Basic properties
| Modulus: | \(2695\) | |
| Conductor: | \(2695\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | 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.de
\(\chi_{2695}(8,\cdot)\) \(\chi_{2695}(57,\cdot)\) \(\chi_{2695}(127,\cdot)\) \(\chi_{2695}(162,\cdot)\) \(\chi_{2695}(183,\cdot)\) \(\chi_{2695}(288,\cdot)\) \(\chi_{2695}(337,\cdot)\) \(\chi_{2695}(358,\cdot)\) \(\chi_{2695}(512,\cdot)\) \(\chi_{2695}(547,\cdot)\) \(\chi_{2695}(568,\cdot)\) \(\chi_{2695}(673,\cdot)\) \(\chi_{2695}(722,\cdot)\) \(\chi_{2695}(743,\cdot)\) \(\chi_{2695}(778,\cdot)\) \(\chi_{2695}(827,\cdot)\) \(\chi_{2695}(897,\cdot)\) \(\chi_{2695}(953,\cdot)\) \(\chi_{2695}(1058,\cdot)\) \(\chi_{2695}(1107,\cdot)\) \(\chi_{2695}(1163,\cdot)\) \(\chi_{2695}(1212,\cdot)\) \(\chi_{2695}(1282,\cdot)\) \(\chi_{2695}(1317,\cdot)\) \(\chi_{2695}(1338,\cdot)\) \(\chi_{2695}(1443,\cdot)\) \(\chi_{2695}(1492,\cdot)\) \(\chi_{2695}(1513,\cdot)\) \(\chi_{2695}(1548,\cdot)\) \(\chi_{2695}(1597,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((2157,1816,981)\) → \((-i,e\left(\frac{6}{7}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 2695 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{123}{140}\right)\) |