Basic properties
Modulus: | \(2347\) | |
Conductor: | \(2347\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2347.i
\(\chi_{2347}(24,\cdot)\) \(\chi_{2347}(40,\cdot)\) \(\chi_{2347}(234,\cdot)\) \(\chi_{2347}(272,\cdot)\) \(\chi_{2347}(279,\cdot)\) \(\chi_{2347}(301,\cdot)\) \(\chi_{2347}(390,\cdot)\) \(\chi_{2347}(465,\cdot)\) \(\chi_{2347}(489,\cdot)\) \(\chi_{2347}(576,\cdot)\) \(\chi_{2347}(603,\cdot)\) \(\chi_{2347}(650,\cdot)\) \(\chi_{2347}(775,\cdot)\) \(\chi_{2347}(815,\cdot)\) \(\chi_{2347}(849,\cdot)\) \(\chi_{2347}(960,\cdot)\) \(\chi_{2347}(1005,\cdot)\) \(\chi_{2347}(1102,\cdot)\) \(\chi_{2347}(1227,\cdot)\) \(\chi_{2347}(1415,\cdot)\) \(\chi_{2347}(1576,\cdot)\) \(\chi_{2347}(1600,\cdot)\) \(\chi_{2347}(1675,\cdot)\) \(\chi_{2347}(1770,\cdot)\) \(\chi_{2347}(1772,\cdot)\) \(\chi_{2347}(1892,\cdot)\) \(\chi_{2347}(2002,\cdot)\) \(\chi_{2347}(2018,\cdot)\) \(\chi_{2347}(2045,\cdot)\) \(\chi_{2347}(2074,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\(3\) → \(e\left(\frac{43}{51}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2347 }(24, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) |