Basic properties
Modulus: | \(1507\) | |
Conductor: | \(1507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(680\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1507.bf
\(\chi_{1507}(6,\cdot)\) \(\chi_{1507}(13,\cdot)\) \(\chi_{1507}(24,\cdot)\) \(\chi_{1507}(29,\cdot)\) \(\chi_{1507}(35,\cdot)\) \(\chi_{1507}(40,\cdot)\) \(\chi_{1507}(46,\cdot)\) \(\chi_{1507}(51,\cdot)\) \(\chi_{1507}(52,\cdot)\) \(\chi_{1507}(57,\cdot)\) \(\chi_{1507}(62,\cdot)\) \(\chi_{1507}(79,\cdot)\) \(\chi_{1507}(83,\cdot)\) \(\chi_{1507}(84,\cdot)\) \(\chi_{1507}(85,\cdot)\) \(\chi_{1507}(90,\cdot)\) \(\chi_{1507}(94,\cdot)\) \(\chi_{1507}(95,\cdot)\) \(\chi_{1507}(106,\cdot)\) \(\chi_{1507}(116,\cdot)\) \(\chi_{1507}(117,\cdot)\) \(\chi_{1507}(134,\cdot)\) \(\chi_{1507}(140,\cdot)\) \(\chi_{1507}(149,\cdot)\) \(\chi_{1507}(150,\cdot)\) \(\chi_{1507}(160,\cdot)\) \(\chi_{1507}(161,\cdot)\) \(\chi_{1507}(172,\cdot)\) \(\chi_{1507}(182,\cdot)\) \(\chi_{1507}(183,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{680})$ |
Fixed field: | Number field defined by a degree 680 polynomial (not computed) |
Values on generators
\((1234,551)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{136}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1507 }(277, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{340}\right)\) | \(e\left(\frac{549}{680}\right)\) | \(e\left(\frac{59}{170}\right)\) | \(e\left(\frac{647}{680}\right)\) | \(e\left(\frac{667}{680}\right)\) | \(e\left(\frac{3}{340}\right)\) | \(e\left(\frac{177}{340}\right)\) | \(e\left(\frac{209}{340}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{21}{136}\right)\) |