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lfunc_lfunctions • Show schema
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{'Lhash': '1400739157834194482163853710064', 'a10': [0, 0], 'a2': [1.224744871391589, 0.7071067811865476], 'a3': [0.8660254037844386, 1.5], 'a4': [1.0, 1.7320508075688772], 'a5': [0, 0], 'a6': [0, 2.449489742783178], 'a7': [2.8612270578730263, -6.388535021684961], 'a8': [0, 2.8284271247461903], 'a9': [-1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.224744871391589, -0.7071067811865476]]], [3, [[1.0, 0], [-0.8660254037844386, -1.5]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.8612270578730263, 6.388535021684961]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.649', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1276315173943508370778585741329', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.224744871391589, -0.7071067811865476]], [[1.0, 0], [-0.8660254037844386, -1.5]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 36, 'label': '2-1050-35.19-c2-0-36', 'leading_term': '3.253254645668709448886781157695884948635143585059938819', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/3/q/e/649/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.2532546456687093, 3.2304210138226765, 3.1858363253962114, 3.1200154316840174, 3.03349618996317, 2.9268582940149024, 2.8007473101849603, 2.6559024061086975, 2.493186084690148, 2.313614141663177, 2.1183840486707157, 1.908900018477218, 1.6867931252058126, 1.4539350199033505, 1.2124439902048862, 0.9646823535850401, 0.7132444394790501, 0.4609347008275865, 0.21073579591523212, -0.03423320708817847, -0.27076803151922807, -0.4956390061358214, -0.7056583782499388, -0.8977537014188842, 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'4.96028253358974915634332643837812', '6.18310770278231807001088391287231', '7.23073234957400720714848909535756', '7.75958684502507513705053254465905', '8.933346668843456701509821447231138', '9.669307847789920915773929222816586'], 'prelabel': '2-1050-35.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.17803641981944915, 'root_number': '0.8476172314431928451366360128020341637586519461564040446 - 0.5306081689538683067410497229307398695126658919034303589*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.08901820990972459', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10498836002760038932962353302', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56607244789170499790834106560', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80884010804755691674922087045', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.19', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/q/e/649/10'], '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': '2-1050-35.19-c2-0-36', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-35.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.08901820990972457, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10498836002760038932962353302', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1400739157834194482163853710064', 'Lhash_array': ['1400739157834194482163853710064'], 'label': '2-1050-35.19-c2-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/q/e/649/10'}