Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(71,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.ba (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 575.16 | ||
Character | \(\chi\) | \(=\) | 756.575 |
Dual form | 756.2.ba.a.71.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.246614 | + | 1.39255i | −0.174382 | + | 0.984678i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.87836 | − | 0.686842i | −0.939182 | − | 0.343421i | ||||
\(5\) | 3.28588 | − | 1.89710i | 1.46949 | − | 0.848410i | 0.470075 | − | 0.882626i | \(-0.344227\pi\) |
0.999414 | + | 0.0342161i | \(0.0108934\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | − | 0.500000i | −0.327327 | − | 0.188982i | ||||
\(8\) | 1.41969 | − | 2.44632i | 0.501936 | − | 0.864905i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.83146 | + | 5.04359i | 0.579158 | + | 1.59492i | ||||
\(11\) | −0.147235 | + | 0.255018i | −0.0443930 | + | 0.0768909i | −0.887368 | − | 0.461062i | \(-0.847469\pi\) |
0.842975 | + | 0.537953i | \(0.180802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.99299 | − | 3.45197i | −0.552757 | − | 0.957404i | −0.998074 | − | 0.0620307i | \(-0.980242\pi\) |
0.445317 | − | 0.895373i | \(-0.353091\pi\) | |||||||
\(14\) | 0.909846 | − | 1.08267i | 0.243167 | − | 0.289356i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.05650 | + | 2.58028i | 0.764124 | + | 0.645069i | ||||
\(17\) | 3.60857i | 0.875207i | 0.899168 | + | 0.437603i | \(0.144173\pi\) | ||||
−0.899168 | + | 0.437603i | \(0.855827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.02570i | − | 1.38239i | −0.722668 | − | 0.691195i | \(-0.757085\pi\) | ||
0.722668 | − | 0.691195i | \(-0.242915\pi\) | |||||||
\(20\) | −7.47508 | + | 1.30657i | −1.67148 | + | 0.292158i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.318814 | − | 0.267922i | −0.0679715 | − | 0.0571212i | ||||
\(23\) | −2.37532 | − | 4.11418i | −0.495289 | − | 0.857865i | 0.504696 | − | 0.863297i | \(-0.331604\pi\) |
−0.999985 | + | 0.00543156i | \(0.998271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.69800 | − | 8.13717i | 0.939600 | − | 1.62743i | ||||
\(26\) | 5.29852 | − | 1.92403i | 1.03913 | − | 0.377334i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.28329 | + | 1.53400i | 0.242519 | + | 0.289900i | ||||
\(29\) | −0.904457 | − | 0.522189i | −0.167954 | − | 0.0969680i | 0.413667 | − | 0.910428i | \(-0.364248\pi\) |
−0.581621 | + | 0.813460i | \(0.697581\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.56802 | − | 3.21470i | 1.00005 | − | 0.577376i | 0.0917836 | − | 0.995779i | \(-0.470743\pi\) |
0.908262 | + | 0.418403i | \(0.137410\pi\) | |||||||
\(32\) | −4.34693 | + | 3.61998i | −0.768435 | + | 0.639928i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.02510 | − | 0.889923i | −0.861797 | − | 0.152621i | ||||
\(35\) | −3.79421 | −0.641338 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.86636 | −0.635626 | −0.317813 | − | 0.948153i | \(-0.602948\pi\) | ||||
−0.317813 | + | 0.948153i | \(0.602948\pi\) | |||||||
\(38\) | 8.39106 | + | 1.48602i | 1.36121 | + | 0.241064i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0240018 | − | 10.7316i | 0.00379502 | − | 1.69682i | ||||
\(41\) | 10.6945 | − | 6.17450i | 1.67021 | − | 0.964295i | 0.702687 | − | 0.711499i | \(-0.251983\pi\) |
0.967520 | − | 0.252796i | \(-0.0813501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.852502 | − | 0.492192i | −0.130005 | − | 0.0750586i | 0.433587 | − | 0.901112i | \(-0.357248\pi\) |
−0.563592 | + | 0.826053i | \(0.690581\pi\) | |||||||
\(44\) | 0.451718 | − | 0.377890i | 0.0680991 | − | 0.0569691i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.31496 | − | 2.29313i | 0.931091 | − | 0.338103i | ||||
\(47\) | −1.68371 | + | 2.91626i | −0.245594 | + | 0.425381i | −0.962298 | − | 0.271996i | \(-0.912316\pi\) |
0.716705 | + | 0.697377i | \(0.245650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 10.1728 | + | 8.54892i | 1.43865 | + | 1.20900i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.37261 | + | 7.85292i | 0.190347 | + | 1.08900i | ||||
\(53\) | 2.03029i | 0.278882i | 0.990230 | + | 0.139441i | \(0.0445306\pi\) | ||||
−0.990230 | + | 0.139441i | \(0.955469\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.11728i | 0.150654i | ||||||||
\(56\) | −2.45265 | + | 1.40873i | −0.327749 | + | 0.188250i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.950223 | − | 1.13072i | 0.124770 | − | 0.148471i | ||||
\(59\) | 4.15275 | + | 7.19278i | 0.540642 | + | 0.936420i | 0.998867 | + | 0.0475837i | \(0.0151521\pi\) |
−0.458225 | + | 0.888836i | \(0.651515\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.48589 | + | 9.50184i | −0.702397 | + | 1.21659i | 0.265226 | + | 0.964186i | \(0.414553\pi\) |
−0.967623 | + | 0.252400i | \(0.918780\pi\) | |||||||
\(62\) | 3.10346 | + | 8.54650i | 0.394140 | + | 1.08541i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.96897 | − | 6.94603i | −0.496121 | − | 0.868253i | ||||
\(65\) | −13.0975 | − | 7.56183i | −1.62454 | − | 0.937930i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.26153 | − | 5.34715i | 1.13148 | − | 0.653258i | 0.187170 | − | 0.982327i | \(-0.440068\pi\) |
0.944306 | + | 0.329069i | \(0.106735\pi\) | |||||||
\(68\) | 2.47852 | − | 6.77821i | 0.300564 | − | 0.821978i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.935704 | − | 5.28360i | 0.111838 | − | 0.631511i | ||||
\(71\) | −2.73284 | −0.324329 | −0.162164 | − | 0.986764i | \(-0.551848\pi\) | ||||
−0.162164 | + | 0.986764i | \(0.551848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.63292 | 1.01041 | 0.505203 | − | 0.863000i | \(-0.331417\pi\) | ||||
0.505203 | + | 0.863000i | \(0.331417\pi\) | |||||||
\(74\) | 0.953498 | − | 5.38408i | 0.110842 | − | 0.625886i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.13870 | + | 11.3185i | −0.474742 | + | 1.29832i | ||||
\(77\) | 0.255018 | − | 0.147235i | 0.0290620 | − | 0.0167790i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.74756 | + | 2.74100i | 0.534142 | + | 0.308387i | 0.742701 | − | 0.669623i | \(-0.233544\pi\) |
−0.208560 | + | 0.978010i | \(0.566878\pi\) | |||||||
\(80\) | 14.9383 | + | 2.67999i | 1.67016 | + | 0.299632i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.96084 | + | 16.4153i | 0.658265 | + | 1.81277i | ||||
\(83\) | −4.07096 | + | 7.05111i | −0.446846 | + | 0.773960i | −0.998179 | − | 0.0603253i | \(-0.980786\pi\) |
0.551333 | + | 0.834286i | \(0.314120\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.84583 | + | 11.8573i | 0.742534 | + | 1.28611i | ||||
\(86\) | 0.895639 | − | 1.06577i | 0.0965792 | − | 0.114925i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.414829 | + | 0.722231i | 0.0442209 | + | 0.0769900i | ||||
\(89\) | 3.35572i | 0.355706i | 0.984057 | + | 0.177853i | \(0.0569151\pi\) | ||||
−0.984057 | + | 0.177853i | \(0.943085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.98599i | 0.417845i | ||||||||
\(92\) | 1.63593 | + | 9.35939i | 0.170557 | + | 0.975784i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.64580 | − | 3.06383i | −0.376036 | − | 0.316010i | ||||
\(95\) | −11.4314 | − | 19.7997i | −1.17283 | − | 2.03141i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.74076 | − | 11.6753i | 0.684421 | − | 1.18545i | −0.289198 | − | 0.957269i | \(-0.593389\pi\) |
0.973619 | − | 0.228182i | \(-0.0732781\pi\) | |||||||
\(98\) | −1.32929 | + | 0.482699i | −0.134278 | + | 0.0487599i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.4135 | + | 12.0578i | −1.44135 | + | 1.20578i | ||||
\(101\) | 11.1419 | + | 6.43278i | 1.10866 | + | 0.640085i | 0.938482 | − | 0.345328i | \(-0.112232\pi\) |
0.170178 | + | 0.985413i | \(0.445566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.71860 | + | 4.45634i | −0.760537 | + | 0.439096i | −0.829488 | − | 0.558524i | \(-0.811368\pi\) |
0.0689517 | + | 0.997620i | \(0.478035\pi\) | |||||||
\(104\) | −11.2741 | − | 0.0252150i | −1.10551 | − | 0.00247254i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.82728 | − | 0.500699i | −0.274609 | − | 0.0486322i | ||||
\(107\) | 2.28113 | 0.220525 | 0.110263 | − | 0.993902i | \(-0.464831\pi\) | ||||
0.110263 | + | 0.993902i | \(0.464831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0544 | −0.963032 | −0.481516 | − | 0.876437i | \(-0.659914\pi\) | ||||
−0.481516 | + | 0.876437i | \(0.659914\pi\) | |||||||
\(110\) | −1.55586 | − | 0.275537i | −0.148346 | − | 0.0262714i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.35687 | − | 3.76283i | −0.128212 | − | 0.355554i | ||||
\(113\) | −6.07706 | + | 3.50859i | −0.571682 | + | 0.330061i | −0.757821 | − | 0.652463i | \(-0.773736\pi\) |
