Properties

Label 4334.bd
Modulus 43344334
Conductor 197197
Order 196196
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, base_ring=CyclotomicField(196))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,59]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(45,4334))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 43344334
Conductor: 197197
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 196196
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 197.i
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(ζ196)\Q(\zeta_{196})
Fixed field: Number field defined by a degree 196 polynomial (not computed)

First 31 of 84 characters in Galois orbit

Character 1-1 11 33 55 77 99 1313 1515 1717 1919 2121 2323
χ4334(45,)\chi_{4334}(45,\cdot) 1-1 11 e(95196)e\left(\frac{95}{196}\right) e(155196)e\left(\frac{155}{196}\right) e(9398)e\left(\frac{93}{98}\right) e(9598)e\left(\frac{95}{98}\right) e(103196)e\left(\frac{103}{196}\right) e(2798)e\left(\frac{27}{98}\right) e(169196)e\left(\frac{169}{196}\right) e(514)e\left(\frac{5}{14}\right) e(85196)e\left(\frac{85}{196}\right) e(649)e\left(\frac{6}{49}\right)
χ4334(67,)\chi_{4334}(67,\cdot) 1-1 11 e(137196)e\left(\frac{137}{196}\right) e(141196)e\left(\frac{141}{196}\right) e(6598)e\left(\frac{65}{98}\right) e(3998)e\left(\frac{39}{98}\right) e(33196)e\left(\frac{33}{196}\right) e(4198)e\left(\frac{41}{98}\right) e(155196)e\left(\frac{155}{196}\right) e(514)e\left(\frac{5}{14}\right) e(71196)e\left(\frac{71}{196}\right) e(2049)e\left(\frac{20}{49}\right)
χ4334(89,)\chi_{4334}(89,\cdot) 1-1 11 e(155196)e\left(\frac{155}{196}\right) e(191196)e\left(\frac{191}{196}\right) e(9598)e\left(\frac{95}{98}\right) e(5798)e\left(\frac{57}{98}\right) e(3196)e\left(\frac{3}{196}\right) e(7598)e\left(\frac{75}{98}\right) e(121196)e\left(\frac{121}{196}\right) e(314)e\left(\frac{3}{14}\right) e(149196)e\left(\frac{149}{196}\right) e(3349)e\left(\frac{33}{49}\right)
χ4334(111,)\chi_{4334}(111,\cdot) 1-1 11 e(89196)e\left(\frac{89}{196}\right) e(73196)e\left(\frac{73}{196}\right) e(8398)e\left(\frac{83}{98}\right) e(8998)e\left(\frac{89}{98}\right) e(113196)e\left(\frac{113}{196}\right) e(8198)e\left(\frac{81}{98}\right) e(115196)e\left(\frac{115}{196}\right) e(114)e\left(\frac{1}{14}\right) e(59196)e\left(\frac{59}{196}\right) e(1849)e\left(\frac{18}{49}\right)
χ4334(199,)\chi_{4334}(199,\cdot) 1-1 11 e(181196)e\left(\frac{181}{196}\right) e(89196)e\left(\frac{89}{196}\right) e(7398)e\left(\frac{73}{98}\right) e(8398)e\left(\frac{83}{98}\right) e(25196)e\left(\frac{25}{196}\right) e(3798)e\left(\frac{37}{98}\right) e(159196)e\left(\frac{159}{196}\right) e(1114)e\left(\frac{11}{14}\right) e(131196)e\left(\frac{131}{196}\right) e(3049)e\left(\frac{30}{49}\right)
