Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(939,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.cn
\(\chi_{6027}(379,\cdot)\) \(\chi_{6027}(631,\cdot)\) \(\chi_{6027}(652,\cdot)\) \(\chi_{6027}(715,\cdot)\) \(\chi_{6027}(1240,\cdot)\) \(\chi_{6027}(1492,\cdot)\) \(\chi_{6027}(1513,\cdot)\) \(\chi_{6027}(1576,\cdot)\) \(\chi_{6027}(2101,\cdot)\) \(\chi_{6027}(2374,\cdot)\) \(\chi_{6027}(2437,\cdot)\) \(\chi_{6027}(2962,\cdot)\) \(\chi_{6027}(3214,\cdot)\) \(\chi_{6027}(3298,\cdot)\) \(\chi_{6027}(4075,\cdot)\) \(\chi_{6027}(4096,\cdot)\) \(\chi_{6027}(4159,\cdot)\) \(\chi_{6027}(4684,\cdot)\) \(\chi_{6027}(4936,\cdot)\) \(\chi_{6027}(4957,\cdot)\) \(\chi_{6027}(5020,\cdot)\) \(\chi_{6027}(5545,\cdot)\) \(\chi_{6027}(5797,\cdot)\) \(\chi_{6027}(5818,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{6}{7}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(4957, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |