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)
|
Galois orbit 8001.na
\(\chi_{8001}(139,\cdot)\) \(\chi_{8001}(601,\cdot)\) \(\chi_{8001}(664,\cdot)\) \(\chi_{8001}(769,\cdot)\) \(\chi_{8001}(853,\cdot)\) \(\chi_{8001}(895,\cdot)\) \(\chi_{8001}(1210,\cdot)\) \(\chi_{8001}(1273,\cdot)\) \(\chi_{8001}(1462,\cdot)\) \(\chi_{8001}(1483,\cdot)\) \(\chi_{8001}(1609,\cdot)\) \(\chi_{8001}(1861,\cdot)\) \(\chi_{8001}(2470,\cdot)\) \(\chi_{8001}(2491,\cdot)\) \(\chi_{8001}(2596,\cdot)\) \(\chi_{8001}(3289,\cdot)\) \(\chi_{8001}(3541,\cdot)\) \(\chi_{8001}(3604,\cdot)\) \(\chi_{8001}(3856,\cdot)\) \(\chi_{8001}(4927,\cdot)\) \(\chi_{8001}(5011,\cdot)\) \(\chi_{8001}(5389,\cdot)\) \(\chi_{8001}(5431,\cdot)\) \(\chi_{8001}(5452,\cdot)\) \(\chi_{8001}(5557,\cdot)\) \(\chi_{8001}(5641,\cdot)\) \(\chi_{8001}(5704,\cdot)\) \(\chi_{8001}(6061,\cdot)\) \(\chi_{8001}(6460,\cdot)\) \(\chi_{8001}(6586,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{19}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{1}{6}\right)\) |