Properties

Label 256.m
Modulus 256256
Conductor 256256
Order 6464
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(256, base_ring=CyclotomicField(64))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,1]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(5,256))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 256256
Conductor: 256256
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 6464
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(ζ64)\Q(\zeta_{64})
Fixed field: Number field defined by a degree 64 polynomial

First 31 of 32 characters in Galois orbit

Character 1-1 11 33 55 77 99 1111 1313 1515 1717 1919 2121
χ256(5,)\chi_{256}(5,\cdot) 11 11 e(3564)e\left(\frac{35}{64}\right) e(164)e\left(\frac{1}{64}\right) e(532)e\left(\frac{5}{32}\right) e(332)e\left(\frac{3}{32}\right) e(2164)e\left(\frac{21}{64}\right) e(4764)e\left(\frac{47}{64}\right) e(916)e\left(\frac{9}{16}\right) e(716)e\left(\frac{7}{16}\right) e(2364)e\left(\frac{23}{64}\right) e(4564)e\left(\frac{45}{64}\right)
χ256(13,)\chi_{256}(13,\cdot) 11 11 e(4564)e\left(\frac{45}{64}\right) e(4764)e\left(\frac{47}{64}\right) e(1132)e\left(\frac{11}{32}\right) e(1332)e\left(\frac{13}{32}\right) e(2764)e\left(\frac{27}{64}\right) e(3364)e\left(\frac{33}{64}\right) e(716)e\left(\frac{7}{16}\right) e(916)e\left(\frac{9}{16}\right) e(5764)e\left(\frac{57}{64}\right) e(364)e\left(\frac{3}{64}\right)
χ256(21,)\chi_{256}(21,\cdot) 11 11 e(3964)e\left(\frac{39}{64}\right) e(4564)e\left(\frac{45}{64}\right) e(132)e\left(\frac{1}{32}\right) e(732)e\left(\frac{7}{32}\right) e(4964)e\left(\frac{49}{64}\right) e(364)e\left(\frac{3}{64}\right) e(516)e\left(\frac{5}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(1164)e\left(\frac{11}{64}\right) e(4164)e\left(\frac{41}{64}\right)
χ256(29,)\chi_{256}(29,\cdot) 11 11 e(1764)e\left(\frac{17}{64}\right) e(5964)e\left(\frac{59}{64}\right) e(732)e\left(\frac{7}{32}\right) e(1732)e\left(\frac{17}{32}\right) e(2364)e\left(\frac{23}{64}\right) e(2164)e\left(\frac{21}{64}\right) e(316)e\left(\frac{3}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(1364)e\left(\frac{13}{64}\right) e(3164)e\left(\frac{31}{64}\right)
χ256(37,)\chi_{256}(37,\cdot) 11 11 e(4364)e\left(\frac{43}{64}\right) e(2564)e\left(\frac{25}{64}\right) e(2932)e\left(\frac{29}{32}\right) e(1132)e\left(\frac{11}{32}\right) e(1364)e\left(\frac{13}{64}\right) e(2364)e\left(\frac{23}{64}\right) e(116)e\left(\frac{1}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(6364)e\left(\frac{63}{64}\right) e(3764)e\left(\frac{37}{64}\right)
χ256(45,)\chi_{256}(45,\cdot) 11 11 e(5364)e\left(\frac{53}{64}\right) e(764)e\left(\frac{7}{64}\right) e(332)e\left(\frac{3}{32}\right) e(2132)e\left(\frac{21}{32}\right) e(1964)e\left(\frac{19}{64}\right) e(964)e\left(\frac{9}{64}\right) e(1516)e\left(\frac{15}{16}\right) e(116)e\left(\frac{1}{16}\right) e(3364)e\left(\frac{33}{64}\right) e(5964)e\left(\frac{59}{64}\right)
χ256(53,)\chi_{256}(53,\cdot) 11 11 e(4764)e\left(\frac{47}{64}\right) e(564)e\left(\frac{5}{64}\right) e(2532)e\left(\frac{25}{32}\right) e(1532)e\left(\frac{15}{32}\right) e(4164)e\left(\frac{41}{64}\right) e(4364)e\left(\frac{43}{64}\right) e(1316)e\left(\frac{13}{16}\right) e(316)e\left(\frac{3}{16}\right) e(5164)e\left(\frac{51}{64}\right) e(3364)e\left(\frac{33}{64}\right)
