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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6001.ep
\(\chi_{6001}(12,\cdot)\) \(\chi_{6001}(20,\cdot)\) \(\chi_{6001}(28,\cdot)\) \(\chi_{6001}(129,\cdot)\) \(\chi_{6001}(142,\cdot)\) \(\chi_{6001}(214,\cdot)\) \(\chi_{6001}(215,\cdot)\) \(\chi_{6001}(228,\cdot)\) \(\chi_{6001}(279,\cdot)\) \(\chi_{6001}(299,\cdot)\) \(\chi_{6001}(301,\cdot)\) \(\chi_{6001}(367,\cdot)\) \(\chi_{6001}(377,\cdot)\) \(\chi_{6001}(380,\cdot)\) \(\chi_{6001}(465,\cdot)\) \(\chi_{6001}(496,\cdot)\) \(\chi_{6001}(498,\cdot)\) \(\chi_{6001}(532,\cdot)\) \(\chi_{6001}(573,\cdot)\) \(\chi_{6001}(626,\cdot)\) \(\chi_{6001}(643,\cdot)\) \(\chi_{6001}(651,\cdot)\) \(\chi_{6001}(711,\cdot)\) \(\chi_{6001}(719,\cdot)\) \(\chi_{6001}(775,\cdot)\) \(\chi_{6001}(811,\cdot)\) \(\chi_{6001}(830,\cdot)\) \(\chi_{6001}(844,\cdot)\) \(\chi_{6001}(949,\cdot)\) \(\chi_{6001}(955,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{352})$ |
Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{3}{16}\right),e\left(\frac{7}{352}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(775, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{73}{352}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{29}{352}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{73}{176}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{89}{176}\right)\) |