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lfunc_lfunctions • Show schema
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{'Lhash': '2818943548372852624328708817182', 'a10': [0.7095585237500319, -1.2289914140786231], 'a2': [0.2706458792394384, 0.2706458792394384], 'a3': [0.0, 0.0], 'a4': [0.0, -1.8535016161014226], 'a5': [-0.9596172160246579, -3.5813402060218222], 'a6': [0.0, 0.0], 'a7': [1.3038503672523667, -2.302167287539259], 'a8': [1.0429343330403664, -1.0429343330403664], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.3038503672523667, 2.302167287539259]]], [13, [[1.0, 0], [-1.6358977937740051, -3.213073047461782]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.271', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '989880472594237988585619093866', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2706458792394384, -0.2706458792394384], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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[2.746732624566198, -4.757480460555665], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-819-91.89-c1-0-40', '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/819/2/et/b/271/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5807902872562287, 1.8364398202957488, 2.100024580518451, 2.369368406819033, 2.637286463404936, 2.8916970064638035, 3.1165230247446245, 3.2931580891627212, 3.402314470034896, 3.426117346291413, 3.3503122326601793, 3.1664184584707895, 2.8736141215398328, 2.4801018564292687, 2.003698093330156, 1.4714224221421657, 0.9179427266238175, 0.38285350029003, -0.0930805845376463, -0.4724133305074188, -0.7257725422005836, -0.836289278587785, -0.803042702826305, -0.6428838625824572, -0.39012416523877064, 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'7.24919746013958632761524394862566', '7.963861838587685708306842524520369', '8.542097499233560262872225592499736', '9.882474589241238228023767211838059', '10.77315056188526580629622214704790'], 'prelabel': '2-819-91.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.7088492566570194, 'root_number': '-0.6100465125130169 + 0.7923656053683208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.354424628329', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.22375435933633960163919880929', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16465861430244262945547086586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77571745182878917560811531555', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.89', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/et/b/271/5'], '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': '2-819-91.89-c1-0-40', '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': '2-819-91.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.3544246283285097, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22375435933633960163919880929', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2818943548372852624328708817182', 'Lhash_array': ['2818943548372852624328708817182'], 'label': '2-819-91.89-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/et/b/271/5'}