Basic properties
| Modulus: | \(4212\) | |
| Conductor: | \(4212\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | 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 4212.eu
\(\chi_{4212}(7,\cdot)\) \(\chi_{4212}(67,\cdot)\) \(\chi_{4212}(331,\cdot)\) \(\chi_{4212}(427,\cdot)\) \(\chi_{4212}(475,\cdot)\) \(\chi_{4212}(535,\cdot)\) \(\chi_{4212}(799,\cdot)\) \(\chi_{4212}(895,\cdot)\) \(\chi_{4212}(943,\cdot)\) \(\chi_{4212}(1003,\cdot)\) \(\chi_{4212}(1267,\cdot)\) \(\chi_{4212}(1363,\cdot)\) \(\chi_{4212}(1411,\cdot)\) \(\chi_{4212}(1471,\cdot)\) \(\chi_{4212}(1735,\cdot)\) \(\chi_{4212}(1831,\cdot)\) \(\chi_{4212}(1879,\cdot)\) \(\chi_{4212}(1939,\cdot)\) \(\chi_{4212}(2203,\cdot)\) \(\chi_{4212}(2299,\cdot)\) \(\chi_{4212}(2347,\cdot)\) \(\chi_{4212}(2407,\cdot)\) \(\chi_{4212}(2671,\cdot)\) \(\chi_{4212}(2767,\cdot)\) \(\chi_{4212}(2815,\cdot)\) \(\chi_{4212}(2875,\cdot)\) \(\chi_{4212}(3139,\cdot)\) \(\chi_{4212}(3235,\cdot)\) \(\chi_{4212}(3283,\cdot)\) \(\chi_{4212}(3343,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2107,3485,3889)\) → \((-1,e\left(\frac{14}{27}\right),e\left(\frac{5}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4212 }(2671, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{1}{18}\right)\) |