Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [473,2,Mod(85,473)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(473, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("473.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 473 = 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 473.k (of order \(10\), degree \(4\), 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: | \(3.77692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 85.6 | ||
Character | \(\chi\) | \(=\) | 473.85 |
Dual form | 473.2.k.b.128.6 |
$q$-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 \(\left(\mathbb{Z}/473\mathbb{Z}\right)^\times\).
\(n\) | \(89\) | \(431\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89979 | + | 1.38028i | −1.34335 | + | 0.976002i | −0.344038 | + | 0.938956i | \(0.611795\pi\) |
−0.999314 | + | 0.0370465i | \(0.988205\pi\) | |||||||
\(3\) | −1.10873 | + | 0.360248i | −0.640125 | + | 0.207989i | −0.611055 | − | 0.791588i | \(-0.709255\pi\) |
−0.0290702 | + | 0.999577i | \(0.509255\pi\) | |||||||
\(4\) | 1.08599 | − | 3.34234i | 0.542997 | − | 1.67117i | ||||
\(5\) | 0.367347 | − | 0.505610i | 0.164283 | − | 0.226116i | −0.718937 | − | 0.695075i | \(-0.755371\pi\) |
0.883220 | + | 0.468960i | \(0.155371\pi\) | |||||||
\(6\) | 1.60911 | − | 2.21475i | 0.656915 | − | 0.904167i | ||||
\(7\) | −0.481036 | + | 1.48048i | −0.181815 | + | 0.559568i | −0.999879 | − | 0.0155590i | \(-0.995047\pi\) |
0.818064 | + | 0.575127i | \(0.195047\pi\) | |||||||
\(8\) | 1.09889 | + | 3.38204i | 0.388517 | + | 1.19573i | ||||
\(9\) | −1.32755 | + | 0.964520i | −0.442516 | + | 0.321507i | ||||
\(10\) | 1.46759i | 0.464093i | ||||||||
\(11\) | −1.26327 | − | 3.06662i | −0.380889 | − | 0.924621i | ||||
\(12\) | 4.09698i | 1.18270i | ||||||||
\(13\) | −0.137295 | − | 0.188970i | −0.0380788 | − | 0.0524109i | 0.789553 | − | 0.613682i | \(-0.210312\pi\) |
−0.827632 | + | 0.561271i | \(0.810312\pi\) | |||||||
\(14\) | −1.12960 | − | 3.47655i | −0.301898 | − | 0.929148i | ||||
\(15\) | −0.225144 | + | 0.692921i | −0.0581318 | + | 0.178911i | ||||
\(16\) | −1.06948 | − | 0.777020i | −0.267369 | − | 0.194255i | ||||
\(17\) | 1.33309 | − | 1.83484i | 0.323322 | − | 0.445015i | −0.616156 | − | 0.787624i | \(-0.711311\pi\) |
0.939478 | + | 0.342610i | \(0.111311\pi\) | |||||||
\(18\) | 1.19075 | − | 3.66476i | 0.280663 | − | 0.863793i | ||||
\(19\) | −1.23266 | − | 3.79372i | −0.282791 | − | 0.870340i | −0.987052 | − | 0.160399i | \(-0.948722\pi\) |
0.704262 | − | 0.709941i | \(-0.251278\pi\) | |||||||
\(20\) | −1.29099 | − | 1.77689i | −0.288673 | − | 0.397324i | ||||
\(21\) | − | 1.81474i | − | 0.396009i | ||||||
\(22\) | 6.63271 | + | 4.08227i | 1.41410 | + | 0.870343i | ||||
\(23\) | 7.38615 | 1.54012 | 0.770059 | − | 0.637972i | \(-0.220227\pi\) | ||||
0.770059 | + | 0.637972i | \(0.220227\pi\) | |||||||
\(24\) | −2.43675 | − | 3.35390i | −0.497399 | − | 0.684611i | ||||
\(25\) | 1.42439 | + | 4.38381i | 0.284878 | + | 0.876763i | ||||
\(26\) | 0.521662 | + | 0.169498i | 0.102306 | + | 0.0332414i | ||||
\(27\) | 3.18012 | − | 4.37706i | 0.612015 | − | 0.842366i | ||||
\(28\) | 4.42586 | + | 3.21558i | 0.836409 | + | 0.607687i | ||||
\(29\) | 1.53137 | − | 4.71307i | 0.284368 | − | 0.875195i | −0.702219 | − | 0.711961i | \(-0.747807\pi\) |
0.986587 | − | 0.163234i | \(-0.0521926\pi\) | |||||||
\(30\) | −0.528697 | − | 1.62716i | −0.0965264 | − | 0.297078i | ||||
\(31\) | −0.871701 | + | 0.633328i | −0.156562 | + | 0.113749i | −0.663308 | − | 0.748346i | \(-0.730848\pi\) |
0.506746 | + | 0.862095i | \(0.330848\pi\) | |||||||
\(32\) | −4.00790 | −0.708504 | ||||||||
\(33\) | 2.50536 | + | 2.94496i | 0.436128 | + | 0.512652i | ||||
\(34\) | 5.32584i | 0.913374i | ||||||||
\(35\) | 0.571836 | + | 0.787065i | 0.0966580 | + | 0.133038i | ||||
\(36\) | 1.78205 | + | 5.48458i | 0.297008 | + | 0.914097i | ||||
\(37\) | 6.42485 | + | 2.08756i | 1.05624 | + | 0.343193i | 0.785114 | − | 0.619351i | \(-0.212604\pi\) |
0.271125 | + | 0.962544i | \(0.412604\pi\) | |||||||
\(38\) | 7.57817 | + | 5.50586i | 1.22934 | + | 0.893168i | ||||
\(39\) | 0.220299 | + | 0.160057i | 0.0352761 | + | 0.0256296i | ||||
\(40\) | 2.11367 | + | 0.686773i | 0.334200 | + | 0.108588i | ||||
\(41\) | −8.19089 | + | 2.66138i | −1.27920 | + | 0.415638i | −0.868299 | − | 0.496041i | \(-0.834787\pi\) |
−0.410903 | + | 0.911679i | \(0.634787\pi\) | |||||||
\(42\) | 2.50484 | + | 3.44762i | 0.386506 | + | 0.531979i | ||||
\(43\) | 6.13533 | + | 2.31467i | 0.935629 | + | 0.352984i | ||||
\(44\) | −11.6216 | + | 0.891937i | −1.75202 | + | 0.134465i | ||||
\(45\) | 1.02554i | 0.152878i | ||||||||
\(46\) | −14.0321 | + | 10.1949i | −2.06892 | + | 1.50316i | ||||
\(47\) | 0.521184 | + | 1.60404i | 0.0760224 | + | 0.233973i | 0.981845 | − | 0.189684i | \(-0.0607463\pi\) |
−0.905823 | + | 0.423657i | \(0.860746\pi\) | |||||||
\(48\) | 1.46568 | + | 0.476229i | 0.211553 | + | 0.0687377i | ||||
\(49\) | 3.70270 | + | 2.69017i | 0.528958 | + | 0.384310i | ||||
\(50\) | −8.75690 | − | 6.36226i | −1.23841 | − | 0.899760i | ||||
\(51\) | −0.817039 | + | 2.51459i | −0.114408 | + | 0.352113i | ||||
\(52\) | −0.780705 | + | 0.253666i | −0.108264 | + | 0.0351772i | ||||
\(53\) | 2.50195 | − | 1.81778i | 0.343670 | − | 0.249691i | −0.402539 | − | 0.915403i | \(-0.631872\pi\) |
0.746209 | + | 0.665712i | \(0.231872\pi\) | |||||||
\(54\) | 12.7049i | 1.72892i | ||||||||
\(55\) | −2.01457 | − | 0.487795i | −0.271645 | − | 0.0657742i | ||||
\(56\) | −5.53564 | −0.739731 | ||||||||
\(57\) | 2.73336 | + | 3.76215i | 0.362043 | + | 0.498309i | ||||
\(58\) | 3.59606 | + | 11.0675i | 0.472186 | + | 1.45324i | ||||
\(59\) | 0.843736 | − | 2.59675i | 0.109845 | − | 0.338068i | −0.880992 | − | 0.473131i | \(-0.843124\pi\) |
0.990837 | + | 0.135063i | \(0.0431237\pi\) | |||||||
\(60\) | 2.07147 | + | 1.50501i | 0.267426 | + | 0.194297i | ||||
\(61\) | 10.3866 | + | 7.54634i | 1.32987 | + | 0.966210i | 0.999752 | + | 0.0222718i | \(0.00708993\pi\) |
0.330122 | + | 0.943938i | \(0.392910\pi\) | |||||||
\(62\) | 0.781878 | − | 2.40637i | 0.0992987 | − | 0.305610i | ||||
\(63\) | −0.789351 | − | 2.42937i | −0.0994489 | − | 0.306072i | ||||
\(64\) | 9.75311 | − | 7.08605i | 1.21914 | − | 0.885756i | ||||
\(65\) | −0.145980 | −0.0181066 | ||||||||
\(66\) | −8.82452 | − | 2.13671i | −1.08622 | − | 0.263011i | ||||
\(67\) | −1.47745 | −0.180499 | −0.0902497 | − | 0.995919i | \(-0.528767\pi\) | ||||
−0.0902497 | + | 0.995919i | \(0.528767\pi\) | |||||||
\(68\) | −4.68495 | − | 6.44827i | −0.568133 | − | 0.781968i | ||||
\(69\) | −8.18924 | + | 2.66085i | −0.985869 | + | 0.320328i | ||||
\(70\) | −2.17273 | − | 0.705964i | −0.259691 | − | 0.0843788i | ||||
\(71\) | 6.50490 | − | 8.95322i | 0.771989 | − | 1.06255i | −0.224132 | − | 0.974559i | \(-0.571955\pi\) |
0.996121 | − | 0.0879931i | \(-0.0280453\pi\) | |||||||
\(72\) | −4.72088 | − | 3.42992i | −0.556361 | − | 0.404220i | ||||
\(73\) | −1.86493 | + | 5.73967i | −0.218274 | + | 0.671777i | 0.780631 | + | 0.624992i | \(0.214898\pi\) |
−0.998905 | + | 0.0467854i | \(0.985102\pi\) | |||||||
\(74\) | −15.0873 | + | 4.90214i | −1.75386 | + | 0.569863i | ||||
\(75\) | −3.15852 | − | 4.34733i | −0.364715 | − | 0.501987i | ||||
\(76\) | −14.0186 | −1.60804 | ||||||||
\(77\) | 5.14774 | − | 0.395080i | 0.586639 | − | 0.0450235i | ||||
\(78\) | −0.639444 | −0.0724027 | ||||||||
\(79\) | 2.60019 | + | 3.57886i | 0.292545 | + | 0.402653i | 0.929839 | − | 0.367968i | \(-0.119946\pi\) |
−0.637294 | + | 0.770621i | \(0.719946\pi\) | |||||||
\(80\) | −0.785738 | + | 0.255302i | −0.0878482 | + | 0.0285436i | ||||
\(81\) | −0.427833 | + | 1.31673i | −0.0475370 | + | 0.146304i | ||||
\(82\) | 11.8875 | − | 16.3617i | 1.31275 | − | 1.80685i | ||||
\(83\) | 9.92083 | − | 13.6548i | 1.08895 | − | 1.49881i | 0.239685 | − | 0.970851i | \(-0.422956\pi\) |
0.849267 | − | 0.527963i | \(-0.177044\pi\) | |||||||
\(84\) | −6.06549 | − | 1.97080i | −0.661799 | − | 0.215032i | ||||
\(85\) | −0.438007 | − | 1.34805i | −0.0475086 | − | 0.146216i | ||||
\(86\) | −14.8507 | + | 4.07107i | −1.60139 | + | 0.438995i | ||||
\(87\) | 5.77719i | 0.619380i | ||||||||
\(88\) | 8.98325 | − | 7.64230i | 0.957618 | − | 0.814672i | ||||
\(89\) | − | 0.0381389i | − | 0.00404271i | −0.999998 | − | 0.00202136i | \(-0.999357\pi\) | ||
0.999998 | − | 0.00202136i | \(-0.000643418\pi\) | |||||||
\(90\) | −1.41552 | − | 1.94830i | −0.149209 | − | 0.205369i | ||||
\(91\) | 0.345810 | − | 0.112360i | 0.0362507 | − | 0.0117786i | ||||
\(92\) | 8.02131 | − | 24.6871i | 0.836279 | − | 2.57380i | ||||
\(93\) | 0.738325 | − | 1.01622i | 0.0765608 | − | 0.105377i | ||||
\(94\) | −3.20415 | − | 2.32795i | −0.330483 | − | 0.240110i | ||||
\(95\) | −2.37096 | − | 0.770370i | −0.243255 | − | 0.0790383i | ||||
\(96\) | 4.44368 | − | 1.44384i | 0.453531 | − | 0.147361i | ||||
\(97\) | −2.44193 | + | 1.77416i | −0.247940 | + | 0.180139i | −0.704813 | − | 0.709393i | \(-0.748969\pi\) |
0.456873 | + | 0.889532i | \(0.348969\pi\) | |||||||
\(98\) | −10.7475 | −1.08566 | ||||||||
\(99\) | 4.63486 | + | 2.85264i | 0.465821 | + | 0.286701i | ||||
\(100\) | 16.1991 | 1.61991 | ||||||||
\(101\) | −0.643484 | − | 0.885679i | −0.0640290 | − | 0.0881284i | 0.775802 | − | 0.630977i | \(-0.217346\pi\) |
