Table lfunc_lfunctions
L-functions
{'Lhash': '1015420596663610127738782314078', 'a10': [-26.905497055367015, 0.0], 'a2': [5.381099411073403, 0.0], 'a3': [-4.563192248458167, 0.0], 'a4': [20.956230871854522, 0.0], 'a5': [-5.0, 0.0], 'a6': [-24.554991120792955, 0.0], 'a7': [-26.271221400683082, 0.0], 'a8': [69.71876631426741, 0.0], 'a9': [-6.177276503611302, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 85.25775995829522, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [5.0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 17], 'central_character': '1445.1', 'coefficient_field': 'CDF', 'conductor': 1445, 'conductor_radical': 85, 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.381099411073403, 0], [8.0, 0]], [[1.0, 0], [4.563192248458167, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [26.271221400683082, 0], [343.0, 0]], [[1.0, 0], [-2.6842421738601376, 0], [1331.0, 0]], [[1.0, 0], [-62.71000881018703, 0], [2197.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [119.64471489003502, 0], [6859.0, 0]], [[1.0, 0], [-173.4902735499326, 0], [12167.0, 0]], [[1.0, 0], [117.42478763191612, 0], [24389.0, 0]], [[1.0, 0], [-145.28994729522626, 0], [29791.0, 0]], [[1.0, 0], [-190.2457962883593, 0], [50653.0, 0]], [[1.0, 0], [-38.06676299681146, 0], [68921.0, 0]], [[1.0, 0], [-450.87502625597034, 0], [79507.0, 0]], [[1.0, 0], [353.5784745274516, 0], [103823.0, 0]], [[1.0, 0], [-24.35836060754111, 0], [148877.0, 0]], [[1.0, 0], [496.4581663080359, 0], [205379.0, 0]], [[1.0, 0], [-825.2054689724699, 0], [226981.0, 0]], [[1.0, 0], [-864.4746428531014, 0], [300763.0, 0]], [[1.0, 0], [-521.2269220089976, 0], [357911.0, 0]], [[1.0, 0], [-192.58856733909246, 0], [389017.0, 0]], [[1.0, 0], [-847.5417859156759, 0], [493039.0, 0]], [[1.0, 0], [-265.8813991929173, 0], [571787.0, 0]], [[1.0, 0], [-718.2206299817655, 0], [704969.0, 0]], [[1.0, 0], [291.14544176705556, 0], [912673.0, 0]], [[1.0, 0], [-539.7807722483466, 0], [1030301.0, 0]], [[1.0, 0], [-1492.3854635737912, 0], [1092727.0, 0]], [[1.0, 0], [1235.1305179590893, 0], [1225043.0, 0]], [[1.0, 0], [844.2658779647261, 0], [1295029.0, 0]], [[1.0, 0], [1307.7497884382474, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20733165, 'index': 103, 'label': '2-1445-1.1-c3-0-103', 'leading_term': '4.43239644640775152317002010470', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1445/4/a/r/1/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [4.432396446407751, 4.404233757383252, 4.320034056048641, 4.1806627717334655, 3.9875632013030016, 3.742757218192966, 3.4488449762218125, 3.1090024038580206, 2.726975056478714, 2.307066745001398, 1.854121298521217, 1.3734958516880165, 0.8710241759260646, 0.3529687947444967, -0.17403906882322387, -0.7030722795943868, -1.2269934294187785, -1.7385529450185555, -2.2304987477697176, -2.6956960000638897, -3.127254928674944, -3.518664195989806, -3.8639268155029227, -4.157695198801341, -4.395401596731208, -4.57337997544763, -4.688975264436809, -4.740635941440713, -4.7279860881713685, -4.651873366377965, -4.514389827195797, -4.318863073618722, -4.069816036795705, -3.772894486421477, -3.4347623529224207, -3.0629659682129513, -2.665769401410436, -2.251964140785915, -1.83065741494616, -1.4110444143551288, -1.0021705277868045, -0.6126904071049875, -0.25063118047822386, 0.0768325842905408, 0.363584535200041, 0.604745421150253, 0.7968183413084858, 0.9377942986960834, 1.0272130737811271, 1.0661757574308386, 1.057306819559061, 1.004665294786278, 0.9136064839175281, 0.7905974359872388, 0.642991319437098, 0.47876753804268773, 0.30624602164060427, 0.13378544961673744, -0.03052382217668525, -0.17916072300037666, -0.3054566954176306, -0.4038498115369938, -0.47009911548523864, -0.5014497174728807, -0.49674079904318225, -0.4564507261112938, -0.38267584161254675, -0.2790421395446815, -0.15055180706448842, -0.0033694482275204328, 0.15544444969715127, 0.31824270411567884, 0.4771309625612567, 0.6243234808840513, 0.7524998494498251, 0.8551467750657854, 0.926869131093182, 0.9636553166729358, 0.9630835177829618, 0.9244577036957188, 0.8488650536245969, 0.7391498878996164, 0.5998029432603463, 0.43676882398883726, 0.2571785006493755, 