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lfunc_lfunctions • Show schema
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{'Lhash': '3707527758328443461841068284346', 'a10': [0.0, 0.0], 'a2': [0.8660254037844386, 0.5], 'a3': [-0.8660254037844386, -1.5], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [6.873352803342883e-62, -1.7320508075688772], 'a7': [-2.598076211353316, -1.5], 'a8': [0.0, -3.0], 'a9': [-1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, 1.5]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.124', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1033800879091944491305872524434', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5], [1.0, 1.7320508075688772]], [[1.0, 0], [0.8660254037844386, 1.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.598076211353316, 1.5], [3.5, 6.06217782649107]], [[1.0, 0], [-1.0, 1.7320508075688772], 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'data': '3.87077696061692530105290520323', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.08743014639196802501939699801', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '45.34', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/k/a/124/2'], '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': '2-15e2-45.34-c1-0-14', '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': '2-15e2-45.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.2873193022858945, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.92472370356700460003154624998', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3707527758328443461841068284346', 'Lhash_array': ['3707527758328443461841068284346'], 'label': '2-15e2-45.34-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/k/a/124/2'}