-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1080726759669098515448517376333', 'a10': [15.167422244949131, 0.0], 'a2': [-2.3617626048255165, 0.0], 'a3': [0.0, 0.0], 'a4': [-2.422077398447791, 0.0], 'a5': [-6.422077398447791, 0.0], 'a6': [0.0, 0.0], 'a7': [-29.493843077006648, 0.0], 'a8': [24.6144726642512, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.3617626048255165, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.422077398447791, 0], [125.0, 0]], [[1.0, 0], [29.493843077006648, 0], [343.0, 0]], [[1.0, 0], [-0.6247152592567918, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [87.72909517351698, 0], [4913.0, 0]], [[1.0, 0], [-82.80184997003408, 0], [6859.0, 0]], [[1.0, 0], [-74.79770746807188, 0], [12167.0, 0]], [[1.0, 0], [226.32918274080038, 0], [24389.0, 0]], [[1.0, 0], [-173.66029807866553, 0], [29791.0, 0]], [[1.0, 0], [-112.02030038971463, 0], [50653.0, 0]], [[1.0, 0], [-267.0110250379993, 0], [68921.0, 0]], [[1.0, 0], [-383.4498342027129, 0], [79507.0, 0]], [[1.0, 0], [337.37956226974484, 0], [103823.0, 0]], [[1.0, 0], [-146.3543150604063, 0], [148877.0, 0]], [[1.0, 0], [-529.1730135759545, 0], [205379.0, 0]], [[1.0, 0], [-203.27168487243244, 0], [226981.0, 0]], [[1.0, 0], [-121.49674175015011, 0], [300763.0, 0]], [[1.0, 0], [-661.3137806272852, 0], [357911.0, 0]], [[1.0, 0], [-167.3414261060735, 0], [389017.0, 0]], [[1.0, 0], [101.39892331475836, 0], [493039.0, 0]], [[1.0, 0], [-506.9851078783554, 0], [571787.0, 0]], [[1.0, 0], [1402.3316189504405, 0], [704969.0, 0]], [[1.0, 0], [-1902.8903901491376, 0], [912673.0, 0]], [[1.0, 0], [1833.0926795617174, 0], [1030301.0, 0]], [[1.0, 0], [-1446.985082591586, 0], [1092727.0, 0]], [[1.0, 0], [-369.28570210616834, 0], [1225043.0, 0]], [[1.0, 0], [815.693531831732, 0], [1295029.0, 0]], [[1.0, 0], [1790.5647803809672, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 78, 'label': '2-39e2-1.1-c3-0-78', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/v/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.7745317003275912e-61, 0.09252983322866937, 0.18271462495568622, 0.2682353597000495, 0.34682521395304866, 0.41629598245653315, 0.4745648469607496, 0.5196815142850982, 0.5498556804333143, 0.5634846956727126, 0.5591812153570426, 0.5358005267130965, 0.49246714691926907, 0.4286001967750284, 0.3439369712534525, 0.2385540572442163, 0.11288529355837883, -0.032264167867449664, -0.1957084547687991, -0.37587696634248685, -0.570816472702384, -0.7781999671674101, -0.9953428254586135, -1.2192267075780807, -1.4465314937649547, -1.6736753774126811, -1.8968630479306847, -2.112141688782536, -2.3154642946401514, -2.5027595817910395, -2.670007533308222, -2.8133193912861154, -2.929020689349844, -3.013735716651028, -3.0644716267971917, -3.0787002587013164, -3.054435628004967, -2.9903049838726488, -2.885611312228355, -2.7403852076339112, -2.5554241355714638, -2.3323172671116876, -2.073454289503464, -1.7820168780857721, -1.4619518542508414, -1.117925446231834, -0.7552585075765902, -0.37984302373752454, 0.0019592601049784374, 0.38343473906325637, 0.757650505978712, 1.1175991891840218, 1.4563532150119063, 1.7672252048606374, 2.0439308415346744, 2.2807502390950942, 2.4726836386121054, 2.6155971414740375, 2.706354192660637, 2.7429286464626608, 2.7244954913580224, 2.6514956805970447, 2.525672008292391, 2.3500735813612788, 2.129027155461699, 1.8680744140821273, 1.5738751563685243, 1.2540772997741985, 0.9171555737783745, 0.5722217537819471, 0.22881023103661957, -0.1033563947970345, -0.41461620922929804, -0.6956251822373949, -0.9376159467341657, -1.1326510514950336, -1.2738633947891322, -1.3556765616020547, -1.3739980207532008, -1.3263785933301488, -1.2121322789073476, -1.0324114121415482, -0.7902332034847094, -0.4904549707446021, -0.13969676307861462, 0.2537884204601959, 0.6802950510669805, 1.1288927794154802, 1.5876965322718763, 2.0441726239907796, 2.485473171459893, 2.8987899428805717, 3.2717178388245625, 3.592617538652965, 3.85096648022881, 4.037687301259636, 4.145443172391745, 4.168890100592095, 4.104877270351637, 3.9525878021187184, 3.713613912776099, 3.391962321353786, 2.99398780360332, 2.5282550015237892, 2.005330870940933, 1.4375124288457592, 0.8384966662656334, 