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Properties

Label 3328.dc
Modulus 33283328
Conductor 33283328
Order 6464
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3328, base_ring=CyclotomicField(64)) M = H._module chi = DirichletCharacter(H, M([32,39,48])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(83,3328)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 33283328
Conductor: 33283328
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 6464
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content 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 1515 1717 1919 2121 2323
χ3328(83,⋅)\chi_{3328}(83,\cdot) 11 11 e(5364)e\left(\frac{53}{64}\right) e(2364)e\left(\frac{23}{64}\right) e(2732)e\left(\frac{27}{32}\right) e(2132)e\left(\frac{21}{32}\right) e(3564)e\left(\frac{35}{64}\right) e(316)e\left(\frac{3}{16}\right) e(916)e\left(\frac{9}{16}\right) e(1764)e\left(\frac{17}{64}\right) e(4364)e\left(\frac{43}{64}\right) e(1732)e\left(\frac{17}{32}\right)
χ3328(203,⋅)\chi_{3328}(203,\cdot) 11 11 e(1564)e\left(\frac{15}{64}\right) e(2164)e\left(\frac{21}{64}\right) e(132)e\left(\frac{1}{32}\right) e(1532)e\left(\frac{15}{32}\right) e(5764)e\left(\frac{57}{64}\right) e(916)e\left(\frac{9}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(3564)e\left(\frac{35}{64}\right) e(1764)e\left(\frac{17}{64}\right) e(332)e\left(\frac{3}{32}\right)
χ3328(291,⋅)\chi_{3328}(291,\cdot) 11 11 e(3364)e\left(\frac{33}{64}\right) e(5964)e\left(\frac{59}{64}\right) e(1532)e\left(\frac{15}{32}\right) e(132)e\left(\frac{1}{32}\right) e(2364)e\left(\frac{23}{64}\right) e(716)e\left(\frac{7}{16}\right) e(516)e\left(\frac{5}{16}\right) e(1364)e\left(\frac{13}{64}\right) e(6364)e\left(\frac{63}{64}\right) e(1332)e\left(\frac{13}{32}\right)
χ3328(411,⋅)\chi_{3328}(411,\cdot) 11 11 e(2764)e\left(\frac{27}{64}\right) e(2564)e\left(\frac{25}{64}\right) e(2132)e\left(\frac{21}{32}\right) e(2732)e\left(\frac{27}{32}\right) e(1364)e\left(\frac{13}{64}\right) e(1316)e\left(\frac{13}{16}\right) e(716)e\left(\frac{7}{16}\right) e(6364)e\left(\frac{63}{64}\right) e(564)e\left(\frac{5}{64}\right) e(3132)e\left(\frac{31}{32}\right)
χ3328(499,⋅)\chi_{3328}(499,\cdot) 11 11 e(1364)e\left(\frac{13}{64}\right) e(3164)e\left(\frac{31}{64}\right) e(332)e\left(\frac{3}{32}\right) e(1332)e\left(\frac{13}{32}\right) e(1164)e\left(\frac{11}{64}\right) e(1116)e\left(\frac{11}{16}\right) e(116)e\left(\frac{1}{16}\right) e(964)e\left(\frac{9}{64}\right) e(1964)e\left(\frac{19}{64}\right) e(932)e\left(\frac{9}{32}\right)
χ3328(619,⋅)\chi_{3328}(619,\cdot) 11 11 e(3964)e\left(\frac{39}{64}\right) e(2964)e\left(\frac{29}{64}\right) e(932)e\left(\frac{9}{32}\right) e(732)e\left(\frac{7}{32}\right) e(3364)e\left(\frac{33}{64}\right) e(116)e\left(\frac{1}{16}\right) e(316)e\left(\frac{3}{16}\right) e(2764)e\left(\frac{27}{64}\right) e(5764)e\left(\frac{57}{64}\right) e(2732)e\left(\frac{27}{32}\right)
χ3328(707,⋅)\chi_{3328}(707,\cdot) 11 11 e(5764)e\left(\frac{57}{64}\right) e(364)e\left(\frac{3}{64}\right) e(2332)e\left(\frac{23}{32}\right) e(2532)e\left(\frac{25}{32}\right) e(6364)e\left(\frac{63}{64}\right) e(1516)e\left(\frac{15}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(564)e\left(\frac{5}{64}\right) e(3964)e\left(\frac{39}{64}\right) e(532)e\left(\frac{5}{32}\right)
