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lfunc_lfunctions • Show schema
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{'Lhash': '2045041556382175288767685691120', 'a10': [0.9955983256992652, 3.446235427544792], 'a2': [1.1343612585151177, 1.1343612585151177], 'a3': [-1.700590008856947, 0.3286238302009289], 'a4': [0.0, 0.5735509296400032], 'a5': [1.9578567761818801, 1.0801837084305128], 'a6': [-2.3018615642699856, -1.5563052810604174], 'a7': [1.8458925531497798, -1.8458925531497798], 'a8': [1.6181085626612857, -1.6181085626612857], 'a9': [2.784012756448142, -1.117708804624003], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7130436939895395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.700590008856947, -0.3286238302009289]]], [5, [[1.0, 0], [-1.9578567761818801, -1.0801837084305128]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 31], 'central_character': '465.218', 'coefficient_field': 'CDF', 'conductor': 465, 'conductor_radical': 465, 'conjugate': '1771244737498173820755919731027', 'degree': 2, 'euler_factors': 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'root_number': '0.7622919751920186 - 0.6472332999451209*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.112037021894', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61325333338222965068394872540', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55374103120521554454257784122', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.58522004564283649982684438886', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.7130436939895395, 'bad_primes': [3, 5, 31], 'central_character': '15.8', 'conductor': 465, 'conductor_radical': 465, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/465/2/k/b/218/23'], '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': '2-465-15.8-c1-0-29', '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': '2-465-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9269259700334986, 'root_angle': -0.11203702189360434, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61325333338222965068394872540', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2045041556382175288767685691120', 'Lhash_array': ['2045041556382175288767685691120'], 'factors': ['2-465-15.8-c1-0-29'], 'label': '2-465-15.8-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/465/2/k/b/218/23'}