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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 605.u
\(\chi_{605}(4,\cdot)\) \(\chi_{605}(14,\cdot)\) \(\chi_{605}(49,\cdot)\) \(\chi_{605}(59,\cdot)\) \(\chi_{605}(64,\cdot)\) \(\chi_{605}(69,\cdot)\) \(\chi_{605}(104,\cdot)\) \(\chi_{605}(114,\cdot)\) \(\chi_{605}(119,\cdot)\) \(\chi_{605}(159,\cdot)\) \(\chi_{605}(169,\cdot)\) \(\chi_{605}(174,\cdot)\) \(\chi_{605}(179,\cdot)\) \(\chi_{605}(214,\cdot)\) \(\chi_{605}(224,\cdot)\) \(\chi_{605}(229,\cdot)\) \(\chi_{605}(234,\cdot)\) \(\chi_{605}(279,\cdot)\) \(\chi_{605}(284,\cdot)\) \(\chi_{605}(289,\cdot)\) \(\chi_{605}(324,\cdot)\) \(\chi_{605}(334,\cdot)\) \(\chi_{605}(339,\cdot)\) \(\chi_{605}(344,\cdot)\) \(\chi_{605}(379,\cdot)\) \(\chi_{605}(389,\cdot)\) \(\chi_{605}(394,\cdot)\) \(\chi_{605}(399,\cdot)\) \(\chi_{605}(434,\cdot)\) \(\chi_{605}(449,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,486)\) → \((-1,e\left(\frac{24}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 605 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{27}{55}\right)\) |