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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': 3, 'A8': 0, 'A9': 1, 'Lhash': '1437179725737066180', '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': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 529.4081654010891, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [13, [1, -1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '66300.1', 'coefficient_field': '1.1.1.1', 'conductor': 66300, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -3, 7], [1, 4, 11], [1, -1], [1, 1], [1, 2, 19], [1, 0, 23], [1, 1, 29], [1, 0, 31], [1, 5, 37], [1, -8, 41], [1, 1, 43], [1, -1, 47], [1, 0, 53], [1, 8, 59], [1, 4, 61], [1, 8, 67], [1, -6, 71], [1, 10, 73], [1, -4, 79], [1, -15, 83], [1, -6, 89], [1, -13, 97]], 'gamma_factors': [[], [0]], 'index': 27, 'label': '2-66300-1.1-c1-0-27', 'leading_term': '5.3973234476', '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/66300/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.209870235521737, 1.626949968708035, 0.7959064268479576, -0.8785731076885386, -2.092918142769775, -1.683312691677037, -0.009965003078689708, 1.007929925285567, -0.1530582593751509, -2.535219850046058, -3.260421176261361, -0.8065042553735284, 2.695981749822319, 3.495595376790034, 0.6919772745511676, -2.506771335556787, -2.780404391485791, -0.832883708513728, 0.05900818578859961, -1.006677652674797, -1.51134544950381, 0.02931396390497373, 1.296887129429647, -0.047820927771707, -1.96205248275188, -0.7674404240473753, 2.688205321657808, 3.730177559854287, 1.067294254130266, -1.166762800661287, -0.3170718032323924, 0.4615284892132944, -1.857934146743257, -4.212759589754761, -2.560413682790059, 0.3409829033015188, -1.184089000749266, -5.873991869788821, -6.919628905919104, -2.886807955917225, 0.4499255375377038, 0.07657959268867956, -0.4082017734317743, 1.122896055318588, 1.528780319440781, -0.2995226578399959, -0.4303138511423909, 2.133338849478586, 2.597068670490538, -0.5092765521834689, -1.93029149048452, 0.2928937049877704, 0.7260348958683054, -2.717063141948517, -4.06773963414403, -0.7918678757195828, 0.7900931039491603, -2.460033814662503, -4.341670647553642, -1.388689751979569, 0.7096296248179516, -1.152409502784263, -1.700431460358331, 1.099497737827276, 1.533633741686242, -1.789338785463076, -2.657114781031309, 0.2286206844359373, 1.017442670021095, -1.082408666638016, -1.12746453509246, 0.4226693009287492, -0.2929170787101409, -0.6432192317452599, 2.632936838378265, 4.188249298346442, 0.313469702136149, -1.436016345613294, 3.836629310012338, 7.653932712290616, 3.771828318130661, -0.6923969426031498, -0.2023935479233202, 0.1920277262965171, -1.679555383032607, -0.9616634193878283, 1.162439485956945, -1.055805000215994, -4.260566626767115, -1.9693602300006, 1.631545781867339, 0.5217534144284798, -1.103753501436495, 0.5959054848097689, 1.073064802258215, -0.7179360501163824, 0.1011685621751192, 1.544571186130404, -1.156684170911655, -2.430673998053403, 2.877187493028215, 6.373387164820143, 2.142502102786116, -1.070552659164457, 1.544169210486941, 2.006306120447853, -1.409022755468386, -0.9166863995649565, 2.460221156909305, 1.637399356449381, -0.6779947534075283, 0.1347196389308505, -0.2527355419336017, -3.015546385729158, -2.037605022153435, 1.172357043919793, 0.2970433634534198, -0.8195386871016567, 2.425821434131931, 3.476880958722304], 'positive_zeros': ['0.8745301558921360', '1.751448565811003', '2.231927124463336', '3.054303696511818', '3.796160165640166', '4.655528112708122', '4.782494594508802', '5.496348859261997', '5.994855474267173', '6.558922949982124', '7.335953769251613', '7.799257230973603', '8.084387747729176', '8.951684702780783', '9.160362476780267', '10.18906431029308', '10.51539716245435', '10.83894289933654', '11.45980137645532', '11.80294761064312', '12.46268392648843', '12.97098442513926', '13.31912118871837', '14.05754690671178', '14.33877254885651', '15.10497161939610', '15.38079589950565', '15.90945318907518', '16.37568309301709', '16.98020780342187', '17.37656786871740', '17.90996464658055', '18.20142633366348', '18.57120443141632', '19.26738658813203', '19.59638447486444'], 'prelabel': '2-66300-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.008871449966623, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1437179725737066180, 'z1': {'__RealLiteral__': 0, 'data': '0.8745301558921360', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.751448565811003', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.231927124463336', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 529.4081654010891, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 66300, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 3, 0, 1, 0, -4, 0, 1, 0, 0, 0, -1, 0, -2, 0, -3, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 4, 0, 0, 0, -5, 0, -1, 0, 8, 0, -1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, -8, 0, -4, 0, 3, 0, 0, 0, -8, 0, 0, 0, 6, 0, -10, 0, 0, 0, -12, 0, 4, 0, 1, 0, 15, 0, 0, 0, 1, 0, 6, 0, 3, 0, 0, 0, 0, 0, 13, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 1, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 5, 37], 'euler41': [1, -8, 41], 'euler43': [1, 1, 43], 'euler47': [1, -1, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, 8, 59], 'euler61': [1, 4, 61], 'euler67': [1, 8, 67], 'euler7': [1, -3, 7], 'euler71': [1, -6, 71], 'euler73': [1, 10, 73], 'euler79': [1, -4, 79], 'euler83': [1, -15, 83], 'euler89': [1, -6, 89], 'euler97': [1, -13, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -3, 7], [1, 4, 11], [1, -1, 0], [1, 1, 0], [1, 2, 19], [1, 0, 23], [1, 1, 29], [1, 0, 31], [1, 5, 37], [1, -8, 41], [1, 1, 43], [1, -1, 47], [1, 0, 53], [1, 8, 59], [1, 4, 61], [1, 8, 67], [1, -6, 71], [1, 10, 73], [1, -4, 79], [1, -15, 83], [1, -6, 89], [1, -13, 97]], 'index': 27, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/66300/r'], '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': '2-66300-1.1-c1-0-27', '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': '2-66300-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.008871449966623, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1437179725737066180, 'z1': {'__RealLiteral__': 0, 'data': '0.8745301558921360', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1437179725737066180', 'Lhash_array': ['1437179725737066180'], 'label': '2-66300-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/66300/r'}