Properties

Label 85600.in
Modulus 8560085600
Conductor 8560085600
Order 21202120
Real no
Primitive yes
Minimal yes
Parity odd

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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([0,1855,2014,280]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(13,85600))
 
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: odd
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 23 of 832 characters in Galois orbit

Character 1-1 11 33 77 99 1111 1313 1717 1919 2121 2323 2727
χ85600(13,)\chi_{85600}(13,\cdot) 1-1 11 e(11032120)e\left(\frac{1103}{2120}\right) e(19106)e\left(\frac{19}{106}\right) e(431060)e\left(\frac{43}{1060}\right) e(10192120)e\left(\frac{1019}{2120}\right) e(512120)e\left(\frac{51}{2120}\right) e(7211060)e\left(\frac{721}{1060}\right) e(11172120)e\left(\frac{1117}{2120}\right) e(14832120)e\left(\frac{1483}{2120}\right) e(471530)e\left(\frac{471}{530}\right) e(11892120)e\left(\frac{1189}{2120}\right)
χ85600(37,)\chi_{85600}(37,\cdot) 1-1 11 e(13132120)e\left(\frac{1313}{2120}\right) e(97106)e\left(\frac{97}{106}\right) e(2531060)e\left(\frac{253}{1060}\right) e(15092120)e\left(\frac{1509}{2120}\right) e(9412120)e\left(\frac{941}{2120}\right) e(7911060)e\left(\frac{791}{1060}\right) e(19872120)e\left(\frac{1987}{2120}\right) e(11332120)e\left(\frac{1133}{2120}\right) e(491530)e\left(\frac{491}{530}\right) e(18192120)e\left(\frac{1819}{2120}\right)
χ85600(117,)\chi_{85600}(117,\cdot) 1-1 11 e(2612120)e\left(\frac{261}{2120}\right) e(103106)e\left(\frac{103}{106}\right) e(2611060)e\left(\frac{261}{1060}\right) e(10332120)e\left(\frac{1033}{2120}\right) e(1372120)e\left(\frac{137}{2120}\right) e(871060)e\left(\frac{87}{1060}\right) e(8392120)e\left(\frac{839}{2120}\right) e(2012120)e\left(\frac{201}{2120}\right) e(517530)e\left(\frac{517}{530}\right) e(7832120)e\left(\frac{783}{2120}\right)
χ85600(197,)\chi_{85600}(197,\cdot) 1-1 11 e(10092120)e\left(\frac{1009}{2120}\right) e(81106)e\left(\frac{81}{106}\right) e(10091060)e\left(\frac{1009}{1060}\right) e(5172120)e\left(\frac{517}{2120}\right) e(18132120)e\left(\frac{1813}{2120}\right) e(10431060)e\left(\frac{1043}{1060}\right) e(10912120)e\left(\frac{1091}{2120}\right) e(5092120)e\left(\frac{509}{2120}\right) e(33530)e\left(\frac{33}{530}\right) e(9072120)e\left(\frac{907}{2120}\right)
χ85600(253,)\chi_{85600}(253,\cdot) 1-1 11 e(992120)e\left(\frac{99}{2120}\right) e(61106)e\left(\frac{61}{106}\right) e(991060)e\left(\frac{99}{1060}\right) e(19272120)e\left(\frac{1927}{2120}\right) e(7832120)e\left(\frac{783}{2120}\right) e(331060)e\left(\frac{33}{1060}\right) e(15612120)e\left(\frac{1561}{2120}\right) e(13192120)e\left(\frac{1319}{2120}\right) e(123530)e\left(\frac{123}{530}\right) e(2972120)e\left(\frac{297}{2120}\right)
