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lfunc_lfunctions • Show schema
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{'Lhash': '2187428262691162321395461194510', 'a10': [0.7915968081574759, 0.6976719080998842], 'a2': [0.4086633574294685, 0.23594189941983992], 'a3': [0.0, 0.0], 'a4': [-0.8886628401963163, -1.5392091900184819], 'a5': [2.1920203702954804, 0.44164091319720855], 'a6': [0.0, 0.0], 'a7': [0.0, -1.1753981852081028], 'a8': [0.0, -1.7824587915183538], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.8272093728194765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.1920203702954804, -0.44164091319720855]]], [19, [[1.0, 0], [1.5703069024525993, 4.066218910992093]]]], 'bad_primes': [3, 5, 19], 'central_character': '855.334', 'coefficient_field': 'CDF', 'conductor': 855, 'conductor_radical': 285, 'conjugate': '1089888122907018541171807517249', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4086633574294685, -0.23594189941983992], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 36, 'label': '2-855-95.49-c1-0-36', '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/855/2/be/d/334/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8280908097341952, 1.997239956784355, 2.1525884052796216, 2.289543487512412, 2.3987283268838304, 2.467219894064084, 2.480402625650764, 2.4241144471363922, 2.2868543484011528, 2.0618817121979656, 1.7490443598299608, 1.3561493489322245, 0.8996711397896325, 0.4045997986144599, -0.09672038852419061, -0.5668217943583439, -0.9663477454456919, -1.2580748914578057, -1.411355017085206, -1.4064742699052244, -1.2383401455574166, -0.9188887867636832, -0.47767512284435176, 0.03972657705015719, 0.5756309146090163, 1.0662590711549214, 1.4493217619154848, 1.6723025450828197, 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'8.634977154604726313123055956014447', '9.383246153031325231870925402639523', '10.30212692704647002337228564268254'], 'prelabel': '2-855-95.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.612892912619933, 'root_angle': 0.3782218211670634, 'root_number': '0.3733128046611938 + 0.9277055297215778*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.189110910584', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72557663941257551390393902325', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86573963849753881525397971391', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01054691090270047640775674489', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.8272093728194765, 'bad_primes': [3, 5, 19], 'central_character': '95.49', 'conductor': 855, 'conductor_radical': 285, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/855/2/be/d/334/4'], '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': '2-855-95.49-c1-0-36', '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': '2-855-95.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.612892912619933, 'root_angle': 0.1891109105835317, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72557663941257551390393902325', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2187428262691162321395461194510', 'Lhash_array': ['2187428262691162321395461194510'], 'label': '2-855-95.49-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/855/2/be/d/334/4'}