Basic properties
| Modulus: | \(4012\) | |
| 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 \(\chi_{1003}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4012.bk
\(\chi_{4012}(37,\cdot)\) \(\chi_{4012}(61,\cdot)\) \(\chi_{4012}(65,\cdot)\) \(\chi_{4012}(73,\cdot)\) \(\chi_{4012}(97,\cdot)\) \(\chi_{4012}(109,\cdot)\) \(\chi_{4012}(113,\cdot)\) \(\chi_{4012}(129,\cdot)\) \(\chi_{4012}(141,\cdot)\) \(\chi_{4012}(165,\cdot)\) \(\chi_{4012}(173,\cdot)\) \(\chi_{4012}(201,\cdot)\) \(\chi_{4012}(209,\cdot)\) \(\chi_{4012}(233,\cdot)\) \(\chi_{4012}(249,\cdot)\) \(\chi_{4012}(269,\cdot)\) \(\chi_{4012}(301,\cdot)\) \(\chi_{4012}(309,\cdot)\) \(\chi_{4012}(313,\cdot)\) \(\chi_{4012}(329,\cdot)\) \(\chi_{4012}(333,\cdot)\) \(\chi_{4012}(337,\cdot)\) \(\chi_{4012}(345,\cdot)\) \(\chi_{4012}(377,\cdot)\) \(\chi_{4012}(385,\cdot)\) \(\chi_{4012}(397,\cdot)\) \(\chi_{4012}(401,\cdot)\) \(\chi_{4012}(437,\cdot)\) \(\chi_{4012}(445,\cdot)\) \(\chi_{4012}(453,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{51}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{245}{464}\right)\) | \(e\left(\frac{41}{464}\right)\) | \(e\left(\frac{7}{464}\right)\) | \(e\left(\frac{13}{232}\right)\) | \(e\left(\frac{427}{464}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{143}{232}\right)\) | \(e\left(\frac{67}{232}\right)\) | \(e\left(\frac{63}{116}\right)\) | \(e\left(\frac{291}{464}\right)\) |