Basic properties
Modulus: | \(959\) | |
Conductor: | \(137\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{137}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 959.ba
\(\chi_{959}(29,\cdot)\) \(\chi_{959}(43,\cdot)\) \(\chi_{959}(57,\cdot)\) \(\chi_{959}(71,\cdot)\) \(\chi_{959}(85,\cdot)\) \(\chi_{959}(92,\cdot)\) \(\chi_{959}(106,\cdot)\) \(\chi_{959}(113,\cdot)\) \(\chi_{959}(134,\cdot)\) \(\chi_{959}(183,\cdot)\) \(\chi_{959}(190,\cdot)\) \(\chi_{959}(204,\cdot)\) \(\chi_{959}(232,\cdot)\) \(\chi_{959}(239,\cdot)\) \(\chi_{959}(253,\cdot)\) \(\chi_{959}(295,\cdot)\) \(\chi_{959}(309,\cdot)\) \(\chi_{959}(316,\cdot)\) \(\chi_{959}(344,\cdot)\) \(\chi_{959}(358,\cdot)\) \(\chi_{959}(365,\cdot)\) \(\chi_{959}(414,\cdot)\) \(\chi_{959}(435,\cdot)\) \(\chi_{959}(442,\cdot)\) \(\chi_{959}(456,\cdot)\) \(\chi_{959}(463,\cdot)\) \(\chi_{959}(477,\cdot)\) \(\chi_{959}(491,\cdot)\) \(\chi_{959}(505,\cdot)\) \(\chi_{959}(519,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{136})$ |
Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((549,414)\) → \((1,e\left(\frac{91}{136}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 959 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{91}{136}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{25}{136}\right)\) | \(e\left(\frac{49}{136}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{7}{136}\right)\) |