−0.839831 | + | 0.542849i | \(0.817346\pi\) | |||||||
\(102\) | −1.91862 | − | 5.90492i | −0.189972 | − | 0.584674i | ||||
\(103\) | 4.40671 | − | 13.5625i | 0.434206 | − | 1.33635i | −0.459692 | − | 0.888078i | \(-0.652040\pi\) |
0.893898 | − | 0.448270i | \(-0.147960\pi\) | |||||||
\(104\) | 0.488233 | − | 0.671995i | 0.0478752 | − | 0.0658946i | ||||
\(105\) | −0.917551 | − | 0.666640i | −0.0895438 | − | 0.0650574i | ||||
\(106\) | −2.24414 | + | 6.90677i | −0.217971 | + | 0.670845i | ||||
\(107\) | 4.57117 | − | 1.48526i | 0.441911 | − | 0.143586i | −0.0796060 | − | 0.996826i | \(-0.525366\pi\) |
0.521517 | + | 0.853241i | \(0.325366\pi\) | |||||||
\(108\) | −11.1761 | − | 15.3825i | −1.07542 | − | 1.48018i | ||||
\(109\) | − | 13.4773i | − | 1.29089i | −0.763805 | − | 0.645447i | \(-0.776671\pi\) | ||
0.763805 | − | 0.645447i | \(-0.223329\pi\) | |||||||
\(110\) | 4.50054 | − | 1.85396i | 0.429110 | − | 0.176768i | ||||
\(111\) | −7.87546 | −0.747506 | ||||||||
\(112\) | 1.66482 | − | 1.20956i | 0.157310 | − | 0.114293i | ||||
\(113\) | 8.37448 | − | 2.72103i | 0.787805 | − | 0.255973i | 0.112636 | − | 0.993636i | \(-0.464071\pi\) |
0.675169 | + | 0.737663i | \(0.264071\pi\) | |||||||
\(114\) | −10.3856 | − | 3.37449i | −0.972702 | − | 0.316050i | ||||
\(115\) | 2.71328 | − | 3.73451i | 0.253015 | − | 0.348245i | ||||
\(116\) | −14.0896 | − | 10.2367i | −1.30819 | − | 0.950455i | ||||
\(117\) | 0.364531 | + | 0.118443i | 0.0337009 | + | 0.0109501i | ||||
\(118\) | 1.98132 | + | 6.09786i | 0.182395 | + | 0.561354i | ||||
\(119\) | 2.07518 | + | 2.85624i | 0.190231 | + | 0.261831i | ||||
\(120\) | −2.59090 | −0.236515 | ||||||||
\(121\) | −7.80832 | + | 7.74791i | −0.709847 | + | 0.704355i | ||||
\(122\) | −30.1484 | −2.72951 | ||||||||
\(123\) | 8.12273 | − | 5.90151i | 0.732401 | − | 0.532121i | ||||
\(124\) | 1.17014 | + | 3.60131i | 0.105081 | + | 0.323407i | ||||
\(125\) | 5.71164 | + | 1.85583i | 0.510865 | + | 0.165990i | ||||
\(126\) | 4.85280 | + | 3.52577i | 0.432322 | + | 0.314100i | ||||
\(127\) | 0.579121 | − | 0.797091i | 0.0513886 | − | 0.0707304i | −0.782549 | − | 0.622589i | \(-0.786081\pi\) |
0.833938 | + | 0.551858i | \(0.186081\pi\) | |||||||
\(128\) | −6.27110 | + | 19.3005i | −0.554293 | + | 1.70594i | ||||
\(129\) | −7.63628 | − | 0.356100i | −0.672337 | − | 0.0313529i | ||||
\(130\) | 0.277331 | − | 0.201493i | 0.0243235 | − | 0.0176721i | ||||
\(131\) | −5.13970 | −0.449057 | −0.224529 | − | 0.974467i | \(-0.572084\pi\) | ||||
−0.224529 | + | 0.974467i | \(0.572084\pi\) | |||||||
\(132\) | 12.5639 | − | 5.17558i | 1.09355 | − | 0.450476i | ||||
\(133\) | 6.20947 | 0.538430 | ||||||||
\(134\) | 2.80684 | − | 2.03929i | 0.242474 | − | 0.176168i | ||||
\(135\) | −1.04488 | − | 3.21580i | −0.0899288 | − | 0.276772i | ||||
\(136\) | 7.67044 | + | 2.49228i | 0.657735 | + | 0.213711i | ||||
\(137\) | −8.85288 | + | 12.1850i | −0.756353 | + | 1.04103i | 0.241156 | + | 0.970486i | \(0.422474\pi\) |
−0.997509 | + | 0.0705442i | \(0.977526\pi\) | |||||||
\(138\) | 11.8851 | − | 16.3585i | 1.01173 | − | 1.39252i | ||||
\(139\) | −18.4588 | − | 5.99762i | −1.56565 | − | 0.508711i | −0.607342 | − | 0.794440i | \(-0.707764\pi\) |
−0.958310 | + | 0.285729i | \(0.907764\pi\) | |||||||
\(140\) | 3.25165 | − | 1.05653i | 0.274815 | − | 0.0892928i | ||||
\(141\) | −1.15570 | − | 1.59069i | −0.0973278 | − | 0.133960i | ||||
\(142\) | 25.9878i | 2.18084i | ||||||||
\(143\) | −0.406060 | + | 0.659751i | −0.0339565 | + | 0.0551712i | ||||
\(144\) | 2.16923 | 0.180769 | ||||||||
\(145\) | −1.82043 | − | 2.50561i | −0.151178 | − | 0.208079i | ||||
\(146\) | −4.37935 | − | 13.4783i | −0.362438 | − | 1.11547i | ||||
\(147\) | −5.07443 | − | 1.64878i | −0.418532 | − | 0.135989i | ||||
\(148\) | 13.9547 | − | 19.2070i | 1.14707 | − | 1.57880i | ||||
\(149\) | −14.7574 | − | 10.7219i | −1.20897 | − | 0.878370i | −0.213836 | − | 0.976870i | \(-0.568596\pi\) |
−0.995137 | + | 0.0984992i | \(0.968596\pi\) | |||||||
\(150\) | 12.0010 | + | 3.89937i | 0.979880 | + | 0.318382i | ||||
\(151\) | −0.157729 | − | 0.485441i | −0.0128358 | − | 0.0395047i | 0.944433 | − | 0.328703i | \(-0.106611\pi\) |
−0.957269 | + | 0.289198i | \(0.906611\pi\) | |||||||
\(152\) | 11.4760 | − | 8.33779i | 0.930825 | − | 0.676284i | ||||
\(153\) | 3.72163i | 0.300876i | ||||||||
\(154\) | −9.23428 | + | 7.85586i | −0.744120 | + | 0.633043i | ||||
\(155\) | 0.673392i | 0.0540881i | ||||||||
\(156\) | 0.774208 | − | 0.562495i | 0.0619862 | − | 0.0450356i | ||||
\(157\) | 6.04515 | − | 1.96419i | 0.482456 | − | 0.156759i | −0.0576837 | − | 0.998335i | \(-0.518371\pi\) |
0.540139 | + | 0.841576i | \(0.318371\pi\) | |||||||
\(158\) | −9.87962 | − | 3.21008i | −0.785981 | − | 0.255381i | ||||
\(159\) | −2.11914 | + | 2.91674i | −0.168059 | + | 0.231313i | ||||
\(160\) | −1.47229 | + | 2.02643i | −0.116395 | + | 0.160204i | ||||
\(161\) | −3.55300 | + | 10.9350i | −0.280016 | + | 0.861801i | ||||
\(162\) | −1.00467 | − | 3.09204i | −0.0789340 | − | 0.242934i | ||||
\(163\) | 0.686696 | + | 0.945155i | 0.0537862 | + | 0.0740303i | 0.835063 | − | 0.550155i | \(-0.185431\pi\) |
−0.781277 | + | 0.624185i | \(0.785431\pi\) | |||||||
\(164\) | 30.2670i | 2.36346i | ||||||||
\(165\) | 2.40934 | − | 0.184913i | 0.187567 | − | 0.0143954i | ||||
\(166\) | 39.6348i | 3.07625i | ||||||||
\(167\) | −1.40795 | − | 1.93788i | −0.108950 | − | 0.149957i | 0.751060 | − | 0.660234i | \(-0.229543\pi\) |
−0.860010 | + | 0.510277i | \(0.829543\pi\) | |||||||
\(168\) | 6.13753 | − | 1.99420i | 0.473521 | − | 0.153856i | ||||
\(169\) | 4.00036 | − | 12.3118i | 0.307720 | − | 0.947065i | ||||
\(170\) | 2.69280 | + | 1.95643i | 0.206528 | + | 0.150051i | ||||
\(171\) | 5.29553 | + | 3.84743i | 0.404960 | + | 0.294220i | ||||
\(172\) | 14.3993 | − | 17.9927i | 1.09794 | − | 1.37193i | ||||
\(173\) | 3.26066 | − | 1.05945i | 0.247904 | − | 0.0805487i | −0.182430 | − | 0.983219i | \(-0.558396\pi\) |
0.430333 | + | 0.902670i | \(0.358396\pi\) | |||||||
\(174\) | −7.97411 | − | 10.9754i | −0.604516 | − | 0.832045i | ||||
\(175\) | −7.17532 | −0.542403 | ||||||||
\(176\) | −1.03179 | + | 4.26126i | −0.0777744 | + | 0.321205i | ||||
\(177\) | 3.18305i | 0.239253i | ||||||||
\(178\) | 0.0526422 | + | 0.0724557i | 0.00394570 | + | 0.00543079i | ||||
\(179\) | 8.17193 | − | 2.65522i | 0.610799 | − | 0.198461i | 0.0127480 | − | 0.999919i | \(-0.495942\pi\) |
0.598051 | + | 0.801458i | \(0.295942\pi\) | |||||||
\(180\) | 3.42769 | + | 1.11372i | 0.255485 | + | 0.0830121i | ||||
\(181\) | 7.68310 | + | 5.58210i | 0.571080 | + | 0.414914i | 0.835497 | − | 0.549494i | \(-0.185180\pi\) |
−0.264417 | + | 0.964408i | \(0.585180\pi\) | |||||||
\(182\) | −0.501877 | + | 0.690774i | −0.0372016 | + | 0.0512036i | ||||
\(183\) | −14.2345 | − | 4.62508i | −1.05225 | − | 0.341896i | ||||
\(184\) | 8.11658 | + | 24.9803i | 0.598363 | + | 1.84157i | ||||
\(185\) | 3.41564 | − | 2.48161i | 0.251123 | − | 0.182451i | ||||
\(186\) | 2.94969i | 0.216282i | ||||||||
\(187\) | −7.31081 | − | 1.77019i | −0.534620 | − | 0.129449i | ||||
\(188\) | 5.92725 | 0.432289 | ||||||||
\(189\) | 4.95039 | + | 6.81362i | 0.360088 | + | 0.495618i | ||||
\(190\) | 5.56763 | − | 1.80903i | 0.403919 | − | 0.131241i | ||||
\(191\) | −10.6505 | − | 3.46055i | −0.770641 | − | 0.250396i | −0.102802 | − | 0.994702i | \(-0.532781\pi\) |
−0.667839 | + | 0.744305i | \(0.732781\pi\) | |||||||
\(192\) | −8.26083 | + | 11.3701i | −0.596174 | + | 0.820563i | ||||
\(193\) | 3.84501 | − | 5.29220i | 0.276770 | − | 0.380941i | −0.647891 | − | 0.761733i | \(-0.724349\pi\) |
0.924661 | + | 0.380792i | \(0.124349\pi\) | |||||||
\(194\) | 2.19030 | − | 6.74106i | 0.157255 | − | 0.483980i | ||||
\(195\) | 0.161853 | − | 0.0525891i | 0.0115905 | − | 0.00376598i | ||||
\(196\) | 13.0126 | − | 9.45420i | 0.929471 | − | 0.675300i | ||||
\(197\) | 10.6950i | 0.761985i | 0.924578 | + | 0.380993i | \(0.124418\pi\) | ||||
−0.924578 | + | 0.380993i | \(0.875582\pi\) | |||||||
\(198\) | −12.7427 | + | 0.977978i | −0.905583 | + | 0.0695019i | ||||
\(199\) | − | 24.7641i | − | 1.75548i | −0.479139 | − | 0.877739i | \(-0.659051\pi\) | ||
0.479139 | − | 0.877739i | \(-0.340949\pi\) | |||||||
\(200\) | −13.2610 | + | 9.63468i | −0.937694 | + | 0.681275i | ||||
\(201\) | 1.63809 | − | 0.532249i | 0.115542 | − | 0.0375419i | ||||
\(202\) | 2.44496 | + | 0.794416i | 0.172027 | + | 0.0558949i | ||||
\(203\) | 6.24094 | + | 4.53431i | 0.438028 | + | 0.318246i | ||||
\(204\) | 7.51732 | + | 5.46165i | 0.526317 | + | 0.382392i | ||||
\(205\) | −1.66328 | + | 5.11905i | −0.116168 | + | 0.357530i | ||||
\(206\) | 10.3481 | + | 31.8482i | 0.720988 | + | 2.21897i | ||||
\(207\) | −9.80547 | + | 7.12409i | −0.681527 | + | 0.495159i | ||||
\(208\) | 0.308780i | 0.0214101i | ||||||||
\(209\) | −10.0767 | + | 8.57257i | −0.697023 | + | 0.592977i | ||||
\(210\) | 2.66330 | 0.183785 | ||||||||
\(211\) | 13.1127 | − | 9.52691i | 0.902713 | − | 0.655860i | −0.0364481 | − | 0.999336i | \(-0.511604\pi\) |
0.939161 | + | 0.343476i | \(0.111604\pi\) | |||||||
\(212\) | −3.35852 | − | 10.3365i | −0.230664 | − | 0.709912i | ||||
\(213\) | −3.98679 | + | 12.2701i | −0.273170 | + | 0.840732i | ||||
\(214\) | −6.63417 | + | 9.13115i | −0.453502 | + | 0.624192i | ||||
