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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 0, 'Lhash': '721696181476211395', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2782.62680963758, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '348480.1', 'coefficient_field': '1.1.1.1', 'conductor': 348480, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, -2, 7], [1], [1, 4, 13], [1, 6, 17], [1, -2, 19], [1, -8, 23], [1, -6, 29], [1, 0, 31], [1, -6, 37], [1, 10, 41], [1, 2, 43], [1, -12, 47], [1, 6, 53], [1, 8, 59], [1, 0, 61], [1, 4, 67], [1, 12, 71], [1, 4, 73], [1, -10, 79], [1, -4, 83], [1, -14, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 127, 'label': '2-348480-1.1-c1-0-127', 'leading_term': '2.93325518826', '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': 0, 'origin': 'EllipticCurve/Q/348480/oz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.933255188256818, 1.924059321335148, -0.3099602367416136, -1.790515801997034, -0.9857579396304449, 1.22344925950125, 2.131511634049275, 0.6578148253649408, -0.8715176402485822, 0.0075330568626416, 1.874992907697229, 1.479926939937154, -0.4761868280494514, 0.3527905239358385, 4.620512459157042, 6.932468896497678, 3.853600662950253, -0.4310984627188116, -0.941995164750531, 0.4035293958653919, -0.144345361703244, -0.4188599729360981, 2.694931966969857, 5.420269110467873, 3.210359594654459, -0.139429575269718, 0.7626402228080728, 2.655380863054231, 0.5655248221014285, -1.928475410574223, -0.5059974784864006, 0.3087433812271418, -3.267578301022306, -5.415540154445988, -2.228951975954495, 0.3490882527187861, -0.7439005272814467, 0.01677026859190116, 3.126451636789274, 2.093757437882327, -1.753322620445317, -1.324911551835757, 0.9744092194370055, -0.8563218493891162, -2.638310006253601, 0.003231759138248749, 1.184689449898752, -1.332387532234967, -0.5674128741690287, 2.808055118695773, 0.9033532380552359, -3.210254428548159, -1.967825822618173, 0.017151171466188, -2.315083186198803, -2.761331634984042, 0.3404881648193761, -0.1351918867783407, -2.580083250982398, -0.7692114732715253, 0.7225529255268601, -1.504800194356254, -0.6994388332912151, 1.93293274148124, -2.135855508668455, -7.31806829763, -4.177834067065561, 0.3178652002492586, -0.6201370890605251, -0.6572556713581079, 1.293516014222286, 0.110135941631789, -0.0370928591952007, 2.977828792289459, 1.502991923478942, -2.142595936925643, 0.7304502774663052, 3.674295915930607, 0.1395304497202562, -0.9066964846726044, 2.490454930463088, 1.477153173029754, -0.6554589827317265, 1.83492160053696, 1.655843329500844, -2.013799919373195, -0.9212666501257762, 1.265970193808659, -0.3802898375017961, 0.1523422752324115, 0.668438887294379, -5.051977549270308, -7.389374759283758, -1.402040177645687, 0.9852528830505773, -0.8126358037722615, 2.005438973372632, 3.751068509854026, 0.3863702931495076, -0.1255110496475586, 0.9116603023525663, -0.2290319786253648, 3.177958574032819, 7.2092442747914, 1.749208781166206, -3.90305002298444, -1.306492491967956, 0.3909838272962047, -0.258527725647609, 1.115251442451426, -1.730071406231379, -5.786180613035368, -0.7648201068427496, 4.419520925492085, 1.479123138491146, 0.103029536192682, 1.316842155458718, -0.1635988672047339, 1.991347628391976, 5.486847796736327, 1.134764697447071], 'positive_zeros': ['0.4659155144989484', '1.113958835709395', '1.831055350244944', '2.249036702454221', '2.927275689802014', '3.218568216706878', '4.214524161071322', '4.654587423558703', '4.970691956350152', '5.306083001683921', '6.229736144054121', '6.415310444980477', '7.040417776729923', '7.556428009873899', '7.788016108742215', '8.669092131538460', '8.874480605965453', '9.248524692094034', '9.874924757188545', '10.36375782358687', '10.68099492795587', '11.24975332459216', '11.62522499533056', '12.03892870024619', '12.54632503245624', '13.20497592525423', '13.25817494268873', '13.96676174770844', '14.23781531646486', '14.81533445009515', '15.09931159737588', '15.55001324297200', '15.91616429452412', '16.71173427301076', '16.91943596371198', '17.32329341599944', '17.76403973221346', '18.00396453538179', '18.58084811882844', '18.96396072171385', '19.50844697861016', '19.82070172884824'], 'prelabel': '2-348480-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.750609566502455, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 721696181476211395, 'z1': {'__RealLiteral__': 0, 'data': '0.4659155144989484', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.113958835709395', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.831055350244944', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2782.62680963758, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 348480, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -6, 0, 2, 0, 0, 0, 8, 0, 1, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, -10, 0, -2, 0, 0, 0, 12, 0, -3, 0, 0, 0, -6, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, -12, 0, -4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 4, 0, -6, 0, 0, 0, 14, 0, -8, 0, 0, 0, 2, 0, 2, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 4, 13], 'euler17': [1, 6, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 10, 41], 'euler43': [1, 2, 43], 'euler47': [1, -12, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 8, 59], 'euler61': [1, 0, 61], 'euler67': [1, 4, 67], 'euler7': [1, -2, 7], 'euler71': [1, 12, 71], 'euler73': [1, 4, 73], 'euler79': [1, -10, 79], 'euler83': [1, -4, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -2, 7], [1, 0, 0], [1, 4, 13], [1, 6, 17], [1, -2, 19], [1, -8, 23], [1, -6, 29], [1, 0, 31], [1, -6, 37], [1, 10, 41], [1, 2, 43], [1, -12, 47], [1, 6, 53], [1, 8, 59], [1, 0, 61], [1, 4, 67], [1, 12, 71], [1, 4, 73], [1, -10, 79], [1, -4, 83], [1, -14, 89], [1, -2, 97]], 'index': 127, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/348480/oz'], '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': '2-348480-1.1-c1-0-127', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-348480-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.750609566502455, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 721696181476211395, 'z1': {'__RealLiteral__': 0, 'data': '0.4659155144989484', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '721696181476211395', 'Lhash_array': ['721696181476211395'], 'label': '2-348480-1.1-c1-0-127', 'type': 'ECQ', 'url': 'EllipticCurve/Q/348480/oz'}