χ3328(827,⋅)\chi_{3328}(827,\cdot) 11 11 e(5164)e\left(\frac{51}{64}\right) e(3364)e\left(\frac{33}{64}\right) e(2932)e\left(\frac{29}{32}\right) e(1932)e\left(\frac{19}{32}\right) e(5364)e\left(\frac{53}{64}\right) e(516)e\left(\frac{5}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(5564)e\left(\frac{55}{64}\right) e(4564)e\left(\frac{45}{64}\right) e(2332)e\left(\frac{23}{32}\right)
χ3328(915,⋅)\chi_{3328}(915,\cdot) 11 11 e(3764)e\left(\frac{37}{64}\right) e(3964)e\left(\frac{39}{64}\right) e(1132)e\left(\frac{11}{32}\right) e(532)e\left(\frac{5}{32}\right) e(5164)e\left(\frac{51}{64}\right) e(316)e\left(\frac{3}{16}\right) e(916)e\left(\frac{9}{16}\right) e(164)e\left(\frac{1}{64}\right) e(5964)e\left(\frac{59}{64}\right) e(132)e\left(\frac{1}{32}\right)
χ3328(1035,⋅)\chi_{3328}(1035,\cdot) 11 11 e(6364)e\left(\frac{63}{64}\right) e(3764)e\left(\frac{37}{64}\right) e(1732)e\left(\frac{17}{32}\right) e(3132)e\left(\frac{31}{32}\right) e(964)e\left(\frac{9}{64}\right) e(916)e\left(\frac{9}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(1964)e\left(\frac{19}{64}\right) e(3364)e\left(\frac{33}{64}\right) e(1932)e\left(\frac{19}{32}\right)
χ3328(1123,⋅)\chi_{3328}(1123,\cdot) 11 11 e(1764)e\left(\frac{17}{64}\right) e(1164)e\left(\frac{11}{64}\right) e(3132)e\left(\frac{31}{32}\right) e(1732)e\left(\frac{17}{32}\right) e(3964)e\left(\frac{39}{64}\right) e(716)e\left(\frac{7}{16}\right) e(516)e\left(\frac{5}{16}\right) e(6164)e\left(\frac{61}{64}\right) e(1564)e\left(\frac{15}{64}\right) e(2932)e\left(\frac{29}{32}\right)
χ3328(1243,⋅)\chi_{3328}(1243,\cdot) 11 11 e(1164)e\left(\frac{11}{64}\right) e(4164)e\left(\frac{41}{64}\right) e(532)e\left(\frac{5}{32}\right) e(1132)e\left(\frac{11}{32}\right) e(2964)e\left(\frac{29}{64}\right) e(1316)e\left(\frac{13}{16}\right) e(716)e\left(\frac{7}{16}\right) e(4764)e\left(\frac{47}{64}\right) e(2164)e\left(\frac{21}{64}\right) e(1532)e\left(\frac{15}{32}\right)
χ3328(1331,⋅)\chi_{3328}(1331,\cdot) 11 11 e(6164)e\left(\frac{61}{64}\right) e(4764)e\left(\frac{47}{64}\right) e(1932)e\left(\frac{19}{32}\right) e(2932)e\left(\frac{29}{32}\right) e(2764)e\left(\frac{27}{64}\right) e(1116)e\left(\frac{11}{16}\right) e(116)e\left(\frac{1}{16}\right) e(5764)e\left(\frac{57}{64}\right) e(3564)e\left(\frac{35}{64}\right) e(2532)e\left(\frac{25}{32}\right)
χ3328(1451,⋅)\chi_{3328}(1451,\cdot) 11 11 e(2364)e\left(\frac{23}{64}\right) e(4564)e\left(\frac{45}{64}\right) e(2532)e\left(\frac{25}{32}\right) e(2332)e\left(\frac{23}{32}\right) e(4964)e\left(\frac{49}{64}\right) e(116)e\left(\frac{1}{16}\right) e(316)e\left(\frac{3}{16}\right) e(1164)e\left(\frac{11}{64}\right) e(964)e\left(\frac{9}{64}\right) e(1132)e\left(\frac{11}{32}\right)
χ3328(1539,⋅)\chi_{3328}(1539,\cdot) 11 11 e(4164)e\left(\frac{41}{64}\right) e(1964)e\left(\frac{19}{64}\right) e(732)e\left(\frac{7}{32}\right) e(932)e\left(\frac{9}{32}\right) e(1564)e\left(\frac{15}{64}\right) e(1516)e\left(\frac{15}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(5364)e\left(\frac{53}{64}\right) e(5564)e\left(\frac{55}{64}\right) e(2132)e\left(\frac{21}{32}\right)
