Basic properties
Modulus: | \(1617\) | |
Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | 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 1617.cd
\(\chi_{1617}(41,\cdot)\) \(\chi_{1617}(62,\cdot)\) \(\chi_{1617}(83,\cdot)\) \(\chi_{1617}(167,\cdot)\) \(\chi_{1617}(272,\cdot)\) \(\chi_{1617}(314,\cdot)\) \(\chi_{1617}(398,\cdot)\) \(\chi_{1617}(503,\cdot)\) \(\chi_{1617}(524,\cdot)\) \(\chi_{1617}(545,\cdot)\) \(\chi_{1617}(629,\cdot)\) \(\chi_{1617}(755,\cdot)\) \(\chi_{1617}(776,\cdot)\) \(\chi_{1617}(860,\cdot)\) \(\chi_{1617}(965,\cdot)\) \(\chi_{1617}(986,\cdot)\) \(\chi_{1617}(1007,\cdot)\) \(\chi_{1617}(1091,\cdot)\) \(\chi_{1617}(1196,\cdot)\) \(\chi_{1617}(1217,\cdot)\) \(\chi_{1617}(1238,\cdot)\) \(\chi_{1617}(1427,\cdot)\) \(\chi_{1617}(1448,\cdot)\) \(\chi_{1617}(1553,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,442)\) → \((-1,e\left(\frac{1}{14}\right),e\left(\frac{9}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1617 }(1007, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{24}{35}\right)\) |