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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 605.w
\(\chi_{605}(2,\cdot)\) \(\chi_{605}(7,\cdot)\) \(\chi_{605}(8,\cdot)\) \(\chi_{605}(13,\cdot)\) \(\chi_{605}(17,\cdot)\) \(\chi_{605}(18,\cdot)\) \(\chi_{605}(28,\cdot)\) \(\chi_{605}(52,\cdot)\) \(\chi_{605}(57,\cdot)\) \(\chi_{605}(62,\cdot)\) \(\chi_{605}(63,\cdot)\) \(\chi_{605}(68,\cdot)\) \(\chi_{605}(72,\cdot)\) \(\chi_{605}(73,\cdot)\) \(\chi_{605}(83,\cdot)\) \(\chi_{605}(107,\cdot)\) \(\chi_{605}(117,\cdot)\) \(\chi_{605}(123,\cdot)\) \(\chi_{605}(127,\cdot)\) \(\chi_{605}(128,\cdot)\) \(\chi_{605}(138,\cdot)\) \(\chi_{605}(162,\cdot)\) \(\chi_{605}(167,\cdot)\) \(\chi_{605}(172,\cdot)\) \(\chi_{605}(173,\cdot)\) \(\chi_{605}(178,\cdot)\) \(\chi_{605}(182,\cdot)\) \(\chi_{605}(183,\cdot)\) \(\chi_{605}(193,\cdot)\) \(\chi_{605}(217,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((122,486)\) → \((-i,e\left(\frac{51}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 605 }(68, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{219}{220}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{17}{220}\right)\) | \(e\left(\frac{23}{110}\right)\) |