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lfunc_lfunctions • Show schema
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{'Lhash': '753822229017626006001685310517,972608180496805685423711192260', 'a10': -40, 'a2': 4, 'a3': -6, 'a4': 12, 'a5': -10, 'a6': -24, 'a7': 0, 'a8': 32, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7522.5799329890115, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4, 4]], [3, [1, 6, 9]], [5, [1, 10, 25]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1470.1', 'coefficient_field': '1.1.1.1', 'conductor': 2160900, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1, -4, 4], [1, 6, 9], [1, 10, 25], [1], [1, -2, -778, -2662, 1771561], [1, 28, 4590, 61516, 4826809], [1, 14, 6434, 68782, 24137569], [1, 42, 10718, 288078, 47045881], [1, -50, 21518, -608350, 148035889], [1, -78, 46858, -1902342, 594823321], [1, 128, 49914, 3813248, 887503681], [1, -238, 84498, -12055414, 2565726409], [1, 292, 104102, 20124932, 4750104241], [1, -278, 92310, -22102946, 6321363049], [1, -62, 205166, -6437026, 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'spectral_label': 'c3e2-0', 'trace_hash': 630463960840855285, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59466088595856532384070395081', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.76725256969207137254230951159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.95256515460251027586205050747', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 7522.5799329890115, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 2160900, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, 4, -6, 12, -10, -24, 0, 32, 27, -40, 2, -72, -28, 0, 60, 80, -14, 108, -42, -120, 0, 8, 50, -192, 75, -112, -108, 0, 78, 240, -128, 192, -12, -56, 0, 324, 238, -168, 168, -320, -292, 0, 278, 24, -270, 200, 62, -480, 0, 300, 84, -336, 226, -432, -20, 0, 252, 312, -76, 720, 242, -512, 0, 448, 280, -48, 82, -168, -300, 0, 744, 864, -320, 952, -450, -504, 0, 672, 1400, -800, 405, -1168, -268, 0, 140, 1112, -468, 64, 1660, -1080, 0, 600, 768, 248, 420, -1152, 264, 0, 54, 900], 'euler11': [1, -2, -778, -2662, 1771561], 'euler13': [1, 28, 4590, 61516, 4826809], 'euler17': [1, 14, 6434, 68782, 24137569], 'euler19': [1, 42, 10718, 288078, 47045881], 'euler2': [1, -4, 4, 0, 0], 'euler23': [1, -50, 21518, -608350, 148035889], 'euler29': [1, -78, 46858, -1902342, 594823321], 'euler3': [1, 6, 9, 0, 0], 'euler31': [1, 128, 49914, 3813248, 887503681], 'euler37': [1, -238, 84498, -12055414, 2565726409], 'euler41': [1, 292, 104102, 20124932, 4750104241], 'euler43': [1, -278, 92310, -22102946, 6321363049], 'euler47': [1, -62, 205166, -6437026, 10779215329], 'euler5': [1, 10, 25, 0, 0], 'euler53': [1, -226, 307082, -33646202, 22164361129], 'euler59': [1, 76, 288326, 15608804, 42180533641], 'euler61': [1, -242, 189882, -54929402, 51520374361], 'euler67': [1, -82, 434598, -24662566, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -744, 799150, -266285784, 128100283921], 'euler73': [1, 320, 459534, 124485440, 151334226289], 'euler79': [1, -1400, 1421022, -690254600, 243087455521], 'euler83': [1, 268, 46646, 153238916, 326940373369], 'euler89': [1, -1660, 2043782, -1170248540, 496981290961], 'euler97': [1, -264, 1498670, -240945672, 832972004929], 'euler_factors': [[1, -4, 4, 0, 0], [1, 6, 9, 0, 0], [1, 10, 25, 0, 0], [1, 0, 0, 0, 0], [1, -2, -778, -2662, 1771561], [1, 28, 4590, 61516, 4826809], [1, 14, 6434, 68782, 24137569], [1, 42, 10718, 288078, 47045881], [1, -50, 21518, -608350, 148035889], [1, -78, 46858, -1902342, 594823321], [1, 128, 49914, 3813248, 887503681], [1, -238, 84498, -12055414, 2565726409], [1, 292, 104102, 20124932, 4750104241], [1, -278, 92310, -22102946, 6321363049], [1, -62, 205166, -6437026, 10779215329], [1, -226, 307082, -33646202, 22164361129], [1, 76, 288326, 15608804, 42180533641], [1, -242, 189882, -54929402, 51520374361], [1, -82, 434598, -24662566, 90458382169], [1, -744, 799150, -266285784, 128100283921], [1, 320, 459534, 124485440, 151334226289], [1, -1400, 1421022, -690254600, 243087455521], [1, 268, 46646, 153238916, 326940373369], [1, -1660, 2043782, -1170248540, 496981290961], [1, -264, 1498670, -240945672, 832972004929]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1470/4/a/bl'], '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': '4-1470e2-1.1-c3e2-0-4', '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': '4-1470e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.313045028799053, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 630463960840855285, 'z1': {'__RealLiteral__': 0, 'data': '0.59466088595856532384070395081', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '753822229017626006001685310517,972608180496805685423711192260', 'Lhash_array': ['753822229017626006001685310517', '972608180496805685423711192260'], 'label': '4-1470e2-1.1-c3e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1470/4/a/bl'}