Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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.dq
\(\chi_{4009}(45,\cdot)\) \(\chi_{4009}(258,\cdot)\) \(\chi_{4009}(273,\cdot)\) \(\chi_{4009}(330,\cdot)\) \(\chi_{4009}(653,\cdot)\) \(\chi_{4009}(657,\cdot)\) \(\chi_{4009}(714,\cdot)\) \(\chi_{4009}(809,\cdot)\) \(\chi_{4009}(980,\cdot)\) \(\chi_{4009}(1014,\cdot)\) \(\chi_{4009}(1227,\cdot)\) \(\chi_{4009}(1303,\cdot)\) \(\chi_{4009}(1318,\cdot)\) \(\chi_{4009}(1322,\cdot)\) \(\chi_{4009}(1455,\cdot)\) \(\chi_{4009}(1474,\cdot)\) \(\chi_{4009}(1493,\cdot)\) \(\chi_{4009}(1793,\cdot)\) \(\chi_{4009}(1892,\cdot)\) \(\chi_{4009}(1968,\cdot)\) \(\chi_{4009}(2002,\cdot)\) \(\chi_{4009}(2025,\cdot)\) \(\chi_{4009}(2116,\cdot)\) \(\chi_{4009}(2154,\cdot)\) \(\chi_{4009}(2249,\cdot)\) \(\chi_{4009}(2325,\cdot)\) \(\chi_{4009}(2367,\cdot)\) \(\chi_{4009}(2405,\cdot)\) \(\chi_{4009}(2420,\cdot)\) \(\chi_{4009}(2610,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{4}{105}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{6}{35}\right)\) |