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.du
\(\chi_{4009}(40,\cdot)\) \(\chi_{4009}(67,\cdot)\) \(\chi_{4009}(223,\cdot)\) \(\chi_{4009}(299,\cdot)\) \(\chi_{4009}(364,\cdot)\) \(\chi_{4009}(485,\cdot)\) \(\chi_{4009}(489,\cdot)\) \(\chi_{4009}(884,\cdot)\) \(\chi_{4009}(907,\cdot)\) \(\chi_{4009}(1067,\cdot)\) \(\chi_{4009}(1143,\cdot)\) \(\chi_{4009}(1306,\cdot)\) \(\chi_{4009}(1333,\cdot)\) \(\chi_{4009}(1419,\cdot)\) \(\chi_{4009}(1630,\cdot)\) \(\chi_{4009}(1751,\cdot)\) \(\chi_{4009}(2122,\cdot)\) \(\chi_{4009}(2150,\cdot)\) \(\chi_{4009}(2198,\cdot)\) \(\chi_{4009}(2263,\cdot)\) \(\chi_{4009}(2333,\cdot)\) \(\chi_{4009}(2388,\cdot)\) \(\chi_{4009}(2409,\cdot)\) \(\chi_{4009}(2599,\cdot)\) \(\chi_{4009}(2806,\cdot)\) \(\chi_{4009}(2966,\cdot)\) \(\chi_{4009}(3017,\cdot)\) \(\chi_{4009}(3042,\cdot)\) \(\chi_{4009}(3107,\cdot)\) \(\chi_{4009}(3205,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{9}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(40, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{17}{21}\right)\) |