Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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.dk
\(\chi_{6027}(209,\cdot)\) \(\chi_{6027}(230,\cdot)\) \(\chi_{6027}(482,\cdot)\) \(\chi_{6027}(1007,\cdot)\) \(\chi_{6027}(1070,\cdot)\) \(\chi_{6027}(1091,\cdot)\) \(\chi_{6027}(1343,\cdot)\) \(\chi_{6027}(1868,\cdot)\) \(\chi_{6027}(1931,\cdot)\) \(\chi_{6027}(1952,\cdot)\) \(\chi_{6027}(2729,\cdot)\) \(\chi_{6027}(2813,\cdot)\) \(\chi_{6027}(3065,\cdot)\) \(\chi_{6027}(3590,\cdot)\) \(\chi_{6027}(3653,\cdot)\) \(\chi_{6027}(3926,\cdot)\) \(\chi_{6027}(4451,\cdot)\) \(\chi_{6027}(4514,\cdot)\) \(\chi_{6027}(4535,\cdot)\) \(\chi_{6027}(4787,\cdot)\) \(\chi_{6027}(5312,\cdot)\) \(\chi_{6027}(5375,\cdot)\) \(\chi_{6027}(5396,\cdot)\) \(\chi_{6027}(5648,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(4451, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) |