Basic properties
| Modulus: | \(8018\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4009}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.dq
\(\chi_{8018}(45,\cdot)\) \(\chi_{8018}(273,\cdot)\) \(\chi_{8018}(653,\cdot)\) \(\chi_{8018}(657,\cdot)\) \(\chi_{8018}(809,\cdot)\) \(\chi_{8018}(1227,\cdot)\) \(\chi_{8018}(1303,\cdot)\) \(\chi_{8018}(1455,\cdot)\) \(\chi_{8018}(1493,\cdot)\) \(\chi_{8018}(1793,\cdot)\) \(\chi_{8018}(2025,\cdot)\) \(\chi_{8018}(2249,\cdot)\) \(\chi_{8018}(2325,\cdot)\) \(\chi_{8018}(2367,\cdot)\) \(\chi_{8018}(2405,\cdot)\) \(\chi_{8018}(2823,\cdot)\) \(\chi_{8018}(2937,\cdot)\) \(\chi_{8018}(3013,\cdot)\) \(\chi_{8018}(3047,\cdot)\) \(\chi_{8018}(3427,\cdot)\) \(\chi_{8018}(3617,\cdot)\) \(\chi_{8018}(3769,\cdot)\) \(\chi_{8018}(3807,\cdot)\) \(\chi_{8018}(4267,\cdot)\) \(\chi_{8018}(4339,\cdot)\) \(\chi_{8018}(4723,\cdot)\) \(\chi_{8018}(4989,\cdot)\) \(\chi_{8018}(5023,\cdot)\) \(\chi_{8018}(5327,\cdot)\) \(\chi_{8018}(5331,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{4}{105}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) |