Basic properties
| Modulus: | \(353\) | |
| Conductor: | \(353\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 353.j
\(\chi_{353}(2,\cdot)\) \(\chi_{353}(8,\cdot)\) \(\chi_{353}(11,\cdot)\) \(\chi_{353}(17,\cdot)\) \(\chi_{353}(21,\cdot)\) \(\chi_{353}(29,\cdot)\) \(\chi_{353}(32,\cdot)\) \(\chi_{353}(44,\cdot)\) \(\chi_{353}(61,\cdot)\) \(\chi_{353}(68,\cdot)\) \(\chi_{353}(73,\cdot)\) \(\chi_{353}(81,\cdot)\) \(\chi_{353}(83,\cdot)\) \(\chi_{353}(84,\cdot)\) \(\chi_{353}(91,\cdot)\) \(\chi_{353}(109,\cdot)\) \(\chi_{353}(111,\cdot)\) \(\chi_{353}(128,\cdot)\) \(\chi_{353}(159,\cdot)\) \(\chi_{353}(176,\cdot)\) \(\chi_{353}(177,\cdot)\) \(\chi_{353}(194,\cdot)\) \(\chi_{353}(225,\cdot)\) \(\chi_{353}(242,\cdot)\) \(\chi_{353}(244,\cdot)\) \(\chi_{353}(262,\cdot)\) \(\chi_{353}(269,\cdot)\) \(\chi_{353}(270,\cdot)\) \(\chi_{353}(272,\cdot)\) \(\chi_{353}(280,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\(3\) → \(e\left(\frac{83}{88}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 353 }(324, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{22}\right)\) |