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lfunc_lfunctions • Show schema
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{'Lhash': '896991698064999218259249134827', 'a10': 5, 'a2': 1, 'a3': -6, 'a4': -7, 'a5': 5, 'a6': -6, 'a7': 0, 'a8': -15, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.455467951406456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -5]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': '1.1.1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[1, -1, 8], [1, 6, 27], [1, -5], [1], [1, 44, 1331], [1, 6, 2197], [1, -24, 4913], [1, -114, 6859], [1, 52, 12167], [1, -146, 24389], [1, -276, 29791], [1, 210, 50653], [1, 444, 68921], [1, -492, 79507], [1, -612, 103823], [1, -50, 148877], [1, 294, 205379], [1, 450, 226981], [1, 668, 300763], [1, 308, 357911], [1, 12, 389017], [1, -596, 493039], [1, -966, 571787], [1, -408, 704969], [1, -1200, 912673], [1, 1098, 1030301], [1, 972, 1092727], [1, -1516, 1225043], [1, -930, 1295029], [1, -1694, 1442897]], 'euler_factors_factorization': [[[[1, -1, 8], 1]], [[[1, 6, 27], 1]], [[[1, -5], 1]], [1], [[[1, 44, 1331], 1]], [[[1, 6, 2197], 1]], [[[1, -24, 4913], 1]], [[[1, -114, 6859], 1]], [[[1, 52, 12167], 1]], [[[1, -146, 24389], 1]], [[[1, -276, 29791], 1]], [[[1, 210, 50653], 1]], [[[1, 444, 68921], 1]], [[[1, -492, 79507], 1]], [[[1, -612, 103823], 1]], [[[1, -50, 148877], 1]], [[[1, 294, 205379], 1]], [[[1, 450, 226981], 1]], [[[1, 668, 300763], 1]], [[[1, 308, 357911], 1]], [[[1, 12, 389017], 1]], [[[1, -596, 493039], 1]], [[[1, -966, 571787], 1]], [[[1, -408, 704969], 1]], [[[1, -1200, 912673], 1]], [[[1, 1098, 1030301], 1]], [[[1, 972, 1092727], 1]], [[[1, -1516, 1225043], 1]], [[[1, -930, 1295029], 1]], [[[1, -1694, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-245-1.1-c3-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/245/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9380469466342116, 0.9078035882793852, 0.8173845306955428, 0.667795283788812, 0.4609435131265226, 0.1999538415281456, -0.11045368515807523, -0.4635760812280304, -0.8503916824708, -1.2593381499300198, -1.6762623000530719, -2.0845910263909535, -2.4657588550793843, -2.799909150993629, -3.0668630396700625, -3.2473236005084543, -3.3242543390598485, -3.2843425836183116, -3.119433126961777, -2.8277984281746655, -2.4151023892581582, -1.8949182073321593, -1.288679379964833, -0.6249776609064929, 0.06182799323793236, 0.7336642656149993, 1.351359436638234, 1.877650642977213, 2.2803438951912542, 2.53533687326959, 2.629187072563932, 2.56091178842787, 2.3427465473798943, 1.9996661219398415, 1.5675839427144311, 1.0902834201709806, 0.6152856136135606, 0.18900522949212817, -0.14832778189532203, -0.36741975106177205, -0.4537505511149404, 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1.0085147318254313, 1.9865276963342495, 2.7993939893474415, 3.194175103573591, 3.0147348223391504, 2.2520508227680733, 1.054233062769416, -0.3077786583980866, -1.5102607634263487, -2.263507746880336, -2.391216565334975, -1.8799101418274111, -0.8839632744924429, 0.3158304887148759, 1.389047332828964, 2.046487784224054, 2.119577995986396, 1.6058291145213668, 0.6673846656716653, -0.41697272869959245, -1.3326335713949287, -1.8195820563256695, -1.7463852489772353], 'positive_zeros': ['0.70760168291128778676896138658603', '2.98874167807381179399889932453532', '4.69012342516492712295988571953007', '5.38955411650657020820502524890667', '6.15153347447503958106153449847262', '7.62987393674825266121058001124963', '8.801811997129755070097570128570631', '10.01368956894195597180246174670328', '10.56668606870212241137361683026400', '11.97693236302079478916350455061617'], 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 242679346499516628, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70760168291128778676896138659', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98874167807381179399889932454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69012342516492712295988571953', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.455467951406456, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'dirichlet_coefficients': [1, 1, -6, -7, 5, -6, 0, -15, 9, 5, -44, 42, -6, 0, -30, 41, 24, 9, 114, -35, 0, -44, -52, 90, 25, -6, 108, 0, 146, -30, 276, 161, 264, 24, 0, -63, -210, 114, 36, -75, -444, 0, 492, 308, 45, -52, 612, -246, 0, 25, -144, 42, 50, 108, -220, 0, -684, 146, -294, 210, -450, 276, 0, -167, -30, 264, -668, -168, 312, 0, -308, -135, -12, -210, -150, -798, 0, 36, 596, 205, -891, -444, 966, 0, 120, 492, -876, 660, 408, 45, 0, 364, -1656, 612, 570, -966, 1200, 0, -396, -175], 'euler11': [1, 44, 1331], 'euler13': [1, 6, 2197], 'euler17': [1, -24, 4913], 'euler19': [1, -114, 6859], 'euler2': [1, -1, 8], 'euler23': [1, 52, 12167], 'euler29': [1, -146, 24389], 'euler3': [1, 6, 27], 'euler31': [1, -276, 29791], 'euler37': [1, 210, 50653], 'euler41': [1, 444, 68921], 'euler43': [1, -492, 79507], 'euler47': [1, -612, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -50, 148877], 'euler59': [1, 294, 205379], 'euler61': [1, 450, 226981], 'euler67': [1, 668, 300763], 'euler7': [1, 0, 0], 'euler71': [1, 308, 357911], 'euler73': [1, 12, 389017], 'euler79': [1, -596, 493039], 'euler83': [1, -966, 571787], 'euler89': [1, -408, 704969], 'euler97': [1, -1200, 912673], 'euler_factors': [[1, -1, 8], [1, 6, 27], [1, -5, 0], [1, 0, 0], [1, 44, 1331], [1, 6, 2197], [1, -24, 4913], [1, -114, 6859], [1, 52, 12167], [1, -146, 24389], [1, -276, 29791], [1, 210, 50653], [1, 444, 68921], [1, -492, 79507], [1, -612, 103823], [1, -50, 148877], [1, 294, 205379], [1, 450, 226981], [1, 668, 300763], [1, 308, 357911], [1, 12, 389017], [1, -596, 493039], [1, -966, 571787], [1, -408, 704969], [1, -1200, 912673]], 'index': 5, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/245/4/a/b'], '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': '2-245-1.1-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 242679346499516628, 'z1': {'__RealLiteral__': 0, 'data': '0.70760168291128778676896138659', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19206435
{'Lhash': '896991698064999218259249134827', 'Lhash_array': ['896991698064999218259249134827'], 'label': '2-245-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/a/b'}
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id: 24554667
{'Lhash': '896991698064999218259249134827', 'Lhash_array': ['896991698064999218259249134827'], 'label': '2-245-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/a/b/1/1'}