Basic properties
| Modulus: | \(5312\) | |
| Conductor: | \(5312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(656\) | 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 5312.bk
\(\chi_{5312}(19,\cdot)\) \(\chi_{5312}(35,\cdot)\) \(\chi_{5312}(43,\cdot)\) \(\chi_{5312}(67,\cdot)\) \(\chi_{5312}(91,\cdot)\) \(\chi_{5312}(107,\cdot)\) \(\chi_{5312}(115,\cdot)\) \(\chi_{5312}(139,\cdot)\) \(\chi_{5312}(155,\cdot)\) \(\chi_{5312}(163,\cdot)\) \(\chi_{5312}(171,\cdot)\) \(\chi_{5312}(179,\cdot)\) \(\chi_{5312}(211,\cdot)\) \(\chi_{5312}(219,\cdot)\) \(\chi_{5312}(251,\cdot)\) \(\chi_{5312}(267,\cdot)\) \(\chi_{5312}(283,\cdot)\) \(\chi_{5312}(291,\cdot)\) \(\chi_{5312}(299,\cdot)\) \(\chi_{5312}(307,\cdot)\) \(\chi_{5312}(315,\cdot)\) \(\chi_{5312}(323,\cdot)\) \(\chi_{5312}(347,\cdot)\) \(\chi_{5312}(371,\cdot)\) \(\chi_{5312}(379,\cdot)\) \(\chi_{5312}(387,\cdot)\) \(\chi_{5312}(403,\cdot)\) \(\chi_{5312}(411,\cdot)\) \(\chi_{5312}(435,\cdot)\) \(\chi_{5312}(467,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{656})$ |
| Fixed field: | Number field defined by a degree 656 polynomial (not computed) |
Values on generators
\((831,3653,3073)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{47}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 5312 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{656}\right)\) | \(e\left(\frac{599}{656}\right)\) | \(e\left(\frac{151}{328}\right)\) | \(e\left(\frac{53}{328}\right)\) | \(e\left(\frac{291}{656}\right)\) | \(e\left(\frac{457}{656}\right)\) | \(e\left(\frac{163}{164}\right)\) | \(e\left(\frac{57}{164}\right)\) | \(e\left(\frac{329}{656}\right)\) | \(e\left(\frac{355}{656}\right)\) |