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lfunc_lfunctions • Show schema
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{'Lhash': '1570123926898818029685583147201', 'a10': 0, 'a2': 0, 'a3': -8, 'a4': 0, 'a5': -10, 'a6': 0, 'a7': -49, 'a8': 0, 'a9': -179, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 71.85195127621535, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 49]]], 'bad_primes': [2, 7], 'central_character': '448.1', 'coefficient_field': '1.1.1.1', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 8, 243], [1, 10, 3125], [1, 49], [1, -340, 161051], [1, -294, 371293], [1, -1226, 1419857], [1, 2432, 2476099], [1, -2000, 6436343], [1, -6746, 20511149], [1, -8856, 28629151], [1, 9182, 69343957], [1, 14574, 115856201], [1, 8108, 147008443], [1, 312, 229345007], [1, -14634, 418195493], [1, -27656, 714924299], [1, 34338, 844596301], [1, 12316, 1350125107], [1, -36920, 1804229351], [1, 61718, 2073071593], [1, 64752, 3077056399], [1, -77056, 3939040643], [1, 8166, 5584059449], [1, -20650, 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'8.781477591953328602132474289966338', '10.02914255892216674031743836548867'], 'prelabel': '2-448-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.476553030342897, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 719074830304305926, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23860938228257135813214668380', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84407447871826044236658906515', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93265446939383881499784269418', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 71.85195127621535, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, -8, 0, -10, 0, -49, 0, -179, 0, 340, 0, 294, 0, 80, 0, 1226, 0, -2432, 0, 392, 0, 2000, 0, -3025, 0, 3376, 0, 6746, 0, 8856, 0, -2720, 0, 490, 0, -9182, 0, -2352, 0, -14574, 0, -8108, 0, 1790, 0, -312, 0, 2401, 0, -9808, 0, 14634, 0, -3400, 0, 19456, 0, 27656, 0, -34338, 0, 8771, 0, -2940, 0, -12316, 0, -16000, 0, 36920, 0, -61718, 0, 24200, 0, -16660, 0, -64752, 0, 16489, 0, 77056, 0, -12260, 0, -53968, 0, -8166, 0, -14406, 0, -70848, 0, 24320, 0, 20650, 0, -60860, 0], 'euler11': [1, -340, 161051], 'euler13': [1, -294, 371293], 'euler17': [1, -1226, 1419857], 'euler19': [1, 2432, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -2000, 6436343], 'euler29': [1, -6746, 20511149], 'euler3': [1, 8, 243], 'euler31': [1, -8856, 28629151], 'euler37': [1, 9182, 69343957], 'euler41': [1, 14574, 115856201], 'euler43': [1, 8108, 147008443], 'euler47': [1, 312, 229345007], 'euler5': [1, 10, 3125], 'euler53': [1, -14634, 418195493], 'euler59': [1, -27656, 714924299], 'euler61': [1, 34338, 844596301], 'euler67': [1, 12316, 1350125107], 'euler7': [1, 49, 0], 'euler71': [1, -36920, 1804229351], 'euler73': [1, 61718, 2073071593], 'euler79': [1, 64752, 3077056399], 'euler83': [1, -77056, 3939040643], 'euler89': [1, 8166, 5584059449], 'euler97': [1, -20650, 8587340257], 'euler_factors': [[1, 0, 0], [1, 8, 243], [1, 10, 3125], [1, 49, 0], [1, -340, 161051], [1, -294, 371293], [1, -1226, 1419857], [1, 2432, 2476099], [1, -2000, 6436343], [1, -6746, 20511149], [1, -8856, 28629151], [1, 9182, 69343957], [1, 14574, 115856201], [1, 8108, 147008443], [1, 312, 229345007], [1, -14634, 418195493], [1, -27656, 714924299], [1, 34338, 844596301], [1, 12316, 1350125107], [1, -36920, 1804229351], [1, 61718, 2073071593], [1, 64752, 3077056399], [1, -77056, 3939040643], [1, 8166, 5584059449], [1, -20650, 8587340257]], 'index': 37, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/6/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/448/6/a/f'], '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': '2-448-1.1-c5-0-37', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-448-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.476553030342897, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 719074830304305926, 'z1': {'__RealLiteral__': 0, 'data': '1.23860938228257135813214668380', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20538965
{'Lhash': '1570123926898818029685583147201', 'Lhash_array': ['1570123926898818029685583147201'], 'factors': ['2-448-1.1-c5-0-37'], 'label': '2-448-1.1-c5-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/6/a/f'}
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id: 24586562
{'Lhash': '1570123926898818029685583147201', 'Lhash_array': ['1570123926898818029685583147201'], 'factors': ['2-448-1.1-c5-0-37'], 'label': '2-448-1.1-c5-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/6/a/f/1/1'}