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lfunc_lfunctions • Show schema
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{'Lhash': '3220175121947141471004243029038', 'a10': [0.8522878526009595, -2.0672700395228594], 'a2': [-0.21256528955297668, 0.9771468659711595], 'a3': [2.0453962713776157, -1.5311644696615996], 'a4': [-0.9096319953545183, -0.41541501300188644], 'a5': [-2.2011932544064448, -0.393380549538947], 'a6': [1.0613923121402629, 2.3241249750925803], 'a7': [0.3610362920934348, -5.047946960563418], 'a8': [0.599277666511347, -0.8005412409243604], 'a9': [0.9939836032870755, -3.385197273379948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.21256528955297668, -0.9771468659711595]]], [5, [[1.0, 0], [2.2011932544064448, 0.393380549538947]]], [23, [[1.0, 0], [4.592002752409915, -1.3832970475858626]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.103', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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[-11.242872223589526, -78.19589390859369]], [[1.0, 0], [2.2163194617175095, -1.2102019860356534], [44.8731878488146, -69.82404322498803]], [[1.0, 0], [1.499582012230021, -10.429821988863273], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [-3.807505491478034, -2.0790552928942727], [52.442159293192965, 81.60159268462458]], [[1.0, 0], [-8.813447254290326, -2.587861607974546], [84.9666068159493, 54.60472256301536]], [[1.0, 0], [-3.628899837579035, 0.7894188392725243], [93.6920955215154, -42.7877463391943]], [[1.0, 0], [2.579092706794229, -3.4452645098145442], [-30.145383582032977, -102.66574817675122]], [[1.0, 0], [7.8722728896750604, 17.237873144892543], [-71.37982000003608, 82.37670360461415]], [[1.0, 0], [-0.8594492460695037, 3.9508244221067423], [-102.78841547506057, -46.94189646921317]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-230-115.103-c1-0-9', '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/230/2/l/a/103/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3643630996399114, 1.4448561843089371, 1.5345117092682508, 1.6327469059018311, 1.7365628184267994, 1.8409610686320046, 1.939463962210117, 2.0246488948469685, 2.088671794852642, 2.1237922438396986, 2.1229194236783653, 2.0801850602744265, 1.9915294737449167, 1.8552671690338112, 1.672582630565481, 1.44789675815718, 1.1890407272062915, 0.9071778224779862, 0.6164256098981771, 0.3331508553037369, 0.0749373480810014, -0.14073919755853206, -0.2980571725473072, -0.38450588737211816, -0.392508830397523, -0.32084360008031776, -0.17567690147343618, 0.028961001350280097, 0.27141113020285834, 0.5234298568218648, 0.7520726199097915, 0.9223616991392061, 1.0005868485410647, 0.9579919417934215, 0.7745164563593863, 0.4421997510144481, -0.03216985701468048, 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'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.11606866877790739, 'root_number': '0.7456537194166993 + 0.6663336481973893*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.116068668778', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.54027026166940410042290934874', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35892592715962111372695159571', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49249020465048987853914333185', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.103', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/l/a/103/5'], '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': '2-230-115.103-c1-0-9', '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': '2-230-115.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.11606866877790739, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.54027026166940410042290934874', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3220175121947141471004243029038', 'Lhash_array': ['3220175121947141471004243029038'], 'factors': ['2-230-115.103-c1-0-9'], 'label': '2-230-115.103-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/l/a/103/5'}