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lfunc_lfunctions • Show schema
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{'Lhash': '2576301004771828625694458127171', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [4.372281323269014, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.3722813232690143, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8205891660851936, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 19], 'central_character': '228.1', 'coefficient_field': 'CDF', 'conductor': 228, 'conductor_radical': 114, 'conjugate': '2576301004771828625694458127171', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.372281323269014, 0], [5.0, 0]], [[1.0, 0], [2.3722813232690143, 0], [7.0, 0]], [[1.0, 0], [4.372281323269014, 0], [11.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [4.372281323269014, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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[0]], 'group': 'GL2', 'index': 2, 'label': '2-228-1.1-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/228/2/a/c/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6912817381109257, 1.6972585623707366, 1.713835821570403, 1.7371536942121342, 1.7613713452555024, 1.7793525690847238, 1.783362081699963, 1.7657020284102674, 1.7192881473040207, 1.6381932700451172, 1.5181794509002204, 1.3572180042619746, 1.1559731087894516, 0.9182059545771514, 0.6510448038597773, 0.3650623040708607, 0.07410508922139625, -0.20516778169923852, -0.4540618178888494, -0.6529375885160092, -0.7825809501051036, -0.8257840499061927, -0.7690327195031855, -0.6041640892047898, -0.32983443297079784, 0.047374257010639804, 0.5123758223001662, 1.0416729180210424, 1.6042211734058207, 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'10.91566874243973867331741815141081', '12.74495527959745433790785591281983'], 'prelabel': '2-228-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3492920981333856, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03234314274610698451890866583', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11087682315179490099576488506', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.07471947894140600627574066538', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8205891660851936, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 228, 'conductor_radical': 114, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/228/2/a/c/1/2'], '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': '2-228-1.1-c1-0-2', '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': '2-228-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3492920981333856, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03234314274610698451890866583', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2576301004771828625694458127171', 'Lhash_array': ['2576301004771828625694458127171'], 'label': '2-228-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/228/2/a/c/1/2'}