Basic properties
Modulus: | \(4056\) | |
Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1352}(205,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.cy
\(\chi_{4056}(205,\cdot)\) \(\chi_{4056}(277,\cdot)\) \(\chi_{4056}(517,\cdot)\) \(\chi_{4056}(589,\cdot)\) \(\chi_{4056}(829,\cdot)\) \(\chi_{4056}(901,\cdot)\) \(\chi_{4056}(1141,\cdot)\) \(\chi_{4056}(1213,\cdot)\) \(\chi_{4056}(1453,\cdot)\) \(\chi_{4056}(1525,\cdot)\) \(\chi_{4056}(1765,\cdot)\) \(\chi_{4056}(2077,\cdot)\) \(\chi_{4056}(2149,\cdot)\) \(\chi_{4056}(2461,\cdot)\) \(\chi_{4056}(2701,\cdot)\) \(\chi_{4056}(2773,\cdot)\) \(\chi_{4056}(3013,\cdot)\) \(\chi_{4056}(3085,\cdot)\) \(\chi_{4056}(3325,\cdot)\) \(\chi_{4056}(3397,\cdot)\) \(\chi_{4056}(3637,\cdot)\) \(\chi_{4056}(3709,\cdot)\) \(\chi_{4056}(3949,\cdot)\) \(\chi_{4056}(4021,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((1,-1,1,e\left(\frac{47}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 4056 }(205, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{31}{78}\right)\) |