Properties

Label 4205.bd
Modulus 42054205
Conductor 42054205
Order 116116
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4205, base_ring=CyclotomicField(116))
 
M = H._module
 
chi = DirichletCharacter(H, M([29,77]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(12,4205))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 42054205
Conductor: 42054205
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 116116
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(ζ116)\Q(\zeta_{116})
Fixed field: Number field defined by a degree 116 polynomial (not computed)

First 31 of 56 characters in Galois orbit

Character 1-1 11 22 33 44 66 77 88 99 1111 1212 1313
χ4205(12,)\chi_{4205}(12,\cdot) 11 11 e(5358)e\left(\frac{53}{58}\right) e(629)e\left(\frac{6}{29}\right) e(2429)e\left(\frac{24}{29}\right) e(758)e\left(\frac{7}{58}\right) e(97116)e\left(\frac{97}{116}\right) e(4358)e\left(\frac{43}{58}\right) e(1229)e\left(\frac{12}{29}\right) e(89116)e\left(\frac{89}{116}\right) e(129)e\left(\frac{1}{29}\right) e(21116)e\left(\frac{21}{116}\right)
χ4205(133,)\chi_{4205}(133,\cdot) 11 11 e(5758)e\left(\frac{57}{58}\right) e(729)e\left(\frac{7}{29}\right) e(2829)e\left(\frac{28}{29}\right) e(1358)e\left(\frac{13}{58}\right) e(31116)e\left(\frac{31}{116}\right) e(5558)e\left(\frac{55}{58}\right) e(1429)e\left(\frac{14}{29}\right) e(99116)e\left(\frac{99}{116}\right) e(629)e\left(\frac{6}{29}\right) e(39116)e\left(\frac{39}{116}\right)
χ4205(157,)\chi_{4205}(157,\cdot) 11 11 e(4958)e\left(\frac{49}{58}\right) e(529)e\left(\frac{5}{29}\right) e(2029)e\left(\frac{20}{29}\right) e(158)e\left(\frac{1}{58}\right) e(105116)e\left(\frac{105}{116}\right) e(3158)e\left(\frac{31}{58}\right) e(1029)e\left(\frac{10}{29}\right) e(21116)e\left(\frac{21}{116}\right) e(2529)e\left(\frac{25}{29}\right) e(61116)e\left(\frac{61}{116}\right)
χ4205(278,)\chi_{4205}(278,\cdot) 11 11 e(358)e\left(\frac{3}{58}\right) e(829)e\left(\frac{8}{29}\right) e(329)e\left(\frac{3}{29}\right) e(1958)e\left(\frac{19}{58}\right) e(23116)e\left(\frac{23}{116}\right) e(958)e\left(\frac{9}{58}\right) e(1629)e\left(\frac{16}{29}\right) e(51116)e\left(\frac{51}{116}\right) e(1129)e\left(\frac{11}{29}\right) e(115116)e\left(\frac{115}{116}\right)
χ4205(302,)\chi_{4205}(302,\cdot) 11 11 e(4558)e\left(\frac{45}{58}\right) e(429)e\left(\frac{4}{29}\right) e(1629)e\left(\frac{16}{29}\right) e(5358)e\left(\frac{53}{58}\right) e(113116)e\left(\frac{113}{116}\right) e(1958)e\left(\frac{19}{58}\right) e(829)e\left(\frac{8}{29}\right) e(69116)e\left(\frac{69}{116}\right) e(2029)e\left(\frac{20}{29}\right) e(101116)e\left(\frac{101}{116}\right)
χ4205(423,)\chi_{4205}(423,\cdot) 11 11 e(758)e\left(\frac{7}{58}\right) e(929)e\left(\frac{9}{29}\right) e(729)e\left(\frac{7}{29}\right) e(2558)e\left(\frac{25}{58}\right) e(15116)e\left(\frac{15}{116}\right) e(2158)e\left(\frac{21}{58}\right) e(1829)e\left(\frac{18}{29}\right) e(3116)e\left(\frac{3}{116}\right) e(1629)e\left(\frac{16}{29}\right) e(75116)e\left(\frac{75}{116}\right)
χ4205(447,)\chi_{4205}(447,\cdot) 11 11 e(4158)e\left(\frac{41}{58}\right) e(329)e\left(\frac{3}{29}\right) e(1229)e\left(\frac{12}{29}\right) e(4758)e\left(\frac{47}{58}\right) e(5116)e\left(\frac{5}{116}\right) e(758)e\left(\frac{7}{58}\right) e(629)e\left(\frac{6}{29}\right) e(1116)e\left(\frac{1}{116}\right) e(1529)e\left(\frac{15}{29}\right) e(25116)e\left(\frac{25}{116}\right)
