Basic properties
Modulus: | \(7623\) | |
Conductor: | \(7623\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fb
\(\chi_{7623}(25,\cdot)\) \(\chi_{7623}(58,\cdot)\) \(\chi_{7623}(214,\cdot)\) \(\chi_{7623}(247,\cdot)\) \(\chi_{7623}(466,\cdot)\) \(\chi_{7623}(499,\cdot)\) \(\chi_{7623}(592,\cdot)\) \(\chi_{7623}(625,\cdot)\) \(\chi_{7623}(718,\cdot)\) \(\chi_{7623}(751,\cdot)\) \(\chi_{7623}(907,\cdot)\) \(\chi_{7623}(940,\cdot)\) \(\chi_{7623}(1159,\cdot)\) \(\chi_{7623}(1192,\cdot)\) \(\chi_{7623}(1285,\cdot)\) \(\chi_{7623}(1318,\cdot)\) \(\chi_{7623}(1411,\cdot)\) \(\chi_{7623}(1444,\cdot)\) \(\chi_{7623}(1633,\cdot)\) \(\chi_{7623}(1852,\cdot)\) \(\chi_{7623}(1885,\cdot)\) \(\chi_{7623}(1978,\cdot)\) \(\chi_{7623}(2011,\cdot)\) \(\chi_{7623}(2104,\cdot)\) \(\chi_{7623}(2137,\cdot)\) \(\chi_{7623}(2293,\cdot)\) \(\chi_{7623}(2545,\cdot)\) \(\chi_{7623}(2578,\cdot)\) \(\chi_{7623}(2704,\cdot)\) \(\chi_{7623}(2797,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{48}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(1978, a) \) | \(1\) | \(1\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{41}{165}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{79}{165}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{164}{165}\right)\) |