Basic properties
Modulus: | \(1617\) | |
Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1617.ca
\(\chi_{1617}(20,\cdot)\) \(\chi_{1617}(104,\cdot)\) \(\chi_{1617}(125,\cdot)\) \(\chi_{1617}(251,\cdot)\) \(\chi_{1617}(335,\cdot)\) \(\chi_{1617}(356,\cdot)\) \(\chi_{1617}(377,\cdot)\) \(\chi_{1617}(482,\cdot)\) \(\chi_{1617}(566,\cdot)\) \(\chi_{1617}(608,\cdot)\) \(\chi_{1617}(713,\cdot)\) \(\chi_{1617}(797,\cdot)\) \(\chi_{1617}(818,\cdot)\) \(\chi_{1617}(839,\cdot)\) \(\chi_{1617}(944,\cdot)\) \(\chi_{1617}(1049,\cdot)\) \(\chi_{1617}(1070,\cdot)\) \(\chi_{1617}(1259,\cdot)\) \(\chi_{1617}(1280,\cdot)\) \(\chi_{1617}(1301,\cdot)\) \(\chi_{1617}(1406,\cdot)\) \(\chi_{1617}(1490,\cdot)\) \(\chi_{1617}(1511,\cdot)\) \(\chi_{1617}(1532,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1079,199,442)\) → \((-1,e\left(\frac{13}{14}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1617 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{35}\right)\) |