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lfunc_lfunctions • Show schema
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{'Lhash': '2162672729285133416464281045370', 'a10': [1.4384471871911697, 0.0], 'a2': [2.5615528128088303, 0.0], 'a3': [0.0, 0.0], 'a4': [4.56155281280883, 0.0], 'a5': [0.5615528128088303, 0.0], 'a6': [0.0, 0.0], 'a7': [3.5615528128088303, 0.0], 'a8': [6.56155281280883, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.145246147436753, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.5615528128088303, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5615528128088303, 0], [5.0, 0]], [[1.0, 0], [-3.5615528128088303, 0], [7.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5615528128088303, 0], [17.0, 0]], [[1.0, 0], [-1.1231056256176606, 0], [19.0, 0]], [[1.0, 0], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 45, 'label': '2-39e2-1.1-c1-0-45', 'leading_term': '5.83255607601916793973158705092', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/2/a/m/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [5.832556076019168, 5.830649511971078, 5.824649285336343, 5.8137293525246125, 5.796563539434761, 5.7713970676955775, 5.736138814229068, 5.688467988515857, 5.625948850602532, 5.546147691106474, 5.446747279790617, 5.325655088703756, 5.181102600435619, 5.01173380290359, 4.816681514647382, 4.595630504784284, 4.348866528428457, 4.077310460315464, 3.782536740233226, 3.4667753943763353, 3.1328970023882667, 2.784380161635376, 2.425261266877219, 2.0600667738790985, 1.6937285410532246, 1.331483329642194, 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'5.96063859230283993864858538008237', '6.71767869519000070985174829873549', '7.73931305784082476419620846140148', '8.300635451467443019539945326495508', '9.657833910237604544020920023975992'], 'prelabel': '2-39e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70604796692066655437177248167', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52774417137176119618141532376', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65157862846727552304585172851', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.145246147436753, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/2/a/m/1/2'], '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': '2-39e2-1.1-c1-0-45', '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': '2-39e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70604796692066655437177248167', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2162672729285133416464281045370', 'Lhash_array': ['2162672729285133416464281045370'], 'label': '2-39e2-1.1-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/2/a/m/1/2'}