Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1859}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9295.fu
\(\chi_{9295}(6,\cdot)\) \(\chi_{9295}(41,\cdot)\) \(\chi_{9295}(46,\cdot)\) \(\chi_{9295}(106,\cdot)\) \(\chi_{9295}(171,\cdot)\) \(\chi_{9295}(206,\cdot)\) \(\chi_{9295}(266,\cdot)\) \(\chi_{9295}(271,\cdot)\) \(\chi_{9295}(336,\cdot)\) \(\chi_{9295}(371,\cdot)\) \(\chi_{9295}(431,\cdot)\) \(\chi_{9295}(436,\cdot)\) \(\chi_{9295}(501,\cdot)\) \(\chi_{9295}(591,\cdot)\) \(\chi_{9295}(656,\cdot)\) \(\chi_{9295}(721,\cdot)\) \(\chi_{9295}(761,\cdot)\) \(\chi_{9295}(821,\cdot)\) \(\chi_{9295}(886,\cdot)\) \(\chi_{9295}(921,\cdot)\) \(\chi_{9295}(981,\cdot)\) \(\chi_{9295}(986,\cdot)\) \(\chi_{9295}(1051,\cdot)\) \(\chi_{9295}(1086,\cdot)\) \(\chi_{9295}(1146,\cdot)\) \(\chi_{9295}(1151,\cdot)\) \(\chi_{9295}(1216,\cdot)\) \(\chi_{9295}(1306,\cdot)\) \(\chi_{9295}(1311,\cdot)\) \(\chi_{9295}(1436,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{125}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{547}{780}\right)\) | \(e\left(\frac{109}{195}\right)\) | \(e\left(\frac{157}{390}\right)\) | \(e\left(\frac{203}{780}\right)\) | \(e\left(\frac{29}{780}\right)\) | \(e\left(\frac{27}{260}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{157}{195}\right)\) |