Basic properties
| Modulus: | \(667\) | |
| Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | 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 667.t
\(\chi_{667}(5,\cdot)\) \(\chi_{667}(33,\cdot)\) \(\chi_{667}(34,\cdot)\) \(\chi_{667}(38,\cdot)\) \(\chi_{667}(42,\cdot)\) \(\chi_{667}(51,\cdot)\) \(\chi_{667}(63,\cdot)\) \(\chi_{667}(67,\cdot)\) \(\chi_{667}(80,\cdot)\) \(\chi_{667}(109,\cdot)\) \(\chi_{667}(120,\cdot)\) \(\chi_{667}(122,\cdot)\) \(\chi_{667}(125,\cdot)\) \(\chi_{667}(129,\cdot)\) \(\chi_{667}(149,\cdot)\) \(\chi_{667}(158,\cdot)\) \(\chi_{667}(178,\cdot)\) \(\chi_{667}(180,\cdot)\) \(\chi_{667}(212,\cdot)\) \(\chi_{667}(237,\cdot)\) \(\chi_{667}(241,\cdot)\) \(\chi_{667}(245,\cdot)\) \(\chi_{667}(267,\cdot)\) \(\chi_{667}(270,\cdot)\) \(\chi_{667}(274,\cdot)\) \(\chi_{667}(283,\cdot)\) \(\chi_{667}(295,\cdot)\) \(\chi_{667}(296,\cdot)\) \(\chi_{667}(332,\cdot)\) \(\chi_{667}(341,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((465,553)\) → \((e\left(\frac{9}{22}\right),e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 667 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{73}{154}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{73}{77}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{25}{77}\right)\) |