Basic properties
Modulus: | \(4592\) | |
Conductor: | \(4592\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4592.id
\(\chi_{4592}(101,\cdot)\) \(\chi_{4592}(117,\cdot)\) \(\chi_{4592}(157,\cdot)\) \(\chi_{4592}(229,\cdot)\) \(\chi_{4592}(381,\cdot)\) \(\chi_{4592}(397,\cdot)\) \(\chi_{4592}(773,\cdot)\) \(\chi_{4592}(885,\cdot)\) \(\chi_{4592}(1053,\cdot)\) \(\chi_{4592}(1405,\cdot)\) \(\chi_{4592}(1461,\cdot)\) \(\chi_{4592}(1573,\cdot)\) \(\chi_{4592}(1629,\cdot)\) \(\chi_{4592}(2061,\cdot)\) \(\chi_{4592}(2117,\cdot)\) \(\chi_{4592}(2229,\cdot)\) \(\chi_{4592}(2285,\cdot)\) \(\chi_{4592}(2637,\cdot)\) \(\chi_{4592}(2805,\cdot)\) \(\chi_{4592}(2917,\cdot)\) \(\chi_{4592}(3293,\cdot)\) \(\chi_{4592}(3309,\cdot)\) \(\chi_{4592}(3461,\cdot)\) \(\chi_{4592}(3533,\cdot)\) \(\chi_{4592}(3573,\cdot)\) \(\chi_{4592}(3589,\cdot)\) \(\chi_{4592}(3965,\cdot)\) \(\chi_{4592}(4037,\cdot)\) \(\chi_{4592}(4093,\cdot)\) \(\chi_{4592}(4189,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,3445,3937,785)\) → \((1,-i,e\left(\frac{5}{6}\right),e\left(\frac{3}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 4592 }(1405, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) |