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lfunc_lfunctions • Show schema
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{'Lhash': '897750637679160319145938542967', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.7607698031784271, 0.0], 'a4': [0.0, 0.0], 'a5': [2.557689984836177, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.10031029978499723, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.47257942544966, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '7448.1', 'coefficient_field': 'CDF', 'conductor': 7448, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.7607698031784271, 0], [3.0, 0]], [[1.0, 0], [-2.557689984836177, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.258952799675192, 0], [11.0, 0]], [[1.0, 0], [0.7156554848152988, 0], [13.0, 0]], [[1.0, 0], [1.4730722707025057, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [5.336857110947149, 0], 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'4.49129637092278342192937371258956', '5.24156598055003580505362632931508', '5.99641850407246342590497670867552', '6.23237947562546831598922009693407', '6.92998695432718607013865111743136', '7.80027605638358286748556007907977'], 'prelabel': '2-7448-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.7118466935909495, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70820038070232299824455572113', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70463816095883219297258525276', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.50775559144956803587605270492', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.47257942544966, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 7448, 'conductor_radical': 266, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7448/2/a/bx/1/3'], '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': '2-7448-1.1-c1-0-53', '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': '2-7448-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.7118466935909495, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70820038070232299824455572113', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '897750637679160319145938542967', 'Lhash_array': ['897750637679160319145938542967'], 'label': '2-7448-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7448/2/a/bx/1/3'}