\(215\) | 3.42412 | − | 2.25180i | 0.233523 | − | 0.153571i | ||||
\(216\) | 18.2980 | + | 5.94539i | 1.24502 | + | 0.404533i | ||||
\(217\) | −0.518307 | − | 1.59519i | −0.0351850 | − | 0.108288i | ||||
\(218\) | 18.6024 | + | 25.6041i | 1.25992 | + | 1.73413i | ||||
\(219\) | − | 7.03558i | − | 0.475420i | ||||||
\(220\) | −3.81819 | + | 6.20364i | −0.257422 | + | 0.418250i | ||||
\(221\) | −0.529757 | −0.0356353 | ||||||||
\(222\) | 14.9617 | − | 10.8703i | 1.00416 | − | 0.729567i | ||||
\(223\) | 15.4947 | − | 5.03453i | 1.03760 | − | 0.337137i | 0.259809 | − | 0.965660i | \(-0.416340\pi\) |
0.777791 | + | 0.628523i | \(0.216340\pi\) | |||||||
\(224\) | 1.92795 | − | 5.93360i | 0.128816 | − | 0.396456i | ||||
\(225\) | −6.11922 | − | 4.44587i | −0.407948 | − | 0.296392i | ||||
\(226\) | −12.1539 | + | 16.7285i | −0.808468 | + | 1.11276i | ||||
\(227\) | −4.19787 | + | 12.9197i | −0.278622 | + | 0.857511i | 0.709616 | + | 0.704589i | \(0.248868\pi\) |
−0.988238 | + | 0.152922i | \(0.951132\pi\) | |||||||
\(228\) | 15.5428 | − | 5.05017i | 1.02935 | − | 0.334456i | ||||
\(229\) | −18.4963 | + | 13.4384i | −1.22227 | + | 0.888031i | −0.996287 | − | 0.0860998i | \(-0.972560\pi\) |
−0.225984 | + | 0.974131i | \(0.572560\pi\) | |||||||
\(230\) | 10.8398i | 0.714758i | ||||||||
\(231\) | −5.56512 | + | 2.29250i | −0.366158 | + | 0.150835i | ||||
\(232\) | 17.6226 | 1.15698 | ||||||||
\(233\) | −12.0575 | + | 8.76032i | −0.789916 | + | 0.573908i | −0.907939 | − | 0.419103i | \(-0.862344\pi\) |
0.118023 | + | 0.993011i | \(0.462344\pi\) | |||||||
\(234\) | −0.856016 | + | 0.278137i | −0.0559595 | + | 0.0181824i | ||||
\(235\) | 1.00247 | + | 0.325723i | 0.0653941 | + | 0.0212478i | ||||
\(236\) | −7.76295 | − | 5.64011i | −0.505325 | − | 0.367140i | ||||
\(237\) | −4.17219 | − | 3.03127i | −0.271013 | − | 0.196902i | ||||
\(238\) | −7.88478 | − | 2.56192i | −0.511095 | − | 0.166065i | ||||
\(239\) | 7.40424 | − | 2.40578i | 0.478940 | − | 0.155617i | −0.0595907 | − | 0.998223i | \(-0.518980\pi\) |
0.538531 | + | 0.842606i | \(0.318980\pi\) | |||||||
\(240\) | 0.779199 | − | 0.566121i | 0.0502971 | − | 0.0365430i | ||||
\(241\) | 11.0061 | 0.708968 | 0.354484 | − | 0.935062i | \(-0.384657\pi\) | ||||
0.354484 | + | 0.935062i | \(0.384657\pi\) | |||||||
\(242\) | 4.13989 | − | 25.4970i | 0.266122 | − | 1.63901i | ||||
\(243\) | 14.6170i | 0.937682i | ||||||||
\(244\) | 36.5023 | − | 26.5205i | 2.33682 | − | 1.69780i | ||||
\(245\) | 2.72035 | − | 0.883897i | 0.173797 | − | 0.0564701i | ||||
\(246\) | −7.28574 | + | 22.4232i | −0.464522 | + | 1.42965i | ||||
\(247\) | −0.547664 | + | 0.753794i | −0.0348470 | + | 0.0479628i | ||||
\(248\) | −3.09985 | − | 2.25217i | −0.196840 | − | 0.143013i | ||||
\(249\) | −6.08038 | + | 18.7135i | −0.385329 | + | 1.18592i | ||||
\(250\) | −13.4125 | + | 4.35797i | −0.848278 | + | 0.275622i | ||||
\(251\) | −19.8910 | + | 14.4516i | −1.25551 | + | 0.912180i | −0.998528 | − | 0.0542370i | \(-0.982727\pi\) |
−0.256980 | + | 0.966417i | \(0.582727\pi\) | |||||||
\(252\) | −8.97703 | −0.565500 | ||||||||
\(253\) | −9.33067 | − | 22.6505i | −0.586614 | − | 1.42403i | ||||
\(254\) | 2.31365i | 0.145171i | ||||||||
\(255\) | 0.971263 | + | 1.33683i | 0.0608229 | + | 0.0837155i | ||||
\(256\) | −7.27550 | − | 22.3917i | −0.454719 | − | 1.39948i | ||||
\(257\) | 16.7584 | + | 5.44513i | 1.04536 | + | 0.339658i | 0.780845 | − | 0.624724i | \(-0.214789\pi\) |
0.264514 | + | 0.964382i | \(0.414789\pi\) | |||||||
\(258\) | 14.9988 | − | 9.86366i | 0.933786 | − | 0.614084i | ||||
\(259\) | −6.18117 | + | 8.50765i | −0.384079 | + | 0.528640i | ||||
\(260\) | −0.158533 | + | 0.487916i | −0.00983183 | + | 0.0302593i | ||||
\(261\) | 2.51288 | + | 7.73386i | 0.155544 | + | 0.478714i | ||||
\(262\) | 9.76433 | − | 7.09420i | 0.603242 | − | 0.438281i | ||||
\(263\) | 4.61664 | 0.284674 | 0.142337 | − | 0.989818i | \(-0.454538\pi\) | ||||
0.142337 | + | 0.989818i | \(0.454538\pi\) | |||||||
\(264\) | −7.20687 | + | 11.7094i | −0.443552 | + | 0.720667i | ||||
\(265\) | − | 1.93277i | − | 0.118729i | ||||||
\(266\) | −11.7967 | + | 8.57078i | −0.723300 | + | 0.525508i | ||||
\(267\) | 0.0137395 | + | 0.0422857i | 0.000840841 | + | 0.00258784i | ||||
\(268\) | −1.60450 | + | 4.93815i | −0.0980105 | + | 0.301645i | ||||
\(269\) | 6.89950 | + | 5.01278i | 0.420670 | + | 0.305634i | 0.777907 | − | 0.628379i | \(-0.216281\pi\) |
−0.357238 | + | 0.934014i | \(0.616281\pi\) | |||||||
\(270\) | 6.42374 | + | 4.66712i | 0.390936 | + | 0.284032i | ||||
\(271\) | −6.26603 | − | 2.03596i | −0.380634 | − | 0.123676i | 0.112449 | − | 0.993657i | \(-0.464130\pi\) |
−0.493084 | + | 0.869982i | \(0.664130\pi\) | |||||||
\(272\) | −2.85142 | + | 0.926482i | −0.172893 | + | 0.0561762i | ||||
\(273\) | −0.342932 | + | 0.249155i | −0.0207552 | + | 0.0150795i | ||||
\(274\) | − | 35.3682i | − | 2.13667i | ||||||
\(275\) | 11.6441 | − | 9.90598i | 0.702167 | − | 0.597353i | ||||
\(276\) | 30.2609i | 1.82149i | ||||||||
\(277\) | −4.19352 | + | 3.04677i | −0.251964 | + | 0.183063i | −0.706597 | − | 0.707616i | \(-0.749770\pi\) |
0.454633 | + | 0.890679i | \(0.349770\pi\) | |||||||
\(278\) | 43.3461 | − | 14.0840i | 2.59973 | − | 0.844702i | ||||
\(279\) | 0.546367 | − | 1.68155i | 0.0327102 | − | 0.100672i | ||||
\(280\) | −2.03350 | + | 2.79888i | −0.121525 | + | 0.167265i | ||||
\(281\) | 14.6753 | − | 20.1988i | 0.875453 | − | 1.20496i | −0.102207 | − | 0.994763i | \(-0.532590\pi\) |
0.977660 | − | 0.210194i | \(-0.0674096\pi\) | |||||||
\(282\) | 4.39118 | + | 1.42678i | 0.261491 | + | 0.0849635i | ||||
\(283\) | −12.5391 | + | 4.07420i | −0.745371 | + | 0.242186i | −0.656988 | − | 0.753901i | \(-0.728170\pi\) |
−0.0883829 | + | 0.996087i | \(0.528170\pi\) | |||||||
\(284\) | −22.8605 | − | 31.4647i | −1.35652 | − | 1.86709i | ||||
\(285\) | 2.90627 | 0.172153 | ||||||||
\(286\) | −0.139211 | − | 1.81386i | −0.00823170 | − | 0.107256i | ||||
\(287\) | − | 13.4066i | − | 0.791369i | ||||||
\(288\) | 5.32068 | − | 3.86570i | 0.313524 | − | 0.227789i | ||||
\(289\) | 3.66377 | + | 11.2759i | 0.215516 | + | 0.663290i | ||||
\(290\) | 6.91685 | + | 2.24742i | 0.406172 | + | 0.131973i | ||||
\(291\) | 2.06830 | − | 2.84677i | 0.121246 | − | 0.166880i | ||||
\(292\) | 17.1586 | + | 12.4665i | 1.00413 | + | 0.729545i | ||||
\(293\) | 18.9687 | + | 6.16331i | 1.10816 | + | 0.360065i | 0.805240 | − | 0.592950i | \(-0.202037\pi\) |
0.302925 | + | 0.953014i | \(0.402037\pi\) | |||||||
\(294\) | 11.9161 | − | 3.87177i | 0.694961 | − | 0.225806i | ||||
\(295\) | −1.00300 | − | 1.38051i | −0.0583969 | − | 0.0803764i | ||||
\(296\) | 24.0231i | 1.39632i | ||||||||
\(297\) | −17.4401 | − | 4.22284i | −1.01198 | − | 0.245034i | ||||
\(298\) | 42.8350 | 2.48137 | ||||||||
\(299\) | −1.01408 | − | 1.39576i | −0.0586458 | − | 0.0807191i | ||||
\(300\) | −17.9604 | + | 5.83569i | −1.03694 | + | 0.336924i | ||||
\(301\) | −6.37813 | + | 7.96978i | −0.367629 | + | 0.459370i | ||||
\(302\) | 0.969695 | + | 0.704525i | 0.0557997 | + | 0.0405408i | ||||
\(303\) | 1.03251 | + | 0.750165i | 0.0593164 | + | 0.0430959i | ||||
\(304\) | −1.62950 | + | 5.01510i | −0.0934585 | + | 0.287636i | ||||
\(305\) | 7.63101 | − | 2.47947i | 0.436950 | − | 0.141974i | ||||
\(306\) | −5.13688 | − | 7.07031i | −0.293656 | − | 0.404183i | ||||
\(307\) | − | 14.9720i | − | 0.854499i | −0.904134 | − | 0.427250i | \(-0.859483\pi\) | ||
0.904134 | − | 0.427250i | \(-0.140517\pi\) | |||||||
\(308\) | 4.26992 | − | 17.6346i | 0.243301 | − | 1.00482i | ||||
\(309\) | 16.6246i | 0.945741i | ||||||||
\(310\) | −0.929466 | − | 1.27930i | −0.0527901 | − | 0.0726594i | ||||
\(311\) | 0.416422 | + | 1.28162i | 0.0236132 | + | 0.0726738i | 0.962169 | − | 0.272454i | \(-0.0878354\pi\) |
−0.938556 | + | 0.345128i | \(0.887835\pi\) | |||||||
\(312\) | −0.299234 | + | 0.920946i | −0.0169408 | + | 0.0521383i | ||||
\(313\) | 1.81491 | − | 2.49800i | 0.102585 | − | 0.141196i | −0.754639 | − | 0.656141i | \(-0.772188\pi\) |
0.857223 | + | 0.514945i | \(0.172188\pi\) | |||||||
\(314\) | −8.77338 | + | 12.0755i | −0.495110 | + | 0.681461i | ||||
\(315\) | −1.51828 | − | 0.493319i | −0.0855454 | − | 0.0277954i | ||||
\(316\) | 14.7856 | − | 4.80412i | 0.831753 | − | 0.270253i | ||||
\(317\) | 11.3497 | − | 8.24608i | 0.637465 | − | 0.463146i | −0.221513 | − | 0.975157i | \(-0.571100\pi\) |
0.858978 | + | 0.512012i | \(0.171100\pi\) | |||||||
\(318\) | − | 8.46619i | − | 0.474760i | ||||||
\(319\) | −16.3877 | + | 1.25773i | −0.917536 | + | 0.0704193i | ||||
\(320\) | − | 7.53431i | − | 0.421181i | ||||||
\(321\) | −4.53312 | + | 3.29351i | −0.253014 | + | 0.183826i | ||||
\(322\) | −8.34340 | − | 25.6783i | −0.464959 | − | 1.43100i | ||||
\(323\) | −8.60413 | − | 2.79565i | −0.478746 | − | 0.155554i | ||||
\(324\) | 3.93636 | + | 2.85993i | 0.218686 | + | 0.158885i | ||||
\(325\) | 0.632849 | − | 0.871042i | 0.0351042 | − | 0.0483167i | ||||
\(326\) | −2.60915 | − | 0.847764i | −0.144507 | − | 0.0469533i | ||||
\(327\) | 4.85519 | + | 14.9427i | 0.268492 | + | 0.826335i | ||||
\(328\) | −18.0018 | − | 24.7774i | −0.993984 | − | 1.36810i | ||||
\(329\) | −2.62545 | −0.144746 | ||||||||
\(330\) | −4.32200 | + | 3.67685i | −0.237918 | + | 0.202404i | ||||
