Basic properties
Modulus: | \(353\) | |
Conductor: | \(353\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(176\) | 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.k
\(\chi_{353}(9,\cdot)\) \(\chi_{353}(15,\cdot)\) \(\chi_{353}(18,\cdot)\) \(\chi_{353}(19,\cdot)\) \(\chi_{353}(23,\cdot)\) \(\chi_{353}(25,\cdot)\) \(\chi_{353}(30,\cdot)\) \(\chi_{353}(38,\cdot)\) \(\chi_{353}(39,\cdot)\) \(\chi_{353}(41,\cdot)\) \(\chi_{353}(43,\cdot)\) \(\chi_{353}(46,\cdot)\) \(\chi_{353}(47,\cdot)\) \(\chi_{353}(50,\cdot)\) \(\chi_{353}(65,\cdot)\) \(\chi_{353}(72,\cdot)\) \(\chi_{353}(76,\cdot)\) \(\chi_{353}(78,\cdot)\) \(\chi_{353}(82,\cdot)\) \(\chi_{353}(86,\cdot)\) \(\chi_{353}(92,\cdot)\) \(\chi_{353}(93,\cdot)\) \(\chi_{353}(94,\cdot)\) \(\chi_{353}(98,\cdot)\) \(\chi_{353}(99,\cdot)\) \(\chi_{353}(113,\cdot)\) \(\chi_{353}(120,\cdot)\) \(\chi_{353}(127,\cdot)\) \(\chi_{353}(130,\cdot)\) \(\chi_{353}(144,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{83}{176}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 353 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{83}{176}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{127}{176}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{13}{44}\right)\) |