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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.cj
\(\chi_{4011}(44,\cdot)\) \(\chi_{4011}(53,\cdot)\) \(\chi_{4011}(74,\cdot)\) \(\chi_{4011}(95,\cdot)\) \(\chi_{4011}(116,\cdot)\) \(\chi_{4011}(137,\cdot)\) \(\chi_{4011}(179,\cdot)\) \(\chi_{4011}(212,\cdot)\) \(\chi_{4011}(233,\cdot)\) \(\chi_{4011}(254,\cdot)\) \(\chi_{4011}(284,\cdot)\) \(\chi_{4011}(296,\cdot)\) \(\chi_{4011}(305,\cdot)\) \(\chi_{4011}(317,\cdot)\) \(\chi_{4011}(359,\cdot)\) \(\chi_{4011}(380,\cdot)\) \(\chi_{4011}(401,\cdot)\) \(\chi_{4011}(410,\cdot)\) \(\chi_{4011}(443,\cdot)\) \(\chi_{4011}(473,\cdot)\) \(\chi_{4011}(494,\cdot)\) \(\chi_{4011}(506,\cdot)\) \(\chi_{4011}(527,\cdot)\) \(\chi_{4011}(557,\cdot)\) \(\chi_{4011}(569,\cdot)\) \(\chi_{4011}(620,\cdot)\) \(\chi_{4011}(662,\cdot)\) \(\chi_{4011}(674,\cdot)\) \(\chi_{4011}(683,\cdot)\) \(\chi_{4011}(704,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{141}{190}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(233, a) \) | \(1\) | \(1\) | \(e\left(\frac{467}{570}\right)\) | \(e\left(\frac{182}{285}\right)\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{87}{190}\right)\) | \(e\left(\frac{26}{285}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{11}{95}\right)\) | \(e\left(\frac{79}{285}\right)\) | \(e\left(\frac{319}{570}\right)\) | \(e\left(\frac{233}{570}\right)\) |