{'Lhash': '2161731218226120303198243862722,2715880005470432333410084310488', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 189.72842995495665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 1]], [5, [1]], [23, [1, -2, 1]]], 'bad_primes': [3, 5, 23], 'central_character': '1725.1', 'coefficient_field': '1.1.1.1', 'conductor': 2975625, 'conductor_radical': 345, 'degree': 4, 'euler_factors': [[1, 0, 2, 0, 4], [1, -2, 1], [1], [1, -2, 7, -14, 49], [1, 8, 36, 88, 121], [1, 4, 28, 52, 169], [1, 2, -15, 34, 289], [1, 4, 24, 76, 361], [1, -2, 1], [1, 10, 81, 290, 841], [1, 14, 103, 434, 961], [1, 6, 83, 222, 1369], [1, 18, 161, 738, 1681], [1, 12, 122, 516, 1849], [1, -20, 192, -940, 2209], [1, 6, 97, 318, 2809], [1, -6, 29, -354, 3481], [1, -8, 136, -488, 3721], [1, -6, 71, -402, 4489], [1, 2, 45, 142, 5041], [1, -12, 164, -876, 5329], [1, 8, 46, 632, 6241], [1, 14, 165, 1162, 6889], [1, 8, -6, 712, 7921], [1, -8, 202, -776, 9409], [1, 6, -31, 606, 10201], [1, -4, 202, -412, 10609], [1, -6, 221, -642, 11449], [1, -20, 300, -2180, 11881], [1, -18, 305, -2034, 12769]], 'euler_factors_factorization': [[[[1, 0, 2, 0, 4], 1]], [[[1, -1], 2]], [1], [[[1, -2, 7, -14, 49], 1]], [[[1, 8, 36, 88, 121], 1]], [[[1, 4, 28, 52, 169], 1]], [[[1, 2, -15, 34, 289], 1]], [[[1, 4, 24, 76, 361], 1]], [[[1, -1], 2]], [[[1, 10, 81, 290, 841], 1]], [[[1, 14, 103, 434, 961], 1]], [[[1, 3, 37], 2]], [[[1, 18, 161, 738, 1681], 1]], [[[1, 6, 43], 2]], [[[1, -20, 192, -940, 2209], 1]], [[[1, 6, 97, 318, 2809], 1]], [[[1, -6, 29, -354, 3481], 1]], [[[1, -8, 136, -488, 3721], 1]], [[[1, -6, 71, -402, 4489], 1]], [[[1, 2, 45, 142, 5041], 1]], [[[1, -12, 164, -876, 5329], 1]], [[[1, 8, 46, 632, 6241], 1]], [[[1, 14, 165, 1162, 6889], 1]], [[[1, 8, -6, 712, 7921], 1]], [[[1, -8, 202, -776, 9409], 1]], [[[1, 6, -31, 606, 10201], 1]], [[[1, -4, 202, -412, 10609], 1]], [[[1, -6, 221, -642, 11449], 1]], [[[1, -20, 300, -2180, 11881], 1]], [[[1, -18, 305, -2034, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'id': 20363398, 'index': 21, 'label': '4-1725e2-1.1-c1e2-0-21', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/1725/2/a/z', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [-7.666710897830352e-120, 0.006159814340733857, 0.024640496729438934, 0.055445364188849766, 0.09857756000512155, 0.15403808085146847, 0.22181997887879262, 0.30190597468646313, 0.3942585077891125, 0.49881806559014213, 0.6154888487829319, 0.7441388298051737, 0.8845812250201132, 1.0365771113339752, 1.1998133415985246, 1.3739083171181392, 1.5583874116453476, 1.7526922391555733, 1.9561550330954423, 2.168011476331368, 2.3873757891457537, 2.6132569091990634, 2.8445362532224774, 3.079986752445048, 3.318255353698636, 3.5578841315789935, 3.797299574494765, 4.034834711382643, 4.268727081499962, 4.497140536667321, 4.718173519537754, 4.929878942809013, 5.130284004009707, 5.317406316952846, 5.489285982998378, 5.643995978037554, 5.779686599558745, 5.894588018788477, 5.987066556885795, 6.055617321706817, 6.098931070704829, 6.115874988576005, 6.10556821219843, 6.067349087751117, 6.000856813299515, 5.905983952448458, 5.782961144812736, 5.632294247554555, 5.454848723723888, 5.251771519590858, 5.024571610754542, 4.775027573760186, 4.5052608843197985, 4.217631063056475, 3.9147986979526355, 3.5996109790403867, 3.2751520572894197, 2.944622663241476, 2.6113762931249758, 2.278797356298121, 1.9503227484284578, 1.6293235151531642, 1.3191125603644025, 