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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': 0, 'Lhash': '2121124656377701610', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2288.9117739400035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1]], [7, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '286650.1', 'coefficient_field': '1.1.1.1', 'conductor': 286650, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1, -1], [1], [1], [1], [1, 0, 11], [1, -1], [1, 6, 17], [1, -4, 19], [1, 0, 23], [1, 6, 29], [1, -4, 31], [1, -10, 37], [1, -6, 41], [1, 8, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, 14, 61], [1, -4, 67], [1, 0, 71], [1, -2, 73], [1, -8, 79], [1, -12, 83], [1, -6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 351, 'label': '2-286650-1.1-c1-0-351', 'leading_term': '12.6122862592', '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/286650/mt', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.775269069131865, 3.513753701350654, 1.488869368267095, -1.62564098923267, -2.808743177800392, -0.9601675402549875, 1.441238856380627, 1.277867194519769, -0.9589779323715087, -1.826164267535334, -0.1159436127353887, 1.245894826453495, -0.00998822168158411, -1.623174869044925, -0.628146709667444, 1.42488310268929, 1.214120676756783, -0.3200058801105088, 0.1151159705111294, 1.604095518809223, 0.5861547022213499, -1.881090202527993, -1.558496553015935, 0.8309603364432468, 0.9706681256966809, -0.2204913345750422, 1.524076161042645, 4.142719783536623, 2.327144251037181, -1.357640325292881, -0.8891282356613583, 0.4680116555860956, -3.785808958539474, -8.782276937331064, -6.072408074328891, -0.2941083388609055, -0.3902933660931582, -2.105323650655927, 2.138053166643717, 6.328738663476542, 2.662806671891041, -2.462077960148569, -1.492357743198134, 0.4458102045761313, -1.281769273980781, -1.631342409293142, 0.6244757703468314, -0.2767560210710626, -2.986471089885267, -1.465790552363666, 1.376984328522197, 0.4679667559246707, -0.5654552079742564, 0.7384454461216082, 0.125862801898149, -1.559246331971504, 0.3523177696241729, 2.128313096331317, -0.4666740329086345, -1.975241550446493, -0.03189558301186433, -0.3457703998448347, -1.680225133201438, 1.034283061625415, 2.429032004015109, -1.059090219968881, -1.10410470042874, 2.467039624685499, -0.568487527647983, -5.984314194255214, -2.823960568105689, 1.650805195842755, -0.7265539620206773, -0.2552053738612531, 5.441580590263236, 3.683731840154949, -3.441689397432203, -2.959039259469195, 0.9182510025690963, -0.3073033068248049, -0.8773414144978686, 0.9958708728913109, -1.134265055059534, -3.207907286775332, 0.089025855726822, 1.784863422962853, -0.1981556101522641, 0.5283750845116608, 1.634894499535184, -0.3115283779570516, 0.04452790647614895, 1.888893240802056, -0.02676048729006192, -0.6664803437623312, 2.26060840779988, 1.511494329603542, -1.052897184915083, 0.3430979061889996, 0.7489201311025075, 0.1655039629758321, 4.698761184478833, 6.732162049569607, 0.9987393518451425, -0.705407417516678, 2.409768480575942, -0.09796841733926447, -1.555650979188081, 2.79331789196784, -0.4888014760462381, -8.540857295700757, -5.148793004218259, 1.393379972551091, -0.9321223208456392, -1.875957039227549, 1.378777042041848, -0.03736013573794396, -0.7770730513329882, 2.661034730417677, 1.015175967589817, -2.700445901515363], 'positive_zeros': ['0.8655793790134818', '1.586161746348575', '2.147476612201964', '2.763278852947059', '3.248817210449974', '3.818633726375058', '4.433072886077378', '4.731187208037989', '5.305946643489700', '5.906082230100062', '6.417886021101832', '6.592814152436214', '7.389798903488248', '7.844747884626273', '8.060764042754454', '9.023589757774243', '9.211148070048841', '9.659538278108796', '10.35517366835805', '10.88666432723297', '11.10585449256841', '11.67152234506112', '11.97566052039350', '12.60385517215265', '13.05957124006076', '13.37237897213839', '13.76468911975086', '14.22193025894256', '14.71593405012313', '15.25490948603878', '15.45199293362148', '15.93007503389200', '16.43011264817737', '16.82085683055888', '17.22794898115918', '17.86600430589833', '18.19719526655622', '18.51303004211658', '19.11889585884419', '19.66240492130438', '19.96877266159748'], 'prelabel': '2-286650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.84257281898627, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2121124656377701610, 'z1': {'__RealLiteral__': 0, 'data': '0.8655793790134818', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.586161746348575', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.147476612201964', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2288.9117739400035, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 286650, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, -6, 0, 4, 0, 0, 0, 0, 0, 0, 1, 0, 0, -6, 0, 4, 1, 0, -6, 0, 0, 10, 4, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 1, -6, 0, 0, 0, 0, -6, -12, 0, -14, 4, 0, 1, 0, 0, 4, -6, 0, 0, 0, 0, 2, 10, 0, 4, 0, 0, 8, 0, 0, 6, 12, 0, 0, -8, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, 6, 17], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -10, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, 14, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -2, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 11], [1, -1, 0], [1, 6, 17], [1, -4, 19], [1, 0, 23], [1, 6, 29], [1, -4, 31], [1, -10, 37], [1, -6, 41], [1, 8, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, 14, 61], [1, -4, 67], [1, 0, 71], [1, -2, 73], [1, -8, 79], [1, -12, 83], [1, -6, 89], [1, -2, 97]], 'index': 351, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/286650/mt'], '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': '2-286650-1.1-c1-0-351', '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': '2-286650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.84257281898627, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2121124656377701610, 'z1': {'__RealLiteral__': 0, 'data': '0.8655793790134818', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2121124656377701610', 'Lhash_array': ['2121124656377701610'], 'label': '2-286650-1.1-c1-0-351', 'type': 'ECQ', 'url': 'EllipticCurve/Q/286650/mt'}