Properties

Label 8043.bd
Modulus 80438043
Conductor 26812681
Order 11461146
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8043, base_ring=CyclotomicField(1146))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,382,879]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(37,8043))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 80438043
Conductor: 26812681
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 11461146
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2681.p
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(ζ573)\Q(\zeta_{573})
Fixed field: Number field defined by a degree 1146 polynomial (not computed)

First 31 of 380 characters in Galois orbit

Character 1-1 11 22 44 55 88 1010 1111 1313 1616 1717 1919
χ8043(37,)\chi_{8043}(37,\cdot) 1-1 11 e(256573)e\left(\frac{256}{573}\right) e(512573)e\left(\frac{512}{573}\right) e(4971146)e\left(\frac{497}{1146}\right) e(65191)e\left(\frac{65}{191}\right) e(10091146)e\left(\frac{1009}{1146}\right) e(5471146)e\left(\frac{547}{1146}\right) e(299382)e\left(\frac{299}{382}\right) e(451573)e\left(\frac{451}{573}\right) e(566573)e\left(\frac{566}{573}\right) e(217573)e\left(\frac{217}{573}\right)
χ8043(79,)\chi_{8043}(79,\cdot) 1-1 11 e(166573)e\left(\frac{166}{573}\right) e(332573)e\left(\frac{332}{573}\right) e(10431146)e\left(\frac{1043}{1146}\right) e(166191)e\left(\frac{166}{191}\right) e(2291146)e\left(\frac{229}{1146}\right) e(5831146)e\left(\frac{583}{1146}\right) e(267382)e\left(\frac{267}{382}\right) e(91573)e\left(\frac{91}{573}\right) e(179573)e\left(\frac{179}{573}\right) e(181573)e\left(\frac{181}{573}\right)
χ8043(88,)\chi_{8043}(88,\cdot) 1-1 11 e(314573)e\left(\frac{314}{573}\right) e(55573)e\left(\frac{55}{573}\right) e(2471146)e\left(\frac{247}{1146}\right) e(123191)e\left(\frac{123}{191}\right) e(8751146)e\left(\frac{875}{1146}\right) e(3711146)e\left(\frac{371}{1146}\right) e(31382)e\left(\frac{31}{382}\right) e(110573)e\left(\frac{110}{573}\right) e(166573)e\left(\frac{166}{573}\right) e(11573)e\left(\frac{11}{573}\right)
χ8043(109,)\chi_{8043}(109,\cdot) 1-1 11 e(482573)e\left(\frac{482}{573}\right) e(391573)e\left(\frac{391}{573}\right) e(9851146)e\left(\frac{985}{1146}\right) e(100191)e\left(\frac{100}{191}\right) e(8031146)e\left(\frac{803}{1146}\right) e(5331146)e\left(\frac{533}{1146}\right) e(269382)e\left(\frac{269}{382}\right) e(209573)e\left(\frac{209}{573}\right) e(430573)e\left(\frac{430}{573}\right) e(422573)e\left(\frac{422}{573}\right)
χ8043(151,)\chi_{8043}(151,\cdot) 1-1 11 e(104573)e\left(\frac{104}{573}\right) e(208573)e\left(\frac{208}{573}\right) e(7571146)e\left(\frac{757}{1146}\right) e(104191)e\left(\frac{104}{191}\right) e(9651146)e\left(\frac{965}{1146}\right) e(4551146)e\left(\frac{455}{1146}\right) e(211382)e\left(\frac{211}{382}\right) e(416573)e\left(\frac{416}{573}\right) e(409573)e\left(\frac{409}{573}\right) e(500573)e\left(\frac{500}{573}\right)
