Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(35937\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(5445\) | 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 35937.cq
\(\chi_{35937}(4,\cdot)\) \(\chi_{35937}(16,\cdot)\) \(\chi_{35937}(25,\cdot)\) \(\chi_{35937}(31,\cdot)\) \(\chi_{35937}(49,\cdot)\) \(\chi_{35937}(58,\cdot)\) \(\chi_{35937}(70,\cdot)\) \(\chi_{35937}(97,\cdot)\) \(\chi_{35937}(103,\cdot)\) \(\chi_{35937}(115,\cdot)\) \(\chi_{35937}(157,\cdot)\) \(\chi_{35937}(169,\cdot)\) \(\chi_{35937}(196,\cdot)\) \(\chi_{35937}(214,\cdot)\) \(\chi_{35937}(223,\cdot)\) \(\chi_{35937}(229,\cdot)\) \(\chi_{35937}(247,\cdot)\) \(\chi_{35937}(256,\cdot)\) \(\chi_{35937}(268,\cdot)\) \(\chi_{35937}(295,\cdot)\) \(\chi_{35937}(301,\cdot)\) \(\chi_{35937}(313,\cdot)\) \(\chi_{35937}(322,\cdot)\) \(\chi_{35937}(328,\cdot)\) \(\chi_{35937}(346,\cdot)\) \(\chi_{35937}(355,\cdot)\) \(\chi_{35937}(367,\cdot)\) \(\chi_{35937}(394,\cdot)\) \(\chi_{35937}(400,\cdot)\) \(\chi_{35937}(412,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{5445})$ |
| Fixed field: | Number field defined by a degree 5445 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{1}{605}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{614}{5445}\right)\) | \(e\left(\frac{1228}{5445}\right)\) | \(e\left(\frac{4681}{5445}\right)\) | \(e\left(\frac{3803}{5445}\right)\) | \(e\left(\frac{614}{1815}\right)\) | \(e\left(\frac{353}{363}\right)\) | \(e\left(\frac{4759}{5445}\right)\) | \(e\left(\frac{4417}{5445}\right)\) | \(e\left(\frac{2456}{5445}\right)\) | \(e\left(\frac{1687}{1815}\right)\) |