Dirichlet character orbit 100315.t

• Label: 100315.t
• Modulus: $100315$
• Conductor: $20063$
• Order: $20062$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$100315$
Conductor:	$20063$
Order:	$20062$
Real:	no
Primitive:	no, induced from 20063.h
Minimal:	yes
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{10031})$
Fixed field:	Number field defined by a degree 20062 polynomial (not computed)

First 31 of 8592 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{100315}(21,\cdot)$	$-1$	$1$	$e\left(\frac{440}{1433}\right)$	$e\left(\frac{9619}{10031}\right)$	$e\left(\frac{880}{1433}\right)$	$e\left(\frac{2668}{10031}\right)$	$e\left(\frac{65}{20062}\right)$	$e\left(\frac{1320}{1433}\right)$	$e\left(\frac{9207}{10031}\right)$	$e\left(\frac{2117}{10031}\right)$	$e\left(\frac{5748}{10031}\right)$	$e\left(\frac{2948}{10031}\right)$
$\chi_{100315}(41,\cdot)$	$-1$	$1$	$e\left(\frac{407}{1433}\right)$	$e\left(\frac{9220}{10031}\right)$	$e\left(\frac{814}{1433}\right)$	$e\left(\frac{2038}{10031}\right)$	$e\left(\frac{8479}{20062}\right)$	$e\left(\frac{1221}{1433}\right)$	$e\left(\frac{8409}{10031}\right)$	$e\left(\frac{7941}{10031}\right)$	$e\left(\frac{4887}{10031}\right)$	$e\left(\frac{2297}{10031}\right)$
$\chi_{100315}(51,\cdot)$	$-1$	$1$	$e\left(\frac{793}{1433}\right)$	$e\left(\frac{3335}{10031}\right)$	$e\left(\frac{153}{1433}\right)$	$e\left(\frac{8886}{10031}\right)$	$e\left(\frac{4465}{20062}\right)$	$e\left(\frac{946}{1433}\right)$	$e\left(\frac{6670}{10031}\right)$	$e\left(\frac{4216}{10031}\right)$	$e\left(\frac{4406}{10031}\right)$	$e\left(\frac{5743}{10031}\right)$
$\chi_{100315}(56,\cdot)$	$-1$	$1$	$e\left(\frac{111}{1433}\right)$	$e\left(\frac{9419}{10031}\right)$	$e\left(\frac{222}{1433}\right)$	$e\left(\frac{165}{10031}\right)$	$e\left(\frac{19769}{20062}\right)$	$e\left(\frac{333}{1433}\right)$	$e\left(\frac{8807}{10031}\right)$	$e\left(\frac{3729}{10031}\right)$	$e\left(\frac{942}{10031}\right)$	$e\left(\frac{6619}{10031}\right)$
$\chi_{100315}(86,\cdot)$	$-1$	$1$	$e\left(\frac{967}{1433}\right)$	$e\left(\frac{9347}{10031}\right)$	$e\left(\frac{501}{1433}\right)$	$e\left(\frac{6085}{10031}\right)$	$e\left(\frac{4393}{20062}\right)$	$e\left(\frac{35}{1433}\right)$	$e\left(\frac{8663}{10031}\right)$	$e\left(\frac{7118}{10031}\right)$	$e\left(\frac{2823}{10031}\right)$	$e\left(\frac{317}{10031}\right)$
$\chi_{100315}(91,\cdot)$	$-1$	$1$	$e\left(\frac{158}{1433}\right)$	$e\left(\frac{9857}{10031}\right)$	$e\left(\frac{316}{1433}\right)$	$e\left(\frac{932}{10031}\right)$	$e\left(\frac{6309}{20062}\right)$	$e\left(\frac{474}{1433}\right)$	$e\left(\frac{9683}{10031}\right)$	$e\left(\frac{9026}{10031}\right)$	$e\left(\frac{2038}{10031}\right)$	$e\left(\frac{6504}{10031}\right)$
$\chi_{100315}(126,\cdot)$	$-1$	$1$	$e\left(\frac{1168}{1433}\right)$	$e\left(\frac{7348}{10031}\right)$	$e\left(\frac{903}{1433}\right)$	$e\left(\frac{5493}{10031}\right)$	$e\left(\frac{9943}{20062}\right)$	$e\left(\frac{638}{1433}\right)$	$e\left(\frac{4665}{10031}\right)$	$e\left(\frac{5776}{10031}\right)$	$e\left(\frac{3638}{10031}\right)$	$e\left(\frac{8972}{10031}\right)$
