Basic properties
| Modulus: | \(1259\) | |
| Conductor: | \(1259\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1259.f
\(\chi_{1259}(18,\cdot)\) \(\chi_{1259}(29,\cdot)\) \(\chi_{1259}(30,\cdot)\) \(\chi_{1259}(41,\cdot)\) \(\chi_{1259}(42,\cdot)\) \(\chi_{1259}(50,\cdot)\) \(\chi_{1259}(70,\cdot)\) \(\chi_{1259}(98,\cdot)\) \(\chi_{1259}(136,\cdot)\) \(\chi_{1259}(277,\cdot)\) \(\chi_{1259}(359,\cdot)\) \(\chi_{1259}(389,\cdot)\) \(\chi_{1259}(418,\cdot)\) \(\chi_{1259}(468,\cdot)\) \(\chi_{1259}(488,\cdot)\) \(\chi_{1259}(503,\cdot)\) \(\chi_{1259}(521,\cdot)\) \(\chi_{1259}(552,\cdot)\) \(\chi_{1259}(561,\cdot)\) \(\chi_{1259}(583,\cdot)\) \(\chi_{1259}(694,\cdot)\) \(\chi_{1259}(719,\cdot)\) \(\chi_{1259}(737,\cdot)\) \(\chi_{1259}(754,\cdot)\) \(\chi_{1259}(780,\cdot)\) \(\chi_{1259}(796,\cdot)\) \(\chi_{1259}(837,\cdot)\) \(\chi_{1259}(907,\cdot)\) \(\chi_{1259}(920,\cdot)\) \(\chi_{1259}(935,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | Number field defined by a degree 74 polynomial |
Values on generators
\(2\) → \(e\left(\frac{15}{74}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1259 }(1066, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{74}\right)\) | \(e\left(\frac{6}{37}\right)\) | \(e\left(\frac{15}{37}\right)\) | \(e\left(\frac{15}{37}\right)\) | \(e\left(\frac{27}{74}\right)\) | \(e\left(\frac{32}{37}\right)\) | \(e\left(\frac{45}{74}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{45}{74}\right)\) | \(e\left(\frac{23}{74}\right)\) |