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lfunc_lfunctions • Show schema
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{'Lhash': '2636496251880207860885297968950', 'a10': [1.9866875017256656, -1.026193339720656], 'a2': [0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.10463424947035019, -2.2336185157357953], 'a6': [0.0, 0.0], 'a7': [-1.399241064175573, -2.2454675335717527], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.10463424947035019, 2.2336185157357953]]], [7, [[1.0, 0], [1.399241064175573, 2.2454675335717527]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '630.269', 'coefficient_field': 'CDF', 'conductor': 630, 'conductor_radical': 210, 'conjugate': '672315492976707436371702727102', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.10463424947035019, 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'label': '2-630-105.59-c1-0-15', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/630/2/bo/b/269/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1364240411089954, 1.3489447848366458, 1.5526746209466409, 1.7475895722670054, 1.9292640038459823, 2.08940221250497, 2.2169302457372013, 2.299415113118007, 2.324645827834657, 2.2822673791907087, 2.1653730153176354, 1.9719418355190974, 1.7059801971566655, 1.3782061831724253, 1.0061188148627533, 0.6133242721170307, 0.22805163101020703, -0.11912244823392326, -0.3982145632122603, -0.5832020300638269, -0.6554728386061882, -0.606934585661788, -0.44232289620116677, -0.18027206630589063, 0.14719994192377014, 0.4969830357005043, 0.8189194536466462, 1.0613268197291492, 1.1774697988339382, 1.132228147755768, 0.9080607092608429, 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'9.999121063538378027113591901626610', '10.83568508968723935626977784846498'], 'prelabel': '2-630-105.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.434592916752026, 'root_number': '0.20403944718675887 + 0.9789626673125599*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.217296458376', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.07982881987002552131539045925', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94590402180687852083730840689', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99253037771462267217204164924', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.030575327340666, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.59', 'conductor': 630, 'conductor_radical': 210, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/630/2/bo/b/269/4'], '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': '2-630-105.59-c1-0-15', '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': '2-630-105.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.217296458376013, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.07982881987002552131539045925', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2636496251880207860885297968950', 'Lhash_array': ['2636496251880207860885297968950'], 'label': '2-630-105.59-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/630/2/bo/b/269/4'}