χ4334(243,)\chi_{4334}(243,\cdot) 1-1 11 e(145196)e\left(\frac{145}{196}\right) e(185196)e\left(\frac{185}{196}\right) e(1398)e\left(\frac{13}{98}\right) e(4798)e\left(\frac{47}{98}\right) e(85196)e\left(\frac{85}{196}\right) e(6798)e\left(\frac{67}{98}\right) e(31196)e\left(\frac{31}{196}\right) e(114)e\left(\frac{1}{14}\right) e(171196)e\left(\frac{171}{196}\right) e(449)e\left(\frac{4}{49}\right)
χ4334(397,)\chi_{4334}(397,\cdot) 1-1 11 e(29196)e\left(\frac{29}{196}\right) e(37196)e\left(\frac{37}{196}\right) e(8198)e\left(\frac{81}{98}\right) e(2998)e\left(\frac{29}{98}\right) e(17196)e\left(\frac{17}{196}\right) e(3398)e\left(\frac{33}{98}\right) e(163196)e\left(\frac{163}{196}\right) e(314)e\left(\frac{3}{14}\right) e(191196)e\left(\frac{191}{196}\right) e(4049)e\left(\frac{40}{49}\right)
χ4334(485,)\chi_{4334}(485,\cdot) 1-1 11 e(179196)e\left(\frac{179}{196}\right) e(127196)e\left(\frac{127}{196}\right) e(3798)e\left(\frac{37}{98}\right) e(8198)e\left(\frac{81}{98}\right) e(159196)e\left(\frac{159}{196}\right) e(5598)e\left(\frac{55}{98}\right) e(141196)e\left(\frac{141}{196}\right) e(514)e\left(\frac{5}{14}\right) e(57196)e\left(\frac{57}{196}\right) e(3449)e\left(\frac{34}{49}\right)
χ4334(573,)\chi_{4334}(573,\cdot) 1-1 11 e(141196)e\left(\frac{141}{196}\right) e(65196)e\left(\frac{65}{196}\right) e(3998)e\left(\frac{39}{98}\right) e(4398)e\left(\frac{43}{98}\right) e(157196)e\left(\frac{157}{196}\right) e(598)e\left(\frac{5}{98}\right) e(191196)e\left(\frac{191}{196}\right) e(314)e\left(\frac{3}{14}\right) e(23196)e\left(\frac{23}{196}\right) e(1249)e\left(\frac{12}{49}\right)
χ4334(639,)\chi_{4334}(639,\cdot) 1-1 11 e(165196)e\left(\frac{165}{196}\right) e(1196)e\left(\frac{1}{196}\right) e(7998)e\left(\frac{79}{98}\right) e(6798)e\left(\frac{67}{98}\right) e(117196)e\left(\frac{117}{196}\right) e(8398)e\left(\frac{83}{98}\right) e(15196)e\left(\frac{15}{196}\right) e(514)e\left(\frac{5}{14}\right) e(127196)e\left(\frac{127}{196}\right) e(1349)e\left(\frac{13}{49}\right)
χ4334(771,)\chi_{4334}(771,\cdot) 1-1 11 e(65196)e\left(\frac{65}{196}\right) e(137196)e\left(\frac{137}{196}\right) e(4398)e\left(\frac{43}{98}\right) e(6598)e\left(\frac{65}{98}\right) e(153196)e\left(\frac{153}{196}\right) e(398)e\left(\frac{3}{98}\right) e(95196)e\left(\frac{95}{196}\right) e(1314)e\left(\frac{13}{14}\right) e(151196)e\left(\frac{151}{196}\right) e(1749)e\left(\frac{17}{49}\right)
