Basic properties
| Modulus: | \(6001\) | |
| Conductor: | \(353\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(176\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{353}(209,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.dy
\(\chi_{6001}(18,\cdot)\) \(\chi_{6001}(86,\cdot)\) \(\chi_{6001}(120,\cdot)\) \(\chi_{6001}(188,\cdot)\) \(\chi_{6001}(307,\cdot)\) \(\chi_{6001}(392,\cdot)\) \(\chi_{6001}(562,\cdot)\) \(\chi_{6001}(579,\cdot)\) \(\chi_{6001}(613,\cdot)\) \(\chi_{6001}(630,\cdot)\) \(\chi_{6001}(681,\cdot)\) \(\chi_{6001}(715,\cdot)\) \(\chi_{6001}(749,\cdot)\) \(\chi_{6001}(800,\cdot)\) \(\chi_{6001}(902,\cdot)\) \(\chi_{6001}(987,\cdot)\) \(\chi_{6001}(1021,\cdot)\) \(\chi_{6001}(1089,\cdot)\) \(\chi_{6001}(1106,\cdot)\) \(\chi_{6001}(1157,\cdot)\) \(\chi_{6001}(1259,\cdot)\) \(\chi_{6001}(1565,\cdot)\) \(\chi_{6001}(1667,\cdot)\) \(\chi_{6001}(1718,\cdot)\) \(\chi_{6001}(1735,\cdot)\) \(\chi_{6001}(1803,\cdot)\) \(\chi_{6001}(1837,\cdot)\) \(\chi_{6001}(1922,\cdot)\) \(\chi_{6001}(2024,\cdot)\) \(\chi_{6001}(2075,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{176})$ |
| Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((1,e\left(\frac{65}{176}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6001 }(562, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{65}{176}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{21}{176}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{44}\right)\) |