Basic properties
Modulus: | \(712\) | |
Conductor: | \(712\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | 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 712.bc
\(\chi_{712}(13,\cdot)\) \(\chi_{712}(29,\cdot)\) \(\chi_{712}(61,\cdot)\) \(\chi_{712}(117,\cdot)\) \(\chi_{712}(149,\cdot)\) \(\chi_{712}(165,\cdot)\) \(\chi_{712}(181,\cdot)\) \(\chi_{712}(197,\cdot)\) \(\chi_{712}(205,\cdot)\) \(\chi_{712}(213,\cdot)\) \(\chi_{712}(221,\cdot)\) \(\chi_{712}(229,\cdot)\) \(\chi_{712}(237,\cdot)\) \(\chi_{712}(253,\cdot)\) \(\chi_{712}(261,\cdot)\) \(\chi_{712}(293,\cdot)\) \(\chi_{712}(325,\cdot)\) \(\chi_{712}(333,\cdot)\) \(\chi_{712}(341,\cdot)\) \(\chi_{712}(349,\cdot)\) \(\chi_{712}(389,\cdot)\) \(\chi_{712}(397,\cdot)\) \(\chi_{712}(421,\cdot)\) \(\chi_{712}(469,\cdot)\) \(\chi_{712}(493,\cdot)\) \(\chi_{712}(501,\cdot)\) \(\chi_{712}(541,\cdot)\) \(\chi_{712}(549,\cdot)\) \(\chi_{712}(557,\cdot)\) \(\chi_{712}(565,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((535,357,537)\) → \((1,-1,e\left(\frac{69}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 712 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{35}{44}\right)\) |