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'0.33290528062476913509838912157', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.69555244571411610459861753690', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 194.01815278235063, 'bad_primes': [7, 79], 'central_character': '1.1', 'conductor': 50417971746154743485317052161, 'conductor_radical': 553, 'degree': 16, 'dirichlet_coefficients': [1, 2, 0, 3, 0, 0, 0, 2, -4, 0, -2, 0, 0, 0, 0, 1, 0, -8, 0, 0, 0, -4, -2, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -4, 0, 6, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 8, -3], 'euler11': [1, 2, 1, -2, -4, -4, -1, 4, 7, 4, -1, -4, -4, -2, 1, 2, 1], 'euler13': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler17': [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], 'euler19': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler2': [1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1], 'euler23': [1, 2, 1, -2, -4, -4, -1, 4, 7, 4, -1, -4, -4, -2, 1, 2, 1], 'euler29': [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], 'euler3': [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], 'euler31': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler37': [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], 'euler41': [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], 'euler43': [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], 'euler47': [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], 'euler5': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler53': [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], 'euler59': [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], 'euler61': [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], 'euler67': [1, 2, 1, -2, -4, -4, -1, 4, 7, 4, -1, -4, -4, -2, 1, 2, 1], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], 'euler73': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler79': [1, 4, 10, 16, 19, 16, 10, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler83': [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], 'euler89': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler97': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler_factors': [[1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1], [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, -2, -4, -4, -1, 4, 7, 4, -1, -4, -4, -2, 1, 2, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 2, 1, -2, -4, -4, -1, 4, 7, 4, -1, -4, -4, -2, 1, 2, 1], [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], [1, 0, 4, 0, 10, 0, 16, 0, 19, 0, 16, 0, 10, 0, 4, 0, 1], [1, 2, 1, -2, -4, -4, -1, 4, 7, 4, -1, -4, -4, -2, 1, 2, 1], [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 4, 10, 16, 19, 16, 10, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3871/1/m/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': '16-3871e8-1.1-c0e8-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '16-3871e8-1.1-c0e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.389921099883857, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e8-0', 'trace_hash': 1448877571786805270, 'z1': {'__RealLiteral__': 0, 'data': '0.31705660321478611486902155074', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '401916993371547186177672430653,422007578803135741921037114429,881717475299712226859001144915,1210912919988627898458044719426,1942356246022662883944083385193,2163888212856643051965569228874,2389623744672432588565874689235,2644552868963238032730590493024', 'Lhash_array': ['401916993371547186177672430653', '422007578803135741921037114429', '881717475299712226859001144915', '1210912919988627898458044719426', '1942356246022662883944083385193', '2163888212856643051965569228874', '2389623744672432588565874689235', '2644552868963238032730590493024'], 'factors': ['2-3871-553.394-c0-0-2', '2-3871-553.473-c0-0-0', '2-3871-553.394-c0-0-7', '2-3871-553.473-c0-0-5', '2-3871-553.394-c0-0-16', '2-3871-553.473-c0-0-13', '2-3871-553.473-c0-0-15', '2-3871-553.394-c0-0-17'], 'label': '16-3871e8-1.1-c0e8-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3871/1/m/e'}