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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1536.bf
\(\chi_{1536}(5,\cdot)\) \(\chi_{1536}(29,\cdot)\) \(\chi_{1536}(53,\cdot)\) \(\chi_{1536}(77,\cdot)\) \(\chi_{1536}(101,\cdot)\) \(\chi_{1536}(125,\cdot)\) \(\chi_{1536}(149,\cdot)\) \(\chi_{1536}(173,\cdot)\) \(\chi_{1536}(197,\cdot)\) \(\chi_{1536}(221,\cdot)\) \(\chi_{1536}(245,\cdot)\) \(\chi_{1536}(269,\cdot)\) \(\chi_{1536}(293,\cdot)\) \(\chi_{1536}(317,\cdot)\) \(\chi_{1536}(341,\cdot)\) \(\chi_{1536}(365,\cdot)\) \(\chi_{1536}(389,\cdot)\) \(\chi_{1536}(413,\cdot)\) \(\chi_{1536}(437,\cdot)\) \(\chi_{1536}(461,\cdot)\) \(\chi_{1536}(485,\cdot)\) \(\chi_{1536}(509,\cdot)\) \(\chi_{1536}(533,\cdot)\) \(\chi_{1536}(557,\cdot)\) \(\chi_{1536}(581,\cdot)\) \(\chi_{1536}(605,\cdot)\) \(\chi_{1536}(629,\cdot)\) \(\chi_{1536}(653,\cdot)\) \(\chi_{1536}(677,\cdot)\) \(\chi_{1536}(701,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((511,517,1025)\) → \((1,e\left(\frac{13}{128}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1536 }(917, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{128}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{17}{128}\right)\) | \(e\left(\frac{35}{128}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{43}{128}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{127}{128}\right)\) | \(e\left(\frac{13}{16}\right)\) |