LMFDB - Dirichlet character orbit 2057.bg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2057, base_ring=CyclotomicField(176)) M = H._module chi = DirichletCharacter(H, M([144,143])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(12,2057)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2057$
Conductor:	$2057$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$176$	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:	$\Q(\zeta_{176})$
Fixed field:	Number field defined by a degree 176 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{2057}(12,\cdot)$	$-1$	$1$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{1}{176}\right)$	$e\left(\frac{117}{176}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{35}{176}\right)$
$\chi_{2057}(23,\cdot)$	$-1$	$1$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{137}{176}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{95}{176}\right)$	$e\left(\frac{81}{176}\right)$
$\chi_{2057}(45,\cdot)$	$-1$	$1$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{65}{176}\right)$	$e\left(\frac{147}{176}\right)$	$e\left(\frac{127}{176}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{41}{176}\right)$
$\chi_{2057}(56,\cdot)$	$-1$	$1$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{51}{176}\right)$	$e\left(\frac{137}{176}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{133}{176}\right)$	$e\left(\frac{43}{176}\right)$
$\chi_{2057}(78,\cdot)$	$-1$	$1$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{133}{176}\right)$	$e\left(\frac{95}{176}\right)$	$e\left(\frac{27}{176}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{176}\right)$	$e\left(\frac{157}{176}\right)$
$\chi_{2057}(133,\cdot)$	$-1$	$1$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{63}{176}\right)$	$e\left(\frac{45}{176}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{167}{176}\right)$
$\chi_{2057}(177,\cdot)$	$-1$	$1$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{29}{176}\right)$	$e\left(\frac{71}{176}\right)$	$e\left(\frac{35}{176}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{155}{176}\right)$	$e\left(\frac{21}{176}\right)$
$\chi_{2057}(199,\cdot)$	$-1$	$1$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{155}{176}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{5}{176}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{173}{176}\right)$	$e\left(\frac{3}{176}\right)$
$\chi_{2057}(210,\cdot)$	$-1$	$1$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{127}{176}\right)$	$e\left(\frac{49}{176}\right)$
$\chi_{2057}(232,\cdot)$	$-1$	$1$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{113}{176}\right)$	$e\left(\frac{131}{176}\right)$	$e\left(\frac{15}{176}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{167}{176}\right)$	$e\left(\frac{9}{176}\right)$
$\chi_{2057}(265,\cdot)$	$-1$	$1$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{176}\right)$	$e\left(\frac{79}{176}\right)$	$e\left(\frac{91}{176}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{51}{176}\right)$	$e\left(\frac{125}{176}\right)$
$\chi_{2057}(309,\cdot)$	$-1$	$1$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{103}{176}\right)$	$e\left(\frac{149}{176}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{65}{176}\right)$	$e\left(\frac{111}{176}\right)$
$\chi_{2057}(320,\cdot)$	$-1$	$1$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{111}{176}\right)$	$e\left(\frac{29}{176}\right)$	$e\left(\frac{49}{176}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{41}{176}\right)$	$e\left(\frac{135}{176}\right)$
$\chi_{2057}(386,\cdot)$	$-1$	$1$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{27}{176}\right)$	$e\left(\frac{145}{176}\right)$	$e\left(\frac{69}{176}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{176}\right)$	$e\left(\frac{147}{176}\right)$
$\chi_{2057}(397,\cdot)$	$-1$	$1$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{57}{176}\right)$	$e\left(\frac{91}{176}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{159}{176}\right)$	$e\left(\frac{17}{176}\right)$
$\chi_{2057}(419,\cdot)$	$-1$	$1$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{115}{176}\right)$	$e\left(\frac{79}{176}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{153}{176}\right)$
$\chi_{2057}(430,\cdot)$	$-1$	$1$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{147}{176}\right)$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{21}{176}\right)$	$e\left(\frac{155}{176}\right)$
$\chi_{2057}(452,\cdot)$	$-1$	$1$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{53}{176}\right)$	$e\left(\frac{63}{176}\right)$	$e\left(\frac{155}{176}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{83}{176}\right)$	$e\left(\frac{93}{176}\right)$
$\chi_{2057}(496,\cdot)$	$-1$	$1$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{133}{176}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{97}{176}\right)$	$e\left(\frac{79}{176}\right)$
$\chi_{2057}(507,\cdot)$	$-1$	$1$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{159}{176}\right)$	$e\left(\frac{13}{176}\right)$	$e\left(\frac{113}{176}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{103}{176}\right)$