\(331\) | − | 13.8890i | − | 0.763410i | −0.924284 | − | 0.381705i | \(-0.875337\pi\) | ||
0.924284 | − | 0.381705i | \(-0.124663\pi\) | |||||||
\(332\) | −34.8652 | − | 47.9879i | −1.91348 | − | 2.63368i | ||||
\(333\) | −10.5428 | + | 3.42556i | −0.577742 | + | 0.187720i | ||||
\(334\) | 5.34961 | + | 1.73819i | 0.292717 | + | 0.0951096i | ||||
\(335\) | −0.542737 | + | 0.747014i | −0.0296529 | + | 0.0408137i | ||||
\(336\) | −1.41009 | + | 1.94082i | −0.0769268 | + | 0.105881i | ||||
\(337\) | −21.9471 | − | 7.13105i | −1.19554 | − | 0.388453i | −0.357419 | − | 0.933944i | \(-0.616343\pi\) |
−0.838117 | + | 0.545491i | \(0.816343\pi\) | |||||||
\(338\) | 9.39391 | + | 28.9115i | 0.510961 | + | 1.57258i | ||||
\(339\) | −8.30479 | + | 6.03378i | −0.451054 | + | 0.327710i | ||||
\(340\) | −4.98131 | −0.270150 | ||||||||
\(341\) | 3.04336 | + | 1.87311i | 0.164807 | + | 0.101435i | ||||
\(342\) | −15.3709 | −0.831163 | ||||||||
\(343\) | −14.5795 | + | 10.5926i | −0.787216 | + | 0.571946i | ||||
\(344\) | −1.08624 | + | 23.2935i | −0.0585661 | + | 1.25590i | ||||
\(345\) | −1.66294 | + | 5.11802i | −0.0895299 | + | 0.275545i | ||||
\(346\) | −4.73222 | + | 6.51335i | −0.254406 | + | 0.350160i | ||||
\(347\) | −14.8096 | − | 10.7598i | −0.795020 | − | 0.577616i | 0.114429 | − | 0.993431i | \(-0.463496\pi\) |
−0.909449 | + | 0.415816i | \(0.863496\pi\) | |||||||
\(348\) | 19.3094 | + | 6.27399i | 1.03509 | + | 0.336321i | ||||
\(349\) | 8.24324 | + | 25.3701i | 0.441250 | + | 1.35803i | 0.886544 | + | 0.462645i | \(0.153099\pi\) |
−0.445293 | + | 0.895385i | \(0.646901\pi\) | |||||||
\(350\) | 13.6316 | − | 9.90391i | 0.728638 | − | 0.529386i | ||||
\(351\) | −1.26375 | −0.0674540 | ||||||||
\(352\) | 5.06304 | + | 12.2907i | 0.269861 | + | 0.655097i | ||||
\(353\) | 1.37635 | 0.0732555 | 0.0366277 | − | 0.999329i | \(-0.488338\pi\) | ||||
0.0366277 | + | 0.999329i | \(0.488338\pi\) | |||||||
\(354\) | −4.39349 | − | 6.04711i | −0.233511 | − | 0.321401i | ||||
\(355\) | −2.13728 | − | 6.57788i | −0.113435 | − | 0.349118i | ||||
\(356\) | −0.127473 | − | 0.0414186i | −0.00675607 | − | 0.00219518i | ||||
\(357\) | −3.32976 | − | 2.41921i | −0.176230 | − | 0.128038i | ||||
\(358\) | −11.8600 | + | 16.3239i | −0.626820 | + | 0.862743i | ||||
\(359\) | 1.09030 | + | 0.354261i | 0.0575441 | + | 0.0186972i | 0.337648 | − | 0.941273i | \(-0.390369\pi\) |
−0.280104 | + | 0.959970i | \(0.590369\pi\) | |||||||
\(360\) | −3.46840 | + | 1.12695i | −0.182801 | + | 0.0593956i | ||||
\(361\) | 2.49842 | − | 1.81521i | 0.131496 | − | 0.0955373i | ||||
\(362\) | −22.3011 | −1.17212 | ||||||||
\(363\) | 5.86615 | − | 11.4033i | 0.307893 | − | 0.598516i | ||||
\(364\) | − | 1.27784i | − | 0.0669769i | ||||||
\(365\) | 2.21696 | + | 3.05138i | 0.116041 | + | 0.159716i | ||||
\(366\) | 33.4265 | − | 10.8609i | 1.74723 | − | 0.567709i | ||||
\(367\) | −8.41586 | + | 25.9013i | −0.439304 | + | 1.35204i | 0.449307 | + | 0.893378i | \(0.351671\pi\) |
−0.888611 | + | 0.458662i | \(0.848329\pi\) | |||||||
\(368\) | −7.89932 | − | 5.73919i | −0.411780 | − | 0.299176i | ||||
\(369\) | 8.30685 | − | 11.4334i | 0.432437 | − | 0.595199i | ||||
\(370\) | −3.06368 | + | 9.42905i | −0.159273 | + | 0.490193i | ||||
\(371\) | 1.48764 | + | 4.57850i | 0.0772346 | + | 0.237704i | ||||
\(372\) | −2.59473 | − | 3.57134i | −0.134531 | − | 0.185165i | ||||
\(373\) | −33.4231 | −1.73058 | −0.865291 | − | 0.501269i | \(-0.832867\pi\) | ||||
−0.865291 | + | 0.501269i | \(0.832867\pi\) | |||||||
\(374\) | 16.3323 | − | 6.72795i | 0.844525 | − | 0.347894i | ||||
\(375\) | −7.00123 | −0.361542 | ||||||||
\(376\) | −4.85220 | + | 3.52533i | −0.250233 | + | 0.181805i | ||||
\(377\) | −1.10088 | + | 0.357697i | −0.0566981 | + | 0.0184223i | ||||
\(378\) | −18.8094 | − | 6.11153i | −0.967449 | − | 0.314343i | ||||
\(379\) | 6.58939 | + | 4.78747i | 0.338474 | + | 0.245916i | 0.744018 | − | 0.668160i | \(-0.232918\pi\) |
−0.405543 | + | 0.914076i | \(0.632918\pi\) | |||||||
\(380\) | −5.14969 | + | 7.08793i | −0.264173 | + | 0.363603i | ||||
\(381\) | −0.354938 | + | 1.09239i | −0.0181840 | + | 0.0559646i | ||||
\(382\) | 25.0101 | − | 8.12628i | 1.27963 | − | 0.415777i | ||||
\(383\) | −14.8832 | − | 20.4850i | −0.760498 | − | 1.04674i | −0.997172 | − | 0.0751467i | \(-0.976057\pi\) |
0.236674 | − | 0.971589i | \(-0.423943\pi\) | |||||||
\(384\) | − | 23.6582i | − | 1.20730i | ||||||
\(385\) | 1.69125 | − | 2.74788i | 0.0861941 | − | 0.140045i | ||||
\(386\) | 15.3612i | 0.781866i | ||||||||
\(387\) | −10.3775 | + | 2.84482i | −0.527518 | + | 0.144610i | ||||
\(388\) | 3.27795 | + | 10.0885i | 0.166413 | + | 0.512165i | ||||
\(389\) | 30.4054 | + | 9.87933i | 1.54162 | + | 0.500902i | 0.951822 | − | 0.306651i | \(-0.0992085\pi\) |
0.589795 | + | 0.807553i | \(0.299208\pi\) | |||||||
\(390\) | −0.234898 | + | 0.323309i | −0.0118945 | + | 0.0163714i | ||||
\(391\) | 9.84641 | − | 13.5524i | 0.497954 | − | 0.685375i | ||||
\(392\) | −5.02940 | + | 15.4789i | −0.254023 | + | 0.781803i | ||||
\(393\) | 5.69854 | − | 1.85157i | 0.287453 | − | 0.0933992i | ||||
\(394\) | −14.7620 | − | 20.3182i | −0.743699 | − | 1.02361i | ||||
\(395\) | 2.76468 | 0.139106 | ||||||||
\(396\) | 14.5679 | − | 12.3934i | 0.732066 | − | 0.622790i | ||||
\(397\) | 1.92527 | 0.0966266 | 0.0483133 | − | 0.998832i | \(-0.484615\pi\) | ||||
0.0483133 | + | 0.998832i | \(0.484615\pi\) | |||||||
\(398\) | 34.1812 | + | 47.0464i | 1.71335 | + | 2.35822i | ||||
\(399\) | −6.88463 | + | 2.23695i | −0.344662 | + | 0.111988i | ||||
\(400\) | 1.88296 | − | 5.79517i | 0.0941482 | − | 0.289758i | ||||
\(401\) | −8.24681 | − | 5.99166i | −0.411826 | − | 0.299209i | 0.362515 | − | 0.931978i | \(-0.381918\pi\) |
−0.774341 | + | 0.632769i | \(0.781918\pi\) | |||||||
\(402\) | −2.37738 | + | 3.27218i | −0.118573 | + | 0.163201i | ||||
\(403\) | 0.239360 | + | 0.0777729i | 0.0119234 | + | 0.00387414i | ||||
\(404\) | −3.65906 | + | 1.18890i | −0.182045 | + | 0.0591501i | ||||
\(405\) | 0.508591 | + | 0.700015i | 0.0252721 | + | 0.0347840i | ||||
\(406\) | −18.1151 | −0.899035 | ||||||||
\(407\) | −1.71453 | − | 22.3397i | −0.0849863 | − | 1.10734i | ||||
\(408\) | −9.40228 | −0.465482 | ||||||||
\(409\) | 17.4402 | − | 12.6710i | 0.862361 | − | 0.626542i | −0.0661651 | − | 0.997809i | \(-0.521076\pi\) |
0.928526 | + | 0.371267i | \(0.121076\pi\) | |||||||
\(410\) | −3.90582 | − | 12.0209i | −0.192895 | − | 0.593669i | ||||
\(411\) | 5.42585 | − | 16.6991i | 0.267637 | − | 0.823703i | ||||
\(412\) | −40.5447 | − | 29.4575i | −1.99750 | − | 1.45127i | ||||
\(413\) | 3.43856 | + | 2.49826i | 0.169201 | + | 0.122931i | ||||
\(414\) | 8.79509 | − | 27.0685i | 0.432255 | − | 1.33034i | ||||
\(415\) | −3.25964 | − | 10.0321i | −0.160009 | − | 0.492458i | ||||
\(416\) | 0.550265 | + | 0.757374i | 0.0269789 | + | 0.0371333i | ||||
\(417\) | 22.6264 | 1.10802 | ||||||||
\(418\) | 7.31115 | − | 30.1947i | 0.357600 | − | 1.47687i | ||||
\(419\) | − | 34.5588i | − | 1.68831i | −0.536101 | − | 0.844154i | \(-0.680104\pi\) | ||
0.536101 | − | 0.844154i | \(-0.319896\pi\) | |||||||
\(420\) | −3.22459 | + | 2.34280i | −0.157344 | + | 0.114317i | ||||
\(421\) | −31.1838 | + | 10.1322i | −1.51980 | + | 0.493814i | −0.945720 | − | 0.324982i | \(-0.894642\pi\) |
−0.574084 | + | 0.818796i | \(0.694642\pi\) | |||||||
\(422\) | −11.7615 | + | 36.1982i | −0.572541 | + | 1.76210i | ||||
\(423\) | −2.23902 | − | 1.62675i | −0.108865 | − | 0.0790951i | ||||
\(424\) | 8.89717 | + | 6.46417i | 0.432085 | + | 0.313928i | ||||
\(425\) | 9.94245 | + | 3.23050i | 0.482279 | + | 0.156702i | ||||
\(426\) | −9.36204 | − | 28.8134i | −0.453592 | − | 1.39601i | ||||
\(427\) | −16.1685 | + | 11.7471i | −0.782450 | + | 0.568483i | ||||
\(428\) | − | 16.8914i | − | 0.816476i | ||||||
\(429\) | 0.212537 | − | 0.877768i | 0.0102614 | − | 0.0423790i | ||||
\(430\) | −3.39699 | + | 9.00416i | −0.163817 | + | 0.434219i | ||||
\(431\) | 12.3616 | + | 17.0143i | 0.595438 | + | 0.819551i | 0.995281 | − | 0.0970332i | \(-0.0309353\pi\) |
−0.399843 | + | 0.916584i | \(0.630935\pi\) | |||||||
\(432\) | −6.80214 | + | 2.21015i | −0.327268 | + | 0.106336i | ||||
\(433\) | −5.92241 | − | 1.92431i | −0.284613 | − | 0.0924764i | 0.163232 | − | 0.986588i | \(-0.447808\pi\) |
−0.447845 | + | 0.894111i | \(0.647808\pi\) | |||||||
\(434\) | 3.18647 | + | 2.31511i | 0.152955 | + | 0.111129i | ||||
\(435\) | 2.92100 | + | 2.12223i | 0.140051 | + | 0.101753i | ||||
\(436\) | −45.0459 | − | 14.6363i | −2.15731 | − | 0.700952i | ||||
\(437\) | −9.10458 | − | 28.0210i | −0.435531 | − | 1.34043i | ||||
\(438\) | 9.71103 | + | 13.3661i | 0.464011 | + | 0.638656i | ||||
\(439\) | − | 12.8737i | − | 0.614426i | −0.951641 | − | 0.307213i | \(-0.900604\pi\) | ||
0.951641 | − | 0.307213i | \(-0.0993965\pi\) | |||||||
\(440\) | −0.564053 | − | 7.34940i | −0.0268902 | − | 0.350369i | ||||
\(441\) | −7.51024 | −0.357631 | ||||||||
\(442\) | 1.00643 | − | 0.731211i | 0.0478708 | − | 0.0347802i | ||||
\(443\) | 7.58749 | + | 23.3519i | 0.360493 | + | 1.10948i | 0.952756 | + | 0.303738i | \(0.0982347\pi\) |
−0.592263 | + | 0.805745i | \(0.701765\pi\) | |||||||
\(444\) | −8.55270 | + | 26.3225i | −0.405893 | + | 1.24921i | ||||
