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.eq
\(\chi_{6001}(31,\cdot)\) \(\chi_{6001}(79,\cdot)\) \(\chi_{6001}(108,\cdot)\) \(\chi_{6001}(163,\cdot)\) \(\chi_{6001}(180,\cdot)\) \(\chi_{6001}(192,\cdot)\) \(\chi_{6001}(278,\cdot)\) \(\chi_{6001}(282,\cdot)\) \(\chi_{6001}(296,\cdot)\) \(\chi_{6001}(300,\cdot)\) \(\chi_{6001}(320,\cdot)\) \(\chi_{6001}(398,\cdot)\) \(\chi_{6001}(448,\cdot)\) \(\chi_{6001}(470,\cdot)\) \(\chi_{6001}(500,\cdot)\) \(\chi_{6001}(503,\cdot)\) \(\chi_{6001}(588,\cdot)\) \(\chi_{6001}(589,\cdot)\) \(\chi_{6001}(617,\cdot)\) \(\chi_{6001}(658,\cdot)\) \(\chi_{6001}(669,\cdot)\) \(\chi_{6001}(709,\cdot)\) \(\chi_{6001}(759,\cdot)\) \(\chi_{6001}(802,\cdot)\) \(\chi_{6001}(881,\cdot)\) \(\chi_{6001}(957,\cdot)\) \(\chi_{6001}(974,\cdot)\) \(\chi_{6001}(980,\cdot)\) \(\chi_{6001}(1115,\cdot)\) \(\chi_{6001}(1144,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{352})$ |
Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{11}{16}\right),e\left(\frac{311}{352}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(398, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{201}{352}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{157}{352}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{25}{176}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{145}{176}\right)\) |