Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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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)
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Galois orbit 6001.er
\(\chi_{6001}(3,\cdot)\) \(\chi_{6001}(5,\cdot)\) \(\chi_{6001}(27,\cdot)\) \(\chi_{6001}(45,\cdot)\) \(\chi_{6001}(74,\cdot)\) \(\chi_{6001}(75,\cdot)\) \(\chi_{6001}(112,\cdot)\) \(\chi_{6001}(124,\cdot)\) \(\chi_{6001}(125,\cdot)\) \(\chi_{6001}(133,\cdot)\) \(\chi_{6001}(147,\cdot)\) \(\chi_{6001}(243,\cdot)\) \(\chi_{6001}(245,\cdot)\) \(\chi_{6001}(379,\cdot)\) \(\chi_{6001}(381,\cdot)\) \(\chi_{6001}(386,\cdot)\) \(\chi_{6001}(405,\cdot)\) \(\chi_{6001}(516,\cdot)\) \(\chi_{6001}(533,\cdot)\) \(\chi_{6001}(568,\cdot)\) \(\chi_{6001}(635,\cdot)\) \(\chi_{6001}(666,\cdot)\) \(\chi_{6001}(675,\cdot)\) \(\chi_{6001}(694,\cdot)\) \(\chi_{6001}(726,\cdot)\) \(\chi_{6001}(768,\cdot)\) \(\chi_{6001}(809,\cdot)\) \(\chi_{6001}(838,\cdot)\) \(\chi_{6001}(856,\cdot)\) \(\chi_{6001}(860,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{352})$ |
Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{5}{16}\right),e\left(\frac{69}{352}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(124, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{179}{352}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{47}{352}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{3}{176}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{167}{176}\right)\) |