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.dj
\(\chi_{6027}(461,\cdot)\) \(\chi_{6027}(713,\cdot)\) \(\chi_{6027}(797,\cdot)\) \(\chi_{6027}(1574,\cdot)\) \(\chi_{6027}(1595,\cdot)\) \(\chi_{6027}(1658,\cdot)\) \(\chi_{6027}(2183,\cdot)\) \(\chi_{6027}(2435,\cdot)\) \(\chi_{6027}(2456,\cdot)\) \(\chi_{6027}(2519,\cdot)\) \(\chi_{6027}(3044,\cdot)\) \(\chi_{6027}(3296,\cdot)\) \(\chi_{6027}(3317,\cdot)\) \(\chi_{6027}(3905,\cdot)\) \(\chi_{6027}(4157,\cdot)\) \(\chi_{6027}(4178,\cdot)\) \(\chi_{6027}(4241,\cdot)\) \(\chi_{6027}(4766,\cdot)\) \(\chi_{6027}(5018,\cdot)\) \(\chi_{6027}(5039,\cdot)\) \(\chi_{6027}(5102,\cdot)\) \(\chi_{6027}(5627,\cdot)\) \(\chi_{6027}(5900,\cdot)\) \(\chi_{6027}(5963,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{3}{14}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(2435, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) |