Properties

Label 85600.ig
Modulus 8560085600
Conductor 8560085600
Order 21202120
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(85600, base_ring=CyclotomicField(2120))
 
M = H._module
 
chi = DirichletCharacter(H, M([1060,265,1484,420]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(59,85600))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 8560085600
Conductor: 8560085600
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 21202120
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(ζ2120)\Q(\zeta_{2120})
Fixed field: Number field defined by a degree 2120 polynomial (not computed)

First 20 of 832 characters in Galois orbit

Character 1-1 11 33 77 99 1111 1313 1717 1919 2121 2323 2727
χ85600(59,)\chi_{85600}(59,\cdot) 11 11 e(13632120)e\left(\frac{1363}{2120}\right) e(163212)e\left(\frac{163}{212}\right) e(3031060)e\left(\frac{303}{1060}\right) e(14492120)e\left(\frac{1449}{2120}\right) e(20112120)e\left(\frac{2011}{2120}\right) e(183530)e\left(\frac{183}{530}\right) e(9072120)e\left(\frac{907}{2120}\right) e(8732120)e\left(\frac{873}{2120}\right) e(2471060)e\left(\frac{247}{1060}\right) e(19692120)e\left(\frac{1969}{2120}\right)
χ85600(139,)\chi_{85600}(139,\cdot) 11 11 e(16472120)e\left(\frac{1647}{2120}\right) e(59212)e\left(\frac{59}{212}\right) e(5871060)e\left(\frac{587}{1060}\right) e(9812120)e\left(\frac{981}{2120}\right) e(15592120)e\left(\frac{1559}{2120}\right) e(407530)e\left(\frac{407}{530}\right) e(20232120)e\left(\frac{2023}{2120}\right) e(1172120)e\left(\frac{117}{2120}\right) e(5031060)e\left(\frac{503}{1060}\right) e(7012120)e\left(\frac{701}{2120}\right)
χ85600(179,)\chi_{85600}(179,\cdot) 11 11 e(5492120)e\left(\frac{549}{2120}\right) e(161212)e\left(\frac{161}{212}\right) e(5491060)e\left(\frac{549}{1060}\right) e(3272120)e\left(\frac{327}{2120}\right) e(19332120)e\left(\frac{1933}{2120}\right) e(489530)e\left(\frac{489}{530}\right) e(13812120)e\left(\frac{1381}{2120}\right) e(392120)e\left(\frac{39}{2120}\right) e(5211060)e\left(\frac{521}{1060}\right) e(16472120)e\left(\frac{1647}{2120}\right)
χ85600(219,)\chi_{85600}(219,\cdot) 11 11 e(4512120)e\left(\frac{451}{2120}\right) e(67212)e\left(\frac{67}{212}\right) e(4511060)e\left(\frac{451}{1060}\right) e(5932120)e\left(\frac{593}{2120}\right) e(3872120)e\left(\frac{387}{2120}\right) e(31530)e\left(\frac{31}{530}\right) e(3392120)e\left(\frac{339}{2120}\right) e(11212120)e\left(\frac{1121}{2120}\right) e(6791060)e\left(\frac{679}{1060}\right) e(13532120)e\left(\frac{1353}{2120}\right)
χ85600(259,)\chi_{85600}(259,\cdot) 11 11 e(332120)e\left(\frac{33}{2120}\right) e(129212)e\left(\frac{129}{212}\right) e(331060)e\left(\frac{33}{1060}\right) e(8192120)e\left(\frac{819}{2120}\right) e(13212120)e\left(\frac{1321}{2120}\right) e(403530)e\left(\frac{403}{530}\right) e(6972120)e\left(\frac{697}{2120}\right) e(13232120)e\left(\frac{1323}{2120}\right) e(8771060)e\left(\frac{877}{1060}\right) e(992120)e\left(\frac{99}{2120}\right)
χ85600(339,)\chi_{85600}(339,\cdot) 11 11 e(7172120)e\left(\frac{717}{2120}\right) e(201212)e\left(\frac{201}{212}\right) e(7171060)e\left(\frac{717}{1060}\right) e(19912120)e\left(\frac{1991}{2120}\right) e(9492120)e\left(\frac{949}{2120}\right) e(517530)e\left(\frac{517}{530}\right) e(16532120)e\left(\frac{1653}{2120}\right) e(6072120)e\left(\frac{607}{2120}\right) e(5531060)e\left(\frac{553}{1060}\right) e(312120)e\left(\frac{31}{2120}\right)
