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
\((4019,493,2794)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(1070, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) |