Basic properties
Modulus: | \(968\) | |
Conductor: | \(484\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{484}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 968.be
\(\chi_{968}(15,\cdot)\) \(\chi_{968}(31,\cdot)\) \(\chi_{968}(47,\cdot)\) \(\chi_{968}(71,\cdot)\) \(\chi_{968}(103,\cdot)\) \(\chi_{968}(119,\cdot)\) \(\chi_{968}(135,\cdot)\) \(\chi_{968}(159,\cdot)\) \(\chi_{968}(191,\cdot)\) \(\chi_{968}(207,\cdot)\) \(\chi_{968}(223,\cdot)\) \(\chi_{968}(247,\cdot)\) \(\chi_{968}(279,\cdot)\) \(\chi_{968}(295,\cdot)\) \(\chi_{968}(311,\cdot)\) \(\chi_{968}(335,\cdot)\) \(\chi_{968}(367,\cdot)\) \(\chi_{968}(383,\cdot)\) \(\chi_{968}(399,\cdot)\) \(\chi_{968}(423,\cdot)\) \(\chi_{968}(455,\cdot)\) \(\chi_{968}(471,\cdot)\) \(\chi_{968}(543,\cdot)\) \(\chi_{968}(559,\cdot)\) \(\chi_{968}(575,\cdot)\) \(\chi_{968}(599,\cdot)\) \(\chi_{968}(631,\cdot)\) \(\chi_{968}(647,\cdot)\) \(\chi_{968}(663,\cdot)\) \(\chi_{968}(687,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((727,485,849)\) → \((-1,1,e\left(\frac{43}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 968 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) |