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.cl
\(\chi_{4011}(47,\cdot)\) \(\chi_{4011}(89,\cdot)\) \(\chi_{4011}(101,\cdot)\) \(\chi_{4011}(110,\cdot)\) \(\chi_{4011}(131,\cdot)\) \(\chi_{4011}(143,\cdot)\) \(\chi_{4011}(164,\cdot)\) \(\chi_{4011}(173,\cdot)\) \(\chi_{4011}(248,\cdot)\) \(\chi_{4011}(278,\cdot)\) \(\chi_{4011}(290,\cdot)\) \(\chi_{4011}(332,\cdot)\) \(\chi_{4011}(362,\cdot)\) \(\chi_{4011}(374,\cdot)\) \(\chi_{4011}(404,\cdot)\) \(\chi_{4011}(458,\cdot)\) \(\chi_{4011}(488,\cdot)\) \(\chi_{4011}(509,\cdot)\) \(\chi_{4011}(530,\cdot)\) \(\chi_{4011}(563,\cdot)\) \(\chi_{4011}(626,\cdot)\) \(\chi_{4011}(635,\cdot)\) \(\chi_{4011}(647,\cdot)\) \(\chi_{4011}(656,\cdot)\) \(\chi_{4011}(668,\cdot)\) \(\chi_{4011}(689,\cdot)\) \(\chi_{4011}(710,\cdot)\) \(\chi_{4011}(719,\cdot)\) \(\chi_{4011}(740,\cdot)\) \(\chi_{4011}(752,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{7}{190}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(143, a) \) | \(-1\) | \(1\) | \(e\left(\frac{259}{570}\right)\) | \(e\left(\frac{259}{285}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{69}{190}\right)\) | \(e\left(\frac{359}{570}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{119}{190}\right)\) | \(e\left(\frac{233}{285}\right)\) | \(e\left(\frac{79}{285}\right)\) | \(e\left(\frac{248}{285}\right)\) |