-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2025393072018577066959111788299', 'a10': [-19.559314719491994, 103.00227443649884], 'a2': [-4.502208788738876, -6.612875019430083], 'a3': [11.022703842524301, 11.022703842524301], 'a4': [-23.46023204520484, 59.545088062619776], 'a5': [-9.2668913895906, -9.2668913895906], 'a6': [23.265248771326245, -122.51827700228364], 'a7': [-320.3732064503815, 0.0], 'a8': [499.3870882788374, -112.9448363599889], 'a9': [0.0, 243.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.04259601375285, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.502208788738876, 6.612875019430083]]], [3, [[1.0, 0], [-11.022703842524301, -11.022703842524301]]]], 'bad_primes': [2, 3], 'central_character': '48.43', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '778883754300442064095882962173', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.502208788738876, 6.612875019430083]], [[1.0, 0], [-11.022703842524301, -11.022703842524301]], [[1.0, 0], [9.2668913895906, 9.2668913895906], [0, 15625.0]], [[1.0, 0], [320.3732064503815, 0], [117649.0, 0]], [[1.0, 0], [-1498.4925403678599, 1498.4925403678599], [0, -1771561.0]], [[1.0, 0], [-2546.471543693318, 2546.471543693318], [0, -4826809.0]], [[1.0, 0], [7232.043656415582, 0], [24137569.0, 0]], [[1.0, 0], [4865.791146848081, 4865.791146848081], [0, 47045881.0]], [[1.0, 0], [-12202.587169630564, 0], [148035889.0, 0]], [[1.0, 0], [-9527.739223102024, 9527.739223102024], [0, -594823321.0]], [[1.0, 0], [0, 13501.804689046403], [-887503681.0, 0]], [[1.0, 0], [964.1221425582268, 964.1221425582268], [0, 2565726409.0]], [[1.0, 0], [0, -94673.70804218497], [-4750104241.0, 0]], [[1.0, 0], [-61457.62735404798, 61457.62735404798], [0, -6321363049.0]], [[1.0, 0], [0, 125324.67465308763], [-10779215329.0, 0]], [[1.0, 0], [-92717.78288644609, -92717.78288644609], [0, 22164361129.0]], [[1.0, 0], [78971.18107474508, -78971.18107474508], [0, -42180533641.0]], [[1.0, 0], [-14025.761138833752, 14025.761138833752], [0, -51520374361.0]], [[1.0, 0], [169382.05709012167, 169382.05709012167], [0, 90458382169.0]], [[1.0, 0], [-239400.33715316383, 0], [128100283921.0, 0]], [[1.0, 0], [0, -668709.6778614824], [-151334226289.0, 0]], [[1.0, 0], [0, 572255.2306389442], [-243087455521.0, 0]], [[1.0, 0], [360997.5142915101, 360997.5142915101], [0, 326940373369.0]], [[1.0, 0], [0, 101645.93630351902], [-496981290961.0, 0]], [[1.0, 0], [1299107.0046615375, 0], [832972004929.0, 0]], [[1.0, 0], [-1183001.752061454, -1183001.752061454], [0, 1061520150601.0]], [[1.0, 0], [640195.7697961569, 0], [1194052296529.0, 0]], [[1.0, 0], [-685435.9927876006, 685435.9927876006], [0, -1500730351849.0]], [[1.0, 0], [1306447.0905916947, -1306447.0905916947], [0, -1677100110841.0]], [[1.0, 0], [99366.87174364136, 0], [2081951752609.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-48-16.11-c6-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/48/7/l/a/43/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1146107776016643, 1.278127257740665, 1.4083472352995274, 1.5009598181574997, 1.5522006589535662, 1.5589313434961916, 1.5187308285719126, 1.4299981233741292, 1.292063667094393, 1.105305089547461, 0.8712613415529885, 0.5927376432830499, 0.27389242322567925, -0.07970348790683149, -0.46104558128645823, -0.861722352932101, -1.27199919833903, -1.680967261008303, -2.0767627061666003, -2.446858860184923, -2.778429913571683, -3.058780534166832, -3.275830941118443, -3.4186419755664947, -3.477959756434542, -3.4467549664045243, -3.3207280482050927, -3.0987489957738497, -2.7831993804521944, -2.3801851009827204, -1.8995913557222672, -1.3549566655729999, -0.7631504445773962, -0.14384847049808247, 0.48118769007915796, 1.0890082347657157, 1.6565169908105826, 2.161611632846964, 2.584364313615139, 2.9081751767744803, 3.1208250741394337, 3.2153520607231565, 3.19067964356613, 3.0519337743742936, 2.810400282487894, 2.483094479302996, 2.091939179779504, 1.6625750467531024, 1.2228561891884724, 0.8011121963669388, 0.4242828985879571, 0.11605168849846166, -0.10488505810822975, -0.22627296061065463, -0.243348601561378, -0.15937274418426825, 0.014430115944908907, 0.25956225492271956, 0.5515609378467743, 0.8618595083636893, 1.160084437422316, 1.4166244265500507, 1.6052704873963093, 1.7057029514135067, 1.7055961804578796, 1.602126681636773, 1.4027060858851335, 1.1248158515818645, 0.7948924282199491, 0.44629486572542343, 0.11647474213745376, -0.1564471047788279, -0.3374196484958928, -0.3981861201584321, -0.3206373050950197, -0.09944312118836385, 0.256347626140766, 0.722975204191729, 1.2630367806721392, 1.8279606278383067, 2.3617562521510362, 2.805774477587795, 3.1040912435667325, 3.209037397528492, 3.0863458663921404, 2.7193859298009238, 2.112006171073427, 1.2896120896913987, 0.29825473830887544, -0.7983089175869758, -1.923421566193568, -2.9938355842630737, -3.92699072643013, -4.648591383040797, -5.099745279749762, -5.242928478373292, -5.066122243331005, -4.584622250387558, -3.8402377636804217, -2.8978580548397685, -1.8396396233255816, -0.7573312057529469, 