Basic properties
Modulus: | \(3971\) | |
Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1710\) | 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 3971.bu
\(\chi_{3971}(2,\cdot)\) \(\chi_{3971}(13,\cdot)\) \(\chi_{3971}(29,\cdot)\) \(\chi_{3971}(40,\cdot)\) \(\chi_{3971}(41,\cdot)\) \(\chi_{3971}(51,\cdot)\) \(\chi_{3971}(52,\cdot)\) \(\chi_{3971}(72,\cdot)\) \(\chi_{3971}(79,\cdot)\) \(\chi_{3971}(90,\cdot)\) \(\chi_{3971}(105,\cdot)\) \(\chi_{3971}(117,\cdot)\) \(\chi_{3971}(128,\cdot)\) \(\chi_{3971}(129,\cdot)\) \(\chi_{3971}(162,\cdot)\) \(\chi_{3971}(167,\cdot)\) \(\chi_{3971}(173,\cdot)\) \(\chi_{3971}(184,\cdot)\) \(\chi_{3971}(193,\cdot)\) \(\chi_{3971}(200,\cdot)\) \(\chi_{3971}(204,\cdot)\) \(\chi_{3971}(205,\cdot)\) \(\chi_{3971}(211,\cdot)\) \(\chi_{3971}(222,\cdot)\) \(\chi_{3971}(238,\cdot)\) \(\chi_{3971}(249,\cdot)\) \(\chi_{3971}(250,\cdot)\) \(\chi_{3971}(260,\cdot)\) \(\chi_{3971}(261,\cdot)\) \(\chi_{3971}(281,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{855})$ |
Fixed field: | Number field defined by a degree 1710 polynomial (not computed) |
Values on generators
\((1806,2168)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{329}{342}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 3971 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{855}\right)\) | \(e\left(\frac{883}{1710}\right)\) | \(e\left(\frac{106}{855}\right)\) | \(e\left(\frac{497}{855}\right)\) | \(e\left(\frac{989}{1710}\right)\) | \(e\left(\frac{569}{570}\right)\) | \(e\left(\frac{53}{285}\right)\) | \(e\left(\frac{28}{855}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{73}{114}\right)\) |