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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 35937.cs
\(\chi_{35937}(2,\cdot)\) \(\chi_{35937}(29,\cdot)\) \(\chi_{35937}(41,\cdot)\) \(\chi_{35937}(50,\cdot)\) \(\chi_{35937}(68,\cdot)\) \(\chi_{35937}(74,\cdot)\) \(\chi_{35937}(83,\cdot)\) \(\chi_{35937}(95,\cdot)\) \(\chi_{35937}(101,\cdot)\) \(\chi_{35937}(128,\cdot)\) \(\chi_{35937}(140,\cdot)\) \(\chi_{35937}(149,\cdot)\) \(\chi_{35937}(167,\cdot)\) \(\chi_{35937}(173,\cdot)\) \(\chi_{35937}(182,\cdot)\) \(\chi_{35937}(194,\cdot)\) \(\chi_{35937}(200,\cdot)\) \(\chi_{35937}(227,\cdot)\) \(\chi_{35937}(248,\cdot)\) \(\chi_{35937}(266,\cdot)\) \(\chi_{35937}(272,\cdot)\) \(\chi_{35937}(281,\cdot)\) \(\chi_{35937}(293,\cdot)\) \(\chi_{35937}(299,\cdot)\) \(\chi_{35937}(326,\cdot)\) \(\chi_{35937}(338,\cdot)\) \(\chi_{35937}(347,\cdot)\) \(\chi_{35937}(365,\cdot)\) \(\chi_{35937}(371,\cdot)\) \(\chi_{35937}(380,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{5445})$ |
| Fixed field: | Number field defined by a degree 10890 polynomial (not computed) |
Values on generators
\((22628,13312)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{1}{1210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 35937 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{307}{5445}\right)\) | \(e\left(\frac{614}{5445}\right)\) | \(e\left(\frac{4681}{10890}\right)\) | \(e\left(\frac{3803}{10890}\right)\) | \(e\left(\frac{307}{1815}\right)\) | \(e\left(\frac{353}{726}\right)\) | \(e\left(\frac{4759}{10890}\right)\) | \(e\left(\frac{4417}{10890}\right)\) | \(e\left(\frac{1228}{5445}\right)\) | \(e\left(\frac{1751}{1815}\right)\) |