Basic properties
| Modulus: | \(9216\) | |
| Conductor: | \(768\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{768}(443,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9216.bu
\(\chi_{9216}(143,\cdot)\) \(\chi_{9216}(431,\cdot)\) \(\chi_{9216}(719,\cdot)\) \(\chi_{9216}(1007,\cdot)\) \(\chi_{9216}(1295,\cdot)\) \(\chi_{9216}(1583,\cdot)\) \(\chi_{9216}(1871,\cdot)\) \(\chi_{9216}(2159,\cdot)\) \(\chi_{9216}(2447,\cdot)\) \(\chi_{9216}(2735,\cdot)\) \(\chi_{9216}(3023,\cdot)\) \(\chi_{9216}(3311,\cdot)\) \(\chi_{9216}(3599,\cdot)\) \(\chi_{9216}(3887,\cdot)\) \(\chi_{9216}(4175,\cdot)\) \(\chi_{9216}(4463,\cdot)\) \(\chi_{9216}(4751,\cdot)\) \(\chi_{9216}(5039,\cdot)\) \(\chi_{9216}(5327,\cdot)\) \(\chi_{9216}(5615,\cdot)\) \(\chi_{9216}(5903,\cdot)\) \(\chi_{9216}(6191,\cdot)\) \(\chi_{9216}(6479,\cdot)\) \(\chi_{9216}(6767,\cdot)\) \(\chi_{9216}(7055,\cdot)\) \(\chi_{9216}(7343,\cdot)\) \(\chi_{9216}(7631,\cdot)\) \(\chi_{9216}(7919,\cdot)\) \(\chi_{9216}(8207,\cdot)\) \(\chi_{9216}(8495,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((8191,2053,4097)\) → \((-1,e\left(\frac{49}{64}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 9216 }(143, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |