-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2827312852065059745596824333939', 'a10': [0.0, 0.0], 'a2': [-0.12493236817324022, -0.7085266683026834], 'a3': [0.9455153673364087, -0.793381596004431], 'a4': [1.39298329849309, -0.5070044574814373], 'a5': [0.0, 0.0], 'a6': [-0.6802574928952138, -0.5708038113939551], 'a7': [0.6459696200993271, -1.1188522021580003], 'a8': [-1.2527117156057346, -2.169760338665906], 'a9': [-0.2563995800100253, 1.4541142766684725], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-2.4058579705567134, 3.6348105075104993]]]], 'bad_primes': [5, 19], 'central_character': '475.351', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1449446630009623033916570849542', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.12493236817324022, 0.7085266683026834], [-1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [-0.9455153673364087, 0.793381596004431], [0.520944533000791, -2.9544232590366244]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.6459696200993271, 1.1188522021580003], [-3.5, -6.06217782649107]], [[1.0, 0], [2.8838118292012527, 4.994908607644711], [-5.5, 9.526279441628825]], [[1.0, 0], [1.801247807042919, 1.5114263705485977], [2.2574263096700946, 12.802500789158705]], [[1.0, 0], [-1.1894828855676502, -6.745892663666227], [-15.974774553360442, 5.814342436536369]], [[1.0, 0], [-2.4058579705567134, 3.6348105075104993]], [[1.0, 0], [-5.328033797834821, 1.9392457095761835], [17.619022191736494, -14.784115022790404]], [[1.0, 0], [1.045558535984671, -5.929657116475974], [-27.251086002791343, -9.918584156444393]], [[1.0, 0], [-1.1944488811006853, 2.0688461491101835], [-15.5, -26.846787517317598]], [[1.0, 0], [-4.531206500493377, 0], [37.0, 0]], [[1.0, 0], [3.511767417031723, -2.9467227444117077], [7.119575284344144, -40.37711787350053]], [[1.0, 0], [-0.26031789056898974, -0.09474796361407883], [32.93991105411605, 27.639867216521193]], [[1.0, 0], [0.08804296745772831, -0.49931648068820816], [-44.16555317693769, -16.07494673630643]], [[1.0, 0], [6.756035461555219, -2.4589958096530236], [40.60035548530583, -34.067743313386586]], [[1.0, 0], [-1.000942035104263, -5.6766243661779585], [-55.44186462636859, 20.179188456214455]], [[1.0, 0], [-6.772734192511464, 2.4650736506711164], [46.728711030257664, -39.2100441908789]], [[1.0, 0], [-1.7750119421190584, 10.066592956944138], [-62.95940559265586, -22.915349602819806]], [[1.0, 0], [-1.0520722639059765, -0.38292298835883215], [54.38915546144744, 45.63792028774429]], [[1.0, 0], [1.8329803466740329, -1.5380531328493838], [12.676316969685915, -71.89096596989118]], [[1.0, 0], [10.796917859766557, -9.059689793981505], [13.718206035687498, -77.79981248796443]], [[1.0, 0], [-0.6086090479751559, 1.0541417930390944], [-41.5, -71.88010851410841]], [[1.0, 0], [6.852394164219455, 5.74984141587789], [15.4546878123568, 87.64789001808651]], [[1.0, 0], [-1.8397729334491641, -10.433870789694987], [-91.15018421623311, 33.17595390258987]], [[1.0, 0], [-1.655498145328928, -1.3891278831601745], [17.538465944359967, 99.46558305423301]], [[1.0, 0], [-4.541542632189763, -7.866182583692764], [-51.5, 89.20061658979718]], [[1.0, 0], [1.9343246753289494, -3.350348616003913], [-53.5, -92.66471820493493]], [[1.0, 0], [-15.685198795987931, -5.7089454802876825], [83.49884429996861, 70.06384945583278]], [[1.0, 0], [-18.082193427754618, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-475-19.9-c1-0-25', '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/475/2/l/b/351/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8192357286339702, 1.9812538145019998, 2.152816327132334, 2.3321519418233856, 2.513373924705331, 2.6869157535278827, 2.8403552103967726, 2.9594646646266844, 3.0294040913865032, 3.036027015027079, 2.9672766959701264, 2.8146232402816778, 2.5744520581860435, 2.2492758700750346, 1.8486162815814775, 1.3893931649980995, 0.8956747220181637, 0.3976801542435173, -0.07001009942705297, -0.4709979986610674, -0.770229447152424, -0.9375366521946314, -0.9512321397496846, -0.8013566113739692, -0.49215174405929357, -0.04334739092761709, 0.5100722296268928, 1.1198261412901769, 1.7280380527648442, 2.2724848606693575, 2.6929686081353514, 2.938181458867467, 2.972278956969679, 2.780305718498532, 2.3716533759024117, 1.780884819644846, 1.065527494777202, 0.30079974828668904, -0.42835148086488317, -1.037109636905405, -1.4514007391604267, -1.617887225702921, -1.511917783439849, -1.142157929553768, -0.5509834856603784, 0.18974674708240524, 0.987274251579275, 1.7399410296487647, 2.3510722598872102, 2.742793717927799, 2.8676919190396366, 2.7164009790203356, 2.3197005652806943, 1.7444836314473984, 1.0838983438411038, 0.4429427053935197, -0.0783702046386312, -0.4016103031873096, -0.48349038374228787, -0.3239242615692036, 0.03308670983057714, 0.5062605927858279, 0.990729850612788, 1.3765369059556325, 1.568843306087066, 1.5062555369034243, 1.1737848895284313, 0.6077275260092997, -0.10891674704481165, -0.8601783785315973, -1.5179405519967228, -1.9662957932953842, -2.124964866070404, -1.9671845674772397, -1.5282316287831195, -0.9023129418651904, -0.22767300891523035, 0.3379277393625471, 0.6471678628437675, 