Basic properties
| Modulus: | \(1350\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(589,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1350.bf
\(\chi_{1350}(79,\cdot)\) \(\chi_{1350}(139,\cdot)\) \(\chi_{1350}(169,\cdot)\) \(\chi_{1350}(229,\cdot)\) \(\chi_{1350}(259,\cdot)\) \(\chi_{1350}(319,\cdot)\) \(\chi_{1350}(409,\cdot)\) \(\chi_{1350}(439,\cdot)\) \(\chi_{1350}(529,\cdot)\) \(\chi_{1350}(589,\cdot)\) \(\chi_{1350}(619,\cdot)\) \(\chi_{1350}(679,\cdot)\) \(\chi_{1350}(709,\cdot)\) \(\chi_{1350}(769,\cdot)\) \(\chi_{1350}(859,\cdot)\) \(\chi_{1350}(889,\cdot)\) \(\chi_{1350}(979,\cdot)\) \(\chi_{1350}(1039,\cdot)\) \(\chi_{1350}(1069,\cdot)\) \(\chi_{1350}(1129,\cdot)\) \(\chi_{1350}(1159,\cdot)\) \(\chi_{1350}(1219,\cdot)\) \(\chi_{1350}(1309,\cdot)\) \(\chi_{1350}(1339,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1001,1027)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 1350 }(589, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{45}\right)\) |