Basic properties
| Modulus: | \(6010\) | |
| Conductor: | \(3005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3005}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6010.cq
\(\chi_{6010}(9,\cdot)\) \(\chi_{6010}(649,\cdot)\) \(\chi_{6010}(789,\cdot)\) \(\chi_{6010}(869,\cdot)\) \(\chi_{6010}(889,\cdot)\) \(\chi_{6010}(1249,\cdot)\) \(\chi_{6010}(1269,\cdot)\) \(\chi_{6010}(1729,\cdot)\) \(\chi_{6010}(1809,\cdot)\) \(\chi_{6010}(1839,\cdot)\) \(\chi_{6010}(1899,\cdot)\) \(\chi_{6010}(2179,\cdot)\) \(\chi_{6010}(2209,\cdot)\) \(\chi_{6010}(2289,\cdot)\) \(\chi_{6010}(2709,\cdot)\) \(\chi_{6010}(3099,\cdot)\) \(\chi_{6010}(3139,\cdot)\) \(\chi_{6010}(3149,\cdot)\) \(\chi_{6010}(3339,\cdot)\) \(\chi_{6010}(3389,\cdot)\) \(\chi_{6010}(3609,\cdot)\) \(\chi_{6010}(3809,\cdot)\) \(\chi_{6010}(4059,\cdot)\) \(\chi_{6010}(4219,\cdot)\) \(\chi_{6010}(4279,\cdot)\) \(\chi_{6010}(4369,\cdot)\) \(\chi_{6010}(4399,\cdot)\) \(\chi_{6010}(4489,\cdot)\) \(\chi_{6010}(4509,\cdot)\) \(\chi_{6010}(4629,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((3607,2411)\) → \((-1,e\left(\frac{1}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6010 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{150}\right)\) | \(e\left(\frac{77}{150}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{7}{75}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{16}{75}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{150}\right)\) | \(e\left(\frac{33}{50}\right)\) |