0.5930016542175695, 0.13247979318419864, -0.7005373373774878, -1.7969833524038852, -2.9890626556337407, -4.07921418317575, -4.876523791138508, -5.233746336340206, -5.0775756741871465, -4.425747665253809, -3.3868776249296575, -2.1422268119891608, -0.9122392214541866, 0.08604816613777193, 0.6824458012304624, 0.7890612101871713, 0.42016651437161784, -0.30820762342411506, -1.1996213209822795, -2.015842372559644, -2.5252972911102445, -2.5515853326325604, -2.011933345866207, -0.937267018164127, 0.530779678194575, 2.1658202034794223, 3.7006368119476605, 4.880108332825218, 5.512073324579349, 5.505320048182415, 4.886543572759799, 3.7926185090447975, 2.439935620748006, 1.0776387556612064, -0.06479374702030166, -0.8239127454926417, -1.1323116380381277, -1.0258099201924245, -0.6266889456924736, -0.10752230509430392, 0.3552482097924283, 0.6264152185259064, 0.644599446817372, 0.4343043086649363, 0.09459725456584189, -0.2324398625305696, -0.40508322948917, -0.32555509848362474, 0.028038015599645087, 0.590448687153053, 1.2224582961186818, 1.7457735834239803, 1.9909942477023386, 1.8461112045512253, 1.2922895076708087, 0.41648421044229905, -0.6038532987487059, -1.5414758432066122, -2.1760122392924495, -2.3524061081297045, -2.025681668787394, -1.2793927282770674, -0.3113958632372874, 0.6111310448800689, 1.2173209910041856, 1.3028775862307056, 0.7869515400836447, -0.25972955256100094, -1.6240518086413396, -2.9962795826316224, -4.042148623279083, -4.4838615373169235, -4.169677016894632, -3.1141155082192196, -1.4979093304549644, 0.3730233459443437, 2.1397045910223857, 3.4752096670227903, 4.161034538427606, 4.13506659261072, 3.498860741883233, 2.482679853882008, 1.3780727949651665, 0.4565634608272175, -0.10314943631691877, -0.25937900202690223, -0.11082337578933364, 0.1416543154584268, 0.26380540857386087, 0.06740611391216791, -0.5230281355395202, -1.4363609173067406, -2.464886051245231, -3.3169541368739472, -3.6984017145855455, -3.400189612547611, -2.3670571557640407, -0.7265439432549999, 1.2316726217658378, 3.1223848074677436, 4.560533863661759, 5.2603797515228035, 5.110896984301668, 4.206125972187089, 2.8213443962538873, 1.3408668554837069, 0.1568232061310184, -0.4334822445915407, -0.3035009201930249, 0.47403069109186, 1.6533046526629793, 2.8882820516569327, 3.8309298385579447, 4.2266638454890275, 3.980039179640038, 3.1727895147825147, 2.030525901240092, 0.8495406475442846, -0.09329260597244338, -0.6200255356042177, -0.6969159511396239, -0.43287221347357974, -0.033220280440601796, 0.27510970022844705, 0.32211867365107305, 0.051307485704758, -0.4640222528657913, -1.0497437900679771, -1.4951839417425117, -1.630879144624916, -1.393156647176071, -0.85279564569601, -0.19658289468066972, 0.3338030157716174, 0.5264799704915885, 0.27967332411538515, -0.3502143168684124, -1.151295961157336, -1.8122648118952651, -2.0168878226373312, -1.548455016602914, -0.3707883905501228, 1.3419145675868658, 3.2392186414613646, 4.885631598973718, 5.883422669216235, 5.990460844046213, 5.196374139227364, 3.731848300290062, 2.0057801418053804, 0.48727192756702553, -0.43286737704893535, -0.5590942670445005, 0.04984077166805515, 1.0990721936521672, 2.148677326999096, 2.750541341405799, 2.5892573407691915, 1.5834351984543635, -0.08439690535399429, -2.0191507194029943, -3.7303377311824812, -4.778896027648935, -4.908123698493311, -4.118084887963389, -2.6606718840981247, -0.9575987283868628, 0.532036507809572, 1.4521800014467237, 1.6536608065519844, 1.2290823120735674, 0.4690202366430522, -0.24459693993686196, -0.5717969126326008, -0.3301806768195051, 0.44510857974147067, 1.516097711382356, 2.525320034011128], 'positive_zeros': ['2.23035657582304366768926290519067', '3.13557116969080116653558464551154', '4.67500065614795419971120434757329', '5.59450435271631669374658353911459', '6.97822927698599317702663826196314', '7.49030236296050061178468351570562', '8.481896635794222410500191570117873', '9.545684114739642754159141421798975', '10.02383923020512664048906019929029', '11.48720294901338311562054031578640'], 'prelabel': '2-475-19.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5699707025442355, 'root_number': '-0.21805341643828244 + 0.9759368358554733*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.284985351272', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.23035657582304366768926290519', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13557116969080116653558464551', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.67500065614795419971120434757', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.9', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/l/b/351/2'], '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': '2-475-19.9-c1-0-25', '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': '2-475-19.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.28498535127211777, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.23035657582304366768926290519', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2827312852065059745596824333939', 'Lhash_array': ['2827312852065059745596824333939'], 'label': '2-475-19.9-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/l/b/351/2'}