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lfunc_lfunctions • Show schema
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{'Lhash': '6803410699030603783216332422591', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 24, 'a8': 0, 'a9': -11, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.47201528004592513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '8.1', 'coefficient_field': '1.1.1.1', 'conductor': 8, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[1], [1, 4, 27], [1, 2, 125], [1, -24, 343], [1, 44, 1331], [1, -22, 2197], [1, -50, 4913], [1, -44, 6859], [1, 56, 12167], [1, -198, 24389], [1, 160, 29791], [1, 162, 50653], [1, 198, 68921], [1, -52, 79507], [1, -528, 103823], [1, 242, 148877], [1, 668, 205379], [1, -550, 226981], [1, -188, 300763], [1, -728, 357911], [1, -154, 389017], [1, 656, 493039], [1, -236, 571787], [1, -714, 704969], [1, 478, 912673], [1, -1566, 1030301], [1, 968, 1092727], [1, 780, 1225043], [1, 1994, 1295029], [1, 942, 1442897]], 'euler_factors_factorization': [[1], [[[1, 4, 27], 1]], [[[1, 2, 125], 1]], [[[1, -24, 343], 1]], [[[1, 44, 1331], 1]], [[[1, -22, 2197], 1]], [[[1, -50, 4913], 1]], [[[1, -44, 6859], 1]], [[[1, 56, 12167], 1]], [[[1, -198, 24389], 1]], [[[1, 160, 29791], 1]], [[[1, 162, 50653], 1]], [[[1, 198, 68921], 1]], [[[1, -52, 79507], 1]], [[[1, -528, 103823], 1]], [[[1, 242, 148877], 1]], [[[1, 668, 205379], 1]], [[[1, -550, 226981], 1]], [[[1, -188, 300763], 1]], [[[1, -728, 357911], 1]], [[[1, -154, 389017], 1]], [[[1, 656, 493039], 1]], [[[1, -236, 571787], 1]], [[[1, -714, 704969], 1]], [[[1, 478, 912673], 1]], [[[1, -1566, 1030301], 1]], [[[1, 968, 1092727], 1]], [[[1, 780, 1225043], 1]], [[[1, 1994, 1295029], 1]], [[[1, 942, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-2e3-1.1-c3-0-0', '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/8/4/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.6900311631233975, 0.6940696894550508, 0.7061578846560187, 0.7262130409300759, 0.7540947571546361, 0.7895990172115337, 0.8324467849877045, 0.8822658281250231, 0.9385655718448591, 1.0007058818483021, 1.067861528295417, 1.1389846541072748, 1.2127679454963392, 1.287611484390475, 1.3615965157928394, 1.4324696006762088, 1.4976408176503873, 1.5541997693695466, 1.5989530749003338, 1.628486716555308, 1.6392559928240762, 1.6277048525620212, 1.5904150114410207, 1.5242834662460216, 1.4267248442846856, 1.295892511448464, 1.1309096159327117, 0.9320984168398712, 0.7011935388187666, 0.44152245193748324, 0.15813478256819574, -0.14213868093804757, -0.45071591319265775, -0.7573990971660425, -1.050628409990282, -1.317861353570387, -1.5460773960751433, -1.7223986187924565, -1.8348067387318037, -1.872925884694114, -1.8288296253367669, 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'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1428639190108832196, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.36694472262759880467468382418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '8.041114144439934942917179504468', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '10.71326597252919103933711342457', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.47201528004592513, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 8, 'conductor_radical': 2, 'degree': 2, 'dirichlet_coefficients': [1, 0, -4, 0, -2, 0, 24, 0, -11, 0, -44, 0, 22, 0, 8, 0, 50, 0, 44, 0, -96, 0, -56, 0, -121, 0, 152, 0, 198, 0, -160, 0, 176, 0, -48, 0, -162, 0, -88, 0, -198, 0, 52, 0, 22, 0, 528, 0, 233, 0, -200, 0, -242, 0, 88, 0, -176, 0, -668, 0, 550, 0, -264, 0, -44, 0, 188, 0, 224, 0, 728, 0, 154, 0, 484, 0, -1056, 0, -656, 0, -311, 0, 236, 0, -100, 0, -792, 0, 714, 0, 528, 0, 640, 0, -88, 0, -478, 0, 484, 0], 'euler11': [1, 44, 1331], 'euler13': [1, -22, 2197], 'euler17': [1, -50, 4913], 'euler19': [1, -44, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 56, 12167], 'euler29': [1, -198, 24389], 'euler3': [1, 4, 27], 'euler31': [1, 160, 29791], 'euler37': [1, 162, 50653], 'euler41': [1, 198, 68921], 'euler43': [1, -52, 79507], 'euler47': [1, -528, 103823], 'euler5': [1, 2, 125], 'euler53': [1, 242, 148877], 'euler59': [1, 668, 205379], 'euler61': [1, -550, 226981], 'euler67': [1, -188, 300763], 'euler7': [1, -24, 343], 'euler71': [1, -728, 357911], 'euler73': [1, -154, 389017], 'euler79': [1, 656, 493039], 'euler83': [1, -236, 571787], 'euler89': [1, -714, 704969], 'euler97': [1, 478, 912673], 'euler_factors': [[1, 0, 0], [1, 4, 27], [1, 2, 125], [1, -24, 343], [1, 44, 1331], [1, -22, 2197], [1, -50, 4913], [1, -44, 6859], [1, 56, 12167], [1, -198, 24389], [1, 160, 29791], [1, 162, 50653], [1, 198, 68921], [1, -52, 79507], [1, -528, 103823], [1, 242, 148877], [1, 668, 205379], [1, -550, 226981], [1, -188, 300763], [1, -728, 357911], [1, -154, 389017], [1, 656, 493039], [1, -236, 571787], [1, -714, 704969], [1, 478, 912673]], 'index': 0, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/8/4/a/a'], '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': '2-2e3-1.1-c3-0-0', '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': '2-2e3-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6870336818860667, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1428639190108832196, 'z1': {'__RealLiteral__': 0, 'data': '5.36694472262759880467468382418', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9955695
{'Lhash': '6803410699030603783216332422591', 'Lhash_array': ['6803410699030603783216332422591'], 'label': '2-2e3-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8/4/a/a'}
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id: 24546226
{'Lhash': '6803410699030603783216332422591', 'Lhash_array': ['6803410699030603783216332422591'], 'label': '2-2e3-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8/4/a/a/1/1'}