\(445\) | −0.0192834 | − | 0.0140102i | −0.000914120 | − | 0.000664147i | ||||
\(446\) | −22.4875 | + | 30.9514i | −1.06482 | + | 1.46559i | ||||
\(447\) | 20.2245 | + | 6.57134i | 0.956586 | + | 0.310814i | ||||
\(448\) | 5.79913 | + | 17.8479i | 0.273983 | + | 0.843234i | ||||
\(449\) | 5.42283 | + | 7.46388i | 0.255919 | + | 0.352242i | 0.917573 | − | 0.397567i | \(-0.130145\pi\) |
−0.661654 | + | 0.749809i | \(0.730145\pi\) | |||||||
\(450\) | 17.7617 | 0.837297 | ||||||||
\(451\) | 18.5087 | + | 21.7563i | 0.871541 | + | 1.02447i | ||||
\(452\) | − | 30.9454i | − | 1.45555i | ||||||
\(453\) | 0.349759 | + | 0.481402i | 0.0164331 | + | 0.0226182i | ||||
\(454\) | −9.85770 | − | 30.3389i | −0.462645 | − | 1.42387i | ||||
\(455\) | 0.0702217 | − | 0.216120i | 0.00329204 | − | 0.0101319i | ||||
\(456\) | −9.72009 | + | 13.3786i | −0.455185 | + | 0.626508i | ||||
\(457\) | 20.3310 | + | 14.7713i | 0.951043 | + | 0.690973i | 0.951053 | − | 0.309027i | \(-0.100003\pi\) |
−1.00312e−5 | 1.00000i | \(0.500003\pi\) | ||||||||
\(458\) | 16.5904 | − | 51.0600i | 0.775218 | − | 2.38588i | ||||
\(459\) | −3.79183 | − | 11.6700i | −0.176987 | − | 0.544711i | ||||
\(460\) | −9.53541 | − | 13.1244i | −0.444591 | − | 0.611927i | ||||
\(461\) | − | 6.03723i | − | 0.281182i | −0.990068 | − | 0.140591i | \(-0.955100\pi\) | ||
0.990068 | − | 0.140591i | \(-0.0449002\pi\) | |||||||
\(462\) | 7.40826 | − | 12.0367i | 0.344663 | − | 0.559996i | ||||
\(463\) | − | 1.79835i | − | 0.0835764i | −0.999126 | − | 0.0417882i | \(-0.986695\pi\) | ||
0.999126 | − | 0.0417882i | \(-0.0133055\pi\) | |||||||
\(464\) | −5.29991 | + | 3.85061i | −0.246042 | + | 0.178760i | ||||
\(465\) | −0.242588 | − | 0.746609i | −0.0112498 | − | 0.0346232i | ||||
\(466\) | 10.8151 | − | 33.2855i | 0.501000 | − | 1.54192i | ||||
\(467\) | −18.8383 | + | 25.9286i | −0.871730 | + | 1.19983i | 0.106913 | + | 0.994268i | \(0.465903\pi\) |
−0.978643 | + | 0.205566i | \(0.934097\pi\) | |||||||
\(468\) | 0.791757 | − | 1.08976i | 0.0365990 | − | 0.0503742i | ||||
\(469\) | 0.710707 | − | 2.18733i | 0.0328174 | − | 0.101002i | ||||
\(470\) | −2.35407 | + | 0.764884i | −0.108585 | + | 0.0352815i | ||||
\(471\) | −5.99485 | + | 4.35551i | −0.276228 | + | 0.200691i | ||||
\(472\) | 9.70950 | 0.446916 | ||||||||
\(473\) | −0.652341 | − | 21.7388i | −0.0299947 | − | 0.999550i | ||||
\(474\) | 12.1103 | 0.556243 | ||||||||
\(475\) | 14.8752 | − | 10.8075i | 0.682521 | − | 0.495881i | ||||
\(476\) | 11.8001 | − | 3.83410i | 0.540859 | − | 0.175736i | ||||
\(477\) | −1.56818 | + | 4.82637i | −0.0718021 | + | 0.220984i | ||||
\(478\) | −10.7458 | + | 14.7904i | −0.491502 | + | 0.676495i | ||||
\(479\) | −19.0644 | + | 26.2399i | −0.871075 | + | 1.19893i | 0.107739 | + | 0.994179i | \(0.465639\pi\) |
−0.978814 | + | 0.204753i | \(0.934361\pi\) | |||||||
\(480\) | 0.902353 | − | 2.77716i | 0.0411866 | − | 0.126759i | ||||
\(481\) | −0.487613 | − | 1.50072i | −0.0222332 | − | 0.0684268i | ||||
\(482\) | −20.9093 | + | 15.1915i | −0.952394 | + | 0.691954i | ||||
\(483\) | − | 13.4039i | − | 0.609901i | ||||||
\(484\) | 17.4164 | + | 34.5123i | 0.791654 | + | 1.56874i | ||||
\(485\) | 1.88640i | 0.0856568i | ||||||||
\(486\) | −20.1755 | − | 27.7692i | −0.915180 | − | 1.25964i | ||||
\(487\) | 13.0195 | + | 40.0699i | 0.589970 | + | 1.81574i | 0.578323 | + | 0.815808i | \(0.303707\pi\) |
0.0116468 | + | 0.999932i | \(0.496293\pi\) | |||||||
\(488\) | −14.1082 | + | 43.4207i | −0.638650 | + | 1.96556i | ||||
\(489\) | −1.10185 | − | 0.800541i | −0.0498274 | − | 0.0362017i | ||||
\(490\) | −3.94807 | + | 5.43405i | −0.178356 | + | 0.245485i | ||||
\(491\) | −6.74776 | + | 20.7675i | −0.304522 | + | 0.937223i | 0.675333 | + | 0.737513i | \(0.264000\pi\) |
−0.979855 | + | 0.199710i | \(0.936000\pi\) | |||||||
\(492\) | −10.9036 | − | 33.5579i | −0.491574 | − | 1.51291i | ||||
\(493\) | −6.60628 | − | 9.09277i | −0.297532 | − | 0.409518i | ||||
\(494\) | − | 2.18798i | − | 0.0984417i | ||||||
\(495\) | 3.14493 | − | 1.29552i | 0.141354 | − | 0.0582294i | ||||
\(496\) | 1.42437 | 0.0639562 | ||||||||
\(497\) | 10.1259 | + | 13.9372i | 0.454211 | + | 0.625168i | ||||
\(498\) | −14.2783 | − | 43.9442i | −0.639828 | − | 1.96919i | ||||
\(499\) | 36.8163 | + | 11.9623i | 1.64812 | + | 0.535508i | 0.978332 | − | 0.207041i | \(-0.0663835\pi\) |
0.669791 | + | 0.742549i | \(0.266384\pi\) | |||||||
\(500\) | 12.4056 | − | 17.0749i | 0.554796 | − | 0.763611i | ||||
\(501\) | 2.25915 | + | 1.64137i | 0.100931 | + | 0.0733310i | ||||
\(502\) | 17.8414 | − | 54.9101i | 0.796299 | − | 2.45076i | ||||
\(503\) | 2.25060 | + | 6.92663i | 0.100349 | + | 0.308843i | 0.988611 | − | 0.150495i | \(-0.0480867\pi\) |
−0.888262 | + | 0.459338i | \(0.848087\pi\) | |||||||
\(504\) | 7.34883 | − | 5.33924i | 0.327343 | − | 0.237829i | ||||
\(505\) | −0.684190 | −0.0304461 | ||||||||
\(506\) | 48.9902 | + | 30.1523i | 2.17788 | + | 1.34043i | ||||
\(507\) | 15.0916i | 0.670243i | ||||||||
\(508\) | −2.03523 | − | 2.80126i | −0.0902988 | − | 0.124286i | ||||
\(509\) | −1.27349 | − | 3.91941i | −0.0564466 | − | 0.173725i | 0.918858 | − | 0.394588i | \(-0.129113\pi\) |
−0.975305 | + | 0.220863i | \(0.929113\pi\) | |||||||
\(510\) | −3.69039 | − | 1.19908i | −0.163413 | − | 0.0530961i | ||||
\(511\) | −7.60034 | − | 5.52197i | −0.336219 | − | 0.244278i | ||||
\(512\) | 11.8927 | + | 8.64053i | 0.525587 | + | 0.381861i | ||||
\(513\) | −20.5254 | − | 6.66910i | −0.906217 | − | 0.294448i | ||||
\(514\) | −39.3531 | + | 12.7866i | −1.73579 | + | 0.563993i | ||||
\(515\) | −5.23852 | − | 7.21021i | −0.230837 | − | 0.317720i | ||||
\(516\) | −9.48316 | + | 25.1364i | −0.417473 | + | 1.10657i | ||||
\(517\) | 4.26058 | − | 3.62460i | 0.187380 | − | 0.159410i | ||||
\(518\) | − | 24.6944i | − | 1.08501i | ||||||
\(519\) | −3.23353 | + | 2.34929i | −0.141936 | + | 0.103123i | ||||
\(520\) | −0.160416 | − | 0.493711i | −0.00703473 | − | 0.0216507i | ||||
\(521\) | −26.0388 | − | 8.46052i | −1.14078 | − | 0.370662i | −0.323118 | − | 0.946359i | \(-0.604731\pi\) |
−0.817663 | + | 0.575697i | \(0.804731\pi\) | |||||||
\(522\) | −15.4488 | − | 11.2242i | −0.676176 | − | 0.491270i | ||||
\(523\) | −11.0460 | − | 8.02538i | −0.483007 | − | 0.350925i | 0.319481 | − | 0.947593i | \(-0.396491\pi\) |
−0.802489 | + | 0.596667i | \(0.796491\pi\) | |||||||
\(524\) | −5.58168 | + | 17.1786i | −0.243837 | + | 0.750452i | ||||
\(525\) | 7.95549 | − | 2.58489i | 0.347206 | − | 0.112814i | ||||
\(526\) | −8.77063 | + | 6.37224i | −0.382418 | + | 0.277843i | ||||
\(527\) | 2.44372i | 0.106450i | ||||||||
\(528\) | −0.391131 | − | 5.09629i | −0.0170218 | − | 0.221788i | ||||
\(529\) | 31.5552 | 1.37197 | ||||||||
\(530\) | 2.66775 | + | 3.67184i | 0.115880 | + | 0.159495i | ||||
\(531\) | 1.38452 | + | 4.26111i | 0.0600830 | + | 0.184917i | ||||
\(532\) | 6.74344 | − | 20.7542i | 0.292365 | − | 0.899808i | ||||
\(533\) | 1.62749 | + | 1.18244i | 0.0704944 | + | 0.0512172i | ||||
\(534\) | −0.0844680 | − | 0.0613696i | −0.00365529 | − | 0.00265572i | ||||
\(535\) | 0.928241 | − | 2.85683i | 0.0401314 | − | 0.123512i | ||||
\(536\) | −1.62356 | − | 4.99680i | −0.0701271 | − | 0.215829i | ||||
\(537\) | −8.10392 | + | 5.88785i | −0.349710 | + | 0.254079i | ||||
\(538\) | −20.0266 | −0.863407 | ||||||||
\(539\) | 3.57224 | − | 14.7532i | 0.153867 | − | 0.635465i | ||||
\(540\) | −11.8831 | −0.511365 | ||||||||
\(541\) | 18.9260 | + | 26.0494i | 0.813693 | + | 1.11995i | 0.990743 | + | 0.135751i | \(0.0433446\pi\) |
−0.177050 | + | 0.984202i | \(0.556655\pi\) | |||||||
\(542\) | 14.7143 | − | 4.78097i | 0.632034 | − | 0.205360i | ||||
\(543\) | −10.5294 | − | 3.42121i | −0.451860 | − | 0.146818i | ||||
\(544\) | −5.34290 | + | 7.35387i | −0.229075 | + | 0.315294i | ||||
\(545\) | −6.81427 | − | 4.95086i | −0.291891 | − | 0.212072i | ||||
\(546\) | 0.307595 | − | 0.946682i | 0.0131639 | − | 0.0405142i | ||||
\(547\) | 32.5219 | − | 10.5670i | 1.39054 | − | 0.451812i | 0.484417 | − | 0.874837i | \(-0.339032\pi\) |
0.906118 | + | 0.423025i | \(0.139032\pi\) | |||||||
\(548\) | 31.1121 | + | 42.8222i | 1.32904 | + | 1.82927i | ||||
\(549\) | −21.0674 | −0.899134 | ||||||||
\(550\) | −8.44835 | + | 34.8913i | −0.360239 | + | 1.48777i | ||||
\(551\) | −19.7677 | −0.842133 | ||||||||
\(552\) | −17.9982 | − | 24.7724i | −0.766054 | − | 1.05438i | ||||
\(553\) | −6.54921 | + | 2.12797i | −0.278501 | + | 0.0904903i | ||||
\(554\) | 3.76141 | − | 11.5764i | 0.159807 | − | 0.491835i | ||||
\(555\) | −2.89303 | + | 3.98191i | −0.122802 | + | 0.169023i | ||||
\(556\) | −40.0922 | + | 55.1822i | −1.70029 | + | 2.34025i | ||||
\(557\) | 6.94873 | + | 2.25778i | 0.294427 | + | 0.0956652i | 0.452506 | − | 0.891761i | \(-0.350530\pi\) |
−0.158079 | + | 0.987426i | \(0.550530\pi\) | |||||||
\(558\) | 1.28302 | + | 3.94872i | 0.0543144 | + | 0.167162i | ||||
\(559\) | −0.404947 | − | 1.47719i | −0.0171274 | − | 0.0624784i | ||||
\(560\) | − | 1.28608i | − | 0.0543467i | ||||||
\(561\) | 8.74342 | − | 0.671042i | 0.369148 | − | 0.0283314i | ||||
\(562\) | 58.6292i | 2.47312i | ||||||||
\(563\) | 15.8155 | + | 21.7682i | 0.666544 | + | 0.917419i | 0.999676 | − | 0.0254612i | \(-0.00810542\pi\) |
−0.333132 | + | 0.942880i | \(0.608105\pi\) | |||||||
