Properties

Label 100315.m
Modulus 100315100315
Conductor 2006320063
Order 14331433
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100315, base_ring=CyclotomicField(2866))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,2572]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(16,100315))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 100315100315
Conductor: 2006320063
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 14331433
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 20063.e
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(ζ1433)\Q(\zeta_{1433})
Fixed field: Number field defined by a degree 1433 polynomial (not computed)

First 31 of 1432 characters in Galois orbit

Character 1-1 11 22 33 44 66 77 88 99 1111 1212 1313
χ100315(16,)\chi_{100315}(16,\cdot) 11 11 e(3991433)e\left(\frac{399}{1433}\right) e(10801433)e\left(\frac{1080}{1433}\right) e(7981433)e\left(\frac{798}{1433}\right) e(461433)e\left(\frac{46}{1433}\right) e(6801433)e\left(\frac{680}{1433}\right) e(11971433)e\left(\frac{1197}{1433}\right) e(7271433)e\left(\frac{727}{1433}\right) e(7531433)e\left(\frac{753}{1433}\right) e(4451433)e\left(\frac{445}{1433}\right) e(13851433)e\left(\frac{1385}{1433}\right)
χ100315(146,)\chi_{100315}(146,\cdot) 11 11 e(11711433)e\left(\frac{1171}{1433}\right) e(12411433)e\left(\frac{1241}{1433}\right) e(9091433)e\left(\frac{909}{1433}\right) e(9791433)e\left(\frac{979}{1433}\right) e(5161433)e\left(\frac{516}{1433}\right) e(6471433)e\left(\frac{647}{1433}\right) e(10491433)e\left(\frac{1049}{1433}\right) e(9171433)e\left(\frac{917}{1433}\right) e(7171433)e\left(\frac{717}{1433}\right) e(13461433)e\left(\frac{1346}{1433}\right)
χ100315(211,)\chi_{100315}(211,\cdot) 11 11 e(9171433)e\left(\frac{917}{1433}\right) e(6721433)e\left(\frac{672}{1433}\right) e(4011433)e\left(\frac{401}{1433}\right) e(1561433)e\left(\frac{156}{1433}\right) e(10601433)e\left(\frac{1060}{1433}\right) e(13181433)e\left(\frac{1318}{1433}\right) e(13441433)e\left(\frac{1344}{1433}\right) e(3731433)e\left(\frac{373}{1433}\right) e(10731433)e\left(\frac{1073}{1433}\right) e(10211433)e\left(\frac{1021}{1433}\right)
χ100315(256,)\chi_{100315}(256,\cdot) 11 11 e(7981433)e\left(\frac{798}{1433}\right) e(7271433)e\left(\frac{727}{1433}\right) e(1631433)e\left(\frac{163}{1433}\right) e(921433)e\left(\frac{92}{1433}\right) e(13601433)e\left(\frac{1360}{1433}\right) e(9611433)e\left(\frac{961}{1433}\right) e(211433)e\left(\frac{21}{1433}\right) e(731433)e\left(\frac{73}{1433}\right) e(8901433)e\left(\frac{890}{1433}\right) e(13371433)e\left(\frac{1337}{1433}\right)
χ100315(281,)\chi_{100315}(281,\cdot) 11 11 e(9281433)e\left(\frac{928}{1433}\right) e(6911433)e\left(\frac{691}{1433}\right) e(4231433)e\left(\frac{423}{1433}\right) e(1861433)e\left(\frac{186}{1433}\right) e(3821433)e\left(\frac{382}{1433}\right) e(13511433)e\left(\frac{1351}{1433}\right) e(13821433)e\left(\frac{1382}{1433}\right) e(10511433)e\left(\frac{1051}{1433}\right) e(11141433)e\left(\frac{1114}{1433}\right) e(10521433)e\left(\frac{1052}{1433}\right)
