Basic properties
Modulus: | \(8036\) | |
Conductor: | \(8036\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | 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 8036.ek
\(\chi_{8036}(59,\cdot)\) \(\chi_{8036}(283,\cdot)\) \(\chi_{8036}(467,\cdot)\) \(\chi_{8036}(551,\cdot)\) \(\chi_{8036}(775,\cdot)\) \(\chi_{8036}(871,\cdot)\) \(\chi_{8036}(1123,\cdot)\) \(\chi_{8036}(1363,\cdot)\) \(\chi_{8036}(1431,\cdot)\) \(\chi_{8036}(1615,\cdot)\) \(\chi_{8036}(1699,\cdot)\) \(\chi_{8036}(1923,\cdot)\) \(\chi_{8036}(2019,\cdot)\) \(\chi_{8036}(2271,\cdot)\) \(\chi_{8036}(2355,\cdot)\) \(\chi_{8036}(2511,\cdot)\) \(\chi_{8036}(2847,\cdot)\) \(\chi_{8036}(3071,\cdot)\) \(\chi_{8036}(3419,\cdot)\) \(\chi_{8036}(3503,\cdot)\) \(\chi_{8036}(3659,\cdot)\) \(\chi_{8036}(3727,\cdot)\) \(\chi_{8036}(3911,\cdot)\) \(\chi_{8036}(3995,\cdot)\) \(\chi_{8036}(4219,\cdot)\) \(\chi_{8036}(4315,\cdot)\) \(\chi_{8036}(4567,\cdot)\) \(\chi_{8036}(4651,\cdot)\) \(\chi_{8036}(4807,\cdot)\) \(\chi_{8036}(4875,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{13}{42}\right),e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 8036 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{58}{105}\right)\) |