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lfunc_lfunctions • Show schema
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{'Lhash': '2315772301228736723458753449111', 'a10': [-3.4215463492821097, 0.0], 'a2': [-1.0, 0.0], 'a3': [2.796826303731396, 0.0], 'a4': [1.0, 0.0], 'a5': [3.4215463492821097, 0.0], 'a6': [-2.796826303731396, 0.0], 'a7': [1.084159392926772, 0.0], 'a8': [-1.0, 0.0], 'a9': [4.822237373243822, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.40400224210669, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [401, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 401], 'central_character': '802.1', 'coefficient_field': 'CDF', 'conductor': 802, 'conductor_radical': 802, 'conjugate': '2315772301228736723458753449111', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.796826303731396, 0], [3.0, 0]], [[1.0, 0], [-3.4215463492821097, 0], [5.0, 0]], [[1.0, 0], [-1.084159392926772, 0], [7.0, 0]], [[1.0, 0], [-2.084159392926772, 0], [11.0, 0]], [[1.0, 0], [2.1446072129836926, 0], [13.0, 0]], [[1.0, 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'4.81565983671438900946919317977711', '6.15093562663001028649515469495444', '6.99328412472064445442025508278058', '7.967976113308136451017001046451262', '8.785948885039996276097987182911337', '9.315678278861577815603375919149037', '9.886130706818787362259055082829806'], 'prelabel': '2-802-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.530613017058651, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82682223383304688089144340427', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16971882112667566608618000647', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45402378736818358350478846445', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.40400224210669, 'bad_primes': [2, 401], 'central_character': '1.1', 'conductor': 802, 'conductor_radical': 802, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/802/2/a/d/1/6'], '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': '2-802-1.1-c1-0-22', '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': '2-802-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.530613017058651, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82682223383304688089144340427', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2315772301228736723458753449111', 'Lhash_array': ['2315772301228736723458753449111'], 'label': '2-802-1.1-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/802/2/a/d/1/6'}