0.186139 | + | 0.982523i | \(0.440403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.6100 | − | 9.01246i | −1.45564 | − | 0.840416i | ||||
\(116\) | 1.34024 | + | 1.60208i | 0.124438 | + | 0.148749i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.0404 | + | 4.00906i | −1.01635 | + | 0.369064i | ||||
\(119\) | 1.80429 | − | 3.12511i | 0.165399 | − | 0.286479i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.45664 | + | 9.45118i | 0.496059 | + | 0.859199i | ||||
\(122\) | −11.8788 | − | 9.98264i | −1.07546 | − | 0.903786i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.6667 | + | 2.21402i | −1.13751 | + | 0.198825i | ||||
\(125\) | − | 16.6793i | − | 1.49184i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.98999i | − | 0.620262i | −0.950694 | − | 0.310131i | \(-0.899627\pi\) | ||
0.950694 | − | 0.310131i | \(-0.100373\pi\) | |||||||
\(128\) | 10.6515 | − | 3.81398i | 0.941465 | − | 0.337112i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.7602 | − | 16.3740i | 1.20685 | − | 1.43609i | ||||
\(131\) | −5.94819 | − | 10.3026i | −0.519696 | − | 0.900139i | −0.999738 | − | 0.0228940i | \(-0.992712\pi\) |
0.480042 | − | 0.877245i | \(-0.340621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.01285 | + | 5.21841i | −0.261247 | + | 0.452493i | ||||
\(134\) | 5.16212 | + | 14.2158i | 0.445939 | + | 1.22806i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.82772 | + | 5.12305i | 0.756971 | + | 0.439297i | ||||
\(137\) | 0.240419 | + | 0.138806i | 0.0205404 | + | 0.0118590i | 0.510235 | − | 0.860035i | \(-0.329558\pi\) |
−0.489695 | + | 0.871894i | \(0.662892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.51784 | + | 5.49513i | −0.807293 | + | 0.466091i | −0.846015 | − | 0.533159i | \(-0.821005\pi\) |
0.0387220 | + | 0.999250i | \(0.487671\pi\) | |||||||
\(140\) | 7.12690 | + | 2.60602i | 0.602333 | + | 0.220249i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.673957 | − | 3.80561i | 0.0565572 | − | 0.319360i | ||||
\(143\) | 1.17375 | 0.0981542 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.96258 | −0.329075 | ||||||||
\(146\) | −2.12900 | + | 12.0217i | −0.176197 | + | 0.994925i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.26243 | + | 2.65558i | 0.596968 | + | 0.218287i | ||||
\(149\) | −7.22393 | + | 4.17074i | −0.591808 | + | 0.341680i | −0.765812 | − | 0.643065i | \(-0.777663\pi\) |
0.174004 | + | 0.984745i | \(0.444329\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.58601 | + | 2.64773i | 0.373204 | + | 0.215469i | 0.674857 | − | 0.737948i | \(-0.264205\pi\) |
−0.301653 | + | 0.953418i | \(0.597539\pi\) | |||||||
\(152\) | −14.7408 | − | 8.55462i | −1.19564 | − | 0.693871i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.142140 | + | 0.391435i | 0.0114540 | + | 0.0315427i | ||||
\(155\) | 12.1972 | − | 21.1262i | 0.979704 | − | 1.69690i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.66952 | + | 8.08784i | 0.372668 | + | 0.645480i | 0.989975 | − | 0.141242i | \(-0.0451097\pi\) |
−0.617307 | + | 0.786722i | \(0.711776\pi\) | |||||||
\(158\) | −4.98778 | + | 5.93522i | −0.396807 | + | 0.472180i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.41600 | + | 20.1414i | −0.586286 | + | 1.59232i | ||||
\(161\) | 4.75064i | 0.374403i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.6620i | − | 1.22674i | −0.789794 | − | 0.613372i | \(-0.789813\pi\) | ||
0.789794 | − | 0.613372i | \(-0.210187\pi\) | |||||||
\(164\) | −24.3291 | + | 4.25249i | −1.89979 | + | 0.332064i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.81504 | − | 7.40790i | −0.684179 | − | 0.574965i | ||||
\(167\) | −1.43448 | − | 2.48460i | −0.111004 | − | 0.192264i | 0.805172 | − | 0.593042i | \(-0.202073\pi\) |
−0.916175 | + | 0.400778i | \(0.868740\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.44406 | + | 2.50118i | −0.111081 | + | 0.192398i | ||||
\(170\) | −18.2001 | + | 6.60895i | −1.39589 | + | 0.506883i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.26325 | + | 1.51005i | 0.0963219 | + | 0.115140i | ||||
\(173\) | −5.95609 | − | 3.43875i | −0.452833 | − | 0.261443i | 0.256193 | − | 0.966626i | \(-0.417532\pi\) |
−0.709026 | + | 0.705182i | \(0.750865\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.13717 | + | 4.69800i | −0.615113 | + | 0.355135i | ||||
\(176\) | −1.10804 | + | 0.399556i | −0.0835217 | + | 0.0301177i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.67299 | − | 0.827567i | −0.350255 | − | 0.0620288i | ||||
\(179\) | 19.3475 | 1.44610 | 0.723050 | − | 0.690796i | \(-0.242740\pi\) | ||||
0.723050 | + | 0.690796i | \(0.242740\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6872 | −0.943032 | −0.471516 | − | 0.881858i | \(-0.656293\pi\) | ||||
−0.471516 | + | 0.881858i | \(0.656293\pi\) | |||||||
\(182\) | −5.55067 | − | 0.983000i | −0.411443 | − | 0.0728648i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.4368 | − | 0.0300522i | −0.990575 | − | 0.00221547i | ||||
\(185\) | −12.7044 | + | 7.33488i | −0.934045 | + | 0.539271i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.920252 | − | 0.531308i | −0.0672955 | − | 0.0388531i | ||||
\(188\) | 5.16562 | − | 4.32136i | 0.376742 | − | 0.315168i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 30.3911 | − | 11.0358i | 2.20480 | − | 0.800622i | ||||
\(191\) | −4.15917 | + | 7.20389i | −0.300947 | + | 0.521255i | −0.976351 | − | 0.216193i | \(-0.930636\pi\) |
0.675404 | + | 0.737448i | \(0.263969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.39565 | + | 9.34554i | 0.388387 | + | 0.672707i | 0.992233 | − | 0.124395i | \(-0.0396989\pi\) |
−0.603845 | + | 0.797101i | \(0.706366\pi\) | |||||||
\(194\) | 14.5961 | + | 12.2661i | 1.04794 | + | 0.880656i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.344359 | − | 1.97013i | −0.0245971 | − | 0.140724i | ||||
\(197\) | 14.3939i | 1.02553i | 0.858530 | + | 0.512763i | \(0.171378\pi\) | ||||
−0.858530 | + | 0.512763i | \(0.828622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.9925i | − | 1.06279i | −0.847124 | − | 0.531395i | \(-0.821668\pi\) | ||
0.847124 | − | 0.531395i | \(-0.178332\pi\) | |||||||
\(200\) | −13.2364 | − | 23.0451i | −0.935958 | − | 1.62953i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.7057 | + | 13.9292i | −0.823609 | + | 0.980054i | ||||
\(203\) | 0.522189 | + | 0.904457i | 0.0366505 | + | 0.0634805i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.4273 | − | 40.5773i | 1.63623 | − | 2.83404i | ||||
\(206\) | −4.30214 | − | 11.8475i | −0.299744 | − | 0.825454i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.81545 | − | 15.6934i | 0.195216 | − | 1.08814i | ||||
\(209\) | 1.53666 | + | 0.887194i | 0.106293 | + | 0.0613685i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.48466 | − | 1.43452i | 0.171051 | − | 0.0987564i | −0.412030 | − | 0.911170i | \(-0.635180\pi\) |
0.583081 | + | 0.812414i | \(0.301847\pi\) | |||||||
\(212\) | 1.39449 | − | 3.81363i | 0.0957740 | − | 0.261921i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.562559 | + | 3.17658i | −0.0384557 | + | 0.217147i | ||||
\(215\) | −3.73496 | −0.254722 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.42939 | −0.436456 | ||||||||
\(218\) | 2.47954 | − | 14.0011i | 0.167936 | − | 0.948277i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.767394 | − | 2.09866i | 0.0517377 | − | 0.141491i | ||||
\(221\) | 12.4567 | − | 7.19186i | 0.837926 | − | 0.483777i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.5462 | + | 8.39828i | 0.974088 | + | 0.562390i | 0.900480 | − | 0.434897i | \(-0.143215\pi\) |
0.0736082 | + | 0.997287i | \(0.476549\pi\) | |||||||
\(224\) | 5.57454 | − | 0.961530i | 0.372464 | − | 0.0642449i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.38719 | − | 9.32785i | −0.225312 | − | 0.620479i | ||||
\(227\) | −14.3890 | + | 24.9225i | −0.955033 | + | 1.65417i | −0.220742 | + | 0.975332i | \(0.570848\pi\) |
−0.734291 | + | 0.678834i | \(0.762485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.30663 | − | 16.1196i | −0.614999 | − | 1.06521i | −0.990385 | − | 0.138341i | \(-0.955823\pi\) |
0.375385 | − | 0.926869i | \(-0.377510\pi\) | |||||||
\(230\) | 16.3999 | − | 19.5151i | 1.08138 | − | 1.28679i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.56149 | + | 1.47125i | −0.168170 | + | 0.0965921i | ||||
\(233\) | − | 25.3473i | − | 1.66056i | −0.557348 | − | 0.830279i | \(-0.688181\pi\) | ||
0.557348 | − | 0.830279i | \(-0.311819\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7767i | 0.833457i | ||||||||
\(236\) | −2.86008 | − | 16.3629i | −0.186175 | − | 1.06514i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.90690 | + | 3.28324i | 0.253247 | + | 0.212821i | ||||
\(239\) | 12.5884 | + | 21.8038i | 0.814279 | + | 1.41037i | 0.909845 | + | 0.414949i | \(0.136201\pi\) |
