Basic properties
Modulus: | \(137\) | |
Conductor: | \(137\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(68\) | 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 137.g
\(\chi_{137}(2,\cdot)\) \(\chi_{137}(7,\cdot)\) \(\chi_{137}(8,\cdot)\) \(\chi_{137}(9,\cdot)\) \(\chi_{137}(11,\cdot)\) \(\chi_{137}(17,\cdot)\) \(\chi_{137}(19,\cdot)\) \(\chi_{137}(25,\cdot)\) \(\chi_{137}(28,\cdot)\) \(\chi_{137}(30,\cdot)\) \(\chi_{137}(32,\cdot)\) \(\chi_{137}(36,\cdot)\) \(\chi_{137}(39,\cdot)\) \(\chi_{137}(44,\cdot)\) \(\chi_{137}(61,\cdot)\) \(\chi_{137}(68,\cdot)\) \(\chi_{137}(69,\cdot)\) \(\chi_{137}(76,\cdot)\) \(\chi_{137}(93,\cdot)\) \(\chi_{137}(98,\cdot)\) \(\chi_{137}(101,\cdot)\) \(\chi_{137}(105,\cdot)\) \(\chi_{137}(107,\cdot)\) \(\chi_{137}(109,\cdot)\) \(\chi_{137}(112,\cdot)\) \(\chi_{137}(118,\cdot)\) \(\chi_{137}(120,\cdot)\) \(\chi_{137}(126,\cdot)\) \(\chi_{137}(128,\cdot)\) \(\chi_{137}(129,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\(3\) → \(e\left(\frac{37}{68}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 137 }(93, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(i\) | \(e\left(\frac{13}{34}\right)\) |