Basic properties
Modulus: | \(605\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(58,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 605.s
\(\chi_{605}(16,\cdot)\) \(\chi_{605}(26,\cdot)\) \(\chi_{605}(31,\cdot)\) \(\chi_{605}(36,\cdot)\) \(\chi_{605}(71,\cdot)\) \(\chi_{605}(86,\cdot)\) \(\chi_{605}(91,\cdot)\) \(\chi_{605}(126,\cdot)\) \(\chi_{605}(136,\cdot)\) \(\chi_{605}(141,\cdot)\) \(\chi_{605}(146,\cdot)\) \(\chi_{605}(181,\cdot)\) \(\chi_{605}(191,\cdot)\) \(\chi_{605}(196,\cdot)\) \(\chi_{605}(201,\cdot)\) \(\chi_{605}(236,\cdot)\) \(\chi_{605}(246,\cdot)\) \(\chi_{605}(256,\cdot)\) \(\chi_{605}(291,\cdot)\) \(\chi_{605}(301,\cdot)\) \(\chi_{605}(306,\cdot)\) \(\chi_{605}(311,\cdot)\) \(\chi_{605}(346,\cdot)\) \(\chi_{605}(356,\cdot)\) \(\chi_{605}(361,\cdot)\) \(\chi_{605}(401,\cdot)\) \(\chi_{605}(411,\cdot)\) \(\chi_{605}(416,\cdot)\) \(\chi_{605}(421,\cdot)\) \(\chi_{605}(456,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((122,486)\) → \((1,e\left(\frac{9}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 605 }(421, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) |