Basic properties
| Modulus: | \(8085\) | |
| Conductor: | \(735\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{735}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8085.ga
\(\chi_{8085}(23,\cdot)\) \(\chi_{8085}(452,\cdot)\) \(\chi_{8085}(683,\cdot)\) \(\chi_{8085}(947,\cdot)\) \(\chi_{8085}(1178,\cdot)\) \(\chi_{8085}(1607,\cdot)\) \(\chi_{8085}(1838,\cdot)\) \(\chi_{8085}(2102,\cdot)\) \(\chi_{8085}(2993,\cdot)\) \(\chi_{8085}(3257,\cdot)\) \(\chi_{8085}(3488,\cdot)\) \(\chi_{8085}(3917,\cdot)\) \(\chi_{8085}(4148,\cdot)\) \(\chi_{8085}(4412,\cdot)\) \(\chi_{8085}(4643,\cdot)\) \(\chi_{8085}(5072,\cdot)\) \(\chi_{8085}(5303,\cdot)\) \(\chi_{8085}(5798,\cdot)\) \(\chi_{8085}(6227,\cdot)\) \(\chi_{8085}(6458,\cdot)\) \(\chi_{8085}(6722,\cdot)\) \(\chi_{8085}(6953,\cdot)\) \(\chi_{8085}(7382,\cdot)\) \(\chi_{8085}(7877,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2696,4852,1816,3676)\) → \((-1,-i,e\left(\frac{19}{21}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
| \( \chi_{ 8085 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{2}{7}\right)\) |