Basic properties
Modulus: | \(7623\) | |
Conductor: | \(1089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(165\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1089}(823,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.ey
\(\chi_{7623}(169,\cdot)\) \(\chi_{7623}(295,\cdot)\) \(\chi_{7623}(400,\cdot)\) \(\chi_{7623}(421,\cdot)\) \(\chi_{7623}(526,\cdot)\) \(\chi_{7623}(610,\cdot)\) \(\chi_{7623}(652,\cdot)\) \(\chi_{7623}(841,\cdot)\) \(\chi_{7623}(862,\cdot)\) \(\chi_{7623}(988,\cdot)\) \(\chi_{7623}(1093,\cdot)\) \(\chi_{7623}(1114,\cdot)\) \(\chi_{7623}(1303,\cdot)\) \(\chi_{7623}(1345,\cdot)\) \(\chi_{7623}(1534,\cdot)\) \(\chi_{7623}(1555,\cdot)\) \(\chi_{7623}(1681,\cdot)\) \(\chi_{7623}(1786,\cdot)\) \(\chi_{7623}(1807,\cdot)\) \(\chi_{7623}(1912,\cdot)\) \(\chi_{7623}(1996,\cdot)\) \(\chi_{7623}(2038,\cdot)\) \(\chi_{7623}(2227,\cdot)\) \(\chi_{7623}(2248,\cdot)\) \(\chi_{7623}(2374,\cdot)\) \(\chi_{7623}(2479,\cdot)\) \(\chi_{7623}(2500,\cdot)\) \(\chi_{7623}(2605,\cdot)\) \(\chi_{7623}(2731,\cdot)\) \(\chi_{7623}(2920,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 165 polynomial (not computed) |
Values on generators
\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{18}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 7623 }(1912, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{34}{165}\right)\) |