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 \(\chi_{847}(558,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fx
\(\chi_{7623}(19,\cdot)\) \(\chi_{7623}(73,\cdot)\) \(\chi_{7623}(145,\cdot)\) \(\chi_{7623}(271,\cdot)\) \(\chi_{7623}(325,\cdot)\) \(\chi_{7623}(514,\cdot)\) \(\chi_{7623}(523,\cdot)\) \(\chi_{7623}(640,\cdot)\) \(\chi_{7623}(712,\cdot)\) \(\chi_{7623}(964,\cdot)\) \(\chi_{7623}(1018,\cdot)\) \(\chi_{7623}(1216,\cdot)\) \(\chi_{7623}(1333,\cdot)\) \(\chi_{7623}(1405,\cdot)\) \(\chi_{7623}(1459,\cdot)\) \(\chi_{7623}(1531,\cdot)\) \(\chi_{7623}(1657,\cdot)\) \(\chi_{7623}(1711,\cdot)\) \(\chi_{7623}(1900,\cdot)\) \(\chi_{7623}(2026,\cdot)\) \(\chi_{7623}(2098,\cdot)\) \(\chi_{7623}(2152,\cdot)\) \(\chi_{7623}(2224,\cdot)\) \(\chi_{7623}(2350,\cdot)\) \(\chi_{7623}(2404,\cdot)\) \(\chi_{7623}(2593,\cdot)\) \(\chi_{7623}(2602,\cdot)\) \(\chi_{7623}(2719,\cdot)\) \(\chi_{7623}(2791,\cdot)\) \(\chi_{7623}(2845,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{43}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 7623 }(1405, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{23}{110}\right)\) |