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.cr
\(\chi_{2695}(64,\cdot)\) \(\chi_{2695}(169,\cdot)\) \(\chi_{2695}(379,\cdot)\) \(\chi_{2695}(449,\cdot)\) \(\chi_{2695}(554,\cdot)\) \(\chi_{2695}(729,\cdot)\) \(\chi_{2695}(764,\cdot)\) \(\chi_{2695}(939,\cdot)\) \(\chi_{2695}(1114,\cdot)\) \(\chi_{2695}(1149,\cdot)\) \(\chi_{2695}(1219,\cdot)\) \(\chi_{2695}(1499,\cdot)\) \(\chi_{2695}(1534,\cdot)\) \(\chi_{2695}(1604,\cdot)\) \(\chi_{2695}(1709,\cdot)\) \(\chi_{2695}(1884,\cdot)\) \(\chi_{2695}(1919,\cdot)\) \(\chi_{2695}(1989,\cdot)\) \(\chi_{2695}(2094,\cdot)\) \(\chi_{2695}(2269,\cdot)\) \(\chi_{2695}(2374,\cdot)\) \(\chi_{2695}(2479,\cdot)\) \(\chi_{2695}(2654,\cdot)\) \(\chi_{2695}(2689,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2157,1816,981)\) → \((-1,e\left(\frac{5}{7}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 2695 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) |