Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 2009 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 140 |
| 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.dx |
| Orbit index | = | 102 |
Galois orbit
\(\chi_{6027}(43,\cdot)\) \(\chi_{6027}(169,\cdot)\) \(\chi_{6027}(484,\cdot)\) \(\chi_{6027}(610,\cdot)\) \(\chi_{6027}(799,\cdot)\) \(\chi_{6027}(841,\cdot)\) \(\chi_{6027}(904,\cdot)\) \(\chi_{6027}(1156,\cdot)\) \(\chi_{6027}(1345,\cdot)\) \(\chi_{6027}(1597,\cdot)\) \(\chi_{6027}(1660,\cdot)\) \(\chi_{6027}(1702,\cdot)\) \(\chi_{6027}(1891,\cdot)\) \(\chi_{6027}(2017,\cdot)\) \(\chi_{6027}(2332,\cdot)\) \(\chi_{6027}(2458,\cdot)\) \(\chi_{6027}(2521,\cdot)\) \(\chi_{6027}(2563,\cdot)\) \(\chi_{6027}(2626,\cdot)\) \(\chi_{6027}(2752,\cdot)\) \(\chi_{6027}(2878,\cdot)\) \(\chi_{6027}(3067,\cdot)\) \(\chi_{6027}(3193,\cdot)\) \(\chi_{6027}(3319,\cdot)\) \(\chi_{6027}(3424,\cdot)\) \(\chi_{6027}(3487,\cdot)\) \(\chi_{6027}(3613,\cdot)\) \(\chi_{6027}(3739,\cdot)\) \(\chi_{6027}(3928,\cdot)\) \(\chi_{6027}(4054,\cdot)\) ...
Inducing primitive character
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{1}{7}\right),e\left(\frac{13}{20}\right))\)
Values
| -1 | 1 | 2 | 4 | 5 | 8 | 10 | 11 | 13 | 16 | 17 | 19 |
| \(1\) | \(1\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{17}{20}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{140})\) |