Basic properties
| Modulus: | \(1617\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(64,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1617.bp
\(\chi_{1617}(64,\cdot)\) \(\chi_{1617}(169,\cdot)\) \(\chi_{1617}(190,\cdot)\) \(\chi_{1617}(379,\cdot)\) \(\chi_{1617}(400,\cdot)\) \(\chi_{1617}(421,\cdot)\) \(\chi_{1617}(526,\cdot)\) \(\chi_{1617}(610,\cdot)\) \(\chi_{1617}(631,\cdot)\) \(\chi_{1617}(652,\cdot)\) \(\chi_{1617}(757,\cdot)\) \(\chi_{1617}(841,\cdot)\) \(\chi_{1617}(862,\cdot)\) \(\chi_{1617}(988,\cdot)\) \(\chi_{1617}(1072,\cdot)\) \(\chi_{1617}(1093,\cdot)\) \(\chi_{1617}(1114,\cdot)\) \(\chi_{1617}(1219,\cdot)\) \(\chi_{1617}(1303,\cdot)\) \(\chi_{1617}(1345,\cdot)\) \(\chi_{1617}(1450,\cdot)\) \(\chi_{1617}(1534,\cdot)\) \(\chi_{1617}(1555,\cdot)\) \(\chi_{1617}(1576,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((1079,199,442)\) → \((1,e\left(\frac{5}{7}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1617 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{16}{35}\right)\) |