Basic properties
Modulus: | \(6027\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(1009,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.dn
\(\chi_{6027}(64,\cdot)\) \(\chi_{6027}(127,\cdot)\) \(\chi_{6027}(400,\cdot)\) \(\chi_{6027}(925,\cdot)\) \(\chi_{6027}(988,\cdot)\) \(\chi_{6027}(1009,\cdot)\) \(\chi_{6027}(1261,\cdot)\) \(\chi_{6027}(1786,\cdot)\) \(\chi_{6027}(1849,\cdot)\) \(\chi_{6027}(1870,\cdot)\) \(\chi_{6027}(2122,\cdot)\) \(\chi_{6027}(2710,\cdot)\) \(\chi_{6027}(2731,\cdot)\) \(\chi_{6027}(2983,\cdot)\) \(\chi_{6027}(3508,\cdot)\) \(\chi_{6027}(3571,\cdot)\) \(\chi_{6027}(3592,\cdot)\) \(\chi_{6027}(3844,\cdot)\) \(\chi_{6027}(4369,\cdot)\) \(\chi_{6027}(4432,\cdot)\) \(\chi_{6027}(4453,\cdot)\) \(\chi_{6027}(5230,\cdot)\) \(\chi_{6027}(5314,\cdot)\) \(\chi_{6027}(5566,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{3}{7}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(1009, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) |