LMFDB - Dirichlet character orbit 2057.bk

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2057, base_ring=CyclotomicField(440)) M = H._module chi = DirichletCharacter(H, M([208,165])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(15,2057)) 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:	$440$	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:	$\Q(\zeta_{440})$
Fixed field:	Number field defined by a degree 440 polynomial (not computed)

First 31 of 160 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{2057}(15,\cdot)$	$1$	$1$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{377}{440}\right)$	$e\left(\frac{307}{440}\right)$	$e\left(\frac{191}{440}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{37}{88}\right)$
$\chi_{2057}(25,\cdot)$	$1$	$1$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{303}{440}\right)$	$e\left(\frac{53}{440}\right)$	$e\left(\frac{129}{440}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{19}{88}\right)$
$\chi_{2057}(26,\cdot)$	$1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{107}{440}\right)$	$e\left(\frac{177}{440}\right)$	$e\left(\frac{381}{440}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{2057}(36,\cdot)$	$1$	$1$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{53}{440}\right)$	$e\left(\frac{63}{440}\right)$	$e\left(\frac{419}{440}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{1}{88}\right)$
$\chi_{2057}(42,\cdot)$	$1$	$1$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{311}{440}\right)$	$e\left(\frac{21}{440}\right)$	$e\left(\frac{433}{440}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{59}{88}\right)$
$\chi_{2057}(49,\cdot)$	$1$	$1$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{129}{440}\right)$	$e\left(\frac{419}{440}\right)$	$e\left(\frac{7}{440}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{2057}(53,\cdot)$	$1$	$1$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{301}{440}\right)$	$e\left(\frac{391}{440}\right)$	$e\left(\frac{163}{440}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{9}{88}\right)$
$\chi_{2057}(59,\cdot)$	$1$	$1$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{287}{440}\right)$	$e\left(\frac{117}{440}\right)$	$e\left(\frac{401}{440}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{2057}(60,\cdot)$	$1$	$1$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{419}{440}\right)$	$e\left(\frac{249}{440}\right)$	$e\left(\frac{357}{440}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{71}{88}\right)$
$\chi_{2057}(70,\cdot)$	$1$	$1$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{237}{440}\right)$	$e\left(\frac{207}{440}\right)$	$e\left(\frac{371}{440}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{2057}(93,\cdot)$	$1$	$1$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{79}{440}\right)$	$e\left(\frac{69}{440}\right)$	$e\left(\frac{417}{440}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{43}{88}\right)$
$\chi_{2057}(104,\cdot)$	$1$	$1$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{149}{440}\right)$	$e\left(\frac{119}{440}\right)$	$e\left(\frac{107}{440}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{2057}(168,\cdot)$	$1$	$1$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{353}{440}\right)$	$e\left(\frac{403}{440}\right)$	$e\left(\frac{159}{440}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{5}{88}\right)$
$\chi_{2057}(179,\cdot)$	$1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{323}{440}\right)$	$e\left(\frac{193}{440}\right)$	$e\left(\frac{229}{440}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{2057}(185,\cdot)$	$1$	$1$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{401}{440}\right)$	$e\left(\frac{211}{440}\right)$	$e\left(\frac{223}{440}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{69}{88}\right)$
$\chi_{2057}(196,\cdot)$	$1$	$1$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{171}{440}\right)$	$e\left(\frac{361}{440}\right)$	$e\left(\frac{173}{440}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{2057}(212,\cdot)$	$1$	$1$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{343}{440}\right)$	$e\left(\frac{333}{440}\right)$	$e\left(\frac{329}{440}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{43}{88}\right)$
$\chi_{2057}(213,\cdot)$	$1$	$1$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{27}{440}\right)$	$e\left(\frac{57}{440}\right)$	$e\left(\frac{421}{440}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{47}{88}\right)$
$\chi_{2057}(223,\cdot)$	$1$	$1$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{93}{440}\right)$	$e\left(\frac{343}{440}\right)$	$e\left(\frac{179}{440}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{25}{88}\right)$
$\chi_{2057}(229,\cdot)$	$1$	$1$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{31}{440}\right)$	$e\left(\frac{261}{440}\right)$	$e\left(\frac{353}{440}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{67}{88}\right)$
$\chi_{2057}(236,\cdot)$	$1$	$1$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{329}{440}\right)$	$e\left(\frac{59}{440}\right)$	$e\left(\frac{127}{440}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{61}{88}\right)$
$\chi_{2057}(240,\cdot)$	$1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{21}{440}\right)$	$e\left(\frac{191}{440}\right)$	$e\left(\frac{83}{440}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{2057}(246,\cdot)$	$1$	$1$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{207}{440}\right)$	$e\left(\frac{437}{440}\right)$	$e\left(\frac{1}{440}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{67}{88}\right)$
$\chi_{2057}(247,\cdot)$	$1$	$1$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{179}{440}\right)$	$e\left(\frac{329}{440}\right)$	$e\left(\frac{37}{440}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{15}{88}\right)$
$\chi_{2057}(257,\cdot)$	$1$	$1$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{157}{440}\right)$	$e\left(\frac{87}{440}\right)$	$e\left(\frac{411}{440}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{2057}(280,\cdot)$	$1$	$1$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{279}{440}\right)$	$e\left(\frac{149}{440}\right)$	$e\left(\frac{97}{440}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{75}{88}\right)$
$\chi_{2057}(291,\cdot)$	$1$	$1$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{349}{440}\right)$	$e\left(\frac{199}{440}\right)$	$e\left(\frac{227}{440}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{73}{88}\right)$
$\chi_{2057}(355,\cdot)$	$1$	$1$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{393}{440}\right)$	$e\left(\frac{243}{440}\right)$	$e\left(\frac{359}{440}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{2057}(383,\cdot)$	$1$	$1$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{331}{440}\right)$	$e\left(\frac{161}{440}\right)$	$e\left(\frac{93}{440}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{71}{88}\right)$