$\chi_{2057}(551,\cdot)$	$-1$	$1$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{125}{176}\right)$	$e\left(\frac{39}{176}\right)$	$e\left(\frac{163}{176}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{43}{176}\right)$	$e\left(\frac{133}{176}\right)$
$\chi_{2057}(573,\cdot)$	$-1$	$1$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{75}{176}\right)$	$e\left(\frac{129}{176}\right)$	$e\left(\frac{133}{176}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{115}{176}\right)$
$\chi_{2057}(584,\cdot)$	$-1$	$1$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{75}{176}\right)$	$e\left(\frac{151}{176}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{176}\right)$	$e\left(\frac{161}{176}\right)$
$\chi_{2057}(617,\cdot)$	$-1$	$1$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{19}{176}\right)$	$e\left(\frac{89}{176}\right)$	$e\left(\frac{29}{176}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{53}{176}\right)$	$e\left(\frac{123}{176}\right)$
$\chi_{2057}(639,\cdot)$	$-1$	$1$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{101}{176}\right)$	$e\left(\frac{47}{176}\right)$	$e\left(\frac{43}{176}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{115}{176}\right)$	$e\left(\frac{61}{176}\right)$
$\chi_{2057}(683,\cdot)$	$-1$	$1$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{117}{176}\right)$	$e\left(\frac{137}{176}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{129}{176}\right)$	$e\left(\frac{47}{176}\right)$
$\chi_{2057}(694,\cdot)$	$-1$	$1$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{31}{176}\right)$	$e\left(\frac{173}{176}\right)$	$e\left(\frac{1}{176}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{105}{176}\right)$	$e\left(\frac{71}{176}\right)$
$\chi_{2057}(738,\cdot)$	$-1$	$1$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{173}{176}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{51}{176}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{75}{176}\right)$	$e\left(\frac{101}{176}\right)$
$\chi_{2057}(760,\cdot)$	$-1$	$1$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{113}{176}\right)$	$e\left(\frac{21}{176}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{93}{176}\right)$	$e\left(\frac{83}{176}\right)$
$\chi_{2057}(771,\cdot)$	$-1$	$1$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{153}{176}\right)$	$e\left(\frac{59}{176}\right)$	$e\left(\frac{39}{176}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{47}{176}\right)$	$e\left(\frac{129}{176}\right)$
$\chi_{2057}(793,\cdot)$	$-1$	$1$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{81}{176}\right)$	$e\left(\frac{83}{176}\right)$	$e\left(\frac{31}{176}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{89}{176}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{2057}(12,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{1}{176}\right)\)	\(e\left(\frac{117}{176}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{35}{176}\right)\)
\(\chi_{2057}(23,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{137}{176}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{95}{176}\right)\)	\(e\left(\frac{81}{176}\right)\)
\(\chi_{2057}(45,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{65}{176}\right)\)	\(e\left(\frac{147}{176}\right)\)	\(e\left(\frac{127}{176}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{41}{176}\right)\)
\(\chi_{2057}(56,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{51}{176}\right)\)	\(e\left(\frac{137}{176}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{133}{176}\right)\)	\(e\left(\frac{43}{176}\right)\)
\(\chi_{2057}(78,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{133}{176}\right)\)	\(e\left(\frac{95}{176}\right)\)	\(e\left(\frac{27}{176}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{176}\right)\)	\(e\left(\frac{157}{176}\right)\)
\(\chi_{2057}(133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{63}{176}\right)\)	\(e\left(\frac{45}{176}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{167}{176}\right)\)
\(\chi_{2057}(177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{29}{176}\right)\)	\(e\left(\frac{71}{176}\right)\)	\(e\left(\frac{35}{176}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{155}{176}\right)\)	\(e\left(\frac{21}{176}\right)\)
\(\chi_{2057}(199,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{155}{176}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{5}{176}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{173}{176}\right)\)	\(e\left(\frac{3}{176}\right)\)
\(\chi_{2057}(210,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{127}{176}\right)\)	\(e\left(\frac{49}{176}\right)\)
\(\chi_{2057}(232,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{113}{176}\right)\)	\(e\left(\frac{131}{176}\right)\)	\(e\left(\frac{15}{176}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{167}{176}\right)\)	\(e\left(\frac{9}{176}\right)\)
\(\chi_{2057}(265,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{176}\right)\)	\(e\left(\frac{79}{176}\right)\)	\(e\left(\frac{91}{176}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{51}{176}\right)\)	\(e\left(\frac{125}{176}\right)\)
