Properties

Label 2001.br
Modulus 20012001
Conductor 20012001
Order 154154
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2001, base_ring=CyclotomicField(154))
 
M = H._module
 
chi = DirichletCharacter(H, M([77,7,121]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(5,2001))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 20012001
Conductor: 20012001
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 154154
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(ζ77)\Q(\zeta_{77})
Fixed field: Number field defined by a degree 154 polynomial (not computed)

First 31 of 60 characters in Galois orbit

Character 1-1 11 22 44 55 77 88 1010 1111 1313 1414 1616
χ2001(5,)\chi_{2001}(5,\cdot) 11 11 e(2977)e\left(\frac{29}{77}\right) e(5877)e\left(\frac{58}{77}\right) e(6477)e\left(\frac{64}{77}\right) e(45154)e\left(\frac{45}{154}\right) e(1077)e\left(\frac{10}{77}\right) e(1677)e\left(\frac{16}{77}\right) e(85154)e\left(\frac{85}{154}\right) e(6077)e\left(\frac{60}{77}\right) e(103154)e\left(\frac{103}{154}\right) e(3977)e\left(\frac{39}{77}\right)
χ2001(38,)\chi_{2001}(38,\cdot) 11 11 e(3177)e\left(\frac{31}{77}\right) e(6277)e\left(\frac{62}{77}\right) e(1077)e\left(\frac{10}{77}\right) e(149154)e\left(\frac{149}{154}\right) e(1677)e\left(\frac{16}{77}\right) e(4177)e\left(\frac{41}{77}\right) e(59154)e\left(\frac{59}{154}\right) e(1977)e\left(\frac{19}{77}\right) e(57154)e\left(\frac{57}{154}\right) e(4777)e\left(\frac{47}{77}\right)
χ2001(80,)\chi_{2001}(80,\cdot) 11 11 e(1977)e\left(\frac{19}{77}\right) e(3877)e\left(\frac{38}{77}\right) e(2677)e\left(\frac{26}{77}\right) e(141154)e\left(\frac{141}{154}\right) e(5777)e\left(\frac{57}{77}\right) e(4577)e\left(\frac{45}{77}\right) e(61154)e\left(\frac{61}{154}\right) e(3477)e\left(\frac{34}{77}\right) e(25154)e\left(\frac{25}{154}\right) e(7677)e\left(\frac{76}{77}\right)
χ2001(122,)\chi_{2001}(122,\cdot) 11 11 e(3477)e\left(\frac{34}{77}\right) e(6877)e\left(\frac{68}{77}\right) e(677)e\left(\frac{6}{77}\right) e(151154)e\left(\frac{151}{154}\right) e(2577)e\left(\frac{25}{77}\right) e(4077)e\left(\frac{40}{77}\right) e(97154)e\left(\frac{97}{154}\right) e(7377)e\left(\frac{73}{77}\right) e(65154)e\left(\frac{65}{154}\right) e(5977)e\left(\frac{59}{77}\right)
χ2001(125,)\chi_{2001}(125,\cdot) 11 11 e(1077)e\left(\frac{10}{77}\right) e(2077)e\left(\frac{20}{77}\right) e(3877)e\left(\frac{38}{77}\right) e(135154)e\left(\frac{135}{154}\right) e(3077)e\left(\frac{30}{77}\right) e(4877)e\left(\frac{48}{77}\right) e(101154)e\left(\frac{101}{154}\right) e(2677)e\left(\frac{26}{77}\right) e(1154)e\left(\frac{1}{154}\right) e(4077)e\left(\frac{40}{77}\right)
χ2001(149,)\chi_{2001}(149,\cdot) 11 11 e(3077)e\left(\frac{30}{77}\right) e(6077)e\left(\frac{60}{77}\right) e(3777)e\left(\frac{37}{77}\right) e(97154)e\left(\frac{97}{154}\right) e(1377)e\left(\frac{13}{77}\right) e(6777)e\left(\frac{67}{77}\right) e(149154)e\left(\frac{149}{154}\right) e(177)e\left(\frac{1}{77}\right) e(3154)e\left(\frac{3}{154}\right) e(4377)e\left(\frac{43}{77}\right)
