Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(560\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.gt
\(\chi_{8023}(55,\cdot)\) \(\chi_{8023}(93,\cdot)\) \(\chi_{8023}(203,\cdot)\) \(\chi_{8023}(209,\cdot)\) \(\chi_{8023}(255,\cdot)\) \(\chi_{8023}(265,\cdot)\) \(\chi_{8023}(269,\cdot)\) \(\chi_{8023}(345,\cdot)\) \(\chi_{8023}(349,\cdot)\) \(\chi_{8023}(366,\cdot)\) \(\chi_{8023}(423,\cdot)\) \(\chi_{8023}(433,\cdot)\) \(\chi_{8023}(447,\cdot)\) \(\chi_{8023}(473,\cdot)\) \(\chi_{8023}(489,\cdot)\) \(\chi_{8023}(528,\cdot)\) \(\chi_{8023}(544,\cdot)\) \(\chi_{8023}(623,\cdot)\) \(\chi_{8023}(635,\cdot)\) \(\chi_{8023}(695,\cdot)\) \(\chi_{8023}(707,\cdot)\) \(\chi_{8023}(788,\cdot)\) \(\chi_{8023}(859,\cdot)\) \(\chi_{8023}(885,\cdot)\) \(\chi_{8023}(958,\cdot)\) \(\chi_{8023}(1007,\cdot)\) \(\chi_{8023}(1022,\cdot)\) \(\chi_{8023}(1041,\cdot)\) \(\chi_{8023}(1050,\cdot)\) \(\chi_{8023}(1055,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{560})$ |
| Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{59}{70}\right),e\left(\frac{45}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{177}{560}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{531}{560}\right)\) | \(e\left(\frac{109}{560}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{177}{280}\right)\) | \(e\left(\frac{463}{560}\right)\) | \(e\left(\frac{241}{280}\right)\) |