Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 151 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 75 |
| 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 | = | 151.k |
| Orbit index | = | 11 |
Galois orbit
\(\chi_{151}(5,\cdot)\) \(\chi_{151}(10,\cdot)\) \(\chi_{151}(11,\cdot)\) \(\chi_{151}(17,\cdot)\) \(\chi_{151}(18,\cdot)\) \(\chi_{151}(21,\cdot)\) \(\chi_{151}(22,\cdot)\) \(\chi_{151}(25,\cdot)\) \(\chi_{151}(31,\cdot)\) \(\chi_{151}(34,\cdot)\) \(\chi_{151}(36,\cdot)\) \(\chi_{151}(37,\cdot)\) \(\chi_{151}(39,\cdot)\) \(\chi_{151}(40,\cdot)\) \(\chi_{151}(42,\cdot)\) \(\chi_{151}(43,\cdot)\) \(\chi_{151}(45,\cdot)\) \(\chi_{151}(47,\cdot)\) \(\chi_{151}(49,\cdot)\) \(\chi_{151}(55,\cdot)\) \(\chi_{151}(58,\cdot)\) \(\chi_{151}(62,\cdot)\) \(\chi_{151}(69,\cdot)\) \(\chi_{151}(74,\cdot)\) \(\chi_{151}(80,\cdot)\) \(\chi_{151}(88,\cdot)\) \(\chi_{151}(90,\cdot)\) \(\chi_{151}(95,\cdot)\) \(\chi_{151}(97,\cdot)\) \(\chi_{151}(99,\cdot)\) ...
Values on generators
\(6\) → \(e\left(\frac{13}{75}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{31}{75}\right)\) | \(e\left(\frac{13}{75}\right)\) | \(e\left(\frac{46}{75}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{22}{75}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{75})\) |