χ85600(333,)\chi_{85600}(333,\cdot) 1-1 11 e(4712120)e\left(\frac{471}{2120}\right) e(75106)e\left(\frac{75}{106}\right) e(4711060)e\left(\frac{471}{1060}\right) e(15232120)e\left(\frac{1523}{2120}\right) e(10272120)e\left(\frac{1027}{2120}\right) e(1571060)e\left(\frac{157}{1060}\right) e(17092120)e\left(\frac{1709}{2120}\right) e(19712120)e\left(\frac{1971}{2120}\right) e(7530)e\left(\frac{7}{530}\right) e(14132120)e\left(\frac{1413}{2120}\right)
χ85600(413,)\chi_{85600}(413,\cdot) 1-1 11 e(832120)e\left(\frac{83}{2120}\right) e(49106)e\left(\frac{49}{106}\right) e(831060)e\left(\frac{83}{1060}\right) e(7592120)e\left(\frac{759}{2120}\right) e(2712120)e\left(\frac{271}{2120}\right) e(3811060)e\left(\frac{381}{1060}\right) e(17372120)e\left(\frac{1737}{2120}\right) e(10632120)e\left(\frac{1063}{2120}\right) e(71530)e\left(\frac{71}{530}\right) e(2492120)e\left(\frac{249}{2120}\right)
χ85600(437,)\chi_{85600}(437,\cdot) 1-1 11 e(10132120)e\left(\frac{1013}{2120}\right) e(31106)e\left(\frac{31}{106}\right) e(10131060)e\left(\frac{1013}{1060}\right) e(8092120)e\left(\frac{809}{2120}\right) e(8812120)e\left(\frac{881}{2120}\right) e(6911060)e\left(\frac{691}{1060}\right) e(10472120)e\left(\frac{1047}{2120}\right) e(16332120)e\left(\frac{1633}{2120}\right) e(311530)e\left(\frac{311}{530}\right) e(9192120)e\left(\frac{919}{2120}\right)
χ85600(517,)\chi_{85600}(517,\cdot) 1-1 11 e(812120)e\left(\frac{81}{2120}\right) e(21106)e\left(\frac{21}{106}\right) e(811060)e\left(\frac{81}{1060}\right) e(6132120)e\left(\frac{613}{2120}\right) e(17972120)e\left(\frac{1797}{2120}\right) e(271060)e\left(\frac{27}{1060}\right) e(6992120)e\left(\frac{699}{2120}\right) e(5012120)e\left(\frac{501}{2120}\right) e(197530)e\left(\frac{197}{530}\right) e(2432120)e\left(\frac{243}{2120}\right)
χ85600(597,)\chi_{85600}(597,\cdot) 1-1 11 e(6692120)e\left(\frac{669}{2120}\right) e(91106)e\left(\frac{91}{106}\right) e(6691060)e\left(\frac{669}{1060}\right) e(11372120)e\left(\frac{1137}{2120}\right) e(4732120)e\left(\frac{473}{2120}\right) e(2231060)e\left(\frac{223}{1060}\right) e(5912120)e\left(\frac{591}{2120}\right) e(3692120)e\left(\frac{369}{2120}\right) e(253530)e\left(\frac{253}{530}\right) e(20072120)e\left(\frac{2007}{2120}\right)
χ85600(653,)\chi_{85600}(653,\cdot) 1-1 11 e(12792120)e\left(\frac{1279}{2120}\right) e(45106)e\left(\frac{45}{106}\right) e(2191060)e\left(\frac{219}{1060}\right) e(11472120)e\left(\frac{1147}{2120}\right) e(14432120)e\left(\frac{1443}{2120}\right) e(731060)e\left(\frac{73}{1060}\right) e(13012120)e\left(\frac{1301}{2120}\right) e(592120)e\left(\frac{59}{2120}\right) e(513530)e\left(\frac{513}{530}\right) e(17172120)e\left(\frac{1717}{2120}\right)
