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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '990535929305841913', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 737.8177146766311, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '92400.1', 'coefficient_field': '1.1.1.1', 'conductor': 92400, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 1], [1, 1], [1, 1, 13], [1, -5, 17], [1, -5, 19], [1, -8, 23], [1, 6, 29], [1, 8, 31], [1, -11, 37], [1, 5, 41], [1, -4, 43], [1, -4, 47], [1, -3, 53], [1, 14, 59], [1, 5, 61], [1, -3, 67], [1, -5, 71], [1, 11, 73], [1, 10, 79], [1, 0, 83], [1, 16, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 190, 'label': '2-92400-1.1-c1-0-190', 'leading_term': '8.60476890084', '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/92400/ep', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.968258353497814, 2.896688117589489, 2.19029126260288, 0.3750219929536122, -0.8939004398559108, -0.1965029605688753, 1.993675180006864, 3.454335472654705, 2.57344285307595, 0.3621817288236036, -0.6815840091266812, 0.1767112982781914, 0.9030931686001693, -0.2456422118866502, -1.7515352591021, -0.7730643900990104, 2.235961614420926, 3.369823728902527, 0.7681399384525663, -2.238966904611267, -1.861802709289539, 0.2630189231141172, -0.3804324998050407, -3.614124072740975, -4.275259585290162, -0.3883581058506882, 3.333082667818313, 2.74371924127263, 0.3673605891461905, 0.2325281544802843, 0.837261578410272, -1.227618419194157, -3.969126287651464, -2.983645069987115, 0.4123089724746885, 1.24653022349053, -0.3687992145878622, -0.2786092515593973, 1.044461237680517, -0.4927560179347398, -3.500269368060777, -2.573039748130141, 1.100227007663023, 0.9737574607311344, -2.531709406169668, -2.256280219295974, 2.180889069975168, 3.270669277711265, -0.4978502483424114, -2.328534303688729, -0.3094369046829616, 0.1229999093583928, -1.793778406389443, -0.9808226645259785, 2.002540350352111, 1.649811700980748, -0.9546455122424621, -0.4557692221677702, 1.510610306189491, 0.418837327736773, -0.7684223193540074, 1.798960763670704, 3.380060979280254, 0.07589918650995879, -2.377655931340981, -0.3003719262183656, 0.4937192756121405, -1.748969556781192, 0.1788736765093177, 6.351298484382857, 7.067499419663809, 1.306654342260608, -1.579001365664083, 0.003177636123433685, -0.2124050851792494, -1.18999963688274, 1.532859858120117, 3.788214699670163, 1.310997074582142, -0.8152393828718415, 0.2507513966554256, -0.5860940901830559, -3.186112729127697, -1.808213191318659, 0.8705580881606023, -0.9267539115497152, -2.49416918721766, 0.7054795247479311, 1.702118283295501, -2.57821031102639, -3.625135289443326, -0.0137546631130942, -0.265130180524277, -3.183823810817964, -0.9484898551821234, 2.328389450291256, -0.2415499027276617, -2.702227346899505, 0.02731517488309092, 1.543839146233099, -0.2578426864540551, 0.4095000366362135, 1.996458056404436, -0.03408334252160284, -0.9544959184175065, 1.829997286535601, 1.810398611330801, -0.8201583688791168, 0.4199014146895984, 1.664773083267341, -2.08745683025969, -2.790499931270087, 3.011632789684764, 4.677320567376001, 0.2496704817741213, -0.5339574689728968, 1.206777315724168, -1.076075468343316, -1.692571038398624, 3.015470991528965], 'positive_zeros': ['1.052372374163079', '1.527200199340632', '2.548806762312773', '2.964819188419492', '3.465940066365609', '4.069771343757917', '4.802306964664563', '5.458046787929301', '5.708694014466464', '6.519909886356769', '7.341242608700894', '7.419042781975679', '7.893704883772824', '8.715016920918117', '9.189853149442091', '9.546156774728265', '9.958796789669853', '10.66634062190583', '11.07306542661712', '11.63149503059246', '12.21975175229489', '12.78973819600895', '13.01986367343340', '13.57874720489109', '14.14534758603401', '14.54854590033056', '15.04751201852986', '15.36028454711797', '16.00444798778692', '16.52944495767102', '16.81277161790790', '17.24143999640698', '18.06277749943550', '18.49946085702631', '18.71489001299913', '19.14462512950501', '19.85261486487404'], 'prelabel': '2-92400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.16280019947559, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 990535929305841913, 'z1': {'__RealLiteral__': 0, 'data': '1.052372374163079', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.527200199340632', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.548806762312773', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 737.8177146766311, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 92400, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -1, 0, 1, 0, -1, 0, -1, 0, 0, 0, 5, 0, 5, 0, -1, 0, 8, 0, 0, 0, 1, 0, -6, 0, -8, 0, -1, 0, 0, 0, 11, 0, -1, 0, -5, 0, 4, 0, 0, 0, 4, 0, 1, 0, 5, 0, 3, 0, 0, 0, 5, 0, -14, 0, -5, 0, -1, 0, 0, 0, 3, 0, 8, 0, 5, 0, -11, 0, 0, 0, 1, 0, -10, 0, 1, 0, 0, 0, 0, 0, -6, 0, -16, 0, 1, 0, -8, 0, 0, 0, 8, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 1, 13], 'euler17': [1, -5, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -11, 37], 'euler41': [1, 5, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -3, 53], 'euler59': [1, 14, 59], 'euler61': [1, 5, 61], 'euler67': [1, -3, 67], 'euler7': [1, 1, 0], 'euler71': [1, -5, 71], 'euler73': [1, 11, 73], 'euler79': [1, 10, 79], 'euler83': [1, 0, 83], 'euler89': [1, 16, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 1, 13], [1, -5, 17], [1, -5, 19], [1, -8, 23], [1, 6, 29], [1, 8, 31], [1, -11, 37], [1, 5, 41], [1, -4, 43], [1, -4, 47], [1, -3, 53], [1, 14, 59], [1, 5, 61], [1, -3, 67], [1, -5, 71], [1, 11, 73], [1, 10, 79], [1, 0, 83], [1, 16, 89], [1, -8, 97]], 'index': 190, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/92400/ep'], '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': '2-92400-1.1-c1-0-190', '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': '2-92400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.16280019947559, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 990535929305841913, 'z1': {'__RealLiteral__': 0, 'data': '1.052372374163079', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '990535929305841913', 'Lhash_array': ['990535929305841913'], 'label': '2-92400-1.1-c1-0-190', 'type': 'ECQ', 'url': 'EllipticCurve/Q/92400/ep'}