Basic properties
Modulus: | \(8027\) | |
Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(3828\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8027.bu
\(\chi_{8027}(7,\cdot)\) \(\chi_{8027}(30,\cdot)\) \(\chi_{8027}(33,\cdot)\) \(\chi_{8027}(34,\cdot)\) \(\chi_{8027}(40,\cdot)\) \(\chi_{8027}(43,\cdot)\) \(\chi_{8027}(44,\cdot)\) \(\chi_{8027}(63,\cdot)\) \(\chi_{8027}(74,\cdot)\) \(\chi_{8027}(84,\cdot)\) \(\chi_{8027}(89,\cdot)\) \(\chi_{8027}(90,\cdot)\) \(\chi_{8027}(97,\cdot)\) \(\chi_{8027}(99,\cdot)\) \(\chi_{8027}(107,\cdot)\) \(\chi_{8027}(112,\cdot)\) \(\chi_{8027}(113,\cdot)\) \(\chi_{8027}(120,\cdot)\) \(\chi_{8027}(129,\cdot)\) \(\chi_{8027}(132,\cdot)\) \(\chi_{8027}(134,\cdot)\) \(\chi_{8027}(149,\cdot)\) \(\chi_{8027}(152,\cdot)\) \(\chi_{8027}(159,\cdot)\) \(\chi_{8027}(166,\cdot)\) \(\chi_{8027}(172,\cdot)\) \(\chi_{8027}(175,\cdot)\) \(\chi_{8027}(176,\cdot)\) \(\chi_{8027}(195,\cdot)\) \(\chi_{8027}(199,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{3828})$ |
Fixed field: | Number field defined by a degree 3828 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{19}{22}\right),e\left(\frac{341}{348}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(30, a) \) | \(1\) | \(1\) | \(e\left(\frac{2707}{3828}\right)\) | \(e\left(\frac{565}{1914}\right)\) | \(e\left(\frac{793}{1914}\right)\) | \(e\left(\frac{524}{957}\right)\) | \(e\left(\frac{3}{1276}\right)\) | \(e\left(\frac{235}{3828}\right)\) | \(e\left(\frac{155}{1276}\right)\) | \(e\left(\frac{565}{957}\right)\) | \(e\left(\frac{325}{1276}\right)\) | \(e\left(\frac{447}{1276}\right)\) |