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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': 0, 'A8': 0, 'A9': -2, 'Lhash': '2156495578734509366', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 626.0271518468385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '78400.1', 'coefficient_field': '1.1.1.1', 'conductor': 78400, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1], [1], [1, 3, 11], [1, 6, 13], [1, -5, 17], [1, 1, 19], [1, -7, 23], [1, 2, 29], [1, 5, 31], [1, -3, 37], [1, 2, 41], [1, 4, 43], [1, 5, 47], [1, 1, 53], [1, 15, 59], [1, -5, 61], [1, 9, 67], [1, 0, 71], [1, 7, 73], [1, -1, 79], [1, -12, 83], [1, -7, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 132, 'label': '2-280e2-1.1-c1-0-132', 'leading_term': '3.74574419548', '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/78400/db', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7868630116348715, 0.7455153719356469, -0.502029172466953, -2.327751412273056, -3.190241354415715, -1.919833577459349, 0.788836044008677, 2.575163299572232, 1.739030108587211, -0.6575549140943672, -1.790872746680015, -0.5861947036558273, 0.5886998806364292, -1.1689625553114, -5.083696582735056, -7.068222996233915, -4.84897381570441, -1.02576681232318, 0.4775050656088343, -0.3723583522272447, -0.5216274516135949, 0.796682823412202, 0.9166820182263057, -1.175202759055382, -2.248686467500665, 0.1349674186525001, 3.043591149103275, 2.4366048326733, -0.2266948320131618, -0.5091404111715204, 1.171709093376671, 0.2216713701932435, -3.475780996242465, -4.356260563035033, -0.5961116136604633, 2.145904819215025, 0.03347319063627813, -2.546166763045693, -0.9161425993404894, 1.847128503157867, 1.119647249458514, -0.7760096194261403, 0.3872050969706273, 2.361487687360713, 1.060384359462182, -1.174776686897509, -0.2606521236519791, 1.406153476653263, -0.0342613986664136, -1.829256052005061, -0.4652212009947069, 0.3376426256434257, -2.985319699590943, -5.206418533869013, -1.31382182018154, 3.266574009126472, 2.112077328647628, -0.8203303358790286, -0.03209209821335603, 0.8113298138478211, -2.015082464091043, -3.054312567711731, 1.56244797535405, 5.314045685022261, 3.136331526992733, 0.0867520850334195, 0.197133507285594, -0.1364182139159513, -1.883667555525274, -0.8146065404862955, 1.714091605478241, 0.3618466648007705, -2.17809837013336, -0.1466261174720513, 2.624222940272035, 0.5541459711330264, -1.507925743174772, 1.08237328677995, 2.139038375511615, -1.879319197600873, -3.441568603880184, 0.1311565058242528, 0.8392380127152371, -2.700324072583694, -2.614125463848454, 0.8964708563279616, 0.6691759586498877, -1.436811998839215, 0.2889123508070878, 2.079623132302319, -0.2661966574730795, -1.776528434221905, -0.1150020123229141, -0.1689852343452089, -1.01967611799727, 2.094605472646537, 4.476103342031275, 0.8131695645613465, -2.123234617716348, 0.291036215324223, 0.4894007779384445, -3.568256503244626, -3.408480860529177, 0.3259113913907717, -0.8363890033996667, -3.685056175607227, -0.8936392353986362, 2.087719835328516, -0.1298316995082141, -1.06644441158954, 1.411670693271791, 0.3410639943562494, -3.005751363130579, -1.820525059620569, 0.6527760126097821, -0.1493328356342088, 0.01482647511283001, 1.579402672226611, -0.08465631653520127, -0.3412136026425819], 'positive_zeros': ['0.6724352550660202', '1.679208438741799', '2.430722725881676', '3.085020063355817', '3.393535237676124', '4.603829717174844', '4.914135179179730', '5.360481954723052', '5.876730310396333', '6.490351921647446', '7.223709495387684', '7.576631083406161', '8.017847181236795', '8.784173183862590', '9.252361570211660', '9.818503043914863', '10.37008788823985', '10.70912974528585', '11.34636686595183', '11.77897245348543', '12.24665637037801', '12.80676181772934', '13.04579475903208', '13.80633271458384', '14.40373704300861', '14.75399774668190', '15.09893810233072', '15.68236654388627', '16.51802045399690', '16.68330277410351', '16.97719711109479', '17.56848745621119', '18.02760510748185', '18.50954366902490', '19.03956553022686', '19.42176429520322', '19.89899767917264'], 'prelabel': '2-280e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.02053460353792, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2156495578734509366, 'z1': {'__RealLiteral__': 0, 'data': '0.6724352550660202', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.679208438741799', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.430722725881676', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 626.0271518468385, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 78400, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, -2, 0, -3, 0, -6, 0, 0, 0, 5, 0, -1, 0, 0, 0, 7, 0, 0, 0, 5, 0, -2, 0, -5, 0, 3, 0, 0, 0, 3, 0, 6, 0, -2, 0, -4, 0, 0, 0, -5, 0, 0, 0, -5, 0, -1, 0, 0, 0, 1, 0, -15, 0, 5, 0, 0, 0, 0, 0, -9, 0, -7, 0, 0, 0, -7, 0, 0, 0, 0, 0, 1, 0, 1, 0, 12, 0, 0, 0, 2, 0, 7, 0, 0, 0, 5, 0, 0, 0, 2, 0, 6, 0], 'euler11': [1, 3, 11], 'euler13': [1, 6, 13], 'euler17': [1, -5, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -7, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 3], 'euler31': [1, 5, 31], 'euler37': [1, -3, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 5, 47], 'euler5': [1, 0, 0], 'euler53': [1, 1, 53], 'euler59': [1, 15, 59], 'euler61': [1, -5, 61], 'euler67': [1, 9, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 7, 73], 'euler79': [1, -1, 79], 'euler83': [1, -12, 83], 'euler89': [1, -7, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 0, 0], [1, 0, 0], [1, 3, 11], [1, 6, 13], [1, -5, 17], [1, 1, 19], [1, -7, 23], [1, 2, 29], [1, 5, 31], [1, -3, 37], [1, 2, 41], [1, 4, 43], [1, 5, 47], [1, 1, 53], [1, 15, 59], [1, -5, 61], [1, 9, 67], [1, 0, 71], [1, 7, 73], [1, -1, 79], [1, -12, 83], [1, -7, 89], [1, -2, 97]], 'index': 132, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/78400/db'], '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': '2-280e2-1.1-c1-0-132', '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': '2-280e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.02053460353792, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2156495578734509366, 'z1': {'__RealLiteral__': 0, 'data': '0.6724352550660202', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2156495578734509366', 'Lhash_array': ['2156495578734509366'], 'factors': ['2-280e2-1.1-c1-0-132'], 'label': '2-280e2-1.1-c1-0-132', 'type': 'ECQ', 'url': 'EllipticCurve/Q/78400/db'}