Basic properties
Modulus: | \(6027\) | |
Conductor: | \(2009\) | 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 \(\chi_{2009}(1808,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.ef
\(\chi_{6027}(4,\cdot)\) \(\chi_{6027}(25,\cdot)\) \(\chi_{6027}(277,\cdot)\) \(\chi_{6027}(310,\cdot)\) \(\chi_{6027}(394,\cdot)\) \(\chi_{6027}(646,\cdot)\) \(\chi_{6027}(865,\cdot)\) \(\chi_{6027}(886,\cdot)\) \(\chi_{6027}(1138,\cdot)\) \(\chi_{6027}(1171,\cdot)\) \(\chi_{6027}(1234,\cdot)\) \(\chi_{6027}(1507,\cdot)\) \(\chi_{6027}(1663,\cdot)\) \(\chi_{6027}(1726,\cdot)\) \(\chi_{6027}(1747,\cdot)\) \(\chi_{6027}(1999,\cdot)\) \(\chi_{6027}(2032,\cdot)\) \(\chi_{6027}(2095,\cdot)\) \(\chi_{6027}(2116,\cdot)\) \(\chi_{6027}(2368,\cdot)\) \(\chi_{6027}(2524,\cdot)\) \(\chi_{6027}(2587,\cdot)\) \(\chi_{6027}(2608,\cdot)\) \(\chi_{6027}(2893,\cdot)\) \(\chi_{6027}(2956,\cdot)\) \(\chi_{6027}(2977,\cdot)\) \(\chi_{6027}(3229,\cdot)\) \(\chi_{6027}(3385,\cdot)\) \(\chi_{6027}(3469,\cdot)\) \(\chi_{6027}(3721,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{4}{21}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(3817, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{109}{210}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{11}{30}\right)\) |