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lfunc_lfunctions • Show schema
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{'Lhash': '219640881194508417119588558161', 'a10': [0.3966129115467633, 3.137307475908984], 'a2': [-0.25004306440747254, -1.39193335542393], 'a3': [-1.4009076870587456, 1.0185566515121856], 'a4': [-1.8749569318834411, 0.6960865632823502], 'a5': [-2.2330466148626473, -0.11620161724550729], 'a6': [1.7680502286528723, 1.6952871110701355], 'a7': [-2.2904106208671786, 2.2904106208671786], 'a8': [1.4377260825752818, 2.43576347609589], 'a9': [0.925084695320568, -2.853807685616473], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25004306440747254, 1.39193335542393]]], [3, [[1.0, 0], [1.4009076870587456, -1.0185566515121856]]], [5, [[1.0, 0], [2.2330466148626473, 0.11620161724550729]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': '3866782578077384944478515669079', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.25004306440747254, 1.39193335542393]], [[1.0, 0], [1.4009076870587456, -1.0185566515121856]], [[1.0, 0], [2.2330466148626473, 0.11620161724550729]], [[1.0, 0], [2.2904106208671786, -2.2904106208671786], [0, -7.0]], [[1.0, 0], [2.283780582032915, 0], [11.0, 0]], [[1.0, 0], [1.0563452319544744, -1.0563452319544744], [0, -13.0]], [[1.0, 0], [3.043908506684475, 3.043908506684475], [0, 17.0]], [[1.0, 0], [-3.368313232840088, 0], [19.0, 0]], [[1.0, 0], [3.6878475329952694, -3.6878475329952694], [0, -23.0]], [[1.0, 0], [0, 2.714611484294485], [-29.0, 0]], [[1.0, 0], [6.4919616243623475, 0], [31.0, 0]], [[1.0, 0], [2.3119680008856136, 2.3119680008856136], [0, 37.0]], [[1.0, 0], [0, -10.805553302053424], [-41.0, 0]], [[1.0, 0], [-1.1638415696397917, 1.1638415696397917], [0, -43.0]], [[1.0, 0], [-1.837678142354133, -1.837678142354133], [0, 47.0]], [[1.0, 0], [-5.82856178749576, -5.82856178749576], [0, 53.0]], [[1.0, 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'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/53/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.14095381415538621, 0.040454142064194315, -0.0672634864044027, -0.1873628286833761, -0.32479564486729406, -0.4839923400389442, -0.6686287472275623, -0.8814394681349271, -1.1240444329635682, -1.3967693630467128, -1.6984585003634372, -2.0262918238188257, -2.375627529842485, -2.739894802110729, -3.1105630201018246, -3.4772122408171406, -3.8277262529615728, -4.148623742457722, -4.425535101886493, -4.643822274513108, -4.789327075100468, -4.849220267363576, -4.8129101662097655, -4.6729567826009335, -4.425926837150148, -4.073117725553618, -3.6210760835222056, -3.081840150293638, -2.4728455061663475, -1.8164512977161134, -1.139068460064139, -0.46990165298613384, 0.1606491804408631, 0.722846118773322, 1.1896140864119327, 1.5385413809722313, 1.7537166454450812, 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'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.6770831010252176, 'root_number': '-0.5280672308876401 - 0.8492025669194952*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.338541550513', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17326610436264061865409740947', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.96707316029091078975077733546', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.36686359855572284247375544399', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/53/7'], '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': '2-120-120.53-c1-0-0', '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': '2-120-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.3385415505126088, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17326610436264061865409740947', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '219640881194508417119588558161', 'Lhash_array': ['219640881194508417119588558161'], 'label': '2-120-120.53-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/53/7'}