Basic properties
| Modulus: | \(4028\) | |
| Conductor: | \(4028\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | 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 4028.cm
\(\chi_{4028}(15,\cdot)\) \(\chi_{4028}(155,\cdot)\) \(\chi_{4028}(203,\cdot)\) \(\chi_{4028}(307,\cdot)\) \(\chi_{4028}(395,\cdot)\) \(\chi_{4028}(439,\cdot)\) \(\chi_{4028}(471,\cdot)\) \(\chi_{4028}(523,\cdot)\) \(\chi_{4028}(599,\cdot)\) \(\chi_{4028}(611,\cdot)\) \(\chi_{4028}(699,\cdot)\) \(\chi_{4028}(735,\cdot)\) \(\chi_{4028}(755,\cdot)\) \(\chi_{4028}(811,\cdot)\) \(\chi_{4028}(819,\cdot)\) \(\chi_{4028}(831,\cdot)\) \(\chi_{4028}(839,\cdot)\) \(\chi_{4028}(895,\cdot)\) \(\chi_{4028}(1003,\cdot)\) \(\chi_{4028}(1123,\cdot)\) \(\chi_{4028}(1155,\cdot)\) \(\chi_{4028}(1287,\cdot)\) \(\chi_{4028}(1371,\cdot)\) \(\chi_{4028}(1427,\cdot)\) \(\chi_{4028}(1447,\cdot)\) \(\chi_{4028}(1459,\cdot)\) \(\chi_{4028}(1579,\cdot)\) \(\chi_{4028}(1667,\cdot)\) \(\chi_{4028}(1687,\cdot)\) \(\chi_{4028}(1743,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,2757,2281)\) → \((-1,e\left(\frac{11}{18}\right),e\left(\frac{3}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{117}\right)\) | \(e\left(\frac{73}{117}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{49}{117}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{13}{18}\right)\) |