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lfunc_lfunctions • Show schema
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{'A10': 4, 'A2': 2, 'A3': -1, 'A4': 2, 'A5': 2, 'A6': -2, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1208258217511462290', 'a10': [1.2649110640673518, 0], 'a2': [1.414213562373095, 0], 'a3': [-0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [-0.8164965809277261, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [7, [1]], [13, [1, -1]], [17, [1, -1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, 1], [1, -2, 5], [1], [1, 5, 11], [1, -1], [1, -1], [1, -8, 19], [1, -6, 23], [1, 8, 29], [1, -9, 31], [1, -9, 37], [1, -7, 41], [1, 1, 43], [1, 12, 47], [1, -3, 53], [1, -12, 59], [1, 10, 61], [1, -4, 67], [1, 9, 71], [1, 6, 73], [1, -14, 79], [1, 12, 83], [1, -8, 89], [1, 9, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-32487-1.1-c1-0-4', 'leading_term': '4.60184955036', '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/32487/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.601849550362218, 3.857044287902297, 1.783025122619685, -0.9469288809897954, -3.045901446351977, -3.225158536808422, -1.255461170355202, 1.543678279299468, 3.154741166883299, 2.571265704619226, 0.7652310236084061, -0.2654655477881587, 0.3994728080696852, 1.601119282211245, 1.47657720490581, -0.2597377026983747, -1.892516373629665, -1.778244438132424, -0.342587970375433, 0.6103452244168738, 0.3258335857240813, -0.1395154778910423, 0.1539392912414118, 0.4743217050707549, -0.1379595430480792, -0.676308639674915, 0.7072202016584868, 3.265544754867473, 3.636521771056539, 0.7442399487733121, -1.285963633520976, 1.867480527996042, 7.484172220743596, 7.566355108493958, -0.6699409909729437, -9.70667097391533, -10.52207613000219, -4.086513615240256, 0.6055547042619857, -0.8283029076243459, -3.17871247802769, -0.8586836134500153, 3.53848385727861, 4.110274564085952, 1.078328803057246, -0.3979135253579442, 1.04318885963465, 1.572464577774941, -0.525818629647096, -2.068761152441601, -0.8922929826429639, 0.6825558970640109, 0.4796941277700964, -0.09664107852953382, 0.2096831799811, -0.1975255914672934, -1.855277405484693, -2.066983982553016, 0.08999018438955869, 1.154103585642944, -0.6384765422322163, -1.615118742541309, 0.6498985453859129, 2.392303721637677, 0.7601223804497521, -0.1140042433172251, 3.060412498852651, 5.011097319488479, 0.5087752430399218, -5.17989994418589, -4.427354017352713, -0.3491469491070683, -0.423169029448422, -2.327751080110725, 0.5262989465523358, 3.853203613108052, -1.595201131025992, -11.46969336322742, -11.76291605465096, -1.178447104691081, 6.630688777290583, 4.474042475681362, -0.1955235482763807, -0.6200309489524769, 0.4097454505920995, -0.04707892080056133, 0.2294084664851968, 1.708507455182633, 1.520273739116025, 0.01625115599402635, 0.05032028005776533, 0.7971277900980435, 0.1203091859337301, -0.2889207751440522, 0.8741588059271534, 0.7506823275302718, -1.345206703099747, -1.566551353255558, 0.124232075413589, -0.5202654897475208, -1.69260666372543, 2.105768108183566, 6.717305679851554, 3.585625068304639, -2.74637676504089, -1.471354228107028, 3.25356206257188, -0.04446130622757627, -6.060517926555063, -1.135818136341838, 9.632836246677618, 9.875954021167836, 0.8049848576581262, -2.947656274289523, 0.4147803427290006, 1.533258606403545, -0.2378340680533258, 0.3894266060114002, 1.323025155262316, -0.6692558433566324, -1.407333877458941], 'positive_zeros': ['0.6636062013137042', '1.610393376708326', '2.636424927601588', '2.910311745884203', '3.718464043902038', '4.561461894664600', '5.136864041002024', '5.424630373400217', '5.962202851789690', '6.416909948454265', '7.306195443100695', '7.652564915664916', '8.483984336099015', '9.435931421319286', '9.680957220135326', '10.29642343666915', '11.10865335330858', '11.35168071602105', '11.94866007442546', '12.61590946280538', '13.16432091685824', '13.37388442288513', '13.70633996945648', '14.49044678901256', '14.93016515323235', '15.44499873101148', '16.09538910493913', '16.26902599630174', '17.01869970312116', '17.78845496055706', '17.94755404282254', '18.47261826708523', '18.95732106700493', '19.77562664658767'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1208258217511462290, 'z1': {'__RealLiteral__': 0, 'data': '0.6636062013137042', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.610393376708326', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.636424927601588', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, 2, -1, 2, 2, -2, 0, 0, 1, 4, -5, -2, 1, 0, -2, -4, 1, 2, 8, 4, 0, -10, 6, 0, -1, 2, -1, 0, -8, -4, 9, -8, 5, 2, 0, 2, 9, 16, -1, 0, 7, 0, -1, -10, 2, 12, -12, 4, 0, -2, -1, 2, 3, -2, -10, 0, -8, -16, 12, -4, -10, 18, 0, -8, 2, 10, 4, 2, -6, 0, -9, 0, -6, 18, 1, 16, 0, -2, 14, -8, 1, 14, -12, 0, 2, -2, 8, 0, 8, 4, 0, 12, -9, -24, 16, 8, -9, 0, -5, -2], 'euler11': [1, 5, 11], 'euler13': [1, -1, 0], 'euler17': [1, -1, 0], 'euler19': [1, -8, 19], 'euler2': [1, -2, 2], 'euler23': [1, -6, 23], 'euler29': [1, 8, 29], 'euler3': [1, 1, 0], 'euler31': [1, -9, 31], 'euler37': [1, -9, 37], 'euler41': [1, -7, 41], 'euler43': [1, 1, 43], 'euler47': [1, 12, 47], 'euler5': [1, -2, 5], 'euler53': [1, -3, 53], 'euler59': [1, -12, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 9, 71], 'euler73': [1, 6, 73], 'euler79': [1, -14, 79], 'euler83': [1, 12, 83], 'euler89': [1, -8, 89], 'euler97': [1, 9, 97], 'euler_factors': [[1, -2, 2], [1, 1, 0], [1, -2, 5], [1, 0, 0], [1, 5, 11], [1, -1, 0], [1, -1, 0], [1, -8, 19], [1, -6, 23], [1, 8, 29], [1, -9, 31], [1, -9, 37], [1, -7, 41], [1, 1, 43], [1, 12, 47], [1, -3, 53], [1, -12, 59], [1, 10, 61], [1, -4, 67], [1, 9, 71], [1, 6, 73], [1, -14, 79], [1, 12, 83], [1, -8, 89], [1, 9, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/l'], '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': '2-32487-1.1-c1-0-4', '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': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1208258217511462290, 'z1': {'__RealLiteral__': 0, 'data': '0.6636062013137042', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1208258217511462290', 'Lhash_array': ['1208258217511462290'], 'label': '2-32487-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/l'}