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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1375.cl
\(\chi_{1375}(28,\cdot)\) \(\chi_{1375}(63,\cdot)\) \(\chi_{1375}(72,\cdot)\) \(\chi_{1375}(73,\cdot)\) \(\chi_{1375}(162,\cdot)\) \(\chi_{1375}(167,\cdot)\) \(\chi_{1375}(227,\cdot)\) \(\chi_{1375}(233,\cdot)\) \(\chi_{1375}(303,\cdot)\) \(\chi_{1375}(338,\cdot)\) \(\chi_{1375}(347,\cdot)\) \(\chi_{1375}(348,\cdot)\) \(\chi_{1375}(437,\cdot)\) \(\chi_{1375}(442,\cdot)\) \(\chi_{1375}(502,\cdot)\) \(\chi_{1375}(508,\cdot)\) \(\chi_{1375}(578,\cdot)\) \(\chi_{1375}(613,\cdot)\) \(\chi_{1375}(622,\cdot)\) \(\chi_{1375}(623,\cdot)\) \(\chi_{1375}(712,\cdot)\) \(\chi_{1375}(717,\cdot)\) \(\chi_{1375}(777,\cdot)\) \(\chi_{1375}(783,\cdot)\) \(\chi_{1375}(853,\cdot)\) \(\chi_{1375}(888,\cdot)\) \(\chi_{1375}(897,\cdot)\) \(\chi_{1375}(898,\cdot)\) \(\chi_{1375}(987,\cdot)\) \(\chi_{1375}(992,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{59}{100}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1375 }(613, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(i\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) |