Basic properties
| Modulus: | \(2156\) | |
| Conductor: | \(2156\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2156.cc
\(\chi_{2156}(83,\cdot)\) \(\chi_{2156}(139,\cdot)\) \(\chi_{2156}(167,\cdot)\) \(\chi_{2156}(447,\cdot)\) \(\chi_{2156}(475,\cdot)\) \(\chi_{2156}(503,\cdot)\) \(\chi_{2156}(699,\cdot)\) \(\chi_{2156}(755,\cdot)\) \(\chi_{2156}(811,\cdot)\) \(\chi_{2156}(1007,\cdot)\) \(\chi_{2156}(1063,\cdot)\) \(\chi_{2156}(1091,\cdot)\) \(\chi_{2156}(1119,\cdot)\) \(\chi_{2156}(1315,\cdot)\) \(\chi_{2156}(1399,\cdot)\) \(\chi_{2156}(1427,\cdot)\) \(\chi_{2156}(1623,\cdot)\) \(\chi_{2156}(1679,\cdot)\) \(\chi_{2156}(1707,\cdot)\) \(\chi_{2156}(1735,\cdot)\) \(\chi_{2156}(1931,\cdot)\) \(\chi_{2156}(1987,\cdot)\) \(\chi_{2156}(2015,\cdot)\) \(\chi_{2156}(2043,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,1277,981)\) → \((-1,e\left(\frac{1}{14}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2156 }(811, a) \) | \(-1\) | \(1\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) |