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.ft
\(\chi_{9295}(97,\cdot)\) \(\chi_{9295}(163,\cdot)\) \(\chi_{9295}(262,\cdot)\) \(\chi_{9295}(323,\cdot)\) \(\chi_{9295}(388,\cdot)\) \(\chi_{9295}(422,\cdot)\) \(\chi_{9295}(423,\cdot)\) \(\chi_{9295}(487,\cdot)\) \(\chi_{9295}(522,\cdot)\) \(\chi_{9295}(553,\cdot)\) \(\chi_{9295}(652,\cdot)\) \(\chi_{9295}(713,\cdot)\) \(\chi_{9295}(812,\cdot)\) \(\chi_{9295}(878,\cdot)\) \(\chi_{9295}(973,\cdot)\) \(\chi_{9295}(977,\cdot)\) \(\chi_{9295}(1038,\cdot)\) \(\chi_{9295}(1072,\cdot)\) \(\chi_{9295}(1137,\cdot)\) \(\chi_{9295}(1138,\cdot)\) \(\chi_{9295}(1203,\cdot)\) \(\chi_{9295}(1237,\cdot)\) \(\chi_{9295}(1268,\cdot)\) \(\chi_{9295}(1302,\cdot)\) \(\chi_{9295}(1367,\cdot)\) \(\chi_{9295}(1428,\cdot)\) \(\chi_{9295}(1527,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((i,e\left(\frac{3}{5}\right),e\left(\frac{17}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(97, a) \) | \(1\) | \(1\) | \(e\left(\frac{187}{195}\right)\) | \(e\left(\frac{49}{780}\right)\) | \(e\left(\frac{179}{195}\right)\) | \(e\left(\frac{17}{780}\right)\) | \(e\left(\frac{43}{390}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{49}{390}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{163}{195}\right)\) |