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lfunc_lfunctions • Show schema
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{'Lhash': '742662858978606706184003832515', 'a10': 0, 'a2': 0, 'a3': 6, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -118, 'a8': 0, 'a9': -207, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.15352792519226, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': '1.1.1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, -6, 243], [1], [1, 118, 16807], [1, 192, 161051], [1, 1106, 371293], [1, 762, 1419857], [1, -2740, 2476099], [1, -1566, 6436343], [1, -5910, 20511149], [1, -6868, 28629151], [1, -5518, 69343957], [1, 378, 115856201], [1, 2434, 147008443], [1, -13122, 229345007], [1, -9174, 418195493], [1, -34980, 714924299], [1, 9838, 844596301], [1, -33722, 1350125107], [1, 70212, 1804229351], [1, 21986, 2073071593], [1, 4520, 3077056399], [1, 109074, 3939040643], [1, -38490, 5584059449], [1, -1918, 8587340257], [1, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-20e2-1.1-c5-0-6', 'leading_term': '1.413078436077240229272922683510000000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/400/6/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.4130784360772402, 1.395120713348812, 1.341515229855721, 1.2530619790194468, 1.1310840740900947, 0.9774124122101087, 0.7943641667610255, 0.5847150870808462, 0.35166560135610403, 0.09880075088931908, -0.1699559659317177, -0.45039469252338415, -0.7380770199307397, -1.0283991563548898, -1.3166599925237998, -1.5981334555647375, -1.8681443930885897, -2.122147071037781, -2.35580520851022, -2.565072315937754, -2.746270955866427, -2.896169414696473, -3.0120541657818345, 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'6.81570278441390885381646879589009', '7.64257352862693891441158175456824', '8.691623183560660187081764180432564', '9.638198094674950953685455977865735', '10.17008314991347024851093134711533'], 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'trace_hash': 624255358810157247, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58585769520788832115448019778', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57799054975783201955172787051', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04517599026005676930035067922', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.15352792519226, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 6, 0, 0, 0, -118, 0, -207, 0, -192, 0, -1106, 0, 0, 0, -762, 0, 2740, 0, -708, 0, 1566, 0, 0, 0, -2700, 0, 5910, 0, 6868, 0, -1152, 0, 0, 0, 5518, 0, -6636, 0, -378, 0, -2434, 0, 0, 0, 13122, 0, -2883, 0, -4572, 0, 9174, 0, 0, 0, 16440, 0, 34980, 0, -9838, 0, 24426, 0, 0, 0, 33722, 0, 9396, 0, -70212, 0, -21986, 0, 0, 0, 22656, 0, -4520, 0, 34101, 0, -109074, 0, 0, 0, 35460, 0, 38490, 0, 130508, 0, 41208, 0, 0, 0, 1918, 0, 39744, 0], 'euler11': [1, 192, 161051], 'euler13': [1, 1106, 371293], 'euler17': [1, 762, 1419857], 'euler19': [1, -2740, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -1566, 6436343], 'euler29': [1, -5910, 20511149], 'euler3': [1, -6, 243], 'euler31': [1, -6868, 28629151], 'euler37': [1, -5518, 69343957], 'euler41': [1, 378, 115856201], 'euler43': [1, 2434, 147008443], 'euler47': [1, -13122, 229345007], 'euler5': [1, 0, 0], 'euler53': [1, -9174, 418195493], 'euler59': [1, -34980, 714924299], 'euler61': [1, 9838, 844596301], 'euler67': [1, -33722, 1350125107], 'euler7': [1, 118, 16807], 'euler71': [1, 70212, 1804229351], 'euler73': [1, 21986, 2073071593], 'euler79': [1, 4520, 3077056399], 'euler83': [1, 109074, 3939040643], 'euler89': [1, -38490, 5584059449], 'euler97': [1, -1918, 8587340257], 'euler_factors': [[1, 0, 0], [1, -6, 243], [1, 0, 0], [1, 118, 16807], [1, 192, 161051], [1, 1106, 371293], [1, 762, 1419857], [1, -2740, 2476099], [1, -1566, 6436343], [1, -5910, 20511149], [1, -6868, 28629151], [1, -5518, 69343957], [1, 378, 115856201], [1, 2434, 147008443], [1, -13122, 229345007], [1, -9174, 418195493], [1, -34980, 714924299], [1, 9838, 844596301], [1, -33722, 1350125107], [1, 70212, 1804229351], [1, 21986, 2073071593], [1, 4520, 3077056399], [1, 109074, 3939040643], [1, -38490, 5584059449], [1, -1918, 8587340257]], 'index': 6, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/6/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/400/6/a/i'], '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': '2-20e2-1.1-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 624255358810157247, 'z1': {'__RealLiteral__': 0, 'data': '0.58585769520788832115448019778', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20381231
{'Lhash': '742662858978606706184003832515', 'Lhash_array': ['742662858978606706184003832515'], 'label': '2-20e2-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/6/a/i'}
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id: 24582251
{'Lhash': '742662858978606706184003832515', 'Lhash_array': ['742662858978606706184003832515'], 'label': '2-20e2-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/6/a/i/1/1'}