Basic properties
Modulus: | \(7623\) | |
Conductor: | \(7623\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fh
\(\chi_{7623}(31,\cdot)\) \(\chi_{7623}(157,\cdot)\) \(\chi_{7623}(313,\cdot)\) \(\chi_{7623}(346,\cdot)\) \(\chi_{7623}(598,\cdot)\) \(\chi_{7623}(691,\cdot)\) \(\chi_{7623}(724,\cdot)\) \(\chi_{7623}(817,\cdot)\) \(\chi_{7623}(1006,\cdot)\) \(\chi_{7623}(1039,\cdot)\) \(\chi_{7623}(1258,\cdot)\) \(\chi_{7623}(1384,\cdot)\) \(\chi_{7623}(1417,\cdot)\) \(\chi_{7623}(1510,\cdot)\) \(\chi_{7623}(1543,\cdot)\) \(\chi_{7623}(1699,\cdot)\) \(\chi_{7623}(1732,\cdot)\) \(\chi_{7623}(1951,\cdot)\) \(\chi_{7623}(1984,\cdot)\) \(\chi_{7623}(2077,\cdot)\) \(\chi_{7623}(2110,\cdot)\) \(\chi_{7623}(2203,\cdot)\) \(\chi_{7623}(2236,\cdot)\) \(\chi_{7623}(2392,\cdot)\) \(\chi_{7623}(2425,\cdot)\) \(\chi_{7623}(2644,\cdot)\) \(\chi_{7623}(2677,\cdot)\) \(\chi_{7623}(2770,\cdot)\) \(\chi_{7623}(2803,\cdot)\) \(\chi_{7623}(2896,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{18}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(6268, a) \) | \(-1\) | \(1\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{73}{330}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{67}{330}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{233}{330}\right)\) |