χ100315(376,)\chi_{100315}(376,\cdot) 11 11 e(14121433)e\left(\frac{1412}{1433}\right) e(941433)e\left(\frac{94}{1433}\right) e(13911433)e\left(\frac{1391}{1433}\right) e(731433)e\left(\frac{73}{1433}\right) e(6431433)e\left(\frac{643}{1433}\right) e(13701433)e\left(\frac{1370}{1433}\right) e(1881433)e\left(\frac{188}{1433}\right) e(7901433)e\left(\frac{790}{1433}\right) e(521433)e\left(\frac{52}{1433}\right) e(9831433)e\left(\frac{983}{1433}\right)
χ100315(446,)\chi_{100315}(446,\cdot) 11 11 e(251433)e\left(\frac{25}{1433}\right) e(4341433)e\left(\frac{434}{1433}\right) e(501433)e\left(\frac{50}{1433}\right) e(4591433)e\left(\frac{459}{1433}\right) e(8041433)e\left(\frac{804}{1433}\right) e(751433)e\left(\frac{75}{1433}\right) e(8681433)e\left(\frac{868}{1433}\right) e(6291433)e\left(\frac{629}{1433}\right) e(4841433)e\left(\frac{484}{1433}\right) e(3311433)e\left(\frac{331}{1433}\right)
χ100315(696,)\chi_{100315}(696,\cdot) 11 11 e(6521433)e\left(\frac{652}{1433}\right) e(841433)e\left(\frac{84}{1433}\right) e(13041433)e\left(\frac{1304}{1433}\right) e(7361433)e\left(\frac{736}{1433}\right) e(8491433)e\left(\frac{849}{1433}\right) e(5231433)e\left(\frac{523}{1433}\right) e(1681433)e\left(\frac{168}{1433}\right) e(5841433)e\left(\frac{584}{1433}\right) e(13881433)e\left(\frac{1388}{1433}\right) e(6651433)e\left(\frac{665}{1433}\right)
χ100315(726,)\chi_{100315}(726,\cdot) 11 11 e(3881433)e\left(\frac{388}{1433}\right) e(10611433)e\left(\frac{1061}{1433}\right) e(7761433)e\left(\frac{776}{1433}\right) e(161433)e\left(\frac{16}{1433}\right) e(13581433)e\left(\frac{1358}{1433}\right) e(11641433)e\left(\frac{1164}{1433}\right) e(6891433)e\left(\frac{689}{1433}\right) e(751433)e\left(\frac{75}{1433}\right) e(4041433)e\left(\frac{404}{1433}\right) e(13541433)e\left(\frac{1354}{1433}\right)
χ100315(796,)\chi_{100315}(796,\cdot) 11 11 e(7411433)e\left(\frac{741}{1433}\right) e(3681433)e\left(\frac{368}{1433}\right) e(491433)e\left(\frac{49}{1433}\right) e(11091433)e\left(\frac{1109}{1433}\right) e(4441433)e\left(\frac{444}{1433}\right) e(7901433)e\left(\frac{790}{1433}\right) e(7361433)e\left(\frac{736}{1433}\right) e(9891433)e\left(\frac{989}{1433}\right) e(4171433)e\left(\frac{417}{1433}\right) e(5251433)e\left(\frac{525}{1433}\right)
χ100315(891,)\chi_{100315}(891,\cdot) 11 11 e(9101433)e\left(\frac{910}{1433}\right) e(11811433)e\left(\frac{1181}{1433}\right) e(3871433)e\left(\frac{387}{1433}\right) e(6581433)e\left(\frac{658}{1433}\right) e(3191433)e\left(\frac{319}{1433}\right) e(12971433)e\left(\frac{1297}{1433}\right) e(9291433)e\left(\frac{929}{1433}\right) e(11141433)e\left(\frac{1114}{1433}\right) e(1351433)e\left(\frac{135}{1433}\right) e(8711433)e\left(\frac{871}{1433}\right)
