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lfunc_lfunctions • Show schema
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{'Lhash': '682255617568133618970445471296,1790755619790021714855741144594', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 12, 'a8': 0, 'a9': 50, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5703.639669678928, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 0, 25]]], 'bad_primes': [2, 5], 'central_character': '1280.1', 'coefficient_field': '1.1.1.1', 'conductor': 1638400, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 0, -50, 0, 729], [1, 0, 25], [1, -12, 722, -4116, 117649], [1, 0, 938, 0, 1771561], [1, 0, -1894, 0, 4826809], [1, 60, 10726, 294780, 24137569], [1, 0, -12118, 0, 47045881], [1, -356, 56018, -4331452, 148035889], [1, 0, -21222, 0, 594823321], [1, 40, 59982, 1191640, 887503681], [1, 0, -101206, 0, 2565726409], [1, -500, 200342, -34460500, 4750104241], [1, 0, -138850, 0, 6321363049], [1, 428, 253442, 44436244, 10779215329], [1, 0, -57654, 0, 22164361129], [1, 0, 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'8.874187213699615644288686830089814', '9.131089968054584979756754053158788', '9.488545604752342363081879971220030'], 'prelabel': '4-1280e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.69036505604615, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 186944408549399730, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53820478406691833161297783093', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29823691443167736644770991193', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.41265709925717057253174356607', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5703.639669678928, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1638400, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 12, 0, 50, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 356, 0, -25, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 500, 0, 0, 0, 0, 0, -428, 0, -578, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 0, 0, 200, 0, 460, 0, 0, 0, 0, 0, 2640, 0, 1771, 0, 0, 0, 0, 0, 0, 0, -1748, 0, 0, 0, 0, 0, 0, 0, -620, 0, 0, 0], 'euler11': [1, 0, 938, 0, 1771561], 'euler13': [1, 0, -1894, 0, 4826809], 'euler17': [1, 60, 10726, 294780, 24137569], 'euler19': [1, 0, -12118, 0, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -356, 56018, -4331452, 148035889], 'euler29': [1, 0, -21222, 0, 594823321], 'euler3': [1, 0, -50, 0, 729], 'euler31': [1, 40, 59982, 1191640, 887503681], 'euler37': [1, 0, -101206, 0, 2565726409], 'euler41': [1, -500, 200342, -34460500, 4750104241], 'euler43': [1, 0, -138850, 0, 6321363049], 'euler47': [1, 428, 253442, 44436244, 10779215329], 'euler5': [1, 0, 25, 0, 0], 'euler53': [1, 0, -57654, 0, 22164361129], 'euler59': [1, 0, 229242, 0, 42180533641], 'euler61': [1, 0, -391462, 0, 51520374361], 'euler67': [1, 0, -2450, 0, 90458382169], 'euler7': [1, -12, 722, -4116, 117649], 'euler71': [1, -200, 725822, -71582200, 128100283921], 'euler73': [1, -460, 830934, -178947820, 151334226289], 'euler79': [1, -2640, 2728478, -1301622960, 243087455521], 'euler83': [1, 0, -179250, 0, 326940373369], 'euler89': [1, 1748, 2173814, 1232285812, 496981290961], 'euler97': [1, 620, 1921446, 565857260, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -50, 0, 729], [1, 0, 25, 0, 0], [1, -12, 722, -4116, 117649], [1, 0, 938, 0, 1771561], [1, 0, -1894, 0, 4826809], [1, 60, 10726, 294780, 24137569], [1, 0, -12118, 0, 47045881], [1, -356, 56018, -4331452, 148035889], [1, 0, -21222, 0, 594823321], [1, 40, 59982, 1191640, 887503681], [1, 0, -101206, 0, 2565726409], [1, -500, 200342, -34460500, 4750104241], [1, 0, -138850, 0, 6321363049], [1, 428, 253442, 44436244, 10779215329], [1, 0, -57654, 0, 22164361129], [1, 0, 229242, 0, 42180533641], [1, 0, -391462, 0, 51520374361], [1, 0, -2450, 0, 90458382169], [1, -200, 725822, -71582200, 128100283921], [1, -460, 830934, -178947820, 151334226289], [1, -2640, 2728478, -1301622960, 243087455521], [1, 0, -179250, 0, 326940373369], [1, 1748, 2173814, 1232285812, 496981290961], [1, 620, 1921446, 565857260, 832972004929]], 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1280/4/d/k'], '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': '4-1280e2-1.1-c3e2-0-15', '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': '4-1280e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.69036505604615, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 186944408549399730, 'z1': {'__RealLiteral__': 0, 'data': '0.53820478406691833161297783093', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '682255617568133618970445471296,1790755619790021714855741144594', 'Lhash_array': ['682255617568133618970445471296', '1790755619790021714855741144594'], 'factors': ['2-1280-8.5-c3-0-31', '2-1280-8.5-c3-0-80'], 'label': '4-1280e2-1.1-c3e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1280/4/d/k'}