Basic properties
| Modulus: | \(4275\) | |
| Conductor: | \(4275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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 4275.gz
\(\chi_{4275}(22,\cdot)\) \(\chi_{4275}(337,\cdot)\) \(\chi_{4275}(412,\cdot)\) \(\chi_{4275}(508,\cdot)\) \(\chi_{4275}(547,\cdot)\) \(\chi_{4275}(553,\cdot)\) \(\chi_{4275}(583,\cdot)\) \(\chi_{4275}(637,\cdot)\) \(\chi_{4275}(808,\cdot)\) \(\chi_{4275}(877,\cdot)\) \(\chi_{4275}(1048,\cdot)\) \(\chi_{4275}(1192,\cdot)\) \(\chi_{4275}(1237,\cdot)\) \(\chi_{4275}(1267,\cdot)\) \(\chi_{4275}(1363,\cdot)\) \(\chi_{4275}(1402,\cdot)\) \(\chi_{4275}(1408,\cdot)\) \(\chi_{4275}(1438,\cdot)\) \(\chi_{4275}(1492,\cdot)\) \(\chi_{4275}(1573,\cdot)\) \(\chi_{4275}(1663,\cdot)\) \(\chi_{4275}(1903,\cdot)\) \(\chi_{4275}(2047,\cdot)\) \(\chi_{4275}(2092,\cdot)\) \(\chi_{4275}(2122,\cdot)\) \(\chi_{4275}(2263,\cdot)\) \(\chi_{4275}(2347,\cdot)\) \(\chi_{4275}(2428,\cdot)\) \(\chi_{4275}(2587,\cdot)\) \(\chi_{4275}(2758,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{17}{20}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 4275 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{49}{180}\right)\) | \(e\left(\frac{91}{180}\right)\) |