Basic properties
Modulus: | \(4056\) | |
Conductor: | \(4056\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.dc
\(\chi_{4056}(101,\cdot)\) \(\chi_{4056}(173,\cdot)\) \(\chi_{4056}(413,\cdot)\) \(\chi_{4056}(725,\cdot)\) \(\chi_{4056}(797,\cdot)\) \(\chi_{4056}(1109,\cdot)\) \(\chi_{4056}(1349,\cdot)\) \(\chi_{4056}(1421,\cdot)\) \(\chi_{4056}(1661,\cdot)\) \(\chi_{4056}(1733,\cdot)\) \(\chi_{4056}(1973,\cdot)\) \(\chi_{4056}(2045,\cdot)\) \(\chi_{4056}(2285,\cdot)\) \(\chi_{4056}(2357,\cdot)\) \(\chi_{4056}(2597,\cdot)\) \(\chi_{4056}(2669,\cdot)\) \(\chi_{4056}(2909,\cdot)\) \(\chi_{4056}(2981,\cdot)\) \(\chi_{4056}(3221,\cdot)\) \(\chi_{4056}(3293,\cdot)\) \(\chi_{4056}(3533,\cdot)\) \(\chi_{4056}(3605,\cdot)\) \(\chi_{4056}(3845,\cdot)\) \(\chi_{4056}(3917,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((1,-1,-1,e\left(\frac{35}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 4056 }(101, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{2}{39}\right)\) |