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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': -1, 'A9': 0, 'Lhash': '772202681145464096', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 365.2197687649324, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1, -1]], [11, [1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '45738.1', 'coefficient_field': '1.1.1.1', 'conductor': 45738, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1, 5], [1, -1], [1], [1, -4, 13], [1, 2, 17], [1, 6, 19], [1, -4, 23], [1, -8, 29], [1, 2, 31], [1, -1, 37], [1, 1, 41], [1, 4, 43], [1, 1, 47], [1, -6, 53], [1, 9, 59], [1, 4, 61], [1, 9, 67], [1, -4, 71], [1, -14, 73], [1, 3, 79], [1, 9, 83], [1, 15, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 50, 'label': '2-45738-1.1-c1-0-50', 'leading_term': '4.16640218906', '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/45738/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.943158441903711, 1.320428987100771, 0.7817423548720595, -0.4204368690080107, -1.334994491420415, -1.001969734690087, 0.4607291430973116, 1.588726671478724, 0.8682150093119654, -1.418381227720687, -2.999753857571069, -1.908993655588095, 0.9800170023798882, 2.474687179088971, 0.7260514757396124, -2.19515756934646, -2.549369410079783, 0.186214904938203, 2.148047623725398, -0.1253003751087618, -4.826140454333383, -6.770827885128523, -4.056331351906017, -0.4849880807839408, -0.2263754996699117, -2.233509127984328, -2.410959447628749, -0.05446803201551404, 1.300901247162872, 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0.1876028808029846, -0.1006221443488594, 3.027088741979527, 4.848689831892228, 1.764363468643708, -0.9096036907866246, 0.01415346457413935, -1.186824257169056, -5.53326717958111, -4.053162988460412, 4.621912729576553, 8.594913020693337, 3.257391318446125, -1.140875982471076, 0.6206196716784952, 1.359509927174971, -1.070254485917738, 0.0864320849214859, 4.125581619872947, 3.201124158813876, -1.194081331428979, -1.302515161401993, 1.328824341533214, 0.8913917101140701, 0.1170492248923489, 2.715328445068184, 3.985784333930565, 1.099504957499395, -0.558611094184353, 0.9419105254635818, 0.9967768731792481, -0.31343084626191, 0.6207853215889649, 1.306654609128387, -0.90741063162526, -1.486263192598592, 0.944205976059739, 0.3761597222169901, -2.780373650560136, -1.493517476556676, 1.865917748700114, -0.1544627405369874], 'positive_zeros': ['0.9177761551729414', '1.679314896902835', '2.354724475039825', '3.166662220174916', '3.808578649926965', '4.485475494879266', '4.992586754791590', '6.072408070575985', '6.205290608834863', '7.005384079818644', '7.467315861127866', '8.287535640588366', '8.468506572519074', '8.934951402761016', '9.613113115695960', '10.35728209507741', '10.66133305161745', '11.27119990396553', '11.54844617154450', '12.24783471450344', '12.77027878441841', '13.31082261934393', '13.89504384390755', '14.38970379346031', '15.19368954321157', '15.39691989565114', '15.77034389139354', '16.53095172484600', '16.89076500565198', '17.33259951747815', '18.00764308568594', '18.27131938846691', '18.76635948045264', '19.37913865752667', '19.78430154151025'], 'prelabel': '2-45738-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.110723920483295, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 772202681145464096, 'z1': {'__RealLiteral__': 0, 'data': '0.9177761551729414', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.679314896902835', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.354724475039825', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 365.2197687649324, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 45738, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, 1, -1, 0, 1, 0, 0, 4, -1, 0, 1, -2, 0, -6, -1, 0, 0, 4, 0, -4, -4, 0, 1, 8, 0, -2, -1, 0, 2, -1, 0, 1, 6, 0, 1, -1, 0, -4, 0, 0, -4, -1, 0, 1, 4, 0, 4, 6, 0, 0, -1, 0, -8, -9, 0, -4, 2, 0, 1, -4, 0, -9, -2, 0, 1, 4, 0, 14, -1, 0, -6, 0, 0, -3, -1, 0, 1, -9, 0, 2, 4, 0, 0, -15, 0, 4, 4, 0, 1, 6, 0, 16, -1, 0, -4], 'euler11': [1, 0, 0], 'euler13': [1, -4, 13], 'euler17': [1, 2, 17], 'euler19': [1, 6, 19], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -1, 37], 'euler41': [1, 1, 41], 'euler43': [1, 4, 43], 'euler47': [1, 1, 47], 'euler5': [1, 1, 5], 'euler53': [1, -6, 53], 'euler59': [1, 9, 59], 'euler61': [1, 4, 61], 'euler67': [1, 9, 67], 'euler7': [1, -1, 0], 'euler71': [1, -4, 71], 'euler73': [1, -14, 73], 'euler79': [1, 3, 79], 'euler83': [1, 9, 83], 'euler89': [1, 15, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 5], [1, -1, 0], [1, 0, 0], [1, -4, 13], [1, 2, 17], [1, 6, 19], [1, -4, 23], [1, -8, 29], [1, 2, 31], [1, -1, 37], [1, 1, 41], [1, 4, 43], [1, 1, 47], [1, -6, 53], [1, 9, 59], [1, 4, 61], [1, 9, 67], [1, -4, 71], [1, -14, 73], [1, 3, 79], [1, 9, 83], [1, 15, 89], [1, -16, 97]], 'index': 50, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/45738/t'], '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': '2-45738-1.1-c1-0-50', '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': '2-45738-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.110723920483295, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 772202681145464096, 'z1': {'__RealLiteral__': 0, 'data': '0.9177761551729414', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '772202681145464096', 'Lhash_array': ['772202681145464096'], 'factors': ['2-45738-1.1-c1-0-50'], 'label': '2-45738-1.1-c1-0-50', 'type': 'ECQ', 'url': 'EllipticCurve/Q/45738/t'}