Basic properties
Modulus: | \(4011\) | |
Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1337}(1171,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.bo
\(\chi_{4011}(25,\cdot)\) \(\chi_{4011}(121,\cdot)\) \(\chi_{4011}(298,\cdot)\) \(\chi_{4011}(562,\cdot)\) \(\chi_{4011}(625,\cdot)\) \(\chi_{4011}(709,\cdot)\) \(\chi_{4011}(961,\cdot)\) \(\chi_{4011}(991,\cdot)\) \(\chi_{4011}(1024,\cdot)\) \(\chi_{4011}(1108,\cdot)\) \(\chi_{4011}(1171,\cdot)\) \(\chi_{4011}(1306,\cdot)\) \(\chi_{4011}(1369,\cdot)\) \(\chi_{4011}(1444,\cdot)\) \(\chi_{4011}(1558,\cdot)\) \(\chi_{4011}(1705,\cdot)\) \(\chi_{4011}(1873,\cdot)\) \(\chi_{4011}(1915,\cdot)\) \(\chi_{4011}(2137,\cdot)\) \(\chi_{4011}(2251,\cdot)\) \(\chi_{4011}(2452,\cdot)\) \(\chi_{4011}(2515,\cdot)\) \(\chi_{4011}(2608,\cdot)\) \(\chi_{4011}(2704,\cdot)\) \(\chi_{4011}(2851,\cdot)\) \(\chi_{4011}(2986,\cdot)\) \(\chi_{4011}(3019,\cdot)\) \(\chi_{4011}(3061,\cdot)\) \(\chi_{4011}(3397,\cdot)\) \(\chi_{4011}(3427,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((2675,2866,2311)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{10}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(1171, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) |