0.0690176244011918, -0.11925501880263943, -0.2991215642771066, -0.4624319665620395, -0.6018226113021498, -0.7111050308840949, -0.785603686029766, -0.8224234318215254, -0.8206300038996253, -0.7813305614811816, -0.7076458770945095, -0.6045709864373977, -0.47872677872531094, -0.33801085536444164, -0.1911617247953743, -0.04725573396411778, 0.0848392352935602, 0.19702563309522247, 0.2825235865442098, 0.3363726532179688, 0.3558574940134035, 0.34082918693483955, 0.2938977288785372, 0.22047661324354548, 0.1286670434631579, 0.028977082377826067, -0.06612049061054198, -0.14277903233700384, -0.18649630334039977, -0.18293069633297734, -0.11877882491338325, 0.017327831821085864, 0.2339534093280857, 0.5360631791543811, 0.9243514042299568, 1.3947357228493076, 1.9380566951586282, 2.5400132579551435, 3.1813548837264483, 3.8383396150270728, 4.48345434121737, 5.08638028623272, 5.6151733322464334, 6.037616197389879, 6.3226882987263515, 6.442090011627582, 6.3717515597089704, 6.093253406818019, 5.595085110556531, 4.873673312221138, 3.934116880635868, 2.7905780108739173, 1.4662919314091947, -0.006825752582190639, -1.5889768590985833, -3.2336671691061327, -4.889246048846454, -6.50074513478291, -8.011945550582803, -9.367589373154429, -10.51564087407933, -11.409497087405503, -12.01004595800921, -12.287473947485381, -12.222733513676626, -11.808594078965445, -11.050217455175817, -9.965219460934724, -8.583202710473119, -6.944770171778373, -5.100053881019877, -3.1068169075643333, -1.0282080571118601, 1.069733267597769, 3.1207111561702603, 5.060827114273866, 6.831132266665349, 8.37995987236256, 9.664929729977302, 10.654531166670946, 11.329211298573414, 11.681919158323057, 11.718082913214598, 11.455025384076839, 10.92085096254796, 10.152863336618266, 9.195596757832938, 8.098562647656788, 6.913827090523823, 5.693542421251896, 4.487557236239579, 3.341223650462712, 2.29350876358345, 1.375499724534562, 0.6093694577918146, 0.007844275410822962, -0.4258133056771119, -0.697321617003966, -0.8204391129740193, -0.815632815562444, -0.7084433952778396, -0.527649615930344, -0.3033440088944904, -0.06503414853050805, 0.16012034140088882, 0.34883562234741494, 0.4829133734373669, 0.55007071825616, 0.5443533176356808, 0.4661211800126641, 0.32162357538401903, 0.12220486082823558, -0.11679454536972825, -0.3773597614591783, -0.6402507941857092, -0.8864785626743034, -1.0987068896027108, -1.2624867172116792, -1.3672418685344285, -1.4069439560339203, -1.3804363154531847, -1.2913916209203937, -1.1479134568263316, -0.9618168594039463, -0.7476450248328688, -0.5214975033094794, -0.29975801827923687, -0.09781667761195201, 0.0711186944309931, 0.19703409980907222, 0.2738687514210329, 0.2999656145470472, 0.2781788884707129, 0.21562925022506613, 0.12312354263369059, 0.014280445340547603, -0.09557425697780558, -0.19066150519854333, -0.2560586041422144, -0.2789660264001916, -0.2498344998386563, -0.16326434811578097, -0.018604468411146383, 0.17980069485103173, 0.42274270645651546, 0.6966582394675311, 0.9844867637234977, 1.2668214704152678, 1.523275189858926, 1.7339654132859845, 1.8810115174574937, 1.9499338554749401, 1.9308489338907613, 1.8193672919697539, 1.617120209516668, 1.331866738408823, 0.9771620685835501, 0.5715998483695341, 0.1376725263439885, -0.2996772317564257, -0.7147166493574201, -1.0826792509865633, -1.3814925445917958, -1.5933510395720927, -1.7060169769021232, -1.7137482956750882, -1.6177783148904095, -1.4263027404610298, -1.1539647881854207, -0.8208659613486197, -0.45116567045941736, -0.07136477255013951], 'positive_zeros': ['0.801025611064115405256060537452293', '2.50514737139086232076545907483271', '3.38719825522719364651300482242740', '4.04424775103568744296316575262394', '5.00181173938298349501035637659862', '5.87955361345085514302755720993464', '6.46250448833735111961061389276875', '6.79094221669800660919747694667815', '8.085676885297723195003283249419504', '9.227887657325856007794671499924656'], 'prelabel': '2-1445-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.233512872049035, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.801025611064115405256060537452', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.50514737139086232076545907483', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.38719825522719364651300482243', 'prec': 100}}