Basic properties
| Modulus: | \(4018\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(840\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.cl
\(\chi_{4018}(17,\cdot)\) \(\chi_{4018}(47,\cdot)\) \(\chi_{4018}(75,\cdot)\) \(\chi_{4018}(89,\cdot)\) \(\chi_{4018}(101,\cdot)\) \(\chi_{4018}(145,\cdot)\) \(\chi_{4018}(157,\cdot)\) \(\chi_{4018}(171,\cdot)\) \(\chi_{4018}(199,\cdot)\) \(\chi_{4018}(229,\cdot)\) \(\chi_{4018}(257,\cdot)\) \(\chi_{4018}(299,\cdot)\) \(\chi_{4018}(311,\cdot)\) \(\chi_{4018}(339,\cdot)\) \(\chi_{4018}(341,\cdot)\) \(\chi_{4018}(381,\cdot)\) \(\chi_{4018}(395,\cdot)\) \(\chi_{4018}(397,\cdot)\) \(\chi_{4018}(425,\cdot)\) \(\chi_{4018}(439,\cdot)\) \(\chi_{4018}(479,\cdot)\) \(\chi_{4018}(481,\cdot)\) \(\chi_{4018}(507,\cdot)\) \(\chi_{4018}(563,\cdot)\) \(\chi_{4018}(591,\cdot)\) \(\chi_{4018}(593,\cdot)\) \(\chi_{4018}(621,\cdot)\) \(\chi_{4018}(649,\cdot)\) \(\chi_{4018}(663,\cdot)\) \(\chi_{4018}(675,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{840})$ |
| Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{25}{42}\right),e\left(\frac{33}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{239}{840}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{89}{840}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{173}{210}\right)\) |