Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{241}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.jq
\(\chi_{6025}(51,\cdot)\) \(\chi_{6025}(276,\cdot)\) \(\chi_{6025}(351,\cdot)\) \(\chi_{6025}(426,\cdot)\) \(\chi_{6025}(451,\cdot)\) \(\chi_{6025}(551,\cdot)\) \(\chi_{6025}(801,\cdot)\) \(\chi_{6025}(951,\cdot)\) \(\chi_{6025}(1001,\cdot)\) \(\chi_{6025}(1026,\cdot)\) \(\chi_{6025}(1076,\cdot)\) \(\chi_{6025}(1101,\cdot)\) \(\chi_{6025}(1251,\cdot)\) \(\chi_{6025}(1276,\cdot)\) \(\chi_{6025}(1351,\cdot)\) \(\chi_{6025}(1376,\cdot)\) \(\chi_{6025}(1501,\cdot)\) \(\chi_{6025}(1601,\cdot)\) \(\chi_{6025}(1701,\cdot)\) \(\chi_{6025}(1726,\cdot)\) \(\chi_{6025}(1801,\cdot)\) \(\chi_{6025}(1876,\cdot)\) \(\chi_{6025}(2101,\cdot)\) \(\chi_{6025}(2176,\cdot)\) \(\chi_{6025}(2301,\cdot)\) \(\chi_{6025}(2326,\cdot)\) \(\chi_{6025}(2376,\cdot)\) \(\chi_{6025}(2476,\cdot)\) \(\chi_{6025}(2826,\cdot)\) \(\chi_{6025}(2926,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((1,e\left(\frac{1}{240}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(2176, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{240}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{47}{240}\right)\) |