Basic properties
Modulus: | \(7623\) | |
Conductor: | \(2541\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2541}(2312,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fk
\(\chi_{7623}(107,\cdot)\) \(\chi_{7623}(116,\cdot)\) \(\chi_{7623}(305,\cdot)\) \(\chi_{7623}(359,\cdot)\) \(\chi_{7623}(431,\cdot)\) \(\chi_{7623}(557,\cdot)\) \(\chi_{7623}(611,\cdot)\) \(\chi_{7623}(800,\cdot)\) \(\chi_{7623}(809,\cdot)\) \(\chi_{7623}(926,\cdot)\) \(\chi_{7623}(998,\cdot)\) \(\chi_{7623}(1052,\cdot)\) \(\chi_{7623}(1124,\cdot)\) \(\chi_{7623}(1493,\cdot)\) \(\chi_{7623}(1502,\cdot)\) \(\chi_{7623}(1619,\cdot)\) \(\chi_{7623}(1745,\cdot)\) \(\chi_{7623}(1817,\cdot)\) \(\chi_{7623}(1943,\cdot)\) \(\chi_{7623}(1997,\cdot)\) \(\chi_{7623}(2186,\cdot)\) \(\chi_{7623}(2195,\cdot)\) \(\chi_{7623}(2312,\cdot)\) \(\chi_{7623}(2384,\cdot)\) \(\chi_{7623}(2438,\cdot)\) \(\chi_{7623}(2510,\cdot)\) \(\chi_{7623}(2636,\cdot)\) \(\chi_{7623}(2690,\cdot)\) \(\chi_{7623}(2879,\cdot)\) \(\chi_{7623}(2888,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{101}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(2312, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{56}{165}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{289}{330}\right)\) | \(e\left(\frac{31}{110}\right)\) |