Basic properties
Modulus: | \(896\) | |
Conductor: | \(896\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | 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 896.bu
\(\chi_{896}(37,\cdot)\) \(\chi_{896}(53,\cdot)\) \(\chi_{896}(93,\cdot)\) \(\chi_{896}(109,\cdot)\) \(\chi_{896}(149,\cdot)\) \(\chi_{896}(165,\cdot)\) \(\chi_{896}(205,\cdot)\) \(\chi_{896}(221,\cdot)\) \(\chi_{896}(261,\cdot)\) \(\chi_{896}(277,\cdot)\) \(\chi_{896}(317,\cdot)\) \(\chi_{896}(333,\cdot)\) \(\chi_{896}(373,\cdot)\) \(\chi_{896}(389,\cdot)\) \(\chi_{896}(429,\cdot)\) \(\chi_{896}(445,\cdot)\) \(\chi_{896}(485,\cdot)\) \(\chi_{896}(501,\cdot)\) \(\chi_{896}(541,\cdot)\) \(\chi_{896}(557,\cdot)\) \(\chi_{896}(597,\cdot)\) \(\chi_{896}(613,\cdot)\) \(\chi_{896}(653,\cdot)\) \(\chi_{896}(669,\cdot)\) \(\chi_{896}(709,\cdot)\) \(\chi_{896}(725,\cdot)\) \(\chi_{896}(765,\cdot)\) \(\chi_{896}(781,\cdot)\) \(\chi_{896}(821,\cdot)\) \(\chi_{896}(837,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((127,645,129)\) → \((1,e\left(\frac{7}{32}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 896 }(429, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{37}{48}\right)\) |