Hypergeometric motives over $\Q$

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The table below gives for each degree $d$ and weight $w$ shown, the number of corresponding hypergeometric families.

$w$ \ $d$	1	3	5	7	9	2	4	6	8	10
0	1	3	7	21	13	3	11	23	51	23
2		10	93	426	1836		30	234	1234	4475
4			47	414	2878			84	894	5737
6				142	1263				204	1936
8					363					426
1						10	74	287	1001	2197
3							47	487	3247	14397
5								142	1450	10260
7									363	3407
9										812

Families above are separated by type – those with odd weight and even degree are symplectic, otherwise they are orthogonal. Boxes are blank for combinations of weight and degree which cannot occur.

Some interesting families of hypergeometric motives, a random family or a random hypergeometric motive.

Search for hypergeometric families

Enter values into one or more boxes to restrict the list of families returned.

Degree		e.g. 4	Weight		e.g. 3
Family Hodge vector		e.g. [1,1,1,1]	$A$		e.g. [3,2,2]	$B$		e.g. [6,4]
Prime $p$			$A_p$		e.g. [2,2,1,1]	$B_p$		e.g. [2,2,1,1]
			$A^\perp_p$		e.g. [2,2,1,1]	$B^\perp_p$		e.g. [2,2,1,1]

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Search for individual hypergeometric motives

Enter values into the boxes above and the boxes below to obtain the list of corresponding hypergeometric motives.

Conductor		e.g. a value, like 32, a list, like 32,64, or a range like 1..10000
Hodge vector		e.g. [1,1,1,1]
Specialization point $t$		e.g. 3/2 (1 has an associated degree drop and is always in the database)
Root number $\epsilon$		1 or -1, with -1 occurring only in the symplectic case
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Label
	an HGM label encoding the triple $(A, B, t)$