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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1702482440879818018', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 541.0663240961961, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [7, [1, -1]], [11, [1]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '67760.1', 'coefficient_field': '1.1.1.1', 'conductor': 67760, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, -1], [1, -1], [1], [1, -4, 13], [1, 0, 17], [1, 4, 19], [1, 6, 23], [1, -6, 29], [1, -4, 31], [1, -2, 37], [1, -6, 41], [1, 4, 43], [1, 6, 47], [1, 6, 53], [1, 0, 59], [1, -10, 61], [1, 2, 67], [1, 12, 71], [1, 8, 73], [1, 16, 79], [1, 12, 83], [1, 18, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 66, 'label': '2-67760-1.1-c1-0-66', 'leading_term': '10.9694104928', '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/67760/cl', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.572167694329549, 4.136556050081158, 3.936278247103434, 2.109710191341776, -0.01346752617305056, -0.8073434989772661, 0.1015644534134539, 1.345495866870176, 1.29983575030719, 0.07344177623303715, -0.550090041269025, 0.4889832125408866, 1.819601581130342, 1.307043115465384, -0.7758955260163382, -1.728392061620714, -0.2962090697966751, 0.9103248000289238, -1.263745224495863, -5.491122684944744, -6.930696613279901, -3.826593457959749, -0.316318896411233, -0.6275692320600375, -2.896941940640177, -2.23667175266044, 1.366532671342293, 2.783756341736602, -0.2152776399278827, -3.439482294859848, -2.886301362924354, -0.4861888941257746, 0.1285288307807825, -0.2911366699346214, 0.7032212097720927, 1.683813380888603, 0.0127823260077978, -2.260469688659556, -1.421125759147555, 0.6988390837176179, -0.4331207146621979, -3.160986607871006, -1.76666260948142, 2.770048237862933, 3.449612477675604, -0.2490817713382732, -0.7323855066998572, 4.223851783457339, 6.957576713135474, 3.071149631234812, -1.348921616286152, -0.917027326481956, 0.719913614303767, -0.4966890580919849, -1.787255494628034, -0.6604871978915305, 0.0701613154046683, -0.6389670966018055, 0.5169786274484912, 3.042461451303042, 2.255917982674303, -0.7279417059217111, -0.2529308045357739, 1.93135371824331, -0.6777955450455785, -5.285966960115448, -3.516755032175394, 2.273549186410645, 2.67582881559064, -1.314487290490779, -1.426152455698015, 1.261578502152146, -0.03754014253174003, -2.952011808212304, -1.297984310918892, 1.714182318420474, 0.5879002910767642, -1.185405321698988, 0.3880979256590949, 1.292529692078093, -0.7825233163485551, -1.331016342662585, 0.3982293576382382, 0.2097616160109672, -0.4573003185697736, 1.79225014700369, 2.285258980508925, -2.157437895145084, -3.445377936798187, 2.438271776002223, 5.335396673900302, 0.2077301776847174, -2.940827162523104, 0.2802749552282538, 0.8710080891521684, -3.199892747157985, -3.175244351447706, 1.185750886468673, 1.960301425992754, -0.1501658516185366, 0.1462957432906072, 0.6350351871988485, -0.9145408116272543, -0.7808168127226413, 0.5675768898752087, -0.7253859111801753, -0.9004929687684962, 3.326911252514914, 4.570048775437402, -0.2812058701613136, -1.991422244664493, 1.469908308315295, 1.119811191250509, -1.619017909629299, 2.088275260236767, 6.706038611841431, 2.57646883788683, -3.174702660295532, -1.583689908505417, 1.081462198688137], 'positive_zeros': ['1.247993792531031', '1.731702976356409', '2.514823736831793', '2.917515075399314', '3.660215631225761', '4.287560011960981', '4.655259865210874', '5.808976488312877', '5.895943386976498', '6.658587827366405', '7.236900096483750', '8.086478921231426', '8.311143124746890', '8.622944266543043', '9.251166048764284', '9.894621835898396', '10.20986219033638', '10.84733072338185', '11.48239949160913', '11.80144605379231', '12.64659582130093', '13.10514163641393', '13.43843267252598', '14.13665146007478', '14.28597238743858', '14.69392109082797', '15.42597798685401', '15.77430437721554', '16.21540330427209', '16.89374220911968', '17.41233032272910', '17.86874524342565', '18.24724073986003', '18.83663771148280', '19.30568551820770', '19.70789526485026'], 'prelabel': '2-67760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.260832403338366, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1702482440879818018, 'z1': {'__RealLiteral__': 0, 'data': '1.247993792531031', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.731702976356409', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.514823736831793', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 541.0663240961961, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 67760, 'conductor_radical': 770, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 4, 0, 2, 0, 0, 0, -4, 0, 2, 0, -6, 0, 1, 0, -4, 0, 6, 0, 4, 0, 0, 0, 1, 0, 2, 0, 8, 0, 6, 0, -4, 0, 1, 0, -6, 0, 1, 0, 0, 0, -6, 0, 0, 0, -8, 0, 0, 0, 10, 0, 1, 0, 4, 0, -2, 0, -12, 0, -12, 0, -8, 0, 2, 0, 0, 0, -16, 0, -11, 0, -12, 0, 0, 0, 12, 0, -18, 0, 4, 0, 8, 0, -4, 0, -10, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -6, 29], 'euler3': [1, -2, 3], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 6, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -10, 61], 'euler67': [1, 2, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, 8, 73], 'euler79': [1, 16, 79], 'euler83': [1, 12, 83], 'euler89': [1, 18, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -4, 13], [1, 0, 17], [1, 4, 19], [1, 6, 23], [1, -6, 29], [1, -4, 31], [1, -2, 37], [1, -6, 41], [1, 4, 43], [1, 6, 47], [1, 6, 53], [1, 0, 59], [1, -10, 61], [1, 2, 67], [1, 12, 71], [1, 8, 73], [1, 16, 79], [1, 12, 83], [1, 18, 89], [1, 10, 97]], 'index': 66, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/67760/cl'], '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': '2-67760-1.1-c1-0-66', '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': '2-67760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.260832403338366, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1702482440879818018, 'z1': {'__RealLiteral__': 0, 'data': '1.247993792531031', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1702482440879818018', 'Lhash_array': ['1702482440879818018'], 'label': '2-67760-1.1-c1-0-66', 'type': 'ECQ', 'url': 'EllipticCurve/Q/67760/cl'}