Basic properties
| Modulus: | \(3675\) | |
| Conductor: | \(3675\) | 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 3675.de
\(\chi_{3675}(8,\cdot)\) \(\chi_{3675}(92,\cdot)\) \(\chi_{3675}(113,\cdot)\) \(\chi_{3675}(302,\cdot)\) \(\chi_{3675}(323,\cdot)\) \(\chi_{3675}(428,\cdot)\) \(\chi_{3675}(512,\cdot)\) \(\chi_{3675}(533,\cdot)\) \(\chi_{3675}(617,\cdot)\) \(\chi_{3675}(722,\cdot)\) \(\chi_{3675}(827,\cdot)\) \(\chi_{3675}(848,\cdot)\) \(\chi_{3675}(953,\cdot)\) \(\chi_{3675}(1037,\cdot)\) \(\chi_{3675}(1058,\cdot)\) \(\chi_{3675}(1142,\cdot)\) \(\chi_{3675}(1163,\cdot)\) \(\chi_{3675}(1247,\cdot)\) \(\chi_{3675}(1352,\cdot)\) \(\chi_{3675}(1478,\cdot)\) \(\chi_{3675}(1562,\cdot)\) \(\chi_{3675}(1583,\cdot)\) \(\chi_{3675}(1688,\cdot)\) \(\chi_{3675}(1772,\cdot)\) \(\chi_{3675}(1877,\cdot)\) \(\chi_{3675}(1898,\cdot)\) \(\chi_{3675}(2003,\cdot)\) \(\chi_{3675}(2087,\cdot)\) \(\chi_{3675}(2192,\cdot)\) \(\chi_{3675}(2213,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((1226,1177,2551)\) → \((-1,e\left(\frac{3}{20}\right),e\left(\frac{6}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 3675 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{19}{140}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{101}{140}\right)\) |