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 \(\chi_{287}(58,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 861.ck
\(\chi_{861}(58,\cdot)\) \(\chi_{861}(67,\cdot)\) \(\chi_{861}(88,\cdot)\) \(\chi_{861}(130,\cdot)\) \(\chi_{861}(142,\cdot)\) \(\chi_{861}(151,\cdot)\) \(\chi_{861}(193,\cdot)\) \(\chi_{861}(235,\cdot)\) \(\chi_{861}(268,\cdot)\) \(\chi_{861}(298,\cdot)\) \(\chi_{861}(340,\cdot)\) \(\chi_{861}(352,\cdot)\) \(\chi_{861}(382,\cdot)\) \(\chi_{861}(403,\cdot)\) \(\chi_{861}(436,\cdot)\) \(\chi_{861}(445,\cdot)\) \(\chi_{861}(457,\cdot)\) \(\chi_{861}(466,\cdot)\) \(\chi_{861}(499,\cdot)\) \(\chi_{861}(520,\cdot)\) \(\chi_{861}(550,\cdot)\) \(\chi_{861}(562,\cdot)\) \(\chi_{861}(604,\cdot)\) \(\chi_{861}(634,\cdot)\) \(\chi_{861}(667,\cdot)\) \(\chi_{861}(709,\cdot)\) \(\chi_{861}(751,\cdot)\) \(\chi_{861}(760,\cdot)\) \(\chi_{861}(772,\cdot)\) \(\chi_{861}(814,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,493,211)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{33}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 861 }(58, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) |