χ85600(677,)\chi_{85600}(677,\cdot) 1-1 11 e(3372120)e\left(\frac{337}{2120}\right) e(1106)e\left(\frac{1}{106}\right) e(3371060)e\left(\frac{337}{1060}\right) e(2212120)e\left(\frac{221}{2120}\right) e(15092120)e\left(\frac{1509}{2120}\right) e(8191060)e\left(\frac{819}{1060}\right) e(32120)e\left(\frac{3}{2120}\right) e(3572120)e\left(\frac{357}{2120}\right) e(499530)e\left(\frac{499}{530}\right) e(10112120)e\left(\frac{1011}{2120}\right)
χ85600(813,)\chi_{85600}(813,\cdot) 1-1 11 e(5032120)e\left(\frac{503}{2120}\right) e(99106)e\left(\frac{99}{106}\right) e(5031060)e\left(\frac{503}{1060}\right) e(17392120)e\left(\frac{1739}{2120}\right) e(20512120)e\left(\frac{2051}{2120}\right) e(5211060)e\left(\frac{521}{1060}\right) e(13572120)e\left(\frac{1357}{2120}\right) e(3632120)e\left(\frac{363}{2120}\right) e(111530)e\left(\frac{111}{530}\right) e(15092120)e\left(\frac{1509}{2120}\right)
χ85600(917,)\chi_{85600}(917,\cdot) 1-1 11 e(612120)e\left(\frac{61}{2120}\right) e(59106)e\left(\frac{59}{106}\right) e(611060)e\left(\frac{61}{1060}\right) e(12732120)e\left(\frac{1273}{2120}\right) e(972120)e\left(\frac{97}{2120}\right) e(7271060)e\left(\frac{727}{1060}\right) e(9192120)e\left(\frac{919}{2120}\right) e(12412120)e\left(\frac{1241}{2120}\right) e(397530)e\left(\frac{397}{530}\right) e(1832120)e\left(\frac{183}{2120}\right)
χ85600(973,)\chi_{85600}(973,\cdot) 1-1 11 e(3672120)e\left(\frac{367}{2120}\right) e(103106)e\left(\frac{103}{106}\right) e(3671060)e\left(\frac{367}{1060}\right) e(2912120)e\left(\frac{291}{2120}\right) e(19392120)e\left(\frac{1939}{2120}\right) e(8291060)e\left(\frac{829}{1060}\right) e(7332120)e\left(\frac{733}{2120}\right) e(3072120)e\left(\frac{307}{2120}\right) e(199530)e\left(\frac{199}{530}\right) e(11012120)e\left(\frac{1101}{2120}\right)
χ85600(997,)\chi_{85600}(997,\cdot) 1-1 11 e(2892120)e\left(\frac{289}{2120}\right) e(71106)e\left(\frac{71}{106}\right) e(2891060)e\left(\frac{289}{1060}\right) e(9572120)e\left(\frac{957}{2120}\right) e(20932120)e\left(\frac{2093}{2120}\right) e(8031060)e\left(\frac{803}{1060}\right) e(5312120)e\left(\frac{531}{2120}\right) e(17092120)e\left(\frac{1709}{2120}\right) e(343530)e\left(\frac{343}{530}\right) e(8672120)e\left(\frac{867}{2120}\right)
χ85600(1053,)\chi_{85600}(1053,\cdot) 1-1 11 e(15392120)e\left(\frac{1539}{2120}\right) e(81106)e\left(\frac{81}{106}\right) e(4791060)e\left(\frac{479}{1060}\right) e(10472120)e\left(\frac{1047}{2120}\right) e(2232120)e\left(\frac{223}{2120}\right) e(5131060)e\left(\frac{513}{1060}\right) e(5612120)e\left(\frac{561}{2120}\right) e(10392120)e\left(\frac{1039}{2120}\right) e(33530)e\left(\frac{33}{530}\right) e(3772120)e\left(\frac{377}{2120}\right)