\(\chi_{2057}(309,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{103}{176}\right)\)	\(e\left(\frac{149}{176}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{65}{176}\right)\)	\(e\left(\frac{111}{176}\right)\)
\(\chi_{2057}(320,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{111}{176}\right)\)	\(e\left(\frac{29}{176}\right)\)	\(e\left(\frac{49}{176}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{41}{176}\right)\)	\(e\left(\frac{135}{176}\right)\)
\(\chi_{2057}(386,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{27}{176}\right)\)	\(e\left(\frac{145}{176}\right)\)	\(e\left(\frac{69}{176}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{176}\right)\)	\(e\left(\frac{147}{176}\right)\)
\(\chi_{2057}(397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{57}{176}\right)\)	\(e\left(\frac{91}{176}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{159}{176}\right)\)	\(e\left(\frac{17}{176}\right)\)
\(\chi_{2057}(419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{115}{176}\right)\)	\(e\left(\frac{79}{176}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{153}{176}\right)\)
\(\chi_{2057}(430,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{147}{176}\right)\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{21}{176}\right)\)	\(e\left(\frac{155}{176}\right)\)
\(\chi_{2057}(452,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{53}{176}\right)\)	\(e\left(\frac{63}{176}\right)\)	\(e\left(\frac{155}{176}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{83}{176}\right)\)	\(e\left(\frac{93}{176}\right)\)
\(\chi_{2057}(496,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{133}{176}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{97}{176}\right)\)	\(e\left(\frac{79}{176}\right)\)
\(\chi_{2057}(507,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{159}{176}\right)\)	\(e\left(\frac{13}{176}\right)\)	\(e\left(\frac{113}{176}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{103}{176}\right)\)
\(\chi_{2057}(551,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{125}{176}\right)\)	\(e\left(\frac{39}{176}\right)\)	\(e\left(\frac{163}{176}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{43}{176}\right)\)	\(e\left(\frac{133}{176}\right)\)
\(\chi_{2057}(573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{75}{176}\right)\)	\(e\left(\frac{129}{176}\right)\)	\(e\left(\frac{133}{176}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{115}{176}\right)\)
\(\chi_{2057}(584,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{75}{176}\right)\)	\(e\left(\frac{151}{176}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{176}\right)\)	\(e\left(\frac{161}{176}\right)\)
\(\chi_{2057}(617,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{19}{176}\right)\)	\(e\left(\frac{89}{176}\right)\)	\(e\left(\frac{29}{176}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{53}{176}\right)\)	\(e\left(\frac{123}{176}\right)\)
\(\chi_{2057}(639,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{101}{176}\right)\)	\(e\left(\frac{47}{176}\right)\)	\(e\left(\frac{43}{176}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{115}{176}\right)\)	\(e\left(\frac{61}{176}\right)\)
\(\chi_{2057}(683,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{117}{176}\right)\)	\(e\left(\frac{137}{176}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{129}{176}\right)\)	\(e\left(\frac{47}{176}\right)\)
\(\chi_{2057}(694,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{31}{176}\right)\)	\(e\left(\frac{173}{176}\right)\)	\(e\left(\frac{1}{176}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{105}{176}\right)\)	\(e\left(\frac{71}{176}\right)\)
\(\chi_{2057}(738,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{173}{176}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{51}{176}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{75}{176}\right)\)	\(e\left(\frac{101}{176}\right)\)
\(\chi_{2057}(760,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{113}{176}\right)\)	\(e\left(\frac{21}{176}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{93}{176}\right)\)	\(e\left(\frac{83}{176}\right)\)
\(\chi_{2057}(771,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{153}{176}\right)\)	\(e\left(\frac{59}{176}\right)\)	\(e\left(\frac{39}{176}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{47}{176}\right)\)	\(e\left(\frac{129}{176}\right)\)
\(\chi_{2057}(793,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{81}{176}\right)\)	\(e\left(\frac{83}{176}\right)\)	\(e\left(\frac{31}{176}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{89}{176}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 80 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	2057.bg
Modulus	$2057$
Conductor	$2057$
Order	$176$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2057\)
Conductor:	\(2057\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(176\)	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)