Properties

Label 8043.z
Modulus 80438043
Conductor 80438043
Order 11461146
Real no
Primitive yes
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([573,382,402]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(2,8043))
 
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: 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(2,)\chi_{8043}(2,\cdot) 1-1 11 e(1971146)e\left(\frac{197}{1146}\right) e(197573)e\left(\frac{197}{573}\right) e(5931146)e\left(\frac{593}{1146}\right) e(197382)e\left(\frac{197}{382}\right) e(395573)e\left(\frac{395}{573}\right) e(371146)e\left(\frac{37}{1146}\right) e(26191)e\left(\frac{26}{191}\right) e(394573)e\left(\frac{394}{573}\right) e(6371146)e\left(\frac{637}{1146}\right) e(154573)e\left(\frac{154}{573}\right)
χ8043(23,)\chi_{8043}(23,\cdot) 1-1 11 e(5271146)e\left(\frac{527}{1146}\right) e(527573)e\left(\frac{527}{573}\right) e(9291146)e\left(\frac{929}{1146}\right) e(145382)e\left(\frac{145}{382}\right) e(155573)e\left(\frac{155}{573}\right) e(11171146)e\left(\frac{1117}{1146}\right) e(119191)e\left(\frac{119}{191}\right) e(481573)e\left(\frac{481}{573}\right) e(3371146)e\left(\frac{337}{1146}\right) e(220573)e\left(\frac{220}{573}\right)
χ8043(32,)\chi_{8043}(32,\cdot) 1-1 11 e(9851146)e\left(\frac{985}{1146}\right) e(412573)e\left(\frac{412}{573}\right) e(6731146)e\left(\frac{673}{1146}\right) e(221382)e\left(\frac{221}{382}\right) e(256573)e\left(\frac{256}{573}\right) e(1851146)e\left(\frac{185}{1146}\right) e(130191)e\left(\frac{130}{191}\right) e(251573)e\left(\frac{251}{573}\right) e(8931146)e\left(\frac{893}{1146}\right) e(197573)e\left(\frac{197}{573}\right)
χ8043(65,)\chi_{8043}(65,\cdot) 1-1 11 e(7491146)e\left(\frac{749}{1146}\right) e(176573)e\left(\frac{176}{573}\right) e(9051146)e\left(\frac{905}{1146}\right) e(367382)e\left(\frac{367}{382}\right) e(254573)e\left(\frac{254}{573}\right) e(3851146)e\left(\frac{385}{1146}\right) e(126191)e\left(\frac{126}{191}\right) e(352573)e\left(\frac{352}{573}\right) e(311146)e\left(\frac{31}{1146}\right) e(379573)e\left(\frac{379}{573}\right)
χ8043(86,)\chi_{8043}(86,\cdot) 1-1 11 e(2931146)e\left(\frac{293}{1146}\right) e(293573)e\left(\frac{293}{573}\right) e(1491146)e\left(\frac{149}{1146}\right) e(293382)e\left(\frac{293}{382}\right) e(221573)e\left(\frac{221}{573}\right) e(2471146)e\left(\frac{247}{1146}\right) e(60191)e\left(\frac{60}{191}\right) e(13573)e\left(\frac{13}{573}\right) e(1331146)e\left(\frac{133}{1146}\right) e(517573)e\left(\frac{517}{573}\right)
χ8043(116,)\chi_{8043}(116,\cdot) 1-1 11 e(7751146)e\left(\frac{775}{1146}\right) e(202573)e\left(\frac{202}{573}\right) e(3551146)e\left(\frac{355}{1146}\right) e(11382)e\left(\frac{11}{382}\right) e(565573)e\left(\frac{565}{573}\right) e(2271146)e\left(\frac{227}{1146}\right) e(175191)e\left(\frac{175}{191}\right) e(404573)e\left(\frac{404}{573}\right) e(5631146)e\left(\frac{563}{1146}\right) e(155573)e\left(\frac{155}{573}\right)
