# lfunc_search downloaded from the LMFDB on 02 May 2026. # Search link: https://www.lmfdb.org/L/2/8624 # Query "{'degree': 2, 'conductor': 8624}" returned 205 lfunc_searchs, sorted by root analytic conductor. # Each entry in the following data list has the form: # [Label, $\alpha$, $A$, $d$, $N$, $\chi$, $\mu$, $\nu$, $w$, prim, arith, $\mathbb{Q}$, self-dual, $\operatorname{Arg}(\epsilon)$, $r$, First zero, Origin] # For more details, see the definitions at the bottom of the file. "2-8624-1.1-c1-0-0" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.096707528347186097368876718601 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/5"] "2-8624-1.1-c1-0-1" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.10251559288994634238880646896 ["ModularForm/GL2/Q/holomorphic/8624/2/a/de/1/2"] "2-8624-1.1-c1-0-10" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.30258361706072399620651671008 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bl/1/1"] "2-8624-1.1-c1-0-100" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.936071559048242997613623229886 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dd/1/4"] "2-8624-1.1-c1-0-101" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.942835376243860514734661121549 ["EllipticCurve/Q/8624/w", "ModularForm/GL2/Q/holomorphic/8624/2/a/w/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/w"] "2-8624-1.1-c1-0-102" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.943225355105721948581236920420 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cu/1/2"] "2-8624-1.1-c1-0-103" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.944682176578822211001332908348 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cd/1/2"] "2-8624-1.1-c1-0-104" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.950007547924136266172055961778 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cw/1/1"] "2-8624-1.1-c1-0-105" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.950294903072132692665701512843 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cr/1/1"] "2-8624-1.1-c1-0-106" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.954433882105245086734176998750 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cq/1/1"] "2-8624-1.1-c1-0-107" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.959312128265039974239357190234 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/8"] "2-8624-1.1-c1-0-108" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.968948037648386637365537444731 ["EllipticCurve/Q/8624/be", "ModularForm/GL2/Q/holomorphic/8624/2/a/be/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/be"] "2-8624-1.1-c1-0-109" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 0.969255775458665212504779315908 ["EllipticCurve/Q/8624/i", "ModularForm/GL2/Q/holomorphic/8624/2/a/i/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/i"] "2-8624-1.1-c1-0-11" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.30423234661907049817444345107 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/3"] "2-8624-1.1-c1-0-110" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.969639852596352880235525834999 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/12"] "2-8624-1.1-c1-0-111" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.971569733419731983638759502665 ["ModularForm/GL2/Q/holomorphic/8624/2/a/by/1/2"] "2-8624-1.1-c1-0-112" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.973028907382995088418632044565 ["ModularForm/GL2/Q/holomorphic/8624/2/a/br/1/1"] "2-8624-1.1-c1-0-113" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 0.979033992832471368219893964268 ["EllipticCurve/Q/8624/j", "ModularForm/GL2/Q/holomorphic/8624/2/a/j/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/j"] "2-8624-1.1-c1-0-114" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.990126139818806984030646148806 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bw/1/1"] "2-8624-1.1-c1-0-115" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.00096275034805857195732354190 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bv/1/1"] "2-8624-1.1-c1-0-116" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.00184938446969175342463812095 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cp/1/3"] "2-8624-1.1-c1-0-117" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.00359487834415383251666804253 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bn/1/1"] "2-8624-1.1-c1-0-118" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.01739207421506705941148561256 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bp/1/1"] "2-8624-1.1-c1-0-119" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.01902961748760814942092863552 ["ModularForm/GL2/Q/holomorphic/8624/2/a/co/1/2"] "2-8624-1.1-c1-0-12" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.31640324540219889555662500084 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bi/1/1"] "2-8624-1.1-c1-0-120" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.02857100009546872706914998523 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/8"] "2-8624-1.1-c1-0-121" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.03455225501079997217363707687 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ct/1/4"] "2-8624-1.1-c1-0-122" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.03961887724386371443510119306 ["EllipticCurve/Q/8624/f", "ModularForm/GL2/Q/holomorphic/8624/2/a/f/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/f"] "2-8624-1.1-c1-0-123" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.04212464652439392878833127473 