Basic properties
Modulus: | \(8007\) | |
Conductor: | \(471\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{471}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.ds
\(\chi_{8007}(35,\cdot)\) \(\chi_{8007}(647,\cdot)\) \(\chi_{8007}(749,\cdot)\) \(\chi_{8007}(953,\cdot)\) \(\chi_{8007}(1055,\cdot)\) \(\chi_{8007}(1208,\cdot)\) \(\chi_{8007}(1973,\cdot)\) \(\chi_{8007}(2228,\cdot)\) \(\chi_{8007}(2279,\cdot)\) \(\chi_{8007}(2330,\cdot)\) \(\chi_{8007}(2636,\cdot)\) \(\chi_{8007}(3554,\cdot)\) \(\chi_{8007}(3758,\cdot)\) \(\chi_{8007}(3962,\cdot)\) \(\chi_{8007}(4727,\cdot)\) \(\chi_{8007}(4982,\cdot)\) \(\chi_{8007}(5033,\cdot)\) \(\chi_{8007}(5390,\cdot)\) \(\chi_{8007}(5492,\cdot)\) \(\chi_{8007}(5849,\cdot)\) \(\chi_{8007}(6563,\cdot)\) \(\chi_{8007}(6665,\cdot)\) \(\chi_{8007}(7328,\cdot)\) \(\chi_{8007}(7583,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5339,1414,7855)\) → \((-1,1,e\left(\frac{37}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 8007 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) |