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lfunc_lfunctions • Show schema
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{'Lhash': '2560926239342643866812137509638', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': -26, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.55085950258329, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1, -2], [1], [1], [1, 26, 343], [1, -28, 1331], [1, 12, 2197], [1, 64, 4913], [1, 60, 6859], [1, 58, 12167], [1, 90, 24389], [1, 128, 29791], [1, 236, 50653], [1, 242, 68921], [1, 362, 79507], [1, -226, 103823], [1, 108, 148877], [1, -20, 205379], [1, -542, 226981], [1, -434, 300763], [1, -1128, 357911], [1, 632, 389017], [1, 720, 493039], [1, 478, 571787], [1, -490, 704969], [1, 1456, 912673], [1, -578, 1030301], [1, 1462, 1092727], [1, -966, 1225043], [1, -370, 1295029], [1, 528, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [1], [1], [[[1, 26, 343], 1]], [[[1, -28, 1331], 1]], [[[1, 12, 2197], 1]], [[[1, 64, 4913], 1]], [[[1, 60, 6859], 1]], [[[1, 58, 12167], 1]], [[[1, 90, 24389], 1]], [[[1, 128, 29791], 1]], [[[1, 236, 50653], 1]], [[[1, 242, 68921], 1]], [[[1, 362, 79507], 1]], [[[1, -226, 103823], 1]], [[[1, 108, 148877], 1]], [[[1, -20, 205379], 1]], [[[1, -542, 226981], 1]], [[[1, -434, 300763], 1]], [[[1, -1128, 357911], 1]], [[[1, 632, 389017], 1]], [[[1, 720, 493039], 1]], [[[1, 478, 571787], 1]], [[[1, -490, 704969], 1]], [[[1, 1456, 912673], 1]], [[[1, -578, 1030301], 1]], [[[1, 1462, 1092727], 1]], [[[1, -966, 1225043], 1]], [[[1, -370, 1295029], 1]], [[[1, 528, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-450-1.1-c3-0-19', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/450/4/a/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [-2.6168265416474684e-60, 0.2759928751021218, 0.5499266741342467, 0.8197389893101366, 1.0833616179394934, 1.3387198017170423, 1.5837339346714396, 1.816324407683607, 2.0344201324595352, 2.235971140633819, 2.4189654893701404, 2.5814505287304788, 2.721558403517573, 2.837535478386455, 2.927775194617743, 2.9908536945728033, 3.02556738972518, 3.0309715042364798, 3.0064185020608214, 2.9515952050960643, 2.8665573363785426, 2.7517601789981603, 2.608084031321234, 2.436853164951593, 2.2398470558805776, 2.019302763104826, 1.7779074734758449, 1.5187804165828804, 1.2454435778418558, 0.961780899195928, 0.6719859510941737, 0.38049838144360887, 0.0919297903221456, -0.18901996471207222, -0.45765466828861145, -0.7093801348629003, -0.9398070332139504, -1.1448557931563978, -1.3208609792260915, -1.4646723106935524, -1.5737493687403907, 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1.4416925480598393, 1.6951125193496441, 1.8572942399605665, 1.919204333718865, 1.8777952604980577, 1.7362781819930444, 1.504010897119755, 1.1960003286612675, 0.8320431136627402, 0.43555099886270343, 0.032128503341418264, -0.35201267046325213, -0.6917058740274575, -0.9644454477974342, -1.1518633708041308, -1.2409700810664306, -1.2250755906744715, -1.1043252742089267, -0.8858075424507338, -0.5832167027301571, -0.21608209128790856, 0.19139766684368237, 0.6118504104619878], 'positive_zeros': ['2.02021459137207957754950848163340', '3.34639866936807531453688209813513', '4.16400255317564643962006062450453', '5.48633302056199884963434598773426', '6.55155528932095901846697571472291', '6.97237505725871307599391348466050', '8.473027275732949666847633909369334', '9.427606068435365467927169499195458', '10.24705929574650852945409835618354'], 'prelabel': '2-450-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.1527526141455, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 637566433717191505, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02021459137207957754950848163', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34639866936807531453688209814', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16400255317564643962006062450', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.55085950258329, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 4, 0, 0, -26, 8, 0, 0, 28, 0, -12, -52, 0, 16, -64, 0, -60, 0, 0, 56, -58, 0, 0, -24, 0, -104, -90, 0, -128, 32, 0, -128, 0, 0, -236, -120, 0, 0, -242, 0, -362, 112, 0, -116, 226, 0, 333, 0, 0, -48, -108, 0, 0, -208, 0, -180, 20, 0, 542, -256, 0, 64, 0, 0, 434, -256, 0, 0, 1128, 0, -632, -472, 0, -240, -728, 0, -720, 0, 0, -484, -478, 0, 0, -724, 0, 224, 490, 0, 312, -232, 0, 452, 0, 0, -1456, 666, 0, 0], 'euler11': [1, -28, 1331], 'euler13': [1, 12, 2197], 'euler17': [1, 64, 4913], 'euler19': [1, 60, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 58, 12167], 'euler29': [1, 90, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 128, 29791], 'euler37': [1, 236, 50653], 'euler41': [1, 242, 68921], 'euler43': [1, 362, 79507], 'euler47': [1, -226, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 108, 148877], 'euler59': [1, -20, 205379], 'euler61': [1, -542, 226981], 'euler67': [1, -434, 300763], 'euler7': [1, 26, 343], 'euler71': [1, -1128, 357911], 'euler73': [1, 632, 389017], 'euler79': [1, 720, 493039], 'euler83': [1, 478, 571787], 'euler89': [1, -490, 704969], 'euler97': [1, 1456, 912673], 'euler_factors': [[1, -2, 0], [1, 0, 0], [1, 0, 0], [1, 26, 343], [1, -28, 1331], [1, 12, 2197], [1, 64, 4913], [1, 60, 6859], [1, 58, 12167], [1, 90, 24389], [1, 128, 29791], [1, 236, 50653], [1, 242, 68921], [1, 362, 79507], [1, -226, 103823], [1, 108, 148877], [1, -20, 205379], [1, -542, 226981], [1, -434, 300763], [1, -1128, 357911], [1, 632, 389017], [1, 720, 493039], [1, 478, 571787], [1, -490, 704969], [1, 1456, 912673]], 'index': 19, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/4/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/450/4/a/k'], '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': '2-450-1.1-c3-0-19', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-450-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.1527526141455, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 637566433717191505, 'z1': {'__RealLiteral__': 0, 'data': '2.02021459137207957754950848163', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20668433
{'Lhash': '2560926239342643866812137509638', 'Lhash_array': ['2560926239342643866812137509638'], 'label': '2-450-1.1-c3-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/4/a/k'}
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id: 24561089
{'Lhash': '2560926239342643866812137509638', 'Lhash_array': ['2560926239342643866812137509638'], 'label': '2-450-1.1-c3-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/4/a/k/1/1'}