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bo/1/1"] "2-8624-1.1-c1-0-124" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.06167590159195657203928361547 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bh/1/1"] "2-8624-1.1-c1-0-125" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.06271186926021691802176623021 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bi/1/2"] "2-8624-1.1-c1-0-126" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.06281337353144312918356625670 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bz/1/1"] "2-8624-1.1-c1-0-127" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.06635800584766769227430616406 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cy/1/4"] "2-8624-1.1-c1-0-128" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.06932176766277946982444878355 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cu/1/4"] "2-8624-1.1-c1-0-129" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.07055595102177968762291052173 ["EllipticCurve/Q/8624/k", "ModularForm/GL2/Q/holomorphic/8624/2/a/k/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/k"] "2-8624-1.1-c1-0-13" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.34269503535730182617994507306 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cd/1/1"] "2-8624-1.1-c1-0-130" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.07696943335018709894615475359 ["EllipticCurve/Q/8624/b", "ModularForm/GL2/Q/holomorphic/8624/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/b"] "2-8624-1.1-c1-0-131" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.07849551585873598538118195366 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/10"] "2-8624-1.1-c1-0-132" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.07893465019443229830299615489 ["ModularForm/GL2/Q/holomorphic/8624/2/a/db/1/2"] "2-8624-1.1-c1-0-133" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.09991191362984260549444044840 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cw/1/2"] "2-8624-1.1-c1-0-134" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.10811208023702151565140234637 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cz/1/4"] "2-8624-1.1-c1-0-135" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.11046195028346012436707118039 ["EllipticCurve/Q/8624/g", "ModularForm/GL2/Q/holomorphic/8624/2/a/g/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/g"] "2-8624-1.1-c1-0-136" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.11299784894513551832789907727 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bq/1/1"] "2-8624-1.1-c1-0-137" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.11543850259996911832558702221 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ck/1/3"] "2-8624-1.1-c1-0-138" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.11562338447763612182076696248 ["ModularForm/GL2/Q/holomorphic/8624/2/a/co/1/1"] "2-8624-1.1-c1-0-139" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.12113155743030734812238244327 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bx/1/1"] "2-8624-1.1-c1-0-14" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.34479783481048107003412693587 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/1"] "2-8624-1.1-c1-0-140" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.12239804975834457710455257380 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cs/1/2"] "2-8624-1.1-c1-0-141" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.12316698870874313447206408447 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dc/1/5"] "2-8624-1.1-c1-0-142" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.12730952737508724650815682186 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bs/1/2"] "2-8624-1.1-c1-0-143" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.14559998201306115747834258066 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cj/1/1"] "2-8624-1.1-c1-0-144" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.15982420448245161462844689986 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ce/1/2"] "2-8624-1.1-c1-0-145" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.16412667189394194124784917880 ["ModularForm/GL2/Q/holomorphic/8624/2/a/de/1/7"] "2-8624-1.1-c1-0-146" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.18290695432917122002954632766 ["EllipticCurve/Q/8624/l", "ModularForm/GL2/Q/holomorphic/8624/2/a/l/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/l"] "2-8624-1.1-c1-0-147" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.19701545800302823373777251700 ["ModularForm/GL2/Q/holomorphic/8624/2/a/da/1/3"] "2-8624-1.1-c1-0-148" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.19711706468737922787565093014 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ci/1/2"] "2-8624-1.1-c1-0-149" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.19714222140847366798974360860 ["ModularForm/GL2/Q/holomorphic/8624/2/a/db/1/5"] "2-8624-1.1-c1-0-15" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.35426505502516818432572323946 ["ModularForm/GL2/Q/holomorphic/8624/2/a/de/1/1"] "2-8624-1.1-c1-0-150" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.21643601698678464376535700472 ["EllipticCurve/Q/8624/n", "ModularForm/GL2/Q/holomorphic/8624/2/a/n/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/n"] "2-8624-1.1-c1-0-151" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.21814054681517508725062809672 ["ModularForm/GL2/Q/holomorphic/8624/2/a/da/1/1"] "2-8624-1.1-c1-0-152" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.22791886809023694657447574030 