Basic properties
Modulus: | \(1617\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{539}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1617.ck
\(\chi_{1617}(40,\cdot)\) \(\chi_{1617}(52,\cdot)\) \(\chi_{1617}(61,\cdot)\) \(\chi_{1617}(73,\cdot)\) \(\chi_{1617}(94,\cdot)\) \(\chi_{1617}(145,\cdot)\) \(\chi_{1617}(250,\cdot)\) \(\chi_{1617}(271,\cdot)\) \(\chi_{1617}(283,\cdot)\) \(\chi_{1617}(292,\cdot)\) \(\chi_{1617}(304,\cdot)\) \(\chi_{1617}(376,\cdot)\) \(\chi_{1617}(409,\cdot)\) \(\chi_{1617}(481,\cdot)\) \(\chi_{1617}(502,\cdot)\) \(\chi_{1617}(514,\cdot)\) \(\chi_{1617}(523,\cdot)\) \(\chi_{1617}(535,\cdot)\) \(\chi_{1617}(556,\cdot)\) \(\chi_{1617}(640,\cdot)\) \(\chi_{1617}(712,\cdot)\) \(\chi_{1617}(733,\cdot)\) \(\chi_{1617}(745,\cdot)\) \(\chi_{1617}(787,\cdot)\) \(\chi_{1617}(838,\cdot)\) \(\chi_{1617}(871,\cdot)\) \(\chi_{1617}(943,\cdot)\) \(\chi_{1617}(964,\cdot)\) \(\chi_{1617}(976,\cdot)\) \(\chi_{1617}(985,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,442)\) → \((1,e\left(\frac{23}{42}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 1617 }(40, a) \) | \(1\) | \(1\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{143}{210}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{39}{70}\right)\) |