Basic properties
Modulus: | \(2850\) | |
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 \(\chi_{475}(309,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.cp
\(\chi_{2850}(139,\cdot)\) \(\chi_{2850}(169,\cdot)\) \(\chi_{2850}(289,\cdot)\) \(\chi_{2850}(529,\cdot)\) \(\chi_{2850}(709,\cdot)\) \(\chi_{2850}(739,\cdot)\) \(\chi_{2850}(769,\cdot)\) \(\chi_{2850}(859,\cdot)\) \(\chi_{2850}(1069,\cdot)\) \(\chi_{2850}(1279,\cdot)\) \(\chi_{2850}(1309,\cdot)\) \(\chi_{2850}(1339,\cdot)\) \(\chi_{2850}(1429,\cdot)\) \(\chi_{2850}(1639,\cdot)\) \(\chi_{2850}(1669,\cdot)\) \(\chi_{2850}(1879,\cdot)\) \(\chi_{2850}(1909,\cdot)\) \(\chi_{2850}(2209,\cdot)\) \(\chi_{2850}(2239,\cdot)\) \(\chi_{2850}(2419,\cdot)\) \(\chi_{2850}(2479,\cdot)\) \(\chi_{2850}(2569,\cdot)\) \(\chi_{2850}(2779,\cdot)\) \(\chi_{2850}(2809,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{8}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 2850 }(2209, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) |