Dirichlet character orbit 100315.r

• Label: 100315.r
• Modulus: $100315$
• Conductor: $100315$
• Order: $5732$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$100315$
Conductor:	$100315$
Order:	$5732$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{5732})$
Fixed field:	Number field defined by a degree 5732 polynomial (not computed)

First 31 of 2864 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{100315}(2,\cdot)$	$-1$	$1$	$e\left(\frac{3265}{5732}\right)$	$e\left(\frac{5379}{5732}\right)$	$e\left(\frac{399}{2866}\right)$	$e\left(\frac{728}{1433}\right)$	$e\left(\frac{2113}{5732}\right)$	$e\left(\frac{4063}{5732}\right)$	$e\left(\frac{2513}{2866}\right)$	$e\left(\frac{1263}{1433}\right)$	$e\left(\frac{445}{5732}\right)$	$e\left(\frac{4251}{5732}\right)$
$\chi_{100315}(8,\cdot)$	$-1$	$1$	$e\left(\frac{4063}{5732}\right)$	$e\left(\frac{4673}{5732}\right)$	$e\left(\frac{1197}{2866}\right)$	$e\left(\frac{751}{1433}\right)$	$e\left(\frac{607}{5732}\right)$	$e\left(\frac{725}{5732}\right)$	$e\left(\frac{1807}{2866}\right)$	$e\left(\frac{923}{1433}\right)$	$e\left(\frac{1335}{5732}\right)$	$e\left(\frac{1289}{5732}\right)$
$\chi_{100315}(32,\cdot)$	$-1$	$1$	$e\left(\frac{4861}{5732}\right)$	$e\left(\frac{3967}{5732}\right)$	$e\left(\frac{1995}{2866}\right)$	$e\left(\frac{774}{1433}\right)$	$e\left(\frac{4833}{5732}\right)$	$e\left(\frac{3119}{5732}\right)$	$e\left(\frac{1101}{2866}\right)$	$e\left(\frac{583}{1433}\right)$	$e\left(\frac{2225}{5732}\right)$	$e\left(\frac{4059}{5732}\right)$
$\chi_{100315}(47,\cdot)$	$-1$	$1$	$e\left(\frac{1585}{5732}\right)$	$e\left(\frac{1435}{5732}\right)$	$e\left(\frac{1585}{2866}\right)$	$e\left(\frac{755}{1433}\right)$	$e\left(\frac{1965}{5732}\right)$	$e\left(\frac{4755}{5732}\right)$	$e\left(\frac{1435}{2866}\right)$	$e\left(\frac{1300}{1433}\right)$	$e\left(\frac{4605}{5732}\right)$	$e\left(\frac{2643}{5732}\right)$
$\chi_{100315}(73,\cdot)$	$-1$	$1$	$e\left(\frac{1419}{5732}\right)$	$e\left(\frac{5317}{5732}\right)$	$e\left(\frac{1419}{2866}\right)$	$e\left(\frac{251}{1433}\right)$	$e\left(\frac{5683}{5732}\right)$	$e\left(\frac{4257}{5732}\right)$	$e\left(\frac{2451}{2866}\right)$	$e\left(\frac{1087}{1433}\right)$	$e\left(\frac{2423}{5732}\right)$	$e\left(\frac{1133}{5732}\right)$
$\chi_{100315}(87,\cdot)$	$-1$	$1$	$e\left(\frac{4277}{5732}\right)$	$e\left(\frac{1395}{5732}\right)$	$e\left(\frac{1411}{2866}\right)$	$e\left(\frac{1418}{1433}\right)$	$e\left(\frac{2789}{5732}\right)$	$e\left(\frac{1367}{5732}\right)$	$e\left(\frac{1395}{2866}\right)$	$e\left(\frac{1094}{1433}\right)$	$e\left(\frac{4217}{5732}\right)$	$e\left(\frac{1371}{5732}\right)$
$\chi_{100315}(128,\cdot)$	$-1$	$1$	$e\left(\frac{5659}{5732}\right)$	$e\left(\frac{3261}{5732}\right)$	$e\left(\frac{2793}{2866}\right)$	$e\left(\frac{797}{1433}\right)$	$e\left(\frac{3327}{5732}\right)$	$e\left(\frac{5513}{5732}\right)$	$e\left(\frac{395}{2866}\right)$	$e\left(\frac{243}{1433}\right)$	$e\left(\frac{3115}{5732}\right)$	$e\left(\frac{1097}{5732}\right)$
