Basic properties
| Modulus: | \(3895\) | |
| Conductor: | \(3895\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(360\) | 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 3895.ge
\(\chi_{3895}(17,\cdot)\) \(\chi_{3895}(28,\cdot)\) \(\chi_{3895}(47,\cdot)\) \(\chi_{3895}(93,\cdot)\) \(\chi_{3895}(142,\cdot)\) \(\chi_{3895}(218,\cdot)\) \(\chi_{3895}(233,\cdot)\) \(\chi_{3895}(252,\cdot)\) \(\chi_{3895}(253,\cdot)\) \(\chi_{3895}(272,\cdot)\) \(\chi_{3895}(302,\cdot)\) \(\chi_{3895}(347,\cdot)\) \(\chi_{3895}(358,\cdot)\) \(\chi_{3895}(403,\cdot)\) \(\chi_{3895}(423,\cdot)\) \(\chi_{3895}(427,\cdot)\) \(\chi_{3895}(503,\cdot)\) \(\chi_{3895}(557,\cdot)\) \(\chi_{3895}(632,\cdot)\) \(\chi_{3895}(643,\cdot)\) \(\chi_{3895}(662,\cdot)\) \(\chi_{3895}(663,\cdot)\) \(\chi_{3895}(682,\cdot)\) \(\chi_{3895}(708,\cdot)\) \(\chi_{3895}(712,\cdot)\) \(\chi_{3895}(757,\cdot)\) \(\chi_{3895}(833,\cdot)\) \(\chi_{3895}(842,\cdot)\) \(\chi_{3895}(917,\cdot)\) \(\chi_{3895}(937,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{360})$ |
| Fixed field: | Number field defined by a degree 360 polynomial (not computed) |
Values on generators
\((3117,2871,1236)\) → \((-i,e\left(\frac{4}{9}\right),e\left(\frac{39}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 3895 }(1073, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{71}{360}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{251}{360}\right)\) |