Basic properties
Modulus: | \(4608\) | |
Conductor: | \(4608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(384\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 4608.cl
\(\chi_{4608}(43,\cdot)\) \(\chi_{4608}(67,\cdot)\) \(\chi_{4608}(115,\cdot)\) \(\chi_{4608}(139,\cdot)\) \(\chi_{4608}(187,\cdot)\) \(\chi_{4608}(211,\cdot)\) \(\chi_{4608}(259,\cdot)\) \(\chi_{4608}(283,\cdot)\) \(\chi_{4608}(331,\cdot)\) \(\chi_{4608}(355,\cdot)\) \(\chi_{4608}(403,\cdot)\) \(\chi_{4608}(427,\cdot)\) \(\chi_{4608}(475,\cdot)\) \(\chi_{4608}(499,\cdot)\) \(\chi_{4608}(547,\cdot)\) \(\chi_{4608}(571,\cdot)\) \(\chi_{4608}(619,\cdot)\) \(\chi_{4608}(643,\cdot)\) \(\chi_{4608}(691,\cdot)\) \(\chi_{4608}(715,\cdot)\) \(\chi_{4608}(763,\cdot)\) \(\chi_{4608}(787,\cdot)\) \(\chi_{4608}(835,\cdot)\) \(\chi_{4608}(859,\cdot)\) \(\chi_{4608}(907,\cdot)\) \(\chi_{4608}(931,\cdot)\) \(\chi_{4608}(979,\cdot)\) \(\chi_{4608}(1003,\cdot)\) \(\chi_{4608}(1051,\cdot)\) \(\chi_{4608}(1075,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{384})$ |
Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{115}{128}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4608 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{217}{384}\right)\) | \(e\left(\frac{61}{192}\right)\) | \(e\left(\frac{77}{384}\right)\) | \(e\left(\frac{151}{384}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{21}{128}\right)\) | \(e\left(\frac{143}{192}\right)\) | \(e\left(\frac{25}{192}\right)\) | \(e\left(\frac{323}{384}\right)\) | \(e\left(\frac{17}{48}\right)\) |