Properties

Label 8043.bb
Modulus 80438043
Conductor 80438043
Order 11461146
Real no
Primitive yes
Minimal yes
Parity even

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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([573,191,468]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(17,8043))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 80438043
Conductor: 80438043
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 11461146
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(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(17,)\chi_{8043}(17,\cdot) 11 11 e(6371146)e\left(\frac{637}{1146}\right) e(64573)e\left(\frac{64}{573}\right) e(425573)e\left(\frac{425}{573}\right) e(255382)e\left(\frac{255}{382}\right) e(3411146)e\left(\frac{341}{1146}\right) e(7131146)e\left(\frac{713}{1146}\right) e(109382)e\left(\frac{109}{382}\right) e(128573)e\left(\frac{128}{573}\right) e(214573)e\left(\frac{214}{573}\right) e(10571146)e\left(\frac{1057}{1146}\right)
χ8043(38,)\chi_{8043}(38,\cdot) 11 11 e(5051146)e\left(\frac{505}{1146}\right) e(505573)e\left(\frac{505}{573}\right) e(14573)e\left(\frac{14}{573}\right) e(123382)e\left(\frac{123}{382}\right) e(5331146)e\left(\frac{533}{1146}\right) e(2811146)e\left(\frac{281}{1146}\right) e(111382)e\left(\frac{111}{382}\right) e(437573)e\left(\frac{437}{573}\right) e(274573)e\left(\frac{274}{573}\right) e(7751146)e\left(\frac{775}{1146}\right)
χ8043(68,)\chi_{8043}(68,\cdot) 11 11 e(10311146)e\left(\frac{1031}{1146}\right) e(458573)e\left(\frac{458}{573}\right) e(445573)e\left(\frac{445}{573}\right) e(267382)e\left(\frac{267}{382}\right) e(7751146)e\left(\frac{775}{1146}\right) e(7871146)e\left(\frac{787}{1146}\right) e(213382)e\left(\frac{213}{382}\right) e(343573)e\left(\frac{343}{573}\right) e(278573)e\left(\frac{278}{573}\right) e(5271146)e\left(\frac{527}{1146}\right)
χ8043(101,)\chi_{8043}(101,\cdot) 11 11 e(2771146)e\left(\frac{277}{1146}\right) e(277573)e\left(\frac{277}{573}\right) e(398573)e\left(\frac{398}{573}\right) e(277382)e\left(\frac{277}{382}\right) e(10731146)e\left(\frac{1073}{1146}\right) e(7851146)e\left(\frac{785}{1146}\right) e(45382)e\left(\frac{45}{382}\right) e(554573)e\left(\frac{554}{573}\right) e(13573)e\left(\frac{13}{573}\right) e(9131146)e\left(\frac{913}{1146}\right)
χ8043(110,)\chi_{8043}(110,\cdot) 11 11 e(8271146)e\left(\frac{827}{1146}\right) e(254573)e\left(\frac{254}{573}\right) e(487573)e\left(\frac{487}{573}\right) e(63382)e\left(\frac{63}{382}\right) e(6551146)e\left(\frac{655}{1146}\right) e(10571146)e\left(\frac{1057}{1146}\right) e(355382)e\left(\frac{355}{382}\right) e(508573)e\left(\frac{508}{573}\right) e(527573)e\left(\frac{527}{573}\right) e(11331146)e\left(\frac{1133}{1146}\right)
