Basic properties
Modulus: | \(107\) | |
Conductor: | \(107\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(106\) | 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 107.d
\(\chi_{107}(2,\cdot)\) \(\chi_{107}(5,\cdot)\) \(\chi_{107}(6,\cdot)\) \(\chi_{107}(7,\cdot)\) \(\chi_{107}(8,\cdot)\) \(\chi_{107}(15,\cdot)\) \(\chi_{107}(17,\cdot)\) \(\chi_{107}(18,\cdot)\) \(\chi_{107}(20,\cdot)\) \(\chi_{107}(21,\cdot)\) \(\chi_{107}(22,\cdot)\) \(\chi_{107}(24,\cdot)\) \(\chi_{107}(26,\cdot)\) \(\chi_{107}(28,\cdot)\) \(\chi_{107}(31,\cdot)\) \(\chi_{107}(32,\cdot)\) \(\chi_{107}(38,\cdot)\) \(\chi_{107}(43,\cdot)\) \(\chi_{107}(45,\cdot)\) \(\chi_{107}(46,\cdot)\) \(\chi_{107}(50,\cdot)\) \(\chi_{107}(51,\cdot)\) \(\chi_{107}(54,\cdot)\) \(\chi_{107}(55,\cdot)\) \(\chi_{107}(58,\cdot)\) \(\chi_{107}(59,\cdot)\) \(\chi_{107}(60,\cdot)\) \(\chi_{107}(63,\cdot)\) \(\chi_{107}(65,\cdot)\) \(\chi_{107}(66,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{53})$ |
Fixed field: | Number field defined by a degree 106 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{77}{106}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 107 }(63, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{106}\right)\) | \(e\left(\frac{45}{53}\right)\) | \(e\left(\frac{24}{53}\right)\) | \(e\left(\frac{15}{106}\right)\) | \(e\left(\frac{61}{106}\right)\) | \(e\left(\frac{25}{106}\right)\) | \(e\left(\frac{19}{106}\right)\) | \(e\left(\frac{37}{53}\right)\) | \(e\left(\frac{46}{53}\right)\) | \(e\left(\frac{52}{53}\right)\) |