Basic properties
Modulus: | \(605\) | |
Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | 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.x
\(\chi_{605}(37,\cdot)\) \(\chi_{605}(38,\cdot)\) \(\chi_{605}(42,\cdot)\) \(\chi_{605}(47,\cdot)\) \(\chi_{605}(48,\cdot)\) \(\chi_{605}(53,\cdot)\) \(\chi_{605}(58,\cdot)\) \(\chi_{605}(82,\cdot)\) \(\chi_{605}(92,\cdot)\) \(\chi_{605}(93,\cdot)\) \(\chi_{605}(97,\cdot)\) \(\chi_{605}(102,\cdot)\) \(\chi_{605}(103,\cdot)\) \(\chi_{605}(108,\cdot)\) \(\chi_{605}(113,\cdot)\) \(\chi_{605}(137,\cdot)\) \(\chi_{605}(147,\cdot)\) \(\chi_{605}(152,\cdot)\) \(\chi_{605}(157,\cdot)\) \(\chi_{605}(158,\cdot)\) \(\chi_{605}(163,\cdot)\) \(\chi_{605}(168,\cdot)\) \(\chi_{605}(192,\cdot)\) \(\chi_{605}(203,\cdot)\) \(\chi_{605}(207,\cdot)\) \(\chi_{605}(212,\cdot)\) \(\chi_{605}(213,\cdot)\) \(\chi_{605}(218,\cdot)\) \(\chi_{605}(223,\cdot)\) \(\chi_{605}(247,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((122,486)\) → \((i,e\left(\frac{21}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 605 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{220}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{197}{220}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{69}{220}\right)\) | \(e\left(\frac{61}{110}\right)\) |