Basic properties
| Modulus: | \(51714\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{8619}(539,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 51714.mu
\(\chi_{51714}(71,\cdot)\) \(\chi_{51714}(215,\cdot)\) \(\chi_{51714}(449,\cdot)\) \(\chi_{51714}(539,\cdot)\) \(\chi_{51714}(1727,\cdot)\) \(\chi_{51714}(1943,\cdot)\) \(\chi_{51714}(1961,\cdot)\) \(\chi_{51714}(2069,\cdot)\) \(\chi_{51714}(2411,\cdot)\) \(\chi_{51714}(2663,\cdot)\) \(\chi_{51714}(2897,\cdot)\) \(\chi_{51714}(3257,\cdot)\) \(\chi_{51714}(3473,\cdot)\) \(\chi_{51714}(3491,\cdot)\) \(\chi_{51714}(3941,\cdot)\) \(\chi_{51714}(4049,\cdot)\) \(\chi_{51714}(4193,\cdot)\) \(\chi_{51714}(4427,\cdot)\) \(\chi_{51714}(4517,\cdot)\) \(\chi_{51714}(5579,\cdot)\) \(\chi_{51714}(5705,\cdot)\) \(\chi_{51714}(5921,\cdot)\) \(\chi_{51714}(5939,\cdot)\) \(\chi_{51714}(6047,\cdot)\) \(\chi_{51714}(6389,\cdot)\) \(\chi_{51714}(6641,\cdot)\) \(\chi_{51714}(6875,\cdot)\) \(\chi_{51714}(7235,\cdot)\) \(\chi_{51714}(7451,\cdot)\) \(\chi_{51714}(7469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((40223,40393,45631)\) → \((-1,e\left(\frac{5}{156}\right),e\left(\frac{13}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 51714 }(539, a) \) | \(-1\) | \(1\) | \(e\left(\frac{177}{208}\right)\) | \(e\left(\frac{229}{624}\right)\) | \(e\left(\frac{305}{624}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{73}{104}\right)\) | \(e\left(\frac{215}{624}\right)\) | \(e\left(\frac{205}{208}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{407}{624}\right)\) |