Basic properties
Modulus: | \(4011\) | |
Conductor: | \(4011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(114\) | 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.bs
\(\chi_{4011}(5,\cdot)\) \(\chi_{4011}(227,\cdot)\) \(\chi_{4011}(341,\cdot)\) \(\chi_{4011}(542,\cdot)\) \(\chi_{4011}(605,\cdot)\) \(\chi_{4011}(698,\cdot)\) \(\chi_{4011}(794,\cdot)\) \(\chi_{4011}(941,\cdot)\) \(\chi_{4011}(1076,\cdot)\) \(\chi_{4011}(1109,\cdot)\) \(\chi_{4011}(1151,\cdot)\) \(\chi_{4011}(1487,\cdot)\) \(\chi_{4011}(1517,\cdot)\) \(\chi_{4011}(1580,\cdot)\) \(\chi_{4011}(1664,\cdot)\) \(\chi_{4011}(1844,\cdot)\) \(\chi_{4011}(1916,\cdot)\) \(\chi_{4011}(1979,\cdot)\) \(\chi_{4011}(2063,\cdot)\) \(\chi_{4011}(2126,\cdot)\) \(\chi_{4011}(2222,\cdot)\) \(\chi_{4011}(2399,\cdot)\) \(\chi_{4011}(2663,\cdot)\) \(\chi_{4011}(2726,\cdot)\) \(\chi_{4011}(2810,\cdot)\) \(\chi_{4011}(3062,\cdot)\) \(\chi_{4011}(3092,\cdot)\) \(\chi_{4011}(3125,\cdot)\) \(\chi_{4011}(3209,\cdot)\) \(\chi_{4011}(3272,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{7}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(341, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{61}{114}\right)\) |