Basic properties
| Modulus: | \(841\) | |
| Conductor: | \(841\) | 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 841.g
\(\chi_{841}(30,\cdot)\) \(\chi_{841}(59,\cdot)\) \(\chi_{841}(88,\cdot)\) \(\chi_{841}(117,\cdot)\) \(\chi_{841}(146,\cdot)\) \(\chi_{841}(175,\cdot)\) \(\chi_{841}(204,\cdot)\) \(\chi_{841}(233,\cdot)\) \(\chi_{841}(262,\cdot)\) \(\chi_{841}(291,\cdot)\) \(\chi_{841}(320,\cdot)\) \(\chi_{841}(349,\cdot)\) \(\chi_{841}(378,\cdot)\) \(\chi_{841}(407,\cdot)\) \(\chi_{841}(436,\cdot)\) \(\chi_{841}(465,\cdot)\) \(\chi_{841}(494,\cdot)\) \(\chi_{841}(523,\cdot)\) \(\chi_{841}(552,\cdot)\) \(\chi_{841}(581,\cdot)\) \(\chi_{841}(610,\cdot)\) \(\chi_{841}(639,\cdot)\) \(\chi_{841}(668,\cdot)\) \(\chi_{841}(697,\cdot)\) \(\chi_{841}(726,\cdot)\) \(\chi_{841}(755,\cdot)\) \(\chi_{841}(784,\cdot)\) \(\chi_{841}(813,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(2\) → \(e\left(\frac{23}{29}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 841 }(668, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) |