Basic properties
| Modulus: | \(7623\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{847}(361,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.ez
\(\chi_{7623}(37,\cdot)\) \(\chi_{7623}(163,\cdot)\) \(\chi_{7623}(235,\cdot)\) \(\chi_{7623}(289,\cdot)\) \(\chi_{7623}(361,\cdot)\) \(\chi_{7623}(478,\cdot)\) \(\chi_{7623}(676,\cdot)\) \(\chi_{7623}(730,\cdot)\) \(\chi_{7623}(982,\cdot)\) \(\chi_{7623}(1054,\cdot)\) \(\chi_{7623}(1171,\cdot)\) \(\chi_{7623}(1180,\cdot)\) \(\chi_{7623}(1369,\cdot)\) \(\chi_{7623}(1423,\cdot)\) \(\chi_{7623}(1549,\cdot)\) \(\chi_{7623}(1621,\cdot)\) \(\chi_{7623}(1675,\cdot)\) \(\chi_{7623}(1747,\cdot)\) \(\chi_{7623}(1864,\cdot)\) \(\chi_{7623}(1873,\cdot)\) \(\chi_{7623}(2062,\cdot)\) \(\chi_{7623}(2116,\cdot)\) \(\chi_{7623}(2242,\cdot)\) \(\chi_{7623}(2314,\cdot)\) \(\chi_{7623}(2368,\cdot)\) \(\chi_{7623}(2440,\cdot)\) \(\chi_{7623}(2557,\cdot)\) \(\chi_{7623}(2566,\cdot)\) \(\chi_{7623}(2755,\cdot)\) \(\chi_{7623}(2809,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{28}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 7623 }(361, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{38}{55}\right)\) |