Basic properties
| Modulus: | \(4007\) | |
| Conductor: | \(4007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4006\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4007.d
\(\chi_{4007}(5,\cdot)\) \(\chi_{4007}(10,\cdot)\) \(\chi_{4007}(11,\cdot)\) \(\chi_{4007}(15,\cdot)\) \(\chi_{4007}(17,\cdot)\) \(\chi_{4007}(19,\cdot)\) \(\chi_{4007}(20,\cdot)\) \(\chi_{4007}(22,\cdot)\) \(\chi_{4007}(30,\cdot)\) \(\chi_{4007}(31,\cdot)\) \(\chi_{4007}(33,\cdot)\) \(\chi_{4007}(34,\cdot)\) \(\chi_{4007}(35,\cdot)\) \(\chi_{4007}(38,\cdot)\) \(\chi_{4007}(40,\cdot)\) \(\chi_{4007}(41,\cdot)\) \(\chi_{4007}(44,\cdot)\) \(\chi_{4007}(45,\cdot)\) \(\chi_{4007}(47,\cdot)\) \(\chi_{4007}(51,\cdot)\) \(\chi_{4007}(53,\cdot)\) \(\chi_{4007}(57,\cdot)\) \(\chi_{4007}(60,\cdot)\) \(\chi_{4007}(62,\cdot)\) \(\chi_{4007}(65,\cdot)\) \(\chi_{4007}(66,\cdot)\) \(\chi_{4007}(67,\cdot)\) \(\chi_{4007}(68,\cdot)\) \(\chi_{4007}(70,\cdot)\) \(\chi_{4007}(76,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2003})$ |
| Fixed field: | Number field defined by a degree 4006 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{3389}{4006}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4007 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{814}{2003}\right)\) | \(e\left(\frac{184}{2003}\right)\) | \(e\left(\frac{1628}{2003}\right)\) | \(e\left(\frac{3389}{4006}\right)\) | \(e\left(\frac{998}{2003}\right)\) | \(e\left(\frac{140}{2003}\right)\) | \(e\left(\frac{439}{2003}\right)\) | \(e\left(\frac{368}{2003}\right)\) | \(e\left(\frac{1011}{4006}\right)\) | \(e\left(\frac{1181}{4006}\right)\) |