Basic properties
| Modulus: | \(3675\) | |
| Conductor: | \(3675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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.dj
\(\chi_{3675}(59,\cdot)\) \(\chi_{3675}(89,\cdot)\) \(\chi_{3675}(164,\cdot)\) \(\chi_{3675}(194,\cdot)\) \(\chi_{3675}(269,\cdot)\) \(\chi_{3675}(404,\cdot)\) \(\chi_{3675}(479,\cdot)\) \(\chi_{3675}(584,\cdot)\) \(\chi_{3675}(614,\cdot)\) \(\chi_{3675}(689,\cdot)\) \(\chi_{3675}(719,\cdot)\) \(\chi_{3675}(794,\cdot)\) \(\chi_{3675}(929,\cdot)\) \(\chi_{3675}(1004,\cdot)\) \(\chi_{3675}(1034,\cdot)\) \(\chi_{3675}(1139,\cdot)\) \(\chi_{3675}(1214,\cdot)\) \(\chi_{3675}(1319,\cdot)\) \(\chi_{3675}(1454,\cdot)\) \(\chi_{3675}(1529,\cdot)\) \(\chi_{3675}(1559,\cdot)\) \(\chi_{3675}(1634,\cdot)\) \(\chi_{3675}(1664,\cdot)\) \(\chi_{3675}(1739,\cdot)\) \(\chi_{3675}(1769,\cdot)\) \(\chi_{3675}(2054,\cdot)\) \(\chi_{3675}(2084,\cdot)\) \(\chi_{3675}(2159,\cdot)\) \(\chi_{3675}(2189,\cdot)\) \(\chi_{3675}(2264,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1226,1177,2551)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{13}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 3675 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{101}{105}\right)\) |