−0.0955656 | + | 0.995423i | \(0.530466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.83687 | + | 8.37771i | −0.311570 | + | 0.539656i | −0.978703 | − | 0.205284i | \(-0.934188\pi\) |
0.667132 | + | 0.744939i | \(0.267522\pi\) | |||||||
\(242\) | −14.5069 | + | 5.26783i | −0.932538 | + | 0.338629i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.8308 | − | 14.0800i | 1.07748 | − | 0.901378i | ||||
\(245\) | 3.28588 | + | 1.89710i | 0.209927 | + | 0.121201i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.8005 | + | 12.0092i | −1.32351 | + | 0.764126i | ||||
\(248\) | 0.0406718 | − | 18.1850i | 0.00258266 | − | 1.15475i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 23.2267 | + | 4.11335i | 1.46899 | + | 0.260151i | ||||
\(251\) | −9.27090 | −0.585174 | −0.292587 | − | 0.956239i | \(-0.594516\pi\) | ||||
−0.292587 | + | 0.956239i | \(0.594516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.39892 | 0.0879494 | ||||||||
\(254\) | 9.73388 | + | 1.72383i | 0.610758 | + | 0.108163i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.68435 | + | 15.7732i | 0.167772 | + | 0.985826i | ||||
\(257\) | −12.1695 | + | 7.02607i | −0.759113 | + | 0.438274i | −0.828977 | − | 0.559282i | \(-0.811077\pi\) |
0.0698640 | + | 0.997557i | \(0.477743\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.34837 | + | 1.93318i | 0.208057 | + | 0.120122i | ||||
\(260\) | 19.4080 | + | 23.1998i | 1.20364 | + | 1.43879i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.8137 | − | 5.74237i | 0.976973 | − | 0.354765i | ||||
\(263\) | −3.96550 | + | 6.86845i | −0.244523 | + | 0.423527i | −0.961997 | − | 0.273058i | \(-0.911965\pi\) |
0.717474 | + | 0.696585i | \(0.245298\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.85168 | + | 6.67130i | 0.236607 | + | 0.409815i | ||||
\(266\) | −6.52386 | − | 5.48246i | −0.400003 | − | 0.336151i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.0692 | + | 3.68268i | −1.28700 | + | 0.224955i | ||||
\(269\) | − | 6.36470i | − | 0.388062i | −0.980995 | − | 0.194031i | \(-0.937844\pi\) | ||
0.980995 | − | 0.194031i | \(-0.0621563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.98241i | 0.181169i | 0.995889 | + | 0.0905844i | \(0.0288735\pi\) | ||||
−0.995889 | + | 0.0905844i | \(0.971127\pi\) | |||||||
\(272\) | −9.31111 | + | 11.0296i | −0.564569 | + | 0.668767i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.252584 | + | 0.300563i | −0.0152592 | + | 0.0181577i | ||||
\(275\) | 1.38342 | + | 2.39615i | 0.0834233 | + | 0.144493i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7876 | + | 18.6847i | −0.648164 | + | 1.12265i | 0.335397 | + | 0.942077i | \(0.391130\pi\) |
−0.983561 | + | 0.180576i | \(0.942204\pi\) | |||||||
\(278\) | −5.30498 | − | 14.6092i | −0.318172 | − | 0.876202i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.38659 | + | 9.28184i | −0.321910 | + | 0.554696i | ||||
\(281\) | 7.00028 | + | 4.04161i | 0.417602 | + | 0.241103i | 0.694051 | − | 0.719926i | \(-0.255824\pi\) |
−0.276449 | + | 0.961029i | \(0.589158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.719769 | + | 0.415559i | −0.0427858 | + | 0.0247024i | −0.521240 | − | 0.853410i | \(-0.674530\pi\) |
0.478455 | + | 0.878112i | \(0.341197\pi\) | |||||||
\(284\) | 5.13327 | + | 1.87703i | 0.304604 | + | 0.111381i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.289464 | + | 1.63451i | −0.0171164 | + | 0.0966503i | ||||
\(287\) | −12.3490 | −0.728938 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.97822 | 0.234013 | ||||||||
\(290\) | 0.977228 | − | 5.51808i | 0.0573848 | − | 0.324033i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.2158 | − | 5.92945i | −0.948956 | − | 0.346995i | ||||
\(293\) | −11.2950 | + | 6.52120i | −0.659864 | + | 0.380972i | −0.792225 | − | 0.610229i | \(-0.791077\pi\) |
0.132361 | + | 0.991202i | \(0.457744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.2909 | + | 15.7564i | 1.58894 | + | 0.917373i | ||||
\(296\) | −5.48903 | + | 9.45835i | −0.319043 | + | 0.549756i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.02642 | − | 11.0882i | −0.233244 | − | 0.642323i | ||||
\(299\) | −9.46801 | + | 16.3991i | −0.547549 | + | 0.948383i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.492192 | + | 0.852502i | 0.0283695 | + | 0.0491374i | ||||
\(302\) | −4.81806 | + | 5.73325i | −0.277248 | + | 0.329912i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.5480 | − | 18.4175i | 0.891737 | − | 1.05632i | ||||
\(305\) | 41.6292i | 2.38368i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.6077i | 1.86102i | 0.366266 | + | 0.930510i | \(0.380636\pi\) | ||||
−0.366266 | + | 0.930510i | \(0.619364\pi\) | |||||||
\(308\) | −0.580144 | + | 0.101403i | −0.0330568 | + | 0.00577800i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 26.4112 | + | 22.1952i | 1.50005 | + | 1.26060i | ||||
\(311\) | 6.47968 | + | 11.2231i | 0.367429 | + | 0.636406i | 0.989163 | − | 0.146823i | \(-0.0469047\pi\) |
−0.621734 | + | 0.783229i | \(0.713571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.72105 | + | 6.44505i | −0.210326 | + | 0.364296i | −0.951817 | − | 0.306668i | \(-0.900786\pi\) |
0.741490 | + | 0.670963i | \(0.234119\pi\) | |||||||
\(314\) | −12.4142 | + | 4.50794i | −0.700576 | + | 0.254398i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.03500 | − | 8.40942i | −0.395750 | − | 0.473067i | ||||
\(317\) | 0.272234 | + | 0.157175i | 0.0152902 | + | 0.00882780i | 0.507626 | − | 0.861578i | \(-0.330523\pi\) |
−0.492335 | + | 0.870406i | \(0.663857\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.266336 | − | 0.153769i | 0.0149119 | − | 0.00860940i | ||||
\(320\) | −26.2189 | − | 15.2943i | −1.46568 | − | 0.854975i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.61548 | − | 1.17157i | −0.368667 | − | 0.0652893i | ||||
\(323\) | 21.7442 | 1.20988 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −37.4524 | −2.07748 | ||||||||
\(326\) | 21.8101 | + | 3.86247i | 1.20795 | + | 0.213923i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.0781187 | − | 34.9281i | 0.00431338 | − | 1.92858i | ||||
\(329\) | 2.91626 | − | 1.68371i | 0.160779 | − | 0.0928257i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.2481 | + | 10.5356i | 1.00301 | + | 0.579087i | 0.909137 | − | 0.416497i | \(-0.136742\pi\) |
0.0938717 | + | 0.995584i | \(0.470076\pi\) | |||||||
\(332\) | 12.4897 | − | 10.4484i | 0.685464 | − | 0.573433i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.81367 | − | 1.38484i | 0.208675 | − | 0.0757753i | ||||
\(335\) | 20.2882 | − | 35.1402i | 1.10846 | − | 1.91991i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.76860 | − | 8.25945i | −0.259762 | − | 0.449921i | 0.706416 | − | 0.707797i | \(-0.250311\pi\) |
−0.966178 | + | 0.257876i | \(0.916977\pi\) | |||||||
\(338\) | −3.12688 | − | 2.62774i | −0.170080 | − | 0.142930i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.71485 | − | 26.9744i | −0.255699 | − | 1.46289i | ||||
\(341\) | 1.89326i | 0.102526i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −2.41435 | + | 1.38673i | −0.130173 | + | 0.0747677i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.25746 | − | 7.44608i | 0.336403 | − | 0.400303i | ||||
\(347\) | 6.87336 | + | 11.9050i | 0.368981 | + | 0.639095i | 0.989407 | − | 0.145171i | \(-0.0463733\pi\) |
−0.620425 | + | 0.784266i | \(0.713040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.69604 | − | 15.0620i | 0.465488 | − | 0.806249i | −0.533735 | − | 0.845652i | \(-0.679212\pi\) |
0.999223 | + | 0.0394024i | \(0.0125454\pi\) | |||||||
\(350\) | −4.53544 | − | 12.4900i | −0.242429 | − | 0.667617i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.283142 | − | 1.64153i | −0.0150915 | − | 0.0874940i | ||||
\(353\) | 16.2716 | + | 9.39439i | 0.866047 | + | 0.500013i | 0.866033 | − | 0.499987i | \(-0.166662\pi\) |
1.46597e−5 | 1.00000i | \(0.499995\pi\) | ||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.97979 | + | 5.18449i | −0.476598 | + | 0.275164i | ||||
\(356\) | 2.30485 | − | 6.30326i | 0.122157 | − | 0.334072i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.77136 | + | 26.9423i | −0.252174 | + | 1.42394i | ||||
\(359\) | 14.2512 | 0.752151 | 0.376076 | − | 0.926589i | \(-0.377273\pi\) | ||||
0.376076 | + | 0.926589i | \(0.377273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3091 | −0.911003 | ||||||||
\(362\) | 3.12884 | − | 17.6675i | 0.164448 | − | 0.928582i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.73774 | − | 7.48714i | 0.143497 | − | 0.392433i | ||||
\(365\) | 28.3667 | − | 16.3775i | 1.48478 | − | 0.857240i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.87665 | − | 1.08348i | −0.0979604 | − | 0.0565574i | 0.450219 | − | 0.892918i | \(-0.351346\pi\) |
