Basic properties
| Modulus: | \(959\) | |
| Conductor: | \(959\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | 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 959.bb
\(\chi_{959}(6,\cdot)\) \(\chi_{959}(13,\cdot)\) \(\chi_{959}(20,\cdot)\) \(\chi_{959}(27,\cdot)\) \(\chi_{959}(48,\cdot)\) \(\chi_{959}(55,\cdot)\) \(\chi_{959}(62,\cdot)\) \(\chi_{959}(83,\cdot)\) \(\chi_{959}(90,\cdot)\) \(\chi_{959}(97,\cdot)\) \(\chi_{959}(104,\cdot)\) \(\chi_{959}(111,\cdot)\) \(\chi_{959}(125,\cdot)\) \(\chi_{959}(132,\cdot)\) \(\chi_{959}(160,\cdot)\) \(\chi_{959}(188,\cdot)\) \(\chi_{959}(195,\cdot)\) \(\chi_{959}(216,\cdot)\) \(\chi_{959}(223,\cdot)\) \(\chi_{959}(251,\cdot)\) \(\chi_{959}(279,\cdot)\) \(\chi_{959}(286,\cdot)\) \(\chi_{959}(300,\cdot)\) \(\chi_{959}(307,\cdot)\) \(\chi_{959}(314,\cdot)\) \(\chi_{959}(321,\cdot)\) \(\chi_{959}(328,\cdot)\) \(\chi_{959}(349,\cdot)\) \(\chi_{959}(356,\cdot)\) \(\chi_{959}(363,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((549,414)\) → \((-1,e\left(\frac{95}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 959 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{27}{136}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{121}{136}\right)\) | \(e\left(\frac{25}{136}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{23}{136}\right)\) |