Basic properties
Modulus: | \(4015\) | |
Conductor: | \(4015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | 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 4015.fo
\(\chi_{4015}(103,\cdot)\) \(\chi_{4015}(202,\cdot)\) \(\chi_{4015}(212,\cdot)\) \(\chi_{4015}(313,\cdot)\) \(\chi_{4015}(372,\cdot)\) \(\chi_{4015}(577,\cdot)\) \(\chi_{4015}(773,\cdot)\) \(\chi_{4015}(928,\cdot)\) \(\chi_{4015}(1043,\cdot)\) \(\chi_{4015}(1138,\cdot)\) \(\chi_{4015}(1307,\cdot)\) \(\chi_{4015}(1467,\cdot)\) \(\chi_{4015}(1477,\cdot)\) \(\chi_{4015}(1842,\cdot)\) \(\chi_{4015}(1868,\cdot)\) \(\chi_{4015}(1928,\cdot)\) \(\chi_{4015}(2027,\cdot)\) \(\chi_{4015}(2138,\cdot)\) \(\chi_{4015}(2293,\cdot)\) \(\chi_{4015}(2392,\cdot)\) \(\chi_{4015}(2402,\cdot)\) \(\chi_{4015}(2572,\cdot)\) \(\chi_{4015}(2753,\cdot)\) \(\chi_{4015}(2963,\cdot)\) \(\chi_{4015}(3023,\cdot)\) \(\chi_{4015}(3118,\cdot)\) \(\chi_{4015}(3122,\cdot)\) \(\chi_{4015}(3292,\cdot)\) \(\chi_{4015}(3657,\cdot)\) \(\chi_{4015}(3667,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-i,e\left(\frac{1}{5}\right),e\left(\frac{5}{24}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 4015 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) |