Basic properties
Modulus: | \(861\) | |
Conductor: | \(861\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 861.cj
\(\chi_{861}(17,\cdot)\) \(\chi_{861}(26,\cdot)\) \(\chi_{861}(47,\cdot)\) \(\chi_{861}(89,\cdot)\) \(\chi_{861}(101,\cdot)\) \(\chi_{861}(110,\cdot)\) \(\chi_{861}(152,\cdot)\) \(\chi_{861}(194,\cdot)\) \(\chi_{861}(227,\cdot)\) \(\chi_{861}(257,\cdot)\) \(\chi_{861}(299,\cdot)\) \(\chi_{861}(311,\cdot)\) \(\chi_{861}(341,\cdot)\) \(\chi_{861}(362,\cdot)\) \(\chi_{861}(395,\cdot)\) \(\chi_{861}(404,\cdot)\) \(\chi_{861}(416,\cdot)\) \(\chi_{861}(425,\cdot)\) \(\chi_{861}(458,\cdot)\) \(\chi_{861}(479,\cdot)\) \(\chi_{861}(509,\cdot)\) \(\chi_{861}(521,\cdot)\) \(\chi_{861}(563,\cdot)\) \(\chi_{861}(593,\cdot)\) \(\chi_{861}(626,\cdot)\) \(\chi_{861}(668,\cdot)\) \(\chi_{861}(710,\cdot)\) \(\chi_{861}(719,\cdot)\) \(\chi_{861}(731,\cdot)\) \(\chi_{861}(773,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,493,211)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{33}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 861 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) |