$\chi_{100315}(131,\cdot)$	$-1$	$1$	$e\left(\frac{891}{1433}\right)$	$e\left(\frac{3608}{10031}\right)$	$e\left(\frac{349}{1433}\right)$	$e\left(\frac{9845}{10031}\right)$	$e\left(\frac{9267}{20062}\right)$	$e\left(\frac{1240}{1433}\right)$	$e\left(\frac{7216}{10031}\right)$	$e\left(\frac{1815}{10031}\right)$	$e\left(\frac{6051}{10031}\right)$	$e\left(\frac{381}{10031}\right)$
$\chi_{100315}(136,\cdot)$	$-1$	$1$	$e\left(\frac{464}{1433}\right)$	$e\left(\frac{3135}{10031}\right)$	$e\left(\frac{928}{1433}\right)$	$e\left(\frac{6383}{10031}\right)$	$e\left(\frac{4107}{20062}\right)$	$e\left(\frac{1392}{1433}\right)$	$e\left(\frac{6270}{10031}\right)$	$e\left(\frac{5828}{10031}\right)$	$e\left(\frac{9631}{10031}\right)$	$e\left(\frac{9414}{10031}\right)$
$\chi_{100315}(161,\cdot)$	$-1$	$1$	$e\left(\frac{1265}{1433}\right)$	$e\left(\frac{3831}{10031}\right)$	$e\left(\frac{1097}{1433}\right)$	$e\left(\frac{2655}{10031}\right)$	$e\left(\frac{18995}{20062}\right)$	$e\left(\frac{929}{1433}\right)$	$e\left(\frac{7662}{10031}\right)$	$e\left(\frac{9848}{10031}\right)$	$e\left(\frac{1479}{10031}\right)$	$e\left(\frac{3460}{10031}\right)$
$\chi_{100315}(181,\cdot)$	$-1$	$1$	$e\left(\frac{1170}{1433}\right)$	$e\left(\frac{3464}{10031}\right)$	$e\left(\frac{907}{1433}\right)$	$e\left(\frac{1623}{10031}\right)$	$e\left(\frac{18639}{20062}\right)$	$e\left(\frac{644}{1433}\right)$	$e\left(\frac{6928}{10031}\right)$	$e\left(\frac{8593}{10031}\right)$	$e\left(\frac{9813}{10031}\right)$	$e\left(\frac{7839}{10031}\right)$
$\chi_{100315}(191,\cdot)$	$-1$	$1$	$e\left(\frac{1329}{1433}\right)$	$e\left(\frac{7080}{10031}\right)$	$e\left(\frac{1225}{1433}\right)$	$e\left(\frac{6352}{10031}\right)$	$e\left(\frac{10667}{20062}\right)$	$e\left(\frac{1121}{1433}\right)$	$e\left(\frac{4129}{10031}\right)$	$e\left(\frac{1115}{10031}\right)$	$e\left(\frac{5624}{10031}\right)$	$e\left(\frac{4462}{10031}\right)$
$\chi_{100315}(206,\cdot)$	$-1$	$1$	$e\left(\frac{883}{1433}\right)$	$e\left(\frac{7680}{10031}\right)$	$e\left(\frac{333}{1433}\right)$	$e\left(\frac{3830}{10031}\right)$	$e\left(\frac{11741}{20062}\right)$	$e\left(\frac{1216}{1433}\right)$	$e\left(\frac{5329}{10031}\right)$	$e\left(\frac{6310}{10031}\right)$	$e\left(\frac{10011}{10031}\right)$	$e\left(\frac{3480}{10031}\right)$
$\chi_{100315}(221,\cdot)$	$-1$	$1$	$e\left(\frac{511}{1433}\right)$	$e\left(\frac{3573}{10031}\right)$	$e\left(\frac{1022}{1433}\right)$	$e\left(\frac{7150}{10031}\right)$	$e\left(\frac{10709}{20062}\right)$	$e\left(\frac{100}{1433}\right)$	$e\left(\frac{7146}{10031}\right)$	$e\left(\frac{1094}{10031}\right)$	$e\left(\frac{696}{10031}\right)$	$e\left(\frac{9299}{10031}\right)$
$\chi_{100315}(231,\cdot)$	$-1$	$1$	$e\left(\frac{270}{1433}\right)$	$e\left(\frac{4437}{10031}\right)$	$e\left(\frac{540}{1433}\right)$	$e\left(\frac{6327}{10031}\right)$	$e\left(\frac{14663}{20062}\right)$	$e\left(\frac{810}{1433}\right)$	$e\left(\frac{8874}{10031}\right)$	$e\left(\frac{550}{10031}\right)$	$e\left(\frac{8217}{10031}\right)$	$e\left(\frac{4675}{10031}\right)$