\(564\) | −6.57172 | + | 2.13528i | −0.276719 | + | 0.0899115i | ||||
\(565\) | 1.70056 | − | 5.23378i | 0.0715431 | − | 0.220187i | ||||
\(566\) | 18.1981 | − | 25.0475i | 0.764922 | − | 1.05282i | ||||
\(567\) | −1.74359 | − | 1.26679i | −0.0732240 | − | 0.0532003i | ||||
\(568\) | 37.4284 | + | 12.1612i | 1.57046 | + | 0.510273i | ||||
\(569\) | 16.2120 | − | 5.26760i | 0.679643 | − | 0.220829i | 0.0512037 | − | 0.998688i | \(-0.483694\pi\) |
0.628439 | + | 0.777859i | \(0.283694\pi\) | |||||||
\(570\) | −5.52130 | + | 4.01146i | −0.231262 | + | 0.168022i | ||||
\(571\) | 17.2855 | 0.723374 | 0.361687 | − | 0.932300i | \(-0.382201\pi\) | ||||
0.361687 | + | 0.932300i | \(0.382201\pi\) | |||||||
\(572\) | 1.76414 | + | 2.07368i | 0.0737622 | + | 0.0867048i | ||||
\(573\) | 13.0551 | 0.545387 | ||||||||
\(574\) | 18.5049 | + | 25.4698i | 0.772378 | + | 1.06309i | ||||
\(575\) | 10.5207 | + | 32.3795i | 0.438745 | + | 1.35032i | ||||
\(576\) | −6.11309 | + | 18.8141i | −0.254712 | + | 0.783923i | ||||
\(577\) | 6.73260 | − | 9.26663i | 0.280282 | − | 0.385775i | −0.645545 | − | 0.763722i | \(-0.723370\pi\) |
0.925827 | + | 0.377947i | \(0.123370\pi\) | |||||||
\(578\) | −22.5243 | − | 16.3649i | −0.936887 | − | 0.680688i | ||||
\(579\) | −2.35657 | + | 7.25278i | −0.0979357 | + | 0.301415i | ||||
\(580\) | −10.3516 | + | 3.36343i | −0.429826 | + | 0.139659i | ||||
\(581\) | 15.4434 | + | 21.2560i | 0.640700 | + | 0.881849i | ||||
\(582\) | 8.26307i | 0.342515i | ||||||||
\(583\) | −8.73506 | − | 5.37621i | −0.361769 | − | 0.222660i | ||||
\(584\) | −21.4612 | −0.888069 | ||||||||
\(585\) | 0.193796 | − | 0.140801i | 0.00801247 | − | 0.00582140i | ||||
\(586\) | −44.5436 | + | 14.4731i | −1.84008 | + | 0.597878i | ||||
\(587\) | 34.7612 | + | 11.2946i | 1.43475 | + | 0.466178i | 0.920256 | − | 0.391318i | \(-0.127981\pi\) |
0.514492 | + | 0.857495i | \(0.327981\pi\) | |||||||
\(588\) | −11.0216 | + | 15.1699i | −0.454522 | + | 0.625597i | ||||
\(589\) | 3.47718 | + | 2.52632i | 0.143275 | + | 0.104095i | ||||
\(590\) | 3.81097 | + | 1.23826i | 0.156895 | + | 0.0509783i | ||||
\(591\) | −3.85284 | − | 11.8578i | −0.158485 | − | 0.487766i | ||||
\(592\) | −5.24915 | − | 7.22484i | −0.215739 | − | 0.296939i | ||||
\(593\) | −5.45620 | −0.224059 | −0.112030 | − | 0.993705i | \(-0.535735\pi\) | ||||
−0.112030 | + | 0.993705i | \(0.535735\pi\) | |||||||
\(594\) | 38.9612 | − | 16.0497i | 1.59860 | − | 0.658527i | ||||
\(595\) | 2.20645 | 0.0904557 | ||||||||
\(596\) | −51.8626 | + | 37.6804i | −2.12438 | + | 1.54345i | ||||
\(597\) | 8.92121 | + | 27.4566i | 0.365121 | + | 1.12373i | ||||
\(598\) | 3.85307 | + | 1.25194i | 0.157564 | + | 0.0511956i | ||||
\(599\) | 9.28606 | + | 6.74672i | 0.379418 | + | 0.275663i | 0.761105 | − | 0.648628i | \(-0.224657\pi\) |
−0.381687 | + | 0.924291i | \(0.624657\pi\) | |||||||
\(600\) | 11.2320 | − | 15.4595i | 0.458544 | − | 0.631132i | ||||
\(601\) | −8.82886 | + | 27.1724i | −0.360137 | + | 1.10839i | 0.592834 | + | 0.805325i | \(0.298009\pi\) |
−0.952971 | + | 0.303062i | \(0.901991\pi\) | |||||||
\(602\) | 1.11659 | − | 23.9445i | 0.0455090 | − | 0.975903i | ||||
\(603\) | 1.96139 | − | 1.42503i | 0.0798739 | − | 0.0580318i | ||||
\(604\) | −1.79381 | −0.0729889 | ||||||||
\(605\) | 1.04906 | + | 6.79414i | 0.0426502 | + | 0.276221i | ||||
\(606\) | −2.99699 | −0.121744 | ||||||||
\(607\) | −4.77809 | + | 3.47148i | −0.193937 | + | 0.140903i | −0.680516 | − | 0.732733i | \(-0.738244\pi\) |
0.486580 | + | 0.873636i | \(0.338244\pi\) | |||||||
\(608\) | 4.94036 | + | 15.2049i | 0.200358 | + | 0.616639i | ||||
\(609\) | −8.55300 | − | 2.77904i | −0.346585 | − | 0.112612i | ||||
\(610\) | −11.0749 | + | 15.2433i | −0.448411 | + | 0.617185i | ||||
\(611\) | 0.231560 | − | 0.318715i | 0.00936790 | − | 0.0128938i | ||||
\(612\) | 12.4390 | + | 4.04167i | 0.502816 | + | 0.163375i | ||||
\(613\) | 15.5247 | − | 5.04429i | 0.627037 | − | 0.203737i | 0.0217751 | − | 0.999763i | \(-0.493068\pi\) |
0.605262 | + | 0.796026i | \(0.293068\pi\) | |||||||
\(614\) | 20.6655 | + | 28.4437i | 0.833993 | + | 1.14789i | ||||
\(615\) | − | 6.27483i | − | 0.253026i | ||||||
\(616\) | 6.99298 | + | 16.9757i | 0.281755 | + | 0.683971i | ||||
\(617\) | −18.4838 | −0.744128 | −0.372064 | − | 0.928207i | \(-0.621350\pi\) | ||||
−0.372064 | + | 0.928207i | \(0.621350\pi\) | |||||||
\(618\) | −22.9465 | − | 31.5832i | −0.923045 | − | 1.27046i | ||||
\(619\) | −15.3198 | − | 47.1495i | −0.615754 | − | 1.89510i | −0.389487 | − | 0.921032i | \(-0.627348\pi\) |
−0.226267 | − | 0.974065i | \(-0.572652\pi\) | |||||||
\(620\) | 2.25071 | + | 0.731299i | 0.0903905 | + | 0.0293697i | ||||
\(621\) | 23.4889 | − | 32.3297i | 0.942576 | − | 1.29734i | ||||
\(622\) | −2.56010 | − | 1.86002i | −0.102651 | − | 0.0745800i | ||||
\(623\) | 0.0564637 | + | 0.0183462i | 0.00226217 | + | 0.000735024i | ||||
\(624\) | −0.111238 | − | 0.342354i | −0.00445306 | − | 0.0137051i | ||||
\(625\) | −15.6090 | + | 11.3406i | −0.624360 | + | 0.453624i | ||||
\(626\) | 7.25074i | 0.289798i | ||||||||
\(627\) | 8.08413 | − | 13.1348i | 0.322849 | − | 0.524553i | ||||
\(628\) | − | 22.3381i | − | 0.891386i | ||||||
\(629\) | 12.3953 | − | 9.00568i | 0.494231 | − | 0.359080i | ||||
\(630\) | 3.56533 | − | 1.15844i | 0.142046 | − | 0.0461535i | ||||
\(631\) | −30.1162 | − | 9.78536i | −1.19891 | − | 0.389549i | −0.359549 | − | 0.933126i | \(-0.617069\pi\) |
−0.839359 | + | 0.543577i | \(0.817069\pi\) | |||||||
\(632\) | −9.24652 | + | 12.7267i | −0.367807 | + | 0.506243i | ||||
\(633\) | −11.1064 | + | 15.2866i | −0.441438 | + | 0.607587i | ||||
\(634\) | −10.1802 | + | 31.3316i | −0.404309 | + | 1.24434i | ||||
\(635\) | −0.190279 | − | 0.585618i | −0.00755099 | − | 0.0232395i | ||||
\(636\) | 7.44739 | + | 10.2505i | 0.295308 | + | 0.406457i | ||||
\(637\) | − | 1.06905i | − | 0.0423572i | ||||||
\(638\) | 29.3971 | − | 25.0090i | 1.16384 | − | 0.990115i | ||||
\(639\) | 18.1599i | 0.718396i | ||||||||
\(640\) | 7.45484 | + | 10.2607i | 0.294678 | + | 0.405590i | ||||
\(641\) | −41.8826 | + | 13.6085i | −1.65426 | + | 0.537503i | −0.979658 | − | 0.200676i | \(-0.935686\pi\) |
−0.674605 | + | 0.738179i | \(0.735686\pi\) | |||||||
\(642\) | 4.06602 | − | 12.5139i | 0.160473 | − | 0.493885i | ||||
\(643\) | −3.72801 | − | 2.70856i | −0.147018 | − | 0.106815i | 0.511845 | − | 0.859078i | \(-0.328962\pi\) |
−0.658863 | + | 0.752263i | \(0.728962\pi\) | |||||||
\(644\) | 32.6901 | + | 23.7507i | 1.28817 | + | 0.935910i | ||||
\(645\) | −2.98521 | + | 3.73017i | −0.117543 | + | 0.146875i | ||||
\(646\) | 20.2048 | − | 6.56493i | 0.794946 | − | 0.258294i | ||||
\(647\) | 9.95665 | + | 13.7042i | 0.391436 | + | 0.538766i | 0.958569 | − | 0.284860i | \(-0.0919473\pi\) |
−0.567133 | + | 0.823627i | \(0.691947\pi\) | |||||||
\(648\) | −4.92340 | −0.193409 | ||||||||
\(649\) | −9.02911 | + | 0.692969i | −0.354424 | + | 0.0272014i | ||||
\(650\) | 2.52830i | 0.0991681i | ||||||||
\(651\) | 1.14933 | + | 1.58191i | 0.0450456 | + | 0.0620000i | ||||
\(652\) | 3.90478 | − | 1.26874i | 0.152923 | − | 0.0496877i | ||||
\(653\) | −8.25564 | − | 2.68242i | −0.323068 | − | 0.104971i | 0.142993 | − | 0.989724i | \(-0.454327\pi\) |
−0.466061 | + | 0.884752i | \(0.654327\pi\) | |||||||
\(654\) | −29.8489 | − | 21.6865i | −1.16718 | − | 0.848009i | ||||
\(655\) | −1.88805 | + | 2.59868i | −0.0737723 | + | 0.101539i | ||||
\(656\) | 10.8279 | + | 3.51820i | 0.422759 | + | 0.137363i | ||||
\(657\) | −3.06024 | − | 9.41845i | −0.119391 | − | 0.367449i | ||||
\(658\) | 4.98779 | − | 3.62384i | 0.194444 | − | 0.141272i | ||||
\(659\) | − | 25.8267i | − | 1.00606i | −0.864268 | − | 0.503032i | \(-0.832218\pi\) | ||
0.864268 | − | 0.503032i | \(-0.167782\pi\) | |||||||
\(660\) | 1.99849 | − | 8.25366i | 0.0777910 | − | 0.321273i | ||||
\(661\) | 18.0868 | 0.703495 | 0.351748 | − | 0.936095i | \(-0.385588\pi\) | ||||
0.351748 | + | 0.936095i | \(0.385588\pi\) | |||||||
\(662\) | 19.1707 | + | 26.3862i | 0.745090 | + | 1.02553i | ||||
\(663\) | 0.587358 | − | 0.190844i | 0.0228111 | − | 0.00741177i | ||||
\(664\) | 57.0832 | + | 18.5475i | 2.21526 | + | 0.719781i | ||||
\(665\) | 2.28103 | − | 3.13957i | 0.0884546 | − | 0.121747i | ||||
\(666\) | 15.3008 | − | 21.0598i | 0.592895 | − | 0.816050i | ||||
\(667\) | 11.3109 | − | 34.8114i | 0.437960 | − | 1.34790i | ||||
\(668\) | −8.00607 | + | 2.60133i | −0.309764 | + | 0.100648i | ||||
\(669\) | −15.3657 | + | 11.1639i | −0.594073 | + | 0.431620i | ||||
\(670\) | − | 2.16829i | − | 0.0837685i | ||||||
\(671\) | 10.0207 | − | 41.3849i | 0.386844 | − | 1.59765i | ||||
\(672\) | 7.27330i | 0.280574i | ||||||||
\(673\) | −4.53764 | + | 3.29679i | −0.174913 | + | 0.127082i | −0.671797 | − | 0.740735i | \(-0.734477\pi\) |
0.496884 | + | 0.867817i | \(0.334477\pi\) | |||||||
\(674\) | 51.5376 | − | 16.7456i | 1.98516 | − | 0.645016i | ||||
\(675\) | 23.7180 | + | 7.70643i | 0.912905 | + | 0.296621i | ||||
\(676\) | −36.8061 | − | 26.7412i | −1.41562 | − | 1.02851i | ||||
\(677\) | 12.6614 | + | 9.19904i | 0.486617 | + | 0.353548i | 0.803882 | − | 0.594789i | \(-0.202764\pi\) |
−0.317265 | + | 0.948337i | \(0.602764\pi\) | |||||||
\(678\) | 7.44904 | − | 22.9258i | 0.286079 | − | 0.880459i | ||||
