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.cy
\(\chi_{4009}(43,\cdot)\) \(\chi_{4009}(73,\cdot)\) \(\chi_{4009}(101,\cdot)\) \(\chi_{4009}(161,\cdot)\) \(\chi_{4009}(180,\cdot)\) \(\chi_{4009}(245,\cdot)\) \(\chi_{4009}(328,\cdot)\) \(\chi_{4009}(389,\cdot)\) \(\chi_{4009}(917,\cdot)\) \(\chi_{4009}(1023,\cdot)\) \(\chi_{4009}(1309,\cdot)\) \(\chi_{4009}(1320,\cdot)\) \(\chi_{4009}(1594,\cdot)\) \(\chi_{4009}(1638,\cdot)\) \(\chi_{4009}(1650,\cdot)\) \(\chi_{4009}(1657,\cdot)\) \(\chi_{4009}(1662,\cdot)\) \(\chi_{4009}(1849,\cdot)\) \(\chi_{4009}(1866,\cdot)\) \(\chi_{4009}(1867,\cdot)\) \(\chi_{4009}(1868,\cdot)\) \(\chi_{4009}(2077,\cdot)\) \(\chi_{4009}(2144,\cdot)\) \(\chi_{4009}(2183,\cdot)\) \(\chi_{4009}(2422,\cdot)\) \(\chi_{4009}(2494,\cdot)\) \(\chi_{4009}(2797,\cdot)\) \(\chi_{4009}(2988,\cdot)\) \(\chi_{4009}(3008,\cdot)\) \(\chi_{4009}(3133,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2111,1901)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{1}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(1868, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{21}\right)\) |