Basic properties
| Modulus: | \(841\) | |
| Conductor: | \(841\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(203\) | 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.j
\(\chi_{841}(7,\cdot)\) \(\chi_{841}(16,\cdot)\) \(\chi_{841}(20,\cdot)\) \(\chi_{841}(23,\cdot)\) \(\chi_{841}(24,\cdot)\) \(\chi_{841}(25,\cdot)\) \(\chi_{841}(36,\cdot)\) \(\chi_{841}(45,\cdot)\) \(\chi_{841}(49,\cdot)\) \(\chi_{841}(52,\cdot)\) \(\chi_{841}(53,\cdot)\) \(\chi_{841}(54,\cdot)\) \(\chi_{841}(65,\cdot)\) \(\chi_{841}(74,\cdot)\) \(\chi_{841}(78,\cdot)\) \(\chi_{841}(81,\cdot)\) \(\chi_{841}(82,\cdot)\) \(\chi_{841}(83,\cdot)\) \(\chi_{841}(94,\cdot)\) \(\chi_{841}(103,\cdot)\) \(\chi_{841}(107,\cdot)\) \(\chi_{841}(110,\cdot)\) \(\chi_{841}(111,\cdot)\) \(\chi_{841}(112,\cdot)\) \(\chi_{841}(123,\cdot)\) \(\chi_{841}(132,\cdot)\) \(\chi_{841}(136,\cdot)\) \(\chi_{841}(139,\cdot)\) \(\chi_{841}(140,\cdot)\) \(\chi_{841}(141,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{203})$ |
| Fixed field: | Number field defined by a degree 203 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{203}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 841 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{203}\right)\) | \(e\left(\frac{131}{203}\right)\) | \(e\left(\frac{2}{203}\right)\) | \(e\left(\frac{99}{203}\right)\) | \(e\left(\frac{132}{203}\right)\) | \(e\left(\frac{173}{203}\right)\) | \(e\left(\frac{3}{203}\right)\) | \(e\left(\frac{59}{203}\right)\) | \(e\left(\frac{100}{203}\right)\) | \(e\left(\frac{81}{203}\right)\) |