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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.cj
\(\chi_{4028}(47,\cdot)\) \(\chi_{4028}(63,\cdot)\) \(\chi_{4028}(99,\cdot)\) \(\chi_{4028}(119,\cdot)\) \(\chi_{4028}(175,\cdot)\) \(\chi_{4028}(187,\cdot)\) \(\chi_{4028}(195,\cdot)\) \(\chi_{4028}(275,\cdot)\) \(\chi_{4028}(367,\cdot)\) \(\chi_{4028}(415,\cdot)\) \(\chi_{4028}(519,\cdot)\) \(\chi_{4028}(579,\cdot)\) \(\chi_{4028}(651,\cdot)\) \(\chi_{4028}(731,\cdot)\) \(\chi_{4028}(823,\cdot)\) \(\chi_{4028}(947,\cdot)\) \(\chi_{4028}(967,\cdot)\) \(\chi_{4028}(1023,\cdot)\) \(\chi_{4028}(1031,\cdot)\) \(\chi_{4028}(1035,\cdot)\) \(\chi_{4028}(1043,\cdot)\) \(\chi_{4028}(1051,\cdot)\) \(\chi_{4028}(1107,\cdot)\) \(\chi_{4028}(1263,\cdot)\) \(\chi_{4028}(1335,\cdot)\) \(\chi_{4028}(1391,\cdot)\) \(\chi_{4028}(1467,\cdot)\) \(\chi_{4028}(1499,\cdot)\) \(\chi_{4028}(1583,\cdot)\) \(\chi_{4028}(1639,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,2757,2281)\) → \((-1,e\left(\frac{4}{9}\right),e\left(\frac{11}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{155}{234}\right)\) | \(e\left(\frac{103}{117}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{62}{117}\right)\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{106}{117}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{7}{18}\right)\) |