Basic properties
| Modulus: | \(4034\) | |
| Conductor: | \(2017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(252\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2017}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4034.bd
\(\chi_{4034}(11,\cdot)\) \(\chi_{4034}(73,\cdot)\) \(\chi_{4034}(81,\cdot)\) \(\chi_{4034}(217,\cdot)\) \(\chi_{4034}(249,\cdot)\) \(\chi_{4034}(285,\cdot)\) \(\chi_{4034}(309,\cdot)\) \(\chi_{4034}(441,\cdot)\) \(\chi_{4034}(499,\cdot)\) \(\chi_{4034}(529,\cdot)\) \(\chi_{4034}(535,\cdot)\) \(\chi_{4034}(639,\cdot)\) \(\chi_{4034}(673,\cdot)\) \(\chi_{4034}(725,\cdot)\) \(\chi_{4034}(789,\cdot)\) \(\chi_{4034}(827,\cdot)\) \(\chi_{4034}(843,\cdot)\) \(\chi_{4034}(869,\cdot)\) \(\chi_{4034}(919,\cdot)\) \(\chi_{4034}(1007,\cdot)\) \(\chi_{4034}(1093,\cdot)\) \(\chi_{4034}(1127,\cdot)\) \(\chi_{4034}(1217,\cdot)\) \(\chi_{4034}(1271,\cdot)\) \(\chi_{4034}(1365,\cdot)\) \(\chi_{4034}(1423,\cdot)\) \(\chi_{4034}(1451,\cdot)\) \(\chi_{4034}(1467,\cdot)\) \(\chi_{4034}(1627,\cdot)\) \(\chi_{4034}(1633,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{252})$ |
| Fixed field: | Number field defined by a degree 252 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{61}{252}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4034 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{61}{252}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{143}{252}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{197}{252}\right)\) | \(e\left(\frac{23}{63}\right)\) |