Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | 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 6017.ca
\(\chi_{6017}(26,\cdot)\) \(\chi_{6017}(59,\cdot)\) \(\chi_{6017}(102,\cdot)\) \(\chi_{6017}(245,\cdot)\) \(\chi_{6017}(251,\cdot)\) \(\chi_{6017}(366,\cdot)\) \(\chi_{6017}(411,\cdot)\) \(\chi_{6017}(493,\cdot)\) \(\chi_{6017}(500,\cdot)\) \(\chi_{6017}(526,\cdot)\) \(\chi_{6017}(630,\cdot)\) \(\chi_{6017}(653,\cdot)\) \(\chi_{6017}(675,\cdot)\) \(\chi_{6017}(861,\cdot)\) \(\chi_{6017}(863,\cdot)\) \(\chi_{6017}(895,\cdot)\) \(\chi_{6017}(973,\cdot)\) \(\chi_{6017}(1083,\cdot)\) \(\chi_{6017}(1120,\cdot)\) \(\chi_{6017}(1153,\cdot)\) \(\chi_{6017}(1345,\cdot)\) \(\chi_{6017}(1402,\cdot)\) \(\chi_{6017}(1424,\cdot)\) \(\chi_{6017}(1505,\cdot)\) \(\chi_{6017}(1512,\cdot)\) \(\chi_{6017}(1545,\cdot)\) \(\chi_{6017}(1587,\cdot)\) \(\chi_{6017}(1620,\cdot)\) \(\chi_{6017}(1743,\cdot)\) \(\chi_{6017}(1747,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{41}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{283}{390}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{88}{195}\right)\) | \(e\left(\frac{347}{390}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{211}{390}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{43}{78}\right)\) |