−0.548180 | + | 0.836360i | \(0.684679\pi\) | |||||||
\(368\) | 3.35555 | − | 18.7040i | 0.174920 | − | 0.975011i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.08107 | − | 19.5003i | −0.368128 | − | 1.01377i | ||||
\(371\) | 1.01515 | − | 1.75829i | 0.0527038 | − | 0.0912857i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.7324 | − | 28.9814i | −0.866370 | − | 1.50060i | −0.865680 | − | 0.500598i | \(-0.833114\pi\) |
−0.000690393 | − | 1.00000i | \(-0.500220\pi\) | |||||||
\(374\) | 0.966817 | − | 1.15046i | 0.0499929 | − | 0.0594891i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.74378 | + | 8.25907i | 0.244642 | + | 0.425929i | ||||
\(377\) | 4.16288i | 0.214399i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.82998i | − | 0.350832i | −0.984494 | − | 0.175416i | \(-0.943873\pi\) | ||
0.984494 | − | 0.175416i | \(-0.0561271\pi\) | |||||||
\(380\) | 7.87300 | + | 45.0426i | 0.403876 | + | 2.31064i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.00603 | − | 7.56841i | −0.460789 | − | 0.387233i | ||||
\(383\) | 3.69911 | + | 6.40704i | 0.189016 | + | 0.327384i | 0.944922 | − | 0.327295i | \(-0.106137\pi\) |
−0.755907 | + | 0.654679i | \(0.772804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.558640 | − | 0.967592i | 0.0284709 | − | 0.0493131i | ||||
\(386\) | −14.3447 | + | 5.20895i | −0.730128 | + | 0.265128i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −20.6807 | + | 17.3007i | −1.04990 | + | 0.878310i | ||||
\(389\) | −15.0318 | − | 8.67863i | −0.762144 | − | 0.440024i | 0.0679209 | − | 0.997691i | \(-0.478363\pi\) |
−0.830065 | + | 0.557667i | \(0.811697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8463 | − | 8.57151i | 0.750810 | − | 0.433480i | ||||
\(392\) | 2.82842 | + | 0.00632591i | 0.142857 | + | 0.000319507i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.0442 | − | 3.54975i | −1.00981 | − | 0.178834i | ||||
\(395\) | 20.7999 | 1.04655 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.91004 | 0.246428 | 0.123214 | − | 0.992380i | \(-0.460680\pi\) | ||||
0.123214 | + | 0.992380i | \(0.460680\pi\) | |||||||
\(398\) | 20.8777 | + | 3.69736i | 1.04651 | + | 0.185332i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 35.3556 | − | 12.7491i | 1.76778 | − | 0.637455i | ||||
\(401\) | 21.0371 | − | 12.1458i | 1.05054 | − | 0.606532i | 0.127742 | − | 0.991807i | \(-0.459227\pi\) |
0.922802 | + | 0.385276i | \(0.125894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.1941 | − | 12.8137i | −1.10556 | − | 0.638298i | ||||
\(404\) | −16.5102 | − | 19.7358i | −0.821415 | − | 0.981894i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.38828 | + | 0.504120i | −0.0688990 | + | 0.0250190i | ||||
\(407\) | 0.569263 | − | 0.985993i | 0.0282173 | − | 0.0488738i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.1299 | + | 33.1340i | 0.945915 | + | 1.63837i | 0.753909 | + | 0.656979i | \(0.228166\pi\) |
0.192006 | + | 0.981394i | \(0.438501\pi\) | |||||||
\(410\) | 50.7282 | + | 42.6305i | 2.50529 | + | 2.10537i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.5591 | − | 3.06916i | 0.865077 | − | 0.151207i | ||||
\(413\) | − | 8.30551i | − | 0.408687i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.8921i | 1.51644i | ||||||||
\(416\) | 21.1594 | + | 7.79085i | 1.03743 | + | 0.381978i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.61442 | + | 1.92108i | −0.0789638 | + | 0.0939631i | ||||
\(419\) | 9.47453 | + | 16.4104i | 0.462861 | + | 0.801699i | 0.999102 | − | 0.0423659i | \(-0.0134895\pi\) |
−0.536241 | + | 0.844065i | \(0.680156\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6034 | − | 18.3656i | 0.516777 | − | 0.895084i | −0.483033 | − | 0.875602i | \(-0.660465\pi\) |
0.999810 | − | 0.0194821i | \(-0.00620175\pi\) | |||||||
\(422\) | 1.38488 | + | 3.81377i | 0.0674150 | + | 0.185652i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.96675 | + | 2.88239i | 0.241207 | + | 0.139981i | ||||
\(425\) | 29.3636 | + | 16.9531i | 1.42434 | + | 0.822344i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.50184 | − | 5.48589i | 0.459827 | − | 0.265481i | ||||
\(428\) | −4.28480 | − | 1.56678i | −0.207113 | − | 0.0757330i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.921092 | − | 5.20110i | 0.0444190 | − | 0.250819i | ||||
\(431\) | 6.24043 | 0.300591 | 0.150295 | − | 0.988641i | \(-0.451977\pi\) | ||||
0.150295 | + | 0.988641i | \(0.451977\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2312 | 0.587795 | 0.293897 | − | 0.955837i | \(-0.405048\pi\) | ||||
0.293897 | + | 0.955837i | \(0.405048\pi\) | |||||||
\(434\) | 1.58558 | − | 8.95322i | 0.0761101 | − | 0.429768i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.8857 | + | 6.90575i | 0.904462 | + | 0.330725i | ||||
\(437\) | −24.7908 | + | 14.3130i | −1.18590 | + | 0.684682i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.4636 | + | 10.0826i | 0.833492 | + | 0.481217i | 0.855047 | − | 0.518551i | \(-0.173528\pi\) |
−0.0215550 | + | 0.999768i | \(0.506862\pi\) | |||||||
\(440\) | 2.73322 | + | 1.58619i | 0.130301 | + | 0.0756186i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.94300 | + | 19.1201i | 0.330245 | + | 0.909450i | ||||
\(443\) | 14.2028 | − | 24.6000i | 0.674795 | − | 1.16878i | −0.301733 | − | 0.953392i | \(-0.597565\pi\) |
0.976529 | − | 0.215387i | \(-0.0691014\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.36615 | + | 11.0265i | 0.301784 | + | 0.522706i | ||||
\(446\) | −15.2823 | + | 18.1852i | −0.723637 | + | 0.861093i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.0357847 | + | 7.99992i | −0.00169067 | + | 0.377961i | ||||
\(449\) | 8.88596i | 0.419354i | 0.977771 | + | 0.209677i | \(0.0672413\pi\) | ||||
−0.977771 | + | 0.209677i | \(0.932759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.63641i | 0.171232i | ||||||||
\(452\) | 13.8248 | − | 2.41643i | 0.650263 | − | 0.113659i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.1572 | − | 26.1836i | −1.46228 | − | 1.22886i | ||||
\(455\) | 7.56183 | + | 13.0975i | 0.354504 | + | 0.614019i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.43702 | − | 9.41720i | 0.254333 | − | 0.440518i | −0.710381 | − | 0.703817i | \(-0.751477\pi\) |
0.964714 | + | 0.263299i | \(0.0848106\pi\) | |||||||
\(458\) | 24.7423 | − | 8.98459i | 1.15613 | − | 0.419822i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 23.1312 | + | 27.6503i | 1.07850 | + | 1.28920i | ||||
\(461\) | −31.3246 | − | 18.0853i | −1.45893 | − | 0.842316i | −0.459974 | − | 0.887932i | \(-0.652141\pi\) |
−0.998959 | + | 0.0456166i | \(0.985475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.50957 | + | 4.33565i | −0.348999 | + | 0.201495i | −0.664244 | − | 0.747516i | \(-0.731247\pi\) |
0.315245 | + | 0.949010i | \(0.397913\pi\) | |||||||
\(464\) | −1.41708 | − | 3.92982i | −0.0657863 | − | 0.182437i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.2973 | + | 6.25100i | 1.63511 | + | 0.289572i | ||||
\(467\) | −13.4993 | −0.624671 | −0.312336 | − | 0.949972i | \(-0.601111\pi\) | ||||
−0.312336 | + | 0.949972i | \(0.601111\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6943 | −0.493817 | ||||||||
\(470\) | −17.7921 | − | 3.15090i | −0.820687 | − | 0.145340i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.4915 | + | 0.0525399i | 1.08128 | + | 0.00241835i | ||||
\(473\) | 0.251036 | − | 0.144936i | 0.0115427 | − | 0.00666416i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −49.0322 | − | 28.3087i | −2.24975 | − | 1.29889i | ||||
\(476\) | −5.53556 | + | 4.63084i | −0.253722 | + | 0.212254i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −33.4673 | + | 12.1529i | −1.53076 | + | 0.555859i | ||||
\(479\) | 19.1408 | − | 33.1529i | 0.874567 | − | 1.51480i | 0.0173444 | − | 0.999850i | \(-0.494479\pi\) |
0.857223 | − | 0.514945i | \(-0.172188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.70563 | + | 13.3465i | 0.351347 | + | 0.608550i | ||||
\(482\) | −10.4735 | − | 8.80163i | −0.477055 | − | 0.400903i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.75809 | − | 21.5006i | −0.170822 | − | 0.977300i | ||||
\(485\) | − | 51.1517i | − | 2.32268i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13.3113i | − | 0.603193i | −0.953436 | − | 0.301597i | \(-0.902480\pi\) | ||
0.953436 | − | 0.301597i | \(-0.0975196\pi\) | |||||||
\(488\) | 15.4563 | + | 26.9099i | 0.699674 | + | 1.21815i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.45214 | + | 4.10788i | −0.155952 | + | 0.185575i | ||||
\(491\) | −1.46735 | − | 2.54153i | −0.0662207 | − | 0.114698i | 0.831014 | − | 0.556251i | \(-0.187761\pi\) |
−0.897235 | + | 0.441554i | \(0.854427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.88435 | − | 3.26380i | 0.0848671 | − | 0.146994i | ||||
