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lfunc_lfunctions • Show schema
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{'Lhash': '647938309697221873784246535999', 'a10': [0.0, 0.0], 'a2': [-1.3330405260081957, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.2230029560197932, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.2622650698377917, 0.0], 'a8': [2.9633530298103987, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.69565540984309, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 31], 'central_character': '6975.1', 'coefficient_field': 'CDF', 'conductor': 6975, 'conductor_radical': 465, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3330405260081957, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.2622650698377917, 0], [7.0, 0]], [[1.0, 0], [4.888450204978956, 0], [11.0, 0]], [[1.0, 0], [-6.0792269444735405, 0], [13.0, 0]], [[1.0, 0], [4.3276545907385335, 0], [17.0, 0]], [[1.0, 0], [7.229733516826456, 0], [19.0, 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'4.33918513014302817336931415111931', '5.09660780501182681368923046276415', '5.88398907283139353629970743217598', '6.67647773975755664071428864854725', '7.59357206172534682704529406401147', '8.144836904877996266975082230398030'], 'prelabel': '2-6975-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.462952191314312, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51113320151512273896084321759', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77070856321670393313696205609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.28284461359980636706485100212', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.69565540984309, 'bad_primes': [3, 5, 31], 'central_character': '1.1', 'conductor': 6975, 'conductor_radical': 465, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6975/2/a/ck/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': '2-6975-1.1-c1-0-32', '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': '2-6975-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.462952191314312, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51113320151512273896084321759', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '647938309697221873784246535999', 'Lhash_array': ['647938309697221873784246535999'], 'label': '2-6975-1.1-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/ck/1/4'}