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lfunc_lfunctions • Show schema
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{'Lhash': '225623359809686127448939981258', 'a10': [2.6199370712877688, 3.353655903212476], 'a2': [-1.6482298766249122, -0.9516059629557766], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.8111078174659819, 1.4048799502673834], 'a5': [-2.0732110585993753, -0.8377325984472952], 'a6': [1.9032119259115532, 3.563074913982485e-61], 'a7': [0.0, 0.0], 'a8': [0.0, 0.7190037090204106], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.869004548564111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, -0.5]]], [5, [[1.0, 0], [2.0732110585993753, 0.8377325984472952]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '735.79', 'coefficient_field': 'CDF', 'conductor': 735, 'conductor_radical': 105, 'conjugate': '1228260359448625498197185946898', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.6482298766249122, 0.9516059629557766], [1.0, 1.7320508075688772]], 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[[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-735-35.9-c1-0-1', '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/735/2/q/e/79/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.1700201212361128, 0.05600535650171795, -0.08377460150624431, -0.2508797371563943, -0.4456871015857768, -0.6659027555739003, -0.9053285503238149, -1.153026202828624, -1.3929680339528947, -1.6042488910890944, -1.7619277778839717, -1.838545298748487, -1.8063133535481883, -1.6398975135949532, -1.3196183429345065, -0.8347982052984123, -0.18689029827119116, 0.608036267561477, 1.5179010075191575, 2.494714129284733, 3.4764807419359958, 4.391042764933472, 5.161769105778337, 5.714744450170168, 5.986842304159029, 5.933836891018245, 5.537552146321295, 4.811002218939217, 3.800574440469107, 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'9.121912527564780364901321279571117', '10.13656000043652073786373537329633'], 'prelabel': '2-735-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.3374185463888474, 'root_number': '0.4888444920477982 - 0.8723709432314503*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.168709273194', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17798544785847505235991490465', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03140870983165599720888098168', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87217821571288034782005773224', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.869004548564111, 'bad_primes': [3, 5, 7], 'central_character': '35.9', 'conductor': 735, 'conductor_radical': 105, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/735/2/q/e/79/2'], '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': '2-735-35.9-c1-0-1', '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': '2-735-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.422602845817719, 'root_angle': -0.1687092731944237, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17798544785847505235991490465', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '225623359809686127448939981258', 'Lhash_array': ['225623359809686127448939981258'], 'label': '2-735-35.9-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/735/2/q/e/79/2'}