Basic properties
| Modulus: | \(1850\) | |
| Conductor: | \(925\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{925}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1850.cb
\(\chi_{1850}(139,\cdot)\) \(\chi_{1850}(169,\cdot)\) \(\chi_{1850}(189,\cdot)\) \(\chi_{1850}(289,\cdot)\) \(\chi_{1850}(469,\cdot)\) \(\chi_{1850}(509,\cdot)\) \(\chi_{1850}(539,\cdot)\) \(\chi_{1850}(559,\cdot)\) \(\chi_{1850}(659,\cdot)\) \(\chi_{1850}(669,\cdot)\) \(\chi_{1850}(839,\cdot)\) \(\chi_{1850}(879,\cdot)\) \(\chi_{1850}(909,\cdot)\) \(\chi_{1850}(929,\cdot)\) \(\chi_{1850}(1029,\cdot)\) \(\chi_{1850}(1039,\cdot)\) \(\chi_{1850}(1209,\cdot)\) \(\chi_{1850}(1279,\cdot)\) \(\chi_{1850}(1409,\cdot)\) \(\chi_{1850}(1579,\cdot)\) \(\chi_{1850}(1619,\cdot)\) \(\chi_{1850}(1669,\cdot)\) \(\chi_{1850}(1769,\cdot)\) \(\chi_{1850}(1779,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1777,1001)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1850 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) |