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lfunc_lfunctions • Show schema
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{'Lhash': '2148409188503824132114150973877', 'a10': -100, 'a2': -4, 'a3': -23, 'a4': 16, 'a5': 25, 'a6': 92, 'a7': 49, 'a8': -64, 'a9': 286, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.226867386908646, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 4]], [5, [1, -25]], [7, [1, -49]]], 'bad_primes': [2, 5, 7], 'central_character': '70.1', 'coefficient_field': '1.1.1.1', 'conductor': 70, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1, 4], [1, 23, 243], [1, -25], [1, -49], [1, -555, 161051], [1, 241, 371293], [1, 1491, 1419857], [1, 2038, 2476099], [1, 1230, 6436343], [1, 5001, 20511149], [1, -5696, 28629151], [1, 5602, 69343957], [1, 2424, 115856201], [1, -602, 147008443], [1, 23163, 229345007], [1, 25296, 418195493], [1, -5724, 714924299], [1, 36112, 844596301], [1, -66104, 1350125107], [1, -16080, 1804229351], [1, 80482, 2073071593], [1, 64147, 3077056399], [1, 106284, 3939040643], [1, 71676, 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'11.02999957150292822004770496216000', '11.68776992082247466515443419629148', '12.80198363756953519382522454739181'], 'prelabel': '2-70-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.35065178538574, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 697311304770950212, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69479601722826609433478555422', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.53436748796406010279818102551', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.09160417362886682952965522090', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.226867386908646, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 70, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, -4, -23, 16, 25, 92, 49, -64, 286, -100, 555, -368, -241, -196, -575, 256, -1491, -1144, -2038, 400, -1127, -2220, -1230, 1472, 625, 964, -989, 784, -5001, 2300, 5696, -1024, -12765, 5964, 1225, 4576, -5602, 8152, 5543, -1600, -2424, 4508, 602, 8880, 7150, 4920, -23163, -5888, 2401, -2500, 34293, -3856, -25296, 3956, 13875, -3136, 46874, 20004, 5724, -9200, -36112, -22784, 14014, 4096, -6025, 51060, 66104, -23856, 28290, -4900, 16080, -18304, -80482, 22408, -14375, -32608, 27195, -22172, -64147, 6400, -46751, 9696, -106284, -18032, -37275, -2408, 115023, -35520, -71676, -28600, -11809, -19680, -131008, 92652, -50950, 23552, 151025, -9604, 158730, 10000], 'euler11': [1, -555, 161051], 'euler13': [1, 241, 371293], 'euler17': [1, 1491, 1419857], 'euler19': [1, 2038, 2476099], 'euler2': [1, 4, 0], 'euler23': [1, 1230, 6436343], 'euler29': [1, 5001, 20511149], 'euler3': [1, 23, 243], 'euler31': [1, -5696, 28629151], 'euler37': [1, 5602, 69343957], 'euler41': [1, 2424, 115856201], 'euler43': [1, -602, 147008443], 'euler47': [1, 23163, 229345007], 'euler5': [1, -25, 0], 'euler53': [1, 25296, 418195493], 'euler59': [1, -5724, 714924299], 'euler61': [1, 36112, 844596301], 'euler67': [1, -66104, 1350125107], 'euler7': [1, -49, 0], 'euler71': [1, -16080, 1804229351], 'euler73': [1, 80482, 2073071593], 'euler79': [1, 64147, 3077056399], 'euler83': [1, 106284, 3939040643], 'euler89': [1, 71676, 5584059449], 'euler97': [1, -151025, 8587340257], 'euler_factors': [[1, 4, 0], [1, 23, 243], [1, -25, 0], [1, -49, 0], [1, -555, 161051], [1, 241, 371293], [1, 1491, 1419857], [1, 2038, 2476099], [1, 1230, 6436343], [1, 5001, 20511149], [1, -5696, 28629151], [1, 5602, 69343957], [1, 2424, 115856201], [1, -602, 147008443], [1, 23163, 229345007], [1, 25296, 418195493], [1, -5724, 714924299], [1, 36112, 844596301], [1, -66104, 1350125107], [1, -16080, 1804229351], [1, 80482, 2073071593], [1, 64147, 3077056399], [1, 106284, 3939040643], [1, 71676, 5584059449], [1, -151025, 8587340257]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/70/6/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/70/6/a/a'], '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': '2-70-1.1-c5-0-4', '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': '2-70-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.35065178538574, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 697311304770950212, 'z1': {'__RealLiteral__': 0, 'data': '1.69479601722826609433478555422', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12393834
{'Lhash': '2148409188503824132114150973877', 'Lhash_array': ['2148409188503824132114150973877'], 'factors': ['2-70-1.1-c5-0-4'], 'label': '2-70-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/70/6/a/a'}
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id: 24552986
{'Lhash': '2148409188503824132114150973877', 'Lhash_array': ['2148409188503824132114150973877'], 'factors': ['2-70-1.1-c5-0-4'], 'label': '2-70-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/70/6/a/a/1/1'}