χ3328(1659,⋅)\chi_{3328}(1659,\cdot) 11 11 e(3564)e\left(\frac{35}{64}\right) e(4964)e\left(\frac{49}{64}\right) e(1332)e\left(\frac{13}{32}\right) e(332)e\left(\frac{3}{32}\right) e(564)e\left(\frac{5}{64}\right) e(516)e\left(\frac{5}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(3964)e\left(\frac{39}{64}\right) e(6164)e\left(\frac{61}{64}\right) e(732)e\left(\frac{7}{32}\right)
χ3328(1747,⋅)\chi_{3328}(1747,\cdot) 11 11 e(2164)e\left(\frac{21}{64}\right) e(5564)e\left(\frac{55}{64}\right) e(2732)e\left(\frac{27}{32}\right) e(2132)e\left(\frac{21}{32}\right) e(364)e\left(\frac{3}{64}\right) e(316)e\left(\frac{3}{16}\right) e(916)e\left(\frac{9}{16}\right) e(4964)e\left(\frac{49}{64}\right) e(1164)e\left(\frac{11}{64}\right) e(1732)e\left(\frac{17}{32}\right)
χ3328(1867,⋅)\chi_{3328}(1867,\cdot) 11 11 e(4764)e\left(\frac{47}{64}\right) e(5364)e\left(\frac{53}{64}\right) e(132)e\left(\frac{1}{32}\right) e(1532)e\left(\frac{15}{32}\right) e(2564)e\left(\frac{25}{64}\right) e(916)e\left(\frac{9}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(364)e\left(\frac{3}{64}\right) e(4964)e\left(\frac{49}{64}\right) e(332)e\left(\frac{3}{32}\right)
χ3328(1955,⋅)\chi_{3328}(1955,\cdot) 11 11 e(164)e\left(\frac{1}{64}\right) e(2764)e\left(\frac{27}{64}\right) e(1532)e\left(\frac{15}{32}\right) e(132)e\left(\frac{1}{32}\right) e(5564)e\left(\frac{55}{64}\right) e(716)e\left(\frac{7}{16}\right) e(516)e\left(\frac{5}{16}\right) e(4564)e\left(\frac{45}{64}\right) e(3164)e\left(\frac{31}{64}\right) e(1332)e\left(\frac{13}{32}\right)
χ3328(2075,⋅)\chi_{3328}(2075,\cdot) 11 11 e(5964)e\left(\frac{59}{64}\right) e(5764)e\left(\frac{57}{64}\right) e(2132)e\left(\frac{21}{32}\right) e(2732)e\left(\frac{27}{32}\right) e(4564)e\left(\frac{45}{64}\right) e(1316)e\left(\frac{13}{16}\right) e(716)e\left(\frac{7}{16}\right) e(3164)e\left(\frac{31}{64}\right) e(3764)e\left(\frac{37}{64}\right) e(3132)e\left(\frac{31}{32}\right)
χ3328(2163,⋅)\chi_{3328}(2163,\cdot) 11 11 e(4564)e\left(\frac{45}{64}\right) e(6364)e\left(\frac{63}{64}\right) e(332)e\left(\frac{3}{32}\right) e(1332)e\left(\frac{13}{32}\right) e(4364)e\left(\frac{43}{64}\right) e(1116)e\left(\frac{11}{16}\right) e(116)e\left(\frac{1}{16}\right) e(4164)e\left(\frac{41}{64}\right) e(5164)e\left(\frac{51}{64}\right) e(932)e\left(\frac{9}{32}\right)
χ3328(2283,⋅)\chi_{3328}(2283,\cdot) 11 11 e(764)e\left(\frac{7}{64}\right) e(6164)e\left(\frac{61}{64}\right) e(932)e\left(\frac{9}{32}\right) e(732)e\left(\frac{7}{32}\right) e(164)e\left(\frac{1}{64}\right) e(116)e\left(\frac{1}{16}\right) e(316)e\left(\frac{3}{16}\right) e(5964)e\left(\frac{59}{64}\right) e(2564)e\left(\frac{25}{64}\right) e(2732)e\left(\frac{27}{32}\right)
χ3328(2371,⋅)\chi_{3328}(2371,\cdot) 11 11 e(2564)e\left(\frac{25}{64}\right) e(3564)e\left(\frac{35}{64}\right) e(2332)e\left(\frac{23}{32}\right) e(2532)e\left(\frac{25}{32}\right) e(3164)e\left(\frac{31}{64}\right) e(1516)e\left(\frac{15}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(3764)e\left(\frac{37}{64}\right) e(764)e\left(\frac{7}{64}\right) e(532)e\left(\frac{5}{32}\right)
