Basic properties
Modulus: | \(8001\) | |
Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.mr
\(\chi_{8001}(866,\cdot)\) \(\chi_{8001}(1319,\cdot)\) \(\chi_{8001}(1559,\cdot)\) \(\chi_{8001}(1949,\cdot)\) \(\chi_{8001}(2063,\cdot)\) \(\chi_{8001}(2189,\cdot)\) \(\chi_{8001}(2201,\cdot)\) \(\chi_{8001}(2327,\cdot)\) \(\chi_{8001}(2693,\cdot)\) \(\chi_{8001}(2957,\cdot)\) \(\chi_{8001}(3146,\cdot)\) \(\chi_{8001}(3209,\cdot)\) \(\chi_{8001}(3764,\cdot)\) \(\chi_{8001}(4016,\cdot)\) \(\chi_{8001}(4079,\cdot)\) \(\chi_{8001}(4331,\cdot)\) \(\chi_{8001}(4406,\cdot)\) \(\chi_{8001}(4847,\cdot)\) \(\chi_{8001}(4910,\cdot)\) \(\chi_{8001}(5024,\cdot)\) \(\chi_{8001}(5150,\cdot)\) \(\chi_{8001}(5162,\cdot)\) \(\chi_{8001}(5225,\cdot)\) \(\chi_{8001}(5351,\cdot)\) \(\chi_{8001}(6107,\cdot)\) \(\chi_{8001}(6158,\cdot)\) \(\chi_{8001}(6170,\cdot)\) \(\chi_{8001}(6347,\cdot)\) \(\chi_{8001}(6359,\cdot)\) \(\chi_{8001}(6410,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{5}{6}\right),e\left(\frac{29}{63}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(866, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{5}{6}\right)\) |