Basic properties
| Modulus: | \(53312\) | |
| Conductor: | \(53312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | 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 53312.zw
\(\chi_{53312}(75,\cdot)\) \(\chi_{53312}(131,\cdot)\) \(\chi_{53312}(283,\cdot)\) \(\chi_{53312}(299,\cdot)\) \(\chi_{53312}(635,\cdot)\) \(\chi_{53312}(915,\cdot)\) \(\chi_{53312}(1907,\cdot)\) \(\chi_{53312}(2147,\cdot)\) \(\chi_{53312}(4427,\cdot)\) \(\chi_{53312}(4483,\cdot)\) \(\chi_{53312}(4651,\cdot)\) \(\chi_{53312}(4987,\cdot)\) \(\chi_{53312}(5171,\cdot)\) \(\chi_{53312}(5267,\cdot)\) \(\chi_{53312}(7691,\cdot)\) \(\chi_{53312}(7747,\cdot)\) \(\chi_{53312}(7899,\cdot)\) \(\chi_{53312}(7915,\cdot)\) \(\chi_{53312}(8531,\cdot)\) \(\chi_{53312}(9523,\cdot)\) \(\chi_{53312}(9763,\cdot)\) \(\chi_{53312}(11163,\cdot)\) \(\chi_{53312}(12043,\cdot)\) \(\chi_{53312}(12099,\cdot)\) \(\chi_{53312}(12267,\cdot)\) \(\chi_{53312}(12603,\cdot)\) \(\chi_{53312}(12787,\cdot)\) \(\chi_{53312}(12883,\cdot)\) \(\chi_{53312}(14115,\cdot)\) \(\chi_{53312}(15363,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((51647,3333,10881,40769)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{17}{42}\right),e\left(\frac{11}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 53312 }(75, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{168}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{11}{168}\right)\) | \(e\left(\frac{89}{112}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{191}{336}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{33}{56}\right)\) |