Basic properties
Modulus: | \(421\) | |
Conductor: | \(421\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\(2\) → \(e\left(\frac{107}{420}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 421 }(116, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{420}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{83}{105}\right)\) |