LMFDB - Dirichlet character orbit 449.k

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(449, base_ring=CyclotomicField(64)) M = H._module chi = DirichletCharacter(H, M([45])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(24,449)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$449$
Conductor:	$449$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$64$	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:	$\Q(\zeta_{64})$
Fixed field:	Number field defined by a degree 64 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{449}(24,\cdot)$	$-1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{449}(37,\cdot)$	$-1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{449}(52,\cdot)$	$-1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{449}(58,\cdot)$	$-1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{449}(71,\cdot)$	$-1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{449}(79,\cdot)$	$-1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{449}(84,\cdot)$	$-1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{449}(95,\cdot)$	$-1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{449}(108,\cdot)$	$-1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{449}(131,\cdot)$	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{449}(155,\cdot)$	$-1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{449}(182,\cdot)$	$-1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{449}(188,\cdot)$	$-1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{449}(203,\cdot)$	$-1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{449}(209,\cdot)$	$-1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{449}(215,\cdot)$	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{449}(234,\cdot)$	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{449}(240,\cdot)$	$-1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{449}(246,\cdot)$	$-1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{449}(261,\cdot)$	$-1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{449}(267,\cdot)$	$-1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{449}(294,\cdot)$	$-1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{449}(318,\cdot)$	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{449}(341,\cdot)$	$-1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{449}(354,\cdot)$	$-1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{449}(365,\cdot)$	$-1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{449}(370,\cdot)$	$-1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{449}(378,\cdot)$	$-1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{449}(391,\cdot)$	$-1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{449}(397,\cdot)$	$-1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{449}(412,\cdot)$	$-1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{8}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{449}(24,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{449}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{449}(52,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{449}(58,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{449}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{449}(79,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{449}(84,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{449}(95,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{449}(108,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{449}(131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{449}(155,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{449}(182,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{449}(188,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{449}(203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{449}(209,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{449}(215,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{449}(234,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{449}(240,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{449}(246,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{449}(261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{449}(267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{449}(294,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{449}(318,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{449}(341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{449}(354,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{449}(365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{449}(370,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{449}(378,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{449}(391,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{449}(397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{449}(412,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)

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	449.k
Modulus	$449$
Conductor	$449$
Order	$64$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(449\)
Conductor:	\(449\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(64\)	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)