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lfunc_lfunctions • Show schema
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{'Lhash': '722062891695020338783458547979,2015176391122883238452770938117', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -2, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 14, -20, 25], [1, 0, -6, 0, 49], [1, 0, -20, 0, 121], [1, 0, -18, 0, 169], [1, -4, 38, -68, 289], [1, -2, 19], [1, 0, -44, 0, 529], [1, 0, -8, 0, 841], [1, 12, 98, 372, 961], [1, 0, 54, 0, 1369], [1, 0, -64, 0, 1681], [1, 0, -86, 0, 1849], [1, 0, -44, 0, 2209], [1, 0, -8, 0, 2809], [1, 16, 182, 944, 3481], [1, 16, 186, 976, 3721], [1, -4, 138, -268, 4489], [1, 16, 206, 1136, 5041], [1, 0, 146, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, -4, 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'4.77119336982004184635187421273957', '5.36368366270603245986997134831266', '5.57221263482427776957652132678600', '5.91695232788834883211118404340288', '6.21323297088349995759190368928125', '6.56653721126262848569220390313940', '7.28228606117241987537414687675654', '7.59024009090100770350262745389483', '7.61204689926753097539005080221250', '8.314135296785240751337418251325327', '8.803836303869388025887237990286647', '9.254953751879335105640281244227979'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 921387328017602053, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56960718636903515176045558222', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58969387208120941012034376764', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.69550106553071754436707702664', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -16, 0, 0, 0, 0, 0, 4, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0], 'euler11': [1, 0, -20, 0, 121], 'euler13': [1, 0, -18, 0, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, -2, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -44, 0, 529], 'euler29': [1, 0, -8, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 12, 98, 372, 961], 'euler37': [1, 0, 54, 0, 1369], 'euler41': [1, 0, -64, 0, 1681], 'euler43': [1, 0, -86, 0, 1849], 'euler47': [1, 0, -44, 0, 2209], 'euler5': [1, -4, 14, -20, 25], 'euler53': [1, 0, -8, 0, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, -4, 138, -268, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, 0, 146, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, -4, 0, 6889], 'euler89': [1, 0, -80, 0, 7921], 'euler97': [1, 0, -186, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 14, -20, 25], [1, 0, -6, 0, 49], [1, 0, -20, 0, 121], [1, 0, -18, 0, 169], [1, -4, 38, -68, 289], [1, -2, 19, 0, 0], [1, 0, -44, 0, 529], [1, 0, -8, 0, 841], [1, 12, 98, 372, 961], [1, 0, 54, 0, 1369], [1, 0, -64, 0, 1681], [1, 0, -86, 0, 1849], [1, 0, -44, 0, 2209], [1, 0, -8, 0, 2809], [1, 16, 182, 944, 3481], [1, 16, 186, 976, 3721], [1, -4, 138, -268, 4489], [1, 16, 206, 1136, 5041], [1, 0, 146, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, -4, 0, 6889], [1, 0, -80, 0, 7921], [1, 0, -186, 0, 9409]], 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/k/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': '4-2736e2-1.1-c1e2-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 921387328017602053, 'z1': {'__RealLiteral__': 0, 'data': '0.56960718636903515176045558222', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '722062891695020338783458547979,2015176391122883238452770938117', 'Lhash_array': ['722062891695020338783458547979', '2015176391122883238452770938117'], 'label': '4-2736e2-1.1-c1e2-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/k/i'}