Basic properties
| Modulus: | \(9216\) | |
| Conductor: | \(1536\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1536}(1259,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9216.cc
\(\chi_{9216}(71,\cdot)\) \(\chi_{9216}(215,\cdot)\) \(\chi_{9216}(359,\cdot)\) \(\chi_{9216}(503,\cdot)\) \(\chi_{9216}(647,\cdot)\) \(\chi_{9216}(791,\cdot)\) \(\chi_{9216}(935,\cdot)\) \(\chi_{9216}(1079,\cdot)\) \(\chi_{9216}(1223,\cdot)\) \(\chi_{9216}(1367,\cdot)\) \(\chi_{9216}(1511,\cdot)\) \(\chi_{9216}(1655,\cdot)\) \(\chi_{9216}(1799,\cdot)\) \(\chi_{9216}(1943,\cdot)\) \(\chi_{9216}(2087,\cdot)\) \(\chi_{9216}(2231,\cdot)\) \(\chi_{9216}(2375,\cdot)\) \(\chi_{9216}(2519,\cdot)\) \(\chi_{9216}(2663,\cdot)\) \(\chi_{9216}(2807,\cdot)\) \(\chi_{9216}(2951,\cdot)\) \(\chi_{9216}(3095,\cdot)\) \(\chi_{9216}(3239,\cdot)\) \(\chi_{9216}(3383,\cdot)\) \(\chi_{9216}(3527,\cdot)\) \(\chi_{9216}(3671,\cdot)\) \(\chi_{9216}(3815,\cdot)\) \(\chi_{9216}(3959,\cdot)\) \(\chi_{9216}(4103,\cdot)\) \(\chi_{9216}(4247,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((8191,2053,4097)\) → \((-1,e\left(\frac{45}{128}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9216 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{128}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{113}{128}\right)\) | \(e\left(\frac{3}{128}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{75}{128}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{95}{128}\right)\) | \(e\left(\frac{5}{16}\right)\) |