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lfunc_lfunctions • Show schema
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{'Lhash': '2430939396596141324485852033635', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.7967896726836443, -1.5378966862259282], 'a4': [0, 0], 'a5': [0.23025243500938175, 0.3988089160027001], 'a6': [0, 0], 'a7': [-0.06653723767426262, -2.6449145158213865], 'a8': [0, 0], 'a9': [-1.7302524350093818, -2.4507603944784373], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.048920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.7967896726836443, 1.5378966862259282]]], [7, [[1.0, 0], [0.06653723767426262, 2.6449145158213865]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.625', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '786377020865428058172625748705', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7967896726836443, 1.5378966862259282]], [[1.0, 0], [-0.23025243500938175, -0.3988089160027001], [-2.5, 4.330127018922194]], 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'group': 'GL2', 'index': 42, 'label': '2-1008-63.58-c1-0-42', 'leading_term': '1.485222920414640880787875206148333921243017002002176614', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1008/2/q/h/625/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.485222920414641, 1.622366720967458, 1.75894421369288, 1.8949998766934755, 2.0302676170674774, 2.1641354252728493, 2.295629347708257, 2.4234163436966702, 2.5458244692170844, 2.6608781971759727, 2.766346490572513, 2.8598013551101604, 2.9386848545599498, 3.000382842580534, 3.04230386159916, 3.0619617427134598, 3.0570604073945415, 3.025579242726588, 2.9658572295162897, 2.87667378282002, 2.757324051722385, 2.6076862500370868, 2.42827847758372, 2.2203024633844533, 1.985671733178552, 1.727021884950115, 1.4477009538428833, 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'8.228728891077519426617115939649309', '8.607414066343825346063273821199558', '9.329856283384574363270827683249793', '10.18723838706135580222466634846194'], 'prelabel': '2-1008-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': 0.7205859246226011, 'root_number': '-0.6388412208946899479709515414832077178845257729541978054 + 0.76933860847209661107353153409441052681756908086907504827*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.36029296231130054', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91767305293625226963001913516', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11528963097026558462445110712', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88964880745718821979782110897', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.048920523745066, 'bad_primes': [2, 3, 7], 'central_character': '63.58', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/2/q/h/625/2'], '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': '2-1008-63.58-c1-0-42', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1008-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': 0.36029296231130054, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91767305293625226963001913516', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2430939396596141324485852033635', 'Lhash_array': ['2430939396596141324485852033635'], 'label': '2-1008-63.58-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/2/q/h/625/2'}