Basic properties
| Modulus: | \(3895\) | |
| Conductor: | \(3895\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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.fn
\(\chi_{3895}(69,\cdot)\) \(\chi_{3895}(179,\cdot)\) \(\chi_{3895}(259,\cdot)\) \(\chi_{3895}(274,\cdot)\) \(\chi_{3895}(354,\cdot)\) \(\chi_{3895}(464,\cdot)\) \(\chi_{3895}(544,\cdot)\) \(\chi_{3895}(559,\cdot)\) \(\chi_{3895}(639,\cdot)\) \(\chi_{3895}(749,\cdot)\) \(\chi_{3895}(844,\cdot)\) \(\chi_{3895}(924,\cdot)\) \(\chi_{3895}(1019,\cdot)\) \(\chi_{3895}(1114,\cdot)\) \(\chi_{3895}(1129,\cdot)\) \(\chi_{3895}(1224,\cdot)\) \(\chi_{3895}(1319,\cdot)\) \(\chi_{3895}(1874,\cdot)\) \(\chi_{3895}(2079,\cdot)\) \(\chi_{3895}(2349,\cdot)\) \(\chi_{3895}(2554,\cdot)\) \(\chi_{3895}(3109,\cdot)\) \(\chi_{3895}(3204,\cdot)\) \(\chi_{3895}(3299,\cdot)\) \(\chi_{3895}(3314,\cdot)\) \(\chi_{3895}(3409,\cdot)\) \(\chi_{3895}(3504,\cdot)\) \(\chi_{3895}(3584,\cdot)\) \(\chi_{3895}(3679,\cdot)\) \(\chi_{3895}(3789,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((3117,2871,1236)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{3}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 3895 }(749, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{79}{120}\right)\) |