Basic properties
| Modulus: | \(847\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | 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 847.bb
\(\chi_{847}(20,\cdot)\) \(\chi_{847}(48,\cdot)\) \(\chi_{847}(69,\cdot)\) \(\chi_{847}(97,\cdot)\) \(\chi_{847}(104,\cdot)\) \(\chi_{847}(125,\cdot)\) \(\chi_{847}(146,\cdot)\) \(\chi_{847}(174,\cdot)\) \(\chi_{847}(181,\cdot)\) \(\chi_{847}(223,\cdot)\) \(\chi_{847}(258,\cdot)\) \(\chi_{847}(279,\cdot)\) \(\chi_{847}(300,\cdot)\) \(\chi_{847}(328,\cdot)\) \(\chi_{847}(335,\cdot)\) \(\chi_{847}(356,\cdot)\) \(\chi_{847}(377,\cdot)\) \(\chi_{847}(405,\cdot)\) \(\chi_{847}(412,\cdot)\) \(\chi_{847}(433,\cdot)\) \(\chi_{847}(454,\cdot)\) \(\chi_{847}(482,\cdot)\) \(\chi_{847}(489,\cdot)\) \(\chi_{847}(510,\cdot)\) \(\chi_{847}(531,\cdot)\) \(\chi_{847}(559,\cdot)\) \(\chi_{847}(566,\cdot)\) \(\chi_{847}(587,\cdot)\) \(\chi_{847}(636,\cdot)\) \(\chi_{847}(643,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,365)\) → \((-1,e\left(\frac{32}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 847 }(335, a) \) | \(-1\) | \(1\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{29}{110}\right)\) |