Basic properties
Modulus: | \(281\) | |
Conductor: | \(281\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | 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 281.k
\(\chi_{281}(4,\cdot)\) \(\chi_{281}(16,\cdot)\) \(\chi_{281}(35,\cdot)\) \(\chi_{281}(50,\cdot)\) \(\chi_{281}(58,\cdot)\) \(\chi_{281}(63,\cdot)\) \(\chi_{281}(64,\cdot)\) \(\chi_{281}(85,\cdot)\) \(\chi_{281}(98,\cdot)\) \(\chi_{281}(101,\cdot)\) \(\chi_{281}(111,\cdot)\) \(\chi_{281}(123,\cdot)\) \(\chi_{281}(140,\cdot)\) \(\chi_{281}(155,\cdot)\) \(\chi_{281}(162,\cdot)\) \(\chi_{281}(163,\cdot)\) \(\chi_{281}(200,\cdot)\) \(\chi_{281}(211,\cdot)\) \(\chi_{281}(236,\cdot)\) \(\chi_{281}(238,\cdot)\) \(\chi_{281}(252,\cdot)\) \(\chi_{281}(256,\cdot)\) \(\chi_{281}(273,\cdot)\) \(\chi_{281}(279,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\(3\) → \(e\left(\frac{12}{35}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 281 }(58, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{26}{35}\right)\) |