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 \(\chi_{475}(434,\cdot)\) | 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
\((77,401)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 950 }(909, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{8}{45}\right)\) |