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lfunc_lfunctions • Show schema
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{'Lhash': '555153187119501217036667708334', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7514276602601766, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.4353564713959166, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.25339398085481, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '9800.1', 'coefficient_field': 'CDF', 'conductor': 9800, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7514276602601766, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.2770158145727954, 0], [11.0, 0]], [[1.0, 0], [2.4353564713959166, 0], [13.0, 0]], [[1.0, 0], [6.126599389516172, 0], [17.0, 0]], [[1.0, 0], [0.4413109583315756, 0], [19.0, 0]], [[1.0, 0], [-3.1867841316560934, 0], [23.0, 0]], [[1.0, 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'4.97212968441580698657893654816791', '5.54202070904177013045966920870647', '6.27859176192138285917871944119955', '7.20060778487400224880835320975316', '7.65000829751330432123821447105159'], 'prelabel': '2-9800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846094843537164, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43793864572741948138550324650', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08349928801170605978572734147', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54027741889267015151983403070', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.25339398085481, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 9800, 'conductor_radical': 70, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9800/2/a/cx/1/4'], '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': '2-9800-1.1-c1-0-18', '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': '2-9800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846094843537164, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43793864572741948138550324650', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '555153187119501217036667708334', 'Lhash_array': ['555153187119501217036667708334'], 'label': '2-9800-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9800/2/a/cx/1/4'}