Basic properties
| Modulus: | \(1337\) | |
| Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(190\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1337.z
\(\chi_{1337}(13,\cdot)\) \(\chi_{1337}(20,\cdot)\) \(\chi_{1337}(27,\cdot)\) \(\chi_{1337}(34,\cdot)\) \(\chi_{1337}(48,\cdot)\) \(\chi_{1337}(90,\cdot)\) \(\chi_{1337}(97,\cdot)\) \(\chi_{1337}(104,\cdot)\) \(\chi_{1337}(118,\cdot)\) \(\chi_{1337}(195,\cdot)\) \(\chi_{1337}(209,\cdot)\) \(\chi_{1337}(237,\cdot)\) \(\chi_{1337}(251,\cdot)\) \(\chi_{1337}(258,\cdot)\) \(\chi_{1337}(272,\cdot)\) \(\chi_{1337}(293,\cdot)\) \(\chi_{1337}(321,\cdot)\) \(\chi_{1337}(335,\cdot)\) \(\chi_{1337}(349,\cdot)\) \(\chi_{1337}(363,\cdot)\) \(\chi_{1337}(384,\cdot)\) \(\chi_{1337}(391,\cdot)\) \(\chi_{1337}(398,\cdot)\) \(\chi_{1337}(405,\cdot)\) \(\chi_{1337}(433,\cdot)\) \(\chi_{1337}(447,\cdot)\) \(\chi_{1337}(454,\cdot)\) \(\chi_{1337}(461,\cdot)\) \(\chi_{1337}(468,\cdot)\) \(\chi_{1337}(482,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{95})$ |
| Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((192,974)\) → \((-1,e\left(\frac{84}{95}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1337 }(258, a) \) | \(-1\) | \(1\) | \(e\left(\frac{86}{95}\right)\) | \(e\left(\frac{13}{190}\right)\) | \(e\left(\frac{77}{95}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{68}{95}\right)\) | \(e\left(\frac{13}{95}\right)\) | \(e\left(\frac{117}{190}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{167}{190}\right)\) |