Basic properties
| Modulus: | \(9464\) | |
| Conductor: | \(9464\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 9464.is
\(\chi_{9464}(291,\cdot)\) \(\chi_{9464}(499,\cdot)\) \(\chi_{9464}(515,\cdot)\) \(\chi_{9464}(723,\cdot)\) \(\chi_{9464}(1019,\cdot)\) \(\chi_{9464}(1227,\cdot)\) \(\chi_{9464}(1243,\cdot)\) \(\chi_{9464}(1747,\cdot)\) \(\chi_{9464}(1955,\cdot)\) \(\chi_{9464}(1971,\cdot)\) \(\chi_{9464}(2179,\cdot)\) \(\chi_{9464}(2475,\cdot)\) \(\chi_{9464}(2683,\cdot)\) \(\chi_{9464}(2699,\cdot)\) \(\chi_{9464}(2907,\cdot)\) \(\chi_{9464}(3203,\cdot)\) \(\chi_{9464}(3411,\cdot)\) \(\chi_{9464}(3427,\cdot)\) \(\chi_{9464}(3635,\cdot)\) \(\chi_{9464}(3931,\cdot)\) \(\chi_{9464}(4139,\cdot)\) \(\chi_{9464}(4363,\cdot)\) \(\chi_{9464}(4659,\cdot)\) \(\chi_{9464}(4867,\cdot)\) \(\chi_{9464}(4883,\cdot)\) \(\chi_{9464}(5091,\cdot)\) \(\chi_{9464}(5387,\cdot)\) \(\chi_{9464}(5595,\cdot)\) \(\chi_{9464}(5611,\cdot)\) \(\chi_{9464}(5819,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2367,4733,2705,9297)\) → \((-1,-1,e\left(\frac{2}{3}\right),e\left(\frac{47}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 9464 }(291, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) |