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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 847.ba
\(\chi_{847}(6,\cdot)\) \(\chi_{847}(13,\cdot)\) \(\chi_{847}(41,\cdot)\) \(\chi_{847}(62,\cdot)\) \(\chi_{847}(83,\cdot)\) \(\chi_{847}(90,\cdot)\) \(\chi_{847}(139,\cdot)\) \(\chi_{847}(160,\cdot)\) \(\chi_{847}(167,\cdot)\) \(\chi_{847}(195,\cdot)\) \(\chi_{847}(216,\cdot)\) \(\chi_{847}(237,\cdot)\) \(\chi_{847}(244,\cdot)\) \(\chi_{847}(272,\cdot)\) \(\chi_{847}(293,\cdot)\) \(\chi_{847}(314,\cdot)\) \(\chi_{847}(321,\cdot)\) \(\chi_{847}(349,\cdot)\) \(\chi_{847}(370,\cdot)\) \(\chi_{847}(391,\cdot)\) \(\chi_{847}(398,\cdot)\) \(\chi_{847}(426,\cdot)\) \(\chi_{847}(447,\cdot)\) \(\chi_{847}(468,\cdot)\) \(\chi_{847}(503,\cdot)\) \(\chi_{847}(545,\cdot)\) \(\chi_{847}(552,\cdot)\) \(\chi_{847}(580,\cdot)\) \(\chi_{847}(601,\cdot)\) \(\chi_{847}(622,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,365)\) → \((-1,e\left(\frac{19}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 847 }(237, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{52}{55}\right)\) |