Basic properties
| Modulus: | \(1501\) | |
| Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | 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 1501.ck
\(\chi_{1501}(34,\cdot)\) \(\chi_{1501}(60,\cdot)\) \(\chi_{1501}(147,\cdot)\) \(\chi_{1501}(154,\cdot)\) \(\chi_{1501}(186,\cdot)\) \(\chi_{1501}(211,\cdot)\) \(\chi_{1501}(224,\cdot)\) \(\chi_{1501}(300,\cdot)\) \(\chi_{1501}(307,\cdot)\) \(\chi_{1501}(314,\cdot)\) \(\chi_{1501}(319,\cdot)\) \(\chi_{1501}(345,\cdot)\) \(\chi_{1501}(363,\cdot)\) \(\chi_{1501}(364,\cdot)\) \(\chi_{1501}(393,\cdot)\) \(\chi_{1501}(401,\cdot)\) \(\chi_{1501}(402,\cdot)\) \(\chi_{1501}(470,\cdot)\) \(\chi_{1501}(504,\cdot)\) \(\chi_{1501}(509,\cdot)\) \(\chi_{1501}(527,\cdot)\) \(\chi_{1501}(528,\cdot)\) \(\chi_{1501}(534,\cdot)\) \(\chi_{1501}(583,\cdot)\) \(\chi_{1501}(592,\cdot)\) \(\chi_{1501}(675,\cdot)\) \(\chi_{1501}(679,\cdot)\) \(\chi_{1501}(706,\cdot)\) \(\chi_{1501}(717,\cdot)\) \(\chi_{1501}(754,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((1028,951)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1501 }(1188, a) \) | \(1\) | \(1\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{34}{117}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{106}{117}\right)\) | \(e\left(\frac{67}{234}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{68}{117}\right)\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{8}{39}\right)\) |