χ100315(941,)\chi_{100315}(941,\cdot) 11 11 e(13261433)e\left(\frac{1326}{1433}\right) e(2061433)e\left(\frac{206}{1433}\right) e(12191433)e\left(\frac{1219}{1433}\right) e(991433)e\left(\frac{99}{1433}\right) e(3421433)e\left(\frac{342}{1433}\right) e(11121433)e\left(\frac{1112}{1433}\right) e(4121433)e\left(\frac{412}{1433}\right) e(10911433)e\left(\frac{1091}{1433}\right) e(14251433)e\left(\frac{1425}{1433}\right) e(13921433)e\left(\frac{1392}{1433}\right)
χ100315(971,)\chi_{100315}(971,\cdot) 11 11 e(13411433)e\left(\frac{1341}{1433}\right) e(7531433)e\left(\frac{753}{1433}\right) e(12491433)e\left(\frac{1249}{1433}\right) e(6611433)e\left(\frac{661}{1433}\right) e(11111433)e\left(\frac{1111}{1433}\right) e(11571433)e\left(\frac{1157}{1433}\right) e(731433)e\left(\frac{73}{1433}\right) e(3221433)e\left(\frac{322}{1433}\right) e(5691433)e\left(\frac{569}{1433}\right) e(13041433)e\left(\frac{1304}{1433}\right)
χ100315(981,)\chi_{100315}(981,\cdot) 11 11 e(11071433)e\left(\frac{1107}{1433}\right) e(13911433)e\left(\frac{1391}{1433}\right) e(7811433)e\left(\frac{781}{1433}\right) e(10651433)e\left(\frac{1065}{1433}\right) e(2921433)e\left(\frac{292}{1433}\right) e(4551433)e\left(\frac{455}{1433}\right) e(13491433)e\left(\frac{1349}{1433}\right) e(11411433)e\left(\frac{1141}{1433}\right) e(7391433)e\left(\frac{739}{1433}\right) e(3841433)e\left(\frac{384}{1433}\right)
χ100315(1096,)\chi_{100315}(1096,\cdot) 11 11 e(7231433)e\left(\frac{723}{1433}\right) e(8581433)e\left(\frac{858}{1433}\right) e(131433)e\left(\frac{13}{1433}\right) e(1481433)e\left(\frac{148}{1433}\right) e(3811433)e\left(\frac{381}{1433}\right) e(7361433)e\left(\frac{736}{1433}\right) e(2831433)e\left(\frac{283}{1433}\right) e(10521433)e\left(\frac{1052}{1433}\right) e(8711433)e\left(\frac{871}{1433}\right) e(3441433)e\left(\frac{344}{1433}\right)
χ100315(1201,)\chi_{100315}(1201,\cdot) 11 11 e(8641433)e\left(\frac{864}{1433}\right) e(8411433)e\left(\frac{841}{1433}\right) e(2951433)e\left(\frac{295}{1433}\right) e(2721433)e\left(\frac{272}{1433}\right) e(1581433)e\left(\frac{158}{1433}\right) e(11591433)e\left(\frac{1159}{1433}\right) e(2491433)e\left(\frac{249}{1433}\right) e(12751433)e\left(\frac{1275}{1433}\right) e(11361433)e\left(\frac{1136}{1433}\right) e(901433)e\left(\frac{90}{1433}\right)
χ100315(1226,)\chi_{100315}(1226,\cdot) 11 11 e(3601433)e\left(\frac{360}{1433}\right) e(2311433)e\left(\frac{231}{1433}\right) e(7201433)e\left(\frac{720}{1433}\right) e(5911433)e\left(\frac{591}{1433}\right) e(12601433)e\left(\frac{1260}{1433}\right) e(10801433)e\left(\frac{1080}{1433}\right) e(4621433)e\left(\frac{462}{1433}\right) e(1731433)e\left(\frac{173}{1433}\right) e(9511433)e\left(\frac{951}{1433}\right) e(7541433)e\left(\frac{754}{1433}\right)
χ100315(1301,)\chi_{100315}(1301,\cdot) 11 11 e(3901433)e\left(\frac{390}{1433}\right) e(13251433)e\left(\frac{1325}{1433}\right) e(7801433)e\left(\frac{780}{1433}\right) e(2821433)e\left(\frac{282}{1433}\right) e(13651433)e\left(\frac{1365}{1433}\right) e(11701433)e\left(\frac{1170}{1433}\right) e(12171433)e\left(\frac{1217}{1433}\right) e(681433)e\left(\frac{68}{1433}\right) e(6721433)e\left(\frac{672}{1433}\right) e(5781433)e\left(\frac{578}{1433}\right)
