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lfunc_lfunctions • Show schema
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{'Lhash': '661802202083967214412255717138', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.6690790882822886, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.123983179505812, 0.0], 'a6': [0.0, 0.0], 'a7': [4.214174997058765, 0.0], 'a8': [0.0, 0.0], 'a9': [4.123983179505812, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.701974435916174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.1', 'coefficient_field': 'CDF', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.6690790882822886, 0], [3.0, 0]], [[1.0, 0], [4.123983179505812, 0], [5.0, 0]], [[1.0, 0], [-4.214174997058765, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.2141749970587647, 0], [13.0, 0]], [[1.0, 0], [3.4549040912235234, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'6.64265791188034580056217829089783', '6.98890758483376570007619622357903', '7.87829602604869502154891104953591', '8.345121360483923043900120446568233'], 'prelabel': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52206988421321736225961631490', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.64620270307687282364260057995', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29221799126032696049378261547', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.701974435916174, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/2/a/q/1/1'], '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': '2-3344-1.1-c1-0-11', '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': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.52206988421321736225961631490', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '661802202083967214412255717138', 'Lhash_array': ['661802202083967214412255717138'], 'label': '2-3344-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/2/a/q/1/1'}