Basic properties
Modulus: | \(8023\) | |
Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.dz
\(\chi_{8023}(535,\cdot)\) \(\chi_{8023}(987,\cdot)\) \(\chi_{8023}(1586,\cdot)\) \(\chi_{8023}(2211,\cdot)\) \(\chi_{8023}(2571,\cdot)\) \(\chi_{8023}(2716,\cdot)\) \(\chi_{8023}(2809,\cdot)\) \(\chi_{8023}(3397,\cdot)\) \(\chi_{8023}(3487,\cdot)\) \(\chi_{8023}(3586,\cdot)\) \(\chi_{8023}(4019,\cdot)\) \(\chi_{8023}(4414,\cdot)\) \(\chi_{8023}(4831,\cdot)\) \(\chi_{8023}(4979,\cdot)\) \(\chi_{8023}(5202,\cdot)\) \(\chi_{8023}(5281,\cdot)\) \(\chi_{8023}(5283,\cdot)\) \(\chi_{8023}(5375,\cdot)\) \(\chi_{8023}(6335,\cdot)\) \(\chi_{8023}(6392,\cdot)\) \(\chi_{8023}(6538,\cdot)\) \(\chi_{8023}(7317,\cdot)\) \(\chi_{8023}(7442,\cdot)\) \(\chi_{8023}(7575,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{11}{35}\right),e\left(\frac{5}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8023 }(535, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) |