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.ed
\(\chi_{4009}(141,\cdot)\) \(\chi_{4009}(160,\cdot)\) \(\chi_{4009}(164,\cdot)\) \(\chi_{4009}(540,\cdot)\) \(\chi_{4009}(791,\cdot)\) \(\chi_{4009}(901,\cdot)\) \(\chi_{4009}(977,\cdot)\) \(\chi_{4009}(1019,\cdot)\) \(\chi_{4009}(1057,\cdot)\) \(\chi_{4009}(1167,\cdot)\) \(\chi_{4009}(1171,\cdot)\) \(\chi_{4009}(1262,\cdot)\) \(\chi_{4009}(1338,\cdot)\) \(\chi_{4009}(1418,\cdot)\) \(\chi_{4009}(1433,\cdot)\) \(\chi_{4009}(1471,\cdot)\) \(\chi_{4009}(1494,\cdot)\) \(\chi_{4009}(1585,\cdot)\) \(\chi_{4009}(1608,\cdot)\) \(\chi_{4009}(1779,\cdot)\) \(\chi_{4009}(1794,\cdot)\) \(\chi_{4009}(2026,\cdot)\) \(\chi_{4009}(2064,\cdot)\) \(\chi_{4009}(2269,\cdot)\) \(\chi_{4009}(2406,\cdot)\) \(\chi_{4009}(2463,\cdot)\) \(\chi_{4009}(2539,\cdot)\) \(\chi_{4009}(2573,\cdot)\) \(\chi_{4009}(2934,\cdot)\) \(\chi_{4009}(2938,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{167}{210}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4009 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{29}{35}\right)\) |