1.022835076932601, 0.7434643541153061, 0.4837061513351977, 0.24598570682171242, 0.03237077811732947, -0.15544609758729702, -0.3162020147710599, -0.44908148658975233, -0.5537456391838135, -0.630345085708831, -0.6795227633416054, -0.7024171330917237, -0.7006392742386165, -0.6762623372570148, -0.6317753708520641, -0.5700561202697166, -0.49430588221571037, -0.40800432021007926, -0.3148312625370218, -0.2186040892582065, -0.12319364715249786, -0.03244679453947522, 0.04989564134905682, 0.12028658441956185, 0.17544465602212364, 0.2124458396110393, 0.22877784135584472, 0.22242809205280745, 0.19191430172289392, 0.13636054598418354, 0.05549971277446565, -0.05027044152723403, -0.17991481161875472, -0.3317320329784608, -0.5034110467457665, -0.6920345934144269, -0.8941610297984848, -1.105862861748659, -1.3228273315592711, -1.5404294191040082, -1.753842500790285, -1.9581417254091185, -2.1484145678094677, -2.3198869732186287, -2.468023109223413, -2.58866353334387, -2.678104026920096, -2.733232638097187, -2.751579200697069, -2.7314367617635287, -2.671876170621567, -2.5728373610198254, -2.435107042514041, -2.260366702144598, -2.0511356317231657, -1.8107653324633202, -1.5433544668952135, -1.2536834274203146, -0.9471118536400995, -0.629452146211859, -0.30686347120870866, 0.014331484229982915, 0.3277400179851501, 0.6271296523660352, 0.9064926045300388, 1.1603084262224341, 1.383564085169113, 1.5720307820783739, 1.7222272431845993, 1.8316905500310063, 1.8988747875317091, 1.9233958039814247, 1.9058631295224884, 1.8480808263714632, 1.7528170538605983, 1.623947476622754, 1.4661733428284651, 1.2850999535387044, 1.0869199172518822, 0.8784263855878747, 0.666682543257047, 0.4589769453393821, 0.26250269115907915, 0.08426941327849168, -0.06918445919975007, -0.19190256745674372, -0.2787445191105041, -0.32549521870984244, -0.3290293276764716, -0.2873933930743465, -0.19989252015613634, -0.06712129942332805, 0.10902701633027809, 0.3254002010379656, 0.5776459500272402, 0.8603344661071587, 1.167067419415053, 1.4906867381366524, 1.82340864469767, 2.157112126079461, 2.483468613570675, 2.7942940682394437, 3.0816436667940863, 3.3382033838106024, 3.5573214399850284, 3.733409778810489, 3.861889971840139, 3.939572904944329, 3.964505826088409, 3.9363003280797, 3.8558783651848403, 3.7257242339815, 3.549539444580718, 3.332403350265154, 3.080358307359865, 2.800474911624671, 2.5003984556728764, 2.188327045185403, 1.8725566527998243, 1.5613921356328586, 1.262730207483308, 0.9839329542322196, 0.7314852984714352, 0.5108665839414902, 0.32631166233906594, 0.1807174491421957, 0.07552530392673171, 0.010695658824631188, -0.015284864300243171, -0.005336410800136792, 0.03633408882003241, 0.1044038665310883, 0.19264081743046302, 0.29417439127809214, 0.4017505678814408, 0.5080826519282047, 0.6061094442669818, 0.6893914047616779, 0.7523251610680798, 0.7905397723738098, 0.8010252986419457, 0.7824787694762929, 0.7353149816225916, 0.66191347681255, 0.5664949281568064, 0.4552293514513975, 0.33597954422450665, 0.2182463365985781, 0.11279920174957152, 0.031455081951841005, -0.013367094938547727, -0.00901393753725739, 0.05692966068136299, 0.1961701728390499, 0.4192598057733449, 0.7350870650291542, 1.1505103781312682, 1.6698873575822486, 2.2948295459673322, 3.0238536771616036, 3.8522819649690954, 4.772094246592538, 5.771975560513941, 6.837433511037919, 7.9509697892748825, 9.092503539710586, 10.239619337921553, 11.368307135975629, 