Basic properties
| Modulus: | \(3001\) | |
| Conductor: | \(3001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(375\) | 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 3001.z
\(\chi_{3001}(16,\cdot)\) \(\chi_{3001}(17,\cdot)\) \(\chi_{3001}(30,\cdot)\) \(\chi_{3001}(31,\cdot)\) \(\chi_{3001}(36,\cdot)\) \(\chi_{3001}(91,\cdot)\) \(\chi_{3001}(98,\cdot)\) \(\chi_{3001}(142,\cdot)\) \(\chi_{3001}(176,\cdot)\) \(\chi_{3001}(178,\cdot)\) \(\chi_{3001}(187,\cdot)\) \(\chi_{3001}(213,\cdot)\) \(\chi_{3001}(244,\cdot)\) \(\chi_{3001}(256,\cdot)\) \(\chi_{3001}(289,\cdot)\) \(\chi_{3001}(295,\cdot)\) \(\chi_{3001}(305,\cdot)\) \(\chi_{3001}(309,\cdot)\) \(\chi_{3001}(330,\cdot)\) \(\chi_{3001}(340,\cdot)\) \(\chi_{3001}(341,\cdot)\) \(\chi_{3001}(346,\cdot)\) \(\chi_{3001}(354,\cdot)\) \(\chi_{3001}(388,\cdot)\) \(\chi_{3001}(396,\cdot)\) \(\chi_{3001}(398,\cdot)\) \(\chi_{3001}(408,\cdot)\) \(\chi_{3001}(425,\cdot)\) \(\chi_{3001}(469,\cdot)\) \(\chi_{3001}(480,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 375 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{97}{375}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3001 }(697, a) \) | \(1\) | \(1\) | \(e\left(\frac{298}{375}\right)\) | \(e\left(\frac{23}{125}\right)\) | \(e\left(\frac{221}{375}\right)\) | \(e\left(\frac{18}{125}\right)\) | \(e\left(\frac{367}{375}\right)\) | \(e\left(\frac{58}{125}\right)\) | \(e\left(\frac{48}{125}\right)\) | \(e\left(\frac{46}{125}\right)\) | \(e\left(\frac{352}{375}\right)\) | \(e\left(\frac{16}{25}\right)\) |