χ8043(128,)\chi_{8043}(128,\cdot) 1-1 11 e(2331146)e\left(\frac{233}{1146}\right) e(233573)e\left(\frac{233}{573}\right) e(7131146)e\left(\frac{713}{1146}\right) e(233382)e\left(\frac{233}{382}\right) e(473573)e\left(\frac{473}{573}\right) e(2591146)e\left(\frac{259}{1146}\right) e(182191)e\left(\frac{182}{191}\right) e(466573)e\left(\frac{466}{573}\right) e(10211146)e\left(\frac{1021}{1146}\right) e(505573)e\left(\frac{505}{573}\right)
χ8043(137,)\chi_{8043}(137,\cdot) 1-1 11 e(3851146)e\left(\frac{385}{1146}\right) e(385573)e\left(\frac{385}{573}\right) e(5831146)e\left(\frac{583}{1146}\right) e(3382)e\left(\frac{3}{382}\right) e(484573)e\left(\frac{484}{573}\right) e(3051146)e\left(\frac{305}{1146}\right) e(13191)e\left(\frac{13}{191}\right) e(197573)e\left(\frac{197}{573}\right) e(6051146)e\left(\frac{605}{1146}\right) e(77573)e\left(\frac{77}{573}\right)
χ8043(149,)\chi_{8043}(149,\cdot) 1-1 11 e(2691146)e\left(\frac{269}{1146}\right) e(269573)e\left(\frac{269}{573}\right) e(8331146)e\left(\frac{833}{1146}\right) e(269382)e\left(\frac{269}{382}\right) e(551573)e\left(\frac{551}{573}\right) e(4811146)e\left(\frac{481}{1146}\right) e(147191)e\left(\frac{147}{191}\right) e(538573)e\left(\frac{538}{573}\right) e(2591146)e\left(\frac{259}{1146}\right) e(283573)e\left(\frac{283}{573}\right)
χ8043(200,)\chi_{8043}(200,\cdot) 1-1 11 e(6311146)e\left(\frac{631}{1146}\right) e(58573)e\left(\frac{58}{573}\right) e(10211146)e\left(\frac{1021}{1146}\right) e(249382)e\left(\frac{249}{382}\right) e(253573)e\left(\frac{253}{573}\right) e(4851146)e\left(\frac{485}{1146}\right) e(124191)e\left(\frac{124}{191}\right) e(116573)e\left(\frac{116}{573}\right) e(1731146)e\left(\frac{173}{1146}\right) e(470573)e\left(\frac{470}{573}\right)
χ8043(242,)\chi_{8043}(242,\cdot) 1-1 11 e(2711146)e\left(\frac{271}{1146}\right) e(271573)e\left(\frac{271}{573}\right) e(9671146)e\left(\frac{967}{1146}\right) e(271382)e\left(\frac{271}{382}\right) e(46573)e\left(\frac{46}{573}\right) e(5571146)e\left(\frac{557}{1146}\right) e(92191)e\left(\frac{92}{191}\right) e(542573)e\left(\frac{542}{573}\right) e(9171146)e\left(\frac{917}{1146}\right) e(398573)e\left(\frac{398}{573}\right)
χ8043(263,)\chi_{8043}(263,\cdot) 1-1 11 e(1871146)e\left(\frac{187}{1146}\right) e(187573)e\left(\frac{187}{573}\right) e(10691146)e\left(\frac{1069}{1146}\right) e(187382)e\left(\frac{187}{382}\right) e(55573)e\left(\frac{55}{573}\right) e(8031146)e\left(\frac{803}{1146}\right) e(110191)e\left(\frac{110}{191}\right) e(374573)e\left(\frac{374}{573}\right) e(7851146)e\left(\frac{785}{1146}\right) e(152573)e\left(\frac{152}{573}\right)
