Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(800\) | 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 4001.u
\(\chi_{4001}(12,\cdot)\) \(\chi_{4001}(39,\cdot)\) \(\chi_{4001}(53,\cdot)\) \(\chi_{4001}(54,\cdot)\) \(\chi_{4001}(55,\cdot)\) \(\chi_{4001}(60,\cdot)\) \(\chi_{4001}(68,\cdot)\) \(\chi_{4001}(73,\cdot)\) \(\chi_{4001}(74,\cdot)\) \(\chi_{4001}(139,\cdot)\) \(\chi_{4001}(151,\cdot)\) \(\chi_{4001}(154,\cdot)\) \(\chi_{4001}(168,\cdot)\) \(\chi_{4001}(184,\cdot)\) \(\chi_{4001}(195,\cdot)\) \(\chi_{4001}(199,\cdot)\) \(\chi_{4001}(206,\cdot)\) \(\chi_{4001}(221,\cdot)\) \(\chi_{4001}(226,\cdot)\) \(\chi_{4001}(243,\cdot)\) \(\chi_{4001}(275,\cdot)\) \(\chi_{4001}(283,\cdot)\) \(\chi_{4001}(285,\cdot)\) \(\chi_{4001}(291,\cdot)\) \(\chi_{4001}(300,\cdot)\) \(\chi_{4001}(323,\cdot)\) \(\chi_{4001}(333,\cdot)\) \(\chi_{4001}(340,\cdot)\) \(\chi_{4001}(344,\cdot)\) \(\chi_{4001}(352,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{800})$ |
| Fixed field: | Number field defined by a degree 800 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{37}{800}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{151}{200}\right)\) | \(e\left(\frac{37}{800}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{641}{800}\right)\) | \(e\left(\frac{109}{200}\right)\) | \(e\left(\frac{53}{200}\right)\) | \(e\left(\frac{37}{400}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{29}{32}\right)\) |