Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | 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.cs
\(\chi_{8023}(480,\cdot)\) \(\chi_{8023}(593,\cdot)\) \(\chi_{8023}(2064,\cdot)\) \(\chi_{8023}(2968,\cdot)\) \(\chi_{8023}(2987,\cdot)\) \(\chi_{8023}(3533,\cdot)\) \(\chi_{8023}(3646,\cdot)\) \(\chi_{8023}(3891,\cdot)\) \(\chi_{8023}(4456,\cdot)\) \(\chi_{8023}(4569,\cdot)\) \(\chi_{8023}(4762,\cdot)\) \(\chi_{8023}(5666,\cdot)\) \(\chi_{8023}(5756,\cdot)\) \(\chi_{8023}(6231,\cdot)\) \(\chi_{8023}(6324,\cdot)\) \(\chi_{8023}(6344,\cdot)\) \(\chi_{8023}(6660,\cdot)\) \(\chi_{8023}(7034,\cdot)\) \(\chi_{8023}(7225,\cdot)\) \(\chi_{8023}(7228,\cdot)\) \(\chi_{8023}(7338,\cdot)\) \(\chi_{8023}(7793,\cdot)\) \(\chi_{8023}(7906,\cdot)\) \(\chi_{8023}(7938,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{2}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(480, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) |