Basic properties
Modulus: | \(401\) | |
Conductor: | \(401\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(400\) | 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 401.o
\(\chi_{401}(3,\cdot)\) \(\chi_{401}(6,\cdot)\) \(\chi_{401}(12,\cdot)\) \(\chi_{401}(13,\cdot)\) \(\chi_{401}(15,\cdot)\) \(\chi_{401}(17,\cdot)\) \(\chi_{401}(19,\cdot)\) \(\chi_{401}(21,\cdot)\) \(\chi_{401}(23,\cdot)\) \(\chi_{401}(24,\cdot)\) \(\chi_{401}(27,\cdot)\) \(\chi_{401}(31,\cdot)\) \(\chi_{401}(34,\cdot)\) \(\chi_{401}(37,\cdot)\) \(\chi_{401}(38,\cdot)\) \(\chi_{401}(42,\cdot)\) \(\chi_{401}(46,\cdot)\) \(\chi_{401}(52,\cdot)\) \(\chi_{401}(53,\cdot)\) \(\chi_{401}(54,\cdot)\) \(\chi_{401}(59,\cdot)\) \(\chi_{401}(60,\cdot)\) \(\chi_{401}(61,\cdot)\) \(\chi_{401}(62,\cdot)\) \(\chi_{401}(65,\cdot)\) \(\chi_{401}(66,\cdot)\) \(\chi_{401}(67,\cdot)\) \(\chi_{401}(71,\cdot)\) \(\chi_{401}(74,\cdot)\) \(\chi_{401}(75,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{400})$ |
Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{69}{400}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 401 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{200}\right)\) | \(e\left(\frac{69}{400}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{263}{400}\right)\) | \(e\left(\frac{139}{200}\right)\) | \(e\left(\frac{91}{200}\right)\) | \(e\left(\frac{69}{200}\right)\) | \(e\left(\frac{153}{200}\right)\) | \(e\left(\frac{93}{200}\right)\) |