-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2294036327573631629928092235316', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.6457513110645907, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.41178332170387, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '4560.1', 'coefficient_field': 'CDF', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.6457513110645907, 0], [7.0, 0]], [[1.0, 0], [5.645751311064591, 0], [11.0, 0]], [[1.0, 0], [5.645751311064591, 0], [13.0, 0]], [[1.0, 0], [4.0, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.2915026221291812, 0], [23.0, 0]], [[1.0, 0], [6.937253933193772, 0], [29.0, 0]], [[1.0, 0], [6.0, 0], [31.0, 0]], [[1.0, 0], [1.6457513110645905, 0], [37.0, 0]], [[1.0, 0], [4.354248688935409, 0], [41.0, 0]], [[1.0, 0], [0.3542486889354094, 0], [43.0, 0]], [[1.0, 0], [9.291502622129181, 0], [47.0, 0]], [[1.0, 0], [-0.7084973778708188, 0], [53.0, 0]], [[1.0, 0], [0.7084973778708188, 0], [59.0, 0]], [[1.0, 0], [0.7084973778708188, 0], [61.0, 0]], [[1.0, 0], [14.583005244258363, 0], [67.0, 0]], [[1.0, 0], [-3.291502622129181, 0], [71.0, 0]], [[1.0, 0], [-10.0, 0], [73.0, 0]], [[1.0, 0], [-14.583005244258363, 0], [79.0, 0]], [[1.0, 0], [6.0, 0], [83.0, 0]], [[1.0, 0], [1.0627460668062283, 0], [89.0, 0]], [[1.0, 0], [-12.937253933193771, 0], [97.0, 0]], [[1.0, 0], [1.2915026221291812, 0], [101.0, 0]], [[1.0, 0], [10.583005244258363, 0], [103.0, 0]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [5.291502622129181, 0], [109.0, 0]], [[1.0, 0], [4.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 71, 'label': '2-4560-1.1-c1-0-71', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4560/2/a/bo/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.0635035875250975e-60, 0.22419994456579143, 0.4478776918692656, 0.6704689491056113, 0.8913277447205896, 1.1096916917568238, 1.32465409955185, 1.5351444911497982, 1.7399185790766067, 1.9375582383591192, 2.12648153521857, 2.304962451349961, 2.471159600848996, 2.623152970555279, 2.758987516732025, 2.8767223088116087, 2.974483810720926, 3.0505218201745206, 3.103266537686714, 3.13138520505444, 3.1338367363277984, 3.1099227642319125, 3.0593335449711385, 2.9821872087279924, 2.8790609166323984, 2.7510125918207873, 2.599592035855022, 2.4268404244074744, 2.235277398412589, 2.0278752278353247, 1.808019822052609, 1.5794586890517561, 1.3462362989618801, 1.1126176779774657, 0.8830014371845689, 0.6618238166076221, 0.45345568644992856, 0.26209478285924154, 0.09165575219466894, -0.05433917658726789, -0.17286588890865626, -0.261497338973482, -0.3184926230400676, -0.3428730966140765, -0.3344826196240603, -0.29402927058826533, -0.2231062252644647, -0.12418994373142912, -0.0006143454171958552, 0.14347973593821525, 0.30321984949016784, 0.47310128597542234, 0.6471090568139876, 0.8188602962646876, 0.9817641504819513, 1.12919552061623, 1.2546783974562292, 1.3520739870912795, 1.4157684039684528, 1.4408544206704257, 1.423301630859917, 1.3601094173794688, 1.249437331097162, 1.0907078821117542, 0.8846773219453801, 0.633470745785669, 0.3405787538145651, 0.010813960046023726, -0.3497732002241944, -0.734018668865626, -1.1338069840032512, -1.540268239480022, -1.9440052469084022, -2.3353451865897825, -2.7046089831419096, -3.0423907589614787, -3.3398390425996665, -3.588930973815445, -3.782730580200655, -3.915622321812733, -3.9835115212677707, -3.9839840184679254, -3.916418402337492, -3.7820454566603012, -3.5839509827471914, -3.327019887467778, -3.0178213011530777, -2.6644364580456763, -2.27623306806373, -1.8635918640542986, -1.4375928527811577, -1.0096704603728606, -0.5912481766020504, -0.19336440556114984, 0.1736980303792147, 0.5007659538246022, 0.7801007875122595, 1.005682282677694, 1.173439910806034, 1.281422253269086, 1.3298965695699383, 1.3213729230998748, 1.26054972823822, 1.154180275502424, 1.0108626022393516, 0.8407579066141783, 0.6552454489306998, 0.4665244417885689, 0.28717569701405893, 0.12969767706158986, 0.006033006608545812, -0.07289763440558161, -0.09763704511339555, -0.06059163252513126, 0.04362570162973066, 0.21792413183522202, 