Basic properties
| Modulus: | \(6025\) | |
| Conductor: | \(1205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1205}(664,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.im
\(\chi_{6025}(49,\cdot)\) \(\chi_{6025}(174,\cdot)\) \(\chi_{6025}(349,\cdot)\) \(\chi_{6025}(374,\cdot)\) \(\chi_{6025}(549,\cdot)\) \(\chi_{6025}(674,\cdot)\) \(\chi_{6025}(1374,\cdot)\) \(\chi_{6025}(1449,\cdot)\) \(\chi_{6025}(1499,\cdot)\) \(\chi_{6025}(1699,\cdot)\) \(\chi_{6025}(1899,\cdot)\) \(\chi_{6025}(2124,\cdot)\) \(\chi_{6025}(2149,\cdot)\) \(\chi_{6025}(2249,\cdot)\) \(\chi_{6025}(2574,\cdot)\) \(\chi_{6025}(2874,\cdot)\) \(\chi_{6025}(3074,\cdot)\) \(\chi_{6025}(3299,\cdot)\) \(\chi_{6025}(3324,\cdot)\) \(\chi_{6025}(3424,\cdot)\) \(\chi_{6025}(3449,\cdot)\) \(\chi_{6025}(3674,\cdot)\) \(\chi_{6025}(3874,\cdot)\) \(\chi_{6025}(4174,\cdot)\) \(\chi_{6025}(4499,\cdot)\) \(\chi_{6025}(4599,\cdot)\) \(\chi_{6025}(4624,\cdot)\) \(\chi_{6025}(4849,\cdot)\) \(\chi_{6025}(5049,\cdot)\) \(\chi_{6025}(5249,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((-1,e\left(\frac{119}{120}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6025 }(3074, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(-i\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{13}{120}\right)\) |