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 \(\chi_{1007}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.cn
\(\chi_{4028}(9,\cdot)\) \(\chi_{4028}(17,\cdot)\) \(\chi_{4028}(25,\cdot)\) \(\chi_{4028}(93,\cdot)\) \(\chi_{4028}(149,\cdot)\) \(\chi_{4028}(237,\cdot)\) \(\chi_{4028}(329,\cdot)\) \(\chi_{4028}(377,\cdot)\) \(\chi_{4028}(441,\cdot)\) \(\chi_{4028}(453,\cdot)\) \(\chi_{4028}(461,\cdot)\) \(\chi_{4028}(481,\cdot)\) \(\chi_{4028}(517,\cdot)\) \(\chi_{4028}(537,\cdot)\) \(\chi_{4028}(541,\cdot)\) \(\chi_{4028}(693,\cdot)\) \(\chi_{4028}(785,\cdot)\) \(\chi_{4028}(833,\cdot)\) \(\chi_{4028}(997,\cdot)\) \(\chi_{4028}(1013,\cdot)\) \(\chi_{4028}(1069,\cdot)\) \(\chi_{4028}(1089,\cdot)\) \(\chi_{4028}(1225,\cdot)\) \(\chi_{4028}(1289,\cdot)\) \(\chi_{4028}(1297,\cdot)\) \(\chi_{4028}(1301,\cdot)\) \(\chi_{4028}(1309,\cdot)\) \(\chi_{4028}(1365,\cdot)\) \(\chi_{4028}(1385,\cdot)\) \(\chi_{4028}(1469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,2757,2281)\) → \((1,e\left(\frac{7}{9}\right),e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{1}{18}\right)\) |