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lfunc_lfunctions • Show schema
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{'Lhash': '4447309088396039789379142200413', 'a10': [3.955581958641115, 5.750517221836899e-61], 'a2': [-0.5, 0.8660254037844386], 'a3': [-1.2670350983613659, -2.1945691653349155], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.9777909793205575, -3.4256344629346125], 'a6': [2.5340701967227317, 6.132587529244607e-61], 'a7': [1.2670350983613659, 2.1945691653349155], 'a8': [1.0, 0.0], 'a9': [-1.7107558809591916, 2.963116105168574], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [37, [[1.0, 0], [0.022209020679442495, 6.082721986035566]]]], 'bad_primes': [2, 37], 'central_character': '74.47', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '1327245764777231944743161356406', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.2670350983613659, 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'14.06007973838360505594506071105461', '14.89233620902077356646101164916838'], 'prelabel': '2-74-37.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.45201373654608934, 'root_number': '0.15018292407838904 + 0.9886582267473755*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.226006868273', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.50830827326973275751603700338', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.44228348321657210616630175821', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.60238576215399886777773952153', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.10', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/c/c/47/1'], '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': '2-74-37.10-c1-0-3', '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': '2-74-37.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.22600686827304467, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.50830827326973275751603700338', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4447309088396039789379142200413', 'Lhash_array': ['4447309088396039789379142200413'], 'label': '2-74-37.10-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/c/c/47/1'}