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.lt
\(\chi_{8001}(166,\cdot)\) \(\chi_{8001}(241,\cdot)\) \(\chi_{8001}(493,\cdot)\) \(\chi_{8001}(556,\cdot)\) \(\chi_{8001}(808,\cdot)\) \(\chi_{8001}(1363,\cdot)\) \(\chi_{8001}(1426,\cdot)\) \(\chi_{8001}(1615,\cdot)\) \(\chi_{8001}(1879,\cdot)\) \(\chi_{8001}(2245,\cdot)\) \(\chi_{8001}(2371,\cdot)\) \(\chi_{8001}(2383,\cdot)\) \(\chi_{8001}(2509,\cdot)\) \(\chi_{8001}(2623,\cdot)\) \(\chi_{8001}(3013,\cdot)\) \(\chi_{8001}(3253,\cdot)\) \(\chi_{8001}(3706,\cdot)\) \(\chi_{8001}(4840,\cdot)\) \(\chi_{8001}(5092,\cdot)\) \(\chi_{8001}(5722,\cdot)\) \(\chi_{8001}(5773,\cdot)\) \(\chi_{8001}(5848,\cdot)\) \(\chi_{8001}(6151,\cdot)\) \(\chi_{8001}(6163,\cdot)\) \(\chi_{8001}(6214,\cdot)\) \(\chi_{8001}(6226,\cdot)\) \(\chi_{8001}(6403,\cdot)\) \(\chi_{8001}(6415,\cdot)\) \(\chi_{8001}(6466,\cdot)\) \(\chi_{8001}(7222,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{95}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(166, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(-1\) |