χ4334(793,)\chi_{4334}(793,\cdot) 1-1 11 e(37196)e\left(\frac{37}{196}\right) e(81196)e\left(\frac{81}{196}\right) e(2998)e\left(\frac{29}{98}\right) e(3798)e\left(\frac{37}{98}\right) e(69196)e\left(\frac{69}{196}\right) e(5998)e\left(\frac{59}{98}\right) e(39196)e\left(\frac{39}{196}\right) e(1314)e\left(\frac{13}{14}\right) e(95196)e\left(\frac{95}{196}\right) e(2449)e\left(\frac{24}{49}\right)
χ4334(815,)\chi_{4334}(815,\cdot) 1-1 11 e(87196)e\left(\frac{87}{196}\right) e(111196)e\left(\frac{111}{196}\right) e(4798)e\left(\frac{47}{98}\right) e(8798)e\left(\frac{87}{98}\right) e(51196)e\left(\frac{51}{196}\right) e(198)e\left(\frac{1}{98}\right) e(97196)e\left(\frac{97}{196}\right) e(914)e\left(\frac{9}{14}\right) e(181196)e\left(\frac{181}{196}\right) e(2249)e\left(\frac{22}{49}\right)
χ4334(859,)\chi_{4334}(859,\cdot) 1-1 11 e(107196)e\left(\frac{107}{196}\right) e(123196)e\left(\frac{123}{196}\right) e(1598)e\left(\frac{15}{98}\right) e(998)e\left(\frac{9}{98}\right) e(83196)e\left(\frac{83}{196}\right) e(1798)e\left(\frac{17}{98}\right) e(81196)e\left(\frac{81}{196}\right) e(1314)e\left(\frac{13}{14}\right) e(137196)e\left(\frac{137}{196}\right) e(3149)e\left(\frac{31}{49}\right)
χ4334(903,)\chi_{4334}(903,\cdot) 1-1 11 e(1196)e\left(\frac{1}{196}\right) e(177196)e\left(\frac{177}{196}\right) e(6798)e\left(\frac{67}{98}\right) e(198)e\left(\frac{1}{98}\right) e(129196)e\left(\frac{129}{196}\right) e(8998)e\left(\frac{89}{98}\right) e(107196)e\left(\frac{107}{196}\right) e(314)e\left(\frac{3}{14}\right) e(135196)e\left(\frac{135}{196}\right) e(4749)e\left(\frac{47}{49}\right)
χ4334(947,)\chi_{4334}(947,\cdot) 1-1 11 e(125196)e\left(\frac{125}{196}\right) e(173196)e\left(\frac{173}{196}\right) e(4598)e\left(\frac{45}{98}\right) e(2798)e\left(\frac{27}{98}\right) e(53196)e\left(\frac{53}{196}\right) e(5198)e\left(\frac{51}{98}\right) e(47196)e\left(\frac{47}{196}\right) e(1114)e\left(\frac{11}{14}\right) e(19196)e\left(\frac{19}{196}\right) e(4449)e\left(\frac{44}{49}\right)
χ4334(1035,)\chi_{4334}(1035,\cdot) 1-1 11 e(59196)e\left(\frac{59}{196}\right) e(55196)e\left(\frac{55}{196}\right) e(3398)e\left(\frac{33}{98}\right) e(5998)e\left(\frac{59}{98}\right) e(163196)e\left(\frac{163}{196}\right) e(5798)e\left(\frac{57}{98}\right) e(41196)e\left(\frac{41}{196}\right) e(914)e\left(\frac{9}{14}\right) e(125196)e\left(\frac{125}{196}\right) e(2949)e\left(\frac{29}{49}\right)
χ4334(1057,)\chi_{4334}(1057,\cdot) 1-1 11 e(13196)e\left(\frac{13}{196}\right) e(145196)e\left(\frac{145}{196}\right) e(8798)e\left(\frac{87}{98}\right) e(1398)e\left(\frac{13}{98}\right) e(109196)e\left(\frac{109}{196}\right) e(7998)e\left(\frac{79}{98}\right) e(19196)e\left(\frac{19}{196}\right) e(1114)e\left(\frac{11}{14}\right) e(187196)e\left(\frac{187}{196}\right) e(2349)e\left(\frac{23}{49}\right)
