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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fp
\(\chi_{7623}(61,\cdot)\) \(\chi_{7623}(250,\cdot)\) \(\chi_{7623}(283,\cdot)\) \(\chi_{7623}(376,\cdot)\) \(\chi_{7623}(409,\cdot)\) \(\chi_{7623}(502,\cdot)\) \(\chi_{7623}(535,\cdot)\) \(\chi_{7623}(754,\cdot)\) \(\chi_{7623}(787,\cdot)\) \(\chi_{7623}(943,\cdot)\) \(\chi_{7623}(976,\cdot)\) \(\chi_{7623}(1069,\cdot)\) \(\chi_{7623}(1102,\cdot)\) \(\chi_{7623}(1195,\cdot)\) \(\chi_{7623}(1228,\cdot)\) \(\chi_{7623}(1447,\cdot)\) \(\chi_{7623}(1480,\cdot)\) \(\chi_{7623}(1636,\cdot)\) \(\chi_{7623}(1669,\cdot)\) \(\chi_{7623}(1762,\cdot)\) \(\chi_{7623}(1795,\cdot)\) \(\chi_{7623}(1888,\cdot)\) \(\chi_{7623}(1921,\cdot)\) \(\chi_{7623}(2140,\cdot)\) \(\chi_{7623}(2173,\cdot)\) \(\chi_{7623}(2329,\cdot)\) \(\chi_{7623}(2362,\cdot)\) \(\chi_{7623}(2455,\cdot)\) \(\chi_{7623}(2488,\cdot)\) \(\chi_{7623}(2614,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{27}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(535, a) \) | \(1\) | \(1\) | \(e\left(\frac{301}{330}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{158}{165}\right)\) | \(e\left(\frac{107}{165}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{34}{165}\right)\) | \(e\left(\frac{161}{330}\right)\) |