0.22300154517243323, -0.39365117546698714, -0.9959790089959792, -1.5687942586986914, -2.097657776776687, -2.56931644977141, -2.972110065858173, -3.2963338784537055, -3.5345443219175037, -3.681796935136086, -3.735807566669265, -3.6970303137624367, -3.5686483148062846, -3.35647638577293, -3.0687774704965407, -2.7159978599199586, -2.310429020420743, -1.865806549967907, -1.3968591510730475, -0.918822477181554, -0.4469341919666084, 0.004072488114546821, 0.42045916737631667, 0.7899392581919317, 1.1020852116581892, 1.3486711687705775, 1.5239383301697649, 1.6247729719816706, 1.6507900871973047, 1.6043190018099238, 1.490290882824025, 1.3160316906017882, 1.0909676939342412, 0.8262540247737074, 0.5343397671155448, 0.2284856271573131, -0.07774778941481282, -0.37102175168244117, -0.6387313012145118, -0.8694875254742355, -1.0535514153076762, -1.1832022250193903, -1.253025664914006, -1.2601102866245868, -1.2041439618389953, -1.0874062726088003, -0.9146567751336266, -0.6929233047121199, -0.43119858689936097, -0.14005723865315628, 0.16879137930588736, 0.48299620979453134, 0.7900831258282145, 1.0779775621103342, 1.3355092077933626, 1.5528773657146788, 1.7220570443623198, 1.8371281778176147, 1.894513483468407, 1.8931142494676045, 1.8343376443725257, 1.7220137849387025, 1.5622055904848946, 1.3629191883623049, 1.1337271071934918, 0.8853205016150074, 0.6290100087453877, 0.37619738112733353, 0.13784164398759907, -0.07605590465050074, -0.25692404156110765, -0.39802909354491556, -0.4947979421498585, -0.545040519102168, -0.5490601108778058, -0.5096447668896178, -0.431938489159039, -0.3231964367600133, -0.1924338565816674, -0.04998360091333701, 0.09301833171501166, 0.22519601707522016, 0.33551958331454446, 0.4138862978432955, 0.45166871783965934, 0.44220276121563296, 0.3811907470752955, 0.2669978688391399, 0.10082507270689957, -0.11325326186980748, -0.3683923328588546, -0.6552195808607295, -0.9622093165313554, -1.2761751439392903, -1.5828600294221586, -1.8675986650085856, -2.116022624253865, -2.3147759305071367, -2.4522072240610164, -2.519004833392739, -2.5087427651052114, -2.4183088919233144, -2.24819132877185, -2.002604962960235, -1.6894471004605125, -1.3200789057147273, -0.9089374043193339, -0.472990915685417, -0.03105850486050923, 0.3969789855260972, 0.7910428906099582, 1.1317577696059022, 1.4013488407029024, 1.5844941320839625, 1.6690906388543756, 1.6468966775796956, 1.5140173872763318, 1.271206763196507, 0.923967468113733, 0.48243861093591633, -0.03892868049987381, -0.6218981750650118, -1.2451585431614232, -1.8851880427543286, -2.5172375876060955, -3.1163895281310485, -3.658644965715016, -4.121990033016662, -4.487391471021728, -4.739674078405545, -4.868237148999549, -4.867573686344434, -4.737564721483873, -4.483531096180839, -4.116036162565203, -3.650444484431801, -3.1062532593060634, -2.506224255540191, -1.8753540307312506, -1.2397285631845847, -0.625314749878537, -0.0567451545700191, 0.44384631121223483, 0.8578815404905906, 1.171236165578927, 1.3749329936748758, 1.465594740803113, 1.4456308551854011, 1.3231456322406576, 1.111568075589933], 'positive_zeros': ['0.852543089929135927742108642245646', '2.43724007709548561130663359665525', '3.58939149680003314698650400328386', '4.28423118064832192250339290215305', '5.45190213179498770103211177960414', '6.49952571990433946354298796321611', '7.24870822471231370101241143971128', '7.945143728784910784341585954332992', '8.918628115732156826341584173651101'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.852543089929135927742108642246', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.43724007709548561130663359666', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58939149680003314698650400328', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 78, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/v/1/2'], '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': '2-39e2-1.1-c3-0-78', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.852543089929135927742108642246', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1080726759669098515448517376333', 'Lhash_array': ['1080726759669098515448517376333'], 'label': '2-39e2-1.1-c3-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/v/1/2'}