Basic properties
| Modulus: | \(8020\) | |
| Conductor: | \(8020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(200\) | 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.dt
\(\chi_{8020}(43,\cdot)\) \(\chi_{8020}(47,\cdot)\) \(\chi_{8020}(103,\cdot)\) \(\chi_{8020}(203,\cdot)\) \(\chi_{8020}(247,\cdot)\) \(\chi_{8020}(263,\cdot)\) \(\chi_{8020}(567,\cdot)\) \(\chi_{8020}(643,\cdot)\) \(\chi_{8020}(747,\cdot)\) \(\chi_{8020}(983,\cdot)\) \(\chi_{8020}(1003,\cdot)\) \(\chi_{8020}(1023,\cdot)\) \(\chi_{8020}(1027,\cdot)\) \(\chi_{8020}(1163,\cdot)\) \(\chi_{8020}(1243,\cdot)\) \(\chi_{8020}(1347,\cdot)\) \(\chi_{8020}(1383,\cdot)\) \(\chi_{8020}(1403,\cdot)\) \(\chi_{8020}(1423,\cdot)\) \(\chi_{8020}(1763,\cdot)\) \(\chi_{8020}(1927,\cdot)\) \(\chi_{8020}(1947,\cdot)\) \(\chi_{8020}(2007,\cdot)\) \(\chi_{8020}(2087,\cdot)\) \(\chi_{8020}(2143,\cdot)\) \(\chi_{8020}(2203,\cdot)\) \(\chi_{8020}(2303,\cdot)\) \(\chi_{8020}(2363,\cdot)\) \(\chi_{8020}(2647,\cdot)\) \(\chi_{8020}(2667,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{200})$ |
| Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((4011,6417,7221)\) → \((-1,-i,e\left(\frac{143}{200}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{93}{200}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{67}{200}\right)\) | \(e\left(\frac{119}{200}\right)\) | \(e\left(\frac{109}{200}\right)\) | \(e\left(\frac{9}{200}\right)\) | \(e\left(\frac{163}{200}\right)\) | \(e\left(\frac{79}{200}\right)\) |