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lfunc_lfunctions • Show schema
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{'Lhash': '816057184096966127950577970925', 'a10': [0.0, 0.0], 'a2': [3.735489498215868, 0.0], 'a3': [-3.0, 0.0], 'a4': [5.953881791281038, 0.0], 'a5': [0.0, 0.0], 'a6': [-11.206468494647604, 0.0], 'a7': [-36.41293698929521, 0.0], 'a8': [-7.643253080777945, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.52686225559712, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [3.0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [13.0, 0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.1', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.735489498215868, 0], [8.0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [36.41293698929521, 0], [343.0, 0]], [[1.0, 0], [-19.194269744117967, 0], [1331.0, 0]], [[1.0, 0], [13.0, 0]], [[1.0, 0], [-83.88391598572694, 0], [4913.0, 0]], [[1.0, 0], [-46.849171671201404, 0], [6859.0, 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'2.61828313547544918889338055266124', '3.52729812527958368136888090986245', '4.16710169683622150056960208152022', '5.45871368128765749224878360256169', '5.98964960471724729511253818829135', '6.66320891844764671386809973367217', '7.54080538794698579330816600017535', '9.113498919825187730729385535812627', '9.687341674229537185438008853142924'], 'prelabel': '2-975-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.584646481913124, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64375560895884257902592056598', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61828313547544918889338055266', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52729812527958368136888090986', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.52686225559712, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/4/a/l/1/3'], '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': '2-975-1.1-c3-0-23', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-975-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.584646481913124, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64375560895884257902592056598', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '816057184096966127950577970925', 'Lhash_array': ['816057184096966127950577970925'], 'label': '2-975-1.1-c3-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/4/a/l/1/3'}