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lfunc_lfunctions • Show schema
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{'Lhash': '632495282512378801387479320473,2377438819076784338512221828097', 'a10': -1, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.95681151086295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [5, [1, 1, 1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '1960.1', 'coefficient_field': '1.1.1.1', 'conductor': 3841600, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, 0, 1, 0, 1], [1, 1, 1], [1], [1, -1, 0, -1, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 1, 0, 1, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 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['0.49895080111073473926780434137245', '1.87546853892448540342866567914976', '2.60555079813967805201716209879150', '2.64981295554159799151061999250138', '3.65057539839967050742999293568117', '3.72097064814655019970564345140005', '4.40631370173048945845939277509692', '4.41936262204184481569765927544491', '5.26641287380979921991738051874880', '5.29941768361267823946218681732580', '6.07864227645811768284050192544854', '6.19170417659035679578922542186179', '6.79473770906631067789140861897791', '7.14933828685915463819293228800629', '7.70304075584915321926070795752683', '7.87013434859997303068917552512600', '8.447999485081896129564081944489590', '8.825314246377564816052352640215279', '9.040653047713604678570768425618499', '9.903016701238506036072904180450014'], 'prelabel': '4-1960e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9890234702779731, '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': 1764739657767781169, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49895080111073473926780434137', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87546853892448540342866567915', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60555079813967805201716209879', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.95681151086295, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 3841600, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, -1, 0, 0, -1, -1, -1, 1, 0, -2, 0, 0, -1, 0, -1, -1, 0, 0, 1, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 2, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, -1, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0], 'euler11': [1, -1, 0, -1, 1], 'euler13': [1, 2, 3, 2, 1], 'euler17': [1, 0, 1, 0, 1], 'euler19': [1, 1, 0, 1, 1], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 1, 0, 1, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 1, 0, 1], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, 1, 0, 1, 1], 'euler41': [1, -2, 3, -2, 1], 'euler43': [1, 0, -2, 0, 1], 'euler47': [1, -1, 0, -1, 1], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, 1, 0, 1, 1], 'euler59': [1, -2, 3, -2, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, 0, 1, 0, 1], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, 1, 0, 1], 'euler79': [1, 0, 1, 0, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, -2, 3, -2, 1], 'euler97': [1, 0, -2, 0, 1], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 1, 0, 1], [1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, -1, 0, -1, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 1, 0, 1, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1960/1/bi/b'], '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': '4-1960e2-1.1-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': '4-1960e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9890234702779731, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1764739657767781169, 'z1': {'__RealLiteral__': 0, 'data': '0.49895080111073473926780434137', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '632495282512378801387479320473,2377438819076784338512221828097', 'Lhash_array': ['632495282512378801387479320473', '2377438819076784338512221828097'], 'label': '4-1960e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/1/bi/b'}