χ256(61,)\chi_{256}(61,\cdot) 11 11 e(2564)e\left(\frac{25}{64}\right) e(1964)e\left(\frac{19}{64}\right) e(3132)e\left(\frac{31}{32}\right) e(2532)e\left(\frac{25}{32}\right) e(1564)e\left(\frac{15}{64}\right) e(6164)e\left(\frac{61}{64}\right) e(1116)e\left(\frac{11}{16}\right) e(516)e\left(\frac{5}{16}\right) e(5364)e\left(\frac{53}{64}\right) e(2364)e\left(\frac{23}{64}\right)
χ256(69,)\chi_{256}(69,\cdot) 11 11 e(5164)e\left(\frac{51}{64}\right) e(4964)e\left(\frac{49}{64}\right) e(2132)e\left(\frac{21}{32}\right) e(1932)e\left(\frac{19}{32}\right) e(564)e\left(\frac{5}{64}\right) e(6364)e\left(\frac{63}{64}\right) e(916)e\left(\frac{9}{16}\right) e(716)e\left(\frac{7}{16}\right) e(3964)e\left(\frac{39}{64}\right) e(2964)e\left(\frac{29}{64}\right)
χ256(77,)\chi_{256}(77,\cdot) 11 11 e(6164)e\left(\frac{61}{64}\right) e(3164)e\left(\frac{31}{64}\right) e(2732)e\left(\frac{27}{32}\right) e(2932)e\left(\frac{29}{32}\right) e(1164)e\left(\frac{11}{64}\right) e(4964)e\left(\frac{49}{64}\right) e(716)e\left(\frac{7}{16}\right) e(916)e\left(\frac{9}{16}\right) e(964)e\left(\frac{9}{64}\right) e(5164)e\left(\frac{51}{64}\right)
χ256(85,)\chi_{256}(85,\cdot) 11 11 e(5564)e\left(\frac{55}{64}\right) e(2964)e\left(\frac{29}{64}\right) e(1732)e\left(\frac{17}{32}\right) e(2332)e\left(\frac{23}{32}\right) e(3364)e\left(\frac{33}{64}\right) e(1964)e\left(\frac{19}{64}\right) e(516)e\left(\frac{5}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(2764)e\left(\frac{27}{64}\right) e(2564)e\left(\frac{25}{64}\right)
χ256(93,)\chi_{256}(93,\cdot) 11 11 e(3364)e\left(\frac{33}{64}\right) e(4364)e\left(\frac{43}{64}\right) e(2332)e\left(\frac{23}{32}\right) e(132)e\left(\frac{1}{32}\right) e(764)e\left(\frac{7}{64}\right) e(3764)e\left(\frac{37}{64}\right) e(316)e\left(\frac{3}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(2964)e\left(\frac{29}{64}\right) e(1564)e\left(\frac{15}{64}\right)
χ256(101,)\chi_{256}(101,\cdot) 11 11 e(5964)e\left(\frac{59}{64}\right) e(964)e\left(\frac{9}{64}\right) e(1332)e\left(\frac{13}{32}\right) e(2732)e\left(\frac{27}{32}\right) e(6164)e\left(\frac{61}{64}\right) e(3964)e\left(\frac{39}{64}\right) e(116)e\left(\frac{1}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(1564)e\left(\frac{15}{64}\right) e(2164)e\left(\frac{21}{64}\right)
χ256(109,)\chi_{256}(109,\cdot) 11 11 e(564)e\left(\frac{5}{64}\right) e(5564)e\left(\frac{55}{64}\right) e(1932)e\left(\frac{19}{32}\right) e(532)e\left(\frac{5}{32}\right) e(364)e\left(\frac{3}{64}\right) e(2564)e\left(\frac{25}{64}\right) e(1516)e\left(\frac{15}{16}\right) e(116)e\left(\frac{1}{16}\right) e(4964)e\left(\frac{49}{64}\right) e(4364)e\left(\frac{43}{64}\right)
χ256(117,)\chi_{256}(117,\cdot) 11 11 e(6364)e\left(\frac{63}{64}\right) e(5364)e\left(\frac{53}{64}\right) e(932)e\left(\frac{9}{32}\right) e(3132)e\left(\frac{31}{32}\right) e(2564)e\left(\frac{25}{64}\right) e(5964)e\left(\frac{59}{64}\right) e(1316)e\left(\frac{13}{16}\right) e(316)e\left(\frac{3}{16}\right) e(364)e\left(\frac{3}{64}\right) e(1764)e\left(\frac{17}{64}\right)