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cg/1/2"] "2-8624-1.1-c1-0-153" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.23470312000295412452900585512 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cx/1/1"] "2-8624-1.1-c1-0-154" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.23478617475981005021292314037 ["ModularForm/GL2/Q/holomorphic/8624/2/a/de/1/8"] "2-8624-1.1-c1-0-155" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.23945863959553211180189013359 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cs/1/4"] "2-8624-1.1-c1-0-156" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.26550311928445429782834289710 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cr/1/2"] "2-8624-1.1-c1-0-157" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.26580086102669104331986720348 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cn/1/3"] "2-8624-1.1-c1-0-158" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.26602469649261530150825126665 ["EllipticCurve/Q/8624/p", "ModularForm/GL2/Q/holomorphic/8624/2/a/p/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/p"] "2-8624-1.1-c1-0-159" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.26991203355811791076606468674 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cv/1/4"] "2-8624-1.1-c1-0-16" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.36134681724684103974056827182 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ck/1/2"] "2-8624-1.1-c1-0-160" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.29602835110322760048880216037 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cs/1/3"] "2-8624-1.1-c1-0-161" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.30616737378324587220528635560 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/10"] "2-8624-1.1-c1-0-162" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.30648916402694460465835732440 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bq/1/2"] "2-8624-1.1-c1-0-163" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 1.31533137676839461678616572811 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ca/1/2"] "2-8624-1.1-c1-0-164" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.32907013756634914495717772180 ["EllipticCurve/Q/8624/c", "ModularForm/GL2/Q/holomorphic/8624/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/c"] "2-8624-1.1-c1-0-165" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.34319356131477999978921545642 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bo/1/2"] "2-8624-1.1-c1-0-166" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.34849648072881836851260434746 ["ModularForm/GL2/Q/holomorphic/8624/2/a/db/1/4"] "2-8624-1.1-c1-0-167" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.34864199103902842222872515778 ["EllipticCurve/Q/8624/q", "ModularForm/GL2/Q/holomorphic/8624/2/a/q/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/q"] "2-8624-1.1-c1-0-168" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.34939095994789021827663944051 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bg/1/2"] "2-8624-1.1-c1-0-169" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.35387629911425067865594370176 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cs/1/1"] "2-8624-1.1-c1-0-17" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.36329876637049930353500898539 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dd/1/2"] "2-8624-1.1-c1-0-170" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.35801922528529719030194429191 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bs/1/1"] "2-8624-1.1-c1-0-171" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.36226365501053462033152194399 ["ModularForm/GL2/Q/holomorphic/8624/2/a/da/1/4"] "2-8624-1.1-c1-0-172" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.37085742552661853239671743807 ["EllipticCurve/Q/8624/y", "ModularForm/GL2/Q/holomorphic/8624/2/a/y/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/y"] "2-8624-1.1-c1-0-173" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.37305950189066983363250464788 ["EllipticCurve/Q/8624/ba", "ModularForm/GL2/Q/holomorphic/8624/2/a/ba/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/ba"] "2-8624-1.1-c1-0-174" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.38218274704641539685547935547 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bn/1/2"] "2-8624-1.1-c1-0-175" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.39134982267066587201348228305 ["EllipticCurve/Q/8624/z", "ModularForm/GL2/Q/holomorphic/8624/2/a/z/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/z"] "2-8624-1.1-c1-0-176" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.41687188543665914502828717952 ["EllipticCurve/Q/8624/bd", "ModularForm/GL2/Q/holomorphic/8624/2/a/bd/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/bd"] "2-8624-1.1-c1-0-177" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.44823371671113145400936870397 ["ModularForm/GL2/Q/holomorphic/8624/2/a/db/1/3"] "2-8624-1.1-c1-0-178" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.45202725639002495320177906613 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cg/1/3"] "2-8624-1.1-c1-0-179" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.45334134792195779769901679273 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bf/1/2"] "2-8624-1.1-c1-0-18" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.36751099267138983390514483759 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cu/1/3"] "2-8624-1.1-c1-0-180" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.46050002511220412703698146679 