Basic properties
| Modulus: | \(2000\) | |
| Conductor: | \(2000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | 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)
|
Galois orbit 2000.ch
\(\chi_{2000}(19,\cdot)\) \(\chi_{2000}(59,\cdot)\) \(\chi_{2000}(139,\cdot)\) \(\chi_{2000}(179,\cdot)\) \(\chi_{2000}(219,\cdot)\) \(\chi_{2000}(259,\cdot)\) \(\chi_{2000}(339,\cdot)\) \(\chi_{2000}(379,\cdot)\) \(\chi_{2000}(419,\cdot)\) \(\chi_{2000}(459,\cdot)\) \(\chi_{2000}(539,\cdot)\) \(\chi_{2000}(579,\cdot)\) \(\chi_{2000}(619,\cdot)\) \(\chi_{2000}(659,\cdot)\) \(\chi_{2000}(739,\cdot)\) \(\chi_{2000}(779,\cdot)\) \(\chi_{2000}(819,\cdot)\) \(\chi_{2000}(859,\cdot)\) \(\chi_{2000}(939,\cdot)\) \(\chi_{2000}(979,\cdot)\) \(\chi_{2000}(1019,\cdot)\) \(\chi_{2000}(1059,\cdot)\) \(\chi_{2000}(1139,\cdot)\) \(\chi_{2000}(1179,\cdot)\) \(\chi_{2000}(1219,\cdot)\) \(\chi_{2000}(1259,\cdot)\) \(\chi_{2000}(1339,\cdot)\) \(\chi_{2000}(1379,\cdot)\) \(\chi_{2000}(1419,\cdot)\) \(\chi_{2000}(1459,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,1377)\) → \((-1,i,e\left(\frac{23}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2000 }(539, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{41}{100}\right)\) |