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lfunc_lfunctions • Show schema
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{'Lhash': '1875464585207696026792819674616', 'a10': -470, 'a2': -5, 'a3': 0, 'a4': -7, 'a5': 94, 'a6': 0, 'a7': 0, 'a8': 195, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[1, 5, 32], [1], [1, -94, 3125], [1], [1, 52, 161051], [1, -770, 371293], [1, 2022, 1419857], [1, 1732, 2476099], [1, -576, 6436343], [1, 5518, 20511149], [1, 6336, 28629151], [1, 7338, 69343957], [1, 3262, 115856201], [1, -5420, 147008443], [1, -864, 229345007], [1, 4182, 418195493], [1, 11220, 714924299], [1, -45602, 844596301], [1, -1396, 1350125107], [1, 18720, 1804229351], [1, 46362, 2073071593], [1, -97424, 3077056399], [1, 81228, 3939040643], [1, 3182, 5584059449], [1, 4914, 8587340257], [1, 166354, 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[0]], 'group': 'GL2', 'index': 66, 'label': '2-21e2-1.1-c5-0-66', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/441/6/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.1941625997067523e-60, 0.18971980304342562, 0.37635594423577384, 0.5568724204559714, 0.7283281328074127, 0.8879232987794254, 1.0330445977363454, 1.1613085977206197, 1.2706029888319497, 1.3591251234398734, 1.4254173383006816, 1.4683985106363353, 1.4873912819237642, 1.4821443721547942, 1.4528494062690356, 1.40015168583787, 1.3251543651865905, 1.2294155339826556, 1.1149377694966272, 0.98414980238532, 0.839880040524329, 0.6853218160772644, 0.5239903609041913, 0.3596716731413758, 0.19636361115459888, 0.03820973717041843, -0.11057337190013367, -0.24577442891118817, -0.3632702387503496, 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'8.959289522120979125219220056616241', '9.686879902953372506515996983685954'], 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1069658246182035931, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47948069039689251462319951770', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.19698957695456137349275900442', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99393072620464901544562362410', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'dirichlet_coefficients': [1, -5, 0, -7, 94, 0, 0, 195, 0, -470, -52, 0, 770, 0, 0, -751, -2022, 0, -1732, -658, 0, 260, 576, 0, 5711, -3850, 0, 0, -5518, 0, -6336, -2485, 0, 10110, 0, 0, -7338, 8660, 0, 18330, -3262, 0, 5420, 364, 0, -2880, 864, 0, 0, -28555, 0, -5390, -4182, 0, -4888, 0, 0, 27590, -11220, 0, 45602, 31680, 0, 36457, 72380, 0, 1396, 14154, 0, 0, -18720, 0, -46362, 36690, 0, 12124, 0, 0, 97424, -70594, 0, 16310, -81228, 0, -190068, -27100, 0, -10140, -3182, 0, 0, -4032, 0, -4320, -162808, 0, -4914, 0, 0, -39977], 'euler11': [1, 52, 161051], 'euler13': [1, -770, 371293], 'euler17': [1, 2022, 1419857], 'euler19': [1, 1732, 2476099], 'euler2': [1, 5, 32], 'euler23': [1, -576, 6436343], 'euler29': [1, 5518, 20511149], 'euler3': [1, 0, 0], 'euler31': [1, 6336, 28629151], 'euler37': [1, 7338, 69343957], 'euler41': [1, 3262, 115856201], 'euler43': [1, -5420, 147008443], 'euler47': [1, -864, 229345007], 'euler5': [1, -94, 3125], 'euler53': [1, 4182, 418195493], 'euler59': [1, 11220, 714924299], 'euler61': [1, -45602, 844596301], 'euler67': [1, -1396, 1350125107], 'euler7': [1, 0, 0], 'euler71': [1, 18720, 1804229351], 'euler73': [1, 46362, 2073071593], 'euler79': [1, -97424, 3077056399], 'euler83': [1, 81228, 3939040643], 'euler89': [1, 3182, 5584059449], 'euler97': [1, 4914, 8587340257], 'euler_factors': [[1, 5, 32], [1, 0, 0], [1, -94, 3125], [1, 0, 0], [1, 52, 161051], [1, -770, 371293], [1, 2022, 1419857], [1, 1732, 2476099], [1, -576, 6436343], [1, 5518, 20511149], [1, 6336, 28629151], [1, 7338, 69343957], [1, 3262, 115856201], [1, -5420, 147008443], [1, -864, 229345007], [1, 4182, 418195493], [1, 11220, 714924299], [1, -45602, 844596301], [1, -1396, 1350125107], [1, 18720, 1804229351], [1, 46362, 2073071593], [1, -97424, 3077056399], [1, 81228, 3939040643], [1, 3182, 5584059449], [1, 4914, 8587340257]], 'index': 66, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/441/6/a/c'], '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': '2-21e2-1.1-c5-0-66', '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': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1069658246182035931, 'z1': {'__RealLiteral__': 0, 'data': '1.47948069039689251462319951770', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20544814
{'Lhash': '1875464585207696026792819674616', 'Lhash_array': ['1875464585207696026792819674616'], 'label': '2-21e2-1.1-c5-0-66', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/c'}
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id: 24585922
{'Lhash': '1875464585207696026792819674616', 'Lhash_array': ['1875464585207696026792819674616'], 'label': '2-21e2-1.1-c5-0-66', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/c/1/1'}