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lfunc_lfunctions • Show schema
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{'Lhash': '1157987372081374185753088290150', 'a10': 0, 'a2': 0, 'a3': -9, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 244, 'a8': 0, 'a9': 81, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.1151459438942, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 9]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '300.1', 'coefficient_field': '1.1.1.1', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, 9], [1], [1, -244, 16807], [1, 144, 161051], [1, 50, 371293], [1, -1914, 1419857], [1, -140, 2476099], [1, -624, 6436343], [1, 3126, 20511149], [1, 5176, 28629151], [1, 15698, 69343957], [1, -12570, 115856201], [1, 11516, 147008443], [1, -26736, 229345007], [1, -19158, 418195493], [1, -27984, 714924299], [1, -22022, 844596301], [1, -12676, 1350125107], [1, 59520, 1804229351], [1, -67102, 2073071593], [1, -11048, 3077056399], [1, -115284, 3939040643], [1, -73650, 5584059449], [1, 35522, 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'5.13141525974496658561464644956703', '5.54500228013529253037622932987136', '7.22876705413046419750484474000761', '7.88116188327387936077369607470786', '8.914535246675628518701448090550453', '10.24983631817767854359640325186155', '10.93648210683167849255548714160031'], 'prelabel': '2-300-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.9365081953310055, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'trace_hash': 469973326837115349, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.913490966574613453564506930109', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.01725202827975941600263018333', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.81078780079936262133727673200', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.1151459438942, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, -9, 0, 0, 0, 244, 0, 81, 0, -144, 0, -50, 0, 0, 0, 1914, 0, 140, 0, -2196, 0, 624, 0, 0, 0, -729, 0, -3126, 0, -5176, 0, 1296, 0, 0, 0, -15698, 0, 450, 0, 12570, 0, -11516, 0, 0, 0, 26736, 0, 42729, 0, -17226, 0, 19158, 0, 0, 0, -1260, 0, 27984, 0, 22022, 0, 19764, 0, 0, 0, 12676, 0, -5616, 0, -59520, 0, 67102, 0, 0, 0, -35136, 0, 11048, 0, 6561, 0, 115284, 0, 0, 0, 28134, 0, 73650, 0, -12200, 0, 46584, 0, 0, 0, -35522, 0, -11664, 0], 'euler11': [1, 144, 161051], 'euler13': [1, 50, 371293], 'euler17': [1, -1914, 1419857], 'euler19': [1, -140, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -624, 6436343], 'euler29': [1, 3126, 20511149], 'euler3': [1, 9, 0], 'euler31': [1, 5176, 28629151], 'euler37': [1, 15698, 69343957], 'euler41': [1, -12570, 115856201], 'euler43': [1, 11516, 147008443], 'euler47': [1, -26736, 229345007], 'euler5': [1, 0, 0], 'euler53': [1, -19158, 418195493], 'euler59': [1, -27984, 714924299], 'euler61': [1, -22022, 844596301], 'euler67': [1, -12676, 1350125107], 'euler7': [1, -244, 16807], 'euler71': [1, 59520, 1804229351], 'euler73': [1, -67102, 2073071593], 'euler79': [1, -11048, 3077056399], 'euler83': [1, -115284, 3939040643], 'euler89': [1, -73650, 5584059449], 'euler97': [1, 35522, 8587340257], 'euler_factors': [[1, 0, 0], [1, 9, 0], [1, 0, 0], [1, -244, 16807], [1, 144, 161051], [1, 50, 371293], [1, -1914, 1419857], [1, -140, 2476099], [1, -624, 6436343], [1, 3126, 20511149], [1, 5176, 28629151], [1, 15698, 69343957], [1, -12570, 115856201], [1, 11516, 147008443], [1, -26736, 229345007], [1, -19158, 418195493], [1, -27984, 714924299], [1, -22022, 844596301], [1, -12676, 1350125107], [1, 59520, 1804229351], [1, -67102, 2073071593], [1, -11048, 3077056399], [1, -115284, 3939040643], [1, -73650, 5584059449], [1, 35522, 8587340257]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/6/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/300/6/a/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': '2-300-1.1-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': 0, 'prelabel': '2-300-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.9365081953310055, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 469973326837115349, 'z1': {'__RealLiteral__': 0, 'data': '0.913490966574613453564506930109', 'prec': 107}}
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lfunc_instances • Show schema
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id: 19980854
{'Lhash': '1157987372081374185753088290150', 'Lhash_array': ['1157987372081374185753088290150'], 'label': '2-300-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/6/a/c'}
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id: 24573062
{'Lhash': '1157987372081374185753088290150', 'Lhash_array': ['1157987372081374185753088290150'], 'label': '2-300-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/6/a/c/1/1'}