Basic properties
| Modulus: | \(7623\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{847}(270,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fs
\(\chi_{7623}(46,\cdot)\) \(\chi_{7623}(172,\cdot)\) \(\chi_{7623}(226,\cdot)\) \(\chi_{7623}(415,\cdot)\) \(\chi_{7623}(424,\cdot)\) \(\chi_{7623}(541,\cdot)\) \(\chi_{7623}(613,\cdot)\) \(\chi_{7623}(667,\cdot)\) \(\chi_{7623}(739,\cdot)\) \(\chi_{7623}(865,\cdot)\) \(\chi_{7623}(919,\cdot)\) \(\chi_{7623}(1108,\cdot)\) \(\chi_{7623}(1117,\cdot)\) \(\chi_{7623}(1234,\cdot)\) \(\chi_{7623}(1306,\cdot)\) \(\chi_{7623}(1360,\cdot)\) \(\chi_{7623}(1432,\cdot)\) \(\chi_{7623}(1558,\cdot)\) \(\chi_{7623}(1612,\cdot)\) \(\chi_{7623}(1801,\cdot)\) \(\chi_{7623}(1810,\cdot)\) \(\chi_{7623}(1999,\cdot)\) \(\chi_{7623}(2053,\cdot)\) \(\chi_{7623}(2125,\cdot)\) \(\chi_{7623}(2251,\cdot)\) \(\chi_{7623}(2305,\cdot)\) \(\chi_{7623}(2494,\cdot)\) \(\chi_{7623}(2503,\cdot)\) \(\chi_{7623}(2620,\cdot)\) \(\chi_{7623}(2692,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{9}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 7623 }(1117, a) \) | \(-1\) | \(1\) | \(e\left(\frac{137}{330}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{64}{165}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{12}{55}\right)\) |