Basic properties
| Modulus: | \(6010\) | |
| Conductor: | \(3005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(600\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3005}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6010.dc
\(\chi_{6010}(7,\cdot)\) \(\chi_{6010}(43,\cdot)\) \(\chi_{6010}(53,\cdot)\) \(\chi_{6010}(93,\cdot)\) \(\chi_{6010}(143,\cdot)\) \(\chi_{6010}(173,\cdot)\) \(\chi_{6010}(253,\cdot)\) \(\chi_{6010}(283,\cdot)\) \(\chi_{6010}(297,\cdot)\) \(\chi_{6010}(317,\cdot)\) \(\chi_{6010}(337,\cdot)\) \(\chi_{6010}(377,\cdot)\) \(\chi_{6010}(487,\cdot)\) \(\chi_{6010}(517,\cdot)\) \(\chi_{6010}(543,\cdot)\) \(\chi_{6010}(557,\cdot)\) \(\chi_{6010}(567,\cdot)\) \(\chi_{6010}(587,\cdot)\) \(\chi_{6010}(657,\cdot)\) \(\chi_{6010}(667,\cdot)\) \(\chi_{6010}(683,\cdot)\) \(\chi_{6010}(737,\cdot)\) \(\chi_{6010}(747,\cdot)\) \(\chi_{6010}(773,\cdot)\) \(\chi_{6010}(783,\cdot)\) \(\chi_{6010}(807,\cdot)\) \(\chi_{6010}(813,\cdot)\) \(\chi_{6010}(833,\cdot)\) \(\chi_{6010}(937,\cdot)\) \(\chi_{6010}(1043,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{600})$ |
| Fixed field: | Number field defined by a degree 600 polynomial (not computed) |
Values on generators
\((3607,2411)\) → \((i,e\left(\frac{1}{600}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6010 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{300}\right)\) | \(e\left(\frac{151}{600}\right)\) | \(e\left(\frac{77}{150}\right)\) | \(e\left(\frac{157}{600}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{541}{600}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{44}{75}\right)\) | \(e\left(\frac{77}{100}\right)\) |