Basic properties
| Modulus: | \(8325\) | |
| 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 \(\chi_{925}(696,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8325.kk
\(\chi_{8325}(136,\cdot)\) \(\chi_{8325}(361,\cdot)\) \(\chi_{8325}(946,\cdot)\) \(\chi_{8325}(1261,\cdot)\) \(\chi_{8325}(1621,\cdot)\) \(\chi_{8325}(1891,\cdot)\) \(\chi_{8325}(2611,\cdot)\) \(\chi_{8325}(3286,\cdot)\) \(\chi_{8325}(3466,\cdot)\) \(\chi_{8325}(3556,\cdot)\) \(\chi_{8325}(3691,\cdot)\) \(\chi_{8325}(4591,\cdot)\) \(\chi_{8325}(5131,\cdot)\) \(\chi_{8325}(5221,\cdot)\) \(\chi_{8325}(5356,\cdot)\) \(\chi_{8325}(5941,\cdot)\) \(\chi_{8325}(6256,\cdot)\) \(\chi_{8325}(6616,\cdot)\) \(\chi_{8325}(6796,\cdot)\) \(\chi_{8325}(6886,\cdot)\) \(\chi_{8325}(7021,\cdot)\) \(\chi_{8325}(7606,\cdot)\) \(\chi_{8325}(7921,\cdot)\) \(\chi_{8325}(8281,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3701,7327,5626)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8325 }(1621, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{37}{90}\right)\) |