Basic properties
Modulus: | \(4003\) | |
Conductor: | \(4003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(69\) | 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 4003.i
\(\chi_{4003}(129,\cdot)\) \(\chi_{4003}(493,\cdot)\) \(\chi_{4003}(534,\cdot)\) \(\chi_{4003}(583,\cdot)\) \(\chi_{4003}(629,\cdot)\) \(\chi_{4003}(651,\cdot)\) \(\chi_{4003}(943,\cdot)\) \(\chi_{4003}(993,\cdot)\) \(\chi_{4003}(1183,\cdot)\) \(\chi_{4003}(1265,\cdot)\) \(\chi_{4003}(1311,\cdot)\) \(\chi_{4003}(1434,\cdot)\) \(\chi_{4003}(1543,\cdot)\) \(\chi_{4003}(1557,\cdot)\) \(\chi_{4003}(1752,\cdot)\) \(\chi_{4003}(1821,\cdot)\) \(\chi_{4003}(1825,\cdot)\) \(\chi_{4003}(1857,\cdot)\) \(\chi_{4003}(1866,\cdot)\) \(\chi_{4003}(1914,\cdot)\) \(\chi_{4003}(2015,\cdot)\) \(\chi_{4003}(2321,\cdot)\) \(\chi_{4003}(2434,\cdot)\) \(\chi_{4003}(2442,\cdot)\) \(\chi_{4003}(2487,\cdot)\) \(\chi_{4003}(2621,\cdot)\) \(\chi_{4003}(2735,\cdot)\) \(\chi_{4003}(2817,\cdot)\) \(\chi_{4003}(2869,\cdot)\) \(\chi_{4003}(2897,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 69 polynomial |
Values on generators
\(2\) → \(e\left(\frac{4}{69}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4003 }(943, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{69}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{19}{69}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{49}{69}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{16}{69}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{23}\right)\) |