χ8043(163,)\chi_{8043}(163,\cdot) 1-1 11 e(130573)e\left(\frac{130}{573}\right) e(260573)e\left(\frac{260}{573}\right) e(8031146)e\left(\frac{803}{1146}\right) e(130191)e\left(\frac{130}{191}\right) e(10631146)e\left(\frac{1063}{1146}\right) e(1391146)e\left(\frac{139}{1146}\right) e(25382)e\left(\frac{25}{382}\right) e(520573)e\left(\frac{520}{573}\right) e(368573)e\left(\frac{368}{573}\right) e(52573)e\left(\frac{52}{573}\right)
χ8043(214,)\chi_{8043}(214,\cdot) 1-1 11 e(347573)e\left(\frac{347}{573}\right) e(121573)e\left(\frac{121}{573}\right) e(851146)e\left(\frac{85}{1146}\right) e(156191)e\left(\frac{156}{191}\right) e(7791146)e\left(\frac{779}{1146}\right) e(5871146)e\left(\frac{587}{1146}\right) e(221382)e\left(\frac{221}{382}\right) e(242573)e\left(\frac{242}{573}\right) e(136573)e\left(\frac{136}{573}\right) e(368573)e\left(\frac{368}{573}\right)
χ8043(247,)\chi_{8043}(247,\cdot) 1-1 11 e(232573)e\left(\frac{232}{573}\right) e(464573)e\left(\frac{464}{573}\right) e(7191146)e\left(\frac{719}{1146}\right) e(41191)e\left(\frac{41}{191}\right) e(371146)e\left(\frac{37}{1146}\right) e(10151146)e\left(\frac{1015}{1146}\right) e(265382)e\left(\frac{265}{382}\right) e(355573)e\left(\frac{355}{573}\right) e(119573)e\left(\frac{119}{573}\right) e(322573)e\left(\frac{322}{573}\right)
χ8043(310,)\chi_{8043}(310,\cdot) 1-1 11 e(142573)e\left(\frac{142}{573}\right) e(284573)e\left(\frac{284}{573}\right) e(1191146)e\left(\frac{119}{1146}\right) e(142191)e\left(\frac{142}{191}\right) e(4031146)e\left(\frac{403}{1146}\right) e(10511146)e\left(\frac{1051}{1146}\right) e(233382)e\left(\frac{233}{382}\right) e(568573)e\left(\frac{568}{573}\right) e(305573)e\left(\frac{305}{573}\right) e(286573)e\left(\frac{286}{573}\right)
χ8043(319,)\chi_{8043}(319,\cdot) 1-1 11 e(209573)e\left(\frac{209}{573}\right) e(418573)e\left(\frac{418}{573}\right) e(10751146)e\left(\frac{1075}{1146}\right) e(18191)e\left(\frac{18}{191}\right) e(3471146)e\left(\frac{347}{1146}\right) e(4131146)e\left(\frac{413}{1146}\right) e(121382)e\left(\frac{121}{382}\right) e(263573)e\left(\frac{263}{573}\right) e(1573)e\left(\frac{1}{573}\right) e(542573)e\left(\frac{542}{573}\right)
χ8043(340,)\chi_{8043}(340,\cdot) 1-1 11 e(239573)e\left(\frac{239}{573}\right) e(478573)e\left(\frac{478}{573}\right) e(5111146)e\left(\frac{511}{1146}\right) e(48191)e\left(\frac{48}{191}\right) e(9891146)e\left(\frac{989}{1146}\right) e(4011146)e\left(\frac{401}{1146}\right) e(259382)e\left(\frac{259}{382}\right) e(383573)e\left(\frac{383}{573}\right) e(130573)e\left(\frac{130}{573}\right) e(554573)e\left(\frac{554}{573}\right)
