Basic properties
Modulus: | \(6043\) | |
Conductor: | \(6043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1007\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6043.m
\(\chi_{6043}(9,\cdot)\) \(\chi_{6043}(14,\cdot)\) \(\chi_{6043}(23,\cdot)\) \(\chi_{6043}(24,\cdot)\) \(\chi_{6043}(26,\cdot)\) \(\chi_{6043}(35,\cdot)\) \(\chi_{6043}(37,\cdot)\) \(\chi_{6043}(38,\cdot)\) \(\chi_{6043}(41,\cdot)\) \(\chi_{6043}(53,\cdot)\) \(\chi_{6043}(60,\cdot)\) \(\chi_{6043}(65,\cdot)\) \(\chi_{6043}(67,\cdot)\) \(\chi_{6043}(77,\cdot)\) \(\chi_{6043}(81,\cdot)\) \(\chi_{6043}(83,\cdot)\) \(\chi_{6043}(94,\cdot)\) \(\chi_{6043}(95,\cdot)\) \(\chi_{6043}(102,\cdot)\) \(\chi_{6043}(107,\cdot)\) \(\chi_{6043}(118,\cdot)\) \(\chi_{6043}(124,\cdot)\) \(\chi_{6043}(126,\cdot)\) \(\chi_{6043}(132,\cdot)\) \(\chi_{6043}(143,\cdot)\) \(\chi_{6043}(150,\cdot)\) \(\chi_{6043}(160,\cdot)\) \(\chi_{6043}(181,\cdot)\) \(\chi_{6043}(194,\cdot)\) \(\chi_{6043}(196,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1007})$ |
Fixed field: | Number field defined by a degree 1007 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{979}{1007}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6043 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{53}\right)\) | \(e\left(\frac{338}{1007}\right)\) | \(e\left(\frac{45}{53}\right)\) | \(e\left(\frac{979}{1007}\right)\) | \(e\left(\frac{262}{1007}\right)\) | \(e\left(\frac{345}{1007}\right)\) | \(e\left(\frac{41}{53}\right)\) | \(e\left(\frac{676}{1007}\right)\) | \(e\left(\frac{903}{1007}\right)\) | \(e\left(\frac{14}{19}\right)\) |