Basic properties
| Modulus: | \(3009\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1003}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3009.bk
\(\chi_{3009}(10,\cdot)\) \(\chi_{3009}(31,\cdot)\) \(\chi_{3009}(37,\cdot)\) \(\chi_{3009}(40,\cdot)\) \(\chi_{3009}(61,\cdot)\) \(\chi_{3009}(73,\cdot)\) \(\chi_{3009}(82,\cdot)\) \(\chi_{3009}(91,\cdot)\) \(\chi_{3009}(97,\cdot)\) \(\chi_{3009}(109,\cdot)\) \(\chi_{3009}(124,\cdot)\) \(\chi_{3009}(142,\cdot)\) \(\chi_{3009}(148,\cdot)\) \(\chi_{3009}(160,\cdot)\) \(\chi_{3009}(190,\cdot)\) \(\chi_{3009}(211,\cdot)\) \(\chi_{3009}(214,\cdot)\) \(\chi_{3009}(232,\cdot)\) \(\chi_{3009}(244,\cdot)\) \(\chi_{3009}(250,\cdot)\) \(\chi_{3009}(283,\cdot)\) \(\chi_{3009}(286,\cdot)\) \(\chi_{3009}(292,\cdot)\) \(\chi_{3009}(301,\cdot)\) \(\chi_{3009}(313,\cdot)\) \(\chi_{3009}(328,\cdot)\) \(\chi_{3009}(334,\cdot)\) \(\chi_{3009}(337,\cdot)\) \(\chi_{3009}(364,\cdot)\) \(\chi_{3009}(367,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((1004,1771,1123)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{7}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3009 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{232}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{307}{464}\right)\) | \(e\left(\frac{109}{464}\right)\) | \(e\left(\frac{55}{232}\right)\) | \(e\left(\frac{189}{464}\right)\) | \(e\left(\frac{153}{464}\right)\) | \(e\left(\frac{21}{116}\right)\) | \(e\left(\frac{455}{464}\right)\) | \(e\left(\frac{57}{58}\right)\) |