Basic properties
Modulus: | \(8003\) | |
Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | 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 8003.bb
\(\chi_{8003}(183,\cdot)\) \(\chi_{8003}(334,\cdot)\) \(\chi_{8003}(420,\cdot)\) \(\chi_{8003}(1391,\cdot)\) \(\chi_{8003}(1477,\cdot)\) \(\chi_{8003}(1844,\cdot)\) \(\chi_{8003}(2448,\cdot)\) \(\chi_{8003}(2750,\cdot)\) \(\chi_{8003}(3354,\cdot)\) \(\chi_{8003}(3807,\cdot)\) \(\chi_{8003}(3893,\cdot)\) \(\chi_{8003}(3958,\cdot)\) \(\chi_{8003}(4044,\cdot)\) \(\chi_{8003}(4109,\cdot)\) \(\chi_{8003}(4713,\cdot)\) \(\chi_{8003}(5101,\cdot)\) \(\chi_{8003}(5554,\cdot)\) \(\chi_{8003}(5770,\cdot)\) \(\chi_{8003}(6158,\cdot)\) \(\chi_{8003}(6460,\cdot)\) \(\chi_{8003}(7064,\cdot)\) \(\chi_{8003}(7517,\cdot)\) \(\chi_{8003}(7668,\cdot)\) \(\chi_{8003}(7819,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((4984,7103)\) → \((e\left(\frac{5}{13}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8003 }(183, a) \) | \(1\) | \(1\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) |