Basic properties
Modulus: | \(1152\) | |
Conductor: | \(1152\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1152.bt
\(\chi_{1152}(5,\cdot)\) \(\chi_{1152}(29,\cdot)\) \(\chi_{1152}(77,\cdot)\) \(\chi_{1152}(101,\cdot)\) \(\chi_{1152}(149,\cdot)\) \(\chi_{1152}(173,\cdot)\) \(\chi_{1152}(221,\cdot)\) \(\chi_{1152}(245,\cdot)\) \(\chi_{1152}(293,\cdot)\) \(\chi_{1152}(317,\cdot)\) \(\chi_{1152}(365,\cdot)\) \(\chi_{1152}(389,\cdot)\) \(\chi_{1152}(437,\cdot)\) \(\chi_{1152}(461,\cdot)\) \(\chi_{1152}(509,\cdot)\) \(\chi_{1152}(533,\cdot)\) \(\chi_{1152}(581,\cdot)\) \(\chi_{1152}(605,\cdot)\) \(\chi_{1152}(653,\cdot)\) \(\chi_{1152}(677,\cdot)\) \(\chi_{1152}(725,\cdot)\) \(\chi_{1152}(749,\cdot)\) \(\chi_{1152}(797,\cdot)\) \(\chi_{1152}(821,\cdot)\) \(\chi_{1152}(869,\cdot)\) \(\chi_{1152}(893,\cdot)\) \(\chi_{1152}(941,\cdot)\) \(\chi_{1152}(965,\cdot)\) \(\chi_{1152}(1013,\cdot)\) \(\chi_{1152}(1037,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((127,901,641)\) → \((1,e\left(\frac{3}{32}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1152 }(893, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |