Basic properties
sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Conductor | = | 349 |
sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Order | = | 87 |
Real | = | No |
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
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Primitive | = | Yes |
sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Parity | = | Even |
Orbit label | = | 349.i |
Orbit index | = | 9 |
Galois orbit
\(\chi_{349}(9,\cdot)\) \(\chi_{349}(12,\cdot)\) \(\chi_{349}(14,\cdot)\) \(\chi_{349}(15,\cdot)\) \(\chi_{349}(16,\cdot)\) \(\chi_{349}(19,\cdot)\) \(\chi_{349}(20,\cdot)\) \(\chi_{349}(23,\cdot)\) \(\chi_{349}(25,\cdot)\) \(\chi_{349}(26,\cdot)\) \(\chi_{349}(51,\cdot)\) \(\chi_{349}(68,\cdot)\) \(\chi_{349}(77,\cdot)\) \(\chi_{349}(81,\cdot)\) \(\chi_{349}(85,\cdot)\) \(\chi_{349}(87,\cdot)\) \(\chi_{349}(94,\cdot)\) \(\chi_{349}(106,\cdot)\) \(\chi_{349}(108,\cdot)\) \(\chi_{349}(111,\cdot)\) \(\chi_{349}(116,\cdot)\) \(\chi_{349}(135,\cdot)\) \(\chi_{349}(143,\cdot)\) \(\chi_{349}(144,\cdot)\) \(\chi_{349}(145,\cdot)\) \(\chi_{349}(147,\cdot)\) \(\chi_{349}(148,\cdot)\) \(\chi_{349}(151,\cdot)\) \(\chi_{349}(158,\cdot)\) \(\chi_{349}(180,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{17}{87}\right)\)
Values
-1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
\(1\) | \(1\) | \(e\left(\frac{17}{87}\right)\) | \(e\left(\frac{7}{87}\right)\) | \(e\left(\frac{34}{87}\right)\) | \(e\left(\frac{31}{87}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{8}{87}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{14}{87}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) |
Related number fields
Field of values | \(\Q(\zeta_{87})\) |