Basic properties
Modulus: | \(3997\) | |
Conductor: | \(3997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(570\) | 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 3997.cr
\(\chi_{3997}(26,\cdot)\) \(\chi_{3997}(68,\cdot)\) \(\chi_{3997}(87,\cdot)\) \(\chi_{3997}(122,\cdot)\) \(\chi_{3997}(166,\cdot)\) \(\chi_{3997}(171,\cdot)\) \(\chi_{3997}(187,\cdot)\) \(\chi_{3997}(194,\cdot)\) \(\chi_{3997}(241,\cdot)\) \(\chi_{3997}(269,\cdot)\) \(\chi_{3997}(290,\cdot)\) \(\chi_{3997}(304,\cdot)\) \(\chi_{3997}(346,\cdot)\) \(\chi_{3997}(355,\cdot)\) \(\chi_{3997}(395,\cdot)\) \(\chi_{3997}(423,\cdot)\) \(\chi_{3997}(425,\cdot)\) \(\chi_{3997}(446,\cdot)\) \(\chi_{3997}(451,\cdot)\) \(\chi_{3997}(535,\cdot)\) \(\chi_{3997}(551,\cdot)\) \(\chi_{3997}(565,\cdot)\) \(\chi_{3997}(586,\cdot)\) \(\chi_{3997}(593,\cdot)\) \(\chi_{3997}(598,\cdot)\) \(\chi_{3997}(619,\cdot)\) \(\chi_{3997}(621,\cdot)\) \(\chi_{3997}(682,\cdot)\) \(\chi_{3997}(703,\cdot)\) \(\chi_{3997}(731,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2285,1716)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{141}{190}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 3997 }(586, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{164}{285}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{191}{570}\right)\) | \(e\left(\frac{131}{190}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{43}{285}\right)\) | \(e\left(\frac{128}{285}\right)\) | \(e\left(\frac{62}{285}\right)\) | \(e\left(\frac{229}{285}\right)\) |