χ100315(1311,)\chi_{100315}(1311,\cdot) 11 11 e(4081433)e\left(\frac{408}{1433}\right) e(8351433)e\left(\frac{835}{1433}\right) e(8161433)e\left(\frac{816}{1433}\right) e(12431433)e\left(\frac{1243}{1433}\right) e(14281433)e\left(\frac{1428}{1433}\right) e(12241433)e\left(\frac{1224}{1433}\right) e(2371433)e\left(\frac{237}{1433}\right) e(51433)e\left(\frac{5}{1433}\right) e(2181433)e\left(\frac{218}{1433}\right) e(7591433)e\left(\frac{759}{1433}\right)
χ100315(1461,)\chi_{100315}(1461,\cdot) 11 11 e(9901433)e\left(\frac{990}{1433}\right) e(2771433)e\left(\frac{277}{1433}\right) e(5471433)e\left(\frac{547}{1433}\right) e(12671433)e\left(\frac{1267}{1433}\right) e(5991433)e\left(\frac{599}{1433}\right) e(1041433)e\left(\frac{104}{1433}\right) e(5541433)e\left(\frac{554}{1433}\right) e(8341433)e\left(\frac{834}{1433}\right) e(8241433)e\left(\frac{824}{1433}\right) e(13571433)e\left(\frac{1357}{1433}\right)
χ100315(1506,)\chi_{100315}(1506,\cdot) 11 11 e(12471433)e\left(\frac{1247}{1433}\right) e(12421433)e\left(\frac{1242}{1433}\right) e(10611433)e\left(\frac{1061}{1433}\right) e(10561433)e\left(\frac{1056}{1433}\right) e(7821433)e\left(\frac{782}{1433}\right) e(8751433)e\left(\frac{875}{1433}\right) e(10511433)e\left(\frac{1051}{1433}\right) e(6511433)e\left(\frac{651}{1433}\right) e(8701433)e\left(\frac{870}{1433}\right) e(5181433)e\left(\frac{518}{1433}\right)
χ100315(1751,)\chi_{100315}(1751,\cdot) 11 11 e(9481433)e\left(\frac{948}{1433}\right) e(4651433)e\left(\frac{465}{1433}\right) e(4631433)e\left(\frac{463}{1433}\right) e(14131433)e\left(\frac{1413}{1433}\right) e(4521433)e\left(\frac{452}{1433}\right) e(14111433)e\left(\frac{1411}{1433}\right) e(9301433)e\left(\frac{930}{1433}\right) e(9811433)e\left(\frac{981}{1433}\right) e(9281433)e\left(\frac{928}{1433}\right) e(4571433)e\left(\frac{457}{1433}\right)
χ100315(1801,)\chi_{100315}(1801,\cdot) 11 11 e(3631433)e\left(\frac{363}{1433}\right) e(6271433)e\left(\frac{627}{1433}\right) e(7261433)e\left(\frac{726}{1433}\right) e(9901433)e\left(\frac{990}{1433}\right) e(5541433)e\left(\frac{554}{1433}\right) e(10891433)e\left(\frac{1089}{1433}\right) e(12541433)e\left(\frac{1254}{1433}\right) e(8791433)e\left(\frac{879}{1433}\right) e(13531433)e\left(\frac{1353}{1433}\right) e(10231433)e\left(\frac{1023}{1433}\right)
χ100315(1826,)\chi_{100315}(1826,\cdot) 11 11 e(12651433)e\left(\frac{1265}{1433}\right) e(7521433)e\left(\frac{752}{1433}\right) e(10971433)e\left(\frac{1097}{1433}\right) e(5841433)e\left(\frac{584}{1433}\right) e(8451433)e\left(\frac{845}{1433}\right) e(9291433)e\left(\frac{929}{1433}\right) e(711433)e\left(\frac{71}{1433}\right) e(5881433)e\left(\frac{588}{1433}\right) e(4161433)e\left(\frac{416}{1433}\right) e(6991433)e\left(\frac{699}{1433}\right)
