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 \(\chi_{4009}(75,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.ee
\(\chi_{8018}(75,\cdot)\) \(\chi_{8018}(303,\cdot)\) \(\chi_{8018}(341,\cdot)\) \(\chi_{8018}(797,\cdot)\) \(\chi_{8018}(835,\cdot)\) \(\chi_{8018}(873,\cdot)\) \(\chi_{8018}(1025,\cdot)\) \(\chi_{8018}(1215,\cdot)\) \(\chi_{8018}(1595,\cdot)\) \(\chi_{8018}(2051,\cdot)\) \(\chi_{8018}(2127,\cdot)\) \(\chi_{8018}(2241,\cdot)\) \(\chi_{8018}(2317,\cdot)\) \(\chi_{8018}(2393,\cdot)\) \(\chi_{8018}(2659,\cdot)\) \(\chi_{8018}(2697,\cdot)\) \(\chi_{8018}(2849,\cdot)\) \(\chi_{8018}(3039,\cdot)\) \(\chi_{8018}(3571,\cdot)\) \(\chi_{8018}(3609,\cdot)\) \(\chi_{8018}(3761,\cdot)\) \(\chi_{8018}(3837,\cdot)\) \(\chi_{8018}(3989,\cdot)\) \(\chi_{8018}(4255,\cdot)\) \(\chi_{8018}(4369,\cdot)\) \(\chi_{8018}(4407,\cdot)\) \(\chi_{8018}(4597,\cdot)\) \(\chi_{8018}(4787,\cdot)\) \(\chi_{8018}(4901,\cdot)\) \(\chi_{8018}(5015,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((-1,e\left(\frac{97}{210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{193}{210}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) |