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.nm
\(\chi_{8001}(220,\cdot)\) \(\chi_{8001}(283,\cdot)\) \(\chi_{8001}(472,\cdot)\) \(\chi_{8001}(565,\cdot)\) \(\chi_{8001}(691,\cdot)\) \(\chi_{8001}(1102,\cdot)\) \(\chi_{8001}(1228,\cdot)\) \(\chi_{8001}(1384,\cdot)\) \(\chi_{8001}(1480,\cdot)\) \(\chi_{8001}(1636,\cdot)\) \(\chi_{8001}(1699,\cdot)\) \(\chi_{8001}(1951,\cdot)\) \(\chi_{8001}(2110,\cdot)\) \(\chi_{8001}(3022,\cdot)\) \(\chi_{8001}(3526,\cdot)\) \(\chi_{8001}(3652,\cdot)\) \(\chi_{8001}(4156,\cdot)\) \(\chi_{8001}(4630,\cdot)\) \(\chi_{8001}(4849,\cdot)\) \(\chi_{8001}(5008,\cdot)\) \(\chi_{8001}(5071,\cdot)\) \(\chi_{8001}(5260,\cdot)\) \(\chi_{8001}(5323,\cdot)\) \(\chi_{8001}(5983,\cdot)\) \(\chi_{8001}(6079,\cdot)\) \(\chi_{8001}(6205,\cdot)\) \(\chi_{8001}(6235,\cdot)\) \(\chi_{8001}(6268,\cdot)\) \(\chi_{8001}(6520,\cdot)\) \(\chi_{8001}(6583,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{47}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(220, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{1}{6}\right)\) |