Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 2009 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 280 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | No |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | Even |
| Orbit label | = | 6027.em |
| Orbit index | = | 117 |
Galois orbit
\(\chi_{6027}(13,\cdot)\) \(\chi_{6027}(34,\cdot)\) \(\chi_{6027}(76,\cdot)\) \(\chi_{6027}(181,\cdot)\) \(\chi_{6027}(265,\cdot)\) \(\chi_{6027}(475,\cdot)\) \(\chi_{6027}(559,\cdot)\) \(\chi_{6027}(580,\cdot)\) \(\chi_{6027}(622,\cdot)\) \(\chi_{6027}(643,\cdot)\) \(\chi_{6027}(727,\cdot)\) \(\chi_{6027}(790,\cdot)\) \(\chi_{6027}(874,\cdot)\) \(\chi_{6027}(895,\cdot)\) \(\chi_{6027}(937,\cdot)\) \(\chi_{6027}(958,\cdot)\) \(\chi_{6027}(1042,\cdot)\) \(\chi_{6027}(1252,\cdot)\) \(\chi_{6027}(1336,\cdot)\) \(\chi_{6027}(1441,\cdot)\) \(\chi_{6027}(1483,\cdot)\) \(\chi_{6027}(1504,\cdot)\) \(\chi_{6027}(1546,\cdot)\) \(\chi_{6027}(1588,\cdot)\) \(\chi_{6027}(1651,\cdot)\) \(\chi_{6027}(1693,\cdot)\) \(\chi_{6027}(1735,\cdot)\) \(\chi_{6027}(1756,\cdot)\) \(\chi_{6027}(1798,\cdot)\) \(\chi_{6027}(1819,\cdot)\) ...
Inducing primitive character
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{11}{14}\right),e\left(\frac{31}{40}\right))\)
Values
| -1 | 1 | 2 | 4 | 5 | 8 | 10 | 11 | 13 | 16 | 17 | 19 |
| \(1\) | \(1\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{280})\) |