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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': 2, 'A8': -1, 'A9': 1, 'Lhash': '1353460008830249439', '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': [0.7559289460184544, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 264.7040827005446, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1]], [13, [1, -1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '33150.1', 'coefficient_field': '1.1.1.1', 'conductor': 33150, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1], [1, -2, 7], [1, 2, 11], [1, -1], [1, 1], [1, 8, 19], [1, 0, 23], [1, 6, 29], [1, -6, 31], [1, 4, 37], [1, -4, 41], [1, -4, 43], [1, -8, 47], [1, -6, 53], [1, 8, 59], [1, 2, 61], [1, -8, 67], [1, 6, 71], [1, 12, 73], [1, -4, 79], [1, -12, 83], [1, -6, 89], [1, 0, 97]], 'gamma_factors': [[], [0]], 'index': 39, 'label': '2-33150-1.1-c1-0-39', 'leading_term': '5.1690468366', '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/33150/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.201772452040938, 1.862585634432226, 1.553199134566044, 0.3099024772454128, -1.128767452035443, -1.723223180801137, -1.068005098428246, 0.02895113122103364, 0.1874000676901006, -1.009329498187341, -2.20648838683493, -1.494969808465313, 1.258179980949651, 3.680975703802412, 3.221884847766981, 0.3115494223477069, -1.614242948880931, 0.004036550049936168, 3.403342720335866, 4.164410530286544, 0.6203032622841939, -3.676864204288935, -4.073147315678323, -0.6331767240099297, 1.980900645645227, 0.6075513275067749, -2.48628258485078, -3.100680262408321, -0.8790779877837971, 0.8132700419308561, 0.1867816086838935, -0.758011864985028, -0.06768203034354557, 0.9746244789036047, 0.5252292931221282, -0.1977277404429382, 1.020734936033709, 3.015766323128846, 2.567664712865695, -0.1640755880752727, -1.497770021197768, -0.2531788929256707, 0.3362476605164434, -1.351590818146668, -1.842483739339207, 1.351719693588496, 4.211967027714318, 2.00770553173323, -2.334694344522565, -2.201476111769785, 1.90216106217298, 3.061204697650639, -0.3586699665916935, -1.945483791625066, 1.589989200591489, 4.670882058428694, 2.53252545170128, -0.8629845916693741, -0.3542283657281506, 1.619229787353031, 0.6348824817250297, -1.084742661404018, 0.5051493314889963, 2.674680950916249, 0.6308395092448316, -3.100246357736382, -2.771162883045328, 0.386262809528559, 0.9646734654611058, -0.5579525247970756, 0.2986499080048178, 2.704702451335556, 2.346359144842287, 0.1663351226131953, 0.2216909753656635, 1.431339831399756, 0.3522348173643699, -1.045137686636983, 0.6908511996202858, 2.751379495478376, 1.181254052597756, -1.165789569759099, -0.5454848331112198, 0.1833404660371427, -1.247117344484199, -0.2308138550776459, 4.412750653572826, 4.331631398648329, -3.539132947424506, -8.036084951052446, -1.550370548998195, 6.147177005051784, 4.609262665022957, -0.3370516213692856, 0.3779881762924038, 2.930090142922506, 0.8629045660879578, -1.922463418915326, -0.7257235614518069, 0.2599800517720276, -2.169156275677771, -3.384114884867339, -1.130383125931866, 0.2600933680711613, -0.1646359958511434, 1.197532192198847, 3.036103327134652, 1.414903007132933, -1.021344592611522, -0.2401685642929997, 0.8117487523665377, -0.2618910954839126, 0.8224845201216182, 4.570303768491856, 4.217023247674764, -0.4048168297218128, -1.203051386713826, 2.091153785238035, 1.886453951537974, -0.9956444376910581], 'positive_zeros': ['1.050603660221127', '1.991464389366869', '2.310154038353045', '3.148163495492574', '4.025772697478621', '4.499682551917193', '5.281826411526067', '6.041565566847808', '6.548207623267127', '7.343383282225082', '7.785642356949014', '8.262930999260067', '8.880859878697407', '9.094374175210044', '9.984824002850299', '10.54237500455287', '10.82311486733435', '11.41623612171966', '12.10574036428782', '12.63821133420728', '13.22675155144856', '13.66290117625983', '14.41406510357575', '14.78807358864999', '15.31849588300008', '15.70486645206561', '16.28837340546273', '16.96454361656709', '17.39686898160147', '17.71662171092912', '18.53236386867775', '18.70284261532612', '19.29262134676491', '19.68678726015958'], 'prelabel': '2-33150-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.26972902972095, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1353460008830249439, 'z1': {'__RealLiteral__': 0, 'data': '1.050603660221127', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.991464389366869', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.310154038353045', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 264.7040827005446, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 33150, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, 2, -1, 1, 0, -2, 1, 1, -2, 0, 1, -1, -1, -8, 0, 2, 2, 0, -1, 0, -1, 1, 2, -6, 0, 6, -1, -2, 1, 0, 1, -4, 8, 1, 0, 4, -2, 4, -2, 0, 0, 8, 1, -3, 0, -1, 1, 6, -1, 0, -2, -8, 6, -8, 0, -2, -6, 2, 1, 0, 2, 8, -1, 0, 0, -6, -1, -12, 4, 0, -8, -4, -1, 4, 0, 1, -4, 12, 2, 0, -4, -6, 2, 6, 0, 2, 0, 6, -8, 0, -1, 0, 3, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, -1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 8, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -6, 31], 'euler37': [1, 4, 37], 'euler41': [1, -4, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 8, 59], 'euler61': [1, 2, 61], 'euler67': [1, -8, 67], 'euler7': [1, -2, 7], 'euler71': [1, 6, 71], 'euler73': [1, 12, 73], 'euler79': [1, -4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 0], [1, -2, 7], [1, 2, 11], [1, -1, 0], [1, 1, 0], [1, 8, 19], [1, 0, 23], [1, 6, 29], [1, -6, 31], [1, 4, 37], [1, -4, 41], [1, -4, 43], [1, -8, 47], [1, -6, 53], [1, 8, 59], [1, 2, 61], [1, -8, 67], [1, 6, 71], [1, 12, 73], [1, -4, 79], [1, -12, 83], [1, -6, 89], [1, 0, 97]], 'index': 39, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/33150/y'], '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': '2-33150-1.1-c1-0-39', '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': '2-33150-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.26972902972095, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1353460008830249439, 'z1': {'__RealLiteral__': 0, 'data': '1.050603660221127', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1353460008830249439', 'Lhash_array': ['1353460008830249439'], 'label': '2-33150-1.1-c1-0-39', 'type': 'ECQ', 'url': 'EllipticCurve/Q/33150/y'}