Basic properties
Modulus: | \(605\) | |
Conductor: | \(605\) | 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 605.v
\(\chi_{605}(19,\cdot)\) \(\chi_{605}(24,\cdot)\) \(\chi_{605}(29,\cdot)\) \(\chi_{605}(39,\cdot)\) \(\chi_{605}(74,\cdot)\) \(\chi_{605}(79,\cdot)\) \(\chi_{605}(84,\cdot)\) \(\chi_{605}(129,\cdot)\) \(\chi_{605}(134,\cdot)\) \(\chi_{605}(139,\cdot)\) \(\chi_{605}(149,\cdot)\) \(\chi_{605}(184,\cdot)\) \(\chi_{605}(189,\cdot)\) \(\chi_{605}(194,\cdot)\) \(\chi_{605}(204,\cdot)\) \(\chi_{605}(244,\cdot)\) \(\chi_{605}(249,\cdot)\) \(\chi_{605}(259,\cdot)\) \(\chi_{605}(294,\cdot)\) \(\chi_{605}(299,\cdot)\) \(\chi_{605}(304,\cdot)\) \(\chi_{605}(314,\cdot)\) \(\chi_{605}(349,\cdot)\) \(\chi_{605}(359,\cdot)\) \(\chi_{605}(369,\cdot)\) \(\chi_{605}(404,\cdot)\) \(\chi_{605}(409,\cdot)\) \(\chi_{605}(414,\cdot)\) \(\chi_{605}(424,\cdot)\) \(\chi_{605}(459,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,486)\) → \((-1,e\left(\frac{91}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 605 }(24, a) \) | \(-1\) | \(1\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) |