0.25652587926431064, 1.1176339245791207, 1.7582636947147625, 2.133962901424854, 2.2278892326547544, 2.052246682628544, 1.6466108084331414, 1.0732722941925066, 0.41007046185252516, -0.2585111984795134, -0.8509943031670129, -1.298194648519948, -1.5510617615870788, -1.5861264064082132, -1.407879091275097, -1.0477592862628282, -0.559842431337854, -0.01372118085170971, 0.5145626101522132, 0.9524153609670601, 1.240169684129714, 1.3389203435769974, 1.2356808504553465, 0.9451486876812869, 0.5077956735499484, -0.015520966096658005, -0.5517633348079721, -1.0256761382616946, -1.370187378872234, -1.5358322030711267, -1.4978824696544601, -1.2601455725753177, -0.8548296292938196, -0.33840423470416925, 0.21605371777554996, 0.7290286043256138, 1.1258608052384813, 1.3475751430054197, 1.3596665484347579, 1.1575097396993597, 0.7675049877185953, 0.24366378201891076, -0.34000304511332713, -0.9002994684131299, -1.3573525294350055, -1.6469943097039337, -1.7311410258371718, -1.6045129001751623, -1.2965157078302123, -0.8677806379460552, -0.4016423556296341, 0.008385714483101324, 0.2734215568536065, 0.3241600028154331, 0.12367204856376739, -0.32401804814171375, -0.971126147729893, -1.729833096002031, -2.482360856023618, -3.0962583517821853, -3.442917598373004, -3.416758211474615, -2.9522909916971014, -2.036449678468066, -0.7141558010795089, 0.9140141444145524, 2.702079051557543, 4.4756819457321, 6.0537233823433505, 7.27167625484188, 8.003317868829862, 8.17774874435903, 7.789171441691746, 6.89790025434579, 5.622324273427432, 4.122868818125544, 2.580193645236161, 1.1707448883995364, 0.04319926168623614, -0.7007708770101374, -1.0186176798911593, -0.9301991955094009, -0.5118429688296137, 0.11777447039647577, 0.8176404308168245, 1.4471176183784697, 1.887763468472045, 2.060842179679469, 1.9378401689332592, 1.5424574887861322, 0.9439580871932627, 0.24318910969298388, -0.4462140238480054, -1.0181384182456685, -1.3923005778936959, -1.5274102008420438, -1.4269739312580427, -1.1368310779954984, -0.7349847527171532, -0.3156694505919236, 0.029364547680064194, 0.22885755975755293, 0.24595982337664546, 0.0854165049855512, -0.20740335964369067, -0.5555483948539757, -0.8659912416370944, -1.0487396936593893, -1.0359411949759914, -0.7972730578415521, -0.34850614561454574, 0.24867280144492152, 0.8958989073058639, 1.4750346081082637, 1.8698391328735247, 1.9884756322853123, 1.7826042251737833, 1.2592684065025863, 0.4829708153145513, -0.43294035591382174, -1.3444908027940985, -2.1019782553324893, -2.577244681688052, -2.688381345048018, -2.417178136074091, -1.8157596250136705, -1.0006856664671209, -0.13502282986719213, 0.5988817075115449, 1.031380545564768, 1.0366691205807128, 0.5574360319337672, -0.38166680416704324, -1.6745636995910056, -3.148697277693898, -4.592179022696284, -5.788687284136071, -6.554130542170666, -6.768619038098745, -6.39797548166674, -5.5007692965396355, -4.219382443820105, -2.7564616059638753, -1.340763931337929, -0.18836843096732656, 0.5338733098899816, 0.7361201915569182, 0.41958166829782806, -0.3256796783729283, -1.338714194495977, -2.4180551989430508, -3.358844172006365, -3.989825071822342, -4.203373608109248, -3.973067175670685], 'positive_zeros': ['1.59775341222094066136884341808986', '4.15370546942672452512336690907732', '6.43398765749147827663945744536186', '6.99143606372750268598805660782572', '8.799293224283402680712141444447223', '9.414770931688585603739472740918362', '11.03485165835466561375944385729077', '12.71693819010871780580629801464798', '13.82578106152467092674876644661937', '14.87812022835028875063571587998797'], 'prelabel': '2-48-16.11-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3230401763675457, 'root_angle': 0.6139332953406165, 'root_number': '-0.35033805016187264 + 0.9366233237586907*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.30696664767', 'prec': 44}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59775341222094066136884341809', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.15370546942672452512336690908', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.43398765749147827663945744536', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.04259601375285, 'bad_primes': [2, 3], 'central_character': '16.11', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/7/l/a/43/7'], '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': '2-48-16.11-c6-0-17', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-48-16.11-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3230401763675457, 'root_angle': 0.30696664767030823, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59775341222094066136884341809', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2025393072018577066959111788299', 'Lhash_array': ['2025393072018577066959111788299'], 'label': '2-48-16.11-c6-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/7/l/a/43/7'}