-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1124758288453994463147899793889', 'a10': [-9.0, -15.588457268119896], 'a2': [-1.0, 1.7320508075688772], 'a3': [-2.5, -4.330127018922194], 'a4': [-2.0, -3.4641016151377544], 'a5': [-4.5, 7.794228634059948], 'a6': [10.0, -1.8669045833583425e-60], 'a7': [0.0, 0.0], 'a8': [8.0, 0.0], 'a9': [1.0, -1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.782187180562583, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.7320508075688772]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '98.79', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'conjugate': '1747327934442118958248752162477', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.7320508075688772]], [[1.0, 0], [2.5, 4.330127018922194], [-13.5, 23.382685902179844]], [[1.0, 0], [4.5, -7.794228634059948], [-62.5, -108.25317547305482]], [[1.0, 0], [0, 0]], [[1.0, 0], [-28.5, -49.363448015713004], [-665.5, 1152.6798124370878]], [[1.0, 0], [-70.0, 0], [2197.0, 0]], [[1.0, 0], [-25.5, -44.16729559300637], [-2456.5, 4254.782808792947]], [[1.0, 0], [-2.5, 4.330127018922194], [-3429.5, -5940.068244557465]], [[1.0, 0], [34.5, -59.75575286112627], [-6083.5, -10536.931087845265]], [[1.0, 0], [-114.0, 0], [24389.0, 0]], [[1.0, 0], [-11.5, -19.91858428704209], [-14895.5, 25799.76280414221]], [[1.0, 0], [-126.5, 219.10442715746296], [-25326.5, -43866.78477789317]], [[1.0, 0], [-42.0, 0], [68921.0, 0]], [[1.0, 0], [124.0, 0], [79507.0, 0]], [[1.0, 0], [-100.5, 174.07110616067217], [-51911.5, -89913.35549711177]], [[1.0, 0], [-196.5, -340.3479836872844], [-74438.5, 128931.26403921588]], [[1.0, 0], [-109.5, -189.65956342879207], [-102689.5, 177863.43140384424]], [[1.0, 0], [354.5, -614.012011283167], [-113490.5, -196571.31217639567]], [[1.0, 0], [209.5, 362.86464418567977], [-150381.5, 260468.39851841913]], [[1.0, 0], [96.0, 0], [357911.0, 0]], [[1.0, 0], [156.5, 271.0659513845293], [-194508.5, 336898.604504011]], [[1.0, 0], [230.5, -399.2377111446262], [-246519.5, -426984.29905647587]], [[1.0, 0], [-588.0, 0], [571787.0, 0]], [[1.0, 0], [508.5, -880.7478356487741], [-352484.5, -610521.062880512]], [[1.0, 0], [-1834.0, 0], [912673.0, 0]], [[1.0, 0], [142.5, 246.81724007856502], [-515150.5, 892266.8395445109]], [[1.0, 0], [249.5, -432.1466764884349], [-546363.5, -946329.3414011582]], [[1.0, 0], [-553.5, 958.6901219893736], [-612521.5, -1060918.3587283]], [[1.0, 0], [461.5, 799.3414476930369], [-647514.5, 1121528.0126375577]], [[1.0, 0], [-1542.0, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-98-7.2-c3-0-1', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/98/4/c/a/79/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0535687154457294, 0.9730666527754396, 0.8694170142838635, 0.7431057664196308, 0.5945272342039445, 0.4241666201158905, 0.23280438636382716, 0.02172757199918239, -0.20706743061798272, -0.45069618395772637, -0.7052468873356272, -0.9656951656234172, -1.2258867158943292, -1.4785999297625074, -1.7156980613316088, -1.928376820845082, -2.107508308882221, -2.2440759691318033, -2.3296878975812234, -2.357147747006344, -2.321054126633678, -2.2183914929074477, -2.0490688557284527, -1.8163580529019816, -1.5271817424272704, -1.1922034129786072, -0.8256782246976729, -0.4450346962521771, -0.07017311261781102, 0.2775134398642537, 0.5763662702187268, 0.8058824017963344, 0.948251122773906, 0.9899045605274002, 0.9229636951379419, 0.7464512568567853, 0.46714259745392744, 0.09993656616990187, -0.3323484590643566, -0.7998130838980745, -1.2669638217817318, -1.6948084162445394, -2.0434614692494164, -2.2751049067001143, -2.357096740773798, -2.2649826678192486, -1.9851437828555196, -1.5168146452797697, -0.8732320471979644, -0.08172691318381241, 0.8173519688161018, 1.7728977425366403, 2.726395733692206, 3.616159626608793, 4.382145556250186, 4.970952162945049, 5.340561175914195, 5.46435904947002, 5.334011353582501, 4.960839544246241, 4.375470973819285, 3.6256889325225528, 2.772586706678296, 1.8853108237321166, 1.0348442728704221, 0.2874107289677829, -0.30184210393705935, -0.6942113721906474, -0.8712544744661992, -0.8365807233252673, -0.6153472254107688, -0.25142985377088944, 0.19749732480184584, 0.6664884831701147, 1.090761611989008, 1.4132055169985902, 1.591072009267425, 1.6010238615835923, 1.4418717560260395, 1.1345890665100398, 0.7195160320391778, 0.25101803403186657, -0.2097972599032831, -0.6034174770739151, -0.8802493308145901, -1.0078086300527445, -0.9757516376497335, -0.7979620087744382, -0.5112681920807649, -0.1708075601212413, 0.1574794411722704, 0.4063120470476622, 0.5172456964652775, 0.4501421251444704, 0.19052451692179806, -0.24637865273950887, -0.8157007800915678, -1.4473773403972576, -2.05460955555735, -2.545399056340991, -2.8356944925242806, -2.862360786541655, -2.5940879631824783, -2.0385291702187174, -1.2443896527036669, -0.2978344136341732, 