χ2001(158,)\chi_{2001}(158,\cdot) 11 11 e(4677)e\left(\frac{46}{77}\right) e(1577)e\left(\frac{15}{77}\right) e(6777)e\left(\frac{67}{77}\right) e(5154)e\left(\frac{5}{154}\right) e(6177)e\left(\frac{61}{77}\right) e(3677)e\left(\frac{36}{77}\right) e(95154)e\left(\frac{95}{154}\right) e(5877)e\left(\frac{58}{77}\right) e(97154)e\left(\frac{97}{154}\right) e(3077)e\left(\frac{30}{77}\right)
χ2001(212,)\chi_{2001}(212,\cdot) 11 11 e(7377)e\left(\frac{73}{77}\right) e(6977)e\left(\frac{69}{77}\right) e(3177)e\left(\frac{31}{77}\right) e(23154)e\left(\frac{23}{154}\right) e(6577)e\left(\frac{65}{77}\right) e(2777)e\left(\frac{27}{77}\right) e(129154)e\left(\frac{129}{154}\right) e(577)e\left(\frac{5}{77}\right) e(15154)e\left(\frac{15}{154}\right) e(6177)e\left(\frac{61}{77}\right)
χ2001(245,)\chi_{2001}(245,\cdot) 11 11 e(5377)e\left(\frac{53}{77}\right) e(2977)e\left(\frac{29}{77}\right) e(3277)e\left(\frac{32}{77}\right) e(61154)e\left(\frac{61}{154}\right) e(577)e\left(\frac{5}{77}\right) e(877)e\left(\frac{8}{77}\right) e(81154)e\left(\frac{81}{154}\right) e(3077)e\left(\frac{30}{77}\right) e(13154)e\left(\frac{13}{154}\right) e(5877)e\left(\frac{58}{77}\right)
χ2001(296,)\chi_{2001}(296,\cdot) 11 11 e(1377)e\left(\frac{13}{77}\right) e(2677)e\left(\frac{26}{77}\right) e(3477)e\left(\frac{34}{77}\right) e(137154)e\left(\frac{137}{154}\right) e(3977)e\left(\frac{39}{77}\right) e(4777)e\left(\frac{47}{77}\right) e(139154)e\left(\frac{139}{154}\right) e(377)e\left(\frac{3}{77}\right) e(9154)e\left(\frac{9}{154}\right) e(5277)e\left(\frac{52}{77}\right)
χ2001(332,)\chi_{2001}(332,\cdot) 11 11 e(3277)e\left(\frac{32}{77}\right) e(6477)e\left(\frac{64}{77}\right) e(6077)e\left(\frac{60}{77}\right) e(47154)e\left(\frac{47}{154}\right) e(1977)e\left(\frac{19}{77}\right) e(1577)e\left(\frac{15}{77}\right) e(123154)e\left(\frac{123}{154}\right) e(3777)e\left(\frac{37}{77}\right) e(111154)e\left(\frac{111}{154}\right) e(5177)e\left(\frac{51}{77}\right)
χ2001(341,)\chi_{2001}(341,\cdot) 11 11 e(6177)e\left(\frac{61}{77}\right) e(4577)e\left(\frac{45}{77}\right) e(4777)e\left(\frac{47}{77}\right) e(15154)e\left(\frac{15}{154}\right) e(2977)e\left(\frac{29}{77}\right) e(3177)e\left(\frac{31}{77}\right) e(131154)e\left(\frac{131}{154}\right) e(2077)e\left(\frac{20}{77}\right) e(137154)e\left(\frac{137}{154}\right) e(1377)e\left(\frac{13}{77}\right)
χ2001(383,)\chi_{2001}(383,\cdot) 11 11 e(2077)e\left(\frac{20}{77}\right) e(4077)e\left(\frac{40}{77}\right) e(7677)e\left(\frac{76}{77}\right) e(39154)e\left(\frac{39}{154}\right) e(6077)e\left(\frac{60}{77}\right) e(1977)e\left(\frac{19}{77}\right) e(125154)e\left(\frac{125}{154}\right) e(5277)e\left(\frac{52}{77}\right) e(79154)e\left(\frac{79}{154}\right) e(377)e\left(\frac{3}{77}\right)
χ2001(410,)\chi_{2001}(410,\cdot) 11 11 e(7277)e\left(\frac{72}{77}\right) e(6777)e\left(\frac{67}{77}\right) e(5877)e\left(\frac{58}{77}\right) e(125154)e\left(\frac{125}{154}\right) e(6277)e\left(\frac{62}{77}\right) e(5377)e\left(\frac{53}{77}\right) e(65154)e\left(\frac{65}{154}\right) e(6477)e\left(\frac{64}{77}\right) e(115154)e\left(\frac{115}{154}\right) e(5777)e\left(\frac{57}{77}\right)
χ2001(419,)\chi_{2001}(419,\cdot) 11 11 e(1877)e\left(\frac{18}{77}\right) e(3677)e\left(\frac{36}{77}\right) e(5377)e\left(\frac{53}{77}\right) e(89154)e\left(\frac{89}{154}\right) e(5477)e\left(\frac{54}{77}\right) e(7177)e\left(\frac{71}{77}\right) e(151154)e\left(\frac{151}{154}\right) e(1677)e\left(\frac{16}{77}\right) e(125154)e\left(\frac{125}{154}\right) e(7277)e\left(\frac{72}{77}\right)
