Basic properties
| Modulus: | \(5077\) | |
| Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(94\) | 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 5077.m
\(\chi_{5077}(25,\cdot)\) \(\chi_{5077}(113,\cdot)\) \(\chi_{5077}(193,\cdot)\) \(\chi_{5077}(252,\cdot)\) \(\chi_{5077}(304,\cdot)\) \(\chi_{5077}(365,\cdot)\) \(\chi_{5077}(394,\cdot)\) \(\chi_{5077}(419,\cdot)\) \(\chi_{5077}(494,\cdot)\) \(\chi_{5077}(633,\cdot)\) \(\chi_{5077}(734,\cdot)\) \(\chi_{5077}(787,\cdot)\) \(\chi_{5077}(1029,\cdot)\) \(\chi_{5077}(1120,\cdot)\) \(\chi_{5077}(1121,\cdot)\) \(\chi_{5077}(1171,\cdot)\) \(\chi_{5077}(1187,\cdot)\) \(\chi_{5077}(1820,\cdot)\) \(\chi_{5077}(1958,\cdot)\) \(\chi_{5077}(1986,\cdot)\) \(\chi_{5077}(2072,\cdot)\) \(\chi_{5077}(2134,\cdot)\) \(\chi_{5077}(2151,\cdot)\) \(\chi_{5077}(2252,\cdot)\) \(\chi_{5077}(2437,\cdot)\) \(\chi_{5077}(2455,\cdot)\) \(\chi_{5077}(2462,\cdot)\) \(\chi_{5077}(2497,\cdot)\) \(\chi_{5077}(2554,\cdot)\) \(\chi_{5077}(2881,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{47})$ |
| Fixed field: | Number field defined by a degree 94 polynomial |
Values on generators
\(2\) → \(e\left(\frac{11}{94}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5077 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{94}\right)\) | \(e\left(\frac{21}{47}\right)\) | \(e\left(\frac{11}{47}\right)\) | \(e\left(\frac{71}{94}\right)\) | \(e\left(\frac{53}{94}\right)\) | \(e\left(\frac{26}{47}\right)\) | \(e\left(\frac{33}{94}\right)\) | \(e\left(\frac{42}{47}\right)\) | \(e\left(\frac{41}{47}\right)\) | \(e\left(\frac{77}{94}\right)\) |