Basic properties
Modulus: | \(4011\) | |
Conductor: | \(4011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(570\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 4011.ci
\(\chi_{4011}(2,\cdot)\) \(\chi_{4011}(23,\cdot)\) \(\chi_{4011}(65,\cdot)\) \(\chi_{4011}(86,\cdot)\) \(\chi_{4011}(128,\cdot)\) \(\chi_{4011}(149,\cdot)\) \(\chi_{4011}(158,\cdot)\) \(\chi_{4011}(170,\cdot)\) \(\chi_{4011}(200,\cdot)\) \(\chi_{4011}(242,\cdot)\) \(\chi_{4011}(263,\cdot)\) \(\chi_{4011}(326,\cdot)\) \(\chi_{4011}(338,\cdot)\) \(\chi_{4011}(347,\cdot)\) \(\chi_{4011}(422,\cdot)\) \(\chi_{4011}(485,\cdot)\) \(\chi_{4011}(515,\cdot)\) \(\chi_{4011}(590,\cdot)\) \(\chi_{4011}(599,\cdot)\) \(\chi_{4011}(632,\cdot)\) \(\chi_{4011}(641,\cdot)\) \(\chi_{4011}(653,\cdot)\) \(\chi_{4011}(767,\cdot)\) \(\chi_{4011}(779,\cdot)\) \(\chi_{4011}(788,\cdot)\) \(\chi_{4011}(809,\cdot)\) \(\chi_{4011}(842,\cdot)\) \(\chi_{4011}(872,\cdot)\) \(\chi_{4011}(884,\cdot)\) \(\chi_{4011}(893,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{22}{95}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{203}{570}\right)\) | \(e\left(\frac{203}{285}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{13}{190}\right)\) | \(e\left(\frac{29}{285}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{89}{95}\right)\) | \(e\left(\frac{121}{285}\right)\) | \(e\left(\frac{301}{570}\right)\) | \(e\left(\frac{256}{285}\right)\) |