Basic properties
| Modulus: | \(2695\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2695.cs
\(\chi_{2695}(6,\cdot)\) \(\chi_{2695}(41,\cdot)\) \(\chi_{2695}(216,\cdot)\) \(\chi_{2695}(321,\cdot)\) \(\chi_{2695}(426,\cdot)\) \(\chi_{2695}(601,\cdot)\) \(\chi_{2695}(706,\cdot)\) \(\chi_{2695}(776,\cdot)\) \(\chi_{2695}(811,\cdot)\) \(\chi_{2695}(986,\cdot)\) \(\chi_{2695}(1091,\cdot)\) \(\chi_{2695}(1161,\cdot)\) \(\chi_{2695}(1196,\cdot)\) \(\chi_{2695}(1476,\cdot)\) \(\chi_{2695}(1546,\cdot)\) \(\chi_{2695}(1581,\cdot)\) \(\chi_{2695}(1756,\cdot)\) \(\chi_{2695}(1931,\cdot)\) \(\chi_{2695}(1966,\cdot)\) \(\chi_{2695}(2141,\cdot)\) \(\chi_{2695}(2246,\cdot)\) \(\chi_{2695}(2316,\cdot)\) \(\chi_{2695}(2526,\cdot)\) \(\chi_{2695}(2631,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2157,1816,981)\) → \((1,e\left(\frac{9}{14}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 2695 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) |