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lfunc_lfunctions • Show schema
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{'Lhash': '1907641131922482291421167435419', 'a10': [1.2282108452946385, -0.33687595970290884], 'a2': [0.5203180405687134, -0.23166051714472186], 'a3': [-1.625889883464084, -0.5970612086286861], 'a4': [-1.121196944580211, 1.2452153582390355], 'a5': [2.2105633092307926, 0.33676379835517933], 'a6': [-0.9842953467025001, 0.06599277305039548], 'a7': [1.5887164178523998, -2.751737554539183], 'a8': [-0.6469185862527567, 1.9910106828027985], 'a9': [2.287035826301705, 1.9415115578364393], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.625889883464084, 0.5970612086286861]]], [5, [[1.0, 0], [-2.2105633092307926, -0.33676379835517933]]]], 'bad_primes': [3, 5], 'central_character': '225.16', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1935883325685889123895368899205', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_number': '0.9880874438756767 + 0.15389348022327473*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.024590631615', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50486351016520498090083715689', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.97207795363037206962742928310', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.42867793057593226971397096853', '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': '225.16', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/16/18'], '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': '2-15e2-225.16-c1-0-12', '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': '2-15e2-225.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.024590631615026993, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50486351016520498090083715689', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1907641131922482291421167435419', 'Lhash_array': ['1907641131922482291421167435419'], 'label': '2-15e2-225.16-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/16/18'}