Basic properties
| Modulus: | \(241\) | |
| Conductor: | \(241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 241.r
\(\chi_{241}(17,\cdot)\) \(\chi_{241}(21,\cdot)\) \(\chi_{241}(23,\cdot)\) \(\chi_{241}(26,\cdot)\) \(\chi_{241}(28,\cdot)\) \(\chi_{241}(33,\cdot)\) \(\chi_{241}(43,\cdot)\) \(\chi_{241}(57,\cdot)\) \(\chi_{241}(73,\cdot)\) \(\chi_{241}(85,\cdot)\) \(\chi_{241}(93,\cdot)\) \(\chi_{241}(101,\cdot)\) \(\chi_{241}(102,\cdot)\) \(\chi_{241}(103,\cdot)\) \(\chi_{241}(105,\cdot)\) \(\chi_{241}(117,\cdot)\) \(\chi_{241}(124,\cdot)\) \(\chi_{241}(136,\cdot)\) \(\chi_{241}(138,\cdot)\) \(\chi_{241}(139,\cdot)\) \(\chi_{241}(140,\cdot)\) \(\chi_{241}(148,\cdot)\) \(\chi_{241}(156,\cdot)\) \(\chi_{241}(168,\cdot)\) \(\chi_{241}(184,\cdot)\) \(\chi_{241}(198,\cdot)\) \(\chi_{241}(208,\cdot)\) \(\chi_{241}(213,\cdot)\) \(\chi_{241}(215,\cdot)\) \(\chi_{241}(218,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\(7\) → \(e\left(\frac{31}{80}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 241 }(93, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(i\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{16}\right)\) |