Basic properties
| Modulus: | \(149\) | |
| Conductor: | \(149\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(148\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 149.f
\(\chi_{149}(2,\cdot)\) \(\chi_{149}(3,\cdot)\) \(\chi_{149}(8,\cdot)\) \(\chi_{149}(10,\cdot)\) \(\chi_{149}(11,\cdot)\) \(\chi_{149}(12,\cdot)\) \(\chi_{149}(13,\cdot)\) \(\chi_{149}(14,\cdot)\) \(\chi_{149}(15,\cdot)\) \(\chi_{149}(18,\cdot)\) \(\chi_{149}(21,\cdot)\) \(\chi_{149}(23,\cdot)\) \(\chi_{149}(27,\cdot)\) \(\chi_{149}(32,\cdot)\) \(\chi_{149}(34,\cdot)\) \(\chi_{149}(38,\cdot)\) \(\chi_{149}(40,\cdot)\) \(\chi_{149}(41,\cdot)\) \(\chi_{149}(43,\cdot)\) \(\chi_{149}(48,\cdot)\) \(\chi_{149}(50,\cdot)\) \(\chi_{149}(51,\cdot)\) \(\chi_{149}(52,\cdot)\) \(\chi_{149}(55,\cdot)\) \(\chi_{149}(56,\cdot)\) \(\chi_{149}(57,\cdot)\) \(\chi_{149}(58,\cdot)\) \(\chi_{149}(59,\cdot)\) \(\chi_{149}(60,\cdot)\) \(\chi_{149}(62,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{148})$ |
| Fixed field: | Number field defined by a degree 148 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{75}{148}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 149 }(147, a) \) | \(-1\) | \(1\) | \(e\left(\frac{75}{148}\right)\) | \(e\left(\frac{13}{148}\right)\) | \(e\left(\frac{1}{74}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{22}{37}\right)\) | \(e\left(\frac{71}{74}\right)\) | \(e\left(\frac{77}{148}\right)\) | \(e\left(\frac{13}{74}\right)\) | \(e\left(\frac{31}{148}\right)\) | \(e\left(\frac{35}{148}\right)\) |