$\chi_{100315}(137,\cdot)$	$-1$	$1$	$e\left(\frac{4561}{5732}\right)$	$e\left(\frac{4491}{5732}\right)$	$e\left(\frac{1695}{2866}\right)$	$e\left(\frac{830}{1433}\right)$	$e\left(\frac{917}{5732}\right)$	$e\left(\frac{2219}{5732}\right)$	$e\left(\frac{1625}{2866}\right)$	$e\left(\frac{129}{1433}\right)$	$e\left(\frac{2149}{5732}\right)$	$e\left(\frac{87}{5732}\right)$
$\chi_{100315}(188,\cdot)$	$-1$	$1$	$e\left(\frac{2383}{5732}\right)$	$e\left(\frac{729}{5732}\right)$	$e\left(\frac{2383}{2866}\right)$	$e\left(\frac{778}{1433}\right)$	$e\left(\frac{459}{5732}\right)$	$e\left(\frac{1417}{5732}\right)$	$e\left(\frac{729}{2866}\right)$	$e\left(\frac{960}{1433}\right)$	$e\left(\frac{5495}{5732}\right)$	$e\left(\frac{5413}{5732}\right)$
$\chi_{100315}(223,\cdot)$	$-1$	$1$	$e\left(\frac{2567}{5732}\right)$	$e\left(\frac{2089}{5732}\right)$	$e\left(\frac{2567}{2866}\right)$	$e\left(\frac{1164}{1433}\right)$	$e\left(\frac{1103}{5732}\right)$	$e\left(\frac{1969}{5732}\right)$	$e\left(\frac{2089}{2866}\right)$	$e\left(\frac{799}{1433}\right)$	$e\left(\frac{1491}{5732}\right)$	$e\left(\frac{2805}{5732}\right)$
$\chi_{100315}(292,\cdot)$	$-1$	$1$	$e\left(\frac{2217}{5732}\right)$	$e\left(\frac{4611}{5732}\right)$	$e\left(\frac{2217}{2866}\right)$	$e\left(\frac{274}{1433}\right)$	$e\left(\frac{4177}{5732}\right)$	$e\left(\frac{919}{5732}\right)$	$e\left(\frac{1745}{2866}\right)$	$e\left(\frac{747}{1433}\right)$	$e\left(\frac{3313}{5732}\right)$	$e\left(\frac{3903}{5732}\right)$
$\chi_{100315}(317,\cdot)$	$-1$	$1$	$e\left(\frac{905}{5732}\right)$	$e\left(\frac{3387}{5732}\right)$	$e\left(\frac{905}{2866}\right)$	$e\left(\frac{1073}{1433}\right)$	$e\left(\frac{5317}{5732}\right)$	$e\left(\frac{2715}{5732}\right)$	$e\left(\frac{521}{2866}\right)$	$e\left(\frac{462}{1433}\right)$	$e\left(\frac{5197}{5732}\right)$	$e\left(\frac{2811}{5732}\right)$
$\chi_{100315}(348,\cdot)$	$-1$	$1$	$e\left(\frac{5075}{5732}\right)$	$e\left(\frac{689}{5732}\right)$	$e\left(\frac{2209}{2866}\right)$	$e\left(\frac{8}{1433}\right)$	$e\left(\frac{1283}{5732}\right)$	$e\left(\frac{3761}{5732}\right)$	$e\left(\frac{689}{2866}\right)$	$e\left(\frac{754}{1433}\right)$	$e\left(\frac{5107}{5732}\right)$	$e\left(\frac{4141}{5732}\right)$
$\chi_{100315}(357,\cdot)$	$-1$	$1$	$e\left(\frac{5285}{5732}\right)$	$e\left(\frac{2615}{5732}\right)$	$e\left(\frac{2419}{2866}\right)$	$e\left(\frac{542}{1433}\right)$	$e\left(\frac{585}{5732}\right)$	$e\left(\frac{4391}{5732}\right)$	$e\left(\frac{2615}{2866}\right)$	$e\left(\frac{212}{1433}\right)$	$e\left(\frac{1721}{5732}\right)$	$e\left(\frac{43}{5732}\right)$
$\chi_{100315}(363,\cdot)$	$-1$	$1$	$e\left(\frac{4019}{5732}\right)$	$e\left(\frac{4597}{5732}\right)$	$e\left(\frac{1153}{2866}\right)$	$e\left(\frac{721}{1433}\right)$	$e\left(\frac{3319}{5732}\right)$	$e\left(\frac{593}{5732}\right)$	$e\left(\frac{1731}{2866}\right)$	$e\left(\frac{245}{1433}\right)$	$e\left(\frac{1171}{5732}\right)$	$e\left(\frac{1165}{5732}\right)$
