Basic properties
| Modulus: | \(801\) | |
| 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 \(\chi_{89}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 801.ba
\(\chi_{801}(19,\cdot)\) \(\chi_{801}(28,\cdot)\) \(\chi_{801}(46,\cdot)\) \(\chi_{801}(82,\cdot)\) \(\chi_{801}(118,\cdot)\) \(\chi_{801}(127,\cdot)\) \(\chi_{801}(145,\cdot)\) \(\chi_{801}(154,\cdot)\) \(\chi_{801}(163,\cdot)\) \(\chi_{801}(172,\cdot)\) \(\chi_{801}(181,\cdot)\) \(\chi_{801}(208,\cdot)\) \(\chi_{801}(226,\cdot)\) \(\chi_{801}(244,\cdot)\) \(\chi_{801}(253,\cdot)\) \(\chi_{801}(280,\cdot)\) \(\chi_{801}(298,\cdot)\) \(\chi_{801}(325,\cdot)\) \(\chi_{801}(343,\cdot)\) \(\chi_{801}(370,\cdot)\) \(\chi_{801}(379,\cdot)\) \(\chi_{801}(397,\cdot)\) \(\chi_{801}(415,\cdot)\) \(\chi_{801}(442,\cdot)\) \(\chi_{801}(451,\cdot)\) \(\chi_{801}(460,\cdot)\) \(\chi_{801}(469,\cdot)\) \(\chi_{801}(478,\cdot)\) \(\chi_{801}(496,\cdot)\) \(\chi_{801}(505,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{88})$ |
| Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((713,181)\) → \((1,e\left(\frac{1}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 801 }(181, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{9}{88}\right)\) | \(e\left(\frac{8}{11}\right)\) |