Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(6025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | 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 6025.iv
\(\chi_{6025}(19,\cdot)\) \(\chi_{6025}(89,\cdot)\) \(\chi_{6025}(219,\cdot)\) \(\chi_{6025}(279,\cdot)\) \(\chi_{6025}(304,\cdot)\) \(\chi_{6025}(329,\cdot)\) \(\chi_{6025}(394,\cdot)\) \(\chi_{6025}(419,\cdot)\) \(\chi_{6025}(444,\cdot)\) \(\chi_{6025}(504,\cdot)\) \(\chi_{6025}(634,\cdot)\) \(\chi_{6025}(704,\cdot)\) \(\chi_{6025}(734,\cdot)\) \(\chi_{6025}(1029,\cdot)\) \(\chi_{6025}(1194,\cdot)\) \(\chi_{6025}(1294,\cdot)\) \(\chi_{6025}(1484,\cdot)\) \(\chi_{6025}(1509,\cdot)\) \(\chi_{6025}(1534,\cdot)\) \(\chi_{6025}(1709,\cdot)\) \(\chi_{6025}(1839,\cdot)\) \(\chi_{6025}(1909,\cdot)\) \(\chi_{6025}(1939,\cdot)\) \(\chi_{6025}(2104,\cdot)\) \(\chi_{6025}(2234,\cdot)\) \(\chi_{6025}(2429,\cdot)\) \(\chi_{6025}(2629,\cdot)\) \(\chi_{6025}(2689,\cdot)\) \(\chi_{6025}(2714,\cdot)\) \(\chi_{6025}(2739,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{17}{48}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{179}{240}\right)\) |