Basic properties
| Modulus: | \(4010\) | |
| Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(200\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2005}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4010.bv
\(\chi_{4010}(9,\cdot)\) \(\chi_{4010}(89,\cdot)\) \(\chi_{4010}(109,\cdot)\) \(\chi_{4010}(159,\cdot)\) \(\chi_{4010}(169,\cdot)\) \(\chi_{4010}(229,\cdot)\) \(\chi_{4010}(289,\cdot)\) \(\chi_{4010}(319,\cdot)\) \(\chi_{4010}(399,\cdot)\) \(\chi_{4010}(409,\cdot)\) \(\chi_{4010}(429,\cdot)\) \(\chi_{4010}(459,\cdot)\) \(\chi_{4010}(479,\cdot)\) \(\chi_{4010}(529,\cdot)\) \(\chi_{4010}(539,\cdot)\) \(\chi_{4010}(599,\cdot)\) \(\chi_{4010}(699,\cdot)\) \(\chi_{4010}(729,\cdot)\) \(\chi_{4010}(759,\cdot)\) \(\chi_{4010}(809,\cdot)\) \(\chi_{4010}(849,\cdot)\) \(\chi_{4010}(1049,\cdot)\) \(\chi_{4010}(1059,\cdot)\) \(\chi_{4010}(1159,\cdot)\) \(\chi_{4010}(1239,\cdot)\) \(\chi_{4010}(1369,\cdot)\) \(\chi_{4010}(1379,\cdot)\) \(\chi_{4010}(1389,\cdot)\) \(\chi_{4010}(1429,\cdot)\) \(\chi_{4010}(1549,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{200})$ |
| Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2407,3211)\) → \((-1,e\left(\frac{1}{200}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4010 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{200}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{19}{200}\right)\) | \(e\left(\frac{83}{200}\right)\) | \(e\left(\frac{163}{200}\right)\) | \(e\left(\frac{63}{200}\right)\) | \(e\left(\frac{191}{200}\right)\) | \(e\left(\frac{103}{200}\right)\) |