0.4625469470359572, 0.7749763363548804, 1.1499370350594655, 1.5795014434898196, 2.0532951211103128, 2.5587977717749073, 3.0817311176353788, 3.606521553431275, 4.116822322706745, 4.596077296514057, 5.028106382618105, 5.397691248547173, 5.691139479954538, 5.8968055631242775, 6.005548192157942, 6.011105339364278, 5.910371239976437, 5.703562845146002, 5.3942672753513055, 4.9893662181898115, 4.498837896273779, 3.9354420028255808, 3.3142976755557387, 2.6523689627260114, 1.9678761442328083, 1.279654534278318, 0.6064848613638048, -0.033579125059986795, -0.6238596205935241, -1.149654602367973, -1.5987643875848858, -1.9619233362220565, -2.2331186252882116, -2.4097823385974473, -2.492848083048658, -2.4866687672202885, -2.3987978436490502, -2.2396419894727884, -2.021998641824404, -1.7604967788369184, -1.4709636227276988, -1.1697433405216322, -0.8729961661289458, -0.5960075416096463, -0.35253680026769824, -0.15423356691510015, -0.01014746332261094, 0.07364703338110162, 0.09429348504489826, 0.052252624240480834, -0.04874761588225267, -0.20191000019825145, -0.3977060771840866, -0.6243403770400366, -0.868320836802702, -1.1151105475980552, -1.3498319324492283, -1.5579917086963864, -1.72619361591843, -1.8428059880072307, -1.8985528418064797, -1.8870002020975596, -1.8049137740574899, -1.652469636060458, -1.433306126693713, -1.1544122605590093, -0.825855511553872, -0.4603593105636909, -0.07274776964775631, 0.3207183722964944, 0.7030851019112955, 1.0574940890816196, 1.367980840955753, 1.620244580712274, 1.8023530545366186, 1.9053478870969942, 1.9237201867899867, 1.8557316893443432, 1.70356358952924, 1.4732830477180818, 1.1746258199650026, 0.8206021585541637, 0.4269416562062942, 0.011400651828001943, -0.4070372120052436, -0.8090310428753482, -1.1757831030486696, -1.4899271299441745, -1.736361955733337, -1.9029896692650314, -1.981321418248427, -1.9669196545038095, -1.8596529429196875, -1.66374806507923, -1.387633661217197, -1.043579626786377, -0.6471464379886193, -0.21646804008128437, 0.2285995771752529, 0.667424904078314, 1.0795980102795324, 1.4459304523143455, 1.7494092527953455, 1.976057608630278, 2.1156587222509518, 2.162305092215355, 2.114743499256332, 1.9764954308088805, 1.7557433645703373, 1.464984676184773, 1.1204664007999503, 0.7414250990045445, 0.3491661010548197, -0.03397508577231224, -0.3857398736810262, -0.6850686378356862, -0.9131825033501325, -1.0545707323857234, -1.09783333146121, -1.0363348276329976, -0.8686337864420824, -0.5986631749864247, -0.23564861781324797, 0.20623562094199238, 0.7084600939067138, 1.248957659653527, 1.8031280975694775, 2.344983103602613, 2.848377269601685, 3.288265601654479, 3.641925986021711, 3.8900859183297496, 4.017896773634945, 4.015705757657576, 3.8795851387228617, 3.6115899744591546, 3.2197287589480954, 2.7176455764417358, 2.124026750185197, 1.4617588895270626, 0.7568779498113059], 'positive_zeros': ['1.80967557397962061215883980846884', '2.25021389140852050145134855534981', '3.14208681812751923497089405648922', '4.38349895758822959219982031547757', '5.15903143566908425991132953717572', '5.32764120326536005248220903749070', '6.70058278207679356763305761095500', '7.59799929049065973024828667310087', '7.76177688667222254413923350502336'], 'prelabel': '2-4560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80967557397962061215883980847', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25021389140852050145134855535', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14208681812751923497089405649', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 36.41178332170387, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'index': 71, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4560/2/a/bo/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': '2-4560-1.1-c1-0-71', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80967557397962061215883980847', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2294036327573631629928092235316', 'Lhash_array': ['2294036327573631629928092235316'], 'label': '2-4560-1.1-c1-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4560/2/a/bo/1/2'}