Basic properties
| Modulus: | \(3001\) | |
| Conductor: | \(3001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1000\) | 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 3001.bd
\(\chi_{3001}(7,\cdot)\) \(\chi_{3001}(21,\cdot)\) \(\chi_{3001}(35,\cdot)\) \(\chi_{3001}(38,\cdot)\) \(\chi_{3001}(47,\cdot)\) \(\chi_{3001}(52,\cdot)\) \(\chi_{3001}(53,\cdot)\) \(\chi_{3001}(56,\cdot)\) \(\chi_{3001}(58,\cdot)\) \(\chi_{3001}(63,\cdot)\) \(\chi_{3001}(77,\cdot)\) \(\chi_{3001}(79,\cdot)\) \(\chi_{3001}(92,\cdot)\) \(\chi_{3001}(105,\cdot)\) \(\chi_{3001}(114,\cdot)\) \(\chi_{3001}(127,\cdot)\) \(\chi_{3001}(137,\cdot)\) \(\chi_{3001}(163,\cdot)\) \(\chi_{3001}(166,\cdot)\) \(\chi_{3001}(168,\cdot)\) \(\chi_{3001}(174,\cdot)\) \(\chi_{3001}(175,\cdot)\) \(\chi_{3001}(189,\cdot)\) \(\chi_{3001}(190,\cdot)\) \(\chi_{3001}(221,\cdot)\) \(\chi_{3001}(227,\cdot)\) \(\chi_{3001}(231,\cdot)\) \(\chi_{3001}(237,\cdot)\) \(\chi_{3001}(238,\cdot)\) \(\chi_{3001}(257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1000})$ |
| Fixed field: | Number field defined by a degree 1000 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{41}{1000}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3001 }(237, a) \) | \(-1\) | \(1\) | \(e\left(\frac{197}{500}\right)\) | \(e\left(\frac{41}{500}\right)\) | \(e\left(\frac{197}{250}\right)\) | \(e\left(\frac{103}{250}\right)\) | \(e\left(\frac{119}{250}\right)\) | \(e\left(\frac{647}{1000}\right)\) | \(e\left(\frac{91}{500}\right)\) | \(e\left(\frac{41}{250}\right)\) | \(e\left(\frac{403}{500}\right)\) | \(e\left(\frac{18}{25}\right)\) |