Basic properties
| Modulus: | \(5184\) | |
| Conductor: | \(5184\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(432\) | 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 5184.db
\(\chi_{5184}(11,\cdot)\) \(\chi_{5184}(59,\cdot)\) \(\chi_{5184}(83,\cdot)\) \(\chi_{5184}(131,\cdot)\) \(\chi_{5184}(155,\cdot)\) \(\chi_{5184}(203,\cdot)\) \(\chi_{5184}(227,\cdot)\) \(\chi_{5184}(275,\cdot)\) \(\chi_{5184}(299,\cdot)\) \(\chi_{5184}(347,\cdot)\) \(\chi_{5184}(371,\cdot)\) \(\chi_{5184}(419,\cdot)\) \(\chi_{5184}(443,\cdot)\) \(\chi_{5184}(491,\cdot)\) \(\chi_{5184}(515,\cdot)\) \(\chi_{5184}(563,\cdot)\) \(\chi_{5184}(587,\cdot)\) \(\chi_{5184}(635,\cdot)\) \(\chi_{5184}(659,\cdot)\) \(\chi_{5184}(707,\cdot)\) \(\chi_{5184}(731,\cdot)\) \(\chi_{5184}(779,\cdot)\) \(\chi_{5184}(803,\cdot)\) \(\chi_{5184}(851,\cdot)\) \(\chi_{5184}(875,\cdot)\) \(\chi_{5184}(923,\cdot)\) \(\chi_{5184}(947,\cdot)\) \(\chi_{5184}(995,\cdot)\) \(\chi_{5184}(1019,\cdot)\) \(\chi_{5184}(1067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{432})$ |
| Fixed field: | Number field defined by a degree 432 polynomial (not computed) |
Values on generators
\((2431,325,1217)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{53}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5184 }(851, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{432}\right)\) | \(e\left(\frac{125}{216}\right)\) | \(e\left(\frac{193}{432}\right)\) | \(e\left(\frac{179}{432}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{97}{144}\right)\) | \(e\left(\frac{91}{216}\right)\) | \(e\left(\frac{5}{216}\right)\) | \(e\left(\frac{55}{432}\right)\) | \(e\left(\frac{17}{27}\right)\) |