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lfunc_lfunctions • Show schema
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{'Lhash': '2674953938165814228516960546108', 'a10': -175, 'a2': -7, 'a3': 0, 'a4': 17, 'a5': 25, 'a6': 0, 'a7': 12, 'a8': 105, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.21727189158413, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -25]]], 'bad_primes': [3, 5], 'central_character': '45.1', 'coefficient_field': '1.1.1.1', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, 7, 32], [1], [1, -25], [1, -12, 16807], [1, 112, 161051], [1, 974, 371293], [1, 2182, 1419857], [1, -1420, 2476099], [1, 3216, 6436343], [1, -4150, 20511149], [1, 5688, 28629151], [1, -6482, 69343957], [1, 5402, 115856201], [1, 21764, 147008443], [1, -368, 229345007], [1, 12586, 418195493], [1, -25520, 714924299], [1, -11782, 844596301], [1, 13188, 1350125107], [1, -35968, 1804229351], [1, -73186, 2073071593], [1, 52440, 3077056399], [1, 69036, 3939040643], [1, -33870, 5584059449], [1, -143042, 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'13.10120249854867078543965018590274', '14.27137294936535674695377748047161'], 'prelabel': '2-45-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6864980721348246, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 1970242761187588572, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11016658508599465163700624335', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.84118619701970776334685250643', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.87701619293363042135713139570', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.21727189158413, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, -7, 0, 17, 25, 0, 12, 105, 0, -175, -112, 0, -974, -84, 0, -1279, -2182, 0, 1420, 425, 0, 784, -3216, 0, 625, 6818, 0, 204, 4150, 0, -5688, 5593, 0, 15274, 300, 0, 6482, -9940, 0, 2625, -5402, 0, -21764, -1904, 0, 22512, 368, 0, -16663, -4375, 0, -16558, -12586, 0, -2800, 1260, 0, -29050, 25520, 0, 11782, 39816, 0, 1777, -24350, 0, -13188, -37094, 0, -2100, 35968, 0, 73186, -45374, 0, 24140, -1344, 0, -52440, -31975, 0, 37814, -69036, 0, -54550, 152348, 0, -11760, 33870, 0, -11688, -54672, 0, -2576, 35500, 0, 143042, 116641, 0, 10625], 'euler11': [1, 112, 161051], 'euler13': [1, 974, 371293], 'euler17': [1, 2182, 1419857], 'euler19': [1, -1420, 2476099], 'euler2': [1, 7, 32], 'euler23': [1, 3216, 6436343], 'euler29': [1, -4150, 20511149], 'euler3': [1, 0, 0], 'euler31': [1, 5688, 28629151], 'euler37': [1, -6482, 69343957], 'euler41': [1, 5402, 115856201], 'euler43': [1, 21764, 147008443], 'euler47': [1, -368, 229345007], 'euler5': [1, -25, 0], 'euler53': [1, 12586, 418195493], 'euler59': [1, -25520, 714924299], 'euler61': [1, -11782, 844596301], 'euler67': [1, 13188, 1350125107], 'euler7': [1, -12, 16807], 'euler71': [1, -35968, 1804229351], 'euler73': [1, -73186, 2073071593], 'euler79': [1, 52440, 3077056399], 'euler83': [1, 69036, 3939040643], 'euler89': [1, -33870, 5584059449], 'euler97': [1, -143042, 8587340257], 'euler_factors': [[1, 7, 32], [1, 0, 0], [1, -25, 0], [1, -12, 16807], [1, 112, 161051], [1, 974, 371293], [1, 2182, 1419857], [1, -1420, 2476099], [1, 3216, 6436343], [1, -4150, 20511149], [1, 5688, 28629151], [1, -6482, 69343957], [1, 5402, 115856201], [1, 21764, 147008443], [1, -368, 229345007], [1, 12586, 418195493], [1, -25520, 714924299], [1, -11782, 844596301], [1, 13188, 1350125107], [1, -35968, 1804229351], [1, -73186, 2073071593], [1, 52440, 3077056399], [1, 69036, 3939040643], [1, -33870, 5584059449], [1, -143042, 8587340257]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/6/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/45/6/a/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': '2-45-1.1-c5-0-4', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-45-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6864980721348246, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1970242761187588572, 'z1': {'__RealLiteral__': 0, 'data': '2.11016658508599465163700624335', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10596402
{'Lhash': '2674953938165814228516960546108', 'Lhash_array': ['2674953938165814228516960546108'], 'label': '2-45-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/6/a/a'}
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id: 24550985
{'Lhash': '2674953938165814228516960546108', 'Lhash_array': ['2674953938165814228516960546108'], 'label': '2-45-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/6/a/a/1/1'}