Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 6027.ei
\(\chi_{6027}(236,\cdot)\) \(\chi_{6027}(269,\cdot)\) \(\chi_{6027}(332,\cdot)\) \(\chi_{6027}(353,\cdot)\) \(\chi_{6027}(605,\cdot)\) \(\chi_{6027}(761,\cdot)\) \(\chi_{6027}(824,\cdot)\) \(\chi_{6027}(845,\cdot)\) \(\chi_{6027}(1130,\cdot)\) \(\chi_{6027}(1193,\cdot)\) \(\chi_{6027}(1214,\cdot)\) \(\chi_{6027}(1466,\cdot)\) \(\chi_{6027}(1622,\cdot)\) \(\chi_{6027}(1706,\cdot)\) \(\chi_{6027}(1958,\cdot)\) \(\chi_{6027}(2054,\cdot)\) \(\chi_{6027}(2075,\cdot)\) \(\chi_{6027}(2327,\cdot)\) \(\chi_{6027}(2483,\cdot)\) \(\chi_{6027}(2546,\cdot)\) \(\chi_{6027}(2819,\cdot)\) \(\chi_{6027}(2852,\cdot)\) \(\chi_{6027}(2915,\cdot)\) \(\chi_{6027}(2936,\cdot)\) \(\chi_{6027}(3188,\cdot)\) \(\chi_{6027}(3344,\cdot)\) \(\chi_{6027}(3407,\cdot)\) \(\chi_{6027}(3428,\cdot)\) \(\chi_{6027}(3680,\cdot)\) \(\chi_{6027}(3713,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{31}{42}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(2936, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{11}{15}\right)\) |