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lfunc_lfunctions • Show schema
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{'Lhash': '2162309552845569807458605850213', 'a10': 0, 'a2': 0, 'a3': 729, 'a4': 0, 'a5': -14850, 'a6': 0, 'a7': 62896, 'a8': 0, 'a9': 531441, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.47084589691812, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -729]]], 'bad_primes': [2, 3], 'central_character': '48.1', 'coefficient_field': '1.1.1.1', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, -729], [1, 14850, 1220703125], [1, -62896, 96889010407], [1, 5104836, 34522712143931], [1, -11484110, 302875106592253], [1, -119964834, 9904578032905937], [1, 332601020, 42052983462257059], [1, 350924184, 504036361936467383], [1, 1761101946, 10260628712958602189], [1, -3934224616, 24417546297445042591], [1, 7803567658, 243569224216081305397], [1, -52882647930, 925103102315013629321], [1, 26018412164, 1718264124282290785243], [1, 142370739936, 5460999706120583177327], [1, -13770034398, 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'6.03392003828959394487577222876703', '7.68771504055974879779442176270464', '8.419499589405583573137361232673854', '9.903179885823731068204446726840055', '11.03098341978973556413686393957103', '12.39454109129735506169261565370113'], 'prelabel': '2-48-1.1-c13-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.1743184970363645, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c13-0', 'trace_hash': 1767177496065788028, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70576147122579746168589844033', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15626178334346068027156895474', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42461377420497324337781825620', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.47084589691812, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 729, 0, -14850, 0, 62896, 0, 531441, 0, -5104836, 0, 11484110, 0, -10825650, 0, 119964834, 0, -332601020, 0, 45851184, 0, -350924184, 0, -1000180625, 0, 387420489, 0, -1761101946, 0, 3934224616, 0, -3721425444, 0, -934005600, 0, -7803567658, 0, 8371916190, 0, 52882647930, 0, -26018412164, 0, -7891898850, 0, -142370739936, 0, -92933103591, 0, 87454363986, 0, 13770034398, 0, 75806814600, 0, -242466143580, 0, -336464984484, 0, -677260793938, 0, 33425513136, 0, -170539033500, 0, -262301598236, 0, -255823730136, 0, -1594961300520, 0, 578812819562, 0, -729131675625, 0, -321073765056, 0, -2495818789448, 0, 282429536481, 0, 2693235578436, 0, -1781477784900, 0, -1283843318634, 0, -7935538832550, 0, 722304582560, 0, 2868049745064, 0, 4939125147000, 0, -7858601662, 0, -2712919148676, 0], 'euler11': [1, 5104836, 34522712143931], 'euler13': [1, -11484110, 302875106592253], 'euler17': [1, -119964834, 9904578032905937], 'euler19': [1, 332601020, 42052983462257059], 'euler2': [1, 0, 0], 'euler23': [1, 350924184, 504036361936467383], 'euler29': [1, 1761101946, 10260628712958602189], 'euler3': [1, -729, 0], 'euler31': [1, -3934224616, 24417546297445042591], 'euler37': [1, 7803567658, 243569224216081305397], 'euler41': [1, -52882647930, 925103102315013629321], 'euler43': [1, 26018412164, 1718264124282290785243], 'euler47': [1, 142370739936, 5460999706120583177327], 'euler5': [1, 14850, 1220703125], 'euler53': [1, -13770034398, 26036721925606486195973], 'euler59': [1, 336464984484, 104972647676132430295979], 'euler61': [1, 677260793938, 161915287432152755657581], 'euler67': [1, 262301598236, 548242166610401428685587], 'euler7': [1, -62896, 96889010407], 'euler71': [1, 1594961300520, 1165087474585497590531111], 'euler73': [1, -578812819562, 1671849507393788885941033], 'euler79': [1, 2495818789448, 4668229371502258117133839], 'euler83': [1, -2693235578436, 8871870642308873326043363], 'euler89': [1, 7935538832550, 21982145917308330487013369], 'euler97': [1, 7858601662, 67302709016557486028618977], 'euler_factors': [[1, 0, 0], [1, -729, 0], [1, 14850, 1220703125], [1, -62896, 96889010407], [1, 5104836, 34522712143931], [1, -11484110, 302875106592253], [1, -119964834, 9904578032905937], [1, 332601020, 42052983462257059], [1, 350924184, 504036361936467383], [1, 1761101946, 10260628712958602189], [1, -3934224616, 24417546297445042591], [1, 7803567658, 243569224216081305397], [1, -52882647930, 925103102315013629321], [1, 26018412164, 1718264124282290785243], [1, 142370739936, 5460999706120583177327], [1, -13770034398, 26036721925606486195973], [1, 336464984484, 104972647676132430295979], [1, 677260793938, 161915287432152755657581], [1, 262301598236, 548242166610401428685587], [1, 1594961300520, 1165087474585497590531111], [1, -578812819562, 1671849507393788885941033], [1, 2495818789448, 4668229371502258117133839], [1, -2693235578436, 8871870642308873326043363], [1, 7935538832550, 21982145917308330487013369], [1, 7858601662, 67302709016557486028618977]], 'index': 11, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/14/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/48/14/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': '2-48-1.1-c13-0-11', 'motivic_weight': 13, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [13], 'order_of_vanishing': 1, 'prelabel': '2-48-1.1-c13-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.1743184970363645, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c13-0', 'trace_hash': 1767177496065788028, 'z1': {'__RealLiteral__': 0, 'data': '1.70576147122579746168589844033', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20628485
{'Lhash': '2162309552845569807458605850213', 'Lhash_array': ['2162309552845569807458605850213'], 'label': '2-48-1.1-c13-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/14/a/d'}
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id: 24575069
{'Lhash': '2162309552845569807458605850213', 'Lhash_array': ['2162309552845569807458605850213'], 'label': '2-48-1.1-c13-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/14/a/d/1/1'}