Basic properties
| Modulus: | \(100016\) | |
| Conductor: | \(100016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(276\) | 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 100016.xj
\(\chi_{100016}(37,\cdot)\) \(\chi_{100016}(949,\cdot)\) \(\chi_{100016}(2165,\cdot)\) \(\chi_{100016}(4293,\cdot)\) \(\chi_{100016}(6269,\cdot)\) \(\chi_{100016}(7485,\cdot)\) \(\chi_{100016}(8549,\cdot)\) \(\chi_{100016}(9461,\cdot)\) \(\chi_{100016}(9613,\cdot)\) \(\chi_{100016}(10677,\cdot)\) \(\chi_{100016}(11589,\cdot)\) \(\chi_{100016}(12805,\cdot)\) \(\chi_{100016}(13869,\cdot)\) \(\chi_{100016}(14933,\cdot)\) \(\chi_{100016}(15845,\cdot)\) \(\chi_{100016}(15997,\cdot)\) \(\chi_{100016}(16909,\cdot)\) \(\chi_{100016}(19037,\cdot)\) \(\chi_{100016}(20101,\cdot)\) \(\chi_{100016}(22381,\cdot)\) \(\chi_{100016}(23293,\cdot)\) \(\chi_{100016}(26485,\cdot)\) \(\chi_{100016}(27549,\cdot)\) \(\chi_{100016}(27701,\cdot)\) \(\chi_{100016}(28613,\cdot)\) \(\chi_{100016}(30741,\cdot)\) \(\chi_{100016}(30893,\cdot)\) \(\chi_{100016}(32869,\cdot)\) \(\chi_{100016}(33021,\cdot)\) \(\chi_{100016}(36061,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{276})$ |
| Fixed field: | Number field defined by a degree 276 polynomial (not computed) |
Values on generators
\((62511,75013,28577,5265,46817)\) → \((1,i,e\left(\frac{2}{3}\right),-1,e\left(\frac{7}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 100016 }(11589, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{276}\right)\) | \(e\left(\frac{245}{276}\right)\) | \(e\left(\frac{1}{138}\right)\) | \(e\left(\frac{13}{276}\right)\) | \(e\left(\frac{55}{92}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{49}{138}\right)\) | \(e\left(\frac{107}{138}\right)\) | \(e\left(\frac{1}{92}\right)\) |