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  • lfunc_lfunctions • Show schema
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'9.600251496929512672666684690144699', '9.852586600787591170889488631820297', '9.911566662500873046289978076542627', '9.982537222008737534609226652196551', '10.27571188425527282388698082214125', '10.56980582940046249418540090388863', '10.85283724201053514863457982439564', '11.41769989513578869643706112696782', '11.53102115725122919783813354262723'], 'prelabel': '8-444e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.882912066386758, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1102240784421815964, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.887688086153105071811725621281', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.48635667794053151497638489993', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.81890710963619590499439279143', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 157.99389597986686, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 38862602496, 'conductor_radical': 222, 'degree': 8, 'dirichlet_coefficients': [1, 0, 6, 0, 0, 0, 0, 0, 21, 0, 0, 0, -14, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 22, 0, 0, 0, 0, 0, 20, 0, -84, 0, 0, 0, -10, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, -38, 0, 0, 0], 'euler11': [1, 0, 44, 0, 726, 0, 5324, 0, 14641], 'euler13': [1, 14, 53, -126, -1312, -1638, 8957, 30758, 28561], 'euler17': [1, 0, 0, 0, -289, 0, 0, 0, 83521], 'euler19': [1, -14, 50, 252, -2497, 4788, 18050, -96026, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 0, 0, 1058, 0, 0, 0, 279841], 'euler29': [1, 0, 0, 0, 1682, 0, 0, 0, 707281], 'euler3': [1, -6, 15, -18, 9, 0, 0, 0, 0], 'euler31': [1, -22, 242, -1980, 12719, -61380, 232562, -655402, 923521], 'euler37': [1, -20, 174, -740, 1369, 0, 0, 0, 0], 'euler41': [1, 0, -82, 0, 5043, 0, -137842, 0, 2825761], 'euler43': [1, 10, 50, -180, -3073, -7740, 92450, 795070, 3418801], 'euler47': [1, 0, -188, 0, 13254, 0, -415292, 0, 4879681], 'euler5': [1, 0, 0, 0, -25, 0, 0, 0, 625], 'euler53': [1, 0, 106, 0, 8427, 0, 297754, 0, 7890481], 'euler59': [1, 0, 0, 0, -3481, 0, 0, 0, 12117361], 'euler61': [1, 26, 170, -1560, -27769, -95160, 632570, 5901506, 13845841], 'euler67': [1, 0, 109, 0, 7392, 0, 489301, 0, 20151121], 'euler7': [1, 0, 13, 0, 120, 0, 637, 0, 2401], 'euler71': [1, 0, 142, 0, 15123, 0, 715822, 0, 25411681], 'euler73': [1, 0, 286, 0, 31107, 0, 1524094, 0, 28398241], 'euler79': [1, -26, 185, 1638, -33952, 129402, 1154585, -12819014, 38950081], 'euler83': [1, 0, 166, 0, 20667, 0, 1143574, 0, 47458321], 'euler89': [1, 0, 0, 0, -7921, 0, 0, 0, 62742241], 'euler97': [1, 38, 722, 10032, 111503, 973104, 6793298, 34681574, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -6, 15, -18, 9, 0, 0, 0, 0], [1, 0, 0, 0, -25, 0, 0, 0, 625], [1, 0, 13, 0, 120, 0, 637, 0, 2401], [1, 0, 44, 0, 726, 0, 5324, 0, 14641], [1, 14, 53, -126, -1312, -1638, 8957, 30758, 28561], [1, 0, 0, 0, -289, 0, 0, 0, 83521], [1, -14, 50, 252, -2497, 4788, 18050, -96026, 130321], [1, 0, 0, 0, 1058, 0, 0, 0, 279841], [1, 0, 0, 0, 1682, 0, 0, 0, 707281], [1, -22, 242, -1980, 12719, -61380, 232562, -655402, 923521], [1, -20, 174, -740, 1369, 0, 0, 0, 0], [1, 0, -82, 0, 5043, 0, -137842, 0, 2825761], [1, 10, 50, -180, -3073, -7740, 92450, 795070, 3418801], [1, 0, -188, 0, 13254, 0, -415292, 0, 4879681], [1, 0, 106, 0, 8427, 0, 297754, 0, 7890481], [1, 0, 0, 0, -3481, 0, 0, 0, 12117361], [1, 26, 170, -1560, -27769, -95160, 632570, 5901506, 13845841], [1, 0, 109, 0, 7392, 0, 489301, 0, 20151121], [1, 0, 142, 0, 15123, 0, 715822, 0, 25411681], [1, 0, 286, 0, 31107, 0, 1524094, 0, 28398241], [1, -26, 185, 1638, -33952, 129402, 1154585, -12819014, 38950081], [1, 0, 166, 0, 20667, 0, 1143574, 0, 47458321], [1, 0, 0, 0, -7921, 0, 0, 0, 62742241], [1, 38, 722, 10032, 111503, 973104, 6793298, 34681574, 88529281]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/444/2/w/b'], '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': '8-444e4-1.1-c1e4-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-444e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.882912066386758, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1102240784421815964, 'z1': {'__RealLiteral__': 0, 'data': '0.887688086153105071811725621281', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1125278335227431856763654153448,1884180934944551834295718851771,2305738689289717601694052329644,3160946976705271476375572224996', 'Lhash_array': ['1125278335227431856763654153448', '1884180934944551834295718851771', '2305738689289717601694052329644', '3160946976705271476375572224996'], 'factors': ['2-444-111.8-c1-0-2', '2-444-111.23-c1-0-6', '2-444-111.29-c1-0-9', '2-444-111.14-c1-0-10'], 'label': '8-444e4-1.1-c1e4-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/444/2/w/b'}