Basic properties
sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Conductor | = | 113 |
sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Order | = | 56 |
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 | = | 113.i |
Orbit index | = | 9 |
Galois orbit
\(\chi_{113}(9,\cdot)\) \(\chi_{113}(11,\cdot)\) \(\chi_{113}(13,\cdot)\) \(\chi_{113}(22,\cdot)\) \(\chi_{113}(25,\cdot)\) \(\chi_{113}(26,\cdot)\) \(\chi_{113}(31,\cdot)\) \(\chi_{113}(36,\cdot)\) \(\chi_{113}(41,\cdot)\) \(\chi_{113}(50,\cdot)\) \(\chi_{113}(51,\cdot)\) \(\chi_{113}(52,\cdot)\) \(\chi_{113}(61,\cdot)\) \(\chi_{113}(62,\cdot)\) \(\chi_{113}(63,\cdot)\) \(\chi_{113}(72,\cdot)\) \(\chi_{113}(77,\cdot)\) \(\chi_{113}(82,\cdot)\) \(\chi_{113}(87,\cdot)\) \(\chi_{113}(88,\cdot)\) \(\chi_{113}(91,\cdot)\) \(\chi_{113}(100,\cdot)\) \(\chi_{113}(102,\cdot)\) \(\chi_{113}(104,\cdot)\)
Values on generators
\(3\) → \(e\left(\frac{37}{56}\right)\)
Values
-1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
\(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) |
Related number fields
Field of values | \(\Q(\zeta_{56})\) |