Basic properties
Modulus: | \(6027\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(1369,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.ds
\(\chi_{6027}(16,\cdot)\) \(\chi_{6027}(37,\cdot)\) \(\chi_{6027}(100,\cdot)\) \(\chi_{6027}(256,\cdot)\) \(\chi_{6027}(529,\cdot)\) \(\chi_{6027}(592,\cdot)\) \(\chi_{6027}(625,\cdot)\) \(\chi_{6027}(877,\cdot)\) \(\chi_{6027}(898,\cdot)\) \(\chi_{6027}(1117,\cdot)\) \(\chi_{6027}(1369,\cdot)\) \(\chi_{6027}(1453,\cdot)\) \(\chi_{6027}(1486,\cdot)\) \(\chi_{6027}(1738,\cdot)\) \(\chi_{6027}(1759,\cdot)\) \(\chi_{6027}(1822,\cdot)\) \(\chi_{6027}(2230,\cdot)\) \(\chi_{6027}(2251,\cdot)\) \(\chi_{6027}(2314,\cdot)\) \(\chi_{6027}(2347,\cdot)\) \(\chi_{6027}(2599,\cdot)\) \(\chi_{6027}(2620,\cdot)\) \(\chi_{6027}(2683,\cdot)\) \(\chi_{6027}(2839,\cdot)\) \(\chi_{6027}(3091,\cdot)\) \(\chi_{6027}(3112,\cdot)\) \(\chi_{6027}(3175,\cdot)\) \(\chi_{6027}(3208,\cdot)\) \(\chi_{6027}(3481,\cdot)\) \(\chi_{6027}(3544,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{11}{21}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(1369, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) |