LMFDB - Dirichlet character orbit 4176.fu

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4176, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([42,63,14,48])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(83,4176)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4176$
Conductor:	$4176$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$84$	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:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$31$	$35$
$\chi_{4176}(83,\cdot)$	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{73}{84}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{4176}(227,\cdot)$	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{61}{84}\right)$	$-1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{4176}(371,\cdot)$	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{37}{84}\right)$	$-1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{4176}(587,\cdot)$	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{67}{84}\right)$	$-1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{4176}(779,\cdot)$	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{59}{84}\right)$	$-1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{4176}(803,\cdot)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{1}{84}\right)$	$-1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{4176}(923,\cdot)$	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{47}{84}\right)$	$-1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{4176}(1067,\cdot)$	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{23}{84}\right)$	$-1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{4176}(1283,\cdot)$	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{53}{84}\right)$	$-1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{4176}(1379,\cdot)$	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{84}\right)$	$-1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{4176}(1499,\cdot)$	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{71}{84}\right)$	$-1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{4176}(2075,\cdot)$	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{83}{84}\right)$	$-1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{4176}(2171,\cdot)$	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{31}{84}\right)$	$-1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{4176}(2315,\cdot)$	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{19}{84}\right)$	$-1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{4176}(2459,\cdot)$	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{79}{84}\right)$	$-1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{4176}(2675,\cdot)$	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{25}{84}\right)$	$-1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{4176}(2867,\cdot)$	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{17}{84}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{4176}(2891,\cdot)$	$1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{43}{84}\right)$	$-1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{4176}(3011,\cdot)$	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{5}{84}\right)$	$-1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{4176}(3155,\cdot)$	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{65}{84}\right)$	$-1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{4176}(3371,\cdot)$	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{11}{84}\right)$	$-1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{4176}(3467,\cdot)$	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{55}{84}\right)$	$-1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{4176}(3587,\cdot)$	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{29}{84}\right)$	$-1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{4176}(4163,\cdot)$	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{41}{84}\right)$	$-1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{28}\right)$

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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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)
\(\chi_{4176}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{4176}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{4176}(371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{4176}(587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(-1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{4176}(779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(-1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{4176}(803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(-1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{4176}(923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(-1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{4176}(1067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{4176}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(-1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{4176}(1379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(-1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{4176}(1499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{4176}(2075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(-1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{4176}(2171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(-1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{4176}(2315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(-1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{4176}(2459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{4176}(2675,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(-1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{4176}(2867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{4176}(2891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{4176}(3011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{4176}(3155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{4176}(3371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(-1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{4176}(3467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(-1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{4176}(3587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(-1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{4176}(4163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(-1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)

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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	4176.fu
Modulus	$4176$
Conductor	$4176$
Order	$84$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4176\)
Conductor:	\(4176\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(84\)	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)