χ8043(352,)\chi_{8043}(352,\cdot) 1-1 11 e(511573)e\left(\frac{511}{573}\right) e(449573)e\left(\frac{449}{573}\right) e(2871146)e\left(\frac{287}{1146}\right) e(129191)e\left(\frac{129}{191}\right) e(1631146)e\left(\frac{163}{1146}\right) e(4451146)e\left(\frac{445}{1146}\right) e(135382)e\left(\frac{135}{382}\right) e(325573)e\left(\frac{325}{573}\right) e(230573)e\left(\frac{230}{573}\right) e(319573)e\left(\frac{319}{573}\right)
χ8043(394,)\chi_{8043}(394,\cdot) 1-1 11 e(496573)e\left(\frac{496}{573}\right) e(419573)e\left(\frac{419}{573}\right) e(5691146)e\left(\frac{569}{1146}\right) e(114191)e\left(\frac{114}{191}\right) e(4151146)e\left(\frac{415}{1146}\right) e(4511146)e\left(\frac{451}{1146}\right) e(257382)e\left(\frac{257}{382}\right) e(265573)e\left(\frac{265}{573}\right) e(452573)e\left(\frac{452}{573}\right) e(313573)e\left(\frac{313}{573}\right)
χ8043(403,)\chi_{8043}(403,\cdot) 1-1 11 e(398573)e\left(\frac{398}{573}\right) e(223573)e\left(\frac{223}{573}\right) e(431146)e\left(\frac{43}{1146}\right) e(16191)e\left(\frac{16}{191}\right) e(8391146)e\left(\frac{839}{1146}\right) e(10251146)e\left(\frac{1025}{1146}\right) e(341382)e\left(\frac{341}{382}\right) e(446573)e\left(\frac{446}{573}\right) e(298573)e\left(\frac{298}{573}\right) e(503573)e\left(\frac{503}{573}\right)
χ8043(424,)\chi_{8043}(424,\cdot) 1-1 11 e(497573)e\left(\frac{497}{573}\right) e(421573)e\left(\frac{421}{573}\right) e(7031146)e\left(\frac{703}{1146}\right) e(115191)e\left(\frac{115}{191}\right) e(5511146)e\left(\frac{551}{1146}\right) e(5271146)e\left(\frac{527}{1146}\right) e(147382)e\left(\frac{147}{382}\right) e(269573)e\left(\frac{269}{573}\right) e(208573)e\left(\frac{208}{573}\right) e(428573)e\left(\frac{428}{573}\right)
χ8043(436,)\chi_{8043}(436,\cdot) 1-1 11 e(106573)e\left(\frac{106}{573}\right) e(212573)e\left(\frac{212}{573}\right) e(10251146)e\left(\frac{1025}{1146}\right) e(106191)e\left(\frac{106}{191}\right) e(911146)e\left(\frac{91}{1146}\right) e(6071146)e\left(\frac{607}{1146}\right) e(373382)e\left(\frac{373}{382}\right) e(424573)e\left(\frac{424}{573}\right) e(494573)e\left(\frac{494}{573}\right) e(157573)e\left(\frac{157}{573}\right)
χ8043(457,)\chi_{8043}(457,\cdot) 1-1 11 e(259573)e\left(\frac{259}{573}\right) e(518573)e\left(\frac{518}{573}\right) e(8991146)e\left(\frac{899}{1146}\right) e(68191)e\left(\frac{68}{191}\right) e(2711146)e\left(\frac{271}{1146}\right) e(7751146)e\left(\frac{775}{1146}\right) e(351382)e\left(\frac{351}{382}\right) e(463573)e\left(\frac{463}{573}\right) e(407573)e\left(\frac{407}{573}\right) e(562573)e\left(\frac{562}{573}\right)
χ8043(466,)\chi_{8043}(466,\cdot) 1-1 11 e(5573)e\left(\frac{5}{573}\right) e(10573)e\left(\frac{10}{573}\right) e(971146)e\left(\frac{97}{1146}\right) e(5191)e\left(\frac{5}{191}\right) e(1071146)e\left(\frac{107}{1146}\right) e(9531146)e\left(\frac{953}{1146}\right) e(23382)e\left(\frac{23}{382}\right) e(20573)e\left(\frac{20}{573}\right) e(499573)e\left(\frac{499}{573}\right) e(2573)e\left(\frac{2}{573}\right)
