Basic properties
Modulus: | \(861\) | |
Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{287}(136,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 861.ci
\(\chi_{861}(19,\cdot)\) \(\chi_{861}(52,\cdot)\) \(\chi_{861}(94,\cdot)\) \(\chi_{861}(136,\cdot)\) \(\chi_{861}(145,\cdot)\) \(\chi_{861}(157,\cdot)\) \(\chi_{861}(199,\cdot)\) \(\chi_{861}(220,\cdot)\) \(\chi_{861}(229,\cdot)\) \(\chi_{861}(304,\cdot)\) \(\chi_{861}(313,\cdot)\) \(\chi_{861}(334,\cdot)\) \(\chi_{861}(376,\cdot)\) \(\chi_{861}(388,\cdot)\) \(\chi_{861}(397,\cdot)\) \(\chi_{861}(439,\cdot)\) \(\chi_{861}(481,\cdot)\) \(\chi_{861}(514,\cdot)\) \(\chi_{861}(544,\cdot)\) \(\chi_{861}(586,\cdot)\) \(\chi_{861}(598,\cdot)\) \(\chi_{861}(628,\cdot)\) \(\chi_{861}(649,\cdot)\) \(\chi_{861}(682,\cdot)\) \(\chi_{861}(691,\cdot)\) \(\chi_{861}(703,\cdot)\) \(\chi_{861}(712,\cdot)\) \(\chi_{861}(745,\cdot)\) \(\chi_{861}(766,\cdot)\) \(\chi_{861}(796,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,493,211)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{31}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 861 }(136, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{97}{120}\right)\) |