Basic properties
Modulus: | \(547\) | |
Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(546\) | 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 547.p
\(\chi_{547}(2,\cdot)\) \(\chi_{547}(5,\cdot)\) \(\chi_{547}(7,\cdot)\) \(\chi_{547}(12,\cdot)\) \(\chi_{547}(17,\cdot)\) \(\chi_{547}(18,\cdot)\) \(\chi_{547}(20,\cdot)\) \(\chi_{547}(22,\cdot)\) \(\chi_{547}(23,\cdot)\) \(\chi_{547}(32,\cdot)\) \(\chi_{547}(33,\cdot)\) \(\chi_{547}(37,\cdot)\) \(\chi_{547}(43,\cdot)\) \(\chi_{547}(45,\cdot)\) \(\chi_{547}(48,\cdot)\) \(\chi_{547}(50,\cdot)\) \(\chi_{547}(57,\cdot)\) \(\chi_{547}(58,\cdot)\) \(\chi_{547}(61,\cdot)\) \(\chi_{547}(63,\cdot)\) \(\chi_{547}(70,\cdot)\) \(\chi_{547}(71,\cdot)\) \(\chi_{547}(75,\cdot)\) \(\chi_{547}(77,\cdot)\) \(\chi_{547}(88,\cdot)\) \(\chi_{547}(91,\cdot)\) \(\chi_{547}(92,\cdot)\) \(\chi_{547}(95,\cdot)\) \(\chi_{547}(104,\cdot)\) \(\chi_{547}(108,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{273})$ |
Fixed field: | Number field defined by a degree 546 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{491}{546}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 547 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{491}{546}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{218}{273}\right)\) | \(e\left(\frac{529}{546}\right)\) | \(e\left(\frac{187}{273}\right)\) | \(e\left(\frac{341}{546}\right)\) | \(e\left(\frac{127}{182}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{79}{91}\right)\) | \(e\left(\frac{37}{39}\right)\) |