Basic properties
| Modulus: | \(3456\) | |
| Conductor: | \(3456\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(288\) | 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 3456.cs
\(\chi_{3456}(11,\cdot)\) \(\chi_{3456}(59,\cdot)\) \(\chi_{3456}(83,\cdot)\) \(\chi_{3456}(131,\cdot)\) \(\chi_{3456}(155,\cdot)\) \(\chi_{3456}(203,\cdot)\) \(\chi_{3456}(227,\cdot)\) \(\chi_{3456}(275,\cdot)\) \(\chi_{3456}(299,\cdot)\) \(\chi_{3456}(347,\cdot)\) \(\chi_{3456}(371,\cdot)\) \(\chi_{3456}(419,\cdot)\) \(\chi_{3456}(443,\cdot)\) \(\chi_{3456}(491,\cdot)\) \(\chi_{3456}(515,\cdot)\) \(\chi_{3456}(563,\cdot)\) \(\chi_{3456}(587,\cdot)\) \(\chi_{3456}(635,\cdot)\) \(\chi_{3456}(659,\cdot)\) \(\chi_{3456}(707,\cdot)\) \(\chi_{3456}(731,\cdot)\) \(\chi_{3456}(779,\cdot)\) \(\chi_{3456}(803,\cdot)\) \(\chi_{3456}(851,\cdot)\) \(\chi_{3456}(875,\cdot)\) \(\chi_{3456}(923,\cdot)\) \(\chi_{3456}(947,\cdot)\) \(\chi_{3456}(995,\cdot)\) \(\chi_{3456}(1019,\cdot)\) \(\chi_{3456}(1067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{288})$ |
| Fixed field: | Number field defined by a degree 288 polynomial (not computed) |
Values on generators
\((2431,2053,2945)\) → \((-1,e\left(\frac{21}{32}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3456 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{288}\right)\) | \(e\left(\frac{89}{144}\right)\) | \(e\left(\frac{193}{288}\right)\) | \(e\left(\frac{179}{288}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{91}{144}\right)\) | \(e\left(\frac{77}{144}\right)\) | \(e\left(\frac{127}{288}\right)\) | \(e\left(\frac{7}{36}\right)\) |