χ8043(143,)\chi_{8043}(143,\cdot) 11 11 e(1931146)e\left(\frac{193}{1146}\right) e(193573)e\left(\frac{193}{573}\right) e(449573)e\left(\frac{449}{573}\right) e(193382)e\left(\frac{193}{382}\right) e(10911146)e\left(\frac{1091}{1146}\right) e(10311146)e\left(\frac{1031}{1146}\right) e(81382)e\left(\frac{81}{382}\right) e(386573)e\left(\frac{386}{573}\right) e(520573)e\left(\frac{520}{573}\right) e(4211146)e\left(\frac{421}{1146}\right)
χ8043(152,)\chi_{8043}(152,\cdot) 11 11 e(8991146)e\left(\frac{899}{1146}\right) e(326573)e\left(\frac{326}{573}\right) e(34573)e\left(\frac{34}{573}\right) e(135382)e\left(\frac{135}{382}\right) e(9671146)e\left(\frac{967}{1146}\right) e(3551146)e\left(\frac{355}{1146}\right) e(215382)e\left(\frac{215}{382}\right) e(79573)e\left(\frac{79}{573}\right) e(338573)e\left(\frac{338}{573}\right) e(2451146)e\left(\frac{245}{1146}\right)
χ8043(173,)\chi_{8043}(173,\cdot) 11 11 e(10791146)e\left(\frac{1079}{1146}\right) e(506573)e\left(\frac{506}{573}\right) e(334573)e\left(\frac{334}{573}\right) e(315382)e\left(\frac{315}{382}\right) e(6011146)e\left(\frac{601}{1146}\right) e(3191146)e\left(\frac{319}{1146}\right) e(247382)e\left(\frac{247}{382}\right) e(439573)e\left(\frac{439}{573}\right) e(152573)e\left(\frac{152}{573}\right) e(3171146)e\left(\frac{317}{1146}\right)
χ8043(185,)\chi_{8043}(185,\cdot) 11 11 e(11051146)e\left(\frac{1105}{1146}\right) e(532573)e\left(\frac{532}{573}\right) e(59573)e\left(\frac{59}{573}\right) e(341382)e\left(\frac{341}{382}\right) e(771146)e\left(\frac{77}{1146}\right) e(1611146)e\left(\frac{161}{1146}\right) e(345382)e\left(\frac{345}{382}\right) e(491573)e\left(\frac{491}{573}\right) e(418573)e\left(\frac{418}{573}\right) e(10151146)e\left(\frac{1015}{1146}\right)
χ8043(206,)\chi_{8043}(206,\cdot) 11 11 e(7571146)e\left(\frac{757}{1146}\right) e(184573)e\left(\frac{184}{573}\right) e(434573)e\left(\frac{434}{573}\right) e(375382)e\left(\frac{375}{382}\right) e(4791146)e\left(\frac{479}{1146}\right) e(6891146)e\left(\frac{689}{1146}\right) e(3382)e\left(\frac{3}{382}\right) e(368573)e\left(\frac{368}{573}\right) e(472573)e\left(\frac{472}{573}\right) e(11051146)e\left(\frac{1105}{1146}\right)
χ8043(227,)\chi_{8043}(227,\cdot) 11 11 e(10811146)e\left(\frac{1081}{1146}\right) e(508573)e\left(\frac{508}{573}\right) e(401573)e\left(\frac{401}{573}\right) e(317382)e\left(\frac{317}{382}\right) e(7371146)e\left(\frac{737}{1146}\right) e(3951146)e\left(\frac{395}{1146}\right) e(137382)e\left(\frac{137}{382}\right) e(443573)e\left(\frac{443}{573}\right) e(481573)e\left(\frac{481}{573}\right) e(5471146)e\left(\frac{547}{1146}\right)
χ8043(248,)\chi_{8043}(248,\cdot) 11 11 e(851146)e\left(\frac{85}{1146}\right) e(85573)e\left(\frac{85}{573}\right) e(269573)e\left(\frac{269}{573}\right) e(85382)e\left(\frac{85}{382}\right) e(6231146)e\left(\frac{623}{1146}\right) e(3651146)e\left(\frac{365}{1146}\right) e(291382)e\left(\frac{291}{382}\right) e(170573)e\left(\frac{170}{573}\right) e(517573)e\left(\frac{517}{573}\right) e(6071146)e\left(\frac{607}{1146}\right)
