Basic properties
Modulus: | \(137\) | |
Conductor: | \(137\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(136\) | 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 137.h
\(\chi_{137}(3,\cdot)\) \(\chi_{137}(5,\cdot)\) \(\chi_{137}(6,\cdot)\) \(\chi_{137}(12,\cdot)\) \(\chi_{137}(13,\cdot)\) \(\chi_{137}(20,\cdot)\) \(\chi_{137}(21,\cdot)\) \(\chi_{137}(23,\cdot)\) \(\chi_{137}(24,\cdot)\) \(\chi_{137}(26,\cdot)\) \(\chi_{137}(27,\cdot)\) \(\chi_{137}(29,\cdot)\) \(\chi_{137}(31,\cdot)\) \(\chi_{137}(33,\cdot)\) \(\chi_{137}(35,\cdot)\) \(\chi_{137}(40,\cdot)\) \(\chi_{137}(42,\cdot)\) \(\chi_{137}(43,\cdot)\) \(\chi_{137}(45,\cdot)\) \(\chi_{137}(46,\cdot)\) \(\chi_{137}(47,\cdot)\) \(\chi_{137}(48,\cdot)\) \(\chi_{137}(51,\cdot)\) \(\chi_{137}(52,\cdot)\) \(\chi_{137}(53,\cdot)\) \(\chi_{137}(54,\cdot)\) \(\chi_{137}(55,\cdot)\) \(\chi_{137}(57,\cdot)\) \(\chi_{137}(58,\cdot)\) \(\chi_{137}(62,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{136})$ |
Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{136}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 137 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{75}{136}\right)\) | \(e\left(\frac{11}{136}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{61}{68}\right)\) |