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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': -4, 'A8': 1, 'A9': 1, 'Lhash': '1182356361169072453', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2463.7841543666073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [11, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '308550.1', 'coefficient_field': '1.1.1.1', 'conductor': 308550, 'conductor_radical': 5610, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1, 4, 7], [1], [1, 2, 13], [1, -1], [1, -4, 19], [1, -4, 23], [1, 2, 29], [1, -4, 31], [1, -6, 37], [1, 2, 41], [1, 12, 43], [1, 8, 47], [1, -2, 53], [1, -12, 59], [1, 2, 61], [1, 4, 67], [1, 4, 71], [1, 14, 73], [1, -12, 79], [1, 4, 83], [1, -10, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 188, 'label': '2-308550-1.1-c1-0-188', 'leading_term': '13.3835447714', '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/308550/hy', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.932787844977183, 3.643871928431152, 1.367444150524901, -2.005165577191722, -3.08760085388136, -0.6090752923525585, 2.683911736647704, 3.114173184967696, 0.7244078725371873, -1.051359797646479, -0.4565265801973786, 0.5000167985456161, 0.1192820934011006, 0.014416928267519, 1.532214278319752, 2.318109969285404, 0.3231457494022339, -1.603095875531346, -0.1393053051138575, 2.129249508682877, 0.9486361807421315, -1.532247756015671, -0.4442544628221686, 2.476644726675653, 2.029545721339293, -0.4736130030479448, -0.2663309364145591, 0.8966757479556718, -1.115099923915192, -2.866083837959226, 0.07803419016113414, 2.371313445917325, -1.693607756830049, -5.640810458374405, -2.265816601467092, 2.269983234789676, 0.6161255744902696, -2.03256132928832, -0.3864915420842398, 0.35360932612414, -1.577270422117517, 1.105591151253635, 7.335581183635002, 6.431113721616531, -0.7369302274094832, -2.75808391553538, 0.3560381825413137, -0.05618630958267537, -2.434181016935443, -0.7941990861194785, 1.470888076539967, 0.5442220748556609, -0.06438236042061395, 0.0920638948307453, -2.07958773492748, -3.22437776716747, -0.4311538402448758, 0.9191563747680374, -0.738565922604438, 0.05895219135337481, 1.82157303627424, -0.06503327123056678, -0.9534081035331349, 1.737035974901753, 1.470589064822589, -0.7884040894841243, 0.8559820102301787, -0.893837929316063, -10.37051791438996, -12.19949441150797, -1.386239006568308, 3.055000939287932, -3.618996812599072, -4.315388760204847, 2.145056208630303, 2.780306562176463, 0.06838523056667052, 0.8145784396234994, -0.0009786595494975755, -2.440175329510406, -0.809995081778699, 0.1979707517637997, -2.366433947756477, -1.066939156104875, 2.545321557411203, 0.6452472025143607, -1.906116361498367, -0.2647923409911686, -0.2568926990153964, -1.367297496051438, 0.9024904787991169, 1.377662809623779, -0.8170155339904323, 0.8670338020567068, 1.724306561537007, -3.227217014372106, -4.538847280430861, -0.1439109196700871, 0.6603510943890442, -0.05658680925470771, 2.004958035868779, 1.001559651205168, -0.9760712262154803, 1.688479911937146, 1.716869033988388, -1.557021014272206, 0.1640856763792159, -0.822666182103945, -8.405976694043403, -5.120258868597187, 7.187866756960131, 6.075441879881362, -2.84379107647725, -1.993191748453279, 0.4436236382190336, -2.02385658999846, -0.6403431427231429, 1.316248206958294, -1.069295304655566, -0.03238122658540786], 'positive_zeros': ['0.8472261654805984', '1.541648415603211', '2.321557594283138', '2.840211992530428', '3.296042986335967', '3.495329187798864', '4.279246918841512', '4.762437903209292', '5.330972762888235', '5.785818981153463', '6.440031527504028', '6.789469178823930', '7.153748059696795', '7.745358945094685', '8.176018660565795', '8.847777095174908', '9.290557526671685', '9.792099107318150', '10.05022914953082', '10.44957769077811', '11.22152224917959', '11.71607633483775', '11.99477324327735', '12.56312712476000', '13.11552248560319', '13.28525188100524', '13.52263395409507', '14.28529131170684', '14.64079768813715', '14.99381493719103', '15.49401035214057', '15.85076857637149', '16.37937435449548', '16.66132375660641', '16.96290008555562', '17.78301678647068', '18.12891236417096', '18.66191522706327', '19.27338265781952', '19.32604838030156', '19.74991176500832'], 'prelabel': '2-308550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 49.63652036924634, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1182356361169072453, 'z1': {'__RealLiteral__': 0, 'data': '0.8472261654805984', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.541648415603211', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.321557594283138', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2463.7841543666073, 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '1.1', 'conductor': 308550, 'conductor_radical': 5610, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, -4, 1, 1, 0, 0, 1, -2, -4, 0, 1, 1, 1, 4, 0, -4, 0, 4, 1, 0, -2, 1, -4, -2, 0, 4, 1, 0, 1, 0, 1, 6, 4, -2, 0, -2, -4, -12, 0, 0, 4, -8, 1, 9, 0, 1, -2, 2, 1, 0, -4, 4, -2, 12, 0, -2, 4, -4, 1, 0, 0, -4, 1, 4, 0, -4, 1, -14, 6, 0, 4, 0, -2, 12, 0, 1, -2, -4, -4, 0, -12, -2, 0, 10, 0, 8, 4, 4, -8, 0, 1, -18, 9, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, -1, 0], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 12, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, -12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 4, 71], 'euler73': [1, 14, 73], 'euler79': [1, -12, 79], 'euler83': [1, 4, 83], 'euler89': [1, -10, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, 4, 7], [1, 0, 0], [1, 2, 13], [1, -1, 0], [1, -4, 19], [1, -4, 23], [1, 2, 29], [1, -4, 31], [1, -6, 37], [1, 2, 41], [1, 12, 43], [1, 8, 47], [1, -2, 53], [1, -12, 59], [1, 2, 61], [1, 4, 67], [1, 4, 71], [1, 14, 73], [1, -12, 79], [1, 4, 83], [1, -10, 89], [1, 18, 97]], 'index': 188, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/308550/hy'], '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': '2-308550-1.1-c1-0-188', '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': '2-308550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 49.63652036924634, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1182356361169072453, 'z1': {'__RealLiteral__': 0, 'data': '0.8472261654805984', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1182356361169072453', 'Lhash_array': ['1182356361169072453'], 'label': '2-308550-1.1-c1-0-188', 'type': 'ECQ', 'url': 'EllipticCurve/Q/308550/hy'}