$\chi_{2057}(389,\cdot)$	$1$	$1$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{217}{440}\right)$	$e\left(\frac{67}{440}\right)$	$e\left(\frac{271}{440}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{2057}(399,\cdot)$	$1$	$1$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{383}{440}\right)$	$e\left(\frac{173}{440}\right)$	$e\left(\frac{89}{440}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{67}{88}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{2057}(15,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{377}{440}\right)\)	\(e\left(\frac{307}{440}\right)\)	\(e\left(\frac{191}{440}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)
\(\chi_{2057}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{303}{440}\right)\)	\(e\left(\frac{53}{440}\right)\)	\(e\left(\frac{129}{440}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)
\(\chi_{2057}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{107}{440}\right)\)	\(e\left(\frac{177}{440}\right)\)	\(e\left(\frac{381}{440}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{2057}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{53}{440}\right)\)	\(e\left(\frac{63}{440}\right)\)	\(e\left(\frac{419}{440}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)
\(\chi_{2057}(42,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{311}{440}\right)\)	\(e\left(\frac{21}{440}\right)\)	\(e\left(\frac{433}{440}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)
\(\chi_{2057}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{129}{440}\right)\)	\(e\left(\frac{419}{440}\right)\)	\(e\left(\frac{7}{440}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{2057}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{301}{440}\right)\)	\(e\left(\frac{391}{440}\right)\)	\(e\left(\frac{163}{440}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)
\(\chi_{2057}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{287}{440}\right)\)	\(e\left(\frac{117}{440}\right)\)	\(e\left(\frac{401}{440}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{2057}(60,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{419}{440}\right)\)	\(e\left(\frac{249}{440}\right)\)	\(e\left(\frac{357}{440}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)
\(\chi_{2057}(70,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{237}{440}\right)\)	\(e\left(\frac{207}{440}\right)\)	\(e\left(\frac{371}{440}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{2057}(93,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{79}{440}\right)\)	\(e\left(\frac{69}{440}\right)\)	\(e\left(\frac{417}{440}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)
\(\chi_{2057}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{149}{440}\right)\)	\(e\left(\frac{119}{440}\right)\)	\(e\left(\frac{107}{440}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{2057}(168,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{353}{440}\right)\)	\(e\left(\frac{403}{440}\right)\)	\(e\left(\frac{159}{440}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)
\(\chi_{2057}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{323}{440}\right)\)	\(e\left(\frac{193}{440}\right)\)	\(e\left(\frac{229}{440}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{2057}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{401}{440}\right)\)	\(e\left(\frac{211}{440}\right)\)	\(e\left(\frac{223}{440}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)
\(\chi_{2057}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{171}{440}\right)\)	\(e\left(\frac{361}{440}\right)\)	\(e\left(\frac{173}{440}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{2057}(212,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{343}{440}\right)\)	\(e\left(\frac{333}{440}\right)\)	\(e\left(\frac{329}{440}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)
\(\chi_{2057}(213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{27}{440}\right)\)	\(e\left(\frac{57}{440}\right)\)	\(e\left(\frac{421}{440}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)
\(\chi_{2057}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{93}{440}\right)\)	\(e\left(\frac{343}{440}\right)\)	\(e\left(\frac{179}{440}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)
\(\chi_{2057}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{31}{440}\right)\)	\(e\left(\frac{261}{440}\right)\)	\(e\left(\frac{353}{440}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)
\(\chi_{2057}(236,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{329}{440}\right)\)	\(e\left(\frac{59}{440}\right)\)	\(e\left(\frac{127}{440}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)
\(\chi_{2057}(240,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{21}{440}\right)\)	\(e\left(\frac{191}{440}\right)\)	\(e\left(\frac{83}{440}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{2057}(246,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{207}{440}\right)\)	\(e\left(\frac{437}{440}\right)\)	\(e\left(\frac{1}{440}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)
\(\chi_{2057}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{179}{440}\right)\)	\(e\left(\frac{329}{440}\right)\)	\(e\left(\frac{37}{440}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)
\(\chi_{2057}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{157}{440}\right)\)	\(e\left(\frac{87}{440}\right)\)	\(e\left(\frac{411}{440}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{2057}(280,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{279}{440}\right)\)	\(e\left(\frac{149}{440}\right)\)	\(e\left(\frac{97}{440}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)
\(\chi_{2057}(291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{349}{440}\right)\)	\(e\left(\frac{199}{440}\right)\)	\(e\left(\frac{227}{440}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)
\(\chi_{2057}(355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{393}{440}\right)\)	\(e\left(\frac{243}{440}\right)\)	\(e\left(\frac{359}{440}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{2057}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{331}{440}\right)\)	\(e\left(\frac{161}{440}\right)\)	\(e\left(\frac{93}{440}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)
\(\chi_{2057}(389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{217}{440}\right)\)	\(e\left(\frac{67}{440}\right)\)	\(e\left(\frac{271}{440}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{2057}(399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{383}{440}\right)\)	\(e\left(\frac{173}{440}\right)\)	\(e\left(\frac{89}{440}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)

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First 31 of 160 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.bk
Modulus	$2057$
Conductor	$2057$
Order	$440$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2057\)
Conductor:	\(2057\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(440\)	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)