Basic properties
Modulus: | \(4009\) | |
Conductor: | \(4009\) | 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 4009.ec
\(\chi_{4009}(8,\cdot)\) \(\chi_{4009}(27,\cdot)\) \(\chi_{4009}(198,\cdot)\) \(\chi_{4009}(297,\cdot)\) \(\chi_{4009}(335,\cdot)\) \(\chi_{4009}(411,\cdot)\) \(\chi_{4009}(430,\cdot)\) \(\chi_{4009}(449,\cdot)\) \(\chi_{4009}(464,\cdot)\) \(\chi_{4009}(620,\cdot)\) \(\chi_{4009}(730,\cdot)\) \(\chi_{4009}(768,\cdot)\) \(\chi_{4009}(886,\cdot)\) \(\chi_{4009}(1152,\cdot)\) \(\chi_{4009}(1190,\cdot)\) \(\chi_{4009}(1395,\cdot)\) \(\chi_{4009}(1452,\cdot)\) \(\chi_{4009}(1566,\cdot)\) \(\chi_{4009}(1623,\cdot)\) \(\chi_{4009}(1756,\cdot)\) \(\chi_{4009}(1817,\cdot)\) \(\chi_{4009}(1874,\cdot)\) \(\chi_{4009}(1927,\cdot)\) \(\chi_{4009}(1988,\cdot)\) \(\chi_{4009}(2045,\cdot)\) \(\chi_{4009}(2178,\cdot)\) \(\chi_{4009}(2212,\cdot)\) \(\chi_{4009}(2349,\cdot)\) \(\chi_{4009}(2592,\cdot)\) \(\chi_{4009}(2630,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{70}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{35}\right)\) |