Basic properties
| Modulus: | \(47320\) | |
| Conductor: | \(47320\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 47320.zc
\(\chi_{47320}(467,\cdot)\) \(\chi_{47320}(1403,\cdot)\) \(\chi_{47320}(1923,\cdot)\) \(\chi_{47320}(3587,\cdot)\) \(\chi_{47320}(4107,\cdot)\) \(\chi_{47320}(5043,\cdot)\) \(\chi_{47320}(5563,\cdot)\) \(\chi_{47320}(7227,\cdot)\) \(\chi_{47320}(7747,\cdot)\) \(\chi_{47320}(8683,\cdot)\) \(\chi_{47320}(9203,\cdot)\) \(\chi_{47320}(10867,\cdot)\) \(\chi_{47320}(11387,\cdot)\) \(\chi_{47320}(12323,\cdot)\) \(\chi_{47320}(14507,\cdot)\) \(\chi_{47320}(15027,\cdot)\) \(\chi_{47320}(15963,\cdot)\) \(\chi_{47320}(16483,\cdot)\) \(\chi_{47320}(18147,\cdot)\) \(\chi_{47320}(18667,\cdot)\) \(\chi_{47320}(20123,\cdot)\) \(\chi_{47320}(21787,\cdot)\) \(\chi_{47320}(23243,\cdot)\) \(\chi_{47320}(23763,\cdot)\) \(\chi_{47320}(25427,\cdot)\) \(\chi_{47320}(25947,\cdot)\) \(\chi_{47320}(26883,\cdot)\) \(\chi_{47320}(27403,\cdot)\) \(\chi_{47320}(29587,\cdot)\) \(\chi_{47320}(30523,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((11831,23661,37857,40561,18761)\) → \((-1,-1,i,e\left(\frac{5}{6}\right),e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 47320 }(29587, a) \) | \(-1\) | \(1\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{41}{156}\right)\) |