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lfunc_lfunctions • Show schema
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{'Lhash': '1751427840586452100662883810602,2108203640913755921666821405546', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, '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, 0, -8, 0, 25], [1, 4, 18, 28, 49], [1, 0, -20, 0, 121], [1, 0, -26, 0, 169], [1, 0, -32, 0, 289], [1, 2, 19], [1, 0, -44, 0, 529], [1, 12, 94, 348, 841], [1, 0, -62, 0, 961], [1, 0, -2, 0, 1369], [1, 12, 118, 492, 1681], [1, -8, 102, -344, 1849], [1, 0, -44, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 118, 0, 3481], [1, 8, 138, 488, 3721], [1, 0, -62, 0, 4489], [1, 24, 286, 1704, 5041], [1, 20, 246, 1460, 5329], [1, 0, -86, 0, 6241], [1, 0, 76, 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'1.66307943256145841616912654842678', '2.62789003179984182275392760249749', '2.86170632736332335582529912841720', '3.51518442895303260884905164114003', '3.52475650272781103264045855467388', '4.40718883959655407034679644922007', '4.56984495967064686692884362074418', '5.16211025902678104156867854742442', '5.65065048162430314843615952901988', '6.14533025279164946267054485542705', '6.15742851137146798289555343564251', '6.90721777719929407468632365187183', '6.94671831811922356897585384103992', '7.55710854004184165992271798826890', '7.67127216582801290875691661685931', '8.503921129058680073655437423422388', '8.601433684672441509933749686452548'], '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': 1784169017124647509, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38163295175431056396445053206', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.66307943256145841616912654843', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.62789003179984182275392760250', '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, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -20, 0, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 0, -32, 0, 289], 'euler19': [1, 2, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -44, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -62, 0, 961], 'euler37': [1, 0, -2, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, -44, 0, 2209], 'euler5': [1, 0, -8, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 8, 138, 488, 3721], 'euler67': [1, 0, -62, 0, 4489], 'euler7': [1, 4, 18, 28, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, 0, -86, 0, 6241], 'euler83': [1, 0, 76, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, -122, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -8, 0, 25], [1, 4, 18, 28, 49], [1, 0, -20, 0, 121], [1, 0, -26, 0, 169], [1, 0, -32, 0, 289], [1, 2, 19, 0, 0], [1, 0, -44, 0, 529], [1, 12, 94, 348, 841], [1, 0, -62, 0, 961], [1, 0, -2, 0, 1369], [1, 12, 118, 492, 1681], [1, -8, 102, -344, 1849], [1, 0, -44, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, 118, 0, 3481], [1, 8, 138, 488, 3721], [1, 0, -62, 0, 4489], [1, 24, 286, 1704, 5041], [1, 20, 246, 1460, 5329], [1, 0, -86, 0, 6241], [1, 0, 76, 0, 6889], [1, 12, 214, 1068, 7921], [1, 0, -122, 0, 9409]], 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/f/a'], '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-c1e2-0-42', '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': 2, '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': 1784169017124647509, 'z1': {'__RealLiteral__': 0, 'data': '1.38163295175431056396445053206', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1751427840586452100662883810602,2108203640913755921666821405546', 'Lhash_array': ['1751427840586452100662883810602', '2108203640913755921666821405546'], 'label': '4-2736e2-1.1-c1e2-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/f/a'}