Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(176\) | 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 6001.dh
\(\chi_{6001}(43,\cdot)\) \(\chi_{6001}(76,\cdot)\) \(\chi_{6001}(93,\cdot)\) \(\chi_{6001}(223,\cdot)\) \(\chi_{6001}(508,\cdot)\) \(\chi_{6001}(553,\cdot)\) \(\chi_{6001}(756,\cdot)\) \(\chi_{6001}(859,\cdot)\) \(\chi_{6001}(903,\cdot)\) \(\chi_{6001}(960,\cdot)\) \(\chi_{6001}(1369,\cdot)\) \(\chi_{6001}(1453,\cdot)\) \(\chi_{6001}(1494,\cdot)\) \(\chi_{6001}(1498,\cdot)\) \(\chi_{6001}(1504,\cdot)\) \(\chi_{6001}(1579,\cdot)\) \(\chi_{6001}(1596,\cdot)\) \(\chi_{6001}(1613,\cdot)\) \(\chi_{6001}(1719,\cdot)\) \(\chi_{6001}(1885,\cdot)\) \(\chi_{6001}(1946,\cdot)\) \(\chi_{6001}(1953,\cdot)\) \(\chi_{6001}(1991,\cdot)\) \(\chi_{6001}(2093,\cdot)\) \(\chi_{6001}(2100,\cdot)\) \(\chi_{6001}(2157,\cdot)\) \(\chi_{6001}(2327,\cdot)\) \(\chi_{6001}(2406,\cdot)\) \(\chi_{6001}(2433,\cdot)\) \(\chi_{6001}(2480,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{176})$ |
Fixed field: | Number field defined by a degree 176 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{69}{176}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(903, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{47}{176}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{91}{176}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{57}{88}\right)\) |