Basic properties
| Modulus: | \(4025\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(144,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.cs
\(\chi_{4025}(29,\cdot)\) \(\chi_{4025}(64,\cdot)\) \(\chi_{4025}(169,\cdot)\) \(\chi_{4025}(239,\cdot)\) \(\chi_{4025}(519,\cdot)\) \(\chi_{4025}(554,\cdot)\) \(\chi_{4025}(694,\cdot)\) \(\chi_{4025}(729,\cdot)\) \(\chi_{4025}(834,\cdot)\) \(\chi_{4025}(869,\cdot)\) \(\chi_{4025}(1044,\cdot)\) \(\chi_{4025}(1254,\cdot)\) \(\chi_{4025}(1359,\cdot)\) \(\chi_{4025}(1429,\cdot)\) \(\chi_{4025}(1534,\cdot)\) \(\chi_{4025}(1639,\cdot)\) \(\chi_{4025}(1779,\cdot)\) \(\chi_{4025}(2059,\cdot)\) \(\chi_{4025}(2129,\cdot)\) \(\chi_{4025}(2164,\cdot)\) \(\chi_{4025}(2234,\cdot)\) \(\chi_{4025}(2304,\cdot)\) \(\chi_{4025}(2339,\cdot)\) \(\chi_{4025}(2444,\cdot)\) \(\chi_{4025}(2479,\cdot)\) \(\chi_{4025}(2584,\cdot)\) \(\chi_{4025}(2654,\cdot)\) \(\chi_{4025}(2864,\cdot)\) \(\chi_{4025}(2934,\cdot)\) \(\chi_{4025}(2969,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{9}{10}\right),1,e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 4025 }(2444, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) |