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.ct
\(\chi_{8023}(49,\cdot)\) \(\chi_{8023}(222,\cdot)\) \(\chi_{8023}(1146,\cdot)\) \(\chi_{8023}(1497,\cdot)\) \(\chi_{8023}(1578,\cdot)\) \(\chi_{8023}(2083,\cdot)\) \(\chi_{8023}(2401,\cdot)\) \(\chi_{8023}(2592,\cdot)\) \(\chi_{8023}(2855,\cdot)\) \(\chi_{8023}(2954,\cdot)\) \(\chi_{8023}(3213,\cdot)\) \(\chi_{8023}(4287,\cdot)\) \(\chi_{8023}(4310,\cdot)\) \(\chi_{8023}(5115,\cdot)\) \(\chi_{8023}(5327,\cdot)\) \(\chi_{8023}(5567,\cdot)\) \(\chi_{8023}(5699,\cdot)\) \(\chi_{8023}(5791,\cdot)\) \(\chi_{8023}(6469,\cdot)\) \(\chi_{8023}(6663,\cdot)\) \(\chi_{8023}(7564,\cdot)\) \(\chi_{8023}(7601,\cdot)\) \(\chi_{8023}(7680,\cdot)\) \(\chi_{8023}(8016,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{1}{35}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) |