\(494\) | −11.5936 | − | 31.9273i | −0.521622 | − | 1.43648i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.3134 | + | 4.54131i | 1.13661 | + | 0.203911i | ||||
\(497\) | 2.36671 | + | 1.36642i | 0.106162 | + | 0.0612924i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.3491 | − | 18.6768i | 1.44815 | − | 0.836088i | 0.449775 | − | 0.893142i | \(-0.351504\pi\) |
0.998371 | + | 0.0570538i | \(0.0181707\pi\) | |||||||
\(500\) | −11.4561 | + | 31.3298i | −0.512331 | + | 1.40111i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.28633 | − | 12.9101i | 0.102044 | − | 0.576208i | ||||
\(503\) | −29.1509 | −1.29978 | −0.649888 | − | 0.760030i | \(-0.725184\pi\) | ||||
−0.649888 | + | 0.760030i | \(0.725184\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.8146 | 2.17222 | ||||||||
\(506\) | −0.344993 | + | 1.94806i | −0.0153368 | + | 0.0866019i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.80102 | + | 13.1297i | −0.213011 | + | 0.582538i | ||||
\(509\) | 19.4308 | − | 11.2184i | 0.861255 | − | 0.497246i | −0.00317707 | − | 0.999995i | \(-0.501011\pi\) |
0.864432 | + | 0.502749i | \(0.167678\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.47633 | − | 4.31646i | −0.330733 | − | 0.190949i | ||||
\(512\) | −22.6269 | − | 0.151821i | −0.999977 | − | 0.00670960i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.78295 | − | 18.6793i | −0.299183 | − | 0.823909i | ||||
\(515\) | −16.9083 | + | 29.2860i | −0.745067 | + | 1.29049i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.495801 | − | 0.858752i | −0.0218053 | − | 0.0377679i | ||||
\(518\) | −3.51779 | + | 4.18600i | −0.154563 | + | 0.183922i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −37.0930 | + | 21.3052i | −1.62664 | + | 0.934294i | ||||
\(521\) | 19.1422i | 0.838636i | 0.907839 | + | 0.419318i | \(0.137731\pi\) | ||||
−0.907839 | + | 0.419318i | \(0.862269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.09271i | 0.310143i | 0.987903 | + | 0.155071i | \(0.0495607\pi\) | ||||
−0.987903 | + | 0.155071i | \(0.950439\pi\) | |||||||
\(524\) | 4.09663 | + | 23.4374i | 0.178962 | + | 1.02387i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.58668 | − | 7.21600i | −0.374397 | − | 0.314632i | ||||
\(527\) | 11.6005 | + | 20.0926i | 0.505324 | + | 0.875246i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.215696 | − | 0.373597i | 0.00937809 | − | 0.0162433i | ||||
\(530\) | −10.2400 | + | 3.71840i | −0.444796 | + | 0.161517i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.24345 | − | 7.73272i | 0.400754 | − | 0.335256i | ||||
\(533\) | −42.6283 | − | 24.6115i | −1.84644 | − | 1.06604i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.49553 | − | 4.32754i | 0.324060 | − | 0.187096i | ||||
\(536\) | 0.0676512 | − | 30.2480i | 0.00292209 | − | 1.30651i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.86313 | + | 1.56962i | 0.382116 | + | 0.0676712i | ||||
\(539\) | −0.294470 | −0.0126837 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.6391 | 0.672376 | 0.336188 | − | 0.941795i | \(-0.390862\pi\) | ||||
0.336188 | + | 0.941795i | \(0.390862\pi\) | |||||||
\(542\) | −4.15315 | − | 0.735505i | −0.178393 | − | 0.0315926i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.0629 | − | 15.6862i | −0.560069 | − | 0.672540i | ||||
\(545\) | −33.0374 | + | 19.0741i | −1.41517 | + | 0.817047i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.46377 | + | 3.15451i | 0.233614 | + | 0.134877i | 0.612238 | − | 0.790673i | \(-0.290269\pi\) |
−0.378624 | + | 0.925551i | \(0.623603\pi\) | |||||||
\(548\) | −0.356257 | − | 0.425858i | −0.0152185 | − | 0.0181918i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.67792 | + | 1.33555i | −0.156827 | + | 0.0569480i | ||||
\(551\) | −3.14655 | + | 5.44999i | −0.134048 | + | 0.232177i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.74100 | − | 4.74756i | −0.116559 | − | 0.201887i | ||||
\(554\) | −23.3589 | − | 19.6301i | −0.992424 | − | 0.834004i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.6523 | − | 3.78460i | 0.918260 | − | 0.160503i | ||||
\(557\) | − | 22.2489i | − | 0.942714i | −0.881942 | − | 0.471357i | \(-0.843764\pi\) | ||
0.881942 | − | 0.471357i | \(-0.156236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.92375i | 0.165957i | ||||||||
\(560\) | −11.5970 | − | 9.79010i | −0.490062 | − | 0.413707i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.35450 | + | 8.75149i | −0.310231 | + | 0.369159i | ||||
\(563\) | −18.9723 | − | 32.8609i | −0.799585 | − | 1.38492i | −0.919887 | − | 0.392185i | \(-0.871719\pi\) |
0.120301 | − | 0.992737i | \(-0.461614\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.3123 | + | 23.0576i | −0.560054 | + | 0.970042i | ||||
\(566\) | −0.401179 | − | 1.10479i | −0.0168628 | − | 0.0464379i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.87979 | + | 6.68541i | −0.162792 | + | 0.280514i | ||||
\(569\) | −8.24731 | − | 4.76159i | −0.345745 | − | 0.199616i | 0.317064 | − | 0.948404i | \(-0.397303\pi\) |
−0.662810 | + | 0.748788i | \(0.730636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.0510 | + | 12.1538i | −0.880958 | + | 0.508621i | −0.870974 | − | 0.491329i | \(-0.836511\pi\) |
−0.00998391 | + | 0.999950i | \(0.503178\pi\) | |||||||
\(572\) | −2.20474 | − | 0.806183i | −0.0921847 | − | 0.0337082i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.04543 | − | 17.1965i | 0.127114 | − | 0.717769i | ||||
\(575\) | −44.6370 | −1.86149 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.6033 | −0.566311 | −0.283156 | − | 0.959074i | \(-0.591381\pi\) | ||||
−0.283156 | + | 0.959074i | \(0.591381\pi\) | |||||||
\(578\) | −0.981085 | + | 5.53985i | −0.0408077 | + | 0.230428i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.44317 | + | 2.72167i | 0.309061 | + | 0.113011i | ||||
\(581\) | 7.05111 | − | 4.07096i | 0.292529 | − | 0.168892i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.517763 | − | 0.298930i | −0.0214435 | − | 0.0123804i | ||||
\(584\) | 12.2561 | − | 21.1189i | 0.507159 | − | 0.873906i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.29555 | − | 17.3371i | −0.260067 | − | 0.716188i | ||||
\(587\) | −3.27395 | + | 5.67065i | −0.135130 | + | 0.234053i | −0.925647 | − | 0.378388i | \(-0.876479\pi\) |
0.790517 | + | 0.612440i | \(0.209812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3708 | − | 33.5512i | −0.798159 | − | 1.38245i | ||||
\(590\) | −28.6718 | + | 34.1180i | −1.18040 | + | 1.40462i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.8175 | − | 9.97628i | −0.485697 | − | 0.410022i | ||||
\(593\) | 11.1137i | 0.456386i | 0.973616 | + | 0.228193i | \(0.0732818\pi\) | ||||
−0.973616 | + | 0.228193i | \(0.926718\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 13.6917i | − | 0.561303i | ||||||
\(596\) | 16.4338 | − | 2.87247i | 0.673155 | − | 0.117661i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −20.5015 | − | 17.2289i | −0.838369 | − | 0.704541i | ||||
\(599\) | 6.36905 | + | 11.0315i | 0.260232 | + | 0.450736i | 0.966304 | − | 0.257405i | \(-0.0828675\pi\) |
−0.706071 | + | 0.708141i | \(0.749534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.5547 | + | 25.2095i | −0.593699 | + | 1.02832i | 0.400030 | + | 0.916502i | \(0.369000\pi\) |
−0.993729 | + | 0.111815i | \(0.964334\pi\) | |||||||
\(602\) | −1.30853 | + | 0.475161i | −0.0533317 | + | 0.0193661i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.79561 | − | 8.12326i | −0.276510 | − | 0.330531i | ||||
\(605\) | 35.8597 | + | 20.7036i | 1.45791 | + | 0.841722i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.5285 | + | 18.7804i | −1.32029 | + | 0.762272i | −0.983775 | − | 0.179406i | \(-0.942583\pi\) |
−0.336518 | + | 0.941677i | \(0.609249\pi\) | |||||||
\(608\) | 21.8129 | + | 26.1933i | 0.884630 | + | 1.06228i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −57.9706 | − | 10.2663i | −2.34716 | − | 0.415672i | ||||
\(611\) | 13.4225 | 0.543015 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5622 | 0.830501 | 0.415250 | − | 0.909707i | \(-0.363694\pi\) | ||||
0.415250 | + | 0.909707i | \(0.363694\pi\) | |||||||
\(614\) | −45.4077 | − | 8.04151i | −1.83251 | − | 0.324529i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.00186279 | − | 0.832885i | 7.50540e−5 | − | 0.0335579i | ||||
\(617\) | −29.4852 | + | 17.0233i | −1.18703 | + | 0.685333i | −0.957631 | − | 0.288000i | \(-0.907010\pi\) |
−0.229400 | + | 0.973332i | \(0.573677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9073 | + | 18.9990i | 1.32265 | + | 0.763635i | 0.984151 | − | 0.177330i | \(-0.0567461\pi\) |
0.338503 | + | 0.940965i | \(0.390079\pi\) | |||||||
