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lfunc_lfunctions • Show schema
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{'Lhash': '1766955630800982826226768136707', 'a10': [2.0031222401069138, 0.993730995385099], 'a2': [0.9781476007338057, -0.20791169081775934], 'a3': [0.20085485661080218, 1.7203654630850544], 'a4': [0.9135454576426009, -0.4067366430758002], 'a5': [1.752740921668573, 1.3884881207660371], 'a6': [0.5541497883440799, 1.641011277255038], 'a7': [0.74613251263916, 1.2923394210700525], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [-2.9193146531517082, 0.6910875168122499], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.593268090957619, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9781476007338057, 0.20791169081775934]]], [3, [[1.0, 0], [-0.20085485661080218, -1.7203654630850544]]], [5, [[1.0, 0], [-1.752740921668573, -1.3884881207660371]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.121', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': 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[-77.27366045797065, -16.42502357460299]], [[1.0, 0], [15.08129497384685, 6.714625133956067], [55.53784032778523, 61.68102051462372]], [[1.0, 0], [-2.1214368055867983, 6.529111131712147], [-72.00251249937033, -52.31288745403011]], [[1.0, 0], [-0.05596452649711798, 0.5324669016015773], [-94.88031727117915, -20.167434009322655]], [[1.0, 0], [4.777246821855814, 8.274434215751215], [-50.5, 87.4685657822283]], [[1.0, 0], [-8.779875741858255, 3.90905253371986], [68.9204524549624, -76.5439170241716]], [[1.0, 0], [-13.270942722764778, 0], [107.0, 0]], [[1.0, 0], [-5.513926547813773, -16.970120961400028], [-88.18285238686927, 64.06859249987957]], [[1.0, 0], [6.722181289607608, 1.4288437418415485], [103.2306367136139, 45.96124066756542]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-450-225.121-c1-0-14', '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/450/2/q/c/121/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.374972747315142, 2.2481524545247416, 2.1257549045526734, 1.9991620069678055, 1.8585122192841466, 1.6943852140134923, 1.4992762171236054, 1.268753864109725, 1.002299167581661, 0.7038452135686959, 0.38201275331031664, 0.050006168247624945, -0.27488024654463417, -0.5721874867667035, -0.8196608156358484, -0.9950287457433706, -1.0781018305709458, -1.0530414588921053, -0.9105941873713553, -0.6500461717317828, -0.28063355035137105, 0.1778444336884341, 0.6954173195265688, 1.2334668982716337, 1.7473955182176155, 2.1903158368082005, 2.517492623104581, 2.6911299629695375, 2.6849892032147693, 2.4882644614635576, 2.1081505102327482, 1.5706228102940023, 0.9191125788394547, 0.21099091128504396, -0.48794681756889347, -1.1105143235876516, -1.5959393890995037, -1.8974991471490075, -1.9889572384361769, -1.8688237655160134, 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'root_angle': -0.3497067756085929, 'root_number': '0.45481109471686865 - 0.8905879339640996*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.174853387804', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39388221839902724123245096453', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57887877300024417704869706473', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16201475540800126117106608079', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.593268090957619, 'bad_primes': [2, 3, 5], 'central_character': '225.121', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/2/q/c/121/8'], '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': '2-450-225.121-c1-0-14', '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': '2-450-225.121-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8955917521865353, 'root_angle': -0.17485338780429646, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39388221839902724123245096453', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1766955630800982826226768136707', 'Lhash_array': ['1766955630800982826226768136707'], 'label': '2-450-225.121-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/2/q/c/121/8'}