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lfunc_lfunctions • Show schema
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{'Lhash': '220843603397667282926181448273', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [-16.0, 27.712812921102035], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 95.58309420929984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, 4.330127018922194]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.541', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '1848393478397554583569800104497', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, 4.330127018922194]], [[1.0, 0], [16.0, -27.712812921102035], [-171.5, -297.04671349806245]], [[1.0, 0], [18.0, -31.176914536239792], [-665.5, -1152.6798124370878]], [[1.0, 0], [-5.0, -8.660254037844387], [-1098.5, 1902.6578121144116]], [[1.0, 0], [78.0, 0], 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'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17421488488855393119858874445', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.916182371466648722003163065475', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.67356631562821885401949476438', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 95.58309420929984, 'bad_primes': [2, 3, 5], 'central_character': '9.7', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/4/i/a/541/1'], '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': '2-1620-9.7-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1620-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.776660688051921, 'root_angle': 0.4444444444444444, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17421488488855393119858874445', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '220843603397667282926181448273', 'Lhash_array': ['220843603397667282926181448273'], 'label': '2-1620-9.7-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/4/i/a/541/1'}