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lfunc_lfunctions • Show schema
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{'Lhash': '1623327557465523710337309311699', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [4.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.847069993022323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.5, 2.598076211353316]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.577', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '1073150552849653525119122970989', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-4.0, 0], [7.0, 0]], [[1.0, 0], [-3.0, 0], [11.0, 0]], [[1.0, 0], [1.0, -1.7320508075688772], [-6.5, -11.258330249197702]], [[1.0, 0], [3.0, 5.196152422706632], [-8.5, 14.722431864335457]], [[1.0, 0], [-3.5, 2.598076211353316]], [[1.0, 0], [-3.0, 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-1.0151317665395516], 'positive_zeros': ['1.28057964645246709468571462560304', '1.92066422338471273666688719567305', '3.38410425171896998797815321963829', '4.11220154871372790066642210529830', '5.14055131386955070080165044730393', '5.58974977633622392681504014934411', '6.73228229957901982452071099600119', '7.47048054528617358571003891895502', '8.130877166547134200525843133548695', '8.866965424272802510991259639093536'], 'prelabel': '2-2736-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.1978267572087798, 'root_number': '0.81301117816884032351440209511977384091655159862157482836 + 0.58224807786072954570011168939974070428290544625585496123*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0989133786043899', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28057964645246709468571462560', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92066422338471273666688719567', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38410425171896998797815321964', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.847069993022323, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/s/m/577/1'], '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': '2-2736-19.7-c1-0-37', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2736-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0989133786043899, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28057964645246709468571462560', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1623327557465523710337309311699', 'Lhash_array': ['1623327557465523710337309311699'], 'label': '2-2736-19.7-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/s/m/577/1'}