Basic properties
Modulus: | \(1201\) | |
Conductor: | \(1201\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1200\) | 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 1201.bd
\(\chi_{1201}(11,\cdot)\) \(\chi_{1201}(17,\cdot)\) \(\chi_{1201}(22,\cdot)\) \(\chi_{1201}(26,\cdot)\) \(\chi_{1201}(29,\cdot)\) \(\chi_{1201}(31,\cdot)\) \(\chi_{1201}(33,\cdot)\) \(\chi_{1201}(34,\cdot)\) \(\chi_{1201}(37,\cdot)\) \(\chi_{1201}(39,\cdot)\) \(\chi_{1201}(46,\cdot)\) \(\chi_{1201}(52,\cdot)\) \(\chi_{1201}(65,\cdot)\) \(\chi_{1201}(69,\cdot)\) \(\chi_{1201}(71,\cdot)\) \(\chi_{1201}(73,\cdot)\) \(\chi_{1201}(77,\cdot)\) \(\chi_{1201}(78,\cdot)\) \(\chi_{1201}(82,\cdot)\) \(\chi_{1201}(88,\cdot)\) \(\chi_{1201}(92,\cdot)\) \(\chi_{1201}(94,\cdot)\) \(\chi_{1201}(101,\cdot)\) \(\chi_{1201}(106,\cdot)\) \(\chi_{1201}(113,\cdot)\) \(\chi_{1201}(115,\cdot)\) \(\chi_{1201}(116,\cdot)\) \(\chi_{1201}(119,\cdot)\) \(\chi_{1201}(123,\cdot)\) \(\chi_{1201}(124,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1200})$ |
Fixed field: | Number field defined by a degree 1200 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{1}{1200}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1201 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{283}{300}\right)\) | \(e\left(\frac{97}{300}\right)\) | \(e\left(\frac{133}{150}\right)\) | \(e\left(\frac{421}{600}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{97}{150}\right)\) | \(e\left(\frac{129}{200}\right)\) | \(e\left(\frac{1}{1200}\right)\) |