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lfunc_lfunctions • Show schema
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{'Lhash': '1538682059297886090806764626738', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 13, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.700573001722194, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '300.1', 'coefficient_field': '1.1.1.1', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, -3], [1], [1, -13, 343], [1, -6, 1331], [1, 5, 2197], [1, -78, 4913], [1, -65, 6859], [1, 138, 12167], [1, -66, 24389], [1, -299, 29791], [1, -214, 50653], [1, -360, 68921], [1, 203, 79507], [1, 78, 103823], [1, 636, 148877], [1, -786, 205379], [1, -467, 226981], [1, -217, 300763], [1, 360, 357911], [1, -286, 389017], [1, -272, 493039], [1, 498, 571787], [1, 0, 704969], [1, -511, 912673], [1, 1812, 1030301], [1, -1708, 1092727], [1, 1236, 1225043], [1, 1543, 1295029], [1, 1884, 1442897]], 'euler_factors_factorization': [[1], [[[1, -3], 1]], [1], [[[1, -13, 343], 1]], [[[1, -6, 1331], 1]], [[[1, 5, 2197], 1]], [[[1, -78, 4913], 1]], [[[1, -65, 6859], 1]], [[[1, 138, 12167], 1]], [[[1, -66, 24389], 1]], [[[1, -299, 29791], 1]], [[[1, -214, 50653], 1]], [[[1, -360, 68921], 1]], [[[1, 203, 79507], 1]], [[[1, 78, 103823], 1]], [[[1, 636, 148877], 1]], [[[1, -786, 205379], 1]], [[[1, -467, 226981], 1]], [[[1, -217, 300763], 1]], [[[1, 360, 357911], 1]], [[[1, -286, 389017], 1]], [[[1, -272, 493039], 1]], [[[1, 498, 571787], 1]], [[[1, 0, 704969], 1]], [[[1, -511, 912673], 1]], [[[1, 1812, 1030301], 1]], [[[1, -1708, 1092727], 1]], [[[1, 1236, 1225043], 1]], [[[1, 1543, 1295029], 1]], [[[1, 1884, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-300-1.1-c3-0-3', 'leading_term': '2.56651002309610727695413880710000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, '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/300/4/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [2.5665100230961073, 2.5563740203093923, 2.5260081509580505, 2.475541423108727, 2.4051973545372056, 2.315306270876287, 2.2063216249987203, 2.078839481841741, 1.93362012546145, 1.771610595393796, 1.5939668510572693, 1.4020741978975175, 1.1975645878152859, 0.9823294287587764, 0.7585266032676465, 0.5285805020359529, 0.29517402491690553, 0.061231686824196024, -0.1701068119347341, -0.3955229343110502, -0.6115656683746888, -0.8147076791065783, -1.0014106861821885, -1.168199146598797, -1.311740955478481, -1.4289335143886306, -1.5169931654222295, -1.5735456637382084, -1.596715074931356, -1.5852082506999157, -1.5383918710782056, -1.4563589577374714, -1.3399817730877708, -1.1909481348364055, -1.0117784034291715, -0.8058207453630608, 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True, 'rational': True, 'root_analytic_conductor': 4.207204891816204, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 689497916705877597, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21380612214506098606079871789', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69118882015012861156818223027', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00933457553956148010146370143', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.700573001722194, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, 0, 0, 13, 0, 9, 0, 6, 0, -5, 0, 0, 0, 78, 0, 65, 0, 39, 0, -138, 0, 0, 0, 27, 0, 66, 0, 299, 0, 18, 0, 0, 0, 214, 0, -15, 0, 360, 0, -203, 0, 0, 0, -78, 0, -174, 0, 234, 0, -636, 0, 0, 0, 195, 0, 786, 0, 467, 0, 117, 0, 0, 0, 217, 0, -414, 0, -360, 0, 286, 0, 0, 0, 78, 0, 272, 0, 81, 0, -498, 0, 0, 0, 198, 0, 0, 0, -65, 0, 897, 0, 0, 0, 511, 0, 54, 0], 'euler11': [1, -6, 1331], 'euler13': [1, 5, 2197], 'euler17': [1, -78, 4913], 'euler19': [1, -65, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 138, 12167], 'euler29': [1, -66, 24389], 'euler3': [1, -3, 0], 'euler31': [1, -299, 29791], 'euler37': [1, -214, 50653], 'euler41': [1, -360, 68921], 'euler43': [1, 203, 79507], 'euler47': [1, 78, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 636, 148877], 'euler59': [1, -786, 205379], 'euler61': [1, -467, 226981], 'euler67': [1, -217, 300763], 'euler7': [1, -13, 343], 'euler71': [1, 360, 357911], 'euler73': [1, -286, 389017], 'euler79': [1, -272, 493039], 'euler83': [1, 498, 571787], 'euler89': [1, 0, 704969], 'euler97': [1, -511, 912673], 'euler_factors': [[1, 0, 0], [1, -3, 0], [1, 0, 0], [1, -13, 343], [1, -6, 1331], [1, 5, 2197], [1, -78, 4913], [1, -65, 6859], [1, 138, 12167], [1, -66, 24389], [1, -299, 29791], [1, -214, 50653], [1, -360, 68921], [1, 203, 79507], [1, 78, 103823], [1, 636, 148877], [1, -786, 205379], [1, -467, 226981], [1, -217, 300763], [1, 360, 357911], [1, -286, 389017], [1, -272, 493039], [1, 498, 571787], [1, 0, 704969], [1, -511, 912673]], 'index': 3, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/4/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/300/4/a/h'], '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': '2-300-1.1-c3-0-3', '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': '2-300-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.207204891816204, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 689497916705877597, 'z1': {'__RealLiteral__': 0, 'data': '1.21380612214506098606079871789', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20576173
{'Lhash': '1538682059297886090806764626738', 'Lhash_array': ['1538682059297886090806764626738'], 'label': '2-300-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/4/a/h'}
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id: 24556307
{'Lhash': '1538682059297886090806764626738', 'Lhash_array': ['1538682059297886090806764626738'], 'label': '2-300-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/4/a/h/1/1'}