Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | 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.cz
\(\chi_{4009}(123,\cdot)\) \(\chi_{4009}(199,\cdot)\) \(\chi_{4009}(359,\cdot)\) \(\chi_{4009}(480,\cdot)\) \(\chi_{4009}(593,\cdot)\) \(\chi_{4009}(777,\cdot)\) \(\chi_{4009}(804,\cdot)\) \(\chi_{4009}(902,\cdot)\) \(\chi_{4009}(967,\cdot)\) \(\chi_{4009}(992,\cdot)\) \(\chi_{4009}(1043,\cdot)\) \(\chi_{4009}(1203,\cdot)\) \(\chi_{4009}(1410,\cdot)\) \(\chi_{4009}(1600,\cdot)\) \(\chi_{4009}(1621,\cdot)\) \(\chi_{4009}(1676,\cdot)\) \(\chi_{4009}(1746,\cdot)\) \(\chi_{4009}(1811,\cdot)\) \(\chi_{4009}(1859,\cdot)\) \(\chi_{4009}(1887,\cdot)\) \(\chi_{4009}(2258,\cdot)\) \(\chi_{4009}(2379,\cdot)\) \(\chi_{4009}(2590,\cdot)\) \(\chi_{4009}(2676,\cdot)\) \(\chi_{4009}(2703,\cdot)\) \(\chi_{4009}(2866,\cdot)\) \(\chi_{4009}(2942,\cdot)\) \(\chi_{4009}(3102,\cdot)\) \(\chi_{4009}(3125,\cdot)\) \(\chi_{4009}(3520,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{2}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{13}{21}\right)\) |