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lfunc_lfunctions • Show schema
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{'Lhash': '893899033073569847570715385728', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.23606797749979, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -2.8284271247461903], 'a8': [0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.552128646809734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '3200.449', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '461501243201152553014783482407', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.23606797749979, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-7.0, 0]], [[1.0, 0], [0, -2.23606797749979], [-11.0, 0]], [[1.0, 0], [6.324555320336759, 0], [13.0, 0]], [[1.0, 0], [0, -5.0], [-17.0, 0]], [[1.0, 0], [0, -2.23606797749979], [-19.0, 0]], [[1.0, 0], [0, 5.656854249492381], [-23.0, 0]], [[1.0, 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'5.83704132985375205997116213277359', '6.21774970982900809527807989284332', '7.36404333651414282818571525407031', '7.77526052302832037500498520257702', '9.164682270507401831741271956473466'], 'prelabel': '2-3200-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70516200040660348069073472688', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33440120821207507857513306277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00894460282619592593678535657', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.552128646809734, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/2/f/r/449/2'], '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': '2-3200-40.29-c1-0-30', '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': '2-3200-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70516200040660348069073472688', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '893899033073569847570715385728', 'Lhash_array': ['893899033073569847570715385728'], 'label': '2-3200-40.29-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/2/f/r/449/2'}