Basic properties
| Modulus: | \(4608\) | |
| 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 \(\chi_{1536}(611,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.cc
\(\chi_{4608}(35,\cdot)\) \(\chi_{4608}(107,\cdot)\) \(\chi_{4608}(179,\cdot)\) \(\chi_{4608}(251,\cdot)\) \(\chi_{4608}(323,\cdot)\) \(\chi_{4608}(395,\cdot)\) \(\chi_{4608}(467,\cdot)\) \(\chi_{4608}(539,\cdot)\) \(\chi_{4608}(611,\cdot)\) \(\chi_{4608}(683,\cdot)\) \(\chi_{4608}(755,\cdot)\) \(\chi_{4608}(827,\cdot)\) \(\chi_{4608}(899,\cdot)\) \(\chi_{4608}(971,\cdot)\) \(\chi_{4608}(1043,\cdot)\) \(\chi_{4608}(1115,\cdot)\) \(\chi_{4608}(1187,\cdot)\) \(\chi_{4608}(1259,\cdot)\) \(\chi_{4608}(1331,\cdot)\) \(\chi_{4608}(1403,\cdot)\) \(\chi_{4608}(1475,\cdot)\) \(\chi_{4608}(1547,\cdot)\) \(\chi_{4608}(1619,\cdot)\) \(\chi_{4608}(1691,\cdot)\) \(\chi_{4608}(1763,\cdot)\) \(\chi_{4608}(1835,\cdot)\) \(\chi_{4608}(1907,\cdot)\) \(\chi_{4608}(1979,\cdot)\) \(\chi_{4608}(2051,\cdot)\) \(\chi_{4608}(2123,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{27}{128}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(611, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{128}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{119}{128}\right)\) | \(e\left(\frac{53}{128}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{45}{128}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{57}{128}\right)\) | \(e\left(\frac{3}{16}\right)\) |