$\chi_{100315}(236,\cdot)$	$-1$	$1$	$e\left(\frac{142}{1433}\right)$	$e\left(\frac{9403}{10031}\right)$	$e\left(\frac{284}{1433}\right)$	$e\left(\frac{366}{10031}\right)$	$e\left(\frac{14123}{20062}\right)$	$e\left(\frac{426}{1433}\right)$	$e\left(\frac{8775}{10031}\right)$	$e\left(\frac{2253}{10031}\right)$	$e\left(\frac{1360}{10031}\right)$	$e\left(\frac{4104}{10031}\right)$
$\chi_{100315}(246,\cdot)$	$-1$	$1$	$e\left(\frac{1135}{1433}\right)$	$e\left(\frac{6949}{10031}\right)$	$e\left(\frac{837}{1433}\right)$	$e\left(\frac{4863}{10031}\right)$	$e\left(\frac{18357}{20062}\right)$	$e\left(\frac{539}{1433}\right)$	$e\left(\frac{3867}{10031}\right)$	$e\left(\frac{1569}{10031}\right)$	$e\left(\frac{2777}{10031}\right)$	$e\left(\frac{8321}{10031}\right)$
$\chi_{100315}(266,\cdot)$	$-1$	$1$	$e\left(\frac{1104}{1433}\right)$	$e\left(\frac{5532}{10031}\right)$	$e\left(\frac{775}{1433}\right)$	$e\left(\frac{3229}{10031}\right)$	$e\left(\frac{1075}{20062}\right)$	$e\left(\frac{446}{1433}\right)$	$e\left(\frac{1033}{10031}\right)$	$e\left(\frac{8777}{10031}\right)$	$e\left(\frac{926}{10031}\right)$	$e\left(\frac{9403}{10031}\right)$
$\chi_{100315}(311,\cdot)$	$-1$	$1$	$e\left(\frac{824}{1433}\right)$	$e\left(\frac{453}{10031}\right)$	$e\left(\frac{215}{1433}\right)$	$e\left(\frac{6221}{10031}\right)$	$e\left(\frac{13149}{20062}\right)$	$e\left(\frac{1039}{1433}\right)$	$e\left(\frac{906}{10031}\right)$	$e\left(\frac{4173}{10031}\right)$	$e\left(\frac{1958}{10031}\right)$	$e\left(\frac{362}{10031}\right)$
$\chi_{100315}(316,\cdot)$	$-1$	$1$	$e\left(\frac{1383}{1433}\right)$	$e\left(\frac{2522}{10031}\right)$	$e\left(\frac{1333}{1433}\right)$	$e\left(\frac{2172}{10031}\right)$	$e\left(\frac{4715}{20062}\right)$	$e\left(\frac{1283}{1433}\right)$	$e\left(\frac{5044}{10031}\right)$	$e\left(\frac{6957}{10031}\right)$	$e\left(\frac{1822}{10031}\right)$	$e\left(\frac{3964}{10031}\right)$
$\chi_{100315}(326,\cdot)$	$-1$	$1$	$e\left(\frac{409}{1433}\right)$	$e\left(\frac{2470}{10031}\right)$	$e\left(\frac{818}{1433}\right)$	$e\left(\frac{5333}{10031}\right)$	$e\left(\frac{11443}{20062}\right)$	$e\left(\frac{1227}{1433}\right)$	$e\left(\frac{4940}{10031}\right)$	$e\left(\frac{2160}{10031}\right)$	$e\left(\frac{8196}{10031}\right)$	$e\left(\frac{8329}{10031}\right)$
$\chi_{100315}(336,\cdot)$	$-1$	$1$	$e\left(\frac{839}{1433}\right)$	$e\left(\frac{7148}{10031}\right)$	$e\left(\frac{245}{1433}\right)$	$e\left(\frac{2990}{10031}\right)$	$e\left(\frac{9585}{20062}\right)$	$e\left(\frac{1084}{1433}\right)$	$e\left(\frac{4265}{10031}\right)$	$e\left(\frac{7388}{10031}\right)$	$e\left(\frac{8863}{10031}\right)$	$e\left(\frac{2612}{10031}\right)$
$\chi_{100315}(356,\cdot)$	$-1$	$1$	$e\left(\frac{667}{1433}\right)$	$e\left(\frac{5850}{10031}\right)$	$e\left(\frac{1334}{1433}\right)$	$e\left(\frac{488}{10031}\right)$	$e\left(\frac{15487}{20062}\right)$	$e\left(\frac{568}{1433}\right)$	$e\left(\frac{1669}{10031}\right)$	$e\left(\frac{3004}{10031}\right)$	$e\left(\frac{5157}{10031}\right)$	$e\left(\frac{5472}{10031}\right)$
