Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(352\) | 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 6001.et
\(\chi_{6001}(24,\cdot)\) \(\chi_{6001}(54,\cdot)\) \(\chi_{6001}(62,\cdot)\) \(\chi_{6001}(107,\cdot)\) \(\chi_{6001}(114,\cdot)\) \(\chi_{6001}(139,\cdot)\) \(\chi_{6001}(143,\cdot)\) \(\chi_{6001}(150,\cdot)\) \(\chi_{6001}(193,\cdot)\) \(\chi_{6001}(224,\cdot)\) \(\chi_{6001}(227,\cdot)\) \(\chi_{6001}(235,\cdot)\) \(\chi_{6001}(419,\cdot)\) \(\chi_{6001}(504,\cdot)\) \(\chi_{6001}(555,\cdot)\) \(\chi_{6001}(601,\cdot)\) \(\chi_{6001}(602,\cdot)\) \(\chi_{6001}(619,\cdot)\) \(\chi_{6001}(640,\cdot)\) \(\chi_{6001}(649,\cdot)\) \(\chi_{6001}(743,\cdot)\) \(\chi_{6001}(751,\cdot)\) \(\chi_{6001}(762,\cdot)\) \(\chi_{6001}(839,\cdot)\) \(\chi_{6001}(853,\cdot)\) \(\chi_{6001}(964,\cdot)\) \(\chi_{6001}(979,\cdot)\) \(\chi_{6001}(996,\cdot)\) \(\chi_{6001}(997,\cdot)\) \(\chi_{6001}(1064,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{352})$ |
Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{7}{16}\right),e\left(\frac{81}{352}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(997, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{235}{352}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{103}{352}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{59}{176}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{153}{176}\right)\) |