Basic properties
| Modulus: | \(1208\) | |
| Conductor: | \(604\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{604}(247,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1208.bv
\(\chi_{1208}(7,\cdot)\) \(\chi_{1208}(15,\cdot)\) \(\chi_{1208}(63,\cdot)\) \(\chi_{1208}(71,\cdot)\) \(\chi_{1208}(111,\cdot)\) \(\chi_{1208}(199,\cdot)\) \(\chi_{1208}(207,\cdot)\) \(\chi_{1208}(247,\cdot)\) \(\chi_{1208}(255,\cdot)\) \(\chi_{1208}(263,\cdot)\) \(\chi_{1208}(271,\cdot)\) \(\chi_{1208}(391,\cdot)\) \(\chi_{1208}(431,\cdot)\) \(\chi_{1208}(535,\cdot)\) \(\chi_{1208}(559,\cdot)\) \(\chi_{1208}(567,\cdot)\) \(\chi_{1208}(583,\cdot)\) \(\chi_{1208}(599,\cdot)\) \(\chi_{1208}(639,\cdot)\) \(\chi_{1208}(655,\cdot)\) \(\chi_{1208}(719,\cdot)\) \(\chi_{1208}(767,\cdot)\) \(\chi_{1208}(807,\cdot)\) \(\chi_{1208}(863,\cdot)\) \(\chi_{1208}(895,\cdot)\) \(\chi_{1208}(919,\cdot)\) \(\chi_{1208}(967,\cdot)\) \(\chi_{1208}(983,\cdot)\) \(\chi_{1208}(999,\cdot)\) \(\chi_{1208}(1015,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((303,605,761)\) → \((-1,1,e\left(\frac{131}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1208 }(247, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{61}{75}\right)\) | \(e\left(\frac{1}{75}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{89}{150}\right)\) | \(e\left(\frac{121}{150}\right)\) | \(e\left(\frac{4}{75}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{75}\right)\) |