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lfunc_lfunctions • Show schema
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{'Lhash': '1995658157115657284925498196142', 'a10': [-3.562107333688151, 1.7690566180563618], 'a2': [1.408870928957493, -0.12281166694760907], 'a3': [0.9888308262251285, 0.14904226617617444], 'a4': [1.969834588923099, -0.3460515745985925], 'a5': [-2.6179051302238627, 1.0274520506814613], 'a6': [1.4114391338803476, 0.08854135390366726], 'a7': [2.6374480744919566, 0.20944606551250833], 'a8': [2.7327435164623903, -0.7294606728486263], 'a9': [0.9555728057861407, 0.2947551744109042], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.408870928957493, 0.12281166694760907]]], [3, [[1.0, 0], [-0.9888308262251285, -0.14904226617617444]]], [7, [[1.0, 0], [-2.6374480744919566, -0.20944606551250833]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.187', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '2314868920431136255973279388078', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.408870928957493, 0.12281166694760907]], [[1.0, 0], [-0.9888308262251285, -0.14904226617617444]], [[1.0, 0], [2.6179051302238627, -1.0274520506814613], [3.6652593591491316, -3.400863688854597]], [[1.0, 0], [-2.6374480744919566, -0.20944606551250833]], [[1.0, 0], [-0.07414093604707471, -0.24035901124961925], [-9.088626517475944, 6.196520638699842]], [[1.0, 0], [-1.9981705895544217, -0.4560693977841154], [11.71259528273145, 5.640488608528256]], [[1.0, 0], [-0.5536914812372925, 0.8121162459211416], [-6.210797414228716, -15.824853726951472]], [[1.0, 0], [2.110452756075751, -3.655411400496967], [-9.5, -16.454482671904334]], [[1.0, 0], [4.145048535135917, 6.079669580599612], [-8.402843560427085, 21.410096218816697]], [[1.0, 0], [-0.9897850290071085, 0.476655348045497], [18.081204253903273, -22.673112991572864]], [[1.0, 0], [-4.3677363085525505, -7.565141200476352], [-15.5, 26.846787517317598]], [[1.0, 0], 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[[1.0, 0], [-0.4326834618866906, -1.8957101097535847], [-74.78041603590079, 36.01235034675732]], [[1.0, 0], [0.34039525824854, -1.1035343235311907], [-73.53525091412354, -50.13548516766236]], [[1.0, 0], [0, 5.114502253635588], [-97.0, 0]], [[1.0, 0], [0.7699525714254042, -5.108301536805623], [-96.51285338440022, -29.770272615501327]], [[1.0, 0], [-0.17763893076333473, -0.45261661394745856], [-75.50434279847211, 70.0577919904047]], [[1.0, 0], [5.2277892167713915, -16.948076382078142], [-88.40754885181146, -60.27524621280756]], [[1.0, 0], [-6.358640021360556, 1.961380689324206], [90.06002640044345, -61.4018863289348]], [[1.0, 0], [-4.631271037617624, -20.290924198345845], [-101.80948207297337, 49.028862520284065]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-588-196.187-c1-0-34', '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/588/2/ba/a/187/27', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.054165946636958, 3.0159974148153745, 2.9771294420745575, 2.9283469640344295, 2.8569791236319384, 2.7489390090955528, 2.5907734728097287, 2.3714982509156264, 2.0841416106794037, 1.7269752721659384, 1.3043977110509901, 0.8273997369491407, 0.31351924282970195, -0.21380389355623622, -0.7265279487667706, -1.1939597946971479, -1.5852720280595178, -1.8724151415736485, -2.0331678771694617, -2.0539999546473595, -1.9323823222967196, -1.6781829561927757, -1.3138393659762528, -0.873104892382537, -0.39831971007191314, 0.06365400892046584, 0.4664912317333998, 0.7699278031611887, 0.9450755246253121, 0.9787859305525669, 0.8763484200496457, 0.6619467907439838, 0.37654385601721074, 0.07319621996503023, -0.18981755806776376, -0.3572946061693815, -0.3857569025600702, -0.2511881722262634, 0.04542172232570417, 0.4758204899678466, 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'root_angle': -0.06272789950305006, 'root_number': '0.9806453507238301 - 0.19579248224519824*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0313639497515', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57429670033395360774494584471', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10707653525933921145559693607', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15686664429609268549938554724', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'bad_primes': [2, 3, 7], 'central_character': '196.187', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/2/ba/a/187/27'], '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': '2-588-196.187-c1-0-34', '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': '2-588-196.187-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': -0.03136394975152503, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57429670033395360774494584471', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1995658157115657284925498196142', 'Lhash_array': ['1995658157115657284925498196142'], 'label': '2-588-196.187-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/2/ba/a/187/27'}