LMFDB - Dirichlet character orbit 8041.fr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8041, base_ring=CyclotomicField(420)) M = H._module chi = DirichletCharacter(H, M([42,105,320])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,8041)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8041$
Conductor:	$8041$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$420$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{8041}(13,\cdot)$	$-1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{341}{420}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{8041}(310,\cdot)$	$-1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{8041}(404,\cdot)$	$-1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{233}{420}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{420}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{8041}(497,\cdot)$	$-1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{211}{420}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{8041}(574,\cdot)$	$-1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{8041}(633,\cdot)$	$-1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{319}{420}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{8041}(701,\cdot)$	$-1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{419}{420}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{8041}(744,\cdot)$	$-1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{257}{420}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{8041}(1041,\cdot)$	$-1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{311}{420}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{8041}(1084,\cdot)$	$-1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{8041}(1135,\cdot)$	$-1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{8041}(1228,\cdot)$	$-1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{8041}(1262,\cdot)$	$-1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{179}{420}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{8041}(1271,\cdot)$	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{169}{420}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{8041}(1305,\cdot)$	$-1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{197}{420}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{8041}(1432,\cdot)$	$-1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{83}{420}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{8041}(1823,\cdot)$	$-1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{23}{420}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{8041}(1866,\cdot)$	$-1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{8041}(1993,\cdot)$	$-1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{8041}(2087,\cdot)$	$-1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{13}{420}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{8041}(2163,\cdot)$	$-1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{8041}(2206,\cdot)$	$-1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{8041}(2274,\cdot)$	$-1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{349}{420}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{8041}(2461,\cdot)$	$-1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{169}{420}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{8041}(2503,\cdot)$	$-1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{419}{420}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{227}{420}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{8041}(2554,\cdot)$	$-1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{8041}(2648,\cdot)$	$-1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{353}{420}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{8041}(2690,\cdot)$	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{8041}(2724,\cdot)$	$-1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{8041}(2767,\cdot)$	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{29}{420}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{137}{420}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{8041}(2818,\cdot)$	$-1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{17}{84}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{8041}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{341}{420}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{8041}(310,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{8041}(404,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{233}{420}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{8041}(497,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{211}{420}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{8041}(574,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{8041}(633,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{319}{420}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{8041}(701,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{419}{420}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{8041}(744,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{257}{420}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{8041}(1041,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{311}{420}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{8041}(1084,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{8041}(1135,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{8041}(1228,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{8041}(1262,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{179}{420}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{8041}(1271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{169}{420}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{8041}(1305,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{197}{420}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{8041}(1432,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{83}{420}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{8041}(1823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{23}{420}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{8041}(1866,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{8041}(1993,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{8041}(2087,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{13}{420}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{8041}(2163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{8041}(2206,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{8041}(2274,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{349}{420}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{8041}(2461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{169}{420}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{8041}(2503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{419}{420}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{227}{420}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{8041}(2554,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{8041}(2648,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{353}{420}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{8041}(2690,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{8041}(2724,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{8041}(2767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{137}{420}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{8041}(2818,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)

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First 31 of 96 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	8041.fr
Modulus	$8041$
Conductor	$8041$
Order	$420$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(8041\)
Conductor:	\(8041\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(420\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)