12.453219512509518, 13.468705301521352, 14.388996812781112, 15.189481507800451, 15.846737676968523, 16.33996063957344, 16.650774193465598, 16.764708484159296, 16.670734118918567, 16.36268083657831, 15.838469721806954, 15.101366522270743, 14.158921794335704, 13.023969962921194, 11.71332336629598, 10.24845609474161, 8.654031175715838, 6.958243554409635, 5.19128557486798, 3.3853618024138283, 1.5732127414780899, -0.21214934075589878, -1.9387373535020966, -3.5760535618286524, -5.096099337507619, -6.473941078161204, -7.688351545548489, -8.722373138064519, -9.5635466949034, -10.204375569328855, -10.64214098931972, -10.879191060218572, -10.922385768650207, -10.783165654867265, -10.476708744934822, -10.021769828029178, -9.439660923265194, -8.753888693078245, -7.989085636163507, -7.170504881162604, -6.323029073468366, -5.470604006490679, -4.635436183027499, -3.837456192771019, -3.0937863796624985, -2.418320162906731, -1.8215022154715963, -1.3100917500891587, -0.8872545292177904, -0.5525492241007618, -0.30228942653402024, -0.12975691365030023, -0.025758326408626117, 0.020967079090106717, 0.02309269079376751, -0.005833637587596818, -0.052039541619178876, -0.10211059733222504, -0.143541985541677, -0.1652700211024885, -0.15805518707507915, -0.11487307469022005, -0.03109160009892307, 0.09534896178469478, 0.2639639581143793, 0.471795294562291, 0.7136075453657841, 0.9822134359016639, 1.2687716873813242, 1.5633335927901653, 1.85515860674933, 2.133416822318527, 2.3874351720844436, 2.607469190903976, 2.784804385285564, 2.912502967107256, 2.985309449238464, 3.0002852647470566, 2.956500832868728, 2.8554919205645763, 2.7007567280944462, 2.497999033191764, 2.2544821648109727, 1.979060212864261, 1.6814654548361994, 1.3721641647427645, 1.061665905260126, 0.7602688104598054, 0.47747606867595166, 0.22171220085145546, -8.5533283901282e-05, -0.1826962060908969, -0.32281034851403023, -0.41913343991104757, -0.4723648787290364, -0.4851303126260518, -0.46177815219163115, -0.4081286754806855, -0.33115239875981556, -0.23855960074766847, -0.1384443235069852, -0.038769427022931374, 0.052935212226123074, 0.13011558558375405, 0.18736344131749688, 0.2209033131736791, 0.228577513396424, 0.21020205112616983, 0.1673480850480703, 0.10351464534866275, 0.023725779593640202, -0.06549808208499293, -0.15667347096183276, -0.24156329586407016, -0.31176196340204326, -0.35902847212679484, -0.3758341750867234, -0.35573498075396837, -0.2937989562572681, -0.18692009306449045, -0.034065307943790535, 0.16356325951332368, 0.4024875991344939, 0.6770141511106146, 0.9793843239314961, 1.3000926225328393, 1.628173412549947, 1.951768010723993, 2.258461755803048, 2.536046841360475, 2.772807627909523, 2.958389394342651, 3.083932268457777, 3.142934265624687, 3.131155613985151, 3.047362044696438, 2.892958537958629, 2.6725170705860064, 2.3931457336342623, 2.064741536392216, 1.6991492031915851, 1.310128245543469, 0.9123966524966298, 0.5213538440835872, 0.15213001142123192, -0.1808467316827717, -0.4646698727369464, -0.688422670011325, -0.8437590009562993, -0.9252752861482209, -0.9307835216597633, -0.8614683079297777, -0.7218356894720419, -0.5195721654307212, -0.26521108130083226, 0.028337017352346932, 0.3463056171321461, 0.672840794204638, 0.9915771468104462, 1.2866181812109847, 1.543018522773161, 1.7478456523546728, 1.8904308715500133, 1.9633612740223967, 1.9623983231474469, 1.8872560669353153, 1.7411423944208997, 1.5312144641833565, 1.2677641599152105, 