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lfunc_lfunctions • Show schema
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{'Lhash': '1958771870790788777997705871489', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -3.4641016151377544], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.930660344511594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [-1.0, 3.4641016151377544]]]], 'bad_primes': [2, 3, 13], 'central_character': '2496.961', 'coefficient_field': 'CDF', 'conductor': 2496, 'conductor_radical': 78, 'conjugate': '635441488596082575919924042991', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-5.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-7.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-11.0, 0]], [[1.0, 0], [-1.0, 3.4641016151377544]], [[1.0, 0], [6.0, 0], [17.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-19.0, 0]], [[1.0, 0], [0, 0], [23.0, 0]], 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'8.685986583575293769474638392246248', '8.878723343131379539166875428447884'], 'prelabel': '2-2496-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.464376814798634, 'root_angle': 0.5894561875110335, 'root_number': '-0.2773500981126145610091708667284996881731766595265574010 + 0.9607689228305228008995220186061222247804553812294855860*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.29472809375551673', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54519855111347640862829567898', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49603684641702680291154491293', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31720134533750425500634746113', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.930660344511594, 'bad_primes': [2, 3, 13], 'central_character': '13.12', 'conductor': 2496, 'conductor_radical': 78, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2496/2/c/k/961/1'], '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': '2-2496-13.12-c1-0-44', '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': '2-2496-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.464376814798634, 'root_angle': 0.29472809375551673, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54519855111347640862829567898', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1958771870790788777997705871489', 'Lhash_array': ['1958771870790788777997705871489'], 'label': '2-2496-13.12-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2496/2/c/k/961/1'}