Basic properties
| Modulus: | \(6002\) | |
| Conductor: | \(3001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1000\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3001}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6002.bd
\(\chi_{6002}(7,\cdot)\) \(\chi_{6002}(21,\cdot)\) \(\chi_{6002}(35,\cdot)\) \(\chi_{6002}(47,\cdot)\) \(\chi_{6002}(53,\cdot)\) \(\chi_{6002}(63,\cdot)\) \(\chi_{6002}(77,\cdot)\) \(\chi_{6002}(79,\cdot)\) \(\chi_{6002}(105,\cdot)\) \(\chi_{6002}(127,\cdot)\) \(\chi_{6002}(137,\cdot)\) \(\chi_{6002}(163,\cdot)\) \(\chi_{6002}(175,\cdot)\) \(\chi_{6002}(189,\cdot)\) \(\chi_{6002}(221,\cdot)\) \(\chi_{6002}(227,\cdot)\) \(\chi_{6002}(231,\cdot)\) \(\chi_{6002}(237,\cdot)\) \(\chi_{6002}(257,\cdot)\) \(\chi_{6002}(315,\cdot)\) \(\chi_{6002}(327,\cdot)\) \(\chi_{6002}(343,\cdot)\) \(\chi_{6002}(381,\cdot)\) \(\chi_{6002}(383,\cdot)\) \(\chi_{6002}(385,\cdot)\) \(\chi_{6002}(391,\cdot)\) \(\chi_{6002}(395,\cdot)\) \(\chi_{6002}(397,\cdot)\) \(\chi_{6002}(411,\cdot)\) \(\chi_{6002}(423,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1000})$ |
| Fixed field: | Number field defined by a degree 1000 polynomial (not computed) |
Values on generators
\(3015\) → \(e\left(\frac{657}{1000}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6002 }(63, a) \) | \(-1\) | \(1\) | \(e\left(\frac{157}{500}\right)\) | \(e\left(\frac{181}{250}\right)\) | \(e\left(\frac{319}{1000}\right)\) | \(e\left(\frac{157}{250}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{53}{200}\right)\) | \(e\left(\frac{19}{500}\right)\) | \(e\left(\frac{42}{125}\right)\) | \(e\left(\frac{33}{200}\right)\) | \(e\left(\frac{633}{1000}\right)\) |