Basic properties
| Modulus: | \(841\) | |
| Conductor: | \(841\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(406\) | 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.k
\(\chi_{841}(4,\cdot)\) \(\chi_{841}(5,\cdot)\) \(\chi_{841}(6,\cdot)\) \(\chi_{841}(9,\cdot)\) \(\chi_{841}(13,\cdot)\) \(\chi_{841}(22,\cdot)\) \(\chi_{841}(33,\cdot)\) \(\chi_{841}(34,\cdot)\) \(\chi_{841}(35,\cdot)\) \(\chi_{841}(38,\cdot)\) \(\chi_{841}(42,\cdot)\) \(\chi_{841}(51,\cdot)\) \(\chi_{841}(62,\cdot)\) \(\chi_{841}(64,\cdot)\) \(\chi_{841}(67,\cdot)\) \(\chi_{841}(71,\cdot)\) \(\chi_{841}(80,\cdot)\) \(\chi_{841}(91,\cdot)\) \(\chi_{841}(92,\cdot)\) \(\chi_{841}(93,\cdot)\) \(\chi_{841}(96,\cdot)\) \(\chi_{841}(100,\cdot)\) \(\chi_{841}(109,\cdot)\) \(\chi_{841}(120,\cdot)\) \(\chi_{841}(121,\cdot)\) \(\chi_{841}(122,\cdot)\) \(\chi_{841}(125,\cdot)\) \(\chi_{841}(129,\cdot)\) \(\chi_{841}(138,\cdot)\) \(\chi_{841}(149,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{203})$ |
| Fixed field: | Number field defined by a degree 406 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{309}{406}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 841 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{309}{406}\right)\) | \(e\left(\frac{285}{406}\right)\) | \(e\left(\frac{106}{203}\right)\) | \(e\left(\frac{172}{203}\right)\) | \(e\left(\frac{94}{203}\right)\) | \(e\left(\frac{34}{203}\right)\) | \(e\left(\frac{115}{406}\right)\) | \(e\left(\frac{82}{203}\right)\) | \(e\left(\frac{247}{406}\right)\) | \(e\left(\frac{263}{406}\right)\) |