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lfunc_lfunctions • Show schema
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{'Lhash': '973010670564584878164206490918,1142018575377907007559502820809', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5012.964553428746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 9]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1', 'coefficient_field': '1.1.1.1', 'conductor': 1440000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, 9], [1], [1, 0, -286, 0, 117649], [1, -112, 5798, -149072, 1771561], [1, 0, 3002, 0, 4826809], [1, 0, 1410, 0, 24137569], [1, -8, 13734, -54872, 47045881], [1, 0, -5838, 0, 148035889], [1, -412, 91214, -10048268, 594823321], [1, -304, 82686, -9056464, 887503681], [1, 0, -21782, 0, 2565726409], [1, 492, 198358, 33909132, 4750104241], [1, 0, 10730, 0, 6321363049], [1, 0, -206046, 0, 10779215329], [1, 0, -281878, 0, 22164361129], [1, -112, 413894, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5012.964553428746, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1440000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -9, 0, 112, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 412, 0, 304, 0, 0, 0, 0, 0, 0, 0, 0, 0, -492, 0, 0, 0, 0, 0, 0, 0, 286, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 816, 0, 81, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1008, 0], 'euler11': [1, -112, 5798, -149072, 1771561], 'euler13': [1, 0, 3002, 0, 4826809], 'euler17': [1, 0, 1410, 0, 24137569], 'euler19': [1, -8, 13734, -54872, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -5838, 0, 148035889], 'euler29': [1, -412, 91214, -10048268, 594823321], 'euler3': [1, 0, 9, 0, 0], 'euler31': [1, -304, 82686, -9056464, 887503681], 'euler37': [1, 0, -21782, 0, 2565726409], 'euler41': [1, 492, 198358, 33909132, 4750104241], 'euler43': [1, 0, 10730, 0, 6321363049], 'euler47': [1, 0, -206046, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -281878, 0, 22164361129], 'euler59': [1, -112, 413894, -23002448, 42180533641], 'euler61': [1, 4, 453966, 907924, 51520374361], 'euler67': [1, 0, -450982, 0, 90458382169], 'euler7': [1, 0, -286, 0, 117649], 'euler71': [1, -1344, 1167406, -481032384, 128100283921], 'euler73': [1, 0, 590866, 0, 151334226289], 'euler79': [1, -816, 1152542, -402319824, 243087455521], 'euler83': [1, 0, -697350, 0, 326940373369], 'euler89': [1, 132, 1414294, 93055908, 496981290961], 'euler97': [1, 0, -967870, 0, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 9, 0, 0], [1, 0, 0, 0, 0], [1, 0, -286, 0, 117649], [1, -112, 5798, -149072, 1771561], [1, 0, 3002, 0, 4826809], [1, 0, 1410, 0, 24137569], [1, -8, 13734, -54872, 47045881], [1, 0, -5838, 0, 148035889], [1, -412, 91214, -10048268, 594823321], [1, -304, 82686, -9056464, 887503681], [1, 0, -21782, 0, 2565726409], [1, 492, 198358, 33909132, 4750104241], [1, 0, 10730, 0, 6321363049], [1, 0, -206046, 0, 10779215329], [1, 0, -281878, 0, 22164361129], [1, -112, 413894, -23002448, 42180533641], [1, 4, 453966, 907924, 51520374361], [1, 0, -450982, 0, 90458382169], [1, -1344, 1167406, -481032384, 128100283921], [1, 0, 590866, 0, 151334226289], [1, -816, 1152542, -402319824, 243087455521], [1, 0, -697350, 0, 326940373369], [1, 132, 1414294, 93055908, 496981290961], [1, 0, -967870, 0, 832972004929]], 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/4/f/t'], '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': '4-1200e2-1.1-c3e2-0-26', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-1200e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.414409783632408, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1734273472496898658, 'z1': {'__RealLiteral__': 0, 'data': '0.76757007837128213292428623143', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '973010670564584878164206490918,1142018575377907007559502820809', 'Lhash_array': ['973010670564584878164206490918', '1142018575377907007559502820809'], 'label': '4-1200e2-1.1-c3e2-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/4/f/t'}