Basic properties
Modulus: | \(211\) | |
Conductor: | \(211\) | 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 211.l
\(\chi_{211}(5,\cdot)\) \(\chi_{211}(11,\cdot)\) \(\chi_{211}(13,\cdot)\) \(\chi_{211}(25,\cdot)\) \(\chi_{211}(64,\cdot)\) \(\chi_{211}(65,\cdot)\) \(\chi_{211}(76,\cdot)\) \(\chi_{211}(79,\cdot)\) \(\chi_{211}(82,\cdot)\) \(\chi_{211}(87,\cdot)\) \(\chi_{211}(96,\cdot)\) \(\chi_{211}(109,\cdot)\) \(\chi_{211}(113,\cdot)\) \(\chi_{211}(114,\cdot)\) \(\chi_{211}(121,\cdot)\) \(\chi_{211}(122,\cdot)\) \(\chi_{211}(125,\cdot)\) \(\chi_{211}(143,\cdot)\) \(\chi_{211}(151,\cdot)\) \(\chi_{211}(169,\cdot)\) \(\chi_{211}(183,\cdot)\) \(\chi_{211}(184,\cdot)\) \(\chi_{211}(193,\cdot)\) \(\chi_{211}(203,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\(2\) → \(e\left(\frac{31}{35}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 211 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{35}\right)\) |