Basic properties
Modulus: | \(149\) | |
Conductor: | \(149\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(37\) | 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 149.d
\(\chi_{149}(5,\cdot)\) \(\chi_{149}(6,\cdot)\) \(\chi_{149}(16,\cdot)\) \(\chi_{149}(17,\cdot)\) \(\chi_{149}(19,\cdot)\) \(\chi_{149}(25,\cdot)\) \(\chi_{149}(28,\cdot)\) \(\chi_{149}(29,\cdot)\) \(\chi_{149}(30,\cdot)\) \(\chi_{149}(31,\cdot)\) \(\chi_{149}(33,\cdot)\) \(\chi_{149}(36,\cdot)\) \(\chi_{149}(37,\cdot)\) \(\chi_{149}(39,\cdot)\) \(\chi_{149}(46,\cdot)\) \(\chi_{149}(49,\cdot)\) \(\chi_{149}(63,\cdot)\) \(\chi_{149}(67,\cdot)\) \(\chi_{149}(73,\cdot)\) \(\chi_{149}(80,\cdot)\) \(\chi_{149}(81,\cdot)\) \(\chi_{149}(85,\cdot)\) \(\chi_{149}(88,\cdot)\) \(\chi_{149}(95,\cdot)\) \(\chi_{149}(96,\cdot)\) \(\chi_{149}(102,\cdot)\) \(\chi_{149}(104,\cdot)\) \(\chi_{149}(107,\cdot)\) \(\chi_{149}(114,\cdot)\) \(\chi_{149}(123,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{37})$ |
Fixed field: | Number field defined by a degree 37 polynomial |
Values on generators
\(2\) → \(e\left(\frac{25}{37}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 149 }(140, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{29}{37}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{10}{37}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{35}{37}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{35}{37}\right)\) | \(e\left(\frac{24}{37}\right)\) |