χ85600(379,)\chi_{85600}(379,\cdot) 11 11 e(7792120)e\left(\frac{779}{2120}\right) e(135212)e\left(\frac{135}{212}\right) e(7791060)e\left(\frac{779}{1060}\right) e(12172120)e\left(\frac{1217}{2120}\right) e(2832120)e\left(\frac{283}{2120}\right) e(439530)e\left(\frac{439}{530}\right) e(9712120)e\left(\frac{971}{2120}\right) e(92120)e\left(\frac{9}{2120}\right) e(6911060)e\left(\frac{691}{1060}\right) e(2172120)e\left(\frac{217}{2120}\right)
χ85600(419,)\chi_{85600}(419,\cdot) 11 11 e(8012120)e\left(\frac{801}{2120}\right) e(9212)e\left(\frac{9}{212}\right) e(8011060)e\left(\frac{801}{1060}\right) e(17632120)e\left(\frac{1763}{2120}\right) e(4572120)e\left(\frac{457}{2120}\right) e(1530)e\left(\frac{1}{530}\right) e(7292120)e\left(\frac{729}{2120}\right) e(8912120)e\left(\frac{891}{2120}\right) e(5691060)e\left(\frac{569}{1060}\right) e(2832120)e\left(\frac{283}{2120}\right)
χ85600(459,)\chi_{85600}(459,\cdot) 11 11 e(2232120)e\left(\frac{223}{2120}\right) e(43212)e\left(\frac{43}{212}\right) e(2231060)e\left(\frac{223}{1060}\right) e(9092120)e\left(\frac{909}{2120}\right) e(5112120)e\left(\frac{511}{2120}\right) e(523530)e\left(\frac{523}{530}\right) e(7272120)e\left(\frac{727}{2120}\right) e(6532120)e\left(\frac{653}{2120}\right) e(7871060)e\left(\frac{787}{1060}\right) e(6692120)e\left(\frac{669}{2120}\right)
χ85600(619,)\chi_{85600}(619,\cdot) 11 11 e(13112120)e\left(\frac{1311}{2120}\right) e(191212)e\left(\frac{191}{212}\right) e(2511060)e\left(\frac{251}{1060}\right) e(18932120)e\left(\frac{1893}{2120}\right) e(14072120)e\left(\frac{1407}{2120}\right) e(351530)e\left(\frac{351}{530}\right) e(14792120)e\left(\frac{1479}{2120}\right) e(11012120)e\left(\frac{1101}{2120}\right) e(4391060)e\left(\frac{439}{1060}\right) e(18132120)e\left(\frac{1813}{2120}\right)
χ85600(659,)\chi_{85600}(659,\cdot) 11 11 e(3732120)e\left(\frac{373}{2120}\right) e(109212)e\left(\frac{109}{212}\right) e(3731060)e\left(\frac{373}{1060}\right) e(1992120)e\left(\frac{199}{2120}\right) e(5412120)e\left(\frac{541}{2120}\right) e(283530)e\left(\frac{283}{530}\right) e(11972120)e\left(\frac{1197}{2120}\right) e(14632120)e\left(\frac{1463}{2120}\right) e(4371060)e\left(\frac{437}{1060}\right) e(11192120)e\left(\frac{1119}{2120}\right)
χ85600(739,)\chi_{85600}(739,\cdot) 11 11 e(8972120)e\left(\frac{897}{2120}\right) e(153212)e\left(\frac{153}{212}\right) e(8971060)e\left(\frac{897}{1060}\right) e(2912120)e\left(\frac{291}{2120}\right) e(14092120)e\left(\frac{1409}{2120}\right) e(17530)e\left(\frac{17}{530}\right) e(17932120)e\left(\frac{1793}{2120}\right) e(3072120)e\left(\frac{307}{2120}\right) e(1331060)e\left(\frac{133}{1060}\right) e(5712120)e\left(\frac{571}{2120}\right)
χ85600(819,)\chi_{85600}(819,\cdot) 11 11 e(11012120)e\left(\frac{1101}{2120}\right) e(141212)e\left(\frac{141}{212}\right) e(411060)e\left(\frac{41}{1060}\right) e(3432120)e\left(\frac{343}{2120}\right) e(5172120)e\left(\frac{517}{2120}\right) e(51530)e\left(\frac{51}{530}\right) e(16692120)e\left(\frac{1669}{2120}\right) e(3912120)e\left(\frac{391}{2120}\right) e(9291060)e\left(\frac{929}{1060}\right) e(11832120)e\left(\frac{1183}{2120}\right)
