Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.ea
\(\chi_{6027}(8,\cdot)\) \(\chi_{6027}(323,\cdot)\) \(\chi_{6027}(449,\cdot)\) \(\chi_{6027}(512,\cdot)\) \(\chi_{6027}(554,\cdot)\) \(\chi_{6027}(617,\cdot)\) \(\chi_{6027}(743,\cdot)\) \(\chi_{6027}(869,\cdot)\) \(\chi_{6027}(1058,\cdot)\) \(\chi_{6027}(1184,\cdot)\) \(\chi_{6027}(1310,\cdot)\) \(\chi_{6027}(1415,\cdot)\) \(\chi_{6027}(1478,\cdot)\) \(\chi_{6027}(1604,\cdot)\) \(\chi_{6027}(1730,\cdot)\) \(\chi_{6027}(1919,\cdot)\) \(\chi_{6027}(2045,\cdot)\) \(\chi_{6027}(2171,\cdot)\) \(\chi_{6027}(2234,\cdot)\) \(\chi_{6027}(2276,\cdot)\) \(\chi_{6027}(2339,\cdot)\) \(\chi_{6027}(2465,\cdot)\) \(\chi_{6027}(2591,\cdot)\) \(\chi_{6027}(2780,\cdot)\) \(\chi_{6027}(2906,\cdot)\) \(\chi_{6027}(3032,\cdot)\) \(\chi_{6027}(3095,\cdot)\) \(\chi_{6027}(3200,\cdot)\) \(\chi_{6027}(3326,\cdot)\) \(\chi_{6027}(3452,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{6}{7}\right),e\left(\frac{19}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{11}{20}\right)\) |