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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.fg
\(\chi_{7623}(2,\cdot)\) \(\chi_{7623}(95,\cdot)\) \(\chi_{7623}(128,\cdot)\) \(\chi_{7623}(347,\cdot)\) \(\chi_{7623}(380,\cdot)\) \(\chi_{7623}(536,\cdot)\) \(\chi_{7623}(569,\cdot)\) \(\chi_{7623}(662,\cdot)\) \(\chi_{7623}(695,\cdot)\) \(\chi_{7623}(788,\cdot)\) \(\chi_{7623}(821,\cdot)\) \(\chi_{7623}(1040,\cdot)\) \(\chi_{7623}(1073,\cdot)\) \(\chi_{7623}(1229,\cdot)\) \(\chi_{7623}(1262,\cdot)\) \(\chi_{7623}(1355,\cdot)\) \(\chi_{7623}(1388,\cdot)\) \(\chi_{7623}(1481,\cdot)\) \(\chi_{7623}(1514,\cdot)\) \(\chi_{7623}(1733,\cdot)\) \(\chi_{7623}(1766,\cdot)\) \(\chi_{7623}(1922,\cdot)\) \(\chi_{7623}(1955,\cdot)\) \(\chi_{7623}(2081,\cdot)\) \(\chi_{7623}(2174,\cdot)\) \(\chi_{7623}(2207,\cdot)\) \(\chi_{7623}(2426,\cdot)\) \(\chi_{7623}(2459,\cdot)\) \(\chi_{7623}(2615,\cdot)\) \(\chi_{7623}(2648,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{57}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(2174, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{1}{330}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{113}{330}\right)\) | \(e\left(\frac{71}{330}\right)\) |