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lfunc_lfunctions • Show schema
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{'Lhash': '2436505237435183215236009080918', 'a10': [1.2271344421706896, 0.0], 'a2': [1.0, 0.0], 'a3': [0.7728655578293103, 0.0], 'a4': [1.0, 0.0], 'a5': [1.2271344421706896, 0.0], 'a6': [0.7728655578293103, 0.0], 'a7': [3.402678829521189, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.402678829521189, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '418.1', 'coefficient_field': 'CDF', 'conductor': 418, 'conductor_radical': 418, 'conjugate': '2436505237435183215236009080918', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.7728655578293103, 0], [3.0, 0]], [[1.0, 0], [-1.2271344421706896, 0], [5.0, 0]], [[1.0, 0], [-3.402678829521189, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.402678829521189, 0], [13.0, 0]], 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[107.0, 0]], [[1.0, 0], [-6.0, 0], [109.0, 0]], [[1.0, 0], [19.961804092785755, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-418-1.1-c1-0-7', '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/418/2/a/h/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.6198096702891815, 2.625265715498827, 2.63934557520697, 2.655572244303652, 2.6643092390297056, 2.6541260906408843, 2.6132133399309736, 2.5306899587374505, 2.3977626120841453, 2.20874275978626, 1.9619167807539715, 1.6602302758312777, 1.3117163121428446, 0.929581177662009, 0.5318642576042791, 0.14061094217762074, -0.2194628945836413, -0.5227827440914643, -0.7451090506091022, -0.8659532273176136, -0.8709980243472926, -0.7542604250924212, -0.5197155032972715, -0.1821115793881817, 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'6.33486490588264623934865299007922', '7.52081400967267636097075807942397', '8.432071805849707563616367264203970', '9.250074976273593621794054823911337', '10.60163410364056655862680837597378', '11.22934528192453880770479967337490'], 'prelabel': '2-418-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269501373845762, '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': '1.92206372717885493143257013078', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93214087583392821062183713820', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50628536033226800674415192783', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3377468044895218, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 418, 'conductor_radical': 418, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/418/2/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': '2-418-1.1-c1-0-7', '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': '2-418-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8269501373845762, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92206372717885493143257013078', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2436505237435183215236009080918', 'Lhash_array': ['2436505237435183215236009080918'], 'label': '2-418-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/418/2/a/h/1/2'}