Basic properties
| Modulus: | \(605\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 605.t
\(\chi_{605}(6,\cdot)\) \(\chi_{605}(41,\cdot)\) \(\chi_{605}(46,\cdot)\) \(\chi_{605}(51,\cdot)\) \(\chi_{605}(61,\cdot)\) \(\chi_{605}(96,\cdot)\) \(\chi_{605}(101,\cdot)\) \(\chi_{605}(106,\cdot)\) \(\chi_{605}(116,\cdot)\) \(\chi_{605}(151,\cdot)\) \(\chi_{605}(156,\cdot)\) \(\chi_{605}(171,\cdot)\) \(\chi_{605}(206,\cdot)\) \(\chi_{605}(211,\cdot)\) \(\chi_{605}(216,\cdot)\) \(\chi_{605}(226,\cdot)\) \(\chi_{605}(261,\cdot)\) \(\chi_{605}(266,\cdot)\) \(\chi_{605}(271,\cdot)\) \(\chi_{605}(281,\cdot)\) \(\chi_{605}(316,\cdot)\) \(\chi_{605}(321,\cdot)\) \(\chi_{605}(326,\cdot)\) \(\chi_{605}(371,\cdot)\) \(\chi_{605}(376,\cdot)\) \(\chi_{605}(381,\cdot)\) \(\chi_{605}(391,\cdot)\) \(\chi_{605}(426,\cdot)\) \(\chi_{605}(431,\cdot)\) \(\chi_{605}(436,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,486)\) → \((1,e\left(\frac{1}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 605 }(486, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{4}{55}\right)\) |