Basic properties
| Modulus: | \(8018\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4009}(145,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.el
\(\chi_{8018}(145,\cdot)\) \(\chi_{8018}(259,\cdot)\) \(\chi_{8018}(369,\cdot)\) \(\chi_{8018}(373,\cdot)\) \(\chi_{8018}(563,\cdot)\) \(\chi_{8018}(597,\cdot)\) \(\chi_{8018}(635,\cdot)\) \(\chi_{8018}(749,\cdot)\) \(\chi_{8018}(1323,\cdot)\) \(\chi_{8018}(1357,\cdot)\) \(\chi_{8018}(1399,\cdot)\) \(\chi_{8018}(1589,\cdot)\) \(\chi_{8018}(1855,\cdot)\) \(\chi_{8018}(1893,\cdot)\) \(\chi_{8018}(2007,\cdot)\) \(\chi_{8018}(2041,\cdot)\) \(\chi_{8018}(2117,\cdot)\) \(\chi_{8018}(2535,\cdot)\) \(\chi_{8018}(2687,\cdot)\) \(\chi_{8018}(2691,\cdot)\) \(\chi_{8018}(2995,\cdot)\) \(\chi_{8018}(3029,\cdot)\) \(\chi_{8018}(3295,\cdot)\) \(\chi_{8018}(3679,\cdot)\) \(\chi_{8018}(3751,\cdot)\) \(\chi_{8018}(4211,\cdot)\) \(\chi_{8018}(4249,\cdot)\) \(\chi_{8018}(4401,\cdot)\) \(\chi_{8018}(4591,\cdot)\) \(\chi_{8018}(4971,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{101}{210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) |