Basic properties
Modulus: | \(722\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{361}(217,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 722.j
\(\chi_{722}(27,\cdot)\) \(\chi_{722}(31,\cdot)\) \(\chi_{722}(65,\cdot)\) \(\chi_{722}(103,\cdot)\) \(\chi_{722}(107,\cdot)\) \(\chi_{722}(141,\cdot)\) \(\chi_{722}(145,\cdot)\) \(\chi_{722}(179,\cdot)\) \(\chi_{722}(183,\cdot)\) \(\chi_{722}(217,\cdot)\) \(\chi_{722}(221,\cdot)\) \(\chi_{722}(255,\cdot)\) \(\chi_{722}(259,\cdot)\) \(\chi_{722}(297,\cdot)\) \(\chi_{722}(331,\cdot)\) \(\chi_{722}(335,\cdot)\) \(\chi_{722}(369,\cdot)\) \(\chi_{722}(373,\cdot)\) \(\chi_{722}(407,\cdot)\) \(\chi_{722}(411,\cdot)\) \(\chi_{722}(445,\cdot)\) \(\chi_{722}(449,\cdot)\) \(\chi_{722}(483,\cdot)\) \(\chi_{722}(487,\cdot)\) \(\chi_{722}(521,\cdot)\) \(\chi_{722}(525,\cdot)\) \(\chi_{722}(559,\cdot)\) \(\chi_{722}(563,\cdot)\) \(\chi_{722}(597,\cdot)\) \(\chi_{722}(601,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\(363\) → \(e\left(\frac{37}{114}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 722 }(217, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{22}{57}\right)\) |