χ8043(278,)\chi_{8043}(278,\cdot) 11 11 e(10731146)e\left(\frac{1073}{1146}\right) e(500573)e\left(\frac{500}{573}\right) e(133573)e\left(\frac{133}{573}\right) e(309382)e\left(\frac{309}{382}\right) e(1931146)e\left(\frac{193}{1146}\right) e(911146)e\left(\frac{91}{1146}\right) e(195382)e\left(\frac{195}{382}\right) e(427573)e\left(\frac{427}{573}\right) e(311573)e\left(\frac{311}{573}\right) e(7731146)e\left(\frac{773}{1146}\right)
χ8043(353,)\chi_{8043}(353,\cdot) 11 11 e(1751146)e\left(\frac{175}{1146}\right) e(175573)e\left(\frac{175}{573}\right) e(419573)e\left(\frac{419}{573}\right) e(175382)e\left(\frac{175}{382}\right) e(10131146)e\left(\frac{1013}{1146}\right) e(3471146)e\left(\frac{347}{1146}\right) e(307382)e\left(\frac{307}{382}\right) e(350573)e\left(\frac{350}{573}\right) e(424573)e\left(\frac{424}{573}\right) e(6431146)e\left(\frac{643}{1146}\right)
χ8043(395,)\chi_{8043}(395,\cdot) 11 11 e(9251146)e\left(\frac{925}{1146}\right) e(352573)e\left(\frac{352}{573}\right) e(332573)e\left(\frac{332}{573}\right) e(161382)e\left(\frac{161}{382}\right) e(4431146)e\left(\frac{443}{1146}\right) e(1971146)e\left(\frac{197}{1146}\right) e(313382)e\left(\frac{313}{382}\right) e(131573)e\left(\frac{131}{573}\right) e(31573)e\left(\frac{31}{573}\right) e(9431146)e\left(\frac{943}{1146}\right)
χ8043(404,)\chi_{8043}(404,\cdot) 11 11 e(6711146)e\left(\frac{671}{1146}\right) e(98573)e\left(\frac{98}{573}\right) e(418573)e\left(\frac{418}{573}\right) e(289382)e\left(\frac{289}{382}\right) e(3611146)e\left(\frac{361}{1146}\right) e(8591146)e\left(\frac{859}{1146}\right) e(149382)e\left(\frac{149}{382}\right) e(196573)e\left(\frac{196}{573}\right) e(77573)e\left(\frac{77}{573}\right) e(3831146)e\left(\frac{383}{1146}\right)
χ8043(425,)\chi_{8043}(425,\cdot) 11 11 e(6771146)e\left(\frac{677}{1146}\right) e(104573)e\left(\frac{104}{573}\right) e(46573)e\left(\frac{46}{573}\right) e(295382)e\left(\frac{295}{382}\right) e(7691146)e\left(\frac{769}{1146}\right) e(10871146)e\left(\frac{1087}{1146}\right) e(201382)e\left(\frac{201}{382}\right) e(208573)e\left(\frac{208}{573}\right) e(491573)e\left(\frac{491}{573}\right) e(10731146)e\left(\frac{1073}{1146}\right)
χ8043(437,)\chi_{8043}(437,\cdot) 11 11 e(8351146)e\left(\frac{835}{1146}\right) e(262573)e\left(\frac{262}{573}\right) e(182573)e\left(\frac{182}{573}\right) e(71382)e\left(\frac{71}{382}\right) e(531146)e\left(\frac{53}{1146}\right) e(2151146)e\left(\frac{215}{1146}\right) e(297382)e\left(\frac{297}{382}\right) e(524573)e\left(\frac{524}{573}\right) e(124573)e\left(\frac{124}{573}\right) e(9071146)e\left(\frac{907}{1146}\right)