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bp/1/2"] "2-8624-1.1-c1-0-181" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.47095023243090618914894104771 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cw/1/3"] "2-8624-1.1-c1-0-182" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.49162625882582470249531094170 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cl/1/2"] "2-8624-1.1-c1-0-183" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.51042290467858382595985635016 ["ModularForm/GL2/Q/holomorphic/8624/2/a/br/1/2"] "2-8624-1.1-c1-0-184" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.51471020276721031040875107841 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cl/1/3"] "2-8624-1.1-c1-0-185" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.53151915954957183746205942070 ["ModularForm/GL2/Q/holomorphic/8624/2/a/co/1/3"] "2-8624-1.1-c1-0-186" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.53305843654001978763207746133 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cr/1/4"] "2-8624-1.1-c1-0-187" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.54186045717625356686815637812 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bh/1/2"] "2-8624-1.1-c1-0-188" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.55379012059403473162136330487 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bv/1/2"] "2-8624-1.1-c1-0-189" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.56798461407328346854410830145 ["EllipticCurve/Q/8624/bb", "ModularForm/GL2/Q/holomorphic/8624/2/a/bb/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/bb"] "2-8624-1.1-c1-0-19" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.37771363126039603523652140535 ["ModularForm/GL2/Q/holomorphic/8624/2/a/by/1/1"] "2-8624-1.1-c1-0-190" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.58126441160005025325976768153 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bw/1/2"] "2-8624-1.1-c1-0-191" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.60551958084099456823963926961 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cj/1/3"] "2-8624-1.1-c1-0-192" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.63375003262579083175101365065 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cx/1/4"] "2-8624-1.1-c1-0-193" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.63485086704768469597852881476 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cr/1/3"] "2-8624-1.1-c1-0-194" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.64898519759039438656792173194 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bx/1/2"] "2-8624-1.1-c1-0-195" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.65053888384805960601685824736 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cq/1/3"] "2-8624-1.1-c1-0-196" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 1.67915649184277622840650438512 ["EllipticCurve/Q/8624/bc", "ModularForm/GL2/Q/holomorphic/8624/2/a/bc/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/bc"] "2-8624-1.1-c1-0-197" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.71080348386934776096056934897 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cw/1/4"] "2-8624-1.1-c1-0-198" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.72559842940958780983063578551 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ci/1/3"] "2-8624-1.1-c1-0-199" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.73108148196738799400638989997 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cb/1/2"] "2-8624-1.1-c1-0-2" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.13278041516337010587222769294 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cy/1/3"] "2-8624-1.1-c1-0-20" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.39808852543899251811513383656 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dc/1/3"] "2-8624-1.1-c1-0-200" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.74017101017782960366347071916 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cq/1/2"] "2-8624-1.1-c1-0-201" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.77079289911845285757448485392 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bk/1/2"] "2-8624-1.1-c1-0-202" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.78537283136230774896346777660 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cx/1/3"] "2-8624-1.1-c1-0-203" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.81266946316212506150573995311 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bz/1/2"] "2-8624-1.1-c1-0-204" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 1.83973996903744548936120460367 ["ModularForm/GL2/Q/holomorphic/8624/2/a/da/1/5"] "2-8624-1.1-c1-0-21" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.39861436544397949371533853744 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ct/1/1"] "2-8624-1.1-c1-0-22" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.41802710742323758167636495180 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bu/1/1"] "2-8624-1.1-c1-0-23" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.43301819945497587606566235109 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/1"] "2-8624-1.1-c1-0-24" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.43508504253983385297909689778 ["EllipticCurve/Q/8624/o", "ModularForm/GL2/Q/holomorphic/8624/2/a/o/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/o"] "2-8624-1.1-c1-0-25" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.45049324018912481336212576789 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ch/1/1"] "2-8624-1.1-c1-0-26" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.46649884858073800820772991743 