χ4334(1079,)\chi_{4334}(1079,\cdot) 1-1 11 e(171196)e\left(\frac{171}{196}\right) e(83196)e\left(\frac{83}{196}\right) e(8998)e\left(\frac{89}{98}\right) e(7398)e\left(\frac{73}{98}\right) e(107196)e\left(\frac{107}{196}\right) e(2998)e\left(\frac{29}{98}\right) e(69196)e\left(\frac{69}{196}\right) e(914)e\left(\frac{9}{14}\right) e(153196)e\left(\frac{153}{196}\right) e(149)e\left(\frac{1}{49}\right)
χ4334(1255,)\chi_{4334}(1255,\cdot) 1-1 11 e(109196)e\left(\frac{109}{196}\right) e(85196)e\left(\frac{85}{196}\right) e(5198)e\left(\frac{51}{98}\right) e(1198)e\left(\frac{11}{98}\right) e(145196)e\left(\frac{145}{196}\right) e(9798)e\left(\frac{97}{98}\right) e(99196)e\left(\frac{99}{196}\right) e(514)e\left(\frac{5}{14}\right) e(15196)e\left(\frac{15}{196}\right) e(2749)e\left(\frac{27}{49}\right)
χ4334(1277,)\chi_{4334}(1277,\cdot) 1-1 11 e(79196)e\left(\frac{79}{196}\right) e(67196)e\left(\frac{67}{196}\right) e(198)e\left(\frac{1}{98}\right) e(7998)e\left(\frac{79}{98}\right) e(195196)e\left(\frac{195}{196}\right) e(7398)e\left(\frac{73}{98}\right) e(25196)e\left(\frac{25}{196}\right) e(1314)e\left(\frac{13}{14}\right) e(81196)e\left(\frac{81}{196}\right) e(3849)e\left(\frac{38}{49}\right)
χ4334(1299,)\chi_{4334}(1299,\cdot) 1-1 11 e(75196)e\left(\frac{75}{196}\right) e(143196)e\left(\frac{143}{196}\right) e(2798)e\left(\frac{27}{98}\right) e(7598)e\left(\frac{75}{98}\right) e(71196)e\left(\frac{71}{196}\right) e(1198)e\left(\frac{11}{98}\right) e(185196)e\left(\frac{185}{196}\right) e(114)e\left(\frac{1}{14}\right) e(129196)e\left(\frac{129}{196}\right) e(4649)e\left(\frac{46}{49}\right)
χ4334(1321,)\chi_{4334}(1321,\cdot) 1-1 11 e(131196)e\left(\frac{131}{196}\right) e(59196)e\left(\frac{59}{196}\right) e(5598)e\left(\frac{55}{98}\right) e(3398)e\left(\frac{33}{98}\right) e(43196)e\left(\frac{43}{196}\right) e(9598)e\left(\frac{95}{98}\right) e(101196)e\left(\frac{101}{196}\right) e(114)e\left(\frac{1}{14}\right) e(45196)e\left(\frac{45}{196}\right) e(3249)e\left(\frac{32}{49}\right)
χ4334(1387,)\chi_{4334}(1387,\cdot) 1-1 11 e(151196)e\left(\frac{151}{196}\right) e(71196)e\left(\frac{71}{196}\right) e(2398)e\left(\frac{23}{98}\right) e(5398)e\left(\frac{53}{98}\right) e(75196)e\left(\frac{75}{196}\right) e(1398)e\left(\frac{13}{98}\right) e(85196)e\left(\frac{85}{196}\right) e(514)e\left(\frac{5}{14}\right) e(1196)e\left(\frac{1}{196}\right) e(4149)e\left(\frac{41}{49}\right)
