Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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.dn
\(\chi_{8023}(4,\cdot)\) \(\chi_{8023}(64,\cdot)\) \(\chi_{8023}(876,\cdot)\) \(\chi_{8023}(1815,\cdot)\) \(\chi_{8023}(2006,\cdot)\) \(\chi_{8023}(2493,\cdot)\) \(\chi_{8023}(2663,\cdot)\) \(\chi_{8023}(3134,\cdot)\) \(\chi_{8023}(3281,\cdot)\) \(\chi_{8023}(4358,\cdot)\) \(\chi_{8023}(4391,\cdot)\) \(\chi_{8023}(4492,\cdot)\) \(\chi_{8023}(4942,\cdot)\) \(\chi_{8023}(5408,\cdot)\) \(\chi_{8023}(5541,\cdot)\) \(\chi_{8023}(5544,\cdot)\) \(\chi_{8023}(5973,\cdot)\) \(\chi_{8023}(5993,\cdot)\) \(\chi_{8023}(6298,\cdot)\) \(\chi_{8023}(6448,\cdot)\) \(\chi_{8023}(6865,\cdot)\) \(\chi_{8023}(7315,\cdot)\) \(\chi_{8023}(7329,\cdot)\) \(\chi_{8023}(7635,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{6}{35}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) |