Basic properties
| Modulus: | \(8018\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(315\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4009}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.en
\(\chi_{8018}(5,\cdot)\) \(\chi_{8018}(25,\cdot)\) \(\chi_{8018}(169,\cdot)\) \(\chi_{8018}(275,\cdot)\) \(\chi_{8018}(427,\cdot)\) \(\chi_{8018}(435,\cdot)\) \(\chi_{8018}(605,\cdot)\) \(\chi_{8018}(625,\cdot)\) \(\chi_{8018}(709,\cdot)\) \(\chi_{8018}(747,\cdot)\) \(\chi_{8018}(909,\cdot)\) \(\chi_{8018}(1013,\cdot)\) \(\chi_{8018}(1119,\cdot)\) \(\chi_{8018}(1137,\cdot)\) \(\chi_{8018}(1239,\cdot)\) \(\chi_{8018}(1271,\cdot)\) \(\chi_{8018}(1277,\cdot)\) \(\chi_{8018}(1279,\cdot)\) \(\chi_{8018}(1353,\cdot)\) \(\chi_{8018}(1391,\cdot)\) \(\chi_{8018}(1449,\cdot)\) \(\chi_{8018}(1469,\cdot)\) \(\chi_{8018}(1753,\cdot)\) \(\chi_{8018}(1809,\cdot)\) \(\chi_{8018}(1871,\cdot)\) \(\chi_{8018}(1963,\cdot)\) \(\chi_{8018}(1981,\cdot)\) \(\chi_{8018}(2115,\cdot)\) \(\chi_{8018}(2175,\cdot)\) \(\chi_{8018}(2189,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 315 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{22}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{184}{315}\right)\) | \(e\left(\frac{61}{315}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{53}{315}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{302}{315}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{307}{315}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) |