Basic properties
| Modulus: | \(9295\) | |
| Conductor: | \(9295\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | 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.gb
\(\chi_{9295}(24,\cdot)\) \(\chi_{9295}(84,\cdot)\) \(\chi_{9295}(149,\cdot)\) \(\chi_{9295}(184,\cdot)\) \(\chi_{9295}(189,\cdot)\) \(\chi_{9295}(314,\cdot)\) \(\chi_{9295}(349,\cdot)\) \(\chi_{9295}(409,\cdot)\) \(\chi_{9295}(414,\cdot)\) \(\chi_{9295}(479,\cdot)\) \(\chi_{9295}(514,\cdot)\) \(\chi_{9295}(574,\cdot)\) \(\chi_{9295}(579,\cdot)\) \(\chi_{9295}(644,\cdot)\) \(\chi_{9295}(734,\cdot)\) \(\chi_{9295}(739,\cdot)\) \(\chi_{9295}(799,\cdot)\) \(\chi_{9295}(899,\cdot)\) \(\chi_{9295}(904,\cdot)\) \(\chi_{9295}(964,\cdot)\) \(\chi_{9295}(1029,\cdot)\) \(\chi_{9295}(1064,\cdot)\) \(\chi_{9295}(1124,\cdot)\) \(\chi_{9295}(1129,\cdot)\) \(\chi_{9295}(1194,\cdot)\) \(\chi_{9295}(1229,\cdot)\) \(\chi_{9295}(1289,\cdot)\) \(\chi_{9295}(1294,\cdot)\) \(\chi_{9295}(1359,\cdot)\) \(\chi_{9295}(1449,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{127}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(24, a) \) | \(1\) | \(1\) | \(e\left(\frac{323}{780}\right)\) | \(e\left(\frac{97}{390}\right)\) | \(e\left(\frac{323}{390}\right)\) | \(e\left(\frac{517}{780}\right)\) | \(e\left(\frac{241}{780}\right)\) | \(e\left(\frac{63}{260}\right)\) | \(e\left(\frac{97}{195}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{128}{195}\right)\) |