Basic properties
| Modulus: | \(1208\) | |
| Conductor: | \(1208\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1208.bu
\(\chi_{1208}(5,\cdot)\) \(\chi_{1208}(21,\cdot)\) \(\chi_{1208}(37,\cdot)\) \(\chi_{1208}(45,\cdot)\) \(\chi_{1208}(69,\cdot)\) \(\chi_{1208}(173,\cdot)\) \(\chi_{1208}(213,\cdot)\) \(\chi_{1208}(333,\cdot)\) \(\chi_{1208}(341,\cdot)\) \(\chi_{1208}(349,\cdot)\) \(\chi_{1208}(357,\cdot)\) \(\chi_{1208}(397,\cdot)\) \(\chi_{1208}(405,\cdot)\) \(\chi_{1208}(493,\cdot)\) \(\chi_{1208}(533,\cdot)\) \(\chi_{1208}(541,\cdot)\) \(\chi_{1208}(589,\cdot)\) \(\chi_{1208}(597,\cdot)\) \(\chi_{1208}(621,\cdot)\) \(\chi_{1208}(629,\cdot)\) \(\chi_{1208}(653,\cdot)\) \(\chi_{1208}(701,\cdot)\) \(\chi_{1208}(725,\cdot)\) \(\chi_{1208}(741,\cdot)\) \(\chi_{1208}(749,\cdot)\) \(\chi_{1208}(765,\cdot)\) \(\chi_{1208}(773,\cdot)\) \(\chi_{1208}(789,\cdot)\) \(\chi_{1208}(797,\cdot)\) \(\chi_{1208}(813,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((303,605,761)\) → \((1,-1,e\left(\frac{29}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1208 }(621, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{121}{150}\right)\) | \(e\left(\frac{68}{75}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{127}{150}\right)\) | \(e\left(\frac{53}{150}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{32}{75}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{109}{150}\right)\) |