χ3328(2491,⋅)\chi_{3328}(2491,\cdot) 11 11 e(1964)e\left(\frac{19}{64}\right) e(164)e\left(\frac{1}{64}\right) e(2932)e\left(\frac{29}{32}\right) e(1932)e\left(\frac{19}{32}\right) e(2164)e\left(\frac{21}{64}\right) e(516)e\left(\frac{5}{16}\right) e(1516)e\left(\frac{15}{16}\right) e(2364)e\left(\frac{23}{64}\right) e(1364)e\left(\frac{13}{64}\right) e(2332)e\left(\frac{23}{32}\right)
χ3328(2579,⋅)\chi_{3328}(2579,\cdot) 11 11 e(564)e\left(\frac{5}{64}\right) e(764)e\left(\frac{7}{64}\right) e(1132)e\left(\frac{11}{32}\right) e(532)e\left(\frac{5}{32}\right) e(1964)e\left(\frac{19}{64}\right) e(316)e\left(\frac{3}{16}\right) e(916)e\left(\frac{9}{16}\right) e(3364)e\left(\frac{33}{64}\right) e(2764)e\left(\frac{27}{64}\right) e(132)e\left(\frac{1}{32}\right)
χ3328(2699,⋅)\chi_{3328}(2699,\cdot) 11 11 e(3164)e\left(\frac{31}{64}\right) e(564)e\left(\frac{5}{64}\right) e(1732)e\left(\frac{17}{32}\right) e(3132)e\left(\frac{31}{32}\right) e(4164)e\left(\frac{41}{64}\right) e(916)e\left(\frac{9}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(5164)e\left(\frac{51}{64}\right) e(164)e\left(\frac{1}{64}\right) e(1932)e\left(\frac{19}{32}\right)
χ3328(2787,⋅)\chi_{3328}(2787,\cdot) 11 11 e(4964)e\left(\frac{49}{64}\right) e(4364)e\left(\frac{43}{64}\right) e(3132)e\left(\frac{31}{32}\right) e(1732)e\left(\frac{17}{32}\right) e(764)e\left(\frac{7}{64}\right) e(716)e\left(\frac{7}{16}\right) e(516)e\left(\frac{5}{16}\right) e(2964)e\left(\frac{29}{64}\right) e(4764)e\left(\frac{47}{64}\right) e(2932)e\left(\frac{29}{32}\right)
χ3328(2907,⋅)\chi_{3328}(2907,\cdot) 11 11 e(4364)e\left(\frac{43}{64}\right) e(964)e\left(\frac{9}{64}\right) e(532)e\left(\frac{5}{32}\right) e(1132)e\left(\frac{11}{32}\right) e(6164)e\left(\frac{61}{64}\right) e(1316)e\left(\frac{13}{16}\right) e(716)e\left(\frac{7}{16}\right) e(1564)e\left(\frac{15}{64}\right) e(5364)e\left(\frac{53}{64}\right) e(1532)e\left(\frac{15}{32}\right)
χ3328(2995,⋅)\chi_{3328}(2995,\cdot) 11 11 e(2964)e\left(\frac{29}{64}\right) e(1564)e\left(\frac{15}{64}\right) e(1932)e\left(\frac{19}{32}\right) e(2932)e\left(\frac{29}{32}\right) e(5964)e\left(\frac{59}{64}\right) e(1116)e\left(\frac{11}{16}\right) e(116)e\left(\frac{1}{16}\right) e(2564)e\left(\frac{25}{64}\right) e(364)e\left(\frac{3}{64}\right) e(2532)e\left(\frac{25}{32}\right)
χ3328(3115,⋅)\chi_{3328}(3115,\cdot) 11 11 e(5564)e\left(\frac{55}{64}\right) e(1364)e\left(\frac{13}{64}\right) e(2532)e\left(\frac{25}{32}\right) e(2332)e\left(\frac{23}{32}\right) e(1764)e\left(\frac{17}{64}\right) e(116)e\left(\frac{1}{16}\right) e(316)e\left(\frac{3}{16}\right) e(4364)e\left(\frac{43}{64}\right) e(4164)e\left(\frac{41}{64}\right) e(1132)e\left(\frac{11}{32}\right)
χ3328(3203,⋅)\chi_{3328}(3203,\cdot) 11 11 e(964)e\left(\frac{9}{64}\right) e(5164)e\left(\frac{51}{64}\right) e(732)e\left(\frac{7}{32}\right) e(932)e\left(\frac{9}{32}\right) e(4764)e\left(\frac{47}{64}\right) e(1516)e\left(\frac{15}{16}\right) e(1316)e\left(\frac{13}{16}\right) e(2164)e\left(\frac{21}{64}\right) e(2364)e\left(\frac{23}{64}\right) e(2132)e\left(\frac{21}{32}\right)