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lfunc_lfunctions • Show schema
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{'Lhash': '1412046720148882563489889664591,1682645279209762051989985287345', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3879.2111500809283, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1]], [13, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': '1.1.1.1', 'conductor': 60840000, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1], [1, -2, 13, -14, 49], [1, 2, 21, 22, 121], [1, 2, 1], [1, -2, 27, -34, 289], [1, 4, 42, 76, 361], [1, -4, 42, -92, 529], [1, 6, 35, 174, 841], [1, -6, 69, -186, 961], [1, 4, 46, 148, 1369], [1, 0, 50, 0, 1681], [1, 4, 18, 172, 1849], [1, -10, 69, -470, 2209], [1, 6, 107, 318, 2809], [1, 10, 141, 590, 3481], [1, -2, 115, -122, 3721], [1, -10, 141, -670, 4489], [1, 4, 114, 284, 5041], [1, 4, 22, 292, 5329], [1, 12, 186, 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'1.32737307812327504819314845613136', '2.00770662598978189488872407011218', '2.31899830698031171876791112008915', '2.99848048223864324548280557078619', '3.19958270232897897499669005635425', '4.00923235246730581677128086819097', '4.09941838692569730906743495862576', '4.72456304988199802748126408138912', '4.86700783069264527152267584864534', '5.29349847439803882073004442337862', '5.42986288125131486958830049550387', '6.08531503458998691003173646862787', '6.10534376852989647463977389455798', '6.76148596586763014391602417703286', '6.86364996755545557494333988766534', '7.34546056978665090010019695468055', '7.65505552484139893910982204866936'], 'prelabel': '4-7800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1707508729716938269, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11390845387100822871916869345', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.32737307812327504819314845613', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.00770662598978189488872407011', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3879.2111500809283, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 60840000, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 2, 0, 3, 0, -2, 0, -2, 0, 0, 0, 2, 0, -4, 0, -4, 0, 4, 0, 0, 0, -4, 0, -6, 0, 6, 0, 4, 0, 0, 0, -4, 0, 4, 0, 0, 0, -4, 0, 0, 0, 10, 0, -9, 0, -4, 0, -6, 0, 0, 0, 8, 0, -10, 0, 2, 0, 6, 0, 0, 0, 10, 0, -8, 0, -4, 0, -4, 0, 0, 0, -4, 0, -12, 0, 5, 0, 2, 0, 0, 0, 12, 0, 0, 0, -4, 0, -12, 0, 0, 0, -4, 0, -6, 0], 'euler11': [1, 2, 21, 22, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, -2, 27, -34, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 42, -92, 529], 'euler29': [1, 6, 35, 174, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -6, 69, -186, 961], 'euler37': [1, 4, 46, 148, 1369], 'euler41': [1, 0, 50, 0, 1681], 'euler43': [1, 4, 18, 172, 1849], 'euler47': [1, -10, 69, -470, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 6, 107, 318, 2809], 'euler59': [1, 10, 141, 590, 3481], 'euler61': [1, -2, 115, -122, 3721], 'euler67': [1, -10, 141, -670, 4489], 'euler7': [1, -2, 13, -14, 49], 'euler71': [1, 4, 114, 284, 5041], 'euler73': [1, 4, 22, 292, 5329], 'euler79': [1, 12, 186, 948, 6241], 'euler83': [1, -2, 5, -166, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 4, -90, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, 0, 0, 0], [1, -2, 13, -14, 49], [1, 2, 21, 22, 121], [1, 2, 1, 0, 0], [1, -2, 27, -34, 289], [1, 4, 42, 76, 361], [1, -4, 42, -92, 529], [1, 6, 35, 174, 841], [1, -6, 69, -186, 961], [1, 4, 46, 148, 1369], [1, 0, 50, 0, 1681], [1, 4, 18, 172, 1849], [1, -10, 69, -470, 2209], [1, 6, 107, 318, 2809], [1, 10, 141, 590, 3481], [1, -2, 115, -122, 3721], [1, -10, 141, -670, 4489], [1, 4, 114, 284, 5041], [1, 4, 22, 292, 5329], [1, 12, 186, 948, 6241], [1, -2, 5, -166, 6889], [1, 0, 178, 0, 7921], [1, 4, -90, 388, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/z'], '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': '4-7800e2-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-7800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.8919777987902835, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1707508729716938269, 'z1': {'__RealLiteral__': 0, 'data': '1.11390845387100822871916869345', 'prec': 103}}
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{'Lhash': '1412046720148882563489889664591,1682645279209762051989985287345', 'Lhash_array': ['1412046720148882563489889664591', '1682645279209762051989985287345'], 'label': '4-7800e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/z'}