Basic properties
Modulus: | \(8085\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{245}(152,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8085.fx
\(\chi_{8085}(397,\cdot)\) \(\chi_{8085}(628,\cdot)\) \(\chi_{8085}(892,\cdot)\) \(\chi_{8085}(1123,\cdot)\) \(\chi_{8085}(1552,\cdot)\) \(\chi_{8085}(2047,\cdot)\) \(\chi_{8085}(2278,\cdot)\) \(\chi_{8085}(2707,\cdot)\) \(\chi_{8085}(2938,\cdot)\) \(\chi_{8085}(3202,\cdot)\) \(\chi_{8085}(3433,\cdot)\) \(\chi_{8085}(3862,\cdot)\) \(\chi_{8085}(4093,\cdot)\) \(\chi_{8085}(4357,\cdot)\) \(\chi_{8085}(5248,\cdot)\) \(\chi_{8085}(5512,\cdot)\) \(\chi_{8085}(5743,\cdot)\) \(\chi_{8085}(6172,\cdot)\) \(\chi_{8085}(6403,\cdot)\) \(\chi_{8085}(6667,\cdot)\) \(\chi_{8085}(6898,\cdot)\) \(\chi_{8085}(7327,\cdot)\) \(\chi_{8085}(7558,\cdot)\) \(\chi_{8085}(8053,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((2696,4852,1816,3676)\) → \((1,i,e\left(\frac{29}{42}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
\( \chi_{ 8085 }(397, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) |