Basic properties
Modulus: | \(4003\) | |
Conductor: | \(4003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.f
\(\chi_{4003}(102,\cdot)\) \(\chi_{4003}(168,\cdot)\) \(\chi_{4003}(203,\cdot)\) \(\chi_{4003}(413,\cdot)\) \(\chi_{4003}(691,\cdot)\) \(\chi_{4003}(1000,\cdot)\) \(\chi_{4003}(1124,\cdot)\) \(\chi_{4003}(1170,\cdot)\) \(\chi_{4003}(1179,\cdot)\) \(\chi_{4003}(1333,\cdot)\) \(\chi_{4003}(1633,\cdot)\) \(\chi_{4003}(1925,\cdot)\) \(\chi_{4003}(2080,\cdot)\) \(\chi_{4003}(2096,\cdot)\) \(\chi_{4003}(2118,\cdot)\) \(\chi_{4003}(2140,\cdot)\) \(\chi_{4003}(2398,\cdot)\) \(\chi_{4003}(2431,\cdot)\) \(\chi_{4003}(2443,\cdot)\) \(\chi_{4003}(2484,\cdot)\) \(\chi_{4003}(2564,\cdot)\) \(\chi_{4003}(2850,\cdot)\) \(\chi_{4003}(3160,\cdot)\) \(\chi_{4003}(3253,\cdot)\) \(\chi_{4003}(3560,\cdot)\) \(\chi_{4003}(3779,\cdot)\) \(\chi_{4003}(3867,\cdot)\) \(\chi_{4003}(3877,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(2\) → \(e\left(\frac{2}{29}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4003 }(2140, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) |