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cm/1/2"] "2-8624-1.1-c1-0-27" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.48667941164408914338669340400 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cf/1/2"] "2-8624-1.1-c1-0-28" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.48751631672773148444124830194 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dc/1/2"] "2-8624-1.1-c1-0-29" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.49725573699062484119654941596 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cz/1/2"] "2-8624-1.1-c1-0-3" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.13444352485510401529247725280 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/5"] "2-8624-1.1-c1-0-30" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.50274875505931589913121562753 ["ModularForm/GL2/Q/holomorphic/8624/2/a/de/1/5"] "2-8624-1.1-c1-0-31" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.51310905419093884016781307010 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cp/1/1"] "2-8624-1.1-c1-0-32" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.51641007658809724152807885213 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/3"] "2-8624-1.1-c1-0-33" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.52829827162616250167699475047 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cy/1/2"] "2-8624-1.1-c1-0-34" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.52915129449234541001810239465 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cp/1/2"] "2-8624-1.1-c1-0-35" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.53332021707265700610164652776 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bm/1/2"] "2-8624-1.1-c1-0-36" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.54128583886214059430583331692 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ck/1/1"] "2-8624-1.1-c1-0-37" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.54318043848723560823049108407 ["EllipticCurve/Q/8624/x", "ModularForm/GL2/Q/holomorphic/8624/2/a/x/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/x"] "2-8624-1.1-c1-0-38" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.55600085879009648263163944649 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cv/1/3"] "2-8624-1.1-c1-0-39" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.56017564788045941374164955368 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cz/1/1"] "2-8624-1.1-c1-0-4" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.17067010588648956011243187095 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cv/1/1"] "2-8624-1.1-c1-0-40" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.56076212348527213871917060250 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/9"] "2-8624-1.1-c1-0-41" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.56085320779112636302603550485 ["ModularForm/GL2/Q/holomorphic/8624/2/a/de/1/3"] "2-8624-1.1-c1-0-42" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.56318387497208194653992986163 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cu/1/1"] "2-8624-1.1-c1-0-43" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.56442379601835038706137805515 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bm/1/1"] "2-8624-1.1-c1-0-44" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.56668001044820009293041649017 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dd/1/3"] "2-8624-1.1-c1-0-45" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.57139773279138586482545680334 ["EllipticCurve/Q/8624/t", "ModularForm/GL2/Q/holomorphic/8624/2/a/t/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/t"] "2-8624-1.1-c1-0-46" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.57222674983994739528847396613 ["EllipticCurve/Q/8624/m", "ModularForm/GL2/Q/holomorphic/8624/2/a/m/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/m"] "2-8624-1.1-c1-0-47" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.58384294774336093392229107216 ["ModularForm/GL2/Q/holomorphic/8624/2/a/de/1/6"] "2-8624-1.1-c1-0-48" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.60230455664714089519071857164 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ch/1/3"] "2-8624-1.1-c1-0-49" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.60257073181056741753790635536 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bt/1/2"] "2-8624-1.1-c1-0-5" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.19372249126359057993513260598 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bj/1/1"] "2-8624-1.1-c1-0-50" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.60529254407040601479116364865 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cn/1/2"] "2-8624-1.1-c1-0-51" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.63004241918108359512504792398 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cn/1/1"] "2-8624-1.1-c1-0-52" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.63498940801745792889827996688 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/4"] "2-8624-1.1-c1-0-53" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.63715395674397493657863840222 ["EllipticCurve/Q/8624/s", "ModularForm/GL2/Q/holomorphic/8624/2/a/s/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/s"] "2-8624-1.1-c1-0-54" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.63877537931902655978837422699 ["EllipticCurve/Q/8624/a", "ModularForm/GL2/Q/holomorphic/8624/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/a"] "2-8624-1.1-c1-0-55" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.64093989514210016181941489771 