Basic properties
Modulus: | \(4011\) | |
Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1337}(794,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.bv
\(\chi_{4011}(52,\cdot)\) \(\chi_{4011}(136,\cdot)\) \(\chi_{4011}(388,\cdot)\) \(\chi_{4011}(418,\cdot)\) \(\chi_{4011}(451,\cdot)\) \(\chi_{4011}(535,\cdot)\) \(\chi_{4011}(598,\cdot)\) \(\chi_{4011}(733,\cdot)\) \(\chi_{4011}(796,\cdot)\) \(\chi_{4011}(871,\cdot)\) \(\chi_{4011}(985,\cdot)\) \(\chi_{4011}(1132,\cdot)\) \(\chi_{4011}(1300,\cdot)\) \(\chi_{4011}(1342,\cdot)\) \(\chi_{4011}(1564,\cdot)\) \(\chi_{4011}(1678,\cdot)\) \(\chi_{4011}(1879,\cdot)\) \(\chi_{4011}(1942,\cdot)\) \(\chi_{4011}(2035,\cdot)\) \(\chi_{4011}(2131,\cdot)\) \(\chi_{4011}(2278,\cdot)\) \(\chi_{4011}(2413,\cdot)\) \(\chi_{4011}(2446,\cdot)\) \(\chi_{4011}(2488,\cdot)\) \(\chi_{4011}(2824,\cdot)\) \(\chi_{4011}(2854,\cdot)\) \(\chi_{4011}(2917,\cdot)\) \(\chi_{4011}(3001,\cdot)\) \(\chi_{4011}(3181,\cdot)\) \(\chi_{4011}(3253,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{2}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(2131, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{107}{114}\right)\) |