Basic properties
| Modulus: | \(4012\) | |
| Conductor: | \(4012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | 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 4012.x
\(\chi_{4012}(67,\cdot)\) \(\chi_{4012}(339,\cdot)\) \(\chi_{4012}(679,\cdot)\) \(\chi_{4012}(747,\cdot)\) \(\chi_{4012}(1155,\cdot)\) \(\chi_{4012}(1223,\cdot)\) \(\chi_{4012}(1291,\cdot)\) \(\chi_{4012}(1359,\cdot)\) \(\chi_{4012}(1427,\cdot)\) \(\chi_{4012}(1631,\cdot)\) \(\chi_{4012}(1699,\cdot)\) \(\chi_{4012}(1767,\cdot)\) \(\chi_{4012}(1835,\cdot)\) \(\chi_{4012}(1971,\cdot)\) \(\chi_{4012}(2039,\cdot)\) \(\chi_{4012}(2107,\cdot)\) \(\chi_{4012}(2311,\cdot)\) \(\chi_{4012}(2515,\cdot)\) \(\chi_{4012}(2651,\cdot)\) \(\chi_{4012}(2787,\cdot)\) \(\chi_{4012}(2855,\cdot)\) \(\chi_{4012}(2923,\cdot)\) \(\chi_{4012}(3059,\cdot)\) \(\chi_{4012}(3263,\cdot)\) \(\chi_{4012}(3535,\cdot)\) \(\chi_{4012}(3671,\cdot)\) \(\chi_{4012}(3807,\cdot)\) \(\chi_{4012}(3875,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((2007,3777,3129)\) → \((-1,-1,e\left(\frac{3}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) |