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lfunc_lfunctions • Show schema
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{'Lhash': '3280148870917769619209545459223', 'a10': 384, 'a2': 4, 'a3': 0, 'a4': 16, 'a5': 96, 'a6': 0, 'a7': -148, 'a8': 64, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '18.1', 'coefficient_field': '1.1.1.1', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1, -4], [1], [1, -96, 3125], [1, 148, 16807], [1, 384, 161051], [1, 334, 371293], [1, 576, 1419857], [1, 664, 2476099], [1, -3840, 6436343], [1, 96, 20511149], [1, 4564, 28629151], [1, -5798, 69343957], [1, -6720, 115856201], [1, 14872, 147008443], [1, -19200, 229345007], [1, 7776, 418195493], [1, -13056, 714924299], [1, -42782, 844596301], [1, -36656, 1350125107], [1, 64512, 1804229351], [1, 16810, 2073071593], [1, -28076, 3077056399], [1, -66432, 3939040643], [1, -81792, 5584059449], [1, 29938, 8587340257], [1, 178656, 10510100501], [1, 115228, 11592740743], [1, -76032, 14025517307], [1, 231118, 15386239549], [1, 142464, 18424351793]], 'euler_factors_factorization': [[[[1, -4], 1]], [1], [[[1, -96, 3125], 1]], [[[1, 148, 16807], 1]], [[[1, 384, 161051], 1]], [[[1, 334, 371293], 1]], [[[1, 576, 1419857], 1]], [[[1, 664, 2476099], 1]], [[[1, -3840, 6436343], 1]], [[[1, 96, 20511149], 1]], [[[1, 4564, 28629151], 1]], [[[1, -5798, 69343957], 1]], [[[1, -6720, 115856201], 1]], [[[1, 14872, 147008443], 1]], [[[1, -19200, 229345007], 1]], [[[1, 7776, 418195493], 1]], [[[1, -13056, 714924299], 1]], [[[1, -42782, 844596301], 1]], [[[1, -36656, 1350125107], 1]], [[[1, 64512, 1804229351], 1]], [[[1, 16810, 2073071593], 1]], [[[1, -28076, 3077056399], 1]], [[[1, -66432, 3939040643], 1]], [[[1, -81792, 5584059449], 1]], [[[1, 29938, 8587340257], 1]], [[[1, 178656, 10510100501], 1]], [[[1, 115228, 11592740743], 1]], [[[1, -76032, 14025517307], 1]], [[[1, 231118, 15386239549], 1]], [[[1, 142464, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-18-1.1-c5-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/18/6/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [2.123602411270673, 2.1161465644802835, 2.0935213809993725, 2.054973188902293, 1.9993097811892453, 1.9249952894352769, 1.8302809236052748, 1.713369231115169, 1.5726083882624335, 1.4067114555849263, 1.2149934121525534, 0.9976161243493936, 0.7558283103694458, 0.4921842682949633, 0.21072200146217898, -0.08292113948265643, -0.3814785416341039, -0.6761330393036246, -0.9567245579523628, -1.2121017368550762, -1.4306243613915774, -1.6008122533350035, -1.7121224171371634, -1.7558204067635217, -1.7258951627727588, -1.6199504847696187, -1.4399927126927976, 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'13.35310454643201799098019411633596', '14.82156040587080557317119381944807', '16.34251531634846100275437785659065', '17.49466129180326407137472810357145'], 'prelabel': '2-18-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.699090567519475, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1940508483990430124, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.58758120757187154637192667425', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.37391288708458114310503425939', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.71238824062391881201071462974', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 4, 0, 16, 96, 0, -148, 64, 0, 384, -384, 0, -334, -592, 0, 256, -576, 0, -664, 1536, 0, -1536, 3840, 0, 6091, -1336, 0, -2368, -96, 0, -4564, 1024, 0, -2304, -14208, 0, 5798, -2656, 0, 6144, 6720, 0, -14872, -6144, 0, 15360, 19200, 0, 5097, 24364, 0, -5344, -7776, 0, -36864, -9472, 0, -384, 13056, 0, 42782, -18256, 0, 4096, -32064, 0, 36656, -9216, 0, -56832, -64512, 0, -16810, 23192, 0, -10624, 56832, 0, 28076, 24576, 0, 26880, 66432, 0, -55296, -59488, 0, -24576, 81792, 0, 49432, 61440, 0, 76800, -63744, 0, -29938, 20388, 0, 97456], 'euler11': [1, 384, 161051], 'euler13': [1, 334, 371293], 'euler17': [1, 576, 1419857], 'euler19': [1, 664, 2476099], 'euler2': [1, -4, 0], 'euler23': [1, -3840, 6436343], 'euler29': [1, 96, 20511149], 'euler3': [1, 0, 0], 'euler31': [1, 4564, 28629151], 'euler37': [1, -5798, 69343957], 'euler41': [1, -6720, 115856201], 'euler43': [1, 14872, 147008443], 'euler47': [1, -19200, 229345007], 'euler5': [1, -96, 3125], 'euler53': [1, 7776, 418195493], 'euler59': [1, -13056, 714924299], 'euler61': [1, -42782, 844596301], 'euler67': [1, -36656, 1350125107], 'euler7': [1, 148, 16807], 'euler71': [1, 64512, 1804229351], 'euler73': [1, 16810, 2073071593], 'euler79': [1, -28076, 3077056399], 'euler83': [1, -66432, 3939040643], 'euler89': [1, -81792, 5584059449], 'euler97': [1, 29938, 8587340257], 'euler_factors': [[1, -4, 0], [1, 0, 0], [1, -96, 3125], [1, 148, 16807], [1, 384, 161051], [1, 334, 371293], [1, 576, 1419857], [1, 664, 2476099], [1, -3840, 6436343], [1, 96, 20511149], [1, 4564, 28629151], [1, -5798, 69343957], [1, -6720, 115856201], [1, 14872, 147008443], [1, -19200, 229345007], [1, 7776, 418195493], [1, -13056, 714924299], [1, -42782, 844596301], [1, -36656, 1350125107], [1, 64512, 1804229351], [1, 16810, 2073071593], [1, -28076, 3077056399], [1, -66432, 3939040643], [1, -81792, 5584059449], [1, 29938, 8587340257]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/6/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/18/6/a/c'], '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': '2-18-1.1-c5-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-18-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.699090567519475, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1940508483990430124, 'z1': {'__RealLiteral__': 0, 'data': '2.58758120757187154637192667425', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9995086
{'Lhash': '3280148870917769619209545459223', 'Lhash_array': ['3280148870917769619209545459223'], 'label': '2-18-1.1-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/6/a/c'}
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id: 24549111
{'Lhash': '3280148870917769619209545459223', 'Lhash_array': ['3280148870917769619209545459223'], 'label': '2-18-1.1-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/6/a/c/1/1'}