Basic properties
| Modulus: | \(421\) | |
| Conductor: | \(421\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 421.x
\(\chi_{421}(2,\cdot)\) \(\chi_{421}(14,\cdot)\) \(\chi_{421}(18,\cdot)\) \(\chi_{421}(22,\cdot)\) \(\chi_{421}(23,\cdot)\) \(\chi_{421}(24,\cdot)\) \(\chi_{421}(30,\cdot)\) \(\chi_{421}(39,\cdot)\) \(\chi_{421}(40,\cdot)\) \(\chi_{421}(41,\cdot)\) \(\chi_{421}(43,\cdot)\) \(\chi_{421}(50,\cdot)\) \(\chi_{421}(53,\cdot)\) \(\chi_{421}(54,\cdot)\) \(\chi_{421}(57,\cdot)\) \(\chi_{421}(65,\cdot)\) \(\chi_{421}(66,\cdot)\) \(\chi_{421}(71,\cdot)\) \(\chi_{421}(72,\cdot)\) \(\chi_{421}(76,\cdot)\) \(\chi_{421}(83,\cdot)\) \(\chi_{421}(87,\cdot)\) \(\chi_{421}(88,\cdot)\) \(\chi_{421}(90,\cdot)\) \(\chi_{421}(96,\cdot)\) \(\chi_{421}(98,\cdot)\) \(\chi_{421}(102,\cdot)\) \(\chi_{421}(116,\cdot)\) \(\chi_{421}(117,\cdot)\) \(\chi_{421}(134,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{247}{420}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 421 }(90, a) \) | \(-1\) | \(1\) | \(e\left(\frac{247}{420}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{13}{105}\right)\) |