\(679\) | −1.45195 | − | 4.46865i | −0.0557209 | − | 0.171491i | ||||
\(680\) | 4.07783 | − | 2.96272i | 0.156378 | − | 0.113615i | ||||
\(681\) | − | 15.8367i | − | 0.606865i | ||||||
\(682\) | −8.36716 | + | 0.642165i | −0.320395 | + | 0.0245898i | ||||
\(683\) | −4.29905 | −0.164499 | −0.0822493 | − | 0.996612i | \(-0.526210\pi\) | ||||
−0.0822493 | + | 0.996612i | \(0.526210\pi\) | |||||||
\(684\) | 18.6103 | − | 13.5212i | 0.711584 | − | 0.516996i | ||||
\(685\) | 2.90875 | + | 8.95221i | 0.111138 | + | 0.342046i | ||||
\(686\) | 13.0771 | − | 40.2473i | 0.499288 | − | 1.53665i | ||||
\(687\) | 15.6663 | − | 21.5628i | 0.597705 | − | 0.822670i | ||||
\(688\) | −4.76305 | − | 7.24276i | −0.181590 | − | 0.276128i | ||||
\(689\) | −0.687011 | − | 0.223223i | −0.0261730 | − | 0.00850413i | ||||
\(690\) | −3.90503 | − | 12.0185i | −0.148662 | − | 0.457535i | ||||
\(691\) | 13.2031 | + | 18.1724i | 0.502268 | + | 0.691312i | 0.982592 | − | 0.185779i | \(-0.0594808\pi\) |
−0.480324 | + | 0.877091i | \(0.659481\pi\) | |||||||
\(692\) | − | 12.0488i | − | 0.458027i | ||||||
\(693\) | −6.45281 | + | 5.48958i | −0.245122 | + | 0.208532i | ||||
\(694\) | 42.9865 | 1.63175 | ||||||||
\(695\) | −9.81323 | + | 7.12973i | −0.372237 | + | 0.270446i | ||||
\(696\) | −19.5387 | + | 6.34851i | −0.740613 | + | 0.240640i | ||||
\(697\) | −6.03599 | + | 18.5769i | −0.228629 | + | 0.703649i | ||||
\(698\) | −50.6781 | − | 36.8198i | −1.91819 | − | 1.39365i | ||||
\(699\) | 10.2127 | − | 14.0565i | 0.386279 | − | 0.531667i | ||||
\(700\) | −7.79235 | + | 23.9824i | −0.294523 | + | 0.906449i | ||||
\(701\) | 40.2155 | − | 13.0668i | 1.51892 | − | 0.493527i | 0.573451 | − | 0.819240i | \(-0.305604\pi\) |
0.945469 | + | 0.325713i | \(0.105604\pi\) | |||||||
\(702\) | 2.40085 | − | 1.74432i | 0.0906144 | − | 0.0658352i | ||||
\(703\) | − | 26.9474i | − | 1.01634i | ||||||
\(704\) | −34.0510 | − | 20.9575i | −1.28334 | − | 0.789866i | ||||
\(705\) | −1.22881 | −0.0462798 | ||||||||
\(706\) | −2.61476 | + | 1.89974i | −0.0984079 | + | 0.0714975i | ||||
\(707\) | 1.62077 | − | 0.526619i | 0.0609552 | − | 0.0198055i | ||||
\(708\) | 10.6388 | + | 3.45677i | 0.399832 | + | 0.129913i | ||||
\(709\) | −35.1028 | − | 25.5037i | −1.31831 | − | 0.957811i | −0.999952 | − | 0.00984150i | \(-0.996867\pi\) |
−0.318362 | − | 0.947969i | \(-0.603133\pi\) | |||||||
\(710\) | 13.1397 | + | 9.54653i | 0.493123 | + | 0.358275i | ||||
\(711\) | −6.90377 | − | 2.24317i | −0.258911 | − | 0.0841254i | ||||
\(712\) | 0.128987 | − | 0.0419105i | 0.00483400 | − | 0.00157066i | ||||
\(713\) | −6.43851 | + | 4.67785i | −0.241124 | + | 0.175187i | ||||
\(714\) | 9.66502 | 0.361704 | ||||||||
\(715\) | 0.184412 | + | 0.447666i | 0.00689660 | + | 0.0167417i | ||||
\(716\) | − | 30.1970i | − | 1.12851i | ||||||
\(717\) | −7.34262 | + | 5.33472i | −0.274215 | + | 0.199229i | ||||
\(718\) | −2.56032 | + | 0.831899i | −0.0955504 | + | 0.0310462i | ||||
\(719\) | 8.30534 | − | 25.5612i | 0.309737 | − | 0.953272i | −0.668130 | − | 0.744044i | \(-0.732905\pi\) |
0.977867 | − | 0.209227i | \(-0.0670949\pi\) | |||||||
\(720\) | 0.796862 | − | 1.09679i | 0.0296973 | − | 0.0408748i | ||||
\(721\) | 17.9591 | + | 13.0481i | 0.668833 | + | 0.485935i | ||||
\(722\) | −2.24098 | + | 6.89702i | −0.0834006 | + | 0.256681i | ||||
\(723\) | −12.2028 | + | 3.96494i | −0.453828 | + | 0.147458i | ||||
\(724\) | 27.0011 | − | 19.6174i | 1.00349 | − | 0.729076i | ||||
\(725\) | 22.8425 | 0.848348 | ||||||||
\(726\) | 4.59523 | + | 29.7607i | 0.170545 | + | 1.10452i | ||||
\(727\) | − | 32.7743i | − | 1.21553i | −0.794117 | − | 0.607765i | \(-0.792066\pi\) | ||
0.794117 | − | 0.607765i | \(-0.207934\pi\) | |||||||
\(728\) | 0.760016 | + | 1.04607i | 0.0281681 | + | 0.0387700i | ||||
\(729\) | −6.54925 | − | 20.1565i | −0.242565 | − | 0.746538i | ||||
\(730\) | −8.42348 | − | 2.73695i | −0.311767 | − | 0.101299i | ||||
\(731\) | 12.4260 | − | 8.17170i | 0.459593 | − | 0.302241i | ||||
\(732\) | −30.9172 | + | 42.5539i | −1.14273 | + | 1.57284i | ||||
\(733\) | −2.96535 | + | 9.12640i | −0.109528 | + | 0.337091i | −0.990766 | − | 0.135580i | \(-0.956710\pi\) |
0.881239 | + | 0.472671i | \(0.156710\pi\) | |||||||
\(734\) | −19.7627 | − | 60.8232i | −0.729453 | − | 2.24503i | ||||
\(735\) | −2.69772 | + | 1.96000i | −0.0995067 | + | 0.0722959i | ||||
\(736\) | −29.6030 | −1.09118 | ||||||||
\(737\) | 1.86641 | + | 4.53078i | 0.0687502 | + | 0.166893i | ||||
\(738\) | 33.1867i | 1.22162i | ||||||||
\(739\) | 22.5940 | − | 16.4155i | 0.831135 | − | 0.603855i | −0.0887454 | − | 0.996054i | \(-0.528286\pi\) |
0.919880 | + | 0.392200i | \(0.128286\pi\) | |||||||
\(740\) | −4.58503 | − | 14.1113i | −0.168549 | − | 0.518740i | ||||
\(741\) | 0.335658 | − | 1.03305i | 0.0123307 | − | 0.0379500i | ||||
\(742\) | −9.14579 | − | 6.64481i | −0.335753 | − | 0.243939i | ||||
\(743\) | −30.3558 | − | 22.0548i | −1.11364 | − | 0.809110i | −0.130411 | − | 0.991460i | \(-0.541630\pi\) |
−0.983234 | + | 0.182350i | \(0.941630\pi\) | |||||||
\(744\) | 4.24823 | + | 1.38033i | 0.155748 | + | 0.0506055i | ||||
\(745\) | −10.8422 | + | 3.52284i | −0.397226 | + | 0.129067i | ||||
\(746\) | 63.4967 | − | 46.1331i | 2.32478 | − | 1.68905i | ||||
\(747\) | 27.6963i | 1.01335i | ||||||||
\(748\) | −13.8561 | + | 22.5128i | −0.506629 | + | 0.823151i | ||||
\(749\) | 7.48197i | 0.273385i | ||||||||
\(750\) | 13.3008 | − | 9.66362i | 0.485678 | − | 0.352866i | ||||
\(751\) | −15.0077 | + | 4.87630i | −0.547639 | + | 0.177939i | −0.569752 | − | 0.821817i | \(-0.692961\pi\) |
0.0221126 | + | 0.999755i | \(0.492961\pi\) | |||||||
\(752\) | 0.688977 | − | 2.12045i | 0.0251244 | − | 0.0773249i | ||||
\(753\) | 16.8475 | − | 23.1887i | 0.613959 | − | 0.845042i | ||||
\(754\) | 1.59771 | − | 2.19906i | 0.0581853 | − | 0.0800852i | ||||
\(755\) | −0.303385 | − | 0.0985759i | −0.0110413 | − | 0.00358754i | ||||
\(756\) | 28.1496 | − | 9.14635i | 1.02379 | − | 0.332649i | ||||
\(757\) | 20.8075 | + | 28.6390i | 0.756260 | + | 1.04090i | 0.997516 | + | 0.0704414i | \(0.0224408\pi\) |
−0.241256 | + | 0.970462i | \(0.577559\pi\) | |||||||
\(758\) | −19.1265 | −0.694705 | ||||||||
\(759\) | 18.5050 | + | 21.7519i | 0.671689 | + | 0.789546i | ||||
\(760\) | − | 8.86523i | − | 0.321576i | ||||||
\(761\) | −24.6339 | + | 17.8976i | −0.892977 | + | 0.648786i | −0.936653 | − | 0.350260i | \(-0.886093\pi\) |
0.0436753 | + | 0.999046i | \(0.486093\pi\) | |||||||
\(762\) | −0.833488 | − | 2.56521i | −0.0301941 | − | 0.0929278i | ||||
\(763\) | 19.9529 | + | 6.48309i | 0.722343 | + | 0.234703i | ||||
\(764\) | −23.1327 | + | 31.8394i | −0.836911 | + | 1.15191i | ||||
\(765\) | 1.88170 | + | 1.36713i | 0.0680328 | + | 0.0494287i | ||||
\(766\) | 56.5499 | + | 18.3742i | 2.04323 | + | 0.663887i | ||||
\(767\) | −0.606550 | + | 0.197080i | −0.0219012 | + | 0.00711614i | ||||
\(768\) | 16.1331 | + | 22.2053i | 0.582154 | + | 0.801266i | ||||
\(769\) | − | 45.5405i | − | 1.64223i | −0.570760 | − | 0.821117i | \(-0.693351\pi\) | ||
0.570760 | − | 0.821117i | \(-0.306649\pi\) | |||||||
\(770\) | 0.579815 | + | 7.55477i | 0.0208951 | + | 0.272255i | ||||
\(771\) | −20.5421 | −0.739806 | ||||||||
\(772\) | −13.5127 | − | 18.5986i | −0.486333 | − | 0.669380i | ||||
\(773\) | −48.8565 | + | 15.8744i | −1.75725 | + | 0.570964i | −0.996909 | − | 0.0785635i | \(-0.974967\pi\) |
−0.760338 | + | 0.649528i | \(0.774967\pi\) | |||||||
\(774\) | 15.7884 | − | 19.7283i | 0.567502 | − | 0.709121i | ||||
\(775\) | −4.01803 | − | 2.91927i | −0.144332 | − | 0.104863i | ||||
\(776\) | −8.68371 | − | 6.30909i | −0.311727 | − | 0.226483i | ||||
\(777\) | 3.78838 | − | 11.6594i | 0.135907 | − | 0.418280i | ||||
\(778\) | −71.4000 | + | 23.1993i | −2.55982 | + | 0.831734i | ||||
\(779\) | 20.1931 | + | 27.7934i | 0.723493 | + | 0.995802i | ||||
\(780\) | − | 0.598078i | − | 0.0214146i | ||||||
\(781\) | −35.6735 | − | 8.63775i | −1.27650 | − | 0.309083i | ||||
\(782\) | 39.3375i | 1.40670i | ||||||||
\(783\) | −15.7595 | − | 21.6910i | −0.563197 | − | 0.775174i | ||||
\(784\) | −1.86964 | − | 5.75415i | −0.0667728 | − | 0.205505i | ||||
\(785\) | 1.22756 | − | 3.77803i | 0.0438133 | − | 0.134844i | ||||
\(786\) | −8.27033 | + | 11.3831i | −0.294993 | + | 0.406023i | ||||
\(787\) | −13.3156 | + | 18.3273i | −0.474649 | + | 0.653298i | −0.977465 | − | 0.211095i | \(-0.932297\pi\) |
0.502817 | + | 0.864393i | \(0.332297\pi\) | |||||||
\(788\) | 35.7463 | + | 11.6147i | 1.27341 | + | 0.413755i | ||||
\(789\) | −5.11861 | + | 1.66314i | −0.182227 | + | 0.0592092i | ||||
\(790\) | −5.25230 | + | 3.81602i | −0.186869 | + | 0.135768i | ||||
\(791\) | 13.7071i | 0.487370i | ||||||||
\(792\) | −4.55454 | + | 18.8101i | −0.161839 | + | 0.668386i | ||||
\(793\) | − | 2.99884i | − | 0.106492i | ||||||
\(794\) | −3.65761 | + | 2.65741i | −0.129804 | + | 0.0943078i | ||||
\(795\) | 0.696275 | + | 2.14292i | 0.0246943 | + | 0.0760014i | ||||
\(796\) | −82.7700 | − | 26.8936i | −2.93370 | − | 0.953218i | ||||
\(797\) | −14.8676 | − | 10.8019i | −0.526636 | − | 0.382623i | 0.292462 | − | 0.956277i | \(-0.405525\pi\) |
−0.819098 | + | 0.573654i | \(0.805525\pi\) | |||||||
\(798\) | 9.99171 | − | 13.7524i | 0.353703 | − | 0.486830i | ||||
