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lfunc_lfunctions • Show schema
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{'Lhash': '1750410580286930539772823808837', 'a10': [0, 0], 'a2': [1.224744871391589, -0.7071067811865476], 'a3': [0.8660254037844386, -1.5], 'a4': [1.0, -1.7320508075688772], 'a5': [0, 0], 'a6': [0, -2.449489742783178], 'a7': [-4.615239286758338, 5.263037746963477], 'a8': [0, -2.8284271247461903], 'a9': [-1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.224744871391589, 0.7071067811865476]]], [3, [[1.0, 0], [-0.8660254037844386, 1.5]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [4.615239286758338, -5.263037746963477]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.199', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '996591625695943620296608060709', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.224744871391589, 0.7071067811865476]], [[1.0, 0], [-0.8660254037844386, 1.5]], 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[[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-1050-35.24-c2-0-33', 'leading_term': '2.987334524337313613511396221583694612262291087068201309', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/3/q/e/199/16', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.9873345243373137, 3.1352719851180875, 3.2657828595453546, 3.377574547893483, 3.4693230096298477, 3.539676067155268, 3.5872651182771755, 3.6107252878737603, 3.608723664782936, 3.579994911802225, 3.523383217952701, 3.437889291090185, 3.3227208693453845, 3.177345062122614, 3.0015407137225605, 2.795448912431053, 2.5596197426151734, 2.2950533952591265, 2.0032338127840177, 1.6861531472533364, 1.3463254581722963, 0.986788268249792, 0.6110908335722877, 0.22326826862983293, -0.17219900482563413, 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'6.58301297532054787750097793044678', '7.30224588264937506633545000796377', '8.167659392319640695051603510166438', '9.339982248466565187139138013465618', '9.684710561405265611398580090236858'], 'prelabel': '2-1050-35.24-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.5412261704778888, 'root_number': '-0.1291540471948021881802697729980849978384474895046802050 + 0.9916245418973870924100464050471062292500217301382772488*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2706130852389444', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38083047487358458783833425763', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08525270344207983788110662111', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75035587884931853008244656624', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.24', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/q/e/199/16'], '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': '2-1050-35.24-c2-0-33', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-35.24-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.2706130852389444, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38083047487358458783833425763', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1750410580286930539772823808837', 'Lhash_array': ['1750410580286930539772823808837'], 'label': '2-1050-35.24-c2-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/q/e/199/16'}