Basic properties
| Modulus: | \(3009\) | |
| Conductor: | \(3009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3009.bm
\(\chi_{3009}(5,\cdot)\) \(\chi_{3009}(20,\cdot)\) \(\chi_{3009}(29,\cdot)\) \(\chi_{3009}(41,\cdot)\) \(\chi_{3009}(62,\cdot)\) \(\chi_{3009}(71,\cdot)\) \(\chi_{3009}(74,\cdot)\) \(\chi_{3009}(80,\cdot)\) \(\chi_{3009}(95,\cdot)\) \(\chi_{3009}(107,\cdot)\) \(\chi_{3009}(116,\cdot)\) \(\chi_{3009}(122,\cdot)\) \(\chi_{3009}(125,\cdot)\) \(\chi_{3009}(143,\cdot)\) \(\chi_{3009}(146,\cdot)\) \(\chi_{3009}(164,\cdot)\) \(\chi_{3009}(167,\cdot)\) \(\chi_{3009}(182,\cdot)\) \(\chi_{3009}(194,\cdot)\) \(\chi_{3009}(197,\cdot)\) \(\chi_{3009}(218,\cdot)\) \(\chi_{3009}(245,\cdot)\) \(\chi_{3009}(248,\cdot)\) \(\chi_{3009}(284,\cdot)\) \(\chi_{3009}(299,\cdot)\) \(\chi_{3009}(311,\cdot)\) \(\chi_{3009}(317,\cdot)\) \(\chi_{3009}(320,\cdot)\) \(\chi_{3009}(371,\cdot)\) \(\chi_{3009}(380,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((1004,1771,1123)\) → \((-1,e\left(\frac{11}{16}\right),e\left(\frac{1}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3009 }(653, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{232}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{67}{464}\right)\) | \(e\left(\frac{85}{464}\right)\) | \(e\left(\frac{111}{232}\right)\) | \(e\left(\frac{141}{464}\right)\) | \(e\left(\frac{81}{464}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{159}{464}\right)\) | \(e\left(\frac{37}{58}\right)\) |