Basic properties
Modulus: | \(8015\) | |
Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(228\) | 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)
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Galois orbit 8015.fy
\(\chi_{8015}(2,\cdot)\) \(\chi_{8015}(32,\cdot)\) \(\chi_{8015}(123,\cdot)\) \(\chi_{8015}(128,\cdot)\) \(\chi_{8015}(177,\cdot)\) \(\chi_{8015}(207,\cdot)\) \(\chi_{8015}(242,\cdot)\) \(\chi_{8015}(317,\cdot)\) \(\chi_{8015}(338,\cdot)\) \(\chi_{8015}(492,\cdot)\) \(\chi_{8015}(653,\cdot)\) \(\chi_{8015}(807,\cdot)\) \(\chi_{8015}(823,\cdot)\) \(\chi_{8015}(828,\cdot)\) \(\chi_{8015}(968,\cdot)\) \(\chi_{8015}(1017,\cdot)\) \(\chi_{8015}(1143,\cdot)\) \(\chi_{8015}(1467,\cdot)\) \(\chi_{8015}(1633,\cdot)\) \(\chi_{8015}(1717,\cdot)\) \(\chi_{8015}(2048,\cdot)\) \(\chi_{8015}(2083,\cdot)\) \(\chi_{8015}(2167,\cdot)\) \(\chi_{8015}(2258,\cdot)\) \(\chi_{8015}(2298,\cdot)\) \(\chi_{8015}(2433,\cdot)\) \(\chi_{8015}(2727,\cdot)\) \(\chi_{8015}(2802,\cdot)\) \(\chi_{8015}(2832,\cdot)\) \(\chi_{8015}(2893,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{228})$ |
Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{17}{76}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(2433, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{101}{228}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{17}{76}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{1}{228}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{7}{57}\right)\) |