χ8043(446,)\chi_{8043}(446,\cdot) 11 11 e(6291146)e\left(\frac{629}{1146}\right) e(56573)e\left(\frac{56}{573}\right) e(157573)e\left(\frac{157}{573}\right) e(247382)e\left(\frac{247}{382}\right) e(9431146)e\left(\frac{943}{1146}\right) e(4091146)e\left(\frac{409}{1146}\right) e(167382)e\left(\frac{167}{382}\right) e(112573)e\left(\frac{112}{573}\right) e(44573)e\left(\frac{44}{573}\right) e(1371146)e\left(\frac{137}{1146}\right)
χ8043(458,)\chi_{8043}(458,\cdot) 11 11 e(5711146)e\left(\frac{571}{1146}\right) e(571573)e\left(\frac{571}{573}\right) e(506573)e\left(\frac{506}{573}\right) e(189382)e\left(\frac{189}{382}\right) e(4371146)e\left(\frac{437}{1146}\right) e(4971146)e\left(\frac{497}{1146}\right) e(301382)e\left(\frac{301}{382}\right) e(569573)e\left(\frac{569}{573}\right) e(244573)e\left(\frac{244}{573}\right) e(3431146)e\left(\frac{343}{1146}\right)
χ8043(467,)\chi_{8043}(467,\cdot) 11 11 e(6831146)e\left(\frac{683}{1146}\right) e(110573)e\left(\frac{110}{573}\right) e(247573)e\left(\frac{247}{573}\right) e(301382)e\left(\frac{301}{382}\right) e(311146)e\left(\frac{31}{1146}\right) e(1691146)e\left(\frac{169}{1146}\right) e(253382)e\left(\frac{253}{382}\right) e(220573)e\left(\frac{220}{573}\right) e(332573)e\left(\frac{332}{573}\right) e(6171146)e\left(\frac{617}{1146}\right)
χ8043(479,)\chi_{8043}(479,\cdot) 11 11 e(9431146)e\left(\frac{943}{1146}\right) e(370573)e\left(\frac{370}{573}\right) e(362573)e\left(\frac{362}{573}\right) e(179382)e\left(\frac{179}{382}\right) e(5211146)e\left(\frac{521}{1146}\right) e(8811146)e\left(\frac{881}{1146}\right) e(87382)e\left(\frac{87}{382}\right) e(167573)e\left(\frac{167}{573}\right) e(127573)e\left(\frac{127}{573}\right) e(7211146)e\left(\frac{721}{1146}\right)
χ8043(509,)\chi_{8043}(509,\cdot) 11 11 e(6351146)e\left(\frac{635}{1146}\right) e(62573)e\left(\frac{62}{573}\right) e(358573)e\left(\frac{358}{573}\right) e(253382)e\left(\frac{253}{382}\right) e(2051146)e\left(\frac{205}{1146}\right) e(6371146)e\left(\frac{637}{1146}\right) e(219382)e\left(\frac{219}{382}\right) e(124573)e\left(\frac{124}{573}\right) e(458573)e\left(\frac{458}{573}\right) e(8271146)e\left(\frac{827}{1146}\right)
χ8043(521,)\chi_{8043}(521,\cdot) 11 11 e(1091146)e\left(\frac{109}{1146}\right) e(109573)e\left(\frac{109}{573}\right) e(500573)e\left(\frac{500}{573}\right) e(109382)e\left(\frac{109}{382}\right) e(11091146)e\left(\frac{1109}{1146}\right) e(1311146)e\left(\frac{131}{1146}\right) e(117382)e\left(\frac{117}{382}\right) e(218573)e\left(\frac{218}{573}\right) e(454573)e\left(\frac{454}{573}\right) e(10751146)e\left(\frac{1075}{1146}\right)
χ8043(530,)\chi_{8043}(530,\cdot) 11 11 e(471146)e\left(\frac{47}{1146}\right) e(47573)e\left(\frac{47}{573}\right) e(142573)e\left(\frac{142}{573}\right) e(47382)e\left(\frac{47}{382}\right) e(3311146)e\left(\frac{331}{1146}\right) e(671146)e\left(\frac{67}{1146}\right) e(89382)e\left(\frac{89}{382}\right) e(94573)e\left(\frac{94}{573}\right) e(569573)e\left(\frac{569}{573}\right) e(8211146)e\left(\frac{821}{1146}\right)