\(620\) | −37.4212 | + | 31.3051i | −1.50287 | + | 1.25724i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.2267 | + | 6.25547i | −0.690728 | + | 0.250821i | ||||
\(623\) | 1.67786 | − | 2.90614i | 0.0672220 | − | 0.116432i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.15241 | − | 14.1204i | −0.326096 | − | 0.564815i | ||||
\(626\) | −8.05736 | − | 6.77117i | −0.322037 | − | 0.270630i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.21598 | − | 18.3991i | −0.128332 | − | 0.734205i | ||||
\(629\) | − | 13.9520i | − | 0.556304i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 46.8749i | − | 1.86606i | −0.359799 | − | 0.933030i | \(-0.617155\pi\) | ||
0.359799 | − | 0.933030i | \(-0.382845\pi\) | |||||||
\(632\) | 13.4454 | − | 7.72267i | 0.534830 | − | 0.307191i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.286009 | + | 0.340337i | −0.0113589 | + | 0.0135165i | ||||
\(635\) | −13.2607 | − | 22.9683i | −0.526236 | − | 0.911468i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.99299 | − | 3.45197i | 0.0789653 | − | 0.136772i | ||||
\(638\) | 0.148448 | + | 0.408806i | 0.00587712 | + | 0.0161848i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 27.7639 | − | 32.7392i | 1.09746 | − | 1.29413i | ||||
\(641\) | 22.8062 | + | 13.1672i | 0.900792 | + | 0.520073i | 0.877457 | − | 0.479655i | \(-0.159238\pi\) |
0.0233352 | + | 0.999728i | \(0.492571\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.1788 | − | 19.1558i | 1.30844 | − | 0.755430i | 0.326608 | − | 0.945160i | \(-0.394094\pi\) |
0.981836 | + | 0.189730i | \(0.0607611\pi\) | |||||||
\(644\) | 3.26294 | − | 8.92343i | 0.128578 | − | 0.351633i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.36241 | + | 30.2797i | −0.210981 | + | 1.19134i | ||||
\(647\) | −31.8925 | −1.25382 | −0.626912 | − | 0.779090i | \(-0.715682\pi\) | ||||
−0.626912 | + | 0.779090i | \(0.715682\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.44572 | −0.0960030 | ||||||||
\(650\) | 9.23627 | − | 52.1541i | 0.362276 | − | 2.04565i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.7573 | + | 29.4190i | −0.421290 | + | 1.15214i | ||||
\(653\) | −4.99048 | + | 2.88125i | −0.195292 | + | 0.112752i | −0.594458 | − | 0.804127i | \(-0.702633\pi\) |
0.399165 | + | 0.916879i | \(0.369300\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.0901 | − | 22.5687i | −1.52738 | − | 0.881830i | ||||
\(656\) | 48.6197 | + | 8.72255i | 1.89828 | + | 0.340558i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.62545 | + | 4.47625i | 0.0633664 | + | 0.174503i | ||||
\(659\) | 8.37638 | − | 14.5083i | 0.326298 | − | 0.565164i | −0.655477 | − | 0.755216i | \(-0.727532\pi\) |
0.981774 | + | 0.190052i | \(0.0608655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.26733 | − | 14.3194i | −0.321562 | − | 0.556961i | 0.659249 | − | 0.751925i | \(-0.270874\pi\) |
−0.980810 | + | 0.194964i | \(0.937541\pi\) | |||||||
\(662\) | −19.1715 | + | 22.8131i | −0.745122 | + | 0.886658i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.4698 | + | 19.9693i | 0.445114 | + | 0.774958i | ||||
\(665\) | 22.8627i | 0.886579i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.96146i | 0.192109i | ||||||||
\(668\) | 0.987954 | + | 5.65223i | 0.0382251 | + | 0.218692i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 43.9309 | + | 36.9183i | 1.69720 | + | 1.42628i | ||||
\(671\) | −1.61543 | − | 2.79801i | −0.0623630 | − | 0.108016i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.04519 | + | 10.4706i | −0.233025 | + | 0.403611i | −0.958697 | − | 0.284430i | \(-0.908196\pi\) |
0.725672 | + | 0.688041i | \(0.241529\pi\) | |||||||
\(674\) | 12.6777 | − | 4.60359i | 0.488325 | − | 0.177324i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.43038 | − | 3.70628i | 0.170399 | − | 0.142549i | ||||
\(677\) | 21.2204 | + | 12.2516i | 0.815567 | + | 0.470868i | 0.848885 | − | 0.528577i | \(-0.177274\pi\) |
−0.0333185 | + | 0.999445i | \(0.510608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.6753 | + | 6.74076i | −0.448058 | + | 0.258687i | ||||
\(680\) | 38.7258 | + | 0.0866122i | 1.48507 | + | 0.00332143i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.63645 | − | 0.466905i | −0.100955 | − | 0.0178787i | ||||
\(683\) | −50.4915 | −1.93200 | −0.966002 | − | 0.258534i | \(-0.916761\pi\) | ||||
−0.966002 | + | 0.258534i | \(0.916761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.05332 | 0.0402452 | ||||||||
\(686\) | 1.39255 | + | 0.246614i | 0.0531676 | + | 0.00941576i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.33568 | − | 3.70408i | −0.0509222 | − | 0.141217i | ||||
\(689\) | 7.00851 | − | 4.04637i | 0.267003 | − | 0.154154i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.62153 | + | 4.40029i | 0.289937 | + | 0.167395i | 0.637913 | − | 0.770108i | \(-0.279798\pi\) |
−0.347977 | + | 0.937503i | \(0.613131\pi\) | |||||||
\(692\) | 8.82582 | + | 10.5501i | 0.335507 | + | 0.401055i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.2733 | + | 6.63553i | −0.693646 | + | 0.251881i | ||||
\(695\) | −20.8497 | + | 36.1127i | −0.790872 | + | 1.36983i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.2811 | + | 38.5920i | 0.843957 | + | 1.46178i | ||||
\(698\) | 18.8299 | + | 15.8241i | 0.712723 | + | 0.598952i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 18.5114 | − | 3.23560i | 0.699663 | − | 0.122294i | ||||
\(701\) | − | 40.0613i | − | 1.51309i | −0.653940 | − | 0.756546i | \(-0.726885\pi\) | ||
0.653940 | − | 0.756546i | \(-0.273115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.2975i | 0.878682i | ||||||||
\(704\) | 2.35574 | + | 0.0105375i | 0.0887851 | + | 0.000397147i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.0949 | + | 20.3421i | −0.643375 | + | 0.765584i | ||||
\(707\) | −6.43278 | − | 11.1419i | −0.241930 | − | 0.419034i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4387 | + | 23.2765i | −0.504701 | + | 0.874169i | 0.495284 | + | 0.868731i | \(0.335064\pi\) |
−0.999985 | + | 0.00543734i | \(0.998269\pi\) | |||||||
\(710\) | −5.00509 | − | 13.7833i | −0.187838 | − | 0.517279i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.20917 | + | 4.76408i | 0.307652 | + | 0.178541i | ||||
\(713\) | −26.4517 | − | 15.2719i | −0.990622 | − | 0.571936i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.85681 | − | 2.22673i | 0.144237 | − | 0.0832751i | ||||
\(716\) | −36.3416 | − | 13.2887i | −1.35815 | − | 0.496621i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.51455 | + | 19.8455i | −0.131162 | + | 0.740627i | ||||
\(719\) | 40.6857 | 1.51732 | 0.758661 | − | 0.651486i | \(-0.225854\pi\) | ||||
0.758661 | + | 0.651486i | \(0.225854\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.91268 | 0.331925 | ||||||||
\(722\) | 4.26865 | − | 24.1036i | 0.158863 | − | 0.897044i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.8312 | + | 8.71409i | 0.885678 | + | 0.323857i | ||||
\(725\) | −8.49828 | + | 4.90649i | −0.315618 | + | 0.182222i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.36949 | − | 1.94538i | −0.124968 | − | 0.0721501i | 0.436213 | − | 0.899843i | \(-0.356319\pi\) |
−0.561181 | + | 0.827693i | \(0.689653\pi\) | |||||||
\(728\) | 9.75101 | + | 5.65886i | 0.361396 | + | 0.209731i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.8108 | + | 43.5409i | 0.585185 | + | 1.61152i | ||||
\(731\) | 1.77611 | − | 3.07631i | 0.0656918 | − | 0.113782i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.2371 | − | 19.4633i | −0.415053 | − | 0.718893i | 0.580381 | − | 0.814345i | \(-0.302904\pi\) |
−0.995434 | + | 0.0954521i | \(0.969570\pi\) | |||||||
\(734\) | 1.97161 | − | 2.34612i | 0.0727734 | − | 0.0865968i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.2186 | + | 9.28541i | 0.929569 | + | 0.342265i | ||||
\(737\) | 3.14915i | 0.116000i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.2290i | 1.25913i | 0.776947 | + | 0.629567i | \(0.216768\pi\) | ||||
−0.776947 | + | 0.629567i | \(0.783232\pi\) | |||||||
\(740\) | 28.9014 | − | 5.05167i | 1.06244 | − | 0.185703i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.19814 | + | 1.84726i | 0.0806964 | + | 0.0678149i | ||||
\(743\) | 14.2792 | + | 24.7322i | 0.523851 | + | 0.907337i | 0.999615 | + | 0.0277637i | \(0.00883859\pi\) |
−0.475763 | + | 0.879573i | \(0.657828\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8246 | + | 27.4091i | −0.579770 | + | 1.00419i | ||||
\(746\) | 44.4843 | − | 16.1534i | 1.62869 | − | 0.591418i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.36364 | + | 1.63006i | 0.0498597 | + | 0.0596008i | ||||
\(749\) | −1.97552 | − | 1.14057i | −0.0721839 | − | 0.0416754i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.64406 | + | 2.10390i | −0.132974 | + | 0.0767723i | −0.565011 | − | 0.825083i | \(-0.691128\pi\) |