χ4205(568,)\chi_{4205}(568,\cdot) 11 11 e(1158)e\left(\frac{11}{58}\right) e(1029)e\left(\frac{10}{29}\right) e(1129)e\left(\frac{11}{29}\right) e(3158)e\left(\frac{31}{58}\right) e(7116)e\left(\frac{7}{116}\right) e(3358)e\left(\frac{33}{58}\right) e(2029)e\left(\frac{20}{29}\right) e(71116)e\left(\frac{71}{116}\right) e(2129)e\left(\frac{21}{29}\right) e(35116)e\left(\frac{35}{116}\right)
χ4205(592,)\chi_{4205}(592,\cdot) 11 11 e(3758)e\left(\frac{37}{58}\right) e(229)e\left(\frac{2}{29}\right) e(829)e\left(\frac{8}{29}\right) e(4158)e\left(\frac{41}{58}\right) e(13116)e\left(\frac{13}{116}\right) e(5358)e\left(\frac{53}{58}\right) e(429)e\left(\frac{4}{29}\right) e(49116)e\left(\frac{49}{116}\right) e(1029)e\left(\frac{10}{29}\right) e(65116)e\left(\frac{65}{116}\right)
χ4205(713,)\chi_{4205}(713,\cdot) 11 11 e(1558)e\left(\frac{15}{58}\right) e(1129)e\left(\frac{11}{29}\right) e(1529)e\left(\frac{15}{29}\right) e(3758)e\left(\frac{37}{58}\right) e(115116)e\left(\frac{115}{116}\right) e(4558)e\left(\frac{45}{58}\right) e(2229)e\left(\frac{22}{29}\right) e(23116)e\left(\frac{23}{116}\right) e(2629)e\left(\frac{26}{29}\right) e(111116)e\left(\frac{111}{116}\right)
χ4205(737,)\chi_{4205}(737,\cdot) 11 11 e(3358)e\left(\frac{33}{58}\right) e(129)e\left(\frac{1}{29}\right) e(429)e\left(\frac{4}{29}\right) e(3558)e\left(\frac{35}{58}\right) e(21116)e\left(\frac{21}{116}\right) e(4158)e\left(\frac{41}{58}\right) e(229)e\left(\frac{2}{29}\right) e(97116)e\left(\frac{97}{116}\right) e(529)e\left(\frac{5}{29}\right) e(105116)e\left(\frac{105}{116}\right)
χ4205(858,)\chi_{4205}(858,\cdot) 11 11 e(1958)e\left(\frac{19}{58}\right) e(1229)e\left(\frac{12}{29}\right) e(1929)e\left(\frac{19}{29}\right) e(4358)e\left(\frac{43}{58}\right) e(107116)e\left(\frac{107}{116}\right) e(5758)e\left(\frac{57}{58}\right) e(2429)e\left(\frac{24}{29}\right) e(91116)e\left(\frac{91}{116}\right) e(229)e\left(\frac{2}{29}\right) e(71116)e\left(\frac{71}{116}\right)
χ4205(1003,)\chi_{4205}(1003,\cdot) 11 11 e(2358)e\left(\frac{23}{58}\right) e(1329)e\left(\frac{13}{29}\right) e(2329)e\left(\frac{23}{29}\right) e(4958)e\left(\frac{49}{58}\right) e(99116)e\left(\frac{99}{116}\right) e(1158)e\left(\frac{11}{58}\right) e(2629)e\left(\frac{26}{29}\right) e(43116)e\left(\frac{43}{116}\right) e(729)e\left(\frac{7}{29}\right) e(31116)e\left(\frac{31}{116}\right)
χ4205(1027,)\chi_{4205}(1027,\cdot) 11 11 e(2558)e\left(\frac{25}{58}\right) e(2829)e\left(\frac{28}{29}\right) e(2529)e\left(\frac{25}{29}\right) e(2358)e\left(\frac{23}{58}\right) e(37116)e\left(\frac{37}{116}\right) e(1758)e\left(\frac{17}{58}\right) e(2729)e\left(\frac{27}{29}\right) e(77116)e\left(\frac{77}{116}\right) e(2429)e\left(\frac{24}{29}\right) e(69116)e\left(\frac{69}{116}\right)
χ4205(1148,)\chi_{4205}(1148,\cdot) 11 11 e(2758)e\left(\frac{27}{58}\right) e(1429)e\left(\frac{14}{29}\right) e(2729)e\left(\frac{27}{29}\right) e(5558)e\left(\frac{55}{58}\right) e(91116)e\left(\frac{91}{116}\right) e(2358)e\left(\frac{23}{58}\right) e(2829)e\left(\frac{28}{29}\right) e(111116)e\left(\frac{111}{116}\right) e(1229)e\left(\frac{12}{29}\right) e(107116)e\left(\frac{107}{116}\right)
