Basic properties
| Modulus: | \(445\) | |
| Conductor: | \(89\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{89}(66,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 445.y
\(\chi_{445}(6,\cdot)\) \(\chi_{445}(26,\cdot)\) \(\chi_{445}(31,\cdot)\) \(\chi_{445}(41,\cdot)\) \(\chi_{445}(46,\cdot)\) \(\chi_{445}(51,\cdot)\) \(\chi_{445}(56,\cdot)\) \(\chi_{445}(61,\cdot)\) \(\chi_{445}(66,\cdot)\) \(\chi_{445}(76,\cdot)\) \(\chi_{445}(86,\cdot)\) \(\chi_{445}(96,\cdot)\) \(\chi_{445}(116,\cdot)\) \(\chi_{445}(151,\cdot)\) \(\chi_{445}(171,\cdot)\) \(\chi_{445}(181,\cdot)\) \(\chi_{445}(191,\cdot)\) \(\chi_{445}(201,\cdot)\) \(\chi_{445}(206,\cdot)\) \(\chi_{445}(211,\cdot)\) \(\chi_{445}(216,\cdot)\) \(\chi_{445}(221,\cdot)\) \(\chi_{445}(226,\cdot)\) \(\chi_{445}(236,\cdot)\) \(\chi_{445}(241,\cdot)\) \(\chi_{445}(261,\cdot)\) \(\chi_{445}(281,\cdot)\) \(\chi_{445}(286,\cdot)\) \(\chi_{445}(291,\cdot)\) \(\chi_{445}(296,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((357,181)\) → \((1,e\left(\frac{13}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 445 }(66, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{35}{88}\right)\) |