Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(6017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(546\) | 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 6017.cc
\(\chi_{6017}(32,\cdot)\) \(\chi_{6017}(43,\cdot)\) \(\chi_{6017}(109,\cdot)\) \(\chi_{6017}(153,\cdot)\) \(\chi_{6017}(175,\cdot)\) \(\chi_{6017}(186,\cdot)\) \(\chi_{6017}(219,\cdot)\) \(\chi_{6017}(230,\cdot)\) \(\chi_{6017}(241,\cdot)\) \(\chi_{6017}(274,\cdot)\) \(\chi_{6017}(373,\cdot)\) \(\chi_{6017}(417,\cdot)\) \(\chi_{6017}(428,\cdot)\) \(\chi_{6017}(450,\cdot)\) \(\chi_{6017}(461,\cdot)\) \(\chi_{6017}(494,\cdot)\) \(\chi_{6017}(549,\cdot)\) \(\chi_{6017}(604,\cdot)\) \(\chi_{6017}(659,\cdot)\) \(\chi_{6017}(681,\cdot)\) \(\chi_{6017}(747,\cdot)\) \(\chi_{6017}(758,\cdot)\) \(\chi_{6017}(835,\cdot)\) \(\chi_{6017}(901,\cdot)\) \(\chi_{6017}(923,\cdot)\) \(\chi_{6017}(934,\cdot)\) \(\chi_{6017}(967,\cdot)\) \(\chi_{6017}(978,\cdot)\) \(\chi_{6017}(1088,\cdot)\) \(\chi_{6017}(1099,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 546 polynomial (not computed) |
Values on generators
\((3830,2190)\) → \((-1,e\left(\frac{191}{546}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 6017 }(241, a) \) | \(1\) | \(1\) | \(e\left(\frac{232}{273}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{191}{273}\right)\) | \(e\left(\frac{337}{546}\right)\) | \(e\left(\frac{503}{546}\right)\) | \(e\left(\frac{145}{273}\right)\) | \(e\left(\frac{50}{91}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{85}{182}\right)\) | \(e\left(\frac{421}{546}\right)\) |