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lfunc_lfunctions • Show schema
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{'Lhash': '2438994759105081818135437776234', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.4142135623730951, -1.4142135623730951], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, -3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '3200.193', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '1357009383500763427816278335663', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 1.4142135623730951], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], 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'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3200/1/m/d/193/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.9904031252698948, 2.076234676208, 2.1790005317561976, 2.2991546938514356, 2.4361393303259327, 2.58849963921983, 2.7540503969194425, 2.930051644568766, 3.1133655736619406, 3.300583214172173, 3.4881214873752087, 3.6722971839814034, 3.849385941514546, 4.0156733715330315, 4.167503660261641, 4.301329078802335, 4.413762236720123, 4.50163167123862, 4.562040446234863, 4.592426773156125, 4.590625197250021, 4.554926569904935, 4.484134819747249, 4.377618421883764, 4.235354435115566, 4.057963025048204, 3.84673051349269, 3.6036191891099496, 3.3312623784012936, 3.0329436063343973, 2.712559066939102, 2.374563068951399, 2.0238966107048144, 1.6658997604427839, 1.3062090594245395, 0.950641710104315, 0.605068843208348, 0.2752806575285433, -0.03315332407699415, 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'root_angle': 0.5737918088252166, 'root_number': '-0.22975292054736118352393736938184 + 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2868959044126083', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92402761349693846825292498693', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78110614280661601971547883332', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57647308752761538821328187365', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'bad_primes': [2, 5], 'central_character': '40.13', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/m/d/193/2'], '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': '2-3200-40.13-c0-0-9', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3200-40.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.2868959044126083, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92402761349693846825292498693', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2438994759105081818135437776234', 'Lhash_array': ['2438994759105081818135437776234'], 'label': '2-3200-40.13-c0-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/m/d/193/2'}