χ2001(428,)\chi_{2001}(428,\cdot) 11 11 e(2677)e\left(\frac{26}{77}\right) e(5277)e\left(\frac{52}{77}\right) e(6877)e\left(\frac{68}{77}\right) e(43154)e\left(\frac{43}{154}\right) e(177)e\left(\frac{1}{77}\right) e(1777)e\left(\frac{17}{77}\right) e(47154)e\left(\frac{47}{154}\right) e(677)e\left(\frac{6}{77}\right) e(95154)e\left(\frac{95}{154}\right) e(2777)e\left(\frac{27}{77}\right)
χ2001(470,)\chi_{2001}(470,\cdot) 11 11 e(7677)e\left(\frac{76}{77}\right) e(7577)e\left(\frac{75}{77}\right) e(2777)e\left(\frac{27}{77}\right) e(25154)e\left(\frac{25}{154}\right) e(7477)e\left(\frac{74}{77}\right) e(2677)e\left(\frac{26}{77}\right) e(13154)e\left(\frac{13}{154}\right) e(5977)e\left(\frac{59}{77}\right) e(23154)e\left(\frac{23}{154}\right) e(7377)e\left(\frac{73}{77}\right)
χ2001(497,)\chi_{2001}(497,\cdot) 11 11 e(3777)e\left(\frac{37}{77}\right) e(7477)e\left(\frac{74}{77}\right) e(277)e\left(\frac{2}{77}\right) e(153154)e\left(\frac{153}{154}\right) e(3477)e\left(\frac{34}{77}\right) e(3977)e\left(\frac{39}{77}\right) e(135154)e\left(\frac{135}{154}\right) e(5077)e\left(\frac{50}{77}\right) e(73154)e\left(\frac{73}{154}\right) e(7177)e\left(\frac{71}{77}\right)
χ2001(527,)\chi_{2001}(527,\cdot) 11 11 e(3677)e\left(\frac{36}{77}\right) e(7277)e\left(\frac{72}{77}\right) e(2977)e\left(\frac{29}{77}\right) e(101154)e\left(\frac{101}{154}\right) e(3177)e\left(\frac{31}{77}\right) e(6577)e\left(\frac{65}{77}\right) e(71154)e\left(\frac{71}{154}\right) e(3277)e\left(\frac{32}{77}\right) e(19154)e\left(\frac{19}{154}\right) e(6777)e\left(\frac{67}{77}\right)
χ2001(557,)\chi_{2001}(557,\cdot) 11 11 e(6277)e\left(\frac{62}{77}\right) e(4777)e\left(\frac{47}{77}\right) e(2077)e\left(\frac{20}{77}\right) e(67154)e\left(\frac{67}{154}\right) e(3277)e\left(\frac{32}{77}\right) e(577)e\left(\frac{5}{77}\right) e(41154)e\left(\frac{41}{154}\right) e(3877)e\left(\frac{38}{77}\right) e(37154)e\left(\frac{37}{154}\right) e(1777)e\left(\frac{17}{77}\right)
χ2001(701,)\chi_{2001}(701,\cdot) 11 11 e(877)e\left(\frac{8}{77}\right) e(1677)e\left(\frac{16}{77}\right) e(1577)e\left(\frac{15}{77}\right) e(31154)e\left(\frac{31}{154}\right) e(2477)e\left(\frac{24}{77}\right) e(2377)e\left(\frac{23}{77}\right) e(127154)e\left(\frac{127}{154}\right) e(6777)e\left(\frac{67}{77}\right) e(47154)e\left(\frac{47}{154}\right) e(3277)e\left(\frac{32}{77}\right)
χ2001(734,)\chi_{2001}(734,\cdot) 11 11 e(377)e\left(\frac{3}{77}\right) e(677)e\left(\frac{6}{77}\right) e(7377)e\left(\frac{73}{77}\right) e(79154)e\left(\frac{79}{154}\right) e(977)e\left(\frac{9}{77}\right) e(7677)e\left(\frac{76}{77}\right) e(115154)e\left(\frac{115}{154}\right) e(5477)e\left(\frac{54}{77}\right) e(85154)e\left(\frac{85}{154}\right) e(1277)e\left(\frac{12}{77}\right)
χ2001(776,)\chi_{2001}(776,\cdot) 11 11 e(577)e\left(\frac{5}{77}\right) e(1077)e\left(\frac{10}{77}\right) e(1977)e\left(\frac{19}{77}\right) e(29154)e\left(\frac{29}{154}\right) e(1577)e\left(\frac{15}{77}\right) e(2477)e\left(\frac{24}{77}\right) e(89154)e\left(\frac{89}{154}\right) e(1377)e\left(\frac{13}{77}\right) e(39154)e\left(\frac{39}{154}\right) e(2077)e\left(\frac{20}{77}\right)
