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lfunc_lfunctions • Show schema
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{'Lhash': '3188372174209154286936314502348,4650771643881879392625176909954', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0022478196286802696, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [1, 2, 1]], [19, [1, 2, 1]]], 'bad_primes': [5, 19], 'central_character': '95.1', 'coefficient_field': '1.1.1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 2, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 2, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 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'3.66881192896887252833915429072116', '4.29396961792893118367281974002195', '4.75709052287312937184999225316289', '5.92355506824304704240004536395726', '6.82424315532089692950431228434584', '7.14472277853861817875692871455474', '7.88660575820453984407934978438548', '8.588273787705263002746602261300391', '8.691956235481506596317612803993709', '9.566156585394324383794480118049721', '10.64837931859429375334750285041885', '10.72883796175334370510374909404567', '11.35478032774755308995244767083130', '11.97440438418630739376367126083534', '12.22315444399224238023174054159407', '12.93875799995861054376414921190399', '13.27042701489436960383904648519861', '14.13944646882214871532234905578456', '14.61957954625341714164664019559757'], 'prelabel': '4-95e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.21774107605166104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 476004310623190306, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.51518215952811900062369427304', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.66881192896887252833915429072', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29396961792893118367281974002', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.0022478196286802696, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], 'euler11': [1, 0, 2, 0, 1], 'euler13': [1, 0, 0, 0, 1], 'euler17': [1, 0, -2, 0, 1], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 1], 'euler23': [1, 0, -2, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 0, 0, 1], 'euler31': [1, 0, -2, 0, 1], 'euler37': [1, 0, 0, 0, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, 0, -2, 0, 1], 'euler47': [1, 0, -2, 0, 1], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 0, 0, 0, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, 0, 2, 0, 1], 'euler67': [1, 0, 0, 0, 1], 'euler7': [1, 0, -2, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 0, -2, 0, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, -2, 0, 1], 'euler97': [1, 0, 0, 0, 1], 'euler_factors': [[1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 2, 1, 0, 0], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 2, 1, 0, 0], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1]], 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/1/d/b', 'ArtinRepresentation/2.95.8t6.a'], 'is_instance_Artin': True, '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': '4-95e2-1.1-c0e2-0-0', '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': '4-95e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.21774107605166104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 476004310623190306, 'z1': {'__RealLiteral__': 0, 'data': '2.51518215952811900062369427304', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24602850
{'Lhash': '3188372174209154286936314502348,4650771643881879392625176909954', 'Lhash_array': ['3188372174209154286936314502348', '4650771643881879392625176909954'], 'label': '4-95e2-1.1-c0e2-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.95.8t6.a'}
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id: 19808100
{'Lhash': '3188372174209154286936314502348,4650771643881879392625176909954', 'Lhash_array': ['3188372174209154286936314502348', '4650771643881879392625176909954'], 'label': '4-95e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/1/d/b'}