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  • lfunc_lfunctions • Show schema
    {'Lhash': '566322648490203536034537430115,805037379380426425992945489852,1412446275869257417385992352483', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5421.249105625978, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1, 3, 3, 1]]], 'bad_primes': [2, 5, 11], 'central_character': '2200.1', 'coefficient_field': '1.1.1.1', 'conductor': 10648000000, 'conductor_radical': 110, 'degree': 6, 'euler_factors': [[1], [1, 3, 6, 12, 18, 27, 27], [1], [1, 3, 12, 46, 84, 147, 343], [1, 3, 3, 1], [1, -3, 18, -63, 234, -507, 2197], [1, -3, 6, 42, 102, -867, 4913], [1, -3, 60, -115, 1140, -1083, 6859], [1, 6, 75, 271, 1725, 3174, 12167], [1, -12, 123, -727, 3567, -10092, 24389], [1, 3, 48, 259, 1488, 2883, 29791], [1, 12, 138, 884, 5106, 16428, 50653], [1, -6, 120, -472, 4920, -10086, 68921], [1, -3, 117, -246, 5031, -5547, 79507], 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'6.44515523634209317910223154526356', '6.60965751098201312542657254621142', '6.80141232095902593283783879394984', '7.18846712844719106028004406160262', '7.54935573010258722821344517852630', '7.78878792613622072607170191081764', '7.83163558738275652358828872145119', '8.381230539875650900496307410201327', '8.548880320533701841341380684435572', '8.779735000195626485175686026905674', '8.980198449317009464798905650326890', '9.426795212596510906008990318958381'], 'prelabel': '6-2200e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.191311065130061, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 804463112880766858, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44674979713514283605877692824', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.63506251583479429433550521403', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '1.11422364775826936943401366603', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 5421.249105625978, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 10648000000, 'conductor_radical': 110, 'degree': 6, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, -3, 0, 3, 0, -3, 0, 3, 0, 0, 0, 3, 0, 3, 0, 9, 0, -6, 0, 0, 0, -3, 0, 12, 0, -3, 0, 9, 0, 0, 0, -12, 0, -9, 0, 6, 0, 3, 0, 0, 0, -12, 0, -3, 0, -9, 0, 9, 0, 0, 0, -9, 0, 24, 0, -3, 0, -9, 0, 0, 0, -6, 0, 18, 0, -15, 0, 33, 0, 0, 0, 9, 0, 15, 0, 9, 0, -6, 0, 0, 0, -36, 0, 6, 0, -9, 0, 9, 0, 0, 0, 18, 0, -9, 0], 'euler11': [1, 3, 3, 1, 0, 0, 0], 'euler13': [1, -3, 18, -63, 234, -507, 2197], 'euler17': [1, -3, 6, 42, 102, -867, 4913], 'euler19': [1, -3, 60, -115, 1140, -1083, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 6, 75, 271, 1725, 3174, 12167], 'euler29': [1, -12, 123, -727, 3567, -10092, 24389], 'euler3': [1, 3, 6, 12, 18, 27, 27], 'euler31': [1, 3, 48, 259, 1488, 2883, 29791], 'euler37': [1, 12, 138, 884, 5106, 16428, 50653], 'euler41': [1, -6, 120, -472, 4920, -10086, 68921], 'euler43': [1, -3, 117, -246, 5031, -5547, 79507], 'euler47': [1, 12, 132, 1120, 6204, 26508, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -9, 90, -412, 4770, -25281, 148877], 'euler59': [1, -24, 312, -2732, 18408, -83544, 205379], 'euler61': [1, 3, 72, 20, 4392, 11163, 226981], 'euler67': [1, 6, 153, 676, 10251, 26934, 300763], 'euler7': [1, 3, 12, 46, 84, 147, 343], 'euler71': [1, 15, 111, 630, 7881, 75615, 357911], 'euler73': [1, -33, 570, -6002, 41610, -175857, 389017], 'euler79': [1, -15, 258, -2198, 20382, -93615, 493039], 'euler83': [1, 6, 147, 1009, 12201, 41334, 571787], 'euler89': [1, -6, 165, -615, 14685, -47526, 704969], 'euler97': [1, -18, 171, -1015, 16587, -169362, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 3, 6, 12, 18, 27, 27], [1, 0, 0, 0, 0, 0, 0], [1, 3, 12, 46, 84, 147, 343], [1, 3, 3, 1, 0, 0, 0], [1, -3, 18, -63, 234, -507, 2197], [1, -3, 6, 42, 102, -867, 4913], [1, -3, 60, -115, 1140, -1083, 6859], [1, 6, 75, 271, 1725, 3174, 12167], [1, -12, 123, -727, 3567, -10092, 24389], [1, 3, 48, 259, 1488, 2883, 29791], [1, 12, 138, 884, 5106, 16428, 50653], [1, -6, 120, -472, 4920, -10086, 68921], [1, -3, 117, -246, 5031, -5547, 79507], [1, 12, 132, 1120, 6204, 26508, 103823], [1, -9, 90, -412, 4770, -25281, 148877], [1, -24, 312, -2732, 18408, -83544, 205379], [1, 3, 72, 20, 4392, 11163, 226981], [1, 6, 153, 676, 10251, 26934, 300763], [1, 15, 111, 630, 7881, 75615, 357911], [1, -33, 570, -6002, 41610, -175857, 389017], [1, -15, 258, -2198, 20382, -93615, 493039], [1, 6, 147, 1009, 12201, 41334, 571787], [1, -6, 165, -615, 14685, -47526, 704969], [1, -18, 171, -1015, 16587, -169362, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2200/2/a/t'], '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': '6-2200e3-1.1-c1e3-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-2200e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.191311065130061, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 804463112880766858, 'z1': {'__RealLiteral__': 0, 'data': '0.44674979713514283605877692824', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '566322648490203536034537430115,805037379380426425992945489852,1412446275869257417385992352483', 'Lhash_array': ['566322648490203536034537430115', '805037379380426425992945489852', '1412446275869257417385992352483'], 'factors': ['2-2200-1.1-c1-0-1', '2-2200-1.1-c1-0-6', '2-2200-1.1-c1-0-17'], 'label': '6-2200e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2200/2/a/t'}