χ8043(478,)\chi_{8043}(478,\cdot) 1-1 11 e(355573)e\left(\frac{355}{573}\right) e(137573)e\left(\frac{137}{573}\right) e(111146)e\left(\frac{11}{1146}\right) e(164191)e\left(\frac{164}{191}\right) e(7211146)e\left(\frac{721}{1146}\right) e(491146)e\left(\frac{49}{1146}\right) e(105382)e\left(\frac{105}{382}\right) e(274573)e\left(\frac{274}{573}\right) e(476573)e\left(\frac{476}{573}\right) e(142573)e\left(\frac{142}{573}\right)
χ8043(487,)\chi_{8043}(487,\cdot) 1-1 11 e(278573)e\left(\frac{278}{573}\right) e(556573)e\left(\frac{556}{573}\right) e(71146)e\left(\frac{7}{1146}\right) e(87191)e\left(\frac{87}{191}\right) e(5631146)e\left(\frac{563}{1146}\right) e(10731146)e\left(\frac{1073}{1146}\right) e(171382)e\left(\frac{171}{382}\right) e(539573)e\left(\frac{539}{573}\right) e(355573)e\left(\frac{355}{573}\right) e(455573)e\left(\frac{455}{573}\right)
χ8043(508,)\chi_{8043}(508,\cdot) 1-1 11 e(221573)e\left(\frac{221}{573}\right) e(442573)e\left(\frac{442}{573}\right) e(3911146)e\left(\frac{391}{1146}\right) e(30191)e\left(\frac{30}{191}\right) e(8331146)e\left(\frac{833}{1146}\right) e(1791146)e\left(\frac{179}{1146}\right) e(329382)e\left(\frac{329}{382}\right) e(311573)e\left(\frac{311}{573}\right) e(511573)e\left(\frac{511}{573}\right) e(203573)e\left(\frac{203}{573}\right)
χ8043(541,)\chi_{8043}(541,\cdot) 1-1 11 e(169573)e\left(\frac{169}{573}\right) e(338573)e\left(\frac{338}{573}\right) e(2991146)e\left(\frac{299}{1146}\right) e(169191)e\left(\frac{169}{191}\right) e(6371146)e\left(\frac{637}{1146}\right) e(8111146)e\left(\frac{811}{1146}\right) e(319382)e\left(\frac{319}{382}\right) e(103573)e\left(\frac{103}{573}\right) e(20573)e\left(\frac{20}{573}\right) e(526573)e\left(\frac{526}{573}\right)
χ8043(550,)\chi_{8043}(550,\cdot) 1-1 11 e(137573)e\left(\frac{137}{573}\right) e(274573)e\left(\frac{274}{573}\right) e(5951146)e\left(\frac{595}{1146}\right) e(137191)e\left(\frac{137}{191}\right) e(8691146)e\left(\frac{869}{1146}\right) e(6711146)e\left(\frac{671}{1146}\right) e(19382)e\left(\frac{19}{382}\right) e(548573)e\left(\frac{548}{573}\right) e(379573)e\left(\frac{379}{573}\right) e(284573)e\left(\frac{284}{573}\right)
χ8043(562,)\chi_{8043}(562,\cdot) 1-1 11 e(208573)e\left(\frac{208}{573}\right) e(416573)e\left(\frac{416}{573}\right) e(9411146)e\left(\frac{941}{1146}\right) e(17191)e\left(\frac{17}{191}\right) e(2111146)e\left(\frac{211}{1146}\right) e(3371146)e\left(\frac{337}{1146}\right) e(231382)e\left(\frac{231}{382}\right) e(259573)e\left(\frac{259}{573}\right) e(245573)e\left(\frac{245}{573}\right) e(427573)e\left(\frac{427}{573}\right)
