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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4009.ee
\(\chi_{4009}(75,\cdot)\) \(\chi_{4009}(246,\cdot)\) \(\chi_{4009}(303,\cdot)\) \(\chi_{4009}(341,\cdot)\) \(\chi_{4009}(360,\cdot)\) \(\chi_{4009}(398,\cdot)\) \(\chi_{4009}(588,\cdot)\) \(\chi_{4009}(778,\cdot)\) \(\chi_{4009}(797,\cdot)\) \(\chi_{4009}(835,\cdot)\) \(\chi_{4009}(873,\cdot)\) \(\chi_{4009}(892,\cdot)\) \(\chi_{4009}(1006,\cdot)\) \(\chi_{4009}(1025,\cdot)\) \(\chi_{4009}(1196,\cdot)\) \(\chi_{4009}(1215,\cdot)\) \(\chi_{4009}(1424,\cdot)\) \(\chi_{4009}(1595,\cdot)\) \(\chi_{4009}(1652,\cdot)\) \(\chi_{4009}(1690,\cdot)\) \(\chi_{4009}(1804,\cdot)\) \(\chi_{4009}(1956,\cdot)\) \(\chi_{4009}(2032,\cdot)\) \(\chi_{4009}(2051,\cdot)\) \(\chi_{4009}(2127,\cdot)\) \(\chi_{4009}(2222,\cdot)\) \(\chi_{4009}(2241,\cdot)\) \(\chi_{4009}(2317,\cdot)\) \(\chi_{4009}(2393,\cdot)\) \(\chi_{4009}(2412,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((-1,e\left(\frac{97}{210}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{29}{35}\right)\) |