$\chi_{100315}(377,\cdot)$	$-1$	$1$	$e\left(\frac{3149}{5732}\right)$	$e\left(\frac{1531}{5732}\right)$	$e\left(\frac{283}{2866}\right)$	$e\left(\frac{1170}{1433}\right)$	$e\left(\frac{4573}{5732}\right)$	$e\left(\frac{3715}{5732}\right)$	$e\left(\frac{1531}{2866}\right)$	$e\left(\frac{648}{1433}\right)$	$e\left(\frac{2097}{5732}\right)$	$e\left(\frac{3403}{5732}\right)$
$\chi_{100315}(398,\cdot)$	$-1$	$1$	$e\left(\frac{5431}{5732}\right)$	$e\left(\frac{1825}{5732}\right)$	$e\left(\frac{2565}{2866}\right)$	$e\left(\frac{381}{1433}\right)$	$e\left(\frac{5395}{5732}\right)$	$e\left(\frac{4829}{5732}\right)$	$e\left(\frac{1825}{2866}\right)$	$e\left(\frac{1159}{1433}\right)$	$e\left(\frac{1223}{5732}\right)$	$e\left(\frac{3581}{5732}\right)$
$\chi_{100315}(422,\cdot)$	$-1$	$1$	$e\left(\frac{1201}{5732}\right)$	$e\left(\frac{2335}{5732}\right)$	$e\left(\frac{1201}{2866}\right)$	$e\left(\frac{884}{1433}\right)$	$e\left(\frac{621}{5732}\right)$	$e\left(\frac{3603}{5732}\right)$	$e\left(\frac{2335}{2866}\right)$	$e\left(\frac{203}{1433}\right)$	$e\left(\frac{4737}{5732}\right)$	$e\left(\frac{2603}{5732}\right)$
$\chi_{100315}(512,\cdot)$	$-1$	$1$	$e\left(\frac{725}{5732}\right)$	$e\left(\frac{2555}{5732}\right)$	$e\left(\frac{725}{2866}\right)$	$e\left(\frac{820}{1433}\right)$	$e\left(\frac{1821}{5732}\right)$	$e\left(\frac{2175}{5732}\right)$	$e\left(\frac{2555}{2866}\right)$	$e\left(\frac{1336}{1433}\right)$	$e\left(\frac{4005}{5732}\right)$	$e\left(\frac{3867}{5732}\right)$
$\chi_{100315}(548,\cdot)$	$-1$	$1$	$e\left(\frac{5359}{5732}\right)$	$e\left(\frac{3785}{5732}\right)$	$e\left(\frac{2493}{2866}\right)$	$e\left(\frac{853}{1433}\right)$	$e\left(\frac{5143}{5732}\right)$	$e\left(\frac{4613}{5732}\right)$	$e\left(\frac{919}{2866}\right)$	$e\left(\frac{1222}{1433}\right)$	$e\left(\frac{3039}{5732}\right)$	$e\left(\frac{2857}{5732}\right)$
$\chi_{100315}(562,\cdot)$	$-1$	$1$	$e\left(\frac{1245}{5732}\right)$	$e\left(\frac{2411}{5732}\right)$	$e\left(\frac{1245}{2866}\right)$	$e\left(\frac{914}{1433}\right)$	$e\left(\frac{3641}{5732}\right)$	$e\left(\frac{3735}{5732}\right)$	$e\left(\frac{2411}{2866}\right)$	$e\left(\frac{881}{1433}\right)$	$e\left(\frac{4901}{5732}\right)$	$e\left(\frac{2727}{5732}\right)$
$\chi_{100315}(613,\cdot)$	$-1$	$1$	$e\left(\frac{3907}{5732}\right)$	$e\left(\frac{1277}{5732}\right)$	$e\left(\frac{1041}{2866}\right)$	$e\left(\frac{1296}{1433}\right)$	$e\left(\frac{2927}{5732}\right)$	$e\left(\frac{257}{5732}\right)$	$e\left(\frac{1277}{2866}\right)$	$e\left(\frac{343}{1433}\right)$	$e\left(\frac{3359}{5732}\right)$	$e\left(\frac{4497}{5732}\right)$
$\chi_{100315}(627,\cdot)$	$-1$	$1$	$e\left(\frac{3737}{5732}\right)$	$e\left(\frac{4631}{5732}\right)$	$e\left(\frac{871}{2866}\right)$	$e\left(\frac{659}{1433}\right)$	$e\left(\frac{3765}{5732}\right)$	$e\left(\frac{5479}{5732}\right)$	$e\left(\frac{1765}{2866}\right)$	$e\left(\frac{850}{1433}\right)$	$e\left(\frac{641}{5732}\right)$	$e\left(\frac{4539}{5732}\right)$
