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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1331871958799111836', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1032.9448005472836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [7, [1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '129360.1', 'coefficient_field': '1.1.1.1', 'conductor': 129360, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1], [1, -1], [1, 1, 13], [1, 0, 17], [1, 2, 19], [1, -9, 23], [1, 9, 29], [1, 8, 31], [1, -2, 37], [1, -3, 41], [1, -1, 43], [1, 9, 47], [1, -9, 53], [1, 12, 59], [1, 10, 61], [1, -4, 67], [1, 6, 71], [1, -2, 73], [1, -16, 79], [1, 12, 83], [1, 18, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 106, 'label': '2-129360-1.1-c1-0-106', 'leading_term': '4.81557836713', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/129360/br', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.023943293078047, 1.078069999040118, -0.16653865805283, -1.806876833079234, -2.159454831281664, -0.5558155477070269, 1.343006789743832, 0.919111886230784, -2.164941935787275, -4.878198934695234, -4.144764621580041, -0.9259516239916078, 0.7017482607185198, -1.042256524941393, -3.166351496063229, -2.348411206170517, 0.04978464203399332, 0.2397437415476208, -1.807169166278417, -2.340328724873402, -0.2719263282221231, 0.8329560796293943, -0.9575161370994552, -2.199830003619975, 0.01889315488772099, 2.644201833734595, 1.808951359619604, -0.3425361892374666, 0.1289395375151643, 1.276554816470525, -0.9596668299672722, -4.021643382156502, -2.33814472634229, 2.151122336212414, 2.603523093076193, -0.6904357791028741, -1.302636368712288, 0.8806452728982646, -0.3199706766114529, -4.754164623176093, -5.464685812130671, -1.531308174407588, 0.7733303882271167, 0.02537936443568608, 0.5662084624396554, 1.990624463797413, 0.2979046987119062, -2.264396725586143, -1.01878006982715, 1.185260459056572, 0.015395146992085, -0.8387890394446058, 1.697707596913919, 1.54364308497323, -4.292549203991939, -7.243787584111029, -2.539326259546895, 1.607812118961224, 0.02735571296395336, -1.122014631388265, 0.5631226693044677, -0.8123879707562212, -4.592884663578883, -3.638067183448073, 0.4617073336048958, 0.8873226685462843, -0.557505752812192, 0.09384360218000327, -0.9611202324250296, -4.857591432874937, -4.808793382156306, -0.6250626080396192, 0.1127633326354571, -1.627814024106619, 0.4392496123185556, 2.622734162057625, -0.146790120649696, -1.932921797677912, 0.3672144551038422, -0.7822494584808839, -5.542914310488998, -4.723034638705508, -0.2138501534312201, -1.054400517857987, -3.595421898720509, -0.9750624890338299, 0.9875134869847538, -1.948764523194646, -2.721111989944824, 0.1837017860117525, 0.3442426869805134, -0.6873961336872821, 1.20731723249218, 1.289971460037518, -1.708987365112496, -1.160008341292156, 1.168372845368891, -0.8596053485343773, -1.988517094272976, 1.416312041982752, 0.5007741028444087, -5.200176765769582, -4.478969811192801, 0.4433479648164325, -0.892559257534501, -3.447306467963957, 0.210488251463002, 2.746323176020208, 0.3629733653723462, 0.04568578031470567, 1.167757372300182, -0.4677107112782799, 0.4071234154992431, 4.454516618728824, 3.493332563439048, -0.2927279188172712, 0.2713895861909408, 0.7486137826508567, -0.9989843240703102, 1.971227603466612], 'positive_zeros': ['0.7251315502423034', '1.562425734679257', '2.091134374989174', '3.085312170732294', '3.394123280608540', '4.243132604608045', '4.537667838438320', '5.280380975450115', '5.646874366128861', '6.248580540651332', '6.942425478130578', '7.230105607209640', '7.680753280615828', '8.373872837359636', '8.945710513239769', '9.392620626548646', '9.727663355378745', '10.61081198870670', '11.00918181818343', '11.13866157997573', '11.77337400924283', '12.33890355159114', '12.75180396397433', '13.10458683347545', '13.58228594358913', '14.36178445255614', '14.75253081112168', '15.16277699108316', '15.43755519266202', '16.21423556059223', '16.62429323259429', '16.97325686273557', '17.14693067798409', '18.05330060599733', '18.26539131950629', '18.71900471814889', '19.24038423301289', '19.70894420883710', '19.94782785185466'], 'prelabel': '2-129360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.13945862249835, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1331871958799111836, 'z1': {'__RealLiteral__': 0, 'data': '0.7251315502423034', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.562425734679257', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.091134374989174', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1032.9448005472836, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 129360, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 9, 0, 1, 0, -1, 0, -9, 0, -8, 0, -1, 0, 0, 0, 2, 0, 1, 0, 3, 0, 1, 0, -1, 0, -9, 0, 0, 0, 0, 0, 9, 0, -1, 0, 2, 0, -12, 0, -10, 0, 0, 0, 1, 0, 4, 0, -9, 0, -6, 0, 2, 0, -1, 0, 0, 0, 16, 0, 1, 0, -12, 0, 0, 0, 9, 0, -18, 0, 0, 0, 8, 0, 2, 0, 8, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 1, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -9, 23], 'euler29': [1, 9, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -3, 41], 'euler43': [1, -1, 43], 'euler47': [1, 9, 47], 'euler5': [1, 1, 0], 'euler53': [1, -9, 53], 'euler59': [1, 12, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 6, 71], 'euler73': [1, -2, 73], 'euler79': [1, -16, 79], 'euler83': [1, 12, 83], 'euler89': [1, 18, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 13], [1, 0, 17], [1, 2, 19], [1, -9, 23], [1, 9, 29], [1, 8, 31], [1, -2, 37], [1, -3, 41], [1, -1, 43], [1, 9, 47], [1, -9, 53], [1, 12, 59], [1, 10, 61], [1, -4, 67], [1, 6, 71], [1, -2, 73], [1, -16, 79], [1, 12, 83], [1, 18, 89], [1, -8, 97]], 'index': 106, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/129360/br'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-129360-1.1-c1-0-106', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-129360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.13945862249835, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1331871958799111836, 'z1': {'__RealLiteral__': 0, 'data': '0.7251315502423034', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1331871958799111836', 'Lhash_array': ['1331871958799111836'], 'label': '2-129360-1.1-c1-0-106', 'type': 'ECQ', 'url': 'EllipticCurve/Q/129360/br'}