Basic properties
| Modulus: | \(343\) | |
| Conductor: | \(343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(147\) | 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 343.k
\(\chi_{343}(2,\cdot)\) \(\chi_{343}(4,\cdot)\) \(\chi_{343}(9,\cdot)\) \(\chi_{343}(11,\cdot)\) \(\chi_{343}(16,\cdot)\) \(\chi_{343}(23,\cdot)\) \(\chi_{343}(25,\cdot)\) \(\chi_{343}(32,\cdot)\) \(\chi_{343}(37,\cdot)\) \(\chi_{343}(39,\cdot)\) \(\chi_{343}(44,\cdot)\) \(\chi_{343}(46,\cdot)\) \(\chi_{343}(51,\cdot)\) \(\chi_{343}(53,\cdot)\) \(\chi_{343}(58,\cdot)\) \(\chi_{343}(60,\cdot)\) \(\chi_{343}(65,\cdot)\) \(\chi_{343}(72,\cdot)\) \(\chi_{343}(74,\cdot)\) \(\chi_{343}(81,\cdot)\) \(\chi_{343}(86,\cdot)\) \(\chi_{343}(88,\cdot)\) \(\chi_{343}(93,\cdot)\) \(\chi_{343}(95,\cdot)\) \(\chi_{343}(100,\cdot)\) \(\chi_{343}(102,\cdot)\) \(\chi_{343}(107,\cdot)\) \(\chi_{343}(109,\cdot)\) \(\chi_{343}(114,\cdot)\) \(\chi_{343}(121,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{147})$ |
| Fixed field: | Number field defined by a degree 147 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{76}{147}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 343 }(100, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{147}\right)\) | \(e\left(\frac{76}{147}\right)\) | \(e\left(\frac{88}{147}\right)\) | \(e\left(\frac{146}{147}\right)\) | \(e\left(\frac{40}{49}\right)\) | \(e\left(\frac{44}{49}\right)\) | \(e\left(\frac{5}{147}\right)\) | \(e\left(\frac{43}{147}\right)\) | \(e\left(\frac{79}{147}\right)\) | \(e\left(\frac{17}{147}\right)\) |