\(799\) | 3.63794 | + | 1.18204i | 0.128701 | + | 0.0418175i | ||||
\(800\) | −5.70880 | − | 17.5699i | −0.201837 | − | 0.621190i | ||||
\(801\) | 0.0367857 | + | 0.0506312i | 0.00129976 | + | 0.00178897i | ||||
\(802\) | 23.9373 | 0.845256 | ||||||||
\(803\) | 19.9573 | − | 1.53169i | 0.704277 | − | 0.0540520i | ||||
\(804\) | − | 6.05309i | − | 0.213476i | ||||||
\(805\) | 4.22367 | + | 5.81338i | 0.148865 | + | 0.204895i | ||||
\(806\) | −0.562081 | + | 0.182631i | −0.0197985 | + | 0.00643291i | ||||
\(807\) | −9.45552 | − | 3.07228i | −0.332850 | − | 0.108150i | ||||
\(808\) | 2.28829 | − | 3.14956i | 0.0805016 | − | 0.110801i | ||||
\(809\) | 20.3881 | − | 28.0618i | 0.716807 | − | 0.986601i | −0.282817 | − | 0.959174i | \(-0.591269\pi\) |
0.999624 | − | 0.0274266i | \(-0.00873124\pi\) | |||||||
\(810\) | −1.93243 | − | 0.627884i | −0.0678986 | − | 0.0220616i | ||||
\(811\) | −2.35169 | − | 7.23776i | −0.0825790 | − | 0.254152i | 0.901239 | − | 0.433322i | \(-0.142659\pi\) |
−0.983818 | + | 0.179170i | \(0.942659\pi\) | |||||||
\(812\) | 21.9328 | − | 15.9351i | 0.769692 | − | 0.559214i | ||||
\(813\) | 7.68079 | 0.269377 | ||||||||
\(814\) | 34.0922 | + | 40.0742i | 1.19493 | + | 1.40460i | ||||
\(815\) | 0.730136 | 0.0255755 | ||||||||
\(816\) | 2.82769 | − | 2.05444i | 0.0989890 | − | 0.0719197i | ||||
\(817\) | 1.21846 | − | 26.1289i | 0.0426286 | − | 0.914136i | ||||
\(818\) | −15.6431 | + | 48.1445i | −0.546948 | + | 1.68333i | ||||
\(819\) | −0.350705 | + | 0.482705i | −0.0122546 | + | 0.0168671i | ||||
\(820\) | 15.3033 | + | 11.1185i | 0.534414 | + | 0.388275i | ||||
\(821\) | −28.9730 | − | 9.41389i | −1.01116 | − | 0.328547i | −0.243846 | − | 0.969814i | \(-0.578409\pi\) |
−0.767318 | + | 0.641267i | \(0.778409\pi\) | |||||||
\(822\) | 12.7413 | + | 39.2138i | 0.444405 | + | 1.36774i | ||||
\(823\) | −14.6791 | + | 10.6650i | −0.511680 | + | 0.371757i | −0.813461 | − | 0.581620i | \(-0.802419\pi\) |
0.301781 | + | 0.953377i | \(0.402419\pi\) | |||||||
\(824\) | 50.7113 | 1.76661 | ||||||||
\(825\) | −9.34157 | + | 15.1778i | −0.325232 | + | 0.528424i | ||||
\(826\) | −9.98083 | −0.347277 | ||||||||
\(827\) | −12.3461 | − | 16.9929i | −0.429316 | − | 0.590903i | 0.538480 | − | 0.842638i | \(-0.318999\pi\) |
−0.967796 | + | 0.251736i | \(0.918999\pi\) | |||||||
\(828\) | 13.1625 | + | 40.5100i | 0.457428 | + | 1.40782i | ||||
\(829\) | 29.5490 | + | 9.60104i | 1.02628 | + | 0.333458i | 0.773318 | − | 0.634019i | \(-0.218596\pi\) |
0.252960 | + | 0.967477i | \(0.418596\pi\) | |||||||
\(830\) | 20.0397 | + | 14.5597i | 0.695589 | + | 0.505375i | ||||
\(831\) | 3.55188 | − | 4.88875i | 0.123213 | − | 0.169589i | ||||
\(832\) | −2.67811 | − | 0.870169i | −0.0928466 | − | 0.0301677i | ||||
\(833\) | 9.87208 | − | 3.20763i | 0.342047 | − | 0.111138i | ||||
\(834\) | −42.9854 | + | 31.2307i | −1.48846 | + | 1.08143i | ||||
\(835\) | −1.49702 | −0.0518064 | ||||||||
\(836\) | 17.7092 | + | 42.9897i | 0.612485 | + | 1.48683i | ||||
\(837\) | 5.82955i | 0.201499i | ||||||||
\(838\) | 47.7006 | + | 65.6543i | 1.64779 | + | 2.26799i | ||||
\(839\) | −16.0933 | + | 5.22902i | −0.555601 | + | 0.180526i | −0.573341 | − | 0.819317i | \(-0.694353\pi\) |
0.0177399 | + | 0.999843i | \(0.494353\pi\) | |||||||
\(840\) | 1.24631 | − | 3.83576i | 0.0430019 | − | 0.132346i | ||||
\(841\) | 3.59358 | + | 2.61089i | 0.123916 | + | 0.0900306i | ||||
\(842\) | 45.2572 | − | 62.2913i | 1.55967 | − | 2.14670i | ||||
\(843\) | −8.99433 | + | 27.6817i | −0.309781 | + | 0.953408i | ||||
\(844\) | −17.6019 | − | 54.1732i | −0.605884 | − | 1.86472i | ||||
\(845\) | −4.75547 | − | 6.54534i | −0.163593 | − | 0.225167i | ||||
\(846\) | 6.49902 | 0.223441 | ||||||||
\(847\) | −7.71452 | − | 15.2871i | −0.265074 | − | 0.525270i | ||||
\(848\) | −4.08823 | −0.140390 | ||||||||
\(849\) | 12.4347 | − | 9.03436i | 0.426759 | − | 0.310059i | ||||
\(850\) | −23.3475 | + | 7.58606i | −0.800812 | + | 0.260200i | ||||
\(851\) | 47.4549 | + | 15.4190i | 1.62673 | + | 0.528558i | ||||
\(852\) | 36.6812 | + | 26.6504i | 1.25668 | + | 0.913029i | ||||
\(853\) | 27.0197 | − | 37.1894i | 0.925136 | − | 1.27334i | −0.0365903 | − | 0.999330i | \(-0.511650\pi\) |
0.961727 | − | 0.274011i | \(-0.0883503\pi\) | |||||||
\(854\) | 14.5025 | − | 44.6341i | 0.496265 | − | 1.52735i | ||||
\(855\) | 3.89060 | − | 1.26413i | 0.133056 | − | 0.0432324i | ||||
\(856\) | 10.0464 | + | 13.8277i | 0.343380 | + | 0.472622i | ||||
\(857\) | 32.8060i | 1.12063i | 0.828279 | + | 0.560316i | \(0.189320\pi\) | ||||
−0.828279 | + | 0.560316i | \(0.810680\pi\) | |||||||
\(858\) | 0.807787 | + | 1.96093i | 0.0275774 | + | 0.0669451i | ||||
\(859\) | 35.8597i | 1.22352i | 0.791045 | + | 0.611758i | \(0.209537\pi\) | ||||
−0.791045 | + | 0.611758i | \(0.790463\pi\) | |||||||
\(860\) | −3.80772 | − | 13.8900i | −0.129842 | − | 0.473645i | ||||
\(861\) | 4.82972 | + | 14.8643i | 0.164596 | + | 0.506575i | ||||
\(862\) | −46.9689 | − | 15.2611i | −1.59977 | − | 0.519796i | ||||
\(863\) | −18.3988 | + | 25.3238i | −0.626303 | + | 0.862032i | −0.997793 | − | 0.0664049i | \(-0.978847\pi\) |
0.371490 | + | 0.928437i | \(0.378847\pi\) | |||||||
\(864\) | −12.7456 | + | 17.5428i | −0.433615 | + | 0.596820i | ||||
\(865\) | 0.662125 | − | 2.03781i | 0.0225129 | − | 0.0692876i | ||||
\(866\) | 13.9074 | − | 4.51879i | 0.472592 | − | 0.153555i | ||||
\(867\) | −8.12427 | − | 11.1821i | −0.275915 | − | 0.379764i | ||||
\(868\) | −5.89454 | −0.200074 | ||||||||
\(869\) | 7.69027 | − | 12.4949i | 0.260875 | − | 0.423859i | ||||
\(870\) | −8.47855 | −0.287450 | ||||||||
\(871\) | 0.202847 | + | 0.279194i | 0.00687319 | + | 0.00946014i | ||||
\(872\) | 45.5809 | − | 14.8101i | 1.54357 | − | 0.501535i | ||||
\(873\) | 1.53056 | − | 4.71058i | 0.0518016 | − | 0.159429i | ||||
\(874\) | 55.9735 | + | 40.6671i | 1.89333 | + | 1.37559i | ||||
\(875\) | −5.49501 | + | 7.56324i | −0.185765 | + | 0.255684i | ||||
\(876\) | −23.5153 | − | 7.64059i | −0.794509 | − | 0.258152i | ||||
\(877\) | −53.3565 | + | 17.3366i | −1.80172 | + | 0.585415i | −0.999926 | − | 0.0121823i | \(-0.996122\pi\) |
−0.801796 | + | 0.597597i | \(0.796122\pi\) | |||||||
\(878\) | 17.7692 | + | 24.4572i | 0.599681 | + | 0.825391i | ||||
\(879\) | −23.2515 | −0.784254 | ||||||||
\(880\) | 1.77551 | + | 2.08705i | 0.0598524 | + | 0.0703543i | ||||
\(881\) | −25.8442 | −0.870713 | −0.435357 | − | 0.900258i | \(-0.643378\pi\) | ||||
−0.435357 | + | 0.900258i | \(0.643378\pi\) | |||||||
\(882\) | 14.2679 | − | 10.3662i | 0.480424 | − | 0.349048i | ||||
\(883\) | −0.602546 | − | 1.85445i | −0.0202773 | − | 0.0624071i | 0.940406 | − | 0.340054i | \(-0.110445\pi\) |
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(884\) | −0.575313 | + | 1.77063i | −0.0193499 | + | 0.0595528i | ||||
\(885\) | 1.60938 | + | 1.16928i | 0.0540988 | + | 0.0393051i | ||||
\(886\) | −46.6467 | − | 33.8908i | −1.56713 | − | 1.13858i | ||||
\(887\) | −11.2468 | + | 34.6141i | −0.377631 | + | 1.16223i | 0.564055 | + | 0.825737i | \(0.309240\pi\) |
−0.941686 | + | 0.336492i | \(0.890760\pi\) | |||||||
\(888\) | −8.65428 | − | 26.6351i | −0.290419 | − | 0.893817i | ||||
\(889\) | 0.901497 | + | 1.24080i | 0.0302352 | + | 0.0416152i | ||||
\(890\) | 0.0559723 | 0.00187619 | ||||||||
\(891\) | 4.57839 | − | 0.351384i | 0.153382 | − | 0.0117718i | ||||
\(892\) | − | 57.2560i | − | 1.91707i | ||||||
\(893\) | 5.44284 | − | 3.95445i | 0.182138 | − | 0.132331i | ||||
\(894\) | −47.4925 | + | 15.4312i | −1.58839 | + | 0.516098i | ||||
\(895\) | 1.65943 | − | 5.10720i | 0.0554686 | − | 0.170715i | ||||
\(896\) | −25.5573 | − | 18.5684i | −0.853809 | − | 0.620328i | ||||
\(897\) | 1.62716 | + | 1.18220i | 0.0543294 | + | 0.0394726i | ||||
\(898\) | −20.6044 | − | 6.69478i | −0.687578 | − | 0.223408i | ||||
\(899\) | 1.65002 | + | 5.07824i | 0.0550313 | + | 0.169369i | ||||
\(900\) | −21.5051 | + | 15.6243i | −0.716836 | + | 0.520812i | ||||
\(901\) | − | 7.01395i | − | 0.233668i | ||||||
\(902\) | −65.1923 | − | 15.7852i | −2.17067 | − | 0.525591i | ||||
\(903\) | 4.20052 | − | 11.1340i | 0.139785 | − | 0.370518i | ||||
\(904\) | 18.4053 | + | 25.3327i | 0.612151 | + | 0.842554i | ||||
\(905\) | 5.64472 | − | 1.83408i | 0.187637 | − | 0.0609670i | ||||
\(906\) | −1.32893 | − | 0.431797i | −0.0441509 | − | 0.0143455i | ||||
\(907\) | 35.2644 | + | 25.6211i | 1.17093 | + | 0.850734i | 0.991121 | − | 0.132967i | \(-0.0424503\pi\) |
0.179814 | + | 0.983701i | \(0.442450\pi\) | |||||||
\(908\) | 38.6232 | + | 28.0614i | 1.28176 | + | 0.931251i | ||||
\(909\) | 1.70851 | + | 0.555129i | 0.0566677 | + | 0.0184125i | ||||
\(910\) | 0.164899 | + | 0.507508i | 0.00546635 | + | 0.0168237i | ||||
\(911\) | 0.106169 | + | 0.146129i | 0.00351754 | + | 0.00484148i | 0.810772 | − | 0.585362i | \(-0.199048\pi\) |
−0.807255 | + | 0.590203i | \(0.799048\pi\) | |||||||
\(912\) | − | 6.14741i | − | 0.203561i | ||||||
\(913\) | −54.4069 | − | 13.1737i | −1.80060 | − | 0.435986i | ||||
\(914\) | −59.0130 | −1.95198 | ||||||||
\(915\) | −7.56750 | + | 5.49811i | −0.250174 | + | 0.181762i | ||||
\(916\) | 24.8287 | + | 76.4150i | 0.820364 | + | 2.52482i | ||||
\(917\) | 2.47238 | − | 7.60920i | 0.0816452 | − | 0.251278i | ||||
\(918\) | 23.3115 | + | 16.9368i | 0.769396 | + | 0.558999i | ||||