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.gd
\(\chi_{9295}(37,\cdot)\) \(\chi_{9295}(58,\cdot)\) \(\chi_{9295}(93,\cdot)\) \(\chi_{9295}(102,\cdot)\) \(\chi_{9295}(137,\cdot)\) \(\chi_{9295}(158,\cdot)\) \(\chi_{9295}(202,\cdot)\) \(\chi_{9295}(223,\cdot)\) \(\chi_{9295}(267,\cdot)\) \(\chi_{9295}(383,\cdot)\) \(\chi_{9295}(548,\cdot)\) \(\chi_{9295}(592,\cdot)\) \(\chi_{9295}(643,\cdot)\) \(\chi_{9295}(687,\cdot)\) \(\chi_{9295}(708,\cdot)\) \(\chi_{9295}(752,\cdot)\) \(\chi_{9295}(773,\cdot)\) \(\chi_{9295}(808,\cdot)\) \(\chi_{9295}(817,\cdot)\) \(\chi_{9295}(852,\cdot)\) \(\chi_{9295}(873,\cdot)\) \(\chi_{9295}(917,\cdot)\) \(\chi_{9295}(938,\cdot)\) \(\chi_{9295}(982,\cdot)\) \(\chi_{9295}(1098,\cdot)\) \(\chi_{9295}(1142,\cdot)\) \(\chi_{9295}(1307,\cdot)\) \(\chi_{9295}(1358,\cdot)\) \(\chi_{9295}(1402,\cdot)\) \(\chi_{9295}(1423,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((7437,4226,6931)\) → \((i,e\left(\frac{1}{5}\right),e\left(\frac{151}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 9295 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{390}\right)\) | \(e\left(\frac{293}{780}\right)\) | \(e\left(\frac{163}{195}\right)\) | \(e\left(\frac{619}{780}\right)\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{293}{390}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{131}{195}\right)\) |