Basic properties
Modulus: | \(1617\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{539}(160,\cdot)\) | 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
\((1079,199,442)\) → \((1,e\left(\frac{11}{14}\right),e\left(\frac{9}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1617 }(160, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{70}\right)\) |