Basic properties
| Modulus: | \(125\) | |
| Conductor: | \(125\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | 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 125.i
\(\chi_{125}(2,\cdot)\) \(\chi_{125}(3,\cdot)\) \(\chi_{125}(8,\cdot)\) \(\chi_{125}(12,\cdot)\) \(\chi_{125}(13,\cdot)\) \(\chi_{125}(17,\cdot)\) \(\chi_{125}(22,\cdot)\) \(\chi_{125}(23,\cdot)\) \(\chi_{125}(27,\cdot)\) \(\chi_{125}(28,\cdot)\) \(\chi_{125}(33,\cdot)\) \(\chi_{125}(37,\cdot)\) \(\chi_{125}(38,\cdot)\) \(\chi_{125}(42,\cdot)\) \(\chi_{125}(47,\cdot)\) \(\chi_{125}(48,\cdot)\) \(\chi_{125}(52,\cdot)\) \(\chi_{125}(53,\cdot)\) \(\chi_{125}(58,\cdot)\) \(\chi_{125}(62,\cdot)\) \(\chi_{125}(63,\cdot)\) \(\chi_{125}(67,\cdot)\) \(\chi_{125}(72,\cdot)\) \(\chi_{125}(73,\cdot)\) \(\chi_{125}(77,\cdot)\) \(\chi_{125}(78,\cdot)\) \(\chi_{125}(83,\cdot)\) \(\chi_{125}(87,\cdot)\) \(\chi_{125}(88,\cdot)\) \(\chi_{125}(92,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\(2\) → \(e\left(\frac{11}{100}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 125 }(48, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) |