χ4205(1172,)\chi_{4205}(1172,\cdot) 11 11 e(2158)e\left(\frac{21}{58}\right) e(2729)e\left(\frac{27}{29}\right) e(2129)e\left(\frac{21}{29}\right) e(1758)e\left(\frac{17}{58}\right) e(45116)e\left(\frac{45}{116}\right) e(558)e\left(\frac{5}{58}\right) e(2529)e\left(\frac{25}{29}\right) e(9116)e\left(\frac{9}{116}\right) e(1929)e\left(\frac{19}{29}\right) e(109116)e\left(\frac{109}{116}\right)
χ4205(1293,)\chi_{4205}(1293,\cdot) 11 11 e(3158)e\left(\frac{31}{58}\right) e(1529)e\left(\frac{15}{29}\right) e(229)e\left(\frac{2}{29}\right) e(358)e\left(\frac{3}{58}\right) e(83116)e\left(\frac{83}{116}\right) e(3558)e\left(\frac{35}{58}\right) e(129)e\left(\frac{1}{29}\right) e(63116)e\left(\frac{63}{116}\right) e(1729)e\left(\frac{17}{29}\right) e(67116)e\left(\frac{67}{116}\right)
χ4205(1317,)\chi_{4205}(1317,\cdot) 11 11 e(1758)e\left(\frac{17}{58}\right) e(2629)e\left(\frac{26}{29}\right) e(1729)e\left(\frac{17}{29}\right) e(1158)e\left(\frac{11}{58}\right) e(53116)e\left(\frac{53}{116}\right) e(5158)e\left(\frac{51}{58}\right) e(2329)e\left(\frac{23}{29}\right) e(57116)e\left(\frac{57}{116}\right) e(1429)e\left(\frac{14}{29}\right) e(33116)e\left(\frac{33}{116}\right)
χ4205(1438,)\chi_{4205}(1438,\cdot) 11 11 e(3558)e\left(\frac{35}{58}\right) e(1629)e\left(\frac{16}{29}\right) e(629)e\left(\frac{6}{29}\right) e(958)e\left(\frac{9}{58}\right) e(75116)e\left(\frac{75}{116}\right) e(4758)e\left(\frac{47}{58}\right) e(329)e\left(\frac{3}{29}\right) e(15116)e\left(\frac{15}{116}\right) e(2229)e\left(\frac{22}{29}\right) e(27116)e\left(\frac{27}{116}\right)
χ4205(1462,)\chi_{4205}(1462,\cdot) 11 11 e(1358)e\left(\frac{13}{58}\right) e(2529)e\left(\frac{25}{29}\right) e(1329)e\left(\frac{13}{29}\right) e(558)e\left(\frac{5}{58}\right) e(61116)e\left(\frac{61}{116}\right) e(3958)e\left(\frac{39}{58}\right) e(2129)e\left(\frac{21}{29}\right) e(105116)e\left(\frac{105}{116}\right) e(929)e\left(\frac{9}{29}\right) e(73116)e\left(\frac{73}{116}\right)
χ4205(1583,)\chi_{4205}(1583,\cdot) 11 11 e(3958)e\left(\frac{39}{58}\right) e(1729)e\left(\frac{17}{29}\right) e(1029)e\left(\frac{10}{29}\right) e(1558)e\left(\frac{15}{58}\right) e(67116)e\left(\frac{67}{116}\right) e(158)e\left(\frac{1}{58}\right) e(529)e\left(\frac{5}{29}\right) e(83116)e\left(\frac{83}{116}\right) e(2729)e\left(\frac{27}{29}\right) e(103116)e\left(\frac{103}{116}\right)
χ4205(1607,)\chi_{4205}(1607,\cdot) 11 11 e(958)e\left(\frac{9}{58}\right) e(2429)e\left(\frac{24}{29}\right) e(929)e\left(\frac{9}{29}\right) e(5758)e\left(\frac{57}{58}\right) e(69116)e\left(\frac{69}{116}\right) e(2758)e\left(\frac{27}{58}\right) e(1929)e\left(\frac{19}{29}\right) e(37116)e\left(\frac{37}{116}\right) e(429)e\left(\frac{4}{29}\right) e(113116)e\left(\frac{113}{116}\right)
χ4205(1728,)\chi_{4205}(1728,\cdot) 11 11 e(4358)e\left(\frac{43}{58}\right) e(1829)e\left(\frac{18}{29}\right) e(1429)e\left(\frac{14}{29}\right) e(2158)e\left(\frac{21}{58}\right) e(59116)e\left(\frac{59}{116}\right) e(1358)e\left(\frac{13}{58}\right) e(729)e\left(\frac{7}{29}\right) e(35116)e\left(\frac{35}{116}\right) e(329)e\left(\frac{3}{29}\right) e(63116)e\left(\frac{63}{116}\right)