0.432038 | + | 0.901856i | \(0.357795\pi\) | |||||||
\(752\) | −12.6710 | + | 4.56913i | −0.462064 | + | 0.166619i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.79700 | − | 1.02662i | −0.211114 | − | 0.0373874i | ||||
\(755\) | 20.0921 | 0.731226 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.18894 | −0.188595 | −0.0942977 | − | 0.995544i | \(-0.530061\pi\) | ||||
−0.0942977 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(758\) | 9.51105 | + | 1.68437i | 0.345457 | + | 0.0611790i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −64.6654 | − | 0.144628i | −2.34566 | − | 0.00524620i | ||||
\(761\) | −0.558714 | + | 0.322574i | −0.0202534 | + | 0.0116933i | −0.510092 | − | 0.860120i | \(-0.670389\pi\) |
0.489839 | + | 0.871813i | \(0.337056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.70733 | + | 5.02718i | 0.315226 | + | 0.181996i | ||||
\(764\) | 12.7604 | − | 10.6748i | 0.461654 | − | 0.386202i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.83434 | + | 3.57111i | −0.355329 | + | 0.129029i | ||||
\(767\) | 16.5528 | − | 28.6703i | 0.597688 | − | 1.03523i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.6215 | − | 21.8612i | −0.455145 | − | 0.788333i | 0.543552 | − | 0.839376i | \(-0.317079\pi\) |
−0.998697 | + | 0.0510420i | \(0.983746\pi\) | |||||||
\(770\) | 1.20965 | + | 1.01655i | 0.0435927 | + | 0.0366340i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.71608 | − | 21.2603i | −0.133745 | − | 0.765174i | ||||
\(773\) | 8.72610i | 0.313856i | 0.987610 | + | 0.156928i | \(0.0501591\pi\) | ||||
−0.987610 | + | 0.156928i | \(0.949841\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 60.4106i | − | 2.17001i | ||||||
\(776\) | −18.9918 | − | 33.0654i | −0.681768 | − | 1.18698i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.7924 | − | 18.7922i | 0.566187 | − | 0.673734i | ||||
\(779\) | −37.2057 | − | 64.4421i | −1.33303 | − | 2.30888i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.402370 | − | 0.696926i | 0.0143979 | − | 0.0249380i | ||||
\(782\) | 8.27492 | + | 22.7880i | 0.295910 | + | 0.814897i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.706337 | + | 3.93714i | −0.0252263 | + | 0.140612i | ||||
\(785\) | 30.6869 | + | 17.7171i | 1.09526 | + | 0.632351i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.8392 | + | 9.72212i | −0.600253 | + | 0.346556i | −0.769141 | − | 0.639079i | \(-0.779316\pi\) |
0.168888 | + | 0.985635i | \(0.445982\pi\) | |||||||
\(788\) | 9.88636 | − | 27.0370i | 0.352187 | − | 0.963155i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.12953 | + | 28.9647i | −0.182501 | + | 1.03052i | ||||
\(791\) | 7.01719 | 0.249502 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.7334 | 1.55302 | ||||||||
\(794\) | −1.21088 | + | 6.83745i | −0.0429727 | + | 0.242652i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.2975 | + | 28.1614i | −0.364984 | + | 0.998153i | ||||
\(797\) | 46.9719 | − | 27.1193i | 1.66383 | − | 0.960614i | 0.692972 | − | 0.720964i | \(-0.256301\pi\) |
0.970859 | − | 0.239649i | \(-0.0770325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.5235 | − | 6.07577i | −0.372296 | − | 0.214945i | ||||
\(800\) | 9.03453 | + | 52.3783i | 0.319419 | + | 1.85185i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.7255 | + | 32.2905i | 0.414042 | + | 1.14022i | ||||
\(803\) | −1.27107 | + | 2.20155i | −0.0448550 | + | 0.0776911i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.01246 | + | 15.6100i | 0.317647 | + | 0.550182i | ||||
\(806\) | 23.3171 | − | 27.7462i | 0.821309 | − | 0.977317i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 31.5547 | − | 18.1241i | 1.11009 | − | 0.637604i | ||||
\(809\) | 33.5957i | 1.18116i | 0.806979 | + | 0.590581i | \(0.201101\pi\) | ||||
−0.806979 | + | 0.590581i | \(0.798899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.28139i | − | 0.220570i | −0.993900 | − | 0.110285i | \(-0.964824\pi\) | ||
0.993900 | − | 0.110285i | \(-0.0351763\pi\) | |||||||
\(812\) | −0.359641 | − | 2.05756i | −0.0126209 | − | 0.0722062i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.23265 | + | 1.03588i | 0.0432044 | + | 0.0363077i | ||||
\(815\) | −29.7125 | − | 51.4635i | −1.04078 | − | 1.80269i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.96580 | + | 5.13692i | −0.103760 | + | 0.179718i | ||||
\(818\) | −50.8583 | + | 18.4680i | −1.77822 | + | 0.645718i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −71.8752 | + | 60.1281i | −2.50999 | + | 2.09976i | ||||
\(821\) | −16.5450 | − | 9.55229i | −0.577426 | − | 0.333377i | 0.182684 | − | 0.983172i | \(-0.441522\pi\) |
−0.760110 | + | 0.649795i | \(0.774855\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.0543 | − | 24.8574i | 1.50078 | − | 0.866476i | 0.500780 | − | 0.865574i | \(-0.333046\pi\) |
1.00000 | 0.000901331i | \(-0.000286903\pi\) | ||||||||
\(824\) | −0.0563808 | + | 25.2088i | −0.00196412 | + | 0.878190i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.5658 | + | 2.04825i | 0.402425 | + | 0.0712678i | ||||
\(827\) | −4.74479 | −0.164992 | −0.0824962 | − | 0.996591i | \(-0.526289\pi\) | ||||
−0.0824962 | + | 0.996591i | \(0.526289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3890 | 0.395558 | 0.197779 | − | 0.980247i | \(-0.436627\pi\) | ||||
0.197779 | + | 0.980247i | \(0.436627\pi\) | |||||||
\(830\) | −43.0187 | − | 7.61843i | −1.49320 | − | 0.264440i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.0673 | + | 27.5442i | −0.557034 | + | 0.954922i | ||||
\(833\) | −3.12511 | + | 1.80429i | −0.108279 | + | 0.0625148i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.42707 | − | 5.44272i | −0.326237 | − | 0.188353i | ||||
\(836\) | −2.27705 | − | 2.72192i | −0.0787535 | − | 0.0941395i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.1887 | + | 9.14669i | −0.870130 | + | 0.315967i | ||||
\(839\) | 17.0108 | − | 29.4636i | 0.587279 | − | 1.01720i | −0.407308 | − | 0.913291i | \(-0.633532\pi\) |
0.994587 | − | 0.103906i | \(-0.0331343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9546 | − | 24.1701i | −0.481194 | − | 0.833453i | ||||
\(842\) | 22.9600 | + | 19.2949i | 0.791253 | + | 0.664946i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.65238 | + | 0.987980i | −0.194563 | + | 0.0340077i | ||||
\(845\) | 10.9581i | 0.376970i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.9133i | − | 0.374985i | ||||||
\(848\) | −5.23872 | + | 6.20559i | −0.179898 | + | 0.213101i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −30.8494 | + | 36.7092i | −1.05812 | + | 1.25912i | ||||
\(851\) | 9.18385 | + | 15.9069i | 0.314818 | + | 0.545281i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.54802 | − | 14.8056i | 0.292679 | − | 0.506934i | −0.681764 | − | 0.731573i | \(-0.738787\pi\) |
0.974442 | + | 0.224638i | \(0.0721201\pi\) | |||||||
\(854\) | 5.29607 | + | 14.5846i | 0.181228 | + | 0.499076i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.23850 | − | 5.58038i | 0.110690 | − | 0.190734i | ||||
\(857\) | 4.25999 | + | 2.45951i | 0.145518 | + | 0.0840151i | 0.570991 | − | 0.820956i | \(-0.306559\pi\) |
−0.425473 | + | 0.904971i | \(0.639892\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.8381 | − | 14.9176i | 0.881585 | − | 0.508983i | 0.0104044 | − | 0.999946i | \(-0.496688\pi\) |
0.871181 | + | 0.490963i | \(0.163355\pi\) | |||||||
\(860\) | 7.01561 | + | 2.56533i | 0.239230 | + | 0.0874769i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.53898 | + | 8.69008i | −0.0524177 | + | 0.295985i | ||||
\(863\) | −7.21912 | −0.245742 | −0.122871 | − | 0.992423i | \(-0.539210\pi\) | ||||
−0.122871 | + | 0.992423i | \(0.539210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.0946 | −0.887244 | ||||||||
\(866\) | −3.01639 | + | 17.0325i | −0.102501 | + | 0.578788i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.0767 | + | 4.41597i | 0.409911 | + | 0.149888i | ||||
\(869\) | −1.39801 | + | 0.807143i | −0.0474243 | + | 0.0273804i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.9164 | − | 21.3137i | −1.25086 | − | 0.722186i | ||||
\(872\) | −14.2741 | + | 24.5962i | −0.483380 | + | 0.832932i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.8177 | − | 38.0521i | −0.467391 | − | 1.28713i | ||||
\(875\) | −8.33966 | + | 14.4447i | −0.281932 | + | 0.488321i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.56875 | − | 7.91331i | −0.154276 | − | 0.267214i | 0.778519 | − | 0.627621i | \(-0.215971\pi\) |
−0.932795 | + | 0.360407i | \(0.882638\pi\) | |||||||
\(878\) | −18.3472 | + | 21.8323i | −0.619190 | + | 0.736805i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.88289 | + | 3.41496i | −0.0971822 | + | 0.115118i | ||||
