Basic properties
| Modulus: | \(4212\) | |
| Conductor: | \(1053\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1053}(401,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4212.ey
\(\chi_{4212}(41,\cdot)\) \(\chi_{4212}(137,\cdot)\) \(\chi_{4212}(401,\cdot)\) \(\chi_{4212}(461,\cdot)\) \(\chi_{4212}(509,\cdot)\) \(\chi_{4212}(605,\cdot)\) \(\chi_{4212}(869,\cdot)\) \(\chi_{4212}(929,\cdot)\) \(\chi_{4212}(977,\cdot)\) \(\chi_{4212}(1073,\cdot)\) \(\chi_{4212}(1337,\cdot)\) \(\chi_{4212}(1397,\cdot)\) \(\chi_{4212}(1445,\cdot)\) \(\chi_{4212}(1541,\cdot)\) \(\chi_{4212}(1805,\cdot)\) \(\chi_{4212}(1865,\cdot)\) \(\chi_{4212}(1913,\cdot)\) \(\chi_{4212}(2009,\cdot)\) \(\chi_{4212}(2273,\cdot)\) \(\chi_{4212}(2333,\cdot)\) \(\chi_{4212}(2381,\cdot)\) \(\chi_{4212}(2477,\cdot)\) \(\chi_{4212}(2741,\cdot)\) \(\chi_{4212}(2801,\cdot)\) \(\chi_{4212}(2849,\cdot)\) \(\chi_{4212}(2945,\cdot)\) \(\chi_{4212}(3209,\cdot)\) \(\chi_{4212}(3269,\cdot)\) \(\chi_{4212}(3317,\cdot)\) \(\chi_{4212}(3413,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2107,3485,3889)\) → \((1,e\left(\frac{29}{54}\right),e\left(\frac{7}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4212 }(401, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{108}\right)\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{11}{18}\right)\) |