)
\(\chi_{3648}(1477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{35}{144}\right)\)
\(\chi_{3648}(1549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{144}\right)\)
\(\chi_{3648}(1573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{91}{144}\right)\)
\(\chi_{3648}(1693,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{113}{144}\right)\)
\(\chi_{3648}(1789,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{137}{144}\right)\)
\(\chi_{3648}(1837,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{133}{144}\right)\)
\(\chi_{3648}(1933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{125}{144}\right)\)
\(\chi_{3648}(2005,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{103}{144}\right)\)
\(\chi_{3648}(2029,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{144}\right)\)
\(\chi_{3648}(2149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{144}\right)\)
\(\chi_{3648}(2245,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{83}{144}\right)\)
\(\chi_{3648}(2293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{79}{144}\right)\)

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First 31 of 48 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	3648.el
Modulus	$3648$
Conductor	$1216$
Order	$144$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(3648\)
Conductor:	\(1216\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(144\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1216.cf	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)