Basic properties
| Modulus: | \(4012\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1003}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.bf
\(\chi_{4012}(13,\cdot)\) \(\chi_{4012}(89,\cdot)\) \(\chi_{4012}(149,\cdot)\) \(\chi_{4012}(157,\cdot)\) \(\chi_{4012}(217,\cdot)\) \(\chi_{4012}(421,\cdot)\) \(\chi_{4012}(565,\cdot)\) \(\chi_{4012}(633,\cdot)\) \(\chi_{4012}(693,\cdot)\) \(\chi_{4012}(701,\cdot)\) \(\chi_{4012}(769,\cdot)\) \(\chi_{4012}(837,\cdot)\) \(\chi_{4012}(1033,\cdot)\) \(\chi_{4012}(1041,\cdot)\) \(\chi_{4012}(1101,\cdot)\) \(\chi_{4012}(1109,\cdot)\) \(\chi_{4012}(1177,\cdot)\) \(\chi_{4012}(1245,\cdot)\) \(\chi_{4012}(1381,\cdot)\) \(\chi_{4012}(1449,\cdot)\) \(\chi_{4012}(1509,\cdot)\) \(\chi_{4012}(1517,\cdot)\) \(\chi_{4012}(1577,\cdot)\) \(\chi_{4012}(1645,\cdot)\) \(\chi_{4012}(1713,\cdot)\) \(\chi_{4012}(1721,\cdot)\) \(\chi_{4012}(1781,\cdot)\) \(\chi_{4012}(1925,\cdot)\) \(\chi_{4012}(1985,\cdot)\) \(\chi_{4012}(2053,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((1,i,e\left(\frac{45}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{45}{116}\right)\) |