Basic properties
| Modulus: | \(9216\) | |
| Conductor: | \(512\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{512}(157,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9216.cb
\(\chi_{9216}(73,\cdot)\) \(\chi_{9216}(217,\cdot)\) \(\chi_{9216}(361,\cdot)\) \(\chi_{9216}(505,\cdot)\) \(\chi_{9216}(649,\cdot)\) \(\chi_{9216}(793,\cdot)\) \(\chi_{9216}(937,\cdot)\) \(\chi_{9216}(1081,\cdot)\) \(\chi_{9216}(1225,\cdot)\) \(\chi_{9216}(1369,\cdot)\) \(\chi_{9216}(1513,\cdot)\) \(\chi_{9216}(1657,\cdot)\) \(\chi_{9216}(1801,\cdot)\) \(\chi_{9216}(1945,\cdot)\) \(\chi_{9216}(2089,\cdot)\) \(\chi_{9216}(2233,\cdot)\) \(\chi_{9216}(2377,\cdot)\) \(\chi_{9216}(2521,\cdot)\) \(\chi_{9216}(2665,\cdot)\) \(\chi_{9216}(2809,\cdot)\) \(\chi_{9216}(2953,\cdot)\) \(\chi_{9216}(3097,\cdot)\) \(\chi_{9216}(3241,\cdot)\) \(\chi_{9216}(3385,\cdot)\) \(\chi_{9216}(3529,\cdot)\) \(\chi_{9216}(3673,\cdot)\) \(\chi_{9216}(3817,\cdot)\) \(\chi_{9216}(3961,\cdot)\) \(\chi_{9216}(4105,\cdot)\) \(\chi_{9216}(4249,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((8191,2053,4097)\) → \((1,e\left(\frac{91}{128}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9216 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{128}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{55}{128}\right)\) | \(e\left(\frac{117}{128}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{45}{128}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{57}{128}\right)\) | \(e\left(\frac{11}{16}\right)\) |