-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '152575972919866597638477261074', 'a10': [29377.32458887296, 0.0], 'a2': [-16.0, 0.0], 'a3': [-52.459508194416, 0.0], 'a4': [256.0, 0.0], 'a5': [-1836.08278680456, 0.0], 'a6': [839.352131110656, 0.0], 'a7': [0.0, 0.0], 'a8': [-4096.0, 0.0], 'a9': [-16931.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.47351194405958, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [16.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '98.1', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [16.0, 0]], [[1.0, 0], [52.459508194416, 0], [19683.0, 0]], [[1.0, 0], [1836.08278680456, 0], [1953125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-9380.0, 0], [2357947691.0, 0]], [[1.0, 0], [179044.30146754184, 0], [10604499373.0, 0]], [[1.0, 0], [97889.44229078027, 0], [118587876497.0, 0]], [[1.0, 0], [562733.1444015005, 0], [322687697779.0, 0]], [[1.0, 0], [978936.0, 0], [1801152661463.0, 0]], [[1.0, 0], [4317214.0, 0], [14507145975869.0, 0]], [[1.0, 0], [7974579.678665955, 0], [26439622160671.0, 0]], [[1.0, 0], [-2714394.0, 0], [129961739795077.0, 0]], [[1.0, 0], [9002366.363210954, 0], [327381934393961.0, 0]], [[1.0, 0], [34755692.0, 0], [502592611936843.0, 0]], [[1.0, 0], [42177549.507326856, 0], [1119130473102767.0, 0]], [[1.0, 0], [-68067926.0, 0], [3299763591802133.0, 0]], [[1.0, 0], [-34231770.098659635, 0], [8662995818654939.0, 0]], [[1.0, 0], [-165832531.70730275, 0], [11694146092834140, 0]], [[1.0, 0], [-242944420.0, 0], [27206534396294948, 0]], [[1.0, 0], [94292464.0, 0], [45848500718449030, 0]], [[1.0, 0], [133334443.43545216, 0], [58871586708267910, 0]], [[1.0, 0], [-677625160.0, 0], [119851595982618320, 0]], [[1.0, 0], [441313461.8456887, 0], [186940255267540400, 0]], [[1.0, 0], [555277599.0969101, 0], [350356403707485200, 0]], [[1.0, 0], [-1268945666.6901386, 0], [760231058654565200, 0]], [[1.0, 0], [1368299201.3951168, 0], [1093685272684361000, 0]], [[1.0, 0], [-192151519.42794943, 0], [1304773183829244700, 0]], [[1.0, 0], [1048549940.0, 0], [1838459212420154600, 0]], [[1.0, 0], [-2037576178.0, 0], [2171893279442309400, 0]], [[1.0, 0], [470998718.0, 0], [3004041937984268300, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-98-1.1-c9-0-0', 'leading_term': '0.041795057078930304235587396005324', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/98/10/a/d/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.0417950570789303, 0.027480185122207432, -0.015143380449007995, -0.08511830758111008, -0.18086835710035912, -0.3002270679412593, -0.4404773459546807, -0.5984013900079806, -0.7703402335139055, -0.9522620289323251, -1.1398380586183023, -1.3285253192528708, -1.513654400779558, -1.6905212662459403, -1.8544814383414145, -2.0010450139886324, -2.1259708624384293, -2.225358317329523, -2.2957346514758723, -2.3341366270123287, -2.338184445061966, -2.306146480119247, -2.2369932763461295, -2.1304394069735157, -1.9869719544609372, -1.8078645578291024, -1.5951761937610838, -1.3517341079988954, -1.0811005907306344, -0.7875235906777607, -0.475871483166774, -0.15155264243440977, 0.17957918824758118, 0.5113323901335555, 0.8372961487641716, 1.1509683174114582, 1.4458901590863433, 1.715785390472567, 1.954700719418283, 2.157144884130342, 2.3182230749703563, 2.4337635560073814, 2.5004333095008517, 2.515839607266605, 2.478614571897976, 2.388480029800803, 2.24629027672657, 2.05405077259799, 1.8149112513173589, 1.5331322660201772, 1.2140247816614032, 0.8638630634267097, 0.48977177766370183, 0.09958890634890809, -0.298293240540221, -0.6951059663214114, -1.0818975085206126, -1.4497375976116693, -1.7899286211567076, -2.0942183657882714, -2.3550090268129047, -2.565557019948735, -2.720158114108728, -2.8143125372575373, -2.844864994517575, -2.810114980017092, -2.7098933580797953, -2.545601927127709, -2.320213548147237, -2.0382314010134546, -1.7056070040751472, -1.3296177686816537, -0.9187060306464765, -0.4822826719147874, -0.0304995827645596, 0.4260037185513539, 0.8763730320143518, 1.3098248933066277, 1.7159367247361053, 2.0849335424667585, 2.4079628317832555, 2.677349237723587, 2.886821012340264, 3.031700715988581, 3.109053483951619, 3.1177872282601338, 3.058700425820824, 2.9344746174054666, 2.7496103690749187, 2.5103071823677894, 2.22428963011844, 1.900583784450109, 1.5492497326933654, 1.1810775849963964, 0.8072558044837225, 0.43902188037552903, 0.08730626520178668, -0.23761893473390364, -0.5264748256186942, -0.7712826486631943, -0.9656318490732916, -1.1048993702514427, -1.1864116211864808, -1.2095422827626652, -1.1757411390259864, -1.088491383036073, -0.9531952828536122, -0.7769906208282212, -0.5685028508326239, -0.3375403613308358, -0.09474249403004169, 