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lfunc_lfunctions • Show schema
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{'Lhash': '3403853064716047178029923946839', 'a10': [-0.5046578537054978, -3.486575445422432], 'a2': [1.2459314735346767, -0.6690700735018037], 'a3': [-0.6614890747472024, -1.6007598833023302], 'a4': [1.104690473488582, -1.6672309251521136], 'a5': [0.8519970931201162, -2.3408427747884963], 'a6': [-1.8951905904067008, -1.5518545763163187], 'a7': [-0.984807753012208, -0.17364817766693036], 'a8': [0.26087431179734405, -2.816370819591103], 'a9': [-2.12486440798018, 2.1177703481961965], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.2459314735346767, 0.6690700735018037]]], [3, [[1.0, 0], [0.6614890747472024, 1.6007598833023302]]], [7, [[1.0, 0], [0.984807753012208, 0.17364817766693036]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.659', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.47084748292', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.68516660987121625607252085984', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31195387645891334112085304476', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49822875712696749521659657064', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '108.11', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 105, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/cf/a/659/90'], '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': '2-756-108.11-c1-0-105', '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': '2-756-108.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': 0.470847482919992, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.68516660987121625607252085984', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3403853064716047178029923946839', 'Lhash_array': ['3403853064716047178029923946839'], 'factors': ['2-756-108.11-c1-0-105'], 'label': '2-756-108.11-c1-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/cf/a/659/90'}