Basic properties
| Modulus: | \(349\) | |
| Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(348\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 349.l
\(\chi_{349}(2,\cdot)\) \(\chi_{349}(7,\cdot)\) \(\chi_{349}(13,\cdot)\) \(\chi_{349}(18,\cdot)\) \(\chi_{349}(30,\cdot)\) \(\chi_{349}(32,\cdot)\) \(\chi_{349}(33,\cdot)\) \(\chi_{349}(34,\cdot)\) \(\chi_{349}(40,\cdot)\) \(\chi_{349}(43,\cdot)\) \(\chi_{349}(44,\cdot)\) \(\chi_{349}(46,\cdot)\) \(\chi_{349}(50,\cdot)\) \(\chi_{349}(54,\cdot)\) \(\chi_{349}(55,\cdot)\) \(\chi_{349}(59,\cdot)\) \(\chi_{349}(62,\cdot)\) \(\chi_{349}(63,\cdot)\) \(\chi_{349}(71,\cdot)\) \(\chi_{349}(72,\cdot)\) \(\chi_{349}(74,\cdot)\) \(\chi_{349}(82,\cdot)\) \(\chi_{349}(84,\cdot)\) \(\chi_{349}(89,\cdot)\) \(\chi_{349}(90,\cdot)\) \(\chi_{349}(96,\cdot)\) \(\chi_{349}(97,\cdot)\) \(\chi_{349}(99,\cdot)\) \(\chi_{349}(105,\cdot)\) \(\chi_{349}(107,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{348})$ |
| Fixed field: | Number field defined by a degree 348 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{341}{348}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 349 }(30, a) \) | \(-1\) | \(1\) | \(e\left(\frac{341}{348}\right)\) | \(e\left(\frac{83}{174}\right)\) | \(e\left(\frac{167}{174}\right)\) | \(e\left(\frac{119}{174}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{227}{348}\right)\) | \(e\left(\frac{109}{116}\right)\) | \(e\left(\frac{83}{87}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{67}{116}\right)\) |