Basic properties
| Modulus: | \(1536\) | |
| Conductor: | \(1536\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | 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 1536.be
\(\chi_{1536}(11,\cdot)\) \(\chi_{1536}(35,\cdot)\) \(\chi_{1536}(59,\cdot)\) \(\chi_{1536}(83,\cdot)\) \(\chi_{1536}(107,\cdot)\) \(\chi_{1536}(131,\cdot)\) \(\chi_{1536}(155,\cdot)\) \(\chi_{1536}(179,\cdot)\) \(\chi_{1536}(203,\cdot)\) \(\chi_{1536}(227,\cdot)\) \(\chi_{1536}(251,\cdot)\) \(\chi_{1536}(275,\cdot)\) \(\chi_{1536}(299,\cdot)\) \(\chi_{1536}(323,\cdot)\) \(\chi_{1536}(347,\cdot)\) \(\chi_{1536}(371,\cdot)\) \(\chi_{1536}(395,\cdot)\) \(\chi_{1536}(419,\cdot)\) \(\chi_{1536}(443,\cdot)\) \(\chi_{1536}(467,\cdot)\) \(\chi_{1536}(491,\cdot)\) \(\chi_{1536}(515,\cdot)\) \(\chi_{1536}(539,\cdot)\) \(\chi_{1536}(563,\cdot)\) \(\chi_{1536}(587,\cdot)\) \(\chi_{1536}(611,\cdot)\) \(\chi_{1536}(635,\cdot)\) \(\chi_{1536}(659,\cdot)\) \(\chi_{1536}(683,\cdot)\) \(\chi_{1536}(707,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((511,517,1025)\) → \((-1,e\left(\frac{85}{128}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1536 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{128}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{57}{128}\right)\) | \(e\left(\frac{91}{128}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{99}{128}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{23}{128}\right)\) | \(e\left(\frac{13}{16}\right)\) |