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lfunc_lfunctions • Show schema
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{'Lhash': '2901950357620158651646827135352', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [2.449489742783178, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [2.449489742783178, 0.0], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.7947640707448147, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '350.1', 'coefficient_field': 'CDF', 'conductor': 350, 'conductor_radical': 70, 'conjugate': '2901950357620158651646827135352', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.449489742783178, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [4.449489742783178, 0], [13.0, 0]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [-1.550510257216822, 0], [19.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-350-1.1-c1-0-8', '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/350/2/a/h/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.8309825308478973, 2.8409442934577456, 2.868639045294908, 2.907846269259468, 2.949240588209576, 2.981601532301139, 2.9930416974112246, 2.9721175520422727, 2.908803465320036, 2.795356596123437, 2.627090393202418, 2.4030405046807797, 2.1264733051525226, 1.80516555534615, 1.451377510967237, 1.0814513181104883, 0.7149907247686874, 0.37361513140218244, 0.07932790646841413, -0.1474084724182129, -0.28974505538432416, -0.33647506238338565, -0.2837940983837268, -0.13655562181136843, 0.09119991761980656, 0.37661892186373713, 0.6894126961680438, 0.9942387797504059, 1.2539638753893567, 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'9.738844466819335119483763061724952', '10.40695359032285207903865428900737', '11.70456166423393402195005342402061'], 'prelabel': '2-350-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6717547878635834, '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': '2.28923518601867728793453841962', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95437356862933556349589288599', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39664725359770703549679315738', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.7947640707448147, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/2/a/h/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': '2-350-1.1-c1-0-8', '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': '2-350-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6717547878635834, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.28923518601867728793453841962', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2901950357620158651646827135352', 'Lhash_array': ['2901950357620158651646827135352'], 'label': '2-350-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/2/a/h/1/2'}