$\chi_{100315}(697,\cdot)$	$-1$	$1$	$e\left(\frac{5153}{5732}\right)$	$e\left(\frac{2387}{5732}\right)$	$e\left(\frac{2287}{2866}\right)$	$e\left(\frac{452}{1433}\right)$	$e\left(\frac{2989}{5732}\right)$	$e\left(\frac{3995}{5732}\right)$	$e\left(\frac{2387}{2866}\right)$	$e\left(\frac{1044}{1433}\right)$	$e\left(\frac{1229}{5732}\right)$	$e\left(\frac{5403}{5732}\right)$
$\chi_{100315}(752,\cdot)$	$-1$	$1$	$e\left(\frac{3181}{5732}\right)$	$e\left(\frac{23}{5732}\right)$	$e\left(\frac{315}{2866}\right)$	$e\left(\frac{801}{1433}\right)$	$e\left(\frac{4685}{5732}\right)$	$e\left(\frac{3811}{5732}\right)$	$e\left(\frac{23}{2866}\right)$	$e\left(\frac{620}{1433}\right)$	$e\left(\frac{653}{5732}\right)$	$e\left(\frac{2451}{5732}\right)$
$\chi_{100315}(753,\cdot)$	$-1$	$1$	$e\left(\frac{1723}{5732}\right)$	$e\left(\frac{5321}{5732}\right)$	$e\left(\frac{1723}{2866}\right)$	$e\left(\frac{328}{1433}\right)$	$e\left(\frac{1015}{5732}\right)$	$e\left(\frac{5169}{5732}\right)$	$e\left(\frac{2455}{2866}\right)$	$e\left(\frac{821}{1433}\right)$	$e\left(\frac{3035}{5732}\right)$	$e\left(\frac{3553}{5732}\right)$
$\chi_{100315}(877,\cdot)$	$-1$	$1$	$e\left(\frac{3957}{5732}\right)$	$e\left(\frac{5011}{5732}\right)$	$e\left(\frac{1091}{2866}\right)$	$e\left(\frac{809}{1433}\right)$	$e\left(\frac{1669}{5732}\right)$	$e\left(\frac{407}{5732}\right)$	$e\left(\frac{2145}{2866}\right)$	$e\left(\frac{1374}{1433}\right)$	$e\left(\frac{1461}{5732}\right)$	$e\left(\frac{5159}{5732}\right)$
$\chi_{100315}(892,\cdot)$	$-1$	$1$	$e\left(\frac{3365}{5732}\right)$	$e\left(\frac{1383}{5732}\right)$	$e\left(\frac{499}{2866}\right)$	$e\left(\frac{1187}{1433}\right)$	$e\left(\frac{5329}{5732}\right)$	$e\left(\frac{4363}{5732}\right)$	$e\left(\frac{1383}{2866}\right)$	$e\left(\frac{459}{1433}\right)$	$e\left(\frac{2381}{5732}\right)$	$e\left(\frac{5575}{5732}\right)$
$\chi_{100315}(913,\cdot)$	$-1$	$1$	$e\left(\frac{1795}{5732}\right)$	$e\left(\frac{3361}{5732}\right)$	$e\left(\frac{1795}{2866}\right)$	$e\left(\frac{1289}{1433}\right)$	$e\left(\frac{1267}{5732}\right)$	$e\left(\frac{5385}{5732}\right)$	$e\left(\frac{495}{2866}\right)$	$e\left(\frac{758}{1433}\right)$	$e\left(\frac{1219}{5732}\right)$	$e\left(\frac{4277}{5732}\right)$
$\chi_{100315}(917,\cdot)$	$-1$	$1$	$e\left(\frac{5677}{5732}\right)$	$e\left(\frac{2771}{5732}\right)$	$e\left(\frac{2811}{2866}\right)$	$e\left(\frac{679}{1433}\right)$	$e\left(\frac{1957}{5732}\right)$	$e\left(\frac{5567}{5732}\right)$	$e\left(\frac{2771}{2866}\right)$	$e\left(\frac{1302}{1433}\right)$	$e\left(\frac{2661}{5732}\right)$	$e\left(\frac{2711}{5732}\right)$
$\chi_{100315}(958,\cdot)$	$-1$	$1$	$e\left(\frac{279}{5732}\right)$	$e\left(\frac{3869}{5732}\right)$	$e\left(\frac{279}{2866}\right)$	$e\left(\frac{1037}{1433}\right)$	$e\left(\frac{4559}{5732}\right)$	$e\left(\frac{837}{5732}\right)$	$e\left(\frac{1003}{2866}\right)$	$e\left(\frac{1368}{1433}\right)$	$e\left(\frac{4427}{5732}\right)$	$e\left(\frac{2089}{5732}\right)$