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lfunc_lfunctions • Show schema
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{'Lhash': '1951695993465220921821963003113', 'a10': [0.0, 0.0], 'a2': [0.33405264748098007, -0.192865385946651], 'a3': [-1.4256058858072986, 0.9836909363980066], 'a4': [-0.9256058858072987, 1.6031964220030377], 'a5': [0.0, 0.0], 'a6': [-0.2865074883177718, 0.6035545909808404], 'a7': [-2.3697500333053725, -1.1765563223446576], 'a8': [0.0, 1.4855308893894696], 'a9': [1.0647042832968256, -2.8047111774885827], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.192146106117222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4256058858072986, -0.9836909363980066]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.3697500333053725, 1.1765563223446576]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.101', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '245214035908299047955786899971', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.33405264748098007, 0.192865385946651], [1.0, 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7.184247231798755], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-525-21.17-c1-0-28', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/525/2/t/g/101/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.31417509609115535, 0.49161913026982795, 0.6532791056624455, 0.7993187975321229, 0.92625643482081, 1.0271201260091265, 1.092118725406007, 1.1096779377282526, 1.067725923702671, 0.9551503519446203, 0.7633582409811984, 0.4878513702130374, 0.12969737404602497, -0.30325544645245694, -0.7955916633460876, -1.3241428474088435, -1.8585497359914576, -2.3626681108935434, -2.7968365091373895, -3.1209256115928623, -3.297979112076921, -3.2981466499966943, -3.102516231708923, -2.706392732410545, -2.1215556593248293, -1.3770747744288276, 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'9.526484747413626630602497121762118', '10.46050175904670522589962188181552', '10.80454620197755469391894954499434'], 'prelabel': '2-525-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': 0.5807520025697657, 'root_number': '-0.2509774549398649 + 0.9679929323667131*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.290376001285', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53961666812119611754399365543', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.32124490301189422930415205283', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91248279957756894030366677779', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.192146106117222, 'bad_primes': [3, 5, 7], 'central_character': '21.17', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/2/t/g/101/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-525-21.17-c1-0-28', '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': '2-525-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': 0.29037600128488283, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53961666812119611754399365543', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1951695993465220921821963003113', 'Lhash_array': ['1951695993465220921821963003113'], 'label': '2-525-21.17-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/2/t/g/101/2'}