Basic properties
Modulus: | \(2681\) | |
Conductor: | \(2681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(573\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 2681.m
\(\chi_{2681}(2,\cdot)\) \(\chi_{2681}(4,\cdot)\) \(\chi_{2681}(9,\cdot)\) \(\chi_{2681}(16,\cdot)\) \(\chi_{2681}(18,\cdot)\) \(\chi_{2681}(23,\cdot)\) \(\chi_{2681}(25,\cdot)\) \(\chi_{2681}(32,\cdot)\) \(\chi_{2681}(46,\cdot)\) \(\chi_{2681}(51,\cdot)\) \(\chi_{2681}(58,\cdot)\) \(\chi_{2681}(65,\cdot)\) \(\chi_{2681}(67,\cdot)\) \(\chi_{2681}(72,\cdot)\) \(\chi_{2681}(81,\cdot)\) \(\chi_{2681}(86,\cdot)\) \(\chi_{2681}(93,\cdot)\) \(\chi_{2681}(100,\cdot)\) \(\chi_{2681}(102,\cdot)\) \(\chi_{2681}(114,\cdot)\) \(\chi_{2681}(116,\cdot)\) \(\chi_{2681}(121,\cdot)\) \(\chi_{2681}(128,\cdot)\) \(\chi_{2681}(130,\cdot)\) \(\chi_{2681}(137,\cdot)\) \(\chi_{2681}(142,\cdot)\) \(\chi_{2681}(144,\cdot)\) \(\chi_{2681}(149,\cdot)\) \(\chi_{2681}(165,\cdot)\) \(\chi_{2681}(172,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{573})$ |
Fixed field: | Number field defined by a degree 573 polynomial (not computed) |
Values on generators
\((2299,771)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{87}{191}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2681 }(128, a) \) | \(1\) | \(1\) | \(e\left(\frac{403}{573}\right)\) | \(e\left(\frac{44}{573}\right)\) | \(e\left(\frac{233}{573}\right)\) | \(e\left(\frac{70}{573}\right)\) | \(e\left(\frac{149}{191}\right)\) | \(e\left(\frac{21}{191}\right)\) | \(e\left(\frac{88}{573}\right)\) | \(e\left(\frac{473}{573}\right)\) | \(e\left(\frac{416}{573}\right)\) | \(e\left(\frac{277}{573}\right)\) |