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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 484.p
\(\chi_{484}(7,\cdot)\) \(\chi_{484}(19,\cdot)\) \(\chi_{484}(35,\cdot)\) \(\chi_{484}(39,\cdot)\) \(\chi_{484}(51,\cdot)\) \(\chi_{484}(63,\cdot)\) \(\chi_{484}(79,\cdot)\) \(\chi_{484}(83,\cdot)\) \(\chi_{484}(95,\cdot)\) \(\chi_{484}(107,\cdot)\) \(\chi_{484}(123,\cdot)\) \(\chi_{484}(127,\cdot)\) \(\chi_{484}(139,\cdot)\) \(\chi_{484}(151,\cdot)\) \(\chi_{484}(167,\cdot)\) \(\chi_{484}(171,\cdot)\) \(\chi_{484}(183,\cdot)\) \(\chi_{484}(195,\cdot)\) \(\chi_{484}(211,\cdot)\) \(\chi_{484}(227,\cdot)\) \(\chi_{484}(255,\cdot)\) \(\chi_{484}(259,\cdot)\) \(\chi_{484}(271,\cdot)\) \(\chi_{484}(283,\cdot)\) \(\chi_{484}(299,\cdot)\) \(\chi_{484}(303,\cdot)\) \(\chi_{484}(315,\cdot)\) \(\chi_{484}(327,\cdot)\) \(\chi_{484}(343,\cdot)\) \(\chi_{484}(347,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((243,365)\) → \((-1,e\left(\frac{93}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 484 }(459, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) |