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.fa
\(\chi_{7623}(4,\cdot)\) \(\chi_{7623}(16,\cdot)\) \(\chi_{7623}(256,\cdot)\) \(\chi_{7623}(268,\cdot)\) \(\chi_{7623}(394,\cdot)\) \(\chi_{7623}(445,\cdot)\) \(\chi_{7623}(520,\cdot)\) \(\chi_{7623}(697,\cdot)\) \(\chi_{7623}(709,\cdot)\) \(\chi_{7623}(823,\cdot)\) \(\chi_{7623}(949,\cdot)\) \(\chi_{7623}(961,\cdot)\) \(\chi_{7623}(1087,\cdot)\) \(\chi_{7623}(1138,\cdot)\) \(\chi_{7623}(1390,\cdot)\) \(\chi_{7623}(1402,\cdot)\) \(\chi_{7623}(1516,\cdot)\) \(\chi_{7623}(1642,\cdot)\) \(\chi_{7623}(1780,\cdot)\) \(\chi_{7623}(1831,\cdot)\) \(\chi_{7623}(1906,\cdot)\) \(\chi_{7623}(2083,\cdot)\) \(\chi_{7623}(2095,\cdot)\) \(\chi_{7623}(2209,\cdot)\) \(\chi_{7623}(2335,\cdot)\) \(\chi_{7623}(2347,\cdot)\) \(\chi_{7623}(2473,\cdot)\) \(\chi_{7623}(2524,\cdot)\) \(\chi_{7623}(2599,\cdot)\) \(\chi_{7623}(2776,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{51}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(2083, a) \) | \(1\) | \(1\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{133}{165}\right)\) |