Basic properties
Modulus: | \(950\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{475}(234,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 950.bg
\(\chi_{950}(9,\cdot)\) \(\chi_{950}(119,\cdot)\) \(\chi_{950}(139,\cdot)\) \(\chi_{950}(169,\cdot)\) \(\chi_{950}(289,\cdot)\) \(\chi_{950}(309,\cdot)\) \(\chi_{950}(329,\cdot)\) \(\chi_{950}(339,\cdot)\) \(\chi_{950}(359,\cdot)\) \(\chi_{950}(389,\cdot)\) \(\chi_{950}(479,\cdot)\) \(\chi_{950}(519,\cdot)\) \(\chi_{950}(529,\cdot)\) \(\chi_{950}(579,\cdot)\) \(\chi_{950}(669,\cdot)\) \(\chi_{950}(689,\cdot)\) \(\chi_{950}(709,\cdot)\) \(\chi_{950}(719,\cdot)\) \(\chi_{950}(739,\cdot)\) \(\chi_{950}(769,\cdot)\) \(\chi_{950}(859,\cdot)\) \(\chi_{950}(879,\cdot)\) \(\chi_{950}(909,\cdot)\) \(\chi_{950}(929,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((77,401)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{7}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 950 }(709, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{28}{45}\right)\) |