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lfunc_lfunctions • Show schema
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{'Lhash': '3415186491477057766277535687871', 'a10': 0, 'a2': 0, 'a3': 8, 'a4': 0, 'a5': -10, 'a6': 0, 'a7': 16, 'a8': 0, 'a9': 37, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8880611201837005, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '32.1', 'coefficient_field': '1.1.1.1', 'conductor': 32, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[1], [1, -8, 27], [1, 10, 125], [1, -16, 343], [1, 40, 1331], [1, 50, 2197], [1, 30, 4913], [1, -40, 6859], [1, -48, 12167], [1, 34, 24389], [1, -320, 29791], [1, -310, 50653], [1, -410, 68921], [1, -152, 79507], [1, 416, 103823], [1, 410, 148877], [1, 200, 205379], [1, -30, 226981], [1, -776, 300763], [1, -400, 357911], [1, 630, 389017], [1, 1120, 493039], [1, -552, 571787], [1, 326, 704969], [1, 110, 912673], [1, 1098, 1030301], [1, 48, 1092727], [1, -664, 1225043], [1, 370, 1295029], [1, -1490, 1442897]], 'euler_factors_factorization': [[1], [[[1, -8, 27], 1]], [[[1, 10, 125], 1]], [[[1, -16, 343], 1]], [[[1, 40, 1331], 1]], [[[1, 50, 2197], 1]], [[[1, 30, 4913], 1]], [[[1, -40, 6859], 1]], [[[1, -48, 12167], 1]], [[[1, 34, 24389], 1]], [[[1, -320, 29791], 1]], [[[1, -310, 50653], 1]], [[[1, -410, 68921], 1]], [[[1, -152, 79507], 1]], [[[1, 416, 103823], 1]], [[[1, 410, 148877], 1]], [[[1, 200, 205379], 1]], [[[1, -30, 226981], 1]], [[[1, -776, 300763], 1]], [[[1, -400, 357911], 1]], [[[1, 630, 389017], 1]], [[[1, 1120, 493039], 1]], [[[1, -552, 571787], 1]], [[[1, 326, 704969], 1]], [[[1, 110, 912673], 1]], [[[1, 1098, 1030301], 1]], [[[1, 48, 1092727], 1]], [[[1, -664, 1225043], 1]], [[[1, 370, 1295029], 1]], [[[1, -1490, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2e5-1.1-c3-0-1', '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/32/4/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.647789167425126, 1.6476888621478543, 1.6472359517164459, 1.6459791218431172, 1.6431815586252152, 1.6378434166283817, 1.6287322805352074, 1.6144210098728378, 1.5933325556231974, 1.5637915994870863, 1.5240830833163168, 1.472517777727057, 1.407504931244179, 1.3276317291119095, 1.2317487896463084, 1.1190602713719882, 0.9892164029681152, 0.8424054325774384, 0.679441178735377, 0.5018416100018487, 0.31189324475851793, 0.11269570902386386, -0.09181941841554542, -0.2969012467211752, -0.4970290138055634, -0.6860027762612448, -0.8570784967800686, -1.0031489333061798, -1.116969565171748, -1.1914262473243535, -1.2198384486971883, -1.1962889250665558, -1.1159676559001903, -0.9755150259073769, -0.7733467674216512, -0.5099413265811308, -0.18806930364552146, 0.18705533917892633, 0.607721327315055, 1.06377975360848, 1.5428296775159043, 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4.313555658392798, 3.727258434601682, 2.8611570378476867, 1.8571928982540769, 0.8637309255103988, 0.01247019443539595, -0.6010845469414061, -0.9304244930801483, -0.9820947339953855, -0.810489013710167, -0.5044552564383568, -0.16820284620766504, 0.10000395911583873, 0.22749063200603364, 0.1815665692020587, -0.023993346074326356, -0.33162989588601316, -0.6514368855199292, -0.8793369434241947, -0.9187002627658309], 'positive_zeros': ['2.69410710716516310854206677122698', '4.56474133618286482949667896526586', '7.61350884803859455478884620236868', '8.163652281493415771325020581764141', '9.682824502714614814012798336544400', '11.35227830488608030471932546258856', '12.86927620499612524351220202169870', '14.13504791546597104644057823567096', '15.03563193490656579912823293464227', '15.85249179829585567904336618178320'], 'prelabel': '2-2e5-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3740673637721335, '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': 1421853197891527038, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.69410710716516310854206677123', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.56474133618286482949667896527', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.61350884803859455478884620237', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8880611201837005, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 32, 'conductor_radical': 2, 'degree': 2, 'dirichlet_coefficients': [1, 0, 8, 0, -10, 0, 16, 0, 37, 0, -40, 0, -50, 0, -80, 0, -30, 0, 40, 0, 128, 0, 48, 0, -25, 0, 80, 0, -34, 0, 320, 0, -320, 0, -160, 0, 310, 0, -400, 0, 410, 0, 152, 0, -370, 0, -416, 0, -87, 0, -240, 0, -410, 0, 400, 0, 320, 0, -200, 0, 30, 0, 592, 0, 500, 0, 776, 0, 384, 0, 400, 0, -630, 0, -200, 0, -640, 0, -1120, 0, -359, 0, 552, 0, 300, 0, -272, 0, -326, 0, -800, 0, 2560, 0, -400, 0, -110, 0, -1480, 0], 'euler11': [1, 40, 1331], 'euler13': [1, 50, 2197], 'euler17': [1, 30, 4913], 'euler19': [1, -40, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -48, 12167], 'euler29': [1, 34, 24389], 'euler3': [1, -8, 27], 'euler31': [1, -320, 29791], 'euler37': [1, -310, 50653], 'euler41': [1, -410, 68921], 'euler43': [1, -152, 79507], 'euler47': [1, 416, 103823], 'euler5': [1, 10, 125], 'euler53': [1, 410, 148877], 'euler59': [1, 200, 205379], 'euler61': [1, -30, 226981], 'euler67': [1, -776, 300763], 'euler7': [1, -16, 343], 'euler71': [1, -400, 357911], 'euler73': [1, 630, 389017], 'euler79': [1, 1120, 493039], 'euler83': [1, -552, 571787], 'euler89': [1, 326, 704969], 'euler97': [1, 110, 912673], 'euler_factors': [[1, 0, 0], [1, -8, 27], [1, 10, 125], [1, -16, 343], [1, 40, 1331], [1, 50, 2197], [1, 30, 4913], [1, -40, 6859], [1, -48, 12167], [1, 34, 24389], [1, -320, 29791], [1, -310, 50653], [1, -410, 68921], [1, -152, 79507], [1, 416, 103823], [1, 410, 148877], [1, 200, 205379], [1, -30, 226981], [1, -776, 300763], [1, -400, 357911], [1, 630, 389017], [1, 1120, 493039], [1, -552, 571787], [1, 326, 704969], [1, 110, 912673]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/32/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/32/4/a/c'], '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': '2-2e5-1.1-c3-0-1', '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': '2-2e5-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3740673637721335, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1421853197891527038, 'z1': {'__RealLiteral__': 0, 'data': '2.69410710716516310854206677123', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9974766
{'Lhash': '3415186491477057766277535687871', 'Lhash_array': ['3415186491477057766277535687871'], 'factors': ['2-2e5-1.1-c3-0-1'], 'label': '2-2e5-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/4/a/c'}
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id: 24548583
{'Lhash': '3415186491477057766277535687871', 'Lhash_array': ['3415186491477057766277535687871'], 'factors': ['2-2e5-1.1-c3-0-1'], 'label': '2-2e5-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/4/a/c/1/1'}