Basic properties
Modulus: | \(4592\) | |
Conductor: | \(1148\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1148}(95,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4592.il
\(\chi_{4592}(95,\cdot)\) \(\chi_{4592}(527,\cdot)\) \(\chi_{4592}(639,\cdot)\) \(\chi_{4592}(751,\cdot)\) \(\chi_{4592}(767,\cdot)\) \(\chi_{4592}(991,\cdot)\) \(\chi_{4592}(1215,\cdot)\) \(\chi_{4592}(1327,\cdot)\) \(\chi_{4592}(1423,\cdot)\) \(\chi_{4592}(1551,\cdot)\) \(\chi_{4592}(1647,\cdot)\) \(\chi_{4592}(1775,\cdot)\) \(\chi_{4592}(1871,\cdot)\) \(\chi_{4592}(1983,\cdot)\) \(\chi_{4592}(2207,\cdot)\) \(\chi_{4592}(2431,\cdot)\) \(\chi_{4592}(2447,\cdot)\) \(\chi_{4592}(2559,\cdot)\) \(\chi_{4592}(2671,\cdot)\) \(\chi_{4592}(3103,\cdot)\) \(\chi_{4592}(3215,\cdot)\) \(\chi_{4592}(3327,\cdot)\) \(\chi_{4592}(3343,\cdot)\) \(\chi_{4592}(3455,\cdot)\) \(\chi_{4592}(3679,\cdot)\) \(\chi_{4592}(3791,\cdot)\) \(\chi_{4592}(3999,\cdot)\) \(\chi_{4592}(4111,\cdot)\) \(\chi_{4592}(4335,\cdot)\) \(\chi_{4592}(4447,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,3445,3937,785)\) → \((-1,1,e\left(\frac{2}{3}\right),e\left(\frac{31}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 4592 }(95, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) |