Basic properties
Modulus: | \(4009\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | 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 4009.dz
\(\chi_{4009}(110,\cdot)\) \(\chi_{4009}(249,\cdot)\) \(\chi_{4009}(516,\cdot)\) \(\chi_{4009}(659,\cdot)\) \(\chi_{4009}(801,\cdot)\) \(\chi_{4009}(870,\cdot)\) \(\chi_{4009}(876,\cdot)\) \(\chi_{4009}(1001,\cdot)\) \(\chi_{4009}(1021,\cdot)\) \(\chi_{4009}(1212,\cdot)\) \(\chi_{4009}(1515,\cdot)\) \(\chi_{4009}(1587,\cdot)\) \(\chi_{4009}(1826,\cdot)\) \(\chi_{4009}(1865,\cdot)\) \(\chi_{4009}(1932,\cdot)\) \(\chi_{4009}(2141,\cdot)\) \(\chi_{4009}(2142,\cdot)\) \(\chi_{4009}(2143,\cdot)\) \(\chi_{4009}(2160,\cdot)\) \(\chi_{4009}(2347,\cdot)\) \(\chi_{4009}(2352,\cdot)\) \(\chi_{4009}(2359,\cdot)\) \(\chi_{4009}(2371,\cdot)\) \(\chi_{4009}(2415,\cdot)\) \(\chi_{4009}(2689,\cdot)\) \(\chi_{4009}(2700,\cdot)\) \(\chi_{4009}(2986,\cdot)\) \(\chi_{4009}(3092,\cdot)\) \(\chi_{4009}(3620,\cdot)\) \(\chi_{4009}(3681,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{31}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(249, a) \) | \(1\) | \(1\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{21}\right)\) |