Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(9295\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | 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 9295.fn
\(\chi_{9295}(4,\cdot)\) \(\chi_{9295}(49,\cdot)\) \(\chi_{9295}(69,\cdot)\) \(\chi_{9295}(114,\cdot)\) \(\chi_{9295}(179,\cdot)\) \(\chi_{9295}(394,\cdot)\) \(\chi_{9295}(504,\cdot)\) \(\chi_{9295}(719,\cdot)\) \(\chi_{9295}(764,\cdot)\) \(\chi_{9295}(784,\cdot)\) \(\chi_{9295}(829,\cdot)\) \(\chi_{9295}(894,\cdot)\) \(\chi_{9295}(1109,\cdot)\) \(\chi_{9295}(1219,\cdot)\) \(\chi_{9295}(1369,\cdot)\) \(\chi_{9295}(1434,\cdot)\) \(\chi_{9295}(1479,\cdot)\) \(\chi_{9295}(1609,\cdot)\) \(\chi_{9295}(1824,\cdot)\) \(\chi_{9295}(1934,\cdot)\) \(\chi_{9295}(2084,\cdot)\) \(\chi_{9295}(2149,\cdot)\) \(\chi_{9295}(2194,\cdot)\) \(\chi_{9295}(2214,\cdot)\) \(\chi_{9295}(2259,\cdot)\) \(\chi_{9295}(2324,\cdot)\) \(\chi_{9295}(2539,\cdot)\) \(\chi_{9295}(2649,\cdot)\) \(\chi_{9295}(2799,\cdot)\) \(\chi_{9295}(2864,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{195}\right)\) | \(e\left(\frac{269}{390}\right)\) | \(e\left(\frac{83}{195}\right)\) | \(e\left(\frac{157}{390}\right)\) | \(e\left(\frac{53}{195}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{74}{195}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{166}{195}\right)\) |