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lfunc_lfunctions • Show schema
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{'Lhash': '1162951840492079207944293571597', 'a10': [-2.1876657927190593, 0.4627292722174497], 'a2': [0.5, 0.8660254037844386], 'a3': [0.09365412622532852, 0.3495219574113949], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.6930975915445333, 2.125938787593652], 'a6': [-0.2558678311860664, 0.2558678311860664], 'a7': [0.010026655915865178, 0.037419989308019895], 'a8': [-1.0, 0.0], 'a9': [2.484681707999653, -1.4345316529641385], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [0.6930975915445333, -2.125938787593652]]], [37, [[1.0, 0], [6.075009865530375, 0.30700998959091996]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.103', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '3030904767892368685957851987611', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 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[-94.39676901250381, -54.5]], [[1.0, 0], [-6.40021049642432, 3.695163252980849], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-370-185.103-c1-0-3', '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/370/2/q/f/103/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.439820204164564, 1.2651037850765345, 1.0943141806467198, 0.9201474762712467, 0.735773206850652, 0.5360356565343577, 0.3183335856773106, 0.08316649160014183, -0.1656098732136303, -0.4207817435569671, -0.672020235431693, -0.9063808103013284, -1.1090743151606133, -1.2645099075562445, -1.3575821553528964, -1.3751386905954677, -1.307526525717838, -1.1500801201087523, -0.9043881998757763, -0.5791646683806351, -0.1905564427200754, 0.23824900675929817, 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'6.02778343369315268796377728098874', '7.39026119591096240831350655103247', '8.450358471738440968226427722287279', '9.164964937569596128800080702503173', '10.43532032339206365990003896614729', '11.01122445371893837119815677138932'], 'prelabel': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.7176276809416844, 'root_number': '-0.6316638126714472 - 0.7752424316053468*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.358813840471', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.917407241619023335184665623205', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.55652643766222506208043070395', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08733496727011626064329744802', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.103', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/q/f/103/6'], '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': '2-370-185.103-c1-0-3', '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': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.3588138404708422, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.917407241619023335184665623205', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1162951840492079207944293571597', 'Lhash_array': ['1162951840492079207944293571597'], 'label': '2-370-185.103-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/q/f/103/6'}