χ2001(845,)\chi_{2001}(845,\cdot) 11 11 e(1677)e\left(\frac{16}{77}\right) e(3277)e\left(\frac{32}{77}\right) e(3077)e\left(\frac{30}{77}\right) e(139154)e\left(\frac{139}{154}\right) e(4877)e\left(\frac{48}{77}\right) e(4677)e\left(\frac{46}{77}\right) e(23154)e\left(\frac{23}{154}\right) e(5777)e\left(\frac{57}{77}\right) e(17154)e\left(\frac{17}{154}\right) e(6477)e\left(\frac{64}{77}\right)
χ2001(908,)\chi_{2001}(908,\cdot) 11 11 e(5277)e\left(\frac{52}{77}\right) e(2777)e\left(\frac{27}{77}\right) e(5977)e\left(\frac{59}{77}\right) e(9154)e\left(\frac{9}{154}\right) e(277)e\left(\frac{2}{77}\right) e(3477)e\left(\frac{34}{77}\right) e(17154)e\left(\frac{17}{154}\right) e(1277)e\left(\frac{12}{77}\right) e(113154)e\left(\frac{113}{154}\right) e(5477)e\left(\frac{54}{77}\right)
χ2001(941,)\chi_{2001}(941,\cdot) 11 11 e(2577)e\left(\frac{25}{77}\right) e(5077)e\left(\frac{50}{77}\right) e(1877)e\left(\frac{18}{77}\right) e(145154)e\left(\frac{145}{154}\right) e(7577)e\left(\frac{75}{77}\right) e(4377)e\left(\frac{43}{77}\right) e(137154)e\left(\frac{137}{154}\right) e(6577)e\left(\frac{65}{77}\right) e(41154)e\left(\frac{41}{154}\right) e(2377)e\left(\frac{23}{77}\right)
χ2001(950,)\chi_{2001}(950,\cdot) 11 11 e(1277)e\left(\frac{12}{77}\right) e(2477)e\left(\frac{24}{77}\right) e(6177)e\left(\frac{61}{77}\right) e(85154)e\left(\frac{85}{154}\right) e(3677)e\left(\frac{36}{77}\right) e(7377)e\left(\frac{73}{77}\right) e(75154)e\left(\frac{75}{154}\right) e(6277)e\left(\frac{62}{77}\right) e(109154)e\left(\frac{109}{154}\right) e(4877)e\left(\frac{48}{77}\right)
χ2001(962,)\chi_{2001}(962,\cdot) 11 11 e(5077)e\left(\frac{50}{77}\right) e(2377)e\left(\frac{23}{77}\right) e(3677)e\left(\frac{36}{77}\right) e(59154)e\left(\frac{59}{154}\right) e(7377)e\left(\frac{73}{77}\right) e(977)e\left(\frac{9}{77}\right) e(43154)e\left(\frac{43}{154}\right) e(5377)e\left(\frac{53}{77}\right) e(5154)e\left(\frac{5}{154}\right) e(4677)e\left(\frac{46}{77}\right)
χ2001(1019,)\chi_{2001}(1019,\cdot) 11 11 e(2377)e\left(\frac{23}{77}\right) e(4677)e\left(\frac{46}{77}\right) e(7277)e\left(\frac{72}{77}\right) e(41154)e\left(\frac{41}{154}\right) e(6977)e\left(\frac{69}{77}\right) e(1877)e\left(\frac{18}{77}\right) e(9154)e\left(\frac{9}{154}\right) e(2977)e\left(\frac{29}{77}\right) e(87154)e\left(\frac{87}{154}\right) e(1577)e\left(\frac{15}{77}\right)
χ2001(1049,)\chi_{2001}(1049,\cdot) 11 11 e(1577)e\left(\frac{15}{77}\right) e(3077)e\left(\frac{30}{77}\right) e(5777)e\left(\frac{57}{77}\right) e(87154)e\left(\frac{87}{154}\right) e(4577)e\left(\frac{45}{77}\right) e(7277)e\left(\frac{72}{77}\right) e(113154)e\left(\frac{113}{154}\right) e(3977)e\left(\frac{39}{77}\right) e(117154)e\left(\frac{117}{154}\right) e(6077)e\left(\frac{60}{77}\right)
χ2001(1079,)\chi_{2001}(1079,\cdot) 11 11 e(6977)e\left(\frac{69}{77}\right) e(6177)e\left(\frac{61}{77}\right) e(6277)e\left(\frac{62}{77}\right) e(123154)e\left(\frac{123}{154}\right) e(5377)e\left(\frac{53}{77}\right) e(5477)e\left(\frac{54}{77}\right) e(27154)e\left(\frac{27}{154}\right) e(1077)e\left(\frac{10}{77}\right) e(107154)e\left(\frac{107}{154}\right) e(4577)e\left(\frac{45}{77}\right)