Basic properties
| Modulus: | \(4067\) | |
| Conductor: | \(581\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(123\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{581}(30,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4067.u
\(\chi_{4067}(30,\cdot)\) \(\chi_{4067}(116,\cdot)\) \(\chi_{4067}(177,\cdot)\) \(\chi_{4067}(214,\cdot)\) \(\chi_{4067}(275,\cdot)\) \(\chi_{4067}(312,\cdot)\) \(\chi_{4067}(324,\cdot)\) \(\chi_{4067}(361,\cdot)\) \(\chi_{4067}(373,\cdot)\) \(\chi_{4067}(410,\cdot)\) \(\chi_{4067}(422,\cdot)\) \(\chi_{4067}(459,\cdot)\) \(\chi_{4067}(508,\cdot)\) \(\chi_{4067}(557,\cdot)\) \(\chi_{4067}(606,\cdot)\) \(\chi_{4067}(618,\cdot)\) \(\chi_{4067}(667,\cdot)\) \(\chi_{4067}(704,\cdot)\) \(\chi_{4067}(851,\cdot)\) \(\chi_{4067}(863,\cdot)\) \(\chi_{4067}(900,\cdot)\) \(\chi_{4067}(949,\cdot)\) \(\chi_{4067}(961,\cdot)\) \(\chi_{4067}(1047,\cdot)\) \(\chi_{4067}(1059,\cdot)\) \(\chi_{4067}(1096,\cdot)\) \(\chi_{4067}(1108,\cdot)\) \(\chi_{4067}(1157,\cdot)\) \(\chi_{4067}(1206,\cdot)\) \(\chi_{4067}(1243,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{123})$ |
| Fixed field: | Number field defined by a degree 123 polynomial (not computed) |
Values on generators
\((2159,2990)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{9}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 4067 }(30, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{123}\right)\) | \(e\left(\frac{17}{123}\right)\) | \(e\left(\frac{95}{123}\right)\) | \(e\left(\frac{73}{123}\right)\) | \(e\left(\frac{1}{41}\right)\) | \(e\left(\frac{27}{41}\right)\) | \(e\left(\frac{34}{123}\right)\) | \(e\left(\frac{59}{123}\right)\) | \(e\left(\frac{74}{123}\right)\) | \(e\left(\frac{112}{123}\right)\) |