\(881\) | 18.1037i | 0.609930i | 0.952364 | + | 0.304965i | \(0.0986447\pi\) | ||||
−0.952364 | + | 0.304965i | \(0.901355\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.5545i | − | 0.355187i | −0.984104 | − | 0.177593i | \(-0.943169\pi\) | ||
0.984104 | − | 0.177593i | \(-0.0568311\pi\) | |||||||
\(884\) | −28.3378 | + | 4.95317i | −0.953104 | + | 0.166593i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.7540 | + | 25.8447i | 1.03320 | + | 0.868271i | ||||
\(887\) | 4.71464 | + | 8.16599i | 0.158302 | + | 0.274187i | 0.934256 | − | 0.356602i | \(-0.116065\pi\) |
−0.775954 | + | 0.630789i | \(0.782731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.49500 | + | 6.05351i | −0.117218 | + | 0.203028i | ||||
\(890\) | −16.9249 | + | 6.14586i | −0.567323 | + | 0.206010i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.5548 | − | 25.7660i | −0.721709 | − | 0.862709i | ||||
\(893\) | 17.5725 | + | 10.1455i | 0.588042 | + | 0.339506i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.5735 | − | 36.7042i | 2.12503 | − | 1.22689i | ||||
\(896\) | −11.1314 | − | 2.02272i | −0.371875 | − | 0.0675744i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.3741 | − | 2.19140i | −0.412929 | − | 0.0731280i | ||||
\(899\) | −6.71471 | −0.223948 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.32646 | −0.244080 | ||||||||
\(902\) | −5.06386 | − | 0.896788i | −0.168608 | − | 0.0298598i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.0443901 | + | 19.8476i | −0.00147639 | + | 0.660120i | ||||
\(905\) | −41.6886 | + | 24.0689i | −1.38578 | + | 0.800078i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.60015 | + | 3.23325i | 0.185950 | + | 0.107358i | 0.590085 | − | 0.807341i | \(-0.299094\pi\) |
−0.404135 | + | 0.914699i | \(0.632428\pi\) | |||||||
\(908\) | 44.1457 | − | 36.9306i | 1.46503 | − | 1.22558i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −20.1037 | + | 7.30017i | −0.666431 | + | 0.241998i | ||||
\(911\) | −17.1240 | + | 29.6597i | −0.567345 | + | 0.982670i | 0.429482 | + | 0.903075i | \(0.358696\pi\) |
−0.996827 | + | 0.0795950i | \(0.974637\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.19878 | − | 2.07634i | −0.0396737 | − | 0.0687168i | ||||
\(914\) | 11.7730 | + | 9.89371i | 0.389417 | + | 0.327255i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.40965 | + | 36.6706i | 0.211781 | + | 1.21163i | ||||
\(917\) | 11.8964i | 0.392853i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.16854i | − | 0.236468i | −0.992986 | − | 0.118234i | \(-0.962277\pi\) | ||
0.992986 | − | 0.118234i | \(-0.0377233\pi\) | |||||||
\(920\) | −44.2088 | + | 25.3923i | −1.45752 | + | 0.837158i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.9097 | − | 39.1609i | 1.08382 | − | 1.28969i | ||||
\(923\) | 5.44654 | + | 9.43369i | 0.179275 | + | 0.310514i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.1642 | + | 31.4612i | −0.597234 | + | 1.03444i | ||||
\(926\) | −4.18562 | − | 11.5266i | −0.137548 | − | 0.378789i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.82192 | − | 1.00420i | 0.191114 | − | 0.0329645i | ||||
\(929\) | −20.4211 | − | 11.7901i | −0.669993 | − | 0.386821i | 0.126081 | − | 0.992020i | \(-0.459760\pi\) |
−0.796074 | + | 0.605199i | \(0.793093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.21841 | − | 3.01285i | 0.171026 | − | 0.0987422i | ||||
\(932\) | −17.4096 | + | 47.6115i | −0.570270 | + | 1.55957i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.32910 | − | 18.7983i | 0.108932 | − | 0.615100i | ||||
\(935\) | −4.03178 | −0.131853 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.9176 | 0.944698 | 0.472349 | − | 0.881411i | \(-0.343406\pi\) | ||||
0.472349 | + | 0.881411i | \(0.343406\pi\) | |||||||
\(938\) | 2.63736 | − | 14.8923i | 0.0861129 | − | 0.486250i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.77554 | − | 23.9992i | 0.286227 | − | 0.782767i | ||||
\(941\) | 7.14862 | − | 4.12726i | 0.233038 | − | 0.134545i | −0.378935 | − | 0.925423i | \(-0.623709\pi\) |
0.611973 | + | 0.790879i | \(0.290376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.8060 | − | 29.3328i | −1.65447 | − | 0.955208i | ||||
\(944\) | −5.86648 | + | 32.7000i | −0.190938 | + | 1.06429i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.139921 | + | 0.385322i | 0.00454921 | + | 0.0125279i | ||||
\(947\) | 13.0431 | − | 22.5914i | 0.423845 | − | 0.734121i | −0.572467 | − | 0.819928i | \(-0.694013\pi\) |
0.996312 | + | 0.0858067i | \(0.0273468\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.2054 | − | 29.8006i | −0.558510 | − | 0.967367i | ||||
\(950\) | 51.5132 | − | 61.2982i | 1.67131 | − | 1.98878i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.08351 | − | 8.85055i | −0.164757 | − | 0.286848i | ||||
\(953\) | − | 8.16427i | − | 0.264467i | −0.991219 | − | 0.132233i | \(-0.957785\pi\) | ||
0.991219 | − | 0.132233i | \(-0.0422148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.5615i | 1.02131i | ||||||||
\(956\) | −8.66990 | − | 49.6018i | −0.280404 | − | 1.60424i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.4465 | + | 34.8304i | 1.33908 | + | 1.12532i | ||||
\(959\) | −0.138806 | − | 0.240419i | −0.00448228 | − | 0.00776354i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.16854 | − | 8.95217i | 0.166727 | − | 0.288780i | ||||
\(962\) | −20.4860 | + | 7.43900i | −0.660495 | + | 0.239843i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.8396 | − | 12.4142i | 0.477950 | − | 0.399835i | ||||
\(965\) | 35.4589 | + | 20.4722i | 1.14146 | + | 0.659024i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.9368 | + | 27.6763i | −1.54154 | + | 0.890010i | −0.542800 | + | 0.839862i | \(0.682636\pi\) |
−0.998742 | + | 0.0501481i | \(0.984031\pi\) | |||||||
\(968\) | 30.8674 | + | 0.0690365i | 0.992115 | + | 0.00221892i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 71.2310 | + | 12.6147i | 2.28709 | + | 0.405034i | ||||
\(971\) | −11.2138 | −0.359869 | −0.179935 | − | 0.983679i | \(-0.557589\pi\) | ||||
−0.179935 | + | 0.983679i | \(0.557589\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.9903 | 0.352332 | ||||||||
\(974\) | 18.5366 | + | 3.28275i | 0.593951 | + | 0.105186i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −41.2850 | + | 14.8872i | −1.32150 | + | 0.476529i | ||||
\(977\) | 20.0276 | − | 11.5629i | 0.640740 | − | 0.369931i | −0.144160 | − | 0.989554i | \(-0.546048\pi\) |
0.784899 | + | 0.619623i | \(0.212715\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.855770 | − | 0.494079i | −0.0273505 | − | 0.0157908i | ||||
\(980\) | −4.86906 | − | 5.82033i | −0.155537 | − | 0.185924i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.90106 | − | 1.41658i | 0.124488 | − | 0.0452048i | ||||
\(983\) | −16.6695 | + | 28.8724i | −0.531673 | + | 0.920885i | 0.467643 | + | 0.883917i | \(0.345103\pi\) |
−0.999316 | + | 0.0369680i | \(0.988230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.3068 | + | 47.2967i | 0.870067 | + | 1.50700i | ||||
\(986\) | 4.08028 | + | 3.42895i | 0.129943 | + | 0.109200i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 47.3193 | − | 8.27095i | 1.50543 | − | 0.263134i | ||||
\(989\) | 4.67646i | 0.148703i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 27.6317i | − | 0.877749i | −0.898548 | − | 0.438875i | \(-0.855377\pi\) | ||
0.898548 | − | 0.438875i | \(-0.144623\pi\) | |||||||
\(992\) | −12.5666 | + | 34.1301i | −0.398991 | + | 1.08363i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.48647 | + | 2.95877i | −0.0788660 | + | 0.0938466i | ||||
\(995\) | −28.4423 | − | 49.2635i | −0.901682 | − | 1.56176i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.1065 | − | 17.5050i | 0.320077 | − | 0.554390i | −0.660426 | − | 0.750891i | \(-0.729624\pi\) |
0.980504 | + | 0.196500i | \(0.0629577\pi\) | |||||||
\(998\) | 18.0305 | + | 49.6536i | 0.570746 | + | 1.57176i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.ba.a.575.16 | 72 | ||
3.2 | odd | 2 | 252.2.ba.a.155.21 | yes | 72 | ||
4.3 | odd | 2 | inner | 756.2.ba.a.575.27 | 72 | ||
9.4 | even | 3 | 252.2.ba.a.239.10 | yes | 72 | ||
9.5 | odd | 6 | inner | 756.2.ba.a.71.27 | 72 | ||
12.11 | even | 2 | 252.2.ba.a.155.10 | ✓ | 72 | ||
36.23 | even | 6 | inner | 756.2.ba.a.71.16 | 72 | ||
36.31 | odd | 6 | 252.2.ba.a.239.21 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.ba.a.155.10 | ✓ | 72 | 12.11 | even | 2 | ||
252.2.ba.a.155.21 | yes | 72 | 3.2 | odd | 2 | ||
252.2.ba.a.239.10 | yes | 72 | 9.4 | even | 3 | ||
252.2.ba.a.239.21 | yes | 72 | 36.31 | odd | 6 | ||
756.2.ba.a.71.16 | 72 | 36.23 | even | 6 | inner | ||
756.2.ba.a.71.27 | 72 | 9.5 | odd | 6 | inner | ||
756.2.ba.a.575.16 | 72 | 1.1 | even | 1 | trivial | ||
756.2.ba.a.575.27 | 72 | 4.3 | odd | 2 | inner |