Basic properties
| Modulus: | \(736\) | |
| Conductor: | \(736\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 736.bd
\(\chi_{736}(3,\cdot)\) \(\chi_{736}(27,\cdot)\) \(\chi_{736}(35,\cdot)\) \(\chi_{736}(59,\cdot)\) \(\chi_{736}(75,\cdot)\) \(\chi_{736}(123,\cdot)\) \(\chi_{736}(131,\cdot)\) \(\chi_{736}(147,\cdot)\) \(\chi_{736}(163,\cdot)\) \(\chi_{736}(179,\cdot)\) \(\chi_{736}(187,\cdot)\) \(\chi_{736}(211,\cdot)\) \(\chi_{736}(219,\cdot)\) \(\chi_{736}(243,\cdot)\) \(\chi_{736}(259,\cdot)\) \(\chi_{736}(307,\cdot)\) \(\chi_{736}(315,\cdot)\) \(\chi_{736}(331,\cdot)\) \(\chi_{736}(347,\cdot)\) \(\chi_{736}(363,\cdot)\) \(\chi_{736}(371,\cdot)\) \(\chi_{736}(395,\cdot)\) \(\chi_{736}(403,\cdot)\) \(\chi_{736}(427,\cdot)\) \(\chi_{736}(443,\cdot)\) \(\chi_{736}(491,\cdot)\) \(\chi_{736}(499,\cdot)\) \(\chi_{736}(515,\cdot)\) \(\chi_{736}(531,\cdot)\) \(\chi_{736}(547,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((415,645,97)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 736 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{9}{88}\right)\) | \(e\left(\frac{87}{88}\right)\) |