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lfunc_lfunctions • Show schema
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{'Lhash': '1035807427713695229411163933428', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [0.5, 0.8660254037844386], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.935765127447429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1081', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '1636009294957136475108536663459', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-3.5, 6.06217782649107]], [[1.0, 0], [-3.0, -5.196152422706632], [-5.5, 9.526279441628825]], [[1.0, 0], [-0.5, 0.8660254037844386], [-6.5, -11.258330249197702]], [[1.0, 0], [0, 0], [17.0, 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-2.2741590069943993, -1.7962397302068116, -1.2470490156177718], 'positive_zeros': ['0.817107985060873369225355709621235', '2.16232661081501294189568825430072', '3.46317722579935583968584931004327', '4.01050746590354684390878290992691', '5.39609020589636824390682936124036', '6.03255574087117669283223451061249', '6.88927875059497253503524900795548', '7.64949770793006575000847689344424', '8.707507576078659200805731718438736', '9.117103165356682067205774154987853'], 'prelabel': '2-1620-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.596632470443349, 'root_angle': -0.22222222222222227, 'root_number': '0.76604444311897803520239265055541667393583245708039524585 - 0.6427876096865393263226434099072634329075598842056817904*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1111111111111111', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.817107985060873369225355709621', 'prec': 107}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.935765127447429, 'bad_primes': [2, 3, 5], 'central_character': '9.4', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/2/i/j/1081/1'], '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': '2-1620-9.4-c1-0-4', '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': '2-1620-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.596632470443349, 'root_angle': -0.11111111111111113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.817107985060873369225355709621', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1035807427713695229411163933428', 'Lhash_array': ['1035807427713695229411163933428'], 'label': '2-1620-9.4-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/2/i/j/1081/1'}