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cy/1/1"] "2-8624-1.1-c1-0-56" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.64257789246223164260573131937 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cv/1/2"] "2-8624-1.1-c1-0-57" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.64591175088605806411853446143 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/7"] "2-8624-1.1-c1-0-58" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.64890579975858367322492381245 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cz/1/3"] "2-8624-1.1-c1-0-59" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.66871130484537630442843295121 ["EllipticCurve/Q/8624/h", "ModularForm/GL2/Q/holomorphic/8624/2/a/h/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/h"] "2-8624-1.1-c1-0-6" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.22692525678679928252089930112 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cc/1/1"] "2-8624-1.1-c1-0-60" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.67058604573892164337879740676 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ce/1/1"] "2-8624-1.1-c1-0-61" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.67269594652445934033221809223 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bk/1/1"] "2-8624-1.1-c1-0-62" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.68209508998543034793956731997 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/4"] "2-8624-1.1-c1-0-63" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.73560815900512632775081729613 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ca/1/1"] "2-8624-1.1-c1-0-64" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.73661957837081539249498970519 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bl/1/2"] "2-8624-1.1-c1-0-65" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.74009564146833610294267691365 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/2"] "2-8624-1.1-c1-0-66" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.74792191692199101347836075508 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cl/1/1"] "2-8624-1.1-c1-0-67" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.75692655299115052865477991532 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cf/1/1"] "2-8624-1.1-c1-0-68" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.76028039870814896295653153518 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cm/1/1"] "2-8624-1.1-c1-0-69" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.76225224717283288100997784823 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ch/1/2"] "2-8624-1.1-c1-0-7" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.25573304626737201681925288507 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ct/1/2"] "2-8624-1.1-c1-0-70" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.76239078235393209673346963725 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bj/1/2"] "2-8624-1.1-c1-0-71" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.76451561431099188610985575785 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dd/1/5"] "2-8624-1.1-c1-0-72" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.77399069757804528941083402011 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ct/1/3"] "2-8624-1.1-c1-0-73" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.77449661709403716691089193894 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bf/1/1"] "2-8624-1.1-c1-0-74" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.77748453596462356693777529751 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dc/1/4"] "2-8624-1.1-c1-0-75" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.78253682208567568279986497394 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bt/1/1"] "2-8624-1.1-c1-0-76" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.78385397243241047554565051843 ["EllipticCurve/Q/8624/r", "ModularForm/GL2/Q/holomorphic/8624/2/a/r/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/r"] "2-8624-1.1-c1-0-77" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.789378871456842894844166431930 ["ModularForm/GL2/Q/holomorphic/8624/2/a/de/1/4"] "2-8624-1.1-c1-0-78" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.789805138327647939571001075771 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/6"] "2-8624-1.1-c1-0-79" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.792977833938875793466249906557 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cf/1/3"] "2-8624-1.1-c1-0-8" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.27762829919541614904138032469 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/7"] "2-8624-1.1-c1-0-80" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.794928295904989400489230840340 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/2"] "2-8624-1.1-c1-0-81" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.796312446703943196957698605850 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/11"] "2-8624-1.1-c1-0-82" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.796724616371184391113970350001 ["EllipticCurve/Q/8624/u", "ModularForm/GL2/Q/holomorphic/8624/2/a/u/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/u"] "2-8624-1.1-c1-0-83" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.799094839644138814639646614783 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cc/1/2"] "2-8624-1.1-c1-0-84" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.812267295907644305810806467523 