-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1403528620668424079931840614737', 'a10': [-0.06265564530407546, 0.5961286445374737], 'a2': [0.9781476007338057, 0.20791169081775934], 'a3': [-0.523531597538018, -0.9067833263035486], 'a4': [0.9135454576426009, 0.4067366430758002], 'a5': [0.06265564530407546, 0.5961286445374737], 'a6': [-0.32356032146302593, -0.9958162746498876], 'a7': [0.22697595310502142, 2.635997328661785], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [0.9518293327585814, -1.6486167644722465], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.583413076021496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9781476007338057, -0.20791169081775934]]], [7, [[1.0, 0], [-0.22697595310502142, -2.635997328661785]]], [41, [[1.0, 0], [-0.7322044448600963, -6.361122279199412]]]], 'bad_primes': [2, 7, 41], 'central_character': '574.387', 'coefficient_field': 'CDF', 'conductor': 574, 'conductor_radical': 574, 'conjugate': '2244648778592662848267799421085', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [0.523531597538018, 0.9067833263035486], [-1.5, 2.598076211353316]], [[1.0, 0], [-0.06265564530407546, -0.5961286445374737], [-4.8907380036690284, 1.0395584540887968]], [[1.0, 0], [-0.22697595310502142, -2.635997328661785]], [[1.0, 0], [0.6058578658747139, -5.764352543389532], [-10.759623608071863, -2.2870285989953527]], [[1.0, 0], [-0.8075682213445152, -2.4854394199779155], [-10.517220926874316, 7.641208279802151]], [[1.0, 0], [-0.44234322954939026, 4.20861469979074], [-16.628509212474697, -3.5344987439019087]], [[1.0, 0], [-0.7417033832885714, -0.8237450597714411], [-1.986040802085416, 18.895916011997194]], [[1.0, 0], [-4.293162230838816, -0.9125398024787006], [21.01154552577982, 9.354942790743404]], [[1.0, 0], [1.0497699750033125, -0.7627025314630311], [8.961492836873475, -27.580638972559452]], [[1.0, 0], [-0.7007660770727383, 6.667343854425866], [-30.322575622747976, -6.445262415350539]], [[1.0, 0], [0.08065330591102705, 0.7673649468754161], [-36.19146122715081, 7.692732560257095]], [[1.0, 0], [-0.7322044448600963, -6.361122279199412]], [[1.0, 0], [-1.3269957372912822, -4.084072934563117], [-34.78773075812274, 25.274765848576344]], [[1.0, 0], [-0.584114674713344, -0.12415740687807181], [42.936636509202245, 19.116622224562608]], [[1.0, 0], [11.208563055918761, 4.9903737935845385], [35.46392213701949, 39.3866757503019]], [[1.0, 0], [-5.177766495089219, 5.750492268309373], [-6.167179332791555, -58.67679182672813]], [[1.0, 0], [4.980517620764996, 5.53142519994892], [-6.376236259326862, 60.66583561746467]], [[1.0, 0], [-13.793762393038785, -6.141378695710986], [44.8317506260435, 49.790703306985414]], [[1.0, 0], [2.0843225579195277, 1.514348980409454], [21.940206600621266, 67.52501265695591]], [[1.0, 0], [5.437074464992254, 9.417289217901956], [-36.5, 63.21985447626402]], [[1.0, 0], [1.7559105373196118, -3.0413262641831347], [-39.5, -68.41600689897065]], [[1.0, 0], [4.179266604337154, 0], [83.0, 0]], [[1.0, 0], [3.505863298111512, 3.8936556541629948], [-9.303033230821159, 88.51244868777633]], [[1.0, 0], [-10.504209477320684, 7.63175490835044], [29.974648454369902, -92.2524820806299]], [[1.0, 0], [16.85807835037241, -3.583295170518998], [92.2680912219027, -41.08040095065582]], [[1.0, 0], [6.514924027316797, 7.235556157899442], [-10.766431716568308, 102.43575522293216]], [[1.0, 0], [4.840979841689885, 5.376452796216631], [-11.18454556963892, 106.41384280440525]], [[1.0, 0], [2.3208278583988364, 4.019791766368053], [-54.5, 94.39676901250381]], [[1.0, 