Basic properties
| Modulus: | \(3021\) | |
| Conductor: | \(3021\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3021.cn
\(\chi_{3021}(17,\cdot)\) \(\chi_{3021}(62,\cdot)\) \(\chi_{3021}(131,\cdot)\) \(\chi_{3021}(149,\cdot)\) \(\chi_{3021}(176,\cdot)\) \(\chi_{3021}(188,\cdot)\) \(\chi_{3021}(218,\cdot)\) \(\chi_{3021}(272,\cdot)\) \(\chi_{3021}(290,\cdot)\) \(\chi_{3021}(302,\cdot)\) \(\chi_{3021}(308,\cdot)\) \(\chi_{3021}(329,\cdot)\) \(\chi_{3021}(347,\cdot)\) \(\chi_{3021}(377,\cdot)\) \(\chi_{3021}(461,\cdot)\) \(\chi_{3021}(536,\cdot)\) \(\chi_{3021}(587,\cdot)\) \(\chi_{3021}(674,\cdot)\) \(\chi_{3021}(746,\cdot)\) \(\chi_{3021}(785,\cdot)\) \(\chi_{3021}(833,\cdot)\) \(\chi_{3021}(992,\cdot)\) \(\chi_{3021}(1013,\cdot)\) \(\chi_{3021}(1016,\cdot)\) \(\chi_{3021}(1100,\cdot)\) \(\chi_{3021}(1130,\cdot)\) \(\chi_{3021}(1175,\cdot)\) \(\chi_{3021}(1244,\cdot)\) \(\chi_{3021}(1259,\cdot)\) \(\chi_{3021}(1289,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,1750,2281)\) → \((-1,e\left(\frac{5}{9}\right),e\left(\frac{5}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3021 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{50}{117}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{116}{117}\right)\) |