Basic properties
Modulus: | \(241\) | |
Conductor: | \(241\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | 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 241.s
\(\chi_{241}(3,\cdot)\) \(\chi_{241}(12,\cdot)\) \(\chi_{241}(18,\cdot)\) \(\chi_{241}(20,\cdot)\) \(\chi_{241}(29,\cdot)\) \(\chi_{241}(45,\cdot)\) \(\chi_{241}(49,\cdot)\) \(\chi_{241}(50,\cdot)\) \(\chi_{241}(53,\cdot)\) \(\chi_{241}(59,\cdot)\) \(\chi_{241}(67,\cdot)\) \(\chi_{241}(72,\cdot)\) \(\chi_{241}(75,\cdot)\) \(\chi_{241}(77,\cdot)\) \(\chi_{241}(80,\cdot)\) \(\chi_{241}(108,\cdot)\) \(\chi_{241}(133,\cdot)\) \(\chi_{241}(161,\cdot)\) \(\chi_{241}(164,\cdot)\) \(\chi_{241}(166,\cdot)\) \(\chi_{241}(169,\cdot)\) \(\chi_{241}(174,\cdot)\) \(\chi_{241}(182,\cdot)\) \(\chi_{241}(188,\cdot)\) \(\chi_{241}(191,\cdot)\) \(\chi_{241}(192,\cdot)\) \(\chi_{241}(196,\cdot)\) \(\chi_{241}(212,\cdot)\) \(\chi_{241}(221,\cdot)\) \(\chi_{241}(223,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\(7\) → \(e\left(\frac{47}{120}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 241 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(i\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{24}\right)\) |