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lfunc_lfunctions • Show schema
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{'Lhash': '476788664621488435217540830259', 'a10': [0.8487910846218353, 0.0], 'a2': [-1.4518802500876062, 0.0], 'a3': [0.0, 0.0], 'a4': [0.10795626059445011, 0.0], 'a5': [-0.5846150772907196, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [2.7470209375448196, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4518802500876062, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5846150772907196, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.415452716812519, 0], [11.0, 0]], [[1.0, 0], [3.183388161804318, 0], [13.0, 0]], [[1.0, 0], [5.060860738714882, 0], [17.0, 0]], [[1.0, 0], 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'2.27841065739508341763695455909200', '3.77386578814433512821724301001838', '4.11819786209088161364264346220741', '4.89516580333750244021210278257245', '6.01121144918516224197956052257460', '6.69445838126875083877781237701073', '7.16581401328221066968908330942100', '8.038740071560444533207503795267212'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37611993757242477302058544491', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.69464559630353517062665678638', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.27841065739508341763695455909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/t/1/5'], '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': '2-8001-1.1-c1-0-22', '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': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37611993757242477302058544491', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '476788664621488435217540830259', 'Lhash_array': ['476788664621488435217540830259'], 'label': '2-8001-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/t/1/5'}