0.9642993937936547, 0.6364600775323281, 0.30174478464717275, -0.021705437509869283, -0.3156441402319454, -0.5629033843641517, -0.7480449087841543, -0.8583502390638635, -0.8844018953461874, -0.8207519138562154, -0.6662466620093669, -0.42430564804385734, -0.10283538915169096, 0.2858740228775795, 0.7257384072261349, 1.1972796326379713, 1.678728193235347, 2.146568547378268, 2.5770753214429933, 2.9468115557218315, 3.234439218289339, 3.4209715003292454, 3.491642734859492, 3.4357467050126567, 3.2483309418504693, 2.929517616835427, 2.4858077920253923, 1.9288698422330477, 1.27629863136545, 0.5499536491346652, -0.2238927618329548, -1.0164965383003794, -1.7970664281194177, -2.534749536440416, -3.1994895996254358, -3.7637960743689396, -4.203817850164513, -4.500653382209693, -4.641378907867955, -4.6197187181989605, -4.4367700293896, -4.1009482987496515, -3.628200832096591, -3.041256555887042, -2.3692099173383085, -1.6462182510603192, -0.9104518519206293, -0.20247497933358377, 0.43632253146912103, 0.9653695052443815, 1.346781532587594, 1.5467328584450049, 1.5373372434848553, 1.2974944932134114, 0.8144773886245287, 0.08408883698832142, -0.8883180071466262, -2.088417304995929, -3.4926471403785553, -5.069439140955885, -6.779782854198914, -8.578909961682418, -10.417622583420536, -12.244153566465869, -14.006067127714795, -15.651984293560874, -17.13376593829708, -18.407815099764402, -19.437200887838337, -20.19232370560512, -20.65264299042827, -20.80660459755022, -20.652695368127652, -20.19866419626261, -19.46173166423349, -18.46726411000787, -17.248098716289444, -15.842930348480186, -14.294848531863174, -12.649751877765647, -10.954309822320496, -9.254719189170032, -7.594380652314775, -6.013256491381819, -4.545577090818454, -3.21995833773925, -2.057424243542404, -1.0723149969178078, -0.27083514943733905, 0.3473479135614265, 0.7899292679930449, 1.0698891775214643, 1.2057099048233961, 1.2191036194079017, 1.1347466253362664, 0.9781157517187586, 0.7749404204518088, 0.5494212987554096, 0.3236368839381828, 0.11632564983230162, -0.05754384864917732, -0.1873176063431439, -0.2667502633096964, -0.2939905138286332, -0.27126713859615365, -0.20429104870246137, -0.10174929098743853, 0.02546911664843165, 0.16611300775418542, 0.3085418911501225, 0.4375688834397556, 0.5408064664821783], 'positive_zeros': ['1.70530524565437787637489128732181', '2.14245155958705174456577634756774', '2.37537801167682862457734294859286', '3.14729512317652580446090893469211', '3.72039850382617311422326187904931', '3.92056572605140958354773963068232', '4.83103720978379443368330709331261', '4.87959848517060035731484401519593', '5.39765946907930750581724106742246', '5.43929502302073579110953200378297', '6.39538505541761392491487348212175', '7.19613985301677964012109823596798', '7.25787082802819912520353331785391', '7.44656605637553718094564083987867', '8.150379883685608462634338921737364', '8.440044341229474346276289930110273', '8.665138946810729755189058956117733', '8.916918028928612182005946049004035'], 'prelabel': '4-1725e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.7113601750127776, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 114769867642866232, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70530524565437787637489128732', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14245155958705174456577634757', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.37537801167682862457734294859', 'prec': 103}}