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 \(\chi_{847}(368,\cdot)\) | 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
\((848,4357,4600)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{37}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(2062, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{4}{165}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{7}{55}\right)\) |