χ8043(284,)\chi_{8043}(284,\cdot) 1-1 11 e(10991146)e\left(\frac{1099}{1146}\right) e(526573)e\left(\frac{526}{573}\right) e(2891146)e\left(\frac{289}{1146}\right) e(335382)e\left(\frac{335}{382}\right) e(121573)e\left(\frac{121}{573}\right) e(10791146)e\left(\frac{1079}{1146}\right) e(51191)e\left(\frac{51}{191}\right) e(479573)e\left(\frac{479}{573}\right) e(5811146)e\left(\frac{581}{1146}\right) e(449573)e\left(\frac{449}{573}\right)
χ8043(305,)\chi_{8043}(305,\cdot) 1-1 11 e(10751146)e\left(\frac{1075}{1146}\right) e(502573)e\left(\frac{502}{573}\right) e(9731146)e\left(\frac{973}{1146}\right) e(311382)e\left(\frac{311}{382}\right) e(451573)e\left(\frac{451}{573}\right) e(1671146)e\left(\frac{167}{1146}\right) e(138191)e\left(\frac{138}{191}\right) e(431573)e\left(\frac{431}{573}\right) e(7071146)e\left(\frac{707}{1146}\right) e(215573)e\left(\frac{215}{573}\right)
χ8043(317,)\chi_{8043}(317,\cdot) 1-1 11 e(3831146)e\left(\frac{383}{1146}\right) e(383573)e\left(\frac{383}{573}\right) e(4491146)e\left(\frac{449}{1146}\right) e(1382)e\left(\frac{1}{382}\right) e(416573)e\left(\frac{416}{573}\right) e(2291146)e\left(\frac{229}{1146}\right) e(68191)e\left(\frac{68}{191}\right) e(193573)e\left(\frac{193}{573}\right) e(10931146)e\left(\frac{1093}{1146}\right) e(535573)e\left(\frac{535}{573}\right)
χ8043(338,)\chi_{8043}(338,\cdot) 1-1 11 e(5091146)e\left(\frac{509}{1146}\right) e(509573)e\left(\frac{509}{573}\right) e(8691146)e\left(\frac{869}{1146}\right) e(127382)e\left(\frac{127}{382}\right) e(116573)e\left(\frac{116}{573}\right) e(4331146)e\left(\frac{433}{1146}\right) e(41191)e\left(\frac{41}{191}\right) e(445573)e\left(\frac{445}{573}\right) e(1451146)e\left(\frac{145}{1146}\right) e(331573)e\left(\frac{331}{573}\right)
χ8043(368,)\chi_{8043}(368,\cdot) 1-1 11 e(1691146)e\left(\frac{169}{1146}\right) e(169573)e\left(\frac{169}{573}\right) e(10091146)e\left(\frac{1009}{1146}\right) e(169382)e\left(\frac{169}{382}\right) e(16573)e\left(\frac{16}{573}\right) e(1191146)e\left(\frac{119}{1146}\right) e(32191)e\left(\frac{32}{191}\right) e(338573)e\left(\frac{338}{573}\right) e(5931146)e\left(\frac{593}{1146}\right) e(263573)e\left(\frac{263}{573}\right)
χ8043(389,)\chi_{8043}(389,\cdot) 1-1 11 e(9191146)e\left(\frac{919}{1146}\right) e(346573)e\left(\frac{346}{573}\right) e(8351146)e\left(\frac{835}{1146}\right) e(155382)e\left(\frac{155}{382}\right) e(304573)e\left(\frac{304}{573}\right) e(11151146)e\left(\frac{1115}{1146}\right) e(35191)e\left(\frac{35}{191}\right) e(119573)e\left(\frac{119}{573}\right) e(9531146)e\left(\frac{953}{1146}\right) e(413573)e\left(\frac{413}{573}\right)
