Basic properties
Modulus: | \(149\) | |
Conductor: | \(149\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(74\) | 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.e
\(\chi_{149}(4,\cdot)\) \(\chi_{149}(7,\cdot)\) \(\chi_{149}(9,\cdot)\) \(\chi_{149}(20,\cdot)\) \(\chi_{149}(22,\cdot)\) \(\chi_{149}(24,\cdot)\) \(\chi_{149}(26,\cdot)\) \(\chi_{149}(35,\cdot)\) \(\chi_{149}(42,\cdot)\) \(\chi_{149}(45,\cdot)\) \(\chi_{149}(47,\cdot)\) \(\chi_{149}(53,\cdot)\) \(\chi_{149}(54,\cdot)\) \(\chi_{149}(61,\cdot)\) \(\chi_{149}(64,\cdot)\) \(\chi_{149}(68,\cdot)\) \(\chi_{149}(69,\cdot)\) \(\chi_{149}(76,\cdot)\) \(\chi_{149}(82,\cdot)\) \(\chi_{149}(86,\cdot)\) \(\chi_{149}(100,\cdot)\) \(\chi_{149}(103,\cdot)\) \(\chi_{149}(110,\cdot)\) \(\chi_{149}(112,\cdot)\) \(\chi_{149}(113,\cdot)\) \(\chi_{149}(116,\cdot)\) \(\chi_{149}(118,\cdot)\) \(\chi_{149}(119,\cdot)\) \(\chi_{149}(120,\cdot)\) \(\chi_{149}(121,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{37})$ |
Fixed field: | Number field defined by a degree 74 polynomial |
Values on generators
\(2\) → \(e\left(\frac{67}{74}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 149 }(124, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{74}\right)\) | \(e\left(\frac{57}{74}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{6}{37}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{53}{74}\right)\) | \(e\left(\frac{20}{37}\right)\) | \(e\left(\frac{5}{74}\right)\) | \(e\left(\frac{51}{74}\right)\) |