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cm/1/3"] "2-8624-1.1-c1-0-85" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.812475168431352423513783861717 ["ModularForm/GL2/Q/holomorphic/8624/2/a/df/1/6"] "2-8624-1.1-c1-0-86" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.813048474466193814798899274179 ["EllipticCurve/Q/8624/v", "ModularForm/GL2/Q/holomorphic/8624/2/a/v/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/v"] "2-8624-1.1-c1-0-87" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.0 0 0.818644360895583031625407140138 ["EllipticCurve/Q/8624/d", "ModularForm/GL2/Q/holomorphic/8624/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/d"] "2-8624-1.1-c1-0-88" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.818757862097360565881381798610 ["ModularForm/GL2/Q/holomorphic/8624/2/a/ci/1/1"] "2-8624-1.1-c1-0-89" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.827385915203224911554175889531 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cx/1/2"] "2-8624-1.1-c1-0-9" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.29032815628124013994546873312 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dd/1/1"] "2-8624-1.1-c1-0-90" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.830324448467241561206188419656 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bu/1/2"] "2-8624-1.1-c1-0-91" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.836719306110438247135393435622 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dg/1/9"] "2-8624-1.1-c1-0-92" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.843585070768322895363532824153 ["ModularForm/GL2/Q/holomorphic/8624/2/a/da/1/2"] "2-8624-1.1-c1-0-93" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.854791727946214322957728734734 ["ModularForm/GL2/Q/holomorphic/8624/2/a/db/1/1"] "2-8624-1.1-c1-0-94" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true true true 0.5 1 0.857071651185432583891932144181 ["EllipticCurve/Q/8624/e", "ModularForm/GL2/Q/holomorphic/8624/2/a/e/1/1", "ModularForm/GL2/Q/holomorphic/8624/2/a/e"] "2-8624-1.1-c1-0-95" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.861225875643021200475484176073 ["ModularForm/GL2/Q/holomorphic/8624/2/a/bg/1/1"] "2-8624-1.1-c1-0-96" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.866503153579054288206624202194 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cb/1/1"] "2-8624-1.1-c1-0-97" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.885819949915540798491345314927 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cj/1/2"] "2-8624-1.1-c1-0-98" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.0 0 0.888211389250900456568638325855 ["ModularForm/GL2/Q/holomorphic/8624/2/a/dc/1/1"] "2-8624-1.1-c1-0-99" 8.298372533403898 68.86298670315223 2 8624 "1.1" [] [[0.5, 0.0]] 1 true true false true 0.5 1 0.891726066752355893012255697382 ["ModularForm/GL2/Q/holomorphic/8624/2/a/cg/1/1"] # Label -- # Each L-function $L$ has a label of the form d-N-q.k-x-y-i, where # * $d$ is the degree of $L$. # * $N$ is the conductor of $L$. When $N$ is a perfect power $m^n$ we write $N$ as $m$e$n$, since $N$ can be very large for some imprimitive L-functions. # * q.k is the label of the primitive Dirichlet character from which the central character is induced. # * x-y is the spectral label encoding the $\mu_j$ and $\nu_j$ in the analytically normalized functional equation. # * i is a non-negative integer disambiguating between L-functions that would otherwise have the same label. #$\alpha$ (root_analytic_conductor) -- # If $d$ is the degree of the L-function $L(s)$, the **root analytic conductor** $\alpha$ of $L$ is the $d$th root of the analytic conductor of $L$. It plays a role analogous to the root discriminant for number fields. #$A$ (analytic_conductor) -- # The **analytic conductor** of an L-function $L(s)$ with infinity factor $L_{\infty}(s)$ and conductor $N$ is the real number # \[ # A := \mathrm{exp}\left(2\mathrm{Re}\left(\frac{L_{\infty}'(1/2)}{L_{\infty}(1/2)}\right)\right)N. # \] #$d$ (degree) -- # The **degree** of an L-function is the number $J + 2K$ of Gamma factors occurring in its functional equation # \[ # \Lambda(s) := N^{s/2} # \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) # \cdot L(s) = \varepsilon \overline{\Lambda}(1-s). # \] # The degree appears as the first component of the Selberg data of $L(s).$ In all known cases it is the degree of the polynomial of the inverse of the Euler factor at any prime not dividing the conductor. #$N$ (conductor) -- # The **conductor** of an L-function is the integer $N$ occurring in its functional equation # \[ # \Lambda(s) := N^{s/2} # \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) # \cdot L(s) = \varepsilon \overline{\Lambda}(1-s). # \] # The conductor of an analytic L-function is the second component in the Selberg data. For a Dirichlet L-function # associated with a primitive Dirichlet character, the conductor of the L-function is the same as the conductor of the character. For a primitive L-function associated with a cusp form $\phi$ on $GL(2)/\mathbb Q$, the conductor of the L-function is the same as the level of $\phi$. # In the literature, the word _level_ is sometimes used instead of _conductor_. #$\chi$ (central_character) -- # An L-function has an Euler product of the form # $L(s) = \prod_p L_p(p^{-s})^{-1}$ # where $L_p(x) = 1 + a_p x + \ldots + (-1)^d \chi(p) x^d$. The character $\chi$ is a Dirichlet character mod $N$ and is called **central character** of the L-function. # Here, $N$ is the conductor of $L$. #$\mu$ (mus) -- # All known analytic L-functions have a **functional equation** that can be written in the form # \[ # \Lambda(s) := N^{s/2} # \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) # \cdot L(s) = \varepsilon \overline{\Lambda}(1-s), # \] # where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer # or half-integer, # \[ # \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real}, # \] # and $\varepsilon$ is the sign of the functional equation. # With those restrictions on the spectral parameters, the # data in the functional equation is specified uniquely. The integer $d = J + 2 K$ # is the degree of the L-function. The integer $N$ is the conductor (or level) # of the L-function. The pair $[J,K]$ is the signature of the L-function. The parameters # in the functional equation can be used to make up the 4-tuple called the Selberg data. # The axioms of the Selberg class are less restrictive than # given above. # Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$. # For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$, # called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers. #$\nu$ (nus) -- # All known analytic L-functions have a **functional equation** that can be written in the form # \[ # \Lambda(s) := N^{s/2} # \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) # \cdot L(s) = \varepsilon \overline{\Lambda}(1-s), # \] # where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer # or half-integer, # \[ # \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real}, # \] # and $\varepsilon$ is the sign of the functional equation. # With those restrictions on the spectral parameters, the # data in the functional equation is specified uniquely. The integer $d = J + 2 K$ # is the degree of the L-function. The integer $N$ is the conductor (or level) # of the L-function. The pair $[J,K]$ is the signature of the L-function. The parameters # in the functional equation can be used to make up the 4-tuple called the Selberg data. # The axioms of the Selberg class are less restrictive than # given above. # Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$. # For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$, # called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers. #$w$ (motivic_weight) -- # The **motivic weight** (or **arithmetic weight**) of an arithmetic L-function with analytic normalization $L_{an}(s)=\sum_{n=1}^\infty a_nn^{-s}$ is the least nonnegative integer $w$ for which $a_nn^{w/2}$ is an algebraic integer for all $n\ge 1$. # If the L-function arises from a motive, then the weight of the motive has the # same parity as the motivic weight of the L-function, but the weight of the motive # could be larger. This apparent discrepancy comes from the fact that a Tate twist # increases the weight of the motive. This corresponds to the change of variables # $s \mapsto s + j$ in the L-function of the motive. #prim (primitive) -- # An L-function is primitive if it cannot be written as a product of nontrivial L-functions. The "trivial L-function" is the constant function $1$. #arith (algebraic) -- # An L-function $L(s) = \sum_{n=1}^{\infty} a_n n^{-s}$ is called **arithmetic** if its Dirichlet coefficients $a_n$ are algebraic numbers. #$\mathbb{Q}$ (rational) -- # A **rational** L-function $L(s)$ is an arithmetic L-function with coefficient field $\Q$; equivalently, its Euler product in the arithmetic normalization can be written as a product over rational primes # \[ # L(s)=\prod_pL_p(p^{-s})^{-1} # \] # with $L_p\in \Z[T]$. #self-dual (self_dual) -- # An L-function $L(s) = \sum_{n=1}^{\infty} \frac{a_n}{n^s}$ is called **self-dual** if its Dirichlet coefficients $a_n$ are real. #$\operatorname{Arg}(\epsilon)$ (root_angle) -- # The **root angle** of an L-function is the argument of its root number, as a real number $\alpha$ with $-0.5 < \alpha \le 0.5$. #$r$ (order_of_vanishing) -- # The **analytic rank** of an L-function $L(s)$ is its order of vanishing at its central point. # When the analytic rank $r$ is positive, the value listed in the LMFDB is typically an upper bound that is believed to be tight (in the sense that there are known to be $r$ zeroes located very near to the central point). #First zero (z1) -- # The **zeros** of an L-function $L(s)$ are the complex numbers $\rho$ for which $L(\rho)=0$. # Under the Riemann Hypothesis, every non-trivial zero $\rho$ lies on the critical line $\Re(s)=1/2$ (in the analytic normalization). # The **lowest zero** of an L-function $L(s)$ is the least $\gamma>0$ for which $L(1/2+i\gamma)=0$. Note that even when $L(1/2)=0$, the lowest zero is by definition a positive real number. #Origin (instance_urls) -- # L-functions arise from many different sources. Already in degree 2 we have examples of # L-functions associated with holomorphic cusp forms, with Maass forms, with elliptic curves, with characters of number fields (Hecke characters), and with 2-dimensional representations of the Galois group of a number field (Artin L-functions). # Sometimes an L-function may arise from more than one source. For example, the L-functions associated with elliptic curves are also associated with weight 2 cusp forms. A goal of the Langlands program ostensibly is to prove that any degree $d$ L-function is associated with an automorphic form on $\mathrm{GL}(d)$. Because of this representation theoretic genesis, one can associate an L-function not only to an automorphic representation but also to symmetric powers, or exterior powers of that representation, or to the tensor product of two representations (the Rankin-Selberg product of two L-functions).