Basic properties
| Modulus: | \(6001\) | |
| Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(176\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.dq
\(\chi_{6001}(29,\cdot)\) \(\chi_{6001}(44,\cdot)\) \(\chi_{6001}(91,\cdot)\) \(\chi_{6001}(109,\cdot)\) \(\chi_{6001}(244,\cdot)\) \(\chi_{6001}(262,\cdot)\) \(\chi_{6001}(345,\cdot)\) \(\chi_{6001}(351,\cdot)\) \(\chi_{6001}(385,\cdot)\) \(\chi_{6001}(481,\cdot)\) \(\chi_{6001}(677,\cdot)\) \(\chi_{6001}(991,\cdot)\) \(\chi_{6001}(998,\cdot)\) \(\chi_{6001}(1027,\cdot)\) \(\chi_{6001}(1061,\cdot)\) \(\chi_{6001}(1142,\cdot)\) \(\chi_{6001}(1150,\cdot)\) \(\chi_{6001}(1170,\cdot)\) \(\chi_{6001}(1236,\cdot)\) \(\chi_{6001}(1303,\cdot)\) \(\chi_{6001}(1423,\cdot)\) \(\chi_{6001}(1485,\cdot)\) \(\chi_{6001}(1571,\cdot)\) \(\chi_{6001}(1654,\cdot)\) \(\chi_{6001}(1754,\cdot)\) \(\chi_{6001}(1809,\cdot)\) \(\chi_{6001}(1833,\cdot)\) \(\chi_{6001}(1846,\cdot)\) \(\chi_{6001}(1941,\cdot)\) \(\chi_{6001}(2035,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{176})$ |
| Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{13}{16}\right),e\left(\frac{39}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{45}{176}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{1}{176}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{49}{176}\right)\) |