Basic properties
Modulus: | \(4009\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | 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 4009.dv
\(\chi_{4009}(32,\cdot)\) \(\chi_{4009}(33,\cdot)\) \(\chi_{4009}(242,\cdot)\) \(\chi_{4009}(243,\cdot)\) \(\chi_{4009}(261,\cdot)\) \(\chi_{4009}(599,\cdot)\) \(\chi_{4009}(743,\cdot)\) \(\chi_{4009}(877,\cdot)\) \(\chi_{4009}(982,\cdot)\) \(\chi_{4009}(1086,\cdot)\) \(\chi_{4009}(1093,\cdot)\) \(\chi_{4009}(1105,\cdot)\) \(\chi_{4009}(1193,\cdot)\) \(\chi_{4009}(1503,\cdot)\) \(\chi_{4009}(1571,\cdot)\) \(\chi_{4009}(1720,\cdot)\) \(\chi_{4009}(1782,\cdot)\) \(\chi_{4009}(1845,\cdot)\) \(\chi_{4009}(1856,\cdot)\) \(\chi_{4009}(2009,\cdot)\) \(\chi_{4009}(2067,\cdot)\) \(\chi_{4009}(2670,\cdot)\) \(\chi_{4009}(2769,\cdot)\) \(\chi_{4009}(2776,\cdot)\) \(\chi_{4009}(2853,\cdot)\) \(\chi_{4009}(2920,\cdot)\) \(\chi_{4009}(2985,\cdot)\) \(\chi_{4009}(3004,\cdot)\) \(\chi_{4009}(3111,\cdot)\) \(\chi_{4009}(3131,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{25}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(1571, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{16}{21}\right)\) |