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lfunc_lfunctions • Show schema
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{'Lhash': '1062068384239829183851502528314', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, -5], [1, 2, 343], [1, 30, 1331], [1, 4, 2197], [1, -90, 4913], [1, -28, 6859], [1, 120, 12167], [1, -210, 24389], [1, -4, 29791], [1, -200, 50653], [1, -240, 68921], [1, -136, 79507], [1, -120, 103823], [1, 30, 148877], [1, -450, 205379], [1, 166, 226981], [1, 908, 300763], [1, -1020, 357911], [1, 250, 389017], [1, -916, 493039], [1, -1140, 571787], [1, 420, 704969], [1, -1538, 912673], [1, -450, 1030301], [1, -1150, 1092727], [1, -1620, 1225043], [1, 1702, 1295029], [1, -1350, 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'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/720/4/a/w', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.0976601473877627, 2.0838340829953466, 2.042496527255077, 1.9740704544851908, 1.8792642224677663, 1.7590761918881876, 1.614800254093508, 1.4480313811475611, 1.2606701323531488, 1.0549249216758245, 0.8333107770381444, 0.5986433091678693, 0.35402665624351254, 0.1028342805459863, -0.15131833765480035, -0.40460983972952497, -0.6530584191361596, -0.8925766840358529, -1.1190357431617435, -1.328337930781319, -1.5164971968161167, -1.679725795333369, -1.814525521076948, -1.9177813825891052, -1.9868552754504862, -2.0196769441260636, -2.0148293095966716, -1.9716251055342964, -1.8901717202958348, -1.7714211958601647, -1.617202496180914, -1.4302334316327798, -1.2141100153099875, -0.9732715290876816, -0.7129401865694701, 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'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 726593591685499783, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.837824226998049038090069762986', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.28504536800406333302608894255', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31655207623427489151424090499', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 5, 0, -2, 0, 0, 0, -30, 0, -4, 0, 0, 0, 90, 0, 28, 0, 0, 0, -120, 0, 25, 0, 0, 0, 210, 0, 4, 0, 0, 0, -10, 0, 200, 0, 0, 0, 240, 0, 136, 0, 0, 0, 120, 0, -339, 0, 0, 0, -30, 0, -150, 0, 0, 0, 450, 0, -166, 0, 0, 0, -20, 0, -908, 0, 0, 0, 1020, 0, -250, 0, 0, 0, 60, 0, 916, 0, 0, 0, 1140, 0, 450, 0, 0, 0, -420, 0, 8, 0, 0, 0, 140, 0, 1538, 0, 0, 0], 'euler11': [1, 30, 1331], 'euler13': [1, 4, 2197], 'euler17': [1, -90, 4913], 'euler19': [1, -28, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 120, 12167], 'euler29': [1, -210, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -4, 29791], 'euler37': [1, -200, 50653], 'euler41': [1, -240, 68921], 'euler43': [1, -136, 79507], 'euler47': [1, -120, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 30, 148877], 'euler59': [1, -450, 205379], 'euler61': [1, 166, 226981], 'euler67': [1, 908, 300763], 'euler7': [1, 2, 343], 'euler71': [1, -1020, 357911], 'euler73': [1, 250, 389017], 'euler79': [1, -916, 493039], 'euler83': [1, -1140, 571787], 'euler89': [1, 420, 704969], 'euler97': [1, -1538, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -5, 0], [1, 2, 343], [1, 30, 1331], [1, 4, 2197], [1, -90, 4913], [1, -28, 6859], [1, 120, 12167], [1, -210, 24389], [1, -4, 29791], [1, -200, 50653], [1, -240, 68921], [1, -136, 79507], [1, -120, 103823], [1, 30, 148877], [1, -450, 205379], [1, 166, 226981], [1, 908, 300763], [1, -1020, 357911], [1, 250, 389017], [1, -916, 493039], [1, -1140, 571787], [1, 420, 704969], [1, -1538, 912673]], 'index': 9, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/w/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/w'], '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': '2-720-1.1-c3-0-9', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 726593591685499783, 'z1': {'__RealLiteral__': 0, 'data': '0.837824226998049038090069762986', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20472456
{'Lhash': '1062068384239829183851502528314', 'Lhash_array': ['1062068384239829183851502528314'], 'label': '2-720-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/w'}
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id: 24569830
{'Lhash': '1062068384239829183851502528314', 'Lhash_array': ['1062068384239829183851502528314'], 'label': '2-720-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/w/1/1'}