Basic properties
| Modulus: | \(4023\) | |
| Conductor: | \(149\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(74\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{149}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4023.u
\(\chi_{4023}(82,\cdot)\) \(\chi_{4023}(217,\cdot)\) \(\chi_{4023}(352,\cdot)\) \(\chi_{4023}(568,\cdot)\) \(\chi_{4023}(622,\cdot)\) \(\chi_{4023}(649,\cdot)\) \(\chi_{4023}(865,\cdot)\) \(\chi_{4023}(1027,\cdot)\) \(\chi_{4023}(1162,\cdot)\) \(\chi_{4023}(1216,\cdot)\) \(\chi_{4023}(1324,\cdot)\) \(\chi_{4023}(1405,\cdot)\) \(\chi_{4023}(1459,\cdot)\) \(\chi_{4023}(1648,\cdot)\) \(\chi_{4023}(1783,\cdot)\) \(\chi_{4023}(1810,\cdot)\) \(\chi_{4023}(1864,\cdot)\) \(\chi_{4023}(1891,\cdot)\) \(\chi_{4023}(1918,\cdot)\) \(\chi_{4023}(1972,\cdot)\) \(\chi_{4023}(2053,\cdot)\) \(\chi_{4023}(2080,\cdot)\) \(\chi_{4023}(2242,\cdot)\) \(\chi_{4023}(2296,\cdot)\) \(\chi_{4023}(2404,\cdot)\) \(\chi_{4023}(2431,\cdot)\) \(\chi_{4023}(2782,\cdot)\) \(\chi_{4023}(2917,\cdot)\) \(\chi_{4023}(2944,\cdot)\) \(\chi_{4023}(3025,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{37})$ |
| Fixed field: | Number field defined by a degree 74 polynomial |
Values on generators
\((299,3727)\) → \((1,e\left(\frac{19}{74}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4023 }(2296, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{74}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{57}{74}\right)\) | \(e\left(\frac{71}{74}\right)\) | \(e\left(\frac{73}{74}\right)\) | \(e\left(\frac{45}{74}\right)\) | \(e\left(\frac{53}{74}\right)\) | \(e\left(\frac{1}{37}\right)\) |