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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': '1034424770350859001', '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': 1079.8968369357965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [7, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '135240.1', 'coefficient_field': '1.1.1.1', 'conductor': 135240, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1], [1, 2, 11], [1, 0, 13], [1, 7, 17], [1, 4, 19], [1, -1], [1, -9, 29], [1, -9, 31], [1, -3, 37], [1, 2, 41], [1, 1, 43], [1, -8, 47], [1, -9, 53], [1, -13, 59], [1, 2, 61], [1, -16, 67], [1, 5, 71], [1, -6, 73], [1, 12, 79], [1, 11, 83], [1, -16, 89], [1, -9, 97]], 'gamma_factors': [[], [0]], 'index': 32, 'label': '2-135240-1.1-c1-0-32', 'leading_term': '2.03756807608', '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': 0, 'origin': 'EllipticCurve/Q/135240/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.037568076081794, 1.4322445868466, 0.06108014053727784, -0.8645927326545665, -0.149436093388767, 2.022936262437984, 3.736738720049471, 3.161417456772761, 0.9044933961196473, -0.3409915956252872, 0.7642287356505393, 1.943264643823936, 0.02290842660321799, -4.271130361079617, -6.400188288411658, -3.874460481465613, 0.1164776370363474, 1.073719947116711, -0.5577369799500441, -0.818513150640255, 0.9826928310046231, 1.336511357797068, -1.007604672767382, -2.514370483431057, -0.977866478375728, 0.6158725752319971, -0.2457784519781228, -0.8424499286292771, 1.14748386965807, 1.980729988136398, -1.885512102336042, -6.123149885712632, -4.791292097791119, -0.5721170191122222, 0.03221624096340178, -1.62348965622075, 0.4300602872607682, 4.645789201119507, 4.343908885845734, 0.2370539385969449, -1.092346197521721, 0.5947682729320712, 0.3236302851223721, -1.128190760753859, 0.4983051253025674, 2.903929201200285, 1.613744644866976, -0.1200531930729116, 2.226041888496405, 4.478294506606332, 1.95678176177057, -0.8510802075652582, 0.2077390355570449, 0.6264216154991235, -1.902852598303659, -1.811968222512753, 1.239902969845977, -0.2992249360322408, -5.774022030253701, -5.794407651124956, -0.5474485469573757, 0.9078922828559599, -1.330251353502194, -0.6388961845805126, 0.6630992917717095, -2.310887706579126, -4.4743243180675, -1.255735346144096, 1.52343634525641, 0.3749528953586896, 0.1469188800966218, 1.179504642872267, -0.7012567322357502, -2.218070859971348, 0.3719349173037769, 0.9581989176511855, -3.022880043538812, -3.22297720858829, 1.292684881630592, 1.06847582358904, -2.654650363051934, -0.4730037355179376, 3.822639017162958, 1.454986074827757, -2.387045689024108, -1.1189505155779, -0.09729550088754706, -1.607384180055337, 0.003631025877480097, 2.621740332072768, 0.6298010324697536, -1.022118193191514, 1.551823048066217, 2.02239737137418, -0.1510388135687457, 1.515494198982966, 3.605350663075579, 0.595603022350311, -1.093573277254403, 1.471764307012782, 0.5301211274923527, -2.495101961035154, 0.4348963647534231, 3.593397966637978, 0.01196039683891093, -2.117866988499368, 0.9646692089947624, 0.636953745348011, -2.108855166697768, 0.03178808782772741, 1.242144266972812, -3.32237014573545, -4.698234370637108, -0.5968890135307978, 0.7065374452703005, -0.1901426203299888, 0.4852823840645655, -1.336461709088829, -3.910357976119908, -0.9693033867289952, 1.712860974187222], 'positive_zeros': ['0.5110543728525842', '1.021817238465977', '2.123747860204861', '2.378817681678059', '3.001553176115109', '3.990304527592979', '4.419943259687604', '4.874205240834621', '5.408242831773188', '6.113525763723797', '6.458385314539190', '6.882300863632449', '7.406810351447750', '8.306206377324069', '8.505024942730983', '8.973721292087195', '9.767027201431869', '10.16198497479825', '10.54521293452773', '10.95712746176480', '11.68375922011136', '11.79498200514218', '12.63574925850562', '12.97251436826656', '13.32528721866358', '13.88971758814345', '14.23410971894063', '15.03240244419478', '15.35214851275888', '15.82077521913979', '16.09298223702316', '16.82580080857728', '17.32403170810330', '17.46400821212581', '17.93852342775870', '18.47053573316952', '18.82311677186943', '19.42360988302781', '19.81515547930874'], 'prelabel': '2-135240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.861783836788234, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1034424770350859001, 'z1': {'__RealLiteral__': 0, 'data': '0.5110543728525842', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.021817238465977', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.123747860204861', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1079.8968369357965, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 135240, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -1, 0, -7, 0, -4, 0, 0, 0, 1, 0, 1, 0, -1, 0, 9, 0, 9, 0, 2, 0, 0, 0, 3, 0, 0, 0, -2, 0, -1, 0, 1, 0, 8, 0, 0, 0, 7, 0, 9, 0, -2, 0, 4, 0, 13, 0, -2, 0, 0, 0, 0, 0, 16, 0, -1, 0, -5, 0, 6, 0, -1, 0, 0, 0, -12, 0, 1, 0, -11, 0, -7, 0, -9, 0, 16, 0, 0, 0, -9, 0, -4, 0, 9, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 0, 13], 'euler17': [1, 7, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -9, 29], 'euler3': [1, 1, 0], 'euler31': [1, -9, 31], 'euler37': [1, -3, 37], 'euler41': [1, 2, 41], 'euler43': [1, 1, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -9, 53], 'euler59': [1, -13, 59], 'euler61': [1, 2, 61], 'euler67': [1, -16, 67], 'euler7': [1, 0, 0], 'euler71': [1, 5, 71], 'euler73': [1, -6, 73], 'euler79': [1, 12, 79], 'euler83': [1, 11, 83], 'euler89': [1, -16, 89], 'euler97': [1, -9, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 0, 0], [1, 2, 11], [1, 0, 13], [1, 7, 17], [1, 4, 19], [1, -1, 0], [1, -9, 29], [1, -9, 31], [1, -3, 37], [1, 2, 41], [1, 1, 43], [1, -8, 47], [1, -9, 53], [1, -13, 59], [1, 2, 61], [1, -16, 67], [1, 5, 71], [1, -6, 73], [1, 12, 79], [1, 11, 83], [1, -16, 89], [1, -9, 97]], 'index': 32, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/135240/x'], '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': '2-135240-1.1-c1-0-32', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-135240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.861783836788234, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1034424770350859001, 'z1': {'__RealLiteral__': 0, 'data': '0.5110543728525842', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1034424770350859001', 'Lhash_array': ['1034424770350859001'], 'label': '2-135240-1.1-c1-0-32', 'type': 'ECQ', 'url': 'EllipticCurve/Q/135240/x'}