$\chi_{100315}(366,\cdot)$	$-1$	$1$	$e\left(\frac{1248}{1433}\right)$	$e\left(\frac{6752}{10031}\right)$	$e\left(\frac{1063}{1433}\right)$	$e\left(\frac{5457}{10031}\right)$	$e\left(\frac{5265}{20062}\right)$	$e\left(\frac{878}{1433}\right)$	$e\left(\frac{3473}{10031}\right)$	$e\left(\frac{950}{10031}\right)$	$e\left(\frac{4162}{10031}\right)$	$e\left(\frac{8075}{10031}\right)$
$\chi_{100315}(371,\cdot)$	$-1$	$1$	$e\left(\frac{606}{1433}\right)$	$e\left(\frac{9672}{10031}\right)$	$e\left(\frac{1212}{1433}\right)$	$e\left(\frac{3883}{10031}\right)$	$e\left(\frac{2467}{20062}\right)$	$e\left(\frac{385}{1433}\right)$	$e\left(\frac{9313}{10031}\right)$	$e\left(\frac{9514}{10031}\right)$	$e\left(\frac{8125}{10031}\right)$	$e\left(\frac{621}{10031}\right)$
$\chi_{100315}(381,\cdot)$	$-1$	$1$	$e\left(\frac{1048}{1433}\right)$	$e\left(\frac{1077}{10031}\right)$	$e\left(\frac{663}{1433}\right)$	$e\left(\frac{8413}{10031}\right)$	$e\left(\frac{12661}{20062}\right)$	$e\left(\frac{278}{1433}\right)$	$e\left(\frac{2154}{10031}\right)$	$e\left(\frac{1551}{10031}\right)$	$e\left(\frac{5718}{10031}\right)$	$e\left(\frac{8168}{10031}\right)$
$\chi_{100315}(391,\cdot)$	$-1$	$1$	$e\left(\frac{185}{1433}\right)$	$e\left(\frac{7578}{10031}\right)$	$e\left(\frac{370}{1433}\right)$	$e\left(\frac{8873}{10031}\right)$	$e\left(\frac{3333}{20062}\right)$	$e\left(\frac{555}{1433}\right)$	$e\left(\frac{5125}{10031}\right)$	$e\left(\frac{1916}{10031}\right)$	$e\left(\frac{137}{10031}\right)$	$e\left(\frac{6255}{10031}\right)$
$\chi_{100315}(401,\cdot)$	$-1$	$1$	$e\left(\frac{320}{1433}\right)$	$e\left(\frac{6214}{10031}\right)$	$e\left(\frac{640}{1433}\right)$	$e\left(\frac{8454}{10031}\right)$	$e\left(\frac{8515}{20062}\right)$	$e\left(\frac{960}{1433}\right)$	$e\left(\frac{2397}{10031}\right)$	$e\left(\frac{6490}{10031}\right)$	$e\left(\frac{663}{10031}\right)$	$e\left(\frac{5010}{10031}\right)$
$\chi_{100315}(421,\cdot)$	$-1$	$1$	$e\left(\frac{810}{1433}\right)$	$e\left(\frac{4713}{10031}\right)$	$e\left(\frac{187}{1433}\right)$	$e\left(\frac{352}{10031}\right)$	$e\left(\frac{6731}{20062}\right)$	$e\left(\frac{997}{1433}\right)$	$e\left(\frac{9426}{10031}\right)$	$e\left(\frac{5949}{10031}\right)$	$e\left(\frac{6022}{10031}\right)$	$e\left(\frac{5427}{10031}\right)$
$\chi_{100315}(451,\cdot)$	$-1$	$1$	$e\left(\frac{237}{1433}\right)$	$e\left(\frac{4038}{10031}\right)$	$e\left(\frac{474}{1433}\right)$	$e\left(\frac{5697}{10031}\right)$	$e\left(\frac{3015}{20062}\right)$	$e\left(\frac{711}{1433}\right)$	$e\left(\frac{8076}{10031}\right)$	$e\left(\frac{6374}{10031}\right)$	$e\left(\frac{7356}{10031}\right)$	$e\left(\frac{4024}{10031}\right)$
$\chi_{100315}(461,\cdot)$	$-1$	$1$	$e\left(\frac{1198}{1433}\right)$	$e\left(\frac{4975}{10031}\right)$	$e\left(\frac{963}{1433}\right)$	$e\left(\frac{3330}{10031}\right)$	$e\left(\frac{11413}{20062}\right)$	$e\left(\frac{728}{1433}\right)$	$e\left(\frac{9950}{10031}\right)$	$e\left(\frac{5041}{10031}\right)$	$e\left(\frac{1685}{10031}\right)$	$e\left(\frac{7740}{10031}\right)$