χ85600(1213,)\chi_{85600}(1213,\cdot) 1-1 11 e(11632120)e\left(\frac{1163}{2120}\right) e(11106)e\left(\frac{11}{106}\right) e(1031060)e\left(\frac{103}{1060}\right) e(11592120)e\left(\frac{1159}{2120}\right) e(9112120)e\left(\frac{911}{2120}\right) e(7411060)e\left(\frac{741}{1060}\right) e(4572120)e\left(\frac{457}{2120}\right) e(13832120)e\left(\frac{1383}{2120}\right) e(401530)e\left(\frac{401}{530}\right) e(13692120)e\left(\frac{1369}{2120}\right)
χ85600(1317,)\chi_{85600}(1317,\cdot) 1-1 11 e(14412120)e\left(\frac{1441}{2120}\right) e(87106)e\left(\frac{87}{106}\right) e(3811060)e\left(\frac{381}{1060}\right) e(2532120)e\left(\frac{253}{2120}\right) e(7972120)e\left(\frac{797}{2120}\right) e(1271060)e\left(\frac{127}{1060}\right) e(5792120)e\left(\frac{579}{2120}\right) e(10612120)e\left(\frac{1061}{2120}\right) e(377530)e\left(\frac{377}{530}\right) e(832120)e\left(\frac{83}{2120}\right)
χ85600(1373,)\chi_{85600}(1373,\cdot) 1-1 11 e(1872120)e\left(\frac{187}{2120}\right) e(21106)e\left(\frac{21}{106}\right) e(1871060)e\left(\frac{187}{1060}\right) e(19912120)e\left(\frac{1991}{2120}\right) e(14792120)e\left(\frac{1479}{2120}\right) e(7691060)e\left(\frac{769}{1060}\right) e(5932120)e\left(\frac{593}{2120}\right) e(6072120)e\left(\frac{607}{2120}\right) e(409530)e\left(\frac{409}{530}\right) e(5612120)e\left(\frac{561}{2120}\right)
χ85600(1453,)\chi_{85600}(1453,\cdot) 1-1 11 e(11992120)e\left(\frac{1199}{2120}\right) e(91106)e\left(\frac{91}{106}\right) e(1391060)e\left(\frac{139}{1060}\right) e(16672120)e\left(\frac{1667}{2120}\right) e(10032120)e\left(\frac{1003}{2120}\right) e(7531060)e\left(\frac{753}{1060}\right) e(612120)e\left(\frac{61}{2120}\right) e(8992120)e\left(\frac{899}{2120}\right) e(253530)e\left(\frac{253}{530}\right) e(14772120)e\left(\frac{1477}{2120}\right)
χ85600(1477,)\chi_{85600}(1477,\cdot) 1-1 11 e(7372120)e\left(\frac{737}{2120}\right) e(89106)e\left(\frac{89}{106}\right) e(7371060)e\left(\frac{737}{1060}\right) e(18612120)e\left(\frac{1861}{2120}\right) e(15892120)e\left(\frac{1589}{2120}\right) e(5991060)e\left(\frac{599}{1060}\right) e(19632120)e\left(\frac{1963}{2120}\right) e(3972120)e\left(\frac{397}{2120}\right) e(209530)e\left(\frac{209}{530}\right) e(912120)e\left(\frac{91}{2120}\right)
χ85600(1533,)\chi_{85600}(1533,\cdot) 1-1 11 e(12912120)e\left(\frac{1291}{2120}\right) e(1106)e\left(\frac{1}{106}\right) e(2311060)e\left(\frac{231}{1060}\right) e(20232120)e\left(\frac{2023}{2120}\right) e(7672120)e\left(\frac{767}{2120}\right) e(771060)e\left(\frac{77}{1060}\right) e(11692120)e\left(\frac{1169}{2120}\right) e(13112120)e\left(\frac{1311}{2120}\right) e(287530)e\left(\frac{287}{530}\right) e(17532120)e\left(\frac{1753}{2120}\right)