from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(280))
M = H._module
chi = DirichletCharacter(H, M([232,35]))
chi.galois_orbit()
[g,chi] = znchar(Mod(18,8023))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(280\) | 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: | $\Q(\zeta_{280})$ |
| Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8023}(18,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{187}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{39}{280}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{13}{280}\right)\) | \(e\left(\frac{131}{140}\right)\) |
| \(\chi_{8023}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{271}{280}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{67}{280}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{209}{280}\right)\) | \(e\left(\frac{103}{140}\right)\) |
| \(\chi_{8023}(131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{179}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{223}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{261}{280}\right)\) | \(e\left(\frac{67}{140}\right)\) |
| \(\chi_{8023}(157,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{261}{280}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{17}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{99}{280}\right)\) | \(e\left(\frac{93}{140}\right)\) |
| \(\chi_{8023}(182,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{129}{280}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{253}{280}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{271}{280}\right)\) | \(e\left(\frac{17}{140}\right)\) |
| \(\chi_{8023}(357,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{99}{280}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{103}{280}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{221}{280}\right)\) | \(e\left(\frac{127}{140}\right)\) |
| \(\chi_{8023}(434,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{87}{280}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{99}{280}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{33}{280}\right)\) | \(e\left(\frac{31}{140}\right)\) |
| \(\chi_{8023}(521,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{201}{280}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{277}{280}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{279}{280}\right)\) | \(e\left(\frac{33}{140}\right)\) |
| \(\chi_{8023}(547,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{183}{280}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{131}{280}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{137}{280}\right)\) | \(e\left(\frac{99}{140}\right)\) |
| \(\chi_{8023}(583,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{51}{280}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{87}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{29}{280}\right)\) | \(e\left(\frac{23}{140}\right)\) |
| \(\chi_{8023}(722,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{277}{280}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{209}{280}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{163}{280}\right)\) | \(e\left(\frac{81}{140}\right)\) |
| \(\chi_{8023}(860,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{17}{280}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{29}{280}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{103}{280}\right)\) | \(e\left(\frac{101}{140}\right)\) |
| \(\chi_{8023}(973,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{113}{280}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{207}{280}\right)\) | \(e\left(\frac{29}{140}\right)\) |
| \(\chi_{8023}(1148,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{67}{280}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{279}{280}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{93}{280}\right)\) | \(e\left(\frac{11}{140}\right)\) |
| \(\chi_{8023}(1174,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{13}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{121}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{227}{280}\right)\) | \(e\left(\frac{69}{140}\right)\) |
| \(\chi_{8023}(1225,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{47}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{179}{280}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{153}{280}\right)\) | \(e\left(\frac{131}{140}\right)\) |
| \(\chi_{8023}(1287,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{53}{280}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{41}{280}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{53}{140}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{109}{140}\right)\) |
| \(\chi_{8023}(1338,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{39}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{83}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{121}{280}\right)\) | \(e\left(\frac{67}{140}\right)\) |
| \(\chi_{8023}(1564,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{239}{280}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{243}{280}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{81}{280}\right)\) | \(e\left(\frac{127}{140}\right)\) |
| \(\chi_{8023}(1600,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{83}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{83}{140}\right)\) | \(e\left(\frac{157}{280}\right)\) | \(e\left(\frac{139}{140}\right)\) |
| \(\chi_{8023}(1626,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{69}{280}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{233}{280}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{69}{140}\right)\) | \(e\left(\frac{171}{280}\right)\) | \(e\left(\frac{97}{140}\right)\) |
| \(\chi_{8023}(1651,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{257}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{109}{280}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{223}{280}\right)\) | \(e\left(\frac{61}{140}\right)\) |
| \(\chi_{8023}(1713,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{123}{280}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{111}{280}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{37}{280}\right)\) | \(e\left(\frac{39}{140}\right)\) |
| \(\chi_{8023}(1764,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{249}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{13}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{109}{140}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{137}{140}\right)\) |
| \(\chi_{8023}(1790,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{227}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{169}{280}\right)\) | \(e\left(\frac{23}{140}\right)\) |
| \(\chi_{8023}(1852,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{213}{280}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{280}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{187}{280}\right)\) | \(e\left(\frac{129}{140}\right)\) |
| \(\chi_{8023}(1990,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{169}{280}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{173}{280}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{151}{280}\right)\) | \(e\left(\frac{57}{140}\right)\) |
| \(\chi_{8023}(2052,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{139}{280}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{23}{280}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{101}{280}\right)\) | \(e\left(\frac{27}{140}\right)\) |
| \(\chi_{8023}(2078,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{229}{280}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{193}{280}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{251}{280}\right)\) | \(e\left(\frac{117}{140}\right)\) |
| \(\chi_{8023}(2216,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{121}{280}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{157}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{239}{280}\right)\) | \(e\left(\frac{93}{140}\right)\) |
| \(\chi_{8023}(2278,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{3}{280}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{71}{280}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{117}{280}\right)\) | \(e\left(\frac{59}{140}\right)\) |