Basic properties
| Modulus: | \(3328\) | |
| Conductor: | \(3328\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3328.dc
\(\chi_{3328}(83,\cdot)\) \(\chi_{3328}(203,\cdot)\) \(\chi_{3328}(291,\cdot)\) \(\chi_{3328}(411,\cdot)\) \(\chi_{3328}(499,\cdot)\) \(\chi_{3328}(619,\cdot)\) \(\chi_{3328}(707,\cdot)\) \(\chi_{3328}(827,\cdot)\) \(\chi_{3328}(915,\cdot)\) \(\chi_{3328}(1035,\cdot)\) \(\chi_{3328}(1123,\cdot)\) \(\chi_{3328}(1243,\cdot)\) \(\chi_{3328}(1331,\cdot)\) \(\chi_{3328}(1451,\cdot)\) \(\chi_{3328}(1539,\cdot)\) \(\chi_{3328}(1659,\cdot)\) \(\chi_{3328}(1747,\cdot)\) \(\chi_{3328}(1867,\cdot)\) \(\chi_{3328}(1955,\cdot)\) \(\chi_{3328}(2075,\cdot)\) \(\chi_{3328}(2163,\cdot)\) \(\chi_{3328}(2283,\cdot)\) \(\chi_{3328}(2371,\cdot)\) \(\chi_{3328}(2491,\cdot)\) \(\chi_{3328}(2579,\cdot)\) \(\chi_{3328}(2699,\cdot)\) \(\chi_{3328}(2787,\cdot)\) \(\chi_{3328}(2907,\cdot)\) \(\chi_{3328}(2995,\cdot)\) \(\chi_{3328}(3115,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1535,261,769)\) → \((-1,e\left(\frac{21}{64}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3328 }(1035, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{19}{32}\right)\) |