Basic properties
| Modulus: | \(7623\) | |
| Conductor: | \(2541\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2541}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fj
\(\chi_{7623}(17,\cdot)\) \(\chi_{7623}(206,\cdot)\) \(\chi_{7623}(332,\cdot)\) \(\chi_{7623}(404,\cdot)\) \(\chi_{7623}(458,\cdot)\) \(\chi_{7623}(530,\cdot)\) \(\chi_{7623}(656,\cdot)\) \(\chi_{7623}(710,\cdot)\) \(\chi_{7623}(899,\cdot)\) \(\chi_{7623}(908,\cdot)\) \(\chi_{7623}(1025,\cdot)\) \(\chi_{7623}(1097,\cdot)\) \(\chi_{7623}(1151,\cdot)\) \(\chi_{7623}(1223,\cdot)\) \(\chi_{7623}(1349,\cdot)\) \(\chi_{7623}(1403,\cdot)\) \(\chi_{7623}(1592,\cdot)\) \(\chi_{7623}(1601,\cdot)\) \(\chi_{7623}(1718,\cdot)\) \(\chi_{7623}(1790,\cdot)\) \(\chi_{7623}(1844,\cdot)\) \(\chi_{7623}(1916,\cdot)\) \(\chi_{7623}(2042,\cdot)\) \(\chi_{7623}(2096,\cdot)\) \(\chi_{7623}(2285,\cdot)\) \(\chi_{7623}(2294,\cdot)\) \(\chi_{7623}(2483,\cdot)\) \(\chi_{7623}(2537,\cdot)\) \(\chi_{7623}(2609,\cdot)\) \(\chi_{7623}(2735,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{49}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 7623 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{47}{55}\right)\) |