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lfunc_lfunctions • Show schema
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{'Lhash': '1639293766914090546087741423926', 'a10': 0, 'a2': 0, 'a3': -18, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 242, 'a8': 0, 'a9': 81, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.15352792519226, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': '1.1.1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, 18, 243], [1], [1, -242, 16807], [1, 656, 161051], [1, -206, 371293], [1, 1690, 1419857], [1, -1364, 2476099], [1, -2198, 6436343], [1, 2218, 20511149], [1, -1700, 28629151], [1, -846, 69343957], [1, 1818, 115856201], [1, -10534, 147008443], [1, -12074, 229345007], [1, 32586, 418195493], [1, 8668, 714924299], [1, 34670, 844596301], [1, 47566, 1350125107], [1, 948, 1804229351], [1, -63102, 2073071593], [1, 46536, 3077056399], [1, 88778, 3939040643], [1, 104934, 5584059449], [1, -36254, 8587340257], [1, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-20e2-1.1-c5-0-29', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/400/6/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [-1.4208407929335302e-60, 0.1998855342681509, 0.3957611548076778, 0.5836789407139951, 0.7598144873041586, 0.9205274767345375, 1.062420785502476, 1.1823975801706987, 1.277715805480459, 1.3460394161894396, 1.385485649257435, 1.394667580632189, 1.3727311653851695, 1.31938592597479, 1.2349284355982015, 1.1202577463433392, 0.9768819391892383, 0.8069150282774984, 0.6130635380132938, 0.3986021902901325, 0.16733829129150307, -0.07643540740193588, -0.3279993818018005, -0.5822773053336987, -0.8339168078561198, -1.0773802265428267, -1.30704424887457, -1.5173070405828077, 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'8.976036917356459858511551819094394', '10.50084565092449070908953905520465'], 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1093363773751181570, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29317476489101180046459641134', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60821472687615408318832066940', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55720539296373807513050927907', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.15352792519226, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, -18, 0, 0, 0, 242, 0, 81, 0, -656, 0, 206, 0, 0, 0, -1690, 0, 1364, 0, -4356, 0, 2198, 0, 0, 0, 2916, 0, -2218, 0, 1700, 0, 11808, 0, 0, 0, 846, 0, -3708, 0, -1818, 0, 10534, 0, 0, 0, 12074, 0, 41757, 0, 30420, 0, -32586, 0, 0, 0, -24552, 0, -8668, 0, -34670, 0, 19602, 0, 0, 0, -47566, 0, -39564, 0, -948, 0, 63102, 0, 0, 0, -158752, 0, -46536, 0, -72171, 0, -88778, 0, 0, 0, 39924, 0, -104934, 0, 49852, 0, -30600, 0, 0, 0, 36254, 0, -53136, 0], 'euler11': [1, 656, 161051], 'euler13': [1, -206, 371293], 'euler17': [1, 1690, 1419857], 'euler19': [1, -1364, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -2198, 6436343], 'euler29': [1, 2218, 20511149], 'euler3': [1, 18, 243], 'euler31': [1, -1700, 28629151], 'euler37': [1, -846, 69343957], 'euler41': [1, 1818, 115856201], 'euler43': [1, -10534, 147008443], 'euler47': [1, -12074, 229345007], 'euler5': [1, 0, 0], 'euler53': [1, 32586, 418195493], 'euler59': [1, 8668, 714924299], 'euler61': [1, 34670, 844596301], 'euler67': [1, 47566, 1350125107], 'euler7': [1, -242, 16807], 'euler71': [1, 948, 1804229351], 'euler73': [1, -63102, 2073071593], 'euler79': [1, 46536, 3077056399], 'euler83': [1, 88778, 3939040643], 'euler89': [1, 104934, 5584059449], 'euler97': [1, -36254, 8587340257], 'euler_factors': [[1, 0, 0], [1, 18, 243], [1, 0, 0], [1, -242, 16807], [1, 656, 161051], [1, -206, 371293], [1, 1690, 1419857], [1, -1364, 2476099], [1, -2198, 6436343], [1, 2218, 20511149], [1, -1700, 28629151], [1, -846, 69343957], [1, 1818, 115856201], [1, -10534, 147008443], [1, -12074, 229345007], [1, 32586, 418195493], [1, 8668, 714924299], [1, 34670, 844596301], [1, 47566, 1350125107], [1, 948, 1804229351], [1, -63102, 2073071593], [1, 46536, 3077056399], [1, 88778, 3939040643], [1, 104934, 5584059449], [1, -36254, 8587340257]], 'index': 29, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/6/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/400/6/a/b'], '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': '2-20e2-1.1-c5-0-29', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1093363773751181570, 'z1': {'__RealLiteral__': 0, 'data': '1.29317476489101180046459641134', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20237516
{'Lhash': '1639293766914090546087741423926', 'Lhash_array': ['1639293766914090546087741423926'], 'label': '2-20e2-1.1-c5-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/6/a/b'}
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id: 24582244
{'Lhash': '1639293766914090546087741423926', 'Lhash_array': ['1639293766914090546087741423926'], 'label': '2-20e2-1.1-c5-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/6/a/b/1/1'}