Basic properties
| Modulus: | \(1375\) | |
| Conductor: | \(1375\) | 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 1375.cs
\(\chi_{1375}(37,\cdot)\) \(\chi_{1375}(53,\cdot)\) \(\chi_{1375}(97,\cdot)\) \(\chi_{1375}(102,\cdot)\) \(\chi_{1375}(192,\cdot)\) \(\chi_{1375}(213,\cdot)\) \(\chi_{1375}(223,\cdot)\) \(\chi_{1375}(258,\cdot)\) \(\chi_{1375}(312,\cdot)\) \(\chi_{1375}(328,\cdot)\) \(\chi_{1375}(372,\cdot)\) \(\chi_{1375}(377,\cdot)\) \(\chi_{1375}(467,\cdot)\) \(\chi_{1375}(488,\cdot)\) \(\chi_{1375}(498,\cdot)\) \(\chi_{1375}(533,\cdot)\) \(\chi_{1375}(587,\cdot)\) \(\chi_{1375}(603,\cdot)\) \(\chi_{1375}(647,\cdot)\) \(\chi_{1375}(652,\cdot)\) \(\chi_{1375}(742,\cdot)\) \(\chi_{1375}(763,\cdot)\) \(\chi_{1375}(773,\cdot)\) \(\chi_{1375}(808,\cdot)\) \(\chi_{1375}(862,\cdot)\) \(\chi_{1375}(878,\cdot)\) \(\chi_{1375}(922,\cdot)\) \(\chi_{1375}(927,\cdot)\) \(\chi_{1375}(1017,\cdot)\) \(\chi_{1375}(1038,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{19}{100}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1375 }(1038, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) |