Basic properties
| Modulus: | \(8020\) | |
| Conductor: | \(8020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(400\) | 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)
|
Galois orbit 8020.ed
\(\chi_{8020}(19,\cdot)\) \(\chi_{8020}(59,\cdot)\) \(\chi_{8020}(79,\cdot)\) \(\chi_{8020}(139,\cdot)\) \(\chi_{8020}(219,\cdot)\) \(\chi_{8020}(279,\cdot)\) \(\chi_{8020}(339,\cdot)\) \(\chi_{8020}(359,\cdot)\) \(\chi_{8020}(439,\cdot)\) \(\chi_{8020}(519,\cdot)\) \(\chi_{8020}(639,\cdot)\) \(\chi_{8020}(659,\cdot)\) \(\chi_{8020}(679,\cdot)\) \(\chi_{8020}(779,\cdot)\) \(\chi_{8020}(799,\cdot)\) \(\chi_{8020}(819,\cdot)\) \(\chi_{8020}(839,\cdot)\) \(\chi_{8020}(899,\cdot)\) \(\chi_{8020}(919,\cdot)\) \(\chi_{8020}(939,\cdot)\) \(\chi_{8020}(1019,\cdot)\) \(\chi_{8020}(1079,\cdot)\) \(\chi_{8020}(1099,\cdot)\) \(\chi_{8020}(1179,\cdot)\) \(\chi_{8020}(1299,\cdot)\) \(\chi_{8020}(1339,\cdot)\) \(\chi_{8020}(1419,\cdot)\) \(\chi_{8020}(1439,\cdot)\) \(\chi_{8020}(1499,\cdot)\) \(\chi_{8020}(1519,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((4011,6417,7221)\) → \((-1,-1,e\left(\frac{163}{400}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{400}\right)\) | \(e\left(\frac{53}{200}\right)\) | \(e\left(\frac{163}{200}\right)\) | \(e\left(\frac{111}{200}\right)\) | \(e\left(\frac{197}{400}\right)\) | \(e\left(\frac{229}{400}\right)\) | \(e\left(\frac{369}{400}\right)\) | \(e\left(\frac{269}{400}\right)\) | \(e\left(\frac{233}{400}\right)\) | \(e\left(\frac{89}{400}\right)\) |