χ8043(551,)\chi_{8043}(551,\cdot) 11 11 e(6891146)e\left(\frac{689}{1146}\right) e(116573)e\left(\frac{116}{573}\right) e(448573)e\left(\frac{448}{573}\right) e(307382)e\left(\frac{307}{382}\right) e(4391146)e\left(\frac{439}{1146}\right) e(3971146)e\left(\frac{397}{1146}\right) e(305382)e\left(\frac{305}{382}\right) e(232573)e\left(\frac{232}{573}\right) e(173573)e\left(\frac{173}{573}\right) e(1611146)e\left(\frac{161}{1146}\right)
χ8043(572,)\chi_{8043}(572,\cdot) 11 11 e(5871146)e\left(\frac{587}{1146}\right) e(14573)e\left(\frac{14}{573}\right) e(469573)e\left(\frac{469}{573}\right) e(205382)e\left(\frac{205}{382}\right) e(3791146)e\left(\frac{379}{1146}\right) e(11051146)e\left(\frac{1105}{1146}\right) e(185382)e\left(\frac{185}{382}\right) e(28573)e\left(\frac{28}{573}\right) e(11573)e\left(\frac{11}{573}\right) e(10371146)e\left(\frac{1037}{1146}\right)
χ8043(584,)\chi_{8043}(584,\cdot) 11 11 e(4931146)e\left(\frac{493}{1146}\right) e(493573)e\left(\frac{493}{573}\right) e(185573)e\left(\frac{185}{573}\right) e(111382)e\left(\frac{111}{382}\right) e(8631146)e\left(\frac{863}{1146}\right) e(9711146)e\left(\frac{971}{1146}\right) e(7382)e\left(\frac{7}{382}\right) e(413573)e\left(\frac{413}{573}\right) e(19573)e\left(\frac{19}{573}\right) e(5411146)e\left(\frac{541}{1146}\right)
χ8043(626,)\chi_{8043}(626,\cdot) 11 11 e(7451146)e\left(\frac{745}{1146}\right) e(172573)e\left(\frac{172}{573}\right) e(32573)e\left(\frac{32}{573}\right) e(363382)e\left(\frac{363}{382}\right) e(8091146)e\left(\frac{809}{1146}\right) e(2331146)e\left(\frac{233}{1146}\right) e(281382)e\left(\frac{281}{382}\right) e(344573)e\left(\frac{344}{573}\right) e(217573)e\left(\frac{217}{573}\right) e(8711146)e\left(\frac{871}{1146}\right)
χ8043(635,)\chi_{8043}(635,\cdot) 11 11 e(6411146)e\left(\frac{641}{1146}\right) e(68573)e\left(\frac{68}{573}\right) e(559573)e\left(\frac{559}{573}\right) e(259382)e\left(\frac{259}{382}\right) e(6131146)e\left(\frac{613}{1146}\right) e(8651146)e\left(\frac{865}{1146}\right) e(271382)e\left(\frac{271}{382}\right) e(136573)e\left(\frac{136}{573}\right) e(299573)e\left(\frac{299}{573}\right) e(3711146)e\left(\frac{371}{1146}\right)
χ8043(677,)\chi_{8043}(677,\cdot) 11 11 e(531146)e\left(\frac{53}{1146}\right) e(53573)e\left(\frac{53}{573}\right) e(343573)e\left(\frac{343}{573}\right) e(53382)e\left(\frac{53}{382}\right) e(7391146)e\left(\frac{739}{1146}\right) e(2951146)e\left(\frac{295}{1146}\right) e(141382)e\left(\frac{141}{382}\right) e(106573)e\left(\frac{106}{573}\right) e(410573)e\left(\frac{410}{573}\right) e(3651146)e\left(\frac{365}{1146}\right)