χ256(125,)\chi_{256}(125,\cdot) 11 11 e(4164)e\left(\frac{41}{64}\right) e(364)e\left(\frac{3}{64}\right) e(1532)e\left(\frac{15}{32}\right) e(932)e\left(\frac{9}{32}\right) e(6364)e\left(\frac{63}{64}\right) e(1364)e\left(\frac{13}{64}\right) e(1116)e\left(\frac{11}{16}\right) e(516)e\left(\frac{5}{16}\right) e(564)e\left(\frac{5}{64}\right) e(764)e\left(\frac{7}{64}\right)
χ256(133,)\chi_{256}(133,\cdot) 11 11 e(364)e\left(\frac{3}{64}\right) e(3364)e\left(\frac{33}{64}\right) e(532)e\left(\frac{5}{32}\right) e(332)e\left(\frac{3}{32}\right) e(5364)e\left(\frac{53}{64}\right) e(1564)e\left(\frac{15}{64}\right) e(916)e\left(\frac{9}{16}\right) e(716)e\left(\frac{7}{16}\right) e(5564)e\left(\frac{55}{64}\right) e(1364)e\left(\frac{13}{64}\right)
χ256(141,)\chi_{256}(141,\cdot) 11 11 e(1364)e\left(\frac{13}{64}\right) e(1564)e\left(\frac{15}{64}\right) e(1132)e\left(\frac{11}{32}\right) e(1332)e\left(\frac{13}{32}\right) e(5964)e\left(\frac{59}{64}\right) e(164)e\left(\frac{1}{64}\right) e(716)e\left(\frac{7}{16}\right) e(916)e\left(\frac{9}{16}\right) e(2564)e\left(\frac{25}{64}\right) e(3564)e\left(\frac{35}{64}\right)
χ256(149,)\chi_{256}(149,\cdot) 11 11 e(764)e\left(\frac{7}{64}\right) e(1364)e\left(\frac{13}{64}\right) e(132)e\left(\frac{1}{32}\right) e(732)e\left(\frac{7}{32}\right) e(1764)e\left(\frac{17}{64}\right) e(3564)e\left(\frac{35}{64}\right) e(516)e\left(\frac{5}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(4364)e\left(\frac{43}{64}\right) e(964)e\left(\frac{9}{64}\right)
χ256(157,)\chi_{256}(157,\cdot) 11 11 e(4964)e\left(\frac{49}{64}\right) e(2764)e\left(\frac{27}{64}\right) e(732)e\left(\frac{7}{32}\right) e(1732)e\left(\frac{17}{32}\right) e(5564)e\left(\frac{55}{64}\right) e(5364)e\left(\frac{53}{64}\right) e(316)e\left(\frac{3}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(4564)e\left(\frac{45}{64}\right) e(6364)e\left(\frac{63}{64}\right)
χ256(165,)\chi_{256}(165,\cdot) 11 11 e(1164)e\left(\frac{11}{64}\right) e(5764)e\left(\frac{57}{64}\right) e(2932)e\left(\frac{29}{32}\right) e(1132)e\left(\frac{11}{32}\right) e(4564)e\left(\frac{45}{64}\right) e(5564)e\left(\frac{55}{64}\right) e(116)e\left(\frac{1}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(3164)e\left(\frac{31}{64}\right) e(564)e\left(\frac{5}{64}\right)
χ256(173,)\chi_{256}(173,\cdot) 11 11 e(2164)e\left(\frac{21}{64}\right) e(3964)e\left(\frac{39}{64}\right) e(332)e\left(\frac{3}{32}\right) e(2132)e\left(\frac{21}{32}\right) e(5164)e\left(\frac{51}{64}\right) e(4164)e\left(\frac{41}{64}\right) e(1516)e\left(\frac{15}{16}\right) e(116)e\left(\frac{1}{16}\right) e(164)e\left(\frac{1}{64}\right) e(2764)e\left(\frac{27}{64}\right)
χ256(181,)\chi_{256}(181,\cdot) 11 11 e(1564)e\left(\frac{15}{64}\right) e(3764)e\left(\frac{37}{64}\right) e(2532)e\left(\frac{25}{32}\right) e(1532)e\left(\frac{15}{32}\right) e(964)e\left(\frac{9}{64}\right) e(1164)e\left(\frac{11}{64}\right) e(1316)e\left(\frac{13}{16}\right) e(316)e\left(\frac{3}{16}\right) e(1964)e\left(\frac{19}{64}\right) e(164)e\left(\frac{1}{64}\right)
