Basic properties
| Modulus: | \(9025\) | |
| Conductor: | \(9025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(380\) | 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 9025.cg
\(\chi_{9025}(37,\cdot)\) \(\chi_{9025}(113,\cdot)\) \(\chi_{9025}(208,\cdot)\) \(\chi_{9025}(227,\cdot)\) \(\chi_{9025}(303,\cdot)\) \(\chi_{9025}(322,\cdot)\) \(\chi_{9025}(398,\cdot)\) \(\chi_{9025}(417,\cdot)\) \(\chi_{9025}(512,\cdot)\) \(\chi_{9025}(588,\cdot)\) \(\chi_{9025}(683,\cdot)\) \(\chi_{9025}(702,\cdot)\) \(\chi_{9025}(778,\cdot)\) \(\chi_{9025}(797,\cdot)\) \(\chi_{9025}(873,\cdot)\) \(\chi_{9025}(892,\cdot)\) \(\chi_{9025}(987,\cdot)\) \(\chi_{9025}(1063,\cdot)\) \(\chi_{9025}(1158,\cdot)\) \(\chi_{9025}(1177,\cdot)\) \(\chi_{9025}(1253,\cdot)\) \(\chi_{9025}(1272,\cdot)\) \(\chi_{9025}(1348,\cdot)\) \(\chi_{9025}(1367,\cdot)\) \(\chi_{9025}(1462,\cdot)\) \(\chi_{9025}(1538,\cdot)\) \(\chi_{9025}(1633,\cdot)\) \(\chi_{9025}(1652,\cdot)\) \(\chi_{9025}(1728,\cdot)\) \(\chi_{9025}(1747,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{380})$ |
| Fixed field: | Number field defined by a degree 380 polynomial (not computed) |
Values on generators
\((5777,3251)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{5}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 9025 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{221}{380}\right)\) | \(e\left(\frac{167}{380}\right)\) | \(e\left(\frac{31}{190}\right)\) | \(e\left(\frac{2}{95}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{283}{380}\right)\) | \(e\left(\frac{167}{190}\right)\) | \(e\left(\frac{59}{95}\right)\) | \(e\left(\frac{229}{380}\right)\) | \(e\left(\frac{319}{380}\right)\) |