0], [-15.216499825556943, -11.055434250653274], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-574-287.100-c1-0-10', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/574/2/s/a/387/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0688325550650646, 1.9626865949769052, 1.8442815896181208, 1.704915397149274, 1.534045808911268, 1.321206753992061, 1.0578129521138178, 0.7386863952480597, 0.3632510459961009, -0.06362570876282514, -0.5311840637551639, -1.0227802343162582, -1.5164252696083678, -1.9859082565751947, -2.4025128729404734, -2.737270703857519, -2.963617112348953, -3.060236176740704, -3.0138121963603584, -2.821359025935182, -2.4917867289992994, -2.046396858608544, -1.51807771020419, -0.9490975880225115, -0.38755860107068274, 0.1172406705785275, 0.5201011466365106, 0.7852902612650138, 0.891294666501165, 0.834257710743023, 0.6294841840699736, 0.3105815529791696, -0.07391417005968266, -0.46623639780858, -0.8068532811568296, -1.042810952931273, -1.1358219160272107, -1.0688643046608992, -0.8501357122893508, -0.5134765995898604, -0.11482691899388689, 0.27514265738772914, 0.5814538417999636, 0.7369429845073977, 0.6942927448464749, 0.4359918355991996, -0.01964243177951355, -0.6177998609129292, -1.272553962832943, -1.8780194181325116, -2.3240215469067813, -2.5141015671240603, -2.3830467953198355, -1.9109171951854038, -1.1308260398615184, -0.12852992499668772, 0.9668927166736706, 2.000517182590122, 2.814950362255574, 3.276116568878729, 3.297217311170651, 2.856579102370093, 2.0058160940680825, 0.8661536729709172, -0.3873107461855889, -1.5515035682972675, -2.4275695462633515, -2.8541122181231517, -2.735696129961729, -2.0613264970491216, -0.9091361961820629, 0.5641755016499964, 2.1478798649389734, 3.611813740107849, 4.745070472625446, 5.391815313853454, 5.477539330354677, 5.020662986741752, 4.127063403684895, 2.968350258020167, 1.747927975499237, 0.6614011755416335, -0.14084229069059404, -0.5813205221759341, -0.6677230152256282, -0.48715732473027984, -0.1835237141954719, 0.07722630383306157, 0.14649788485609494, -0.07148015149981979, -0.5960457037935708, -1.3638097748534452, -2.241391885506848, -3.054654103067475, -3.628100227272923, -3.8256244644840987, -3.5832502927428727, -2.9260941957379134, -1.965233214038253, -0.8747185335374631, 0.14636645485078323, 0.9182494870397924, 1.3209095204637855, 1.3209543229759055, 0.9782557566325594, 0.4303498353665473, -0.1420649134862983, -0.5605020379866997, -0.6940148599668274, -0.4932522535619228, -0.004476463078852014, 0.6404992190932631, 1.2565923190502815, 1.652440159698615, 1.6806140149953315, 1.2783611037377713, 0.4881385020174013, -0.548024840437873, -1.619819707177258, -2.498481239730192, -2.992997549355966, -2.9984651021232285, -2.5238737667744133, -1.6914937874494962, -0.7071661860763077, 0.1916019536236486, 0.7967421063362942, 0.9840206903411225, 0.7460018312059519, 0.1940035618495832, -0.4725900199769601, -1.0225657158442483, -1.2603400933696283, -1.0865911579023224, -0.534973083466132, 0.22656082780454628, 0.9323078334001362, 1.28559400930922, 1.0395449983461247, 0.07093754441855654, -1.5730922110230747, -3.6695819385838546, -5.859435304888157, -7.724490417544475, -8.884018389107105, -9.086853288945758, -8.275543293005503, -6.605318234346786, -4.411803469970921, -2.134463873611352, -0.21431731095718362, 1.0086027337911483, 1.3721890357911612, 0.9241990201250443, -0.09858169148622752, -1.3379388072343155, -2.410342813143836, -3.005963849958857, -2.9645218842860674, -2.3085155914295825, -1.2262430532919129, -0.010873259035911836, 1.0262106756162863, 1.642848167937932, 1.7297570966459315, 1.333208080635113, 