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
\((122,486)\) → \((-i,e\left(\frac{18}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 605 }(218, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{220}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{9}{220}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{67}{220}\right)\) | \(e\left(\frac{13}{110}\right)\) |