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lfunc_lfunctions • Show schema
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{'Lhash': '2661575928169326777157377640453', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 96, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -239, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.43522868334421, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '196.1', 'coefficient_field': '1.1.1.1', 'conductor': 196, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, -2, 243], [1, -96, 3125], [1], [1, 720, 161051], [1, 572, 371293], [1, 1254, 1419857], [1, -94, 2476099], [1, -96, 6436343], [1, 4374, 20511149], [1, -6244, 28629151], [1, 10798, 69343957], [1, 12006, 115856201], [1, 9160, 147008443], [1, -25836, 229345007], [1, -1014, 418195493], [1, 1242, 714924299], [1, 7592, 844596301], [1, -41132, 1350125107], [1, 37632, 1804229351], [1, -13438, 2073071593], [1, -6248, 3077056399], [1, -25254, 3939040643], [1, -45126, 5584059449], [1, 107222, 8587340257], [1, 47136, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-14e2-1.1-c5-0-15', '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/196/6/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [-1.988447850504068e-60, 0.24687770895843558, 0.4913753672684383, 0.731132784046001, 0.9638295473745663, 1.187205054322069, 1.3990786872555265, 1.5973701486800238, 1.7801199368910203, 1.945509908998654, 2.0918838374357915, 2.2177678221384807, 2.3218903745682984, 2.4032019431228226, 2.460893603827202, 2.494414597141164, 2.503488352894228, 2.488126612403435, 2.4486412313076413, 2.38565323005863, 2.3000986527074367, 2.193230799820596, 2.066618419066022, 1.9221394680009765, 1.7619701083877346, 1.5885686501694634, 1.4046542359433944, 1.2131801428985916, 1.0173016778922381, 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'10.84152863973636487883247785398427'], 'prelabel': '2-14e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.606712823334561, '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': 906857568570812570, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09961319601010981579420234783', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78598837853104579456271448294', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.04176549946548992694004507212', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.43522868334421, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 196, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 96, 0, 0, 0, -239, 0, -720, 0, -572, 0, 192, 0, -1254, 0, 94, 0, 0, 0, 96, 0, 6091, 0, -964, 0, -4374, 0, 6244, 0, -1440, 0, 0, 0, -10798, 0, -1144, 0, -12006, 0, -9160, 0, -22944, 0, 25836, 0, 0, 0, -2508, 0, 1014, 0, -69120, 0, 188, 0, -1242, 0, -7592, 0, 0, 0, -54912, 0, 41132, 0, 192, 0, -37632, 0, 13438, 0, 12182, 0, 0, 0, 6248, 0, 56149, 0, 25254, 0, -120384, 0, -8748, 0, 45126, 0, 0, 0, 12488, 0, 9024, 0, -107222, 0, 172080, 0], 'euler11': [1, 720, 161051], 'euler13': [1, 572, 371293], 'euler17': [1, 1254, 1419857], 'euler19': [1, -94, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -96, 6436343], 'euler29': [1, 4374, 20511149], 'euler3': [1, -2, 243], 'euler31': [1, -6244, 28629151], 'euler37': [1, 10798, 69343957], 'euler41': [1, 12006, 115856201], 'euler43': [1, 9160, 147008443], 'euler47': [1, -25836, 229345007], 'euler5': [1, -96, 3125], 'euler53': [1, -1014, 418195493], 'euler59': [1, 1242, 714924299], 'euler61': [1, 7592, 844596301], 'euler67': [1, -41132, 1350125107], 'euler7': [1, 0, 0], 'euler71': [1, 37632, 1804229351], 'euler73': [1, -13438, 2073071593], 'euler79': [1, -6248, 3077056399], 'euler83': [1, -25254, 3939040643], 'euler89': [1, -45126, 5584059449], 'euler97': [1, 107222, 8587340257], 'euler_factors': [[1, 0, 0], [1, -2, 243], [1, -96, 3125], [1, 0, 0], [1, 720, 161051], [1, 572, 371293], [1, 1254, 1419857], [1, -94, 2476099], [1, -96, 6436343], [1, 4374, 20511149], [1, -6244, 28629151], [1, 10798, 69343957], [1, 12006, 115856201], [1, 9160, 147008443], [1, -25836, 229345007], [1, -1014, 418195493], [1, 1242, 714924299], [1, 7592, 844596301], [1, -41132, 1350125107], [1, 37632, 1804229351], [1, -13438, 2073071593], [1, -6248, 3077056399], [1, -25254, 3939040643], [1, -45126, 5584059449], [1, 107222, 8587340257]], 'index': 15, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/196/6/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/196/6/a/d'], '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': '2-14e2-1.1-c5-0-15', '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': '2-14e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.606712823334561, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 906857568570812570, 'z1': {'__RealLiteral__': 0, 'data': '2.09961319601010981579420234783', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20712499
{'Lhash': '2661575928169326777157377640453', 'Lhash_array': ['2661575928169326777157377640453'], 'label': '2-14e2-1.1-c5-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/196/6/a/d'}
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id: 24563775
{'Lhash': '2661575928169326777157377640453', 'Lhash_array': ['2661575928169326777157377640453'], 'label': '2-14e2-1.1-c5-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/196/6/a/d/1/1'}