0.6317006559400483, -0.12491450427792311, -0.6946160080072971, -0.9164518389499063, -0.7558746133476377, -0.3090542259645372, 0.23420639617660108, 0.6565478505072936, 0.7868038008654625, 0.5578071871145378, 0.02970765407462455, -0.6288220842888974, -1.1956907771329366, -1.4692680505390694, -1.3371861829473346, -0.8174173057828986, -0.05748089395245505, 0.709108434749829, 1.2361541694805782, 1.3447692019029627, 0.9840384734128726, 0.25175581704129557, -0.6330777057017151, -1.3988628630168032, -1.810251430463243, -1.7488439572756371, -1.2587174709195161, -0.5399684446020769, 0.11041592933309907, 0.39392757239256204, 0.11307485959998007, -0.7518872158569956, -2.018513605474849, -3.341198966303469, -4.305253207609392, -4.549708042999578, -3.8821329707653534, -2.34942894754533, -0.24059698885499545, 1.9824917409343756, 3.8082620285267246, 4.817275102775487, 4.800668573403264, 3.819147849360867, 2.1838286223065415, 0.3637666440845709, -1.1524822589770274, -1.9995233108300796, -2.0386240060516196, -1.390544440258143, -0.3880233855816405, 0.5367089504725331, 0.9936585750187761, 0.7611340631421503, -0.14370686113624745, -1.4719342506195965, -2.8247874873998127, -3.7837042933787797, -4.046239293515966, -3.523882129274423, -2.3702587979985075, -0.9309261797521269, 0.36844710385435786, 1.158659778891528, 1.243534330377895, 0.6585078394154198, -0.34732091355784794, -1.3987940942527568, -2.1219565331109735, -2.2679891646668047, -1.792297277559829, -0.8626882874259981, 0.20520414221328487, 1.062305310635393, 1.4504307506537042, 1.29344038846122, 0.7236395866965033, 0.03428109939329627, -0.42535363276096966, -0.37583128994228193, 0.2894661641350794, 1.460354172808952, 2.840547206635306, 4.0428631780909186, 4.716321262793879, 4.661422411771065, 3.8940529600341094, 2.6364486622516567, 1.2392024194871103, 0.062388344375158576, -0.6420374679235012], 'positive_zeros': ['1.10718885820409111901978566338952', '3.09401970704944524517424980904487', '3.97674852640224245321338364500838', '5.03547227052399091701348065438485', '5.74542117169014912314386190705907', '6.88989602219044767667593887865636', '7.961391243794797989405245275956751', '8.829233657017965962853202977185621', '10.22356617339315549980935672930745', '10.83077491445149672917278185455867'], 'prelabel': '2-574-287.100-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1408907202427443, 'root_angle': -0.21537357452941763, 'root_number': '0.7796960733722951 - 0.6261581534786755*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.107686787265', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10718885820409111901978566339', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09401970704944524517424980904', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97674852640224245321338364501', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.583413076021496, 'bad_primes': [2, 7, 41], 'central_character': '287.100', 'conductor': 574, 'conductor_radical': 574, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/574/2/s/a/387/5'], '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': '2-574-287.100-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-574-287.100-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1408907202427443, 'root_angle': -0.10768678726470882, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10718885820409111901978566339', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1403528620668424079931840614737', 'Lhash_array': ['1403528620668424079931840614737'], 'label': '2-574-287.100-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/574/2/s/a/387/5'}