Basic properties
| Modulus: | \(8018\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4009}(417,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.dd
\(\chi_{8018}(417,\cdot)\) \(\chi_{8018}(569,\cdot)\) \(\chi_{8018}(1063,\cdot)\) \(\chi_{8018}(1253,\cdot)\) \(\chi_{8018}(1519,\cdot)\) \(\chi_{8018}(1785,\cdot)\) \(\chi_{8018}(1823,\cdot)\) \(\chi_{8018}(2507,\cdot)\) \(\chi_{8018}(2621,\cdot)\) \(\chi_{8018}(2811,\cdot)\) \(\chi_{8018}(3267,\cdot)\) \(\chi_{8018}(3647,\cdot)\) \(\chi_{8018}(3685,\cdot)\) \(\chi_{8018}(3913,\cdot)\) \(\chi_{8018}(4027,\cdot)\) \(\chi_{8018}(4141,\cdot)\) \(\chi_{8018}(4521,\cdot)\) \(\chi_{8018}(4939,\cdot)\) \(\chi_{8018}(4977,\cdot)\) \(\chi_{8018}(5053,\cdot)\) \(\chi_{8018}(5091,\cdot)\) \(\chi_{8018}(6459,\cdot)\) \(\chi_{8018}(6687,\cdot)\) \(\chi_{8018}(6991,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2111,1901)\) → \((-1,e\left(\frac{9}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(417, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(1\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) |