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lfunc_lfunctions • Show schema
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{'Lhash': '1606840350960737455528451389907', 'a10': 15, 'a2': 3, 'a3': 0, 'a4': 1, 'a5': 5, 'a6': 0, 'a7': 7, 'a8': -21, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.585601651808304, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -5]], [7, [1, -7]]], 'bad_primes': [3, 5, 7], 'central_character': '315.1', 'coefficient_field': '1.1.1.1', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[1, -3, 8], [1], [1, -5], [1, -7], [1, -60, 1331], [1, -38, 2197], [1, 84, 4913], [1, -110, 6859], [1, -120, 12167], [1, -162, 24389], [1, -236, 29791], [1, 376, 50653], [1, 126, 68921], [1, 34, 79507], [1, 6, 103823], [1, -582, 148877], [1, -492, 205379], [1, 880, 226981], [1, 826, 300763], [1, 666, 357911], [1, 826, 389017], [1, 592, 493039], [1, -792, 571787], [1, -1002, 704969], [1, -1442, 912673], [1, 1182, 1030301], [1, -56, 1092727], [1, 1572, 1225043], [1, 1402, 1295029], [1, 846, 1442897]], 'euler_factors_factorization': [[[[1, -3, 8], 1]], [1], [[[1, -5], 1]], [[[1, -7], 1]], [[[1, -60, 1331], 1]], [[[1, -38, 2197], 1]], [[[1, 84, 4913], 1]], [[[1, -110, 6859], 1]], [[[1, -120, 12167], 1]], [[[1, -162, 24389], 1]], [[[1, -236, 29791], 1]], [[[1, 376, 50653], 1]], [[[1, 126, 68921], 1]], [[[1, 34, 79507], 1]], [[[1, 6, 103823], 1]], [[[1, -582, 148877], 1]], [[[1, -492, 205379], 1]], [[[1, 880, 226981], 1]], [[[1, 826, 300763], 1]], [[[1, 666, 357911], 1]], [[[1, 826, 389017], 1]], [[[1, 592, 493039], 1]], [[[1, -792, 571787], 1]], [[[1, -1002, 704969], 1]], [[[1, -1442, 912673], 1]], [[[1, 1182, 1030301], 1]], [[[1, -56, 1092727], 1]], [[[1, 1572, 1225043], 1]], [[[1, 1402, 1295029], 1]], [[[1, 846, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-315-1.1-c3-0-12', 'leading_term': '3.52029253644276711371849269201000000000000000000000000000000000000000000000000000000000000', '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/315/4/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [3.520292536442767, 3.507811910125981, 3.470405350095191, 3.4081819679522902, 3.3213339817820056, 3.2101517428400643, 3.0750437516123115, 2.9165606906478403, 2.735422289390508, 2.5325456672094284, 2.3090736789048822, 2.066401714025608, 1.8062013776350834, 1.5304395048528572, 1.241391033083831, 0.9416443725780217, 0.63409807601464, 0.3219478093166563, 0.00866286684444352, -0.30204824795870594, -0.6062833436679681, -0.9000029896234186, -1.179097352924655, -1.4394625021315623, -1.6770848659666182, -1.8881321476630364, -2.069048622572162, -2.2166524016810927, -2.328231941225198, -2.4016388335477408, -2.435373741642919, -2.428662253605373, -2.381517446291405, -2.2947860705489096, -2.1701755112248127, 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'primitive': True, 'rational': True, 'root_analytic_conductor': 4.311102138874502, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 7513478356611133, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26757353380453565560981955821', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02796480050487528963941092002', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15366849174035422445509180431', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.585601651808304, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'dirichlet_coefficients': [1, 3, 0, 1, 5, 0, 7, -21, 0, 15, 60, 0, 38, 21, 0, -71, -84, 0, 110, 5, 0, 180, 120, 0, 25, 114, 0, 7, 162, 0, 236, -45, 0, -252, 35, 0, -376, 330, 0, -105, -126, 0, -34, 60, 0, 360, -6, 0, 49, 75, 0, 38, 582, 0, 300, -147, 0, 486, 492, 0, -880, 708, 0, 433, 190, 0, -826, -84, 0, 105, -666, 0, -826, -1128, 0, 110, 420, 0, -592, -355, 0, -378, 792, 0, -420, -102, 0, -1260, 1002, 0, 266, 120, 0, -18, 550, 0, 1442, 147, 0, 25], 'euler11': [1, -60, 1331], 'euler13': [1, -38, 2197], 'euler17': [1, 84, 4913], 'euler19': [1, -110, 6859], 'euler2': [1, -3, 8], 'euler23': [1, -120, 12167], 'euler29': [1, -162, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -236, 29791], 'euler37': [1, 376, 50653], 'euler41': [1, 126, 68921], 'euler43': [1, 34, 79507], 'euler47': [1, 6, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -582, 148877], 'euler59': [1, -492, 205379], 'euler61': [1, 880, 226981], 'euler67': [1, 826, 300763], 'euler7': [1, -7, 0], 'euler71': [1, 666, 357911], 'euler73': [1, 826, 389017], 'euler79': [1, 592, 493039], 'euler83': [1, -792, 571787], 'euler89': [1, -1002, 704969], 'euler97': [1, -1442, 912673], 'euler_factors': [[1, -3, 8], [1, 0, 0], [1, -5, 0], [1, -7, 0], [1, -60, 1331], [1, -38, 2197], [1, 84, 4913], [1, -110, 6859], [1, -120, 12167], [1, -162, 24389], [1, -236, 29791], [1, 376, 50653], [1, 126, 68921], [1, 34, 79507], [1, 6, 103823], [1, -582, 148877], [1, -492, 205379], [1, 880, 226981], [1, 826, 300763], [1, 666, 357911], [1, 826, 389017], [1, 592, 493039], [1, -792, 571787], [1, -1002, 704969], [1, -1442, 912673]], 'index': 12, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/4/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/315/4/a/e'], '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': '2-315-1.1-c3-0-12', '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': '2-315-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.311102138874502, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 7513478356611133, 'z1': {'__RealLiteral__': 0, 'data': '1.26757353380453565560981955821', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20661033
{'Lhash': '1606840350960737455528451389907', 'Lhash_array': ['1606840350960737455528451389907'], 'factors': ['2-315-1.1-c3-0-12'], 'label': '2-315-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/4/a/e'}
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id: 24556718
{'Lhash': '1606840350960737455528451389907', 'Lhash_array': ['1606840350960737455528451389907'], 'factors': ['2-315-1.1-c3-0-12'], 'label': '2-315-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/4/a/e/1/1'}