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 \(\chi_{2541}(152,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fr
\(\chi_{7623}(26,\cdot)\) \(\chi_{7623}(80,\cdot)\) \(\chi_{7623}(152,\cdot)\) \(\chi_{7623}(278,\cdot)\) \(\chi_{7623}(467,\cdot)\) \(\chi_{7623}(521,\cdot)\) \(\chi_{7623}(647,\cdot)\) \(\chi_{7623}(719,\cdot)\) \(\chi_{7623}(773,\cdot)\) \(\chi_{7623}(845,\cdot)\) \(\chi_{7623}(962,\cdot)\) \(\chi_{7623}(1160,\cdot)\) \(\chi_{7623}(1214,\cdot)\) \(\chi_{7623}(1466,\cdot)\) \(\chi_{7623}(1538,\cdot)\) \(\chi_{7623}(1655,\cdot)\) \(\chi_{7623}(1664,\cdot)\) \(\chi_{7623}(1853,\cdot)\) \(\chi_{7623}(1907,\cdot)\) \(\chi_{7623}(2033,\cdot)\) \(\chi_{7623}(2105,\cdot)\) \(\chi_{7623}(2159,\cdot)\) \(\chi_{7623}(2231,\cdot)\) \(\chi_{7623}(2348,\cdot)\) \(\chi_{7623}(2357,\cdot)\) \(\chi_{7623}(2546,\cdot)\) \(\chi_{7623}(2600,\cdot)\) \(\chi_{7623}(2726,\cdot)\) \(\chi_{7623}(2798,\cdot)\) \(\chi_{7623}(2852,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{43}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 7623 }(152, a) \) | \(1\) | \(1\) | \(e\left(\frac{313}{330}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{131}{165}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{23}{55}\right)\) |