Basic properties
| Modulus: | \(841\) | |
| Conductor: | \(841\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | 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.h
\(\chi_{841}(28,\cdot)\) \(\chi_{841}(57,\cdot)\) \(\chi_{841}(86,\cdot)\) \(\chi_{841}(115,\cdot)\) \(\chi_{841}(144,\cdot)\) \(\chi_{841}(173,\cdot)\) \(\chi_{841}(202,\cdot)\) \(\chi_{841}(231,\cdot)\) \(\chi_{841}(260,\cdot)\) \(\chi_{841}(289,\cdot)\) \(\chi_{841}(318,\cdot)\) \(\chi_{841}(347,\cdot)\) \(\chi_{841}(376,\cdot)\) \(\chi_{841}(405,\cdot)\) \(\chi_{841}(434,\cdot)\) \(\chi_{841}(463,\cdot)\) \(\chi_{841}(492,\cdot)\) \(\chi_{841}(521,\cdot)\) \(\chi_{841}(550,\cdot)\) \(\chi_{841}(579,\cdot)\) \(\chi_{841}(608,\cdot)\) \(\chi_{841}(637,\cdot)\) \(\chi_{841}(666,\cdot)\) \(\chi_{841}(695,\cdot)\) \(\chi_{841}(724,\cdot)\) \(\chi_{841}(753,\cdot)\) \(\chi_{841}(782,\cdot)\) \(\chi_{841}(811,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\(2\) → \(e\left(\frac{39}{58}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 841 }(695, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{27}{58}\right)\) |