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lfunc_lfunctions • Show schema
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{'Lhash': '2386669795204637218057512610210', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.5, 0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.5, -0.8660254037844386], 'a6': [1.0, 0], 'a7': [0, 0], 'a8': [1.0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.738009097128222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1470.961', 'coefficient_field': 'CDF', 'conductor': 1470, 'conductor_radical': 210, 'conjugate': '1806074334431176233266491606654', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 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2.7287790976424087, 2.048485486663437, 1.3310201935961392, 0.6237602350134448, -0.026803504384739604, -0.5780121723779372, -0.9937639806547378, -1.2468389248600307, -1.3206676994412605, -1.2104239402570212, -0.9233620869926663, -0.4783720874596351, 0.09522633353735396, 0.7595764762512958, 1.4707448196141681], 'positive_zeros': ['1.88275049510877697639334908625561', '2.80464691426811486455528942361284', '3.99334699084575686077331835661055', '4.69879211144352595803550176955791', '5.79373078157689272948009113923637', '6.69033163765125261491709463939507', '7.61499984250085776453189081345347', '8.515144259706806443750926299814293', '9.305626621136665420481177327100504'], 'prelabel': '2-1470-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4260778007990744, 'root_angle': -0.9596540938921078, 'root_number': '-0.99197791640852265169404803750682485961305798168199772605 - 0.1264112865127400184730959576238026966982488495928982352*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4798270469460539', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88275049510877697639334908626', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80464691426811486455528942361', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99334699084575686077331835661', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.738009097128222, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.2', 'conductor': 1470, 'conductor_radical': 210, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1470/2/i/c/961/1'], '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': '2-1470-7.2-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1470-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4260778007990744, 'root_angle': -0.4798270469460539, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88275049510877697639334908626', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2386669795204637218057512610210', 'Lhash_array': ['2386669795204637218057512610210'], 'label': '2-1470-7.2-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1470/2/i/c/961/1'}