0.14880804236424655, 0.38199509081007693, 0.5940868235679838, 0.7751461987183482, 0.9164187494720867, 1.0106827627259034, 1.0525478817012437, 1.0386897072496808, 0.9680100366764162, 0.8417149089125462, 0.6633055409993527, 0.4384804449762099, 0.17495039262741194, -0.11782867743546827, -0.4289963731348503, -0.7466906223451263, -1.0584981747151865, -1.3519362047258527, -1.6149466789833018, -1.8363841175082003, -2.0064770893785644, -2.1172442772673814, -2.162847232514709, -2.139863999522498, -2.0474705598740446, -1.8875204451826673, -1.6645167761119604, -1.385475260028598, -1.0596811568545308, -0.6983477221465099, -0.31418797021961686, 0.0790844204428603, 0.467305793515167, 0.8364427847373151, 1.1731782692442887, 1.4654781384862618, 1.7031141491405548, 1.8781192426179383, 1.9851539452399267, 2.0217656689686607, 1.9885268380208636, 1.8890426219016858, 1.7298244758284202, 1.5200314585144235, 1.2710871742689833, 0.9961859165033555, 0.7097069146621473, 0.42656025582656665, 0.16149183465598219, -0.07162261959796425, -0.260462942255139, -0.39489777080727057, -0.4675353524725289, -0.47416437447964804, -0.4140613212486123, -0.29014610937010105, -0.1089739992517063, 0.11944121545351652, 0.3819702735786996, 0.6628676932644766, 0.9444097188003845, 1.2076466239815398, 1.4332390428374318, 1.6023431938068833, 1.6975065001990068, 1.703533391642899, 1.6082811329389, 1.4033474253467806, 1.0846152346830966, 0.6526257093234293, 0.11275696494854774, -0.5248053396570437, -1.245310668464885, -2.029895001495633, -2.856226818684528, -3.6993242850471035, -4.532511808692573, -5.328476936157872, -6.060382948480379, -6.702988835924113, -7.2337267874681395, -7.63368806614761, -7.888471181612243, -7.988851535981792, -7.931239018428262, -7.717899064893242, -7.356923096758256, -6.8619455446557405, -6.251616333404842, -5.548849201334441, -4.779876995690132, -3.9731545899001417, -3.158157820528869, -2.3641324274530335, -1.618850081810533, -0.9474289987540581, -0.37127427998412693, 0.09281192643812164, 0.43330792945852536, 0.644404895931766, 0.7261728820227974, 0.684451932810599, 0.5304729875164813, 0.280226568039478, -0.04639025614316881, -0.4266069857837454, -0.8359420573583763, -1.2494368792607622, -1.6429000544680417, -1.994099477205112, -2.2838423318822474, -2.496888459784795, -2.622650857632003, -2.655647843325542, -2.595684142260069, -2.4477521746070576, -2.221659441311899, -1.9314023510535452, -1.5943203343104912, -1.2300759224554962, -0.8595159743108026, -0.5034758679576298, -0.1815918449133122, 0.08881343023407655, 0.2937106907428128, 0.4231549093131495, 0.47184289192052986, 0.43940598340269876, 0.3304207493852608, 0.1541361065456714, -0.07606876665596443, -0.3434661726905013, -0.6289579770052759, -0.9121952453992129, -1.1727761397535437, -1.3914537438903227, -1.5512842797390671, -1.6386489100483004, -1.6440889138508514, -1.5629041498810936, -1.395477868252247, -1.147306386404898, -0.8287290599179924, -0.45437140004910737, -0.04233111781617603, 0.38684768214999865], 'positive_zeros': ['0.12036122011254254792983075852297', '2.21196979229354497086175423702049', '3.74422961774375350151341401908449', '5.20782688521304806896483376776638', '6.76825029591838927734460603952390', '7.76157571024312546689075818225970', '8.691130294232481270410143328925843', '9.970244849056229712471789460756283', '11.22709924927035041240914086657372', '11.77731890479229605392023752249431'], 'prelabel': '2-98-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.104471264215205, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12036122011254254792983075852', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21196979229354497086175423702', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74422961774375350151341401908', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 50.47351194405958, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/10/a/d/1/1'], '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': '2-98-1.1-c9-0-0', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-98-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.104471264215205, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12036122011254254792983075852', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '152575972919866597638477261074', 'Lhash_array': ['152575972919866597638477261074'], 'factors': ['2-98-1.1-c9-0-0'], 'label': '2-98-1.1-c9-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/10/a/d/1/1'}