Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(35937\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(10890\) | 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 35937.cr
\(\chi_{35937}(5,\cdot)\) \(\chi_{35937}(14,\cdot)\) \(\chi_{35937}(20,\cdot)\) \(\chi_{35937}(38,\cdot)\) \(\chi_{35937}(47,\cdot)\) \(\chi_{35937}(59,\cdot)\) \(\chi_{35937}(86,\cdot)\) \(\chi_{35937}(92,\cdot)\) \(\chi_{35937}(104,\cdot)\) \(\chi_{35937}(113,\cdot)\) \(\chi_{35937}(119,\cdot)\) \(\chi_{35937}(137,\cdot)\) \(\chi_{35937}(146,\cdot)\) \(\chi_{35937}(158,\cdot)\) \(\chi_{35937}(185,\cdot)\) \(\chi_{35937}(191,\cdot)\) \(\chi_{35937}(203,\cdot)\) \(\chi_{35937}(212,\cdot)\) \(\chi_{35937}(218,\cdot)\) \(\chi_{35937}(236,\cdot)\) \(\chi_{35937}(257,\cdot)\) \(\chi_{35937}(284,\cdot)\) \(\chi_{35937}(290,\cdot)\) \(\chi_{35937}(302,\cdot)\) \(\chi_{35937}(311,\cdot)\) \(\chi_{35937}(317,\cdot)\) \(\chi_{35937}(335,\cdot)\) \(\chi_{35937}(344,\cdot)\) \(\chi_{35937}(356,\cdot)\) \(\chi_{35937}(383,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{5445})$ |
| Fixed field: | Number field defined by a degree 10890 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{279}{605}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4417}{10890}\right)\) | \(e\left(\frac{4417}{5445}\right)\) | \(e\left(\frac{6263}{10890}\right)\) | \(e\left(\frac{5312}{5445}\right)\) | \(e\left(\frac{787}{3630}\right)\) | \(e\left(\frac{356}{363}\right)\) | \(e\left(\frac{2206}{5445}\right)\) | \(e\left(\frac{4151}{10890}\right)\) | \(e\left(\frac{3389}{5445}\right)\) | \(e\left(\frac{1781}{3630}\right)\) |