χ8043(401,)\chi_{8043}(401,\cdot) 1-1 11 e(1131146)e\left(\frac{113}{1146}\right) e(113573)e\left(\frac{113}{573}\right) e(6951146)e\left(\frac{695}{1146}\right) e(113382)e\left(\frac{113}{382}\right) e(404573)e\left(\frac{404}{573}\right) e(2831146)e\left(\frac{283}{1146}\right) e(44191)e\left(\frac{44}{191}\right) e(226573)e\left(\frac{226}{573}\right) e(5051146)e\left(\frac{505}{1146}\right) e(481573)e\left(\frac{481}{573}\right)
χ8043(410,)\chi_{8043}(410,\cdot) 1-1 11 e(8291146)e\left(\frac{829}{1146}\right) e(256573)e\left(\frac{256}{573}\right) e(5351146)e\left(\frac{535}{1146}\right) e(65382)e\left(\frac{65}{382}\right) e(109573)e\left(\frac{109}{573}\right) e(11331146)e\left(\frac{1133}{1146}\right) e(27191)e\left(\frac{27}{191}\right) e(512573)e\left(\frac{512}{573}\right) e(11391146)e\left(\frac{1139}{1146}\right) e(395573)e\left(\frac{395}{573}\right)
χ8043(431,)\chi_{8043}(431,\cdot) 1-1 11 e(9371146)e\left(\frac{937}{1146}\right) e(364573)e\left(\frac{364}{573}\right) e(8951146)e\left(\frac{895}{1146}\right) e(173382)e\left(\frac{173}{382}\right) e(343573)e\left(\frac{343}{573}\right) e(6531146)e\left(\frac{653}{1146}\right) e(113191)e\left(\frac{113}{191}\right) e(155573)e\left(\frac{155}{573}\right) e(11451146)e\left(\frac{1145}{1146}\right) e(302573)e\left(\frac{302}{573}\right)
χ8043(452,)\chi_{8043}(452,\cdot) 1-1 11 e(1031146)e\left(\frac{103}{1146}\right) e(103573)e\left(\frac{103}{573}\right) e(251146)e\left(\frac{25}{1146}\right) e(103382)e\left(\frac{103}{382}\right) e(64573)e\left(\frac{64}{573}\right) e(10491146)e\left(\frac{1049}{1146}\right) e(128191)e\left(\frac{128}{191}\right) e(206573)e\left(\frac{206}{573}\right) e(6531146)e\left(\frac{653}{1146}\right) e(479573)e\left(\frac{479}{573}\right)
χ8043(464,)\chi_{8043}(464,\cdot) 1-1 11 e(231146)e\left(\frac{23}{1146}\right) e(23573)e\left(\frac{23}{573}\right) e(3951146)e\left(\frac{395}{1146}\right) e(23382)e\left(\frac{23}{382}\right) e(209573)e\left(\frac{209}{573}\right) e(3011146)e\left(\frac{301}{1146}\right) e(36191)e\left(\frac{36}{191}\right) e(46573)e\left(\frac{46}{573}\right) e(6911146)e\left(\frac{691}{1146}\right) e(463573)e\left(\frac{463}{573}\right)
χ8043(485,)\chi_{8043}(485,\cdot) 1-1 11 e(9831146)e\left(\frac{983}{1146}\right) e(410573)e\left(\frac{410}{573}\right) e(5391146)e\left(\frac{539}{1146}\right) e(219382)e\left(\frac{219}{382}\right) e(188573)e\left(\frac{188}{573}\right) e(1091146)e\left(\frac{109}{1146}\right) e(185191)e\left(\frac{185}{191}\right) e(247573)e\left(\frac{247}{573}\right) e(2351146)e\left(\frac{235}{1146}\right) e(82573)e\left(\frac{82}{573}\right)
χ8043(527,)\chi_{8043}(527,\cdot) 1-1 11 e(1311146)e\left(\frac{131}{1146}\right) e(131573)e\left(\frac{131}{573}\right) e(7551146)e\left(\frac{755}{1146}\right) e(131382)e\left(\frac{131}{382}\right) e(443573)e\left(\frac{443}{573}\right) e(9671146)e\left(\frac{967}{1146}\right) e(122191)e\left(\frac{122}{191}\right) e(262573)e\left(\frac{262}{573}\right) e(6971146)e\left(\frac{697}{1146}\right) e(370573)e\left(\frac{370}{573}\right)
