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 \(\chi_{2009}(78,\cdot)\) | 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
\((4019,493,2794)\) → \((1,e\left(\frac{3}{7}\right),e\left(\frac{4}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(4096, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |