Basic properties
Modulus: | \(4003\) | |
Conductor: | \(4003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(667\) | 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.m
\(\chi_{4003}(6,\cdot)\) \(\chi_{4003}(11,\cdot)\) \(\chi_{4003}(13,\cdot)\) \(\chi_{4003}(15,\cdot)\) \(\chi_{4003}(17,\cdot)\) \(\chi_{4003}(28,\cdot)\) \(\chi_{4003}(36,\cdot)\) \(\chi_{4003}(64,\cdot)\) \(\chi_{4003}(66,\cdot)\) \(\chi_{4003}(69,\cdot)\) \(\chi_{4003}(70,\cdot)\) \(\chi_{4003}(73,\cdot)\) \(\chi_{4003}(76,\cdot)\) \(\chi_{4003}(78,\cdot)\) \(\chi_{4003}(86,\cdot)\) \(\chi_{4003}(90,\cdot)\) \(\chi_{4003}(93,\cdot)\) \(\chi_{4003}(94,\cdot)\) \(\chi_{4003}(103,\cdot)\) \(\chi_{4003}(121,\cdot)\) \(\chi_{4003}(142,\cdot)\) \(\chi_{4003}(143,\cdot)\) \(\chi_{4003}(149,\cdot)\) \(\chi_{4003}(151,\cdot)\) \(\chi_{4003}(160,\cdot)\) \(\chi_{4003}(165,\cdot)\) \(\chi_{4003}(169,\cdot)\) \(\chi_{4003}(175,\cdot)\) \(\chi_{4003}(183,\cdot)\) \(\chi_{4003}(187,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{667})$ |
Fixed field: | Number field defined by a degree 667 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{519}{667}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4003 }(142, a) \) | \(1\) | \(1\) | \(e\left(\frac{519}{667}\right)\) | \(e\left(\frac{463}{667}\right)\) | \(e\left(\frac{371}{667}\right)\) | \(e\left(\frac{401}{667}\right)\) | \(e\left(\frac{315}{667}\right)\) | \(e\left(\frac{326}{667}\right)\) | \(e\left(\frac{223}{667}\right)\) | \(e\left(\frac{259}{667}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{597}{667}\right)\) |