Basic properties
| Modulus: | \(1003\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1003.k
\(\chi_{1003}(35,\cdot)\) \(\chi_{1003}(86,\cdot)\) \(\chi_{1003}(137,\cdot)\) \(\chi_{1003}(154,\cdot)\) \(\chi_{1003}(171,\cdot)\) \(\chi_{1003}(205,\cdot)\) \(\chi_{1003}(222,\cdot)\) \(\chi_{1003}(239,\cdot)\) \(\chi_{1003}(256,\cdot)\) \(\chi_{1003}(307,\cdot)\) \(\chi_{1003}(324,\cdot)\) \(\chi_{1003}(341,\cdot)\) \(\chi_{1003}(358,\cdot)\) \(\chi_{1003}(375,\cdot)\) \(\chi_{1003}(477,\cdot)\) \(\chi_{1003}(494,\cdot)\) \(\chi_{1003}(579,\cdot)\) \(\chi_{1003}(647,\cdot)\) \(\chi_{1003}(664,\cdot)\) \(\chi_{1003}(698,\cdot)\) \(\chi_{1003}(715,\cdot)\) \(\chi_{1003}(749,\cdot)\) \(\chi_{1003}(783,\cdot)\) \(\chi_{1003}(851,\cdot)\) \(\chi_{1003}(902,\cdot)\) \(\chi_{1003}(936,\cdot)\) \(\chi_{1003}(953,\cdot)\) \(\chi_{1003}(970,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\((768,120)\) → \((1,e\left(\frac{12}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1003 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) |