χ8043(536,)\chi_{8043}(536,\cdot) 1-1 11 e(5531146)e\left(\frac{553}{1146}\right) e(553573)e\left(\frac{553}{573}\right) e(3791146)e\left(\frac{379}{1146}\right) e(171382)e\left(\frac{171}{382}\right) e(466573)e\left(\frac{466}{573}\right) e(9591146)e\left(\frac{959}{1146}\right) e(168191)e\left(\frac{168}{191}\right) e(533573)e\left(\frac{533}{573}\right) e(8691146)e\left(\frac{869}{1146}\right) e(569573)e\left(\frac{569}{573}\right)
χ8043(548,)\chi_{8043}(548,\cdot) 1-1 11 e(7791146)e\left(\frac{779}{1146}\right) e(206573)e\left(\frac{206}{573}\right) e(6231146)e\left(\frac{623}{1146}\right) e(15382)e\left(\frac{15}{382}\right) e(128573)e\left(\frac{128}{573}\right) e(3791146)e\left(\frac{379}{1146}\right) e(65191)e\left(\frac{65}{191}\right) e(412573)e\left(\frac{412}{573}\right) e(7331146)e\left(\frac{733}{1146}\right) e(385573)e\left(\frac{385}{573}\right)
χ8043(557,)\chi_{8043}(557,\cdot) 1-1 11 e(7271146)e\left(\frac{727}{1146}\right) e(154573)e\left(\frac{154}{573}\right) e(5771146)e\left(\frac{577}{1146}\right) e(345382)e\left(\frac{345}{382}\right) e(79573)e\left(\frac{79}{573}\right) e(6951146)e\left(\frac{695}{1146}\right) e(158191)e\left(\frac{158}{191}\right) e(308573)e\left(\frac{308}{573}\right) e(8151146)e\left(\frac{815}{1146}\right) e(260573)e\left(\frac{260}{573}\right)
χ8043(569,)\chi_{8043}(569,\cdot) 1-1 11 e(4131146)e\left(\frac{413}{1146}\right) e(413573)e\left(\frac{413}{573}\right) e(1671146)e\left(\frac{167}{1146}\right) e(31382)e\left(\frac{31}{382}\right) e(290573)e\left(\frac{290}{573}\right) e(2231146)e\left(\frac{223}{1146}\right) e(7191)e\left(\frac{7}{191}\right) e(253573)e\left(\frac{253}{573}\right) e(6491146)e\left(\frac{649}{1146}\right) e(541573)e\left(\frac{541}{573}\right)
χ8043(578,)\chi_{8043}(578,\cdot) 1-1 11 e(3251146)e\left(\frac{325}{1146}\right) e(325573)e\left(\frac{325}{573}\right) e(11146)e\left(\frac{1}{1146}\right) e(325382)e\left(\frac{325}{382}\right) e(163573)e\left(\frac{163}{573}\right) e(3171146)e\left(\frac{317}{1146}\right) e(135191)e\left(\frac{135}{191}\right) e(77573)e\left(\frac{77}{573}\right) e(3471146)e\left(\frac{347}{1146}\right) e(65573)e\left(\frac{65}{573}\right)
χ8043(590,)\chi_{8043}(590,\cdot) 1-1 11 e(4431146)e\left(\frac{443}{1146}\right) e(443573)e\left(\frac{443}{573}\right) e(10311146)e\left(\frac{1031}{1146}\right) e(61382)e\left(\frac{61}{382}\right) e(164573)e\left(\frac{164}{573}\right) e(2171146)e\left(\frac{217}{1146}\right) e(137191)e\left(\frac{137}{191}\right) e(313573)e\left(\frac{313}{573}\right) e(2051146)e\left(\frac{205}{1146}\right) e(547573)e\left(\frac{547}{573}\right)