Basic properties
Modulus: | \(4009\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(63\) | 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.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
\((2111,1901)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{3}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(2676, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{21}\right)\) |