χ100315(1916,)\chi_{100315}(1916,\cdot) 11 11 e(8861433)e\left(\frac{886}{1433}\right) e(8791433)e\left(\frac{879}{1433}\right) e(3391433)e\left(\frac{339}{1433}\right) e(3321433)e\left(\frac{332}{1433}\right) e(2351433)e\left(\frac{235}{1433}\right) e(12251433)e\left(\frac{1225}{1433}\right) e(3251433)e\left(\frac{325}{1433}\right) e(11981433)e\left(\frac{1198}{1433}\right) e(12181433)e\left(\frac{1218}{1433}\right) e(1521433)e\left(\frac{152}{1433}\right)
χ100315(1981,)\chi_{100315}(1981,\cdot) 11 11 e(8621433)e\left(\frac{862}{1433}\right) e(5771433)e\left(\frac{577}{1433}\right) e(2911433)e\left(\frac{291}{1433}\right) e(61433)e\left(\frac{6}{1433}\right) e(1511433)e\left(\frac{151}{1433}\right) e(11531433)e\left(\frac{1153}{1433}\right) e(11541433)e\left(\frac{1154}{1433}\right) e(12821433)e\left(\frac{1282}{1433}\right) e(8681433)e\left(\frac{868}{1433}\right) e(8661433)e\left(\frac{866}{1433}\right)
χ100315(2086,)\chi_{100315}(2086,\cdot) 11 11 e(11171433)e\left(\frac{1117}{1433}\right) e(12781433)e\left(\frac{1278}{1433}\right) e(8011433)e\left(\frac{801}{1433}\right) e(9621433)e\left(\frac{962}{1433}\right) e(3271433)e\left(\frac{327}{1433}\right) e(4851433)e\left(\frac{485}{1433}\right) e(11231433)e\left(\frac{1123}{1433}\right) e(11061433)e\left(\frac{1106}{1433}\right) e(6461433)e\left(\frac{646}{1433}\right) e(8031433)e\left(\frac{803}{1433}\right)
χ100315(2126,)\chi_{100315}(2126,\cdot) 11 11 e(11231433)e\left(\frac{1123}{1433}\right) e(6371433)e\left(\frac{637}{1433}\right) e(8131433)e\left(\frac{813}{1433}\right) e(3271433)e\left(\frac{327}{1433}\right) e(3481433)e\left(\frac{348}{1433}\right) e(5031433)e\left(\frac{503}{1433}\right) e(12741433)e\left(\frac{1274}{1433}\right) e(10851433)e\left(\frac{1085}{1433}\right) e(171433)e\left(\frac{17}{1433}\right) e(13411433)e\left(\frac{1341}{1433}\right)
χ100315(2166,)\chi_{100315}(2166,\cdot) 11 11 e(2471433)e\left(\frac{247}{1433}\right) e(10781433)e\left(\frac{1078}{1433}\right) e(4941433)e\left(\frac{494}{1433}\right) e(13251433)e\left(\frac{1325}{1433}\right) e(1481433)e\left(\frac{148}{1433}\right) e(7411433)e\left(\frac{741}{1433}\right) e(7231433)e\left(\frac{723}{1433}\right) e(12851433)e\left(\frac{1285}{1433}\right) e(1391433)e\left(\frac{139}{1433}\right) e(1751433)e\left(\frac{175}{1433}\right)
χ100315(2181,)\chi_{100315}(2181,\cdot) 11 11 e(11431433)e\left(\frac{1143}{1433}\right) e(4111433)e\left(\frac{411}{1433}\right) e(8531433)e\left(\frac{853}{1433}\right) e(1211433)e\left(\frac{121}{1433}\right) e(4181433)e\left(\frac{418}{1433}\right) e(5631433)e\left(\frac{563}{1433}\right) e(8221433)e\left(\frac{822}{1433}\right) e(10151433)e\left(\frac{1015}{1433}\right) e(12641433)e\left(\frac{1264}{1433}\right) e(7461433)e\left(\frac{746}{1433}\right)
χ100315(2186,)\chi_{100315}(2186,\cdot) 11 11 e(11271433)e\left(\frac{1127}{1433}\right) e(11651433)e\left(\frac{1165}{1433}\right) e(8211433)e\left(\frac{821}{1433}\right) e(8591433)e\left(\frac{859}{1433}\right) e(3621433)e\left(\frac{362}{1433}\right) e(5151433)e\left(\frac{515}{1433}\right) e(8971433)e\left(\frac{897}{1433}\right) e(10711433)e\left(\frac{1071}{1433}\right) e(5531433)e\left(\frac{553}{1433}\right) e(12221433)e\left(\frac{1222}{1433}\right)