Basic properties
Modulus: | \(9216\) | |
Conductor: | \(2304\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2304}(1955,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9216.ch
\(\chi_{9216}(47,\cdot)\) \(\chi_{9216}(239,\cdot)\) \(\chi_{9216}(335,\cdot)\) \(\chi_{9216}(527,\cdot)\) \(\chi_{9216}(623,\cdot)\) \(\chi_{9216}(815,\cdot)\) \(\chi_{9216}(911,\cdot)\) \(\chi_{9216}(1103,\cdot)\) \(\chi_{9216}(1199,\cdot)\) \(\chi_{9216}(1391,\cdot)\) \(\chi_{9216}(1487,\cdot)\) \(\chi_{9216}(1679,\cdot)\) \(\chi_{9216}(1775,\cdot)\) \(\chi_{9216}(1967,\cdot)\) \(\chi_{9216}(2063,\cdot)\) \(\chi_{9216}(2255,\cdot)\) \(\chi_{9216}(2351,\cdot)\) \(\chi_{9216}(2543,\cdot)\) \(\chi_{9216}(2639,\cdot)\) \(\chi_{9216}(2831,\cdot)\) \(\chi_{9216}(2927,\cdot)\) \(\chi_{9216}(3119,\cdot)\) \(\chi_{9216}(3215,\cdot)\) \(\chi_{9216}(3407,\cdot)\) \(\chi_{9216}(3503,\cdot)\) \(\chi_{9216}(3695,\cdot)\) \(\chi_{9216}(3791,\cdot)\) \(\chi_{9216}(3983,\cdot)\) \(\chi_{9216}(4079,\cdot)\) \(\chi_{9216}(4271,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((8191,2053,4097)\) → \((-1,e\left(\frac{43}{64}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 9216 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{192}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{149}{192}\right)\) | \(e\left(\frac{175}{192}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{1}{96}\right)\) | \(e\left(\frac{155}{192}\right)\) | \(e\left(\frac{5}{24}\right)\) |