Basic properties
Modulus: | \(8085\) | |
Conductor: | \(2695\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2695}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8085.fp
\(\chi_{8085}(139,\cdot)\) \(\chi_{8085}(349,\cdot)\) \(\chi_{8085}(1084,\cdot)\) \(\chi_{8085}(1294,\cdot)\) \(\chi_{8085}(1399,\cdot)\) \(\chi_{8085}(1504,\cdot)\) \(\chi_{8085}(2239,\cdot)\) \(\chi_{8085}(2554,\cdot)\) \(\chi_{8085}(2659,\cdot)\) \(\chi_{8085}(3394,\cdot)\) \(\chi_{8085}(3604,\cdot)\) \(\chi_{8085}(3709,\cdot)\) \(\chi_{8085}(3814,\cdot)\) \(\chi_{8085}(4549,\cdot)\) \(\chi_{8085}(4759,\cdot)\) \(\chi_{8085}(4864,\cdot)\) \(\chi_{8085}(4969,\cdot)\) \(\chi_{8085}(5704,\cdot)\) \(\chi_{8085}(5914,\cdot)\) \(\chi_{8085}(6019,\cdot)\) \(\chi_{8085}(7069,\cdot)\) \(\chi_{8085}(7174,\cdot)\) \(\chi_{8085}(7279,\cdot)\) \(\chi_{8085}(8014,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((2696,4852,1816,3676)\) → \((1,-1,e\left(\frac{5}{14}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
\( \chi_{ 8085 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{23}{70}\right)\) |