Basic properties
| Modulus: | \(7623\) | |
| Conductor: | \(7623\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | 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 7623.fu
\(\chi_{7623}(20,\cdot)\) \(\chi_{7623}(104,\cdot)\) \(\chi_{7623}(146,\cdot)\) \(\chi_{7623}(335,\cdot)\) \(\chi_{7623}(356,\cdot)\) \(\chi_{7623}(482,\cdot)\) \(\chi_{7623}(587,\cdot)\) \(\chi_{7623}(713,\cdot)\) \(\chi_{7623}(797,\cdot)\) \(\chi_{7623}(839,\cdot)\) \(\chi_{7623}(1028,\cdot)\) \(\chi_{7623}(1175,\cdot)\) \(\chi_{7623}(1280,\cdot)\) \(\chi_{7623}(1301,\cdot)\) \(\chi_{7623}(1406,\cdot)\) \(\chi_{7623}(1490,\cdot)\) \(\chi_{7623}(1532,\cdot)\) \(\chi_{7623}(1742,\cdot)\) \(\chi_{7623}(1868,\cdot)\) \(\chi_{7623}(1973,\cdot)\) \(\chi_{7623}(1994,\cdot)\) \(\chi_{7623}(2099,\cdot)\) \(\chi_{7623}(2183,\cdot)\) \(\chi_{7623}(2225,\cdot)\) \(\chi_{7623}(2414,\cdot)\) \(\chi_{7623}(2435,\cdot)\) \(\chi_{7623}(2561,\cdot)\) \(\chi_{7623}(2666,\cdot)\) \(\chi_{7623}(2687,\cdot)\) \(\chi_{7623}(2876,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),-1,e\left(\frac{19}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 7623 }(146, a) \) | \(1\) | \(1\) | \(e\left(\frac{169}{330}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{152}{165}\right)\) |