Basic properties
| Modulus: | \(4028\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.cp
\(\chi_{4028}(29,\cdot)\) \(\chi_{4028}(117,\cdot)\) \(\chi_{4028}(165,\cdot)\) \(\chi_{4028}(241,\cdot)\) \(\chi_{4028}(249,\cdot)\) \(\chi_{4028}(269,\cdot)\) \(\chi_{4028}(325,\cdot)\) \(\chi_{4028}(409,\cdot)\) \(\chi_{4028}(433,\cdot)\) \(\chi_{4028}(573,\cdot)\) \(\chi_{4028}(621,\cdot)\) \(\chi_{4028}(661,\cdot)\) \(\chi_{4028}(801,\cdot)\) \(\chi_{4028}(857,\cdot)\) \(\chi_{4028}(865,\cdot)\) \(\chi_{4028}(877,\cdot)\) \(\chi_{4028}(941,\cdot)\) \(\chi_{4028}(965,\cdot)\) \(\chi_{4028}(1077,\cdot)\) \(\chi_{4028}(1085,\cdot)\) \(\chi_{4028}(1097,\cdot)\) \(\chi_{4028}(1117,\cdot)\) \(\chi_{4028}(1153,\cdot)\) \(\chi_{4028}(1173,\cdot)\) \(\chi_{4028}(1257,\cdot)\) \(\chi_{4028}(1389,\cdot)\) \(\chi_{4028}(1421,\cdot)\) \(\chi_{4028}(1541,\cdot)\) \(\chi_{4028}(1649,\cdot)\) \(\chi_{4028}(1705,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,2757,2281)\) → \((1,e\left(\frac{17}{18}\right),e\left(\frac{23}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{117}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{223}{234}\right)\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{34}{117}\right)\) | \(e\left(\frac{43}{117}\right)\) | \(e\left(\frac{7}{18}\right)\) |