χ8043(571,)\chi_{8043}(571,\cdot) 1-1 11 e(449573)e\left(\frac{449}{573}\right) e(325573)e\left(\frac{325}{573}\right) e(11146)e\left(\frac{1}{1146}\right) e(67191)e\left(\frac{67}{191}\right) e(8991146)e\left(\frac{899}{1146}\right) e(3171146)e\left(\frac{317}{1146}\right) e(79382)e\left(\frac{79}{382}\right) e(77573)e\left(\frac{77}{573}\right) e(460573)e\left(\frac{460}{573}\right) e(65573)e\left(\frac{65}{573}\right)
χ8043(592,)\chi_{8043}(592,\cdot) 1-1 11 e(77573)e\left(\frac{77}{573}\right) e(154573)e\left(\frac{154}{573}\right) e(5771146)e\left(\frac{577}{1146}\right) e(77191)e\left(\frac{77}{191}\right) e(7311146)e\left(\frac{731}{1146}\right) e(6951146)e\left(\frac{695}{1146}\right) e(125382)e\left(\frac{125}{382}\right) e(308573)e\left(\frac{308}{573}\right) e(121573)e\left(\frac{121}{573}\right) e(260573)e\left(\frac{260}{573}\right)
χ8043(604,)\chi_{8043}(604,\cdot) 1-1 11 e(301573)e\left(\frac{301}{573}\right) e(29573)e\left(\frac{29}{573}\right) e(7971146)e\left(\frac{797}{1146}\right) e(110191)e\left(\frac{110}{191}\right) e(2531146)e\left(\frac{253}{1146}\right) e(5291146)e\left(\frac{529}{1146}\right) e(315382)e\left(\frac{315}{382}\right) e(58573)e\left(\frac{58}{573}\right) e(473573)e\left(\frac{473}{573}\right) e(235573)e\left(\frac{235}{573}\right)
χ8043(613,)\chi_{8043}(613,\cdot) 1-1 11 e(563573)e\left(\frac{563}{573}\right) e(553573)e\left(\frac{553}{573}\right) e(3791146)e\left(\frac{379}{1146}\right) e(181191)e\left(\frac{181}{191}\right) e(3591146)e\left(\frac{359}{1146}\right) e(9591146)e\left(\frac{959}{1146}\right) e(145382)e\left(\frac{145}{382}\right) e(533573)e\left(\frac{533}{573}\right) e(148573)e\left(\frac{148}{573}\right) e(569573)e\left(\frac{569}{573}\right)
χ8043(697,)\chi_{8043}(697,\cdot) 1-1 11 e(338573)e\left(\frac{338}{573}\right) e(103573)e\left(\frac{103}{573}\right) e(251146)e\left(\frac{25}{1146}\right) e(147191)e\left(\frac{147}{191}\right) e(7011146)e\left(\frac{701}{1146}\right) e(10491146)e\left(\frac{1049}{1146}\right) e(65382)e\left(\frac{65}{382}\right) e(206573)e\left(\frac{206}{573}\right) e(40573)e\left(\frac{40}{573}\right) e(479573)e\left(\frac{479}{573}\right)
χ8043(709,)\chi_{8043}(709,\cdot) 1-1 11 e(133573)e\left(\frac{133}{573}\right) e(266573)e\left(\frac{266}{573}\right) e(591146)e\left(\frac{59}{1146}\right) e(133191)e\left(\frac{133}{191}\right) e(3251146)e\left(\frac{325}{1146}\right) e(3671146)e\left(\frac{367}{1146}\right) e(77382)e\left(\frac{77}{382}\right) e(532573)e\left(\frac{532}{573}\right) e(209573)e\left(\frac{209}{573}\right) e(397573)e\left(\frac{397}{573}\right)
χ8043(718,)\chi_{8043}(718,\cdot) 1-1 11 e(182573)e\left(\frac{182}{573}\right) e(364573)e\left(\frac{364}{573}\right) e(8951146)e\left(\frac{895}{1146}\right) e(182191)e\left(\frac{182}{191}\right) e(1131146)e\left(\frac{113}{1146}\right) e(6531146)e\left(\frac{653}{1146}\right) e(35382)e\left(\frac{35}{382}\right) e(155573)e\left(\frac{155}{573}\right) e(286573)e\left(\frac{286}{573}\right) e(302573)e\left(\frac{302}{573}\right)