χ256(189,)\chi_{256}(189,\cdot) 11 11 e(5764)e\left(\frac{57}{64}\right) e(5164)e\left(\frac{51}{64}\right) e(3132)e\left(\frac{31}{32}\right) e(2532)e\left(\frac{25}{32}\right) e(4764)e\left(\frac{47}{64}\right) e(2964)e\left(\frac{29}{64}\right) e(1116)e\left(\frac{11}{16}\right) e(516)e\left(\frac{5}{16}\right) e(2164)e\left(\frac{21}{64}\right) e(5564)e\left(\frac{55}{64}\right)
χ256(197,)\chi_{256}(197,\cdot) 11 11 e(1964)e\left(\frac{19}{64}\right) e(1764)e\left(\frac{17}{64}\right) e(2132)e\left(\frac{21}{32}\right) e(1932)e\left(\frac{19}{32}\right) e(3764)e\left(\frac{37}{64}\right) e(3164)e\left(\frac{31}{64}\right) e(916)e\left(\frac{9}{16}\right) e(716)e\left(\frac{7}{16}\right) e(764)e\left(\frac{7}{64}\right) e(6164)e\left(\frac{61}{64}\right)
χ256(205,)\chi_{256}(205,\cdot) 11 11 e(2964)e\left(\frac{29}{64}\right) e(6364)e\left(\frac{63}{64}\right) e(2732)e\left(\frac{27}{32}\right) e(2932)e\left(\frac{29}{32}\right) e(4364)e\left(\frac{43}{64}\right) e(1764)e\left(\frac{17}{64}\right) e(716)e\left(\frac{7}{16}\right) e(916)e\left(\frac{9}{16}\right) e(4164)e\left(\frac{41}{64}\right) e(1964)e\left(\frac{19}{64}\right)
χ256(213,)\chi_{256}(213,\cdot) 11 11 e(2364)e\left(\frac{23}{64}\right) e(6164)e\left(\frac{61}{64}\right) e(1732)e\left(\frac{17}{32}\right) e(2332)e\left(\frac{23}{32}\right) e(164)e\left(\frac{1}{64}\right) e(5164)e\left(\frac{51}{64}\right) e(516)e\left(\frac{5}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(5964)e\left(\frac{59}{64}\right) e(5764)e\left(\frac{57}{64}\right)
χ256(221,)\chi_{256}(221,\cdot) 11 11 e(164)e\left(\frac{1}{64}\right) e(1164)e\left(\frac{11}{64}\right) e(2332)e\left(\frac{23}{32}\right) e(132)e\left(\frac{1}{32}\right) e(3964)e\left(\frac{39}{64}\right) e(564)e\left(\frac{5}{64}\right) e(316)e\left(\frac{3}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(6164)e\left(\frac{61}{64}\right) e(4764)e\left(\frac{47}{64}\right)
χ256(229,)\chi_{256}(229,\cdot) 11 11 e(2764)e\left(\frac{27}{64}\right) e(4164)e\left(\frac{41}{64}\right) e(1332)e\left(\frac{13}{32}\right) e(2732)e\left(\frac{27}{32}\right) e(2964)e\left(\frac{29}{64}\right) e(764)e\left(\frac{7}{64}\right) e(116)e\left(\frac{1}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(4764)e\left(\frac{47}{64}\right) e(5364)e\left(\frac{53}{64}\right)
χ256(237,)\chi_{256}(237,\cdot) 11 11 e(3764)e\left(\frac{37}{64}\right) e(2364)e\left(\frac{23}{64}\right) e(1932)e\left(\frac{19}{32}\right) e(532)e\left(\frac{5}{32}\right) e(3564)e\left(\frac{35}{64}\right) e(5764)e\left(\frac{57}{64}\right) e(1516)e\left(\frac{15}{16}\right) e(116)e\left(\frac{1}{16}\right) e(1764)e\left(\frac{17}{64}\right) e(1164)e\left(\frac{11}{64}\right)
χ256(245,)\chi_{256}(245,\cdot) 11 11 e(3164)e\left(\frac{31}{64}\right) e(2164)e\left(\frac{21}{64}\right) e(932)e\left(\frac{9}{32}\right) e(3132)e\left(\frac{31}{32}\right) e(5764)e\left(\frac{57}{64}\right) e(2764)e\left(\frac{27}{64}\right) e(1316)e\left(\frac{13}{16}\right) e(316)e\left(\frac{3}{16}\right) e(3564)e\left(\frac{35}{64}\right) e(4964)e\left(\frac{49}{64}\right)