Basic properties
| Modulus: | \(2695\) | |
| Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{245}(12,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2695.da
\(\chi_{2695}(12,\cdot)\) \(\chi_{2695}(122,\cdot)\) \(\chi_{2695}(243,\cdot)\) \(\chi_{2695}(353,\cdot)\) \(\chi_{2695}(397,\cdot)\) \(\chi_{2695}(507,\cdot)\) \(\chi_{2695}(628,\cdot)\) \(\chi_{2695}(738,\cdot)\) \(\chi_{2695}(782,\cdot)\) \(\chi_{2695}(892,\cdot)\) \(\chi_{2695}(1013,\cdot)\) \(\chi_{2695}(1123,\cdot)\) \(\chi_{2695}(1167,\cdot)\) \(\chi_{2695}(1277,\cdot)\) \(\chi_{2695}(1398,\cdot)\) \(\chi_{2695}(1508,\cdot)\) \(\chi_{2695}(1552,\cdot)\) \(\chi_{2695}(1662,\cdot)\) \(\chi_{2695}(1937,\cdot)\) \(\chi_{2695}(2047,\cdot)\) \(\chi_{2695}(2168,\cdot)\) \(\chi_{2695}(2278,\cdot)\) \(\chi_{2695}(2553,\cdot)\) \(\chi_{2695}(2663,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2157,1816,981)\) → \((i,e\left(\frac{11}{42}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 2695 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{67}{84}\right)\) |