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.fe
\(\chi_{7623}(52,\cdot)\) \(\chi_{7623}(178,\cdot)\) \(\chi_{7623}(292,\cdot)\) \(\chi_{7623}(304,\cdot)\) \(\chi_{7623}(556,\cdot)\) \(\chi_{7623}(607,\cdot)\) \(\chi_{7623}(733,\cdot)\) \(\chi_{7623}(745,\cdot)\) \(\chi_{7623}(871,\cdot)\) \(\chi_{7623}(985,\cdot)\) \(\chi_{7623}(997,\cdot)\) \(\chi_{7623}(1174,\cdot)\) \(\chi_{7623}(1249,\cdot)\) \(\chi_{7623}(1300,\cdot)\) \(\chi_{7623}(1426,\cdot)\) \(\chi_{7623}(1438,\cdot)\) \(\chi_{7623}(1678,\cdot)\) \(\chi_{7623}(1690,\cdot)\) \(\chi_{7623}(1867,\cdot)\) \(\chi_{7623}(1942,\cdot)\) \(\chi_{7623}(1993,\cdot)\) \(\chi_{7623}(2119,\cdot)\) \(\chi_{7623}(2131,\cdot)\) \(\chi_{7623}(2257,\cdot)\) \(\chi_{7623}(2371,\cdot)\) \(\chi_{7623}(2383,\cdot)\) \(\chi_{7623}(2560,\cdot)\) \(\chi_{7623}(2686,\cdot)\) \(\chi_{7623}(2812,\cdot)\) \(\chi_{7623}(2824,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{103}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(1867, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{329}{330}\right)\) |