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lfunc_lfunctions • Show schema
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{'Lhash': '1049270279552996039714619535984,1536037681297506439004696285674', 'a10': -1, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.614594053632576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1]], [5, [1, 1, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '3240.1', 'coefficient_field': '1.1.1.1', 'conductor': 10497600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, -1, 1], [1], [1, 1, 1], [1, 0, -1, 0, 1], [1, 0, -1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, -3, 4, -3, 1], [1, 0, 2, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -3, 4, -3, 1], [1, 3, 4, 3, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], 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['0.827728302549680570199567503576421', '1.21172007572193496484057924199140', '2.48135939208053609214986728750139', '2.65501909914820034429238370498917', '3.17829903633742274743160476212583', '3.55801591570220950716833100702935', '3.99993929063249794312464487497451', '4.44139765229329629851185928633300', '4.68556014356963110531476053952957', '5.12441084845364472506472216576649', '5.63689739952118966535027718403391', '5.78625466329583375377506267024878', '6.37538762640902366912605595906687', '6.72186047110978722716552833667108', '7.21109525321414142132101978869690', '7.50192707701956675179681701891142', '7.83742917416974922249155223261603', '8.186860105875462530177872551970013', '8.811558973847702002655833772939127', '8.872271334701190448041472904084840'], 'prelabel': '4-3240e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2716016046431082, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 87876140844416285, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.827728302549680570199567503576', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.21172007572193496484057924199', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.48135939208053609214986728750', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.614594053632576, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 10497600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 1, 0, 0], 'euler11': [1, 0, -1, 0, 1], 'euler13': [1, 0, -1, 0, 1], 'euler17': [1, 0, 1, 0, 1], 'euler19': [1, -2, 3, -2, 1], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, -1, 0, -1, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -3, 4, -3, 1], 'euler37': [1, 0, 2, 0, 1], 'euler41': [1, 0, -1, 0, 1], 'euler43': [1, 0, 1, 0, 1], 'euler47': [1, -2, 3, -2, 1], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, -2, 3, -2, 1], 'euler59': [1, 0, -1, 0, 1], 'euler61': [1, 3, 4, 3, 1], 'euler67': [1, 0, 1, 0, 1], 'euler7': [1, 0, -1, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, -3, 4, -3, 1], 'euler83': [1, 3, 4, 3, 1], 'euler89': [1, 0, 2, 0, 1], 'euler97': [1, 0, 1, 0, 1], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 1, 1, 0, 0], [1, 0, -1, 0, 1], [1, 0, -1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, -3, 4, -3, 1], [1, 0, 2, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -3, 4, -3, 1], [1, 3, 4, 3, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3240/1/z/g'], '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': '4-3240e2-1.1-c0e2-0-10', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-3240e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2716016046431082, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 87876140844416285, 'z1': {'__RealLiteral__': 0, 'data': '0.827728302549680570199567503576', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1049270279552996039714619535984,1536037681297506439004696285674', 'Lhash_array': ['1049270279552996039714619535984', '1536037681297506439004696285674'], 'label': '4-3240e2-1.1-c0e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3240/1/z/g'}