Basic properties
| Modulus: | \(2695\) | |
| Conductor: | \(2695\) | 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 2695.cx
\(\chi_{2695}(139,\cdot)\) \(\chi_{2695}(314,\cdot)\) \(\chi_{2695}(349,\cdot)\) \(\chi_{2695}(524,\cdot)\) \(\chi_{2695}(629,\cdot)\) \(\chi_{2695}(699,\cdot)\) \(\chi_{2695}(909,\cdot)\) \(\chi_{2695}(1014,\cdot)\) \(\chi_{2695}(1084,\cdot)\) \(\chi_{2695}(1119,\cdot)\) \(\chi_{2695}(1294,\cdot)\) \(\chi_{2695}(1399,\cdot)\) \(\chi_{2695}(1504,\cdot)\) \(\chi_{2695}(1679,\cdot)\) \(\chi_{2695}(1784,\cdot)\) \(\chi_{2695}(1854,\cdot)\) \(\chi_{2695}(1889,\cdot)\) \(\chi_{2695}(2064,\cdot)\) \(\chi_{2695}(2169,\cdot)\) \(\chi_{2695}(2239,\cdot)\) \(\chi_{2695}(2274,\cdot)\) \(\chi_{2695}(2554,\cdot)\) \(\chi_{2695}(2624,\cdot)\) \(\chi_{2695}(2659,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2157,1816,981)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 2695 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) |