0.6866382998564431, 1.5799033830269154, 2.254822900709556, 2.6035783642920514, 2.553304390041033, 2.0777203577883467, 1.2029144708702824, 0.006188363336124788, -1.3921758908416153, -2.843342869151621, -4.188721955267406, -5.280602091173268, -6.001724465180322, -6.280949628128656, -6.102661149434816, -5.508408904157315, -4.590415068858232, -3.477782337276786, -2.317371309441849, -1.2521725138969522, -0.40044274276708314, 0.1611803078729634, 0.407935795713328, 0.3689216919297581, 0.12044390904111435, -0.2282427359921175, -0.5545270749563451, -0.7441839550874649, -0.7116753433605646, -0.41559668916624454, 0.13339389127975995, 0.8736099916441378, 1.7022911952540631, 2.492914048101832, 3.1170056916702973, 3.466772132986613, 3.47463327982787, 3.126207502465653, 2.4643511489822556, 1.5833656371327138, 0.6141851745784562, -0.2970420535427573, -1.0133531157910278, -1.430123659770591, -1.4928862581929836, -1.206595446389405, -0.634588972791842, 0.1126891908888823, 0.8972945548993364, 1.5782705538900006, 2.0366344157055063, 2.196321503037711, 2.0372301444235115, 1.5979196887583207, 0.9674104181478702, 0.267571698175054, -0.37061655361653667, -0.8324319511900163, -1.041531720593185, -0.9745038761454472, -0.6649223576373466, -0.19598336915063372, 0.3169664896191028, 0.7506647609960228, 1.000153947989612, 1.0016872611240148, 0.747533452034774, 0.28938511817040874, -0.2707214534722373, -0.8005627850165437, -1.165233830406525, -1.2566208599559283, -1.0188246072379867, -0.464071210927993, 0.32466817670388626, 1.2056058243074061, 2.002979634262919, 2.540480210218766, 2.6769855047427176, 2.337547769463907, 1.533177332314187, 0.36488521994446066, -0.9896451351252475, -2.305027153832547, -3.3478919808950955, -3.9201502321138366, -3.8975952461419365, -3.256239088727425, -2.080881729080004, -0.55367459193769, 1.0757578948920363, 2.5334692392094347, 3.5697567373222574, 4.004072462895149, 3.757749947016923, 2.868241150844923, 1.4820563571411802, -0.17230429723291588, -1.8262552434064396, -3.219804349489356, -4.147642830655388, -4.493845329662158, -4.248704924008555, -3.504851083518372, -2.4339810171930325, -1.249415235335526, -0.16246186999424833, 0.6583361588034966, 1.1168166950829932, 1.201971421132324, 0.981899752919708, 0.5810680719881705, 0.14658203666658187, -0.18853668239558355, -0.33659388625067027, -0.27393154270395675, -0.043052880390461436, 0.261969177847114, 0.5229954827425273, 0.6313733057812123, 0.5192097648946127, 0.180521843906588, -0.32323261883345655, -0.8750437764675183, -1.3292590086330933, -1.5473844625349304, -1.4342843416374245, -0.9658743694390366, -0.20110799141136435, 0.7254690983239563, 1.6298309637728314, 2.318006417393919, 2.630380494317358, 2.4805981905981707, 1.8797258590644959, 0.9393646306267321, -0.1479619555258779, -1.1476305912085962, -1.8328670319505491, -2.034878190406719, -1.6817980659541445, -0.8172636619631973, 0.40618828452824884, 1.7580954660419372, 2.97901170231277, 3.8367385767429845, 4.177245115465715, 3.958610217390463, 3.259977983520393, 2.263109652321077, 1.2103931070963823], 'positive_zeros': ['0.887277841584653983046864472411999', '3.52422175297173536092827535389873', '4.65532943160658943114519691212514', '6.13690516830978083856269375870256', '8.181234144018956430811129151641696', '8.946764877558296449285425864420794', '10.19176681065728094249705888840740', '11.18782076071581031500476251413689', '11.81024008987487486658733642658224', '13.16259342003854485871889582038202'], 'prelabel': '2-98-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4046178866012338, 'root_angle': -0.2929874272254411, 'root_number': '0.6054643436493674 - 0.7958724323465669*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.146493713613', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.887277841584653983046864472412', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.52422175297173536092827535390', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.65532943160658943114519691213', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.782187180562583, 'bad_primes': [2, 7], 'central_character': '7.2', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/4/c/a/79/1'], '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': '2-98-7.2-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-98-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4046178866012338, 'root_angle': -0.14649371361272054, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887277841584653983046864472412', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1124758288453994463147899793889', 'Lhash_array': ['1124758288453994463147899793889'], 'label': '2-98-7.2-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/4/c/a/79/1'}