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lfunc_lfunctions • Show schema
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{'Lhash': '100734690728594952704340636153', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.18966689810087872, 0.32851270402471094], 'a4': [0, 0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0, 0], 'a7': [-1.8930675031969755, 0], 'a8': [0, 0], 'a9': [1.4280529355295817, 2.473460240235118], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [2.105962326440448, -3.8164017974544473]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.961', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '2339613606201324371650157784429', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.18966689810087872, -0.32851270402471094], [-1.5, -2.598076211353316]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.8930675031969755, 0], [7.0, 0]], [[1.0, 0], 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'0.2051606135090847817384223672278026686210409172154838070', '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/1520/2/q/o/961/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.2051606135090848, 0.05346583826316153, -0.09585300164017484, -0.24267446842076468, -0.38673479000909, -0.5275731488038123, -0.6644903359895057, -0.7965227557280621, -0.9224326355978474, -1.0407143333617719, -1.1496159054972364, -1.2471746283613905, -1.331264895199643, -1.3996567836439489, -1.4500835301329422, -1.4803161051179654, -1.488243021462071, -1.4719534133208902, -1.4298212951176204, -1.36058876201154, -1.2634457428696975, -1.138103785271808, -0.9848612607546174, -0.8046573470233027, -0.599112189244699, -0.370550778411551, -0.12200832084242749, 0.14278478541437878, 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'7.12128345077768583163870633922752', '8.355209226063966526157640088859573', '9.218533502601287286235935209802570'], 'prelabel': '2-1520-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.9260841585847874, 'root_number': '-0.97315939008949021559544023536428012507338880917246667453 + 0.2301321391736743335144825528559993069678703125068360217*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4630420792923937', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.079465659315318079634297236963', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.55082738815426603998228757966', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92881321296041894219250331758', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '19.11', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/q/o/961/2'], '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': '2-1520-19.11-c1-0-0', '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': '2-1520-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.4630420792923937, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.079465659315318079634297236963', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '100734690728594952704340636153', 'Lhash_array': ['100734690728594952704340636153'], 'label': '2-1520-19.11-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/q/o/961/2'}