Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 187 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 80 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | Even |
| Orbit label | = | 187.t |
| Orbit index | = | 20 |
Galois orbit
\(\chi_{187}(6,\cdot)\) \(\chi_{187}(7,\cdot)\) \(\chi_{187}(24,\cdot)\) \(\chi_{187}(28,\cdot)\) \(\chi_{187}(29,\cdot)\) \(\chi_{187}(39,\cdot)\) \(\chi_{187}(40,\cdot)\) \(\chi_{187}(41,\cdot)\) \(\chi_{187}(46,\cdot)\) \(\chi_{187}(57,\cdot)\) \(\chi_{187}(61,\cdot)\) \(\chi_{187}(62,\cdot)\) \(\chi_{187}(63,\cdot)\) \(\chi_{187}(73,\cdot)\) \(\chi_{187}(74,\cdot)\) \(\chi_{187}(79,\cdot)\) \(\chi_{187}(90,\cdot)\) \(\chi_{187}(95,\cdot)\) \(\chi_{187}(96,\cdot)\) \(\chi_{187}(105,\cdot)\) \(\chi_{187}(107,\cdot)\) \(\chi_{187}(112,\cdot)\) \(\chi_{187}(116,\cdot)\) \(\chi_{187}(129,\cdot)\) \(\chi_{187}(139,\cdot)\) \(\chi_{187}(150,\cdot)\) \(\chi_{187}(156,\cdot)\) \(\chi_{187}(160,\cdot)\) \(\chi_{187}(167,\cdot)\) \(\chi_{187}(173,\cdot)\) ...
Values on generators
\((35,122)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{16}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 |
| \(1\) | \(1\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{80})\) |