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lfunc_lfunctions • Show schema
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{'Lhash': '327733788659942871837241359795,1863319373546074705023947306462', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -10, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 556.9960614920828, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': '1.1.1.1', 'conductor': 160000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 0, 10, 0, 729], [1], [1, 0, -670, 0, 117649], [1, 24, 2806, 31944, 1771561], [1, 0, -1030, 0, 4826809], [1, 0, -5470, 0, 24137569], [1, 200, 23718, 1371800, 47045881], [1, 0, -6910, 0, 148035889], [1, -180, 56878, -4390020, 594823321], [1, 304, 82686, 9056464, 887503681], [1, 0, -100150, 0, 2565726409], [1, 876, 329686, 60374796, 4750104241], [1, 0, -157990, 0, 6321363049], [1, 0, -166030, 0, 10779215329], [1, 0, -248470, 0, 22164361129], [1, -840, 587158, -172518360, 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'11.32126578633781093636372224421448'], 'prelabel': '4-20e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.858061753651991, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1883020126629812339, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25853637319379430745198509969', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.46989980773140512980886815240', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.32184008131005847734259956559', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 556.9960614920828, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 160000, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -10, 0, -24, 0, 0, 0, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, -304, 0, 0, 0, 0, 0, 0, 0, 0, 0, -876, 0, 0, 0, 0, 0, 0, 0, 670, 0, 0, 0, 0, 0, 0, 0, 0, 0, 840, 0, 1804, 0, 0, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, -320, 0, -629, 0, 0, 0, 0, 0, 0, 0, -1620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0], 'euler11': [1, 24, 2806, 31944, 1771561], 'euler13': [1, 0, -1030, 0, 4826809], 'euler17': [1, 0, -5470, 0, 24137569], 'euler19': [1, 200, 23718, 1371800, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -6910, 0, 148035889], 'euler29': [1, -180, 56878, -4390020, 594823321], 'euler3': [1, 0, 10, 0, 729], 'euler31': [1, 304, 82686, 9056464, 887503681], 'euler37': [1, 0, -100150, 0, 2565726409], 'euler41': [1, 876, 329686, 60374796, 4750104241], 'euler43': [1, 0, -157990, 0, 6321363049], 'euler47': [1, 0, -166030, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -248470, 0, 22164361129], 'euler59': [1, -840, 587158, -172518360, 42180533641], 'euler61': [1, -1804, 1267566, -409473724, 51520374361], 'euler67': [1, 0, 447050, 0, 90458382169], 'euler7': [1, 0, -670, 0, 117649], 'euler71': [1, 864, 902446, 309235104, 128100283921], 'euler73': [1, 0, -646990, 0, 151334226289], 'euler79': [1, 320, 1011678, 157772480, 243087455521], 'euler83': [1, 0, -1138390, 0, 326940373369], 'euler89': [1, 1620, 2066038, 1142049780, 496981290961], 'euler97': [1, 0, -602110, 0, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 10, 0, 729], [1, 0, 0, 0, 0], [1, 0, -670, 0, 117649], [1, 24, 2806, 31944, 1771561], [1, 0, -1030, 0, 4826809], [1, 0, -5470, 0, 24137569], [1, 200, 23718, 1371800, 47045881], [1, 0, -6910, 0, 148035889], [1, -180, 56878, -4390020, 594823321], [1, 304, 82686, 9056464, 887503681], [1, 0, -100150, 0, 2565726409], [1, 876, 329686, 60374796, 4750104241], [1, 0, -157990, 0, 6321363049], [1, 0, -166030, 0, 10779215329], [1, 0, -248470, 0, 22164361129], [1, -840, 587158, -172518360, 42180533641], [1, -1804, 1267566, -409473724, 51520374361], [1, 0, 447050, 0, 90458382169], [1, 864, 902446, 309235104, 128100283921], [1, 0, -646990, 0, 151334226289], [1, 320, 1011678, 157772480, 243087455521], [1, 0, -1138390, 0, 326940373369], [1, 1620, 2066038, 1142049780, 496981290961], [1, 0, -602110, 0, 832972004929]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/4/c/c'], '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': '4-20e4-1.1-c3e2-0-3', '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': '4-20e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.858061753651991, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1883020126629812339, 'z1': {'__RealLiteral__': 0, 'data': '0.25853637319379430745198509969', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '327733788659942871837241359795,1863319373546074705023947306462', 'Lhash_array': ['327733788659942871837241359795', '1863319373546074705023947306462'], 'factors': ['2-20e2-5.4-c3-0-2', '2-20e2-5.4-c3-0-19'], 'label': '4-20e4-1.1-c3e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/4/c/c'}