χ4334(1409,)\chi_{4334}(1409,\cdot) 1-1 11 e(51196)e\left(\frac{51}{196}\right) e(11196)e\left(\frac{11}{196}\right) e(8598)e\left(\frac{85}{98}\right) e(5198)e\left(\frac{51}{98}\right) e(111196)e\left(\frac{111}{196}\right) e(3198)e\left(\frac{31}{98}\right) e(165196)e\left(\frac{165}{196}\right) e(1314)e\left(\frac{13}{14}\right) e(25196)e\left(\frac{25}{196}\right) e(4549)e\left(\frac{45}{49}\right)
χ4334(1431,)\chi_{4334}(1431,\cdot) 1-1 11 e(183196)e\left(\frac{183}{196}\right) e(51196)e\left(\frac{51}{196}\right) e(1198)e\left(\frac{11}{98}\right) e(8598)e\left(\frac{85}{98}\right) e(87196)e\left(\frac{87}{196}\right) e(1998)e\left(\frac{19}{98}\right) e(177196)e\left(\frac{177}{196}\right) e(314)e\left(\frac{3}{14}\right) e(9196)e\left(\frac{9}{196}\right) e(2649)e\left(\frac{26}{49}\right)
χ4334(1453,)\chi_{4334}(1453,\cdot) 1-1 11 e(45196)e\left(\frac{45}{196}\right) e(125196)e\left(\frac{125}{196}\right) e(7598)e\left(\frac{75}{98}\right) e(4598)e\left(\frac{45}{98}\right) e(121196)e\left(\frac{121}{196}\right) e(8598)e\left(\frac{85}{98}\right) e(111196)e\left(\frac{111}{196}\right) e(914)e\left(\frac{9}{14}\right) e(195196)e\left(\frac{195}{196}\right) e(849)e\left(\frac{8}{49}\right)
χ4334(1497,)\chi_{4334}(1497,\cdot) 1-1 11 e(61196)e\left(\frac{61}{196}\right) e(17196)e\left(\frac{17}{196}\right) e(6998)e\left(\frac{69}{98}\right) e(6198)e\left(\frac{61}{98}\right) e(29196)e\left(\frac{29}{196}\right) e(3998)e\left(\frac{39}{98}\right) e(59196)e\left(\frac{59}{196}\right) e(114)e\left(\frac{1}{14}\right) e(3196)e\left(\frac{3}{196}\right) e(2549)e\left(\frac{25}{49}\right)
χ4334(1519,)\chi_{4334}(1519,\cdot) 1-1 11 e(169196)e\left(\frac{169}{196}\right) e(121196)e\left(\frac{121}{196}\right) e(5398)e\left(\frac{53}{98}\right) e(7198)e\left(\frac{71}{98}\right) e(45196)e\left(\frac{45}{196}\right) e(4798)e\left(\frac{47}{98}\right) e(51196)e\left(\frac{51}{196}\right) e(314)e\left(\frac{3}{14}\right) e(79196)e\left(\frac{79}{196}\right) e(549)e\left(\frac{5}{49}\right)
χ4334(1541,)\chi_{4334}(1541,\cdot) 1-1 11 e(101196)e\left(\frac{101}{196}\right) e(41196)e\left(\frac{41}{196}\right) e(598)e\left(\frac{5}{98}\right) e(398)e\left(\frac{3}{98}\right) e(93196)e\left(\frac{93}{196}\right) e(7198)e\left(\frac{71}{98}\right) e(27196)e\left(\frac{27}{196}\right) e(914)e\left(\frac{9}{14}\right) e(111196)e\left(\frac{111}{196}\right) e(4349)e\left(\frac{43}{49}\right)
χ4334(1563,)\chi_{4334}(1563,\cdot) 1-1 11 e(115196)e\left(\frac{115}{196}\right) e(167196)e\left(\frac{167}{196}\right) e(6198)e\left(\frac{61}{98}\right) e(1798)e\left(\frac{17}{98}\right) e(135196)e\left(\frac{135}{196}\right) e(4398)e\left(\frac{43}{98}\right) e(153196)e\left(\frac{153}{196}\right) e(914)e\left(\frac{9}{14}\right) e(41196)e\left(\frac{41}{196}\right) e(1549)e\left(\frac{15}{49}\right)