χ4205(1752,)\chi_{4205}(1752,\cdot) 11 11 e(558)e\left(\frac{5}{58}\right) e(2329)e\left(\frac{23}{29}\right) e(529)e\left(\frac{5}{29}\right) e(5158)e\left(\frac{51}{58}\right) e(77116)e\left(\frac{77}{116}\right) e(1558)e\left(\frac{15}{58}\right) e(1729)e\left(\frac{17}{29}\right) e(85116)e\left(\frac{85}{116}\right) e(2829)e\left(\frac{28}{29}\right) e(37116)e\left(\frac{37}{116}\right)
χ4205(1873,)\chi_{4205}(1873,\cdot) 11 11 e(4758)e\left(\frac{47}{58}\right) e(1929)e\left(\frac{19}{29}\right) e(1829)e\left(\frac{18}{29}\right) e(2758)e\left(\frac{27}{58}\right) e(51116)e\left(\frac{51}{116}\right) e(2558)e\left(\frac{25}{58}\right) e(929)e\left(\frac{9}{29}\right) e(103116)e\left(\frac{103}{116}\right) e(829)e\left(\frac{8}{29}\right) e(23116)e\left(\frac{23}{116}\right)
χ4205(1897,)\chi_{4205}(1897,\cdot) 11 11 e(158)e\left(\frac{1}{58}\right) e(2229)e\left(\frac{22}{29}\right) e(129)e\left(\frac{1}{29}\right) e(4558)e\left(\frac{45}{58}\right) e(85116)e\left(\frac{85}{116}\right) e(358)e\left(\frac{3}{58}\right) e(1529)e\left(\frac{15}{29}\right) e(17116)e\left(\frac{17}{116}\right) e(2329)e\left(\frac{23}{29}\right) e(77116)e\left(\frac{77}{116}\right)
χ4205(2018,)\chi_{4205}(2018,\cdot) 11 11 e(5158)e\left(\frac{51}{58}\right) e(2029)e\left(\frac{20}{29}\right) e(2229)e\left(\frac{22}{29}\right) e(3358)e\left(\frac{33}{58}\right) e(43116)e\left(\frac{43}{116}\right) e(3758)e\left(\frac{37}{58}\right) e(1129)e\left(\frac{11}{29}\right) e(55116)e\left(\frac{55}{116}\right) e(1329)e\left(\frac{13}{29}\right) e(99116)e\left(\frac{99}{116}\right)
χ4205(2042,)\chi_{4205}(2042,\cdot) 11 11 e(5558)e\left(\frac{55}{58}\right) e(2129)e\left(\frac{21}{29}\right) e(2629)e\left(\frac{26}{29}\right) e(3958)e\left(\frac{39}{58}\right) e(93116)e\left(\frac{93}{116}\right) e(4958)e\left(\frac{49}{58}\right) e(1329)e\left(\frac{13}{29}\right) e(65116)e\left(\frac{65}{116}\right) e(1829)e\left(\frac{18}{29}\right) e(1116)e\left(\frac{1}{116}\right)
χ4205(2163,)\chi_{4205}(2163,\cdot) 11 11 e(5558)e\left(\frac{55}{58}\right) e(2129)e\left(\frac{21}{29}\right) e(2629)e\left(\frac{26}{29}\right) e(3958)e\left(\frac{39}{58}\right) e(35116)e\left(\frac{35}{116}\right) e(4958)e\left(\frac{49}{58}\right) e(1329)e\left(\frac{13}{29}\right) e(7116)e\left(\frac{7}{116}\right) e(1829)e\left(\frac{18}{29}\right) e(59116)e\left(\frac{59}{116}\right)
χ4205(2187,)\chi_{4205}(2187,\cdot) 11 11 e(5158)e\left(\frac{51}{58}\right) e(2029)e\left(\frac{20}{29}\right) e(2229)e\left(\frac{22}{29}\right) e(3358)e\left(\frac{33}{58}\right) e(101116)e\left(\frac{101}{116}\right) e(3758)e\left(\frac{37}{58}\right) e(1129)e\left(\frac{11}{29}\right) e(113116)e\left(\frac{113}{116}\right) e(1329)e\left(\frac{13}{29}\right) e(41116)e\left(\frac{41}{116}\right)
χ4205(2308,)\chi_{4205}(2308,\cdot) 11 11 e(158)e\left(\frac{1}{58}\right) e(2229)e\left(\frac{22}{29}\right) e(129)e\left(\frac{1}{29}\right) e(4558)e\left(\frac{45}{58}\right) e(27116)e\left(\frac{27}{116}\right) e(358)e\left(\frac{3}{58}\right) e(1529)e\left(\frac{15}{29}\right) e(75116)e\left(\frac{75}{116}\right) e(2329)e\left(\frac{23}{29}\right) e(19116)e\left(\frac{19}{116}\right)