χ85600(1059,)\chi_{85600}(1059,\cdot) 11 11 e(1132120)e\left(\frac{113}{2120}\right) e(37212)e\left(\frac{37}{212}\right) e(1131060)e\left(\frac{113}{1060}\right) e(2992120)e\left(\frac{299}{2120}\right) e(17612120)e\left(\frac{1761}{2120}\right) e(63530)e\left(\frac{63}{530}\right) e(19372120)e\left(\frac{1937}{2120}\right) e(4832120)e\left(\frac{483}{2120}\right) e(3371060)e\left(\frac{337}{1060}\right) e(3392120)e\left(\frac{339}{2120}\right)
χ85600(1179,)\chi_{85600}(1179,\cdot) 11 11 e(4992120)e\left(\frac{499}{2120}\right) e(139212)e\left(\frac{139}{212}\right) e(4991060)e\left(\frac{499}{1060}\right) e(19772120)e\left(\frac{1977}{2120}\right) e(19232120)e\left(\frac{1923}{2120}\right) e(39530)e\left(\frac{39}{530}\right) e(19312120)e\left(\frac{1931}{2120}\right) e(18892120)e\left(\frac{1889}{2120}\right) e(9911060)e\left(\frac{991}{1060}\right) e(14972120)e\left(\frac{1497}{2120}\right)
χ85600(1259,)\chi_{85600}(1259,\cdot) 11 11 e(7432120)e\left(\frac{743}{2120}\right) e(187212)e\left(\frac{187}{212}\right) e(7431060)e\left(\frac{743}{1060}\right) e(7092120)e\left(\frac{709}{2120}\right) e(1912120)e\left(\frac{191}{2120}\right) e(433530)e\left(\frac{433}{530}\right) e(13672120)e\left(\frac{1367}{2120}\right) e(4932120)e\left(\frac{493}{2120}\right) e(9871060)e\left(\frac{987}{1060}\right) e(1092120)e\left(\frac{109}{2120}\right)
χ85600(1339,)\chi_{85600}(1339,\cdot) 11 11 e(11472120)e\left(\frac{1147}{2120}\right) e(51212)e\left(\frac{51}{212}\right) e(871060)e\left(\frac{87}{1060}\right) e(5212120)e\left(\frac{521}{2120}\right) e(14592120)e\left(\frac{1459}{2120}\right) e(147530)e\left(\frac{147}{530}\right) e(11632120)e\left(\frac{1163}{2120}\right) e(16572120)e\left(\frac{1657}{2120}\right) e(9631060)e\left(\frac{963}{1060}\right) e(13212120)e\left(\frac{1321}{2120}\right)
χ85600(1379,)\chi_{85600}(1379,\cdot) 11 11 e(18492120)e\left(\frac{1849}{2120}\right) e(97212)e\left(\frac{97}{212}\right) e(7891060)e\left(\frac{789}{1060}\right) e(19472120)e\left(\frac{1947}{2120}\right) e(732120)e\left(\frac{73}{2120}\right) e(529530)e\left(\frac{529}{530}\right) e(19212120)e\left(\frac{1921}{2120}\right) e(6992120)e\left(\frac{699}{2120}\right) e(10211060)e\left(\frac{1021}{1060}\right) e(13072120)e\left(\frac{1307}{2120}\right)
χ85600(1419,)\chi_{85600}(1419,\cdot) 11 11 e(8312120)e\left(\frac{831}{2120}\right) e(107212)e\left(\frac{107}{212}\right) e(8311060)e\left(\frac{831}{1060}\right) e(7732120)e\left(\frac{773}{2120}\right) e(8872120)e\left(\frac{887}{2120}\right) e(271530)e\left(\frac{271}{530}\right) e(3992120)e\left(\frac{399}{2120}\right) e(19012120)e\left(\frac{1901}{2120}\right) e(4991060)e\left(\frac{499}{1060}\right) e(3732120)e\left(\frac{373}{2120}\right)
χ85600(1459,)\chi_{85600}(1459,\cdot) 11 11 e(10532120)e\left(\frac{1053}{2120}\right) e(69212)e\left(\frac{69}{212}\right) e(10531060)e\left(\frac{1053}{1060}\right) e(10792120)e\left(\frac{1079}{2120}\right) e(11012120)e\left(\frac{1101}{2120}\right) e(43530)e\left(\frac{43}{530}\right) e(772120)e\left(\frac{77}{2120}\right) e(17432120)e\left(\frac{1743}{2120}\right) e(6171060)e\left(\frac{617}{1060}\right) e(10392120)e\left(\frac{1039}{2120}\right)