Basic properties
| Modulus: | \(1617\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(90,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1617.by
\(\chi_{1617}(13,\cdot)\) \(\chi_{1617}(118,\cdot)\) \(\chi_{1617}(139,\cdot)\) \(\chi_{1617}(160,\cdot)\) \(\chi_{1617}(349,\cdot)\) \(\chi_{1617}(370,\cdot)\) \(\chi_{1617}(475,\cdot)\) \(\chi_{1617}(580,\cdot)\) \(\chi_{1617}(601,\cdot)\) \(\chi_{1617}(622,\cdot)\) \(\chi_{1617}(706,\cdot)\) \(\chi_{1617}(811,\cdot)\) \(\chi_{1617}(853,\cdot)\) \(\chi_{1617}(937,\cdot)\) \(\chi_{1617}(1042,\cdot)\) \(\chi_{1617}(1063,\cdot)\) \(\chi_{1617}(1084,\cdot)\) \(\chi_{1617}(1168,\cdot)\) \(\chi_{1617}(1294,\cdot)\) \(\chi_{1617}(1315,\cdot)\) \(\chi_{1617}(1399,\cdot)\) \(\chi_{1617}(1504,\cdot)\) \(\chi_{1617}(1525,\cdot)\) \(\chi_{1617}(1546,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,442)\) → \((1,e\left(\frac{5}{14}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1617 }(1168, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{37}{70}\right)\) |