Basic properties
| Modulus: | \(4012\) | |
| Conductor: | \(4012\) | 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 4012.bn
\(\chi_{4012}(3,\cdot)\) \(\chi_{4012}(7,\cdot)\) \(\chi_{4012}(27,\cdot)\) \(\chi_{4012}(63,\cdot)\) \(\chi_{4012}(71,\cdot)\) \(\chi_{4012}(75,\cdot)\) \(\chi_{4012}(79,\cdot)\) \(\chi_{4012}(95,\cdot)\) \(\chi_{4012}(107,\cdot)\) \(\chi_{4012}(139,\cdot)\) \(\chi_{4012}(143,\cdot)\) \(\chi_{4012}(147,\cdot)\) \(\chi_{4012}(159,\cdot)\) \(\chi_{4012}(163,\cdot)\) \(\chi_{4012}(167,\cdot)\) \(\chi_{4012}(175,\cdot)\) \(\chi_{4012}(199,\cdot)\) \(\chi_{4012}(243,\cdot)\) \(\chi_{4012}(299,\cdot)\) \(\chi_{4012}(311,\cdot)\) \(\chi_{4012}(343,\cdot)\) \(\chi_{4012}(363,\cdot)\) \(\chi_{4012}(371,\cdot)\) \(\chi_{4012}(379,\cdot)\) \(\chi_{4012}(403,\cdot)\) \(\chi_{4012}(411,\cdot)\) \(\chi_{4012}(435,\cdot)\) \(\chi_{4012}(439,\cdot)\) \(\chi_{4012}(479,\cdot)\) \(\chi_{4012}(487,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((-1,e\left(\frac{1}{16}\right),e\left(\frac{25}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{309}{464}\right)\) | \(e\left(\frac{225}{464}\right)\) | \(e\left(\frac{327}{464}\right)\) | \(e\left(\frac{77}{232}\right)\) | \(e\left(\frac{227}{464}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{35}{232}\right)\) | \(e\left(\frac{31}{232}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{171}{464}\right)\) |