Basic properties
| Modulus: | \(484\) | |
| Conductor: | \(484\) | 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 484.o
\(\chi_{484}(15,\cdot)\) \(\chi_{484}(31,\cdot)\) \(\chi_{484}(47,\cdot)\) \(\chi_{484}(59,\cdot)\) \(\chi_{484}(71,\cdot)\) \(\chi_{484}(75,\cdot)\) \(\chi_{484}(91,\cdot)\) \(\chi_{484}(103,\cdot)\) \(\chi_{484}(115,\cdot)\) \(\chi_{484}(119,\cdot)\) \(\chi_{484}(135,\cdot)\) \(\chi_{484}(147,\cdot)\) \(\chi_{484}(159,\cdot)\) \(\chi_{484}(163,\cdot)\) \(\chi_{484}(179,\cdot)\) \(\chi_{484}(191,\cdot)\) \(\chi_{484}(203,\cdot)\) \(\chi_{484}(207,\cdot)\) \(\chi_{484}(223,\cdot)\) \(\chi_{484}(235,\cdot)\) \(\chi_{484}(247,\cdot)\) \(\chi_{484}(267,\cdot)\) \(\chi_{484}(279,\cdot)\) \(\chi_{484}(291,\cdot)\) \(\chi_{484}(295,\cdot)\) \(\chi_{484}(311,\cdot)\) \(\chi_{484}(335,\cdot)\) \(\chi_{484}(339,\cdot)\) \(\chi_{484}(355,\cdot)\) \(\chi_{484}(367,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((243,365)\) → \((-1,e\left(\frac{12}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 484 }(203, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) |