Basic properties
Modulus: | \(2304\) | |
Conductor: | \(1152\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1152}(517,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.bz
\(\chi_{2304}(25,\cdot)\) \(\chi_{2304}(121,\cdot)\) \(\chi_{2304}(169,\cdot)\) \(\chi_{2304}(265,\cdot)\) \(\chi_{2304}(313,\cdot)\) \(\chi_{2304}(409,\cdot)\) \(\chi_{2304}(457,\cdot)\) \(\chi_{2304}(553,\cdot)\) \(\chi_{2304}(601,\cdot)\) \(\chi_{2304}(697,\cdot)\) \(\chi_{2304}(745,\cdot)\) \(\chi_{2304}(841,\cdot)\) \(\chi_{2304}(889,\cdot)\) \(\chi_{2304}(985,\cdot)\) \(\chi_{2304}(1033,\cdot)\) \(\chi_{2304}(1129,\cdot)\) \(\chi_{2304}(1177,\cdot)\) \(\chi_{2304}(1273,\cdot)\) \(\chi_{2304}(1321,\cdot)\) \(\chi_{2304}(1417,\cdot)\) \(\chi_{2304}(1465,\cdot)\) \(\chi_{2304}(1561,\cdot)\) \(\chi_{2304}(1609,\cdot)\) \(\chi_{2304}(1705,\cdot)\) \(\chi_{2304}(1753,\cdot)\) \(\chi_{2304}(1849,\cdot)\) \(\chi_{2304}(1897,\cdot)\) \(\chi_{2304}(1993,\cdot)\) \(\chi_{2304}(2041,\cdot)\) \(\chi_{2304}(2137,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1279,2053,1793)\) → \((1,e\left(\frac{1}{32}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2304 }(1561, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) |