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lfunc_lfunctions • Show schema
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{'Lhash': '1291798277070605611293576774126', 'a10': [0.0, 0.0], 'a2': [-2.1773064493969643, 1.2570684646676455], 'a3': [1.191544743238007, 1.2570684646676455], 'a4': [2.160442249723743, -3.7419957433399316], 'a5': [0.0, 0.0], 'a6': [-4.174579179059034, -1.2391699544893988], 'a7': [0.44525564182808686, -0.25706846466764555], 'a8': [0.0, 5.8350214287827775], 'a9': [-0.16044224972374319, 2.995706641930011], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.191544743238007, -1.2570684646676455]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.49', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2411245828387028414938689872761', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1773064493969643, -1.2570684646676455], [1.0, -1.7320508075688772]], [[1.0, 0], [-1.191544743238007, 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'9.609336069632407756861126154677954', '11.04737368879577163051152661460281', '11.61872241512772223894340806119340'], 'prelabel': '2-15e2-45.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.6861075962745408, 'root_number': '-0.5519277773571036 - 0.8338919166064913*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.343053798137', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01904915821286136086626410457', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45914750752995271755829095510', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61518848473022671311554222943', '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': '45.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/k/b/49/1'], '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': '2-15e2-45.4-c1-0-3', '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': '2-15e2-45.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.3430537981372704, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01904915821286136086626410457', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1291798277070605611293576774126', 'Lhash_array': ['1291798277070605611293576774126'], 'label': '2-15e2-45.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/k/b/49/1'}