Basic properties
Modulus: | \(8001\) | |
Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(126\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 8001.mv
\(\chi_{8001}(473,\cdot)\) \(\chi_{8001}(947,\cdot)\) \(\chi_{8001}(1166,\cdot)\) \(\chi_{8001}(1325,\cdot)\) \(\chi_{8001}(1388,\cdot)\) \(\chi_{8001}(1577,\cdot)\) \(\chi_{8001}(1640,\cdot)\) \(\chi_{8001}(2300,\cdot)\) \(\chi_{8001}(2396,\cdot)\) \(\chi_{8001}(2522,\cdot)\) \(\chi_{8001}(2552,\cdot)\) \(\chi_{8001}(2585,\cdot)\) \(\chi_{8001}(2837,\cdot)\) \(\chi_{8001}(2900,\cdot)\) \(\chi_{8001}(3182,\cdot)\) \(\chi_{8001}(3308,\cdot)\) \(\chi_{8001}(3341,\cdot)\) \(\chi_{8001}(3623,\cdot)\) \(\chi_{8001}(3686,\cdot)\) \(\chi_{8001}(3875,\cdot)\) \(\chi_{8001}(4538,\cdot)\) \(\chi_{8001}(4601,\cdot)\) \(\chi_{8001}(4790,\cdot)\) \(\chi_{8001}(4883,\cdot)\) \(\chi_{8001}(5009,\cdot)\) \(\chi_{8001}(5420,\cdot)\) \(\chi_{8001}(5546,\cdot)\) \(\chi_{8001}(5702,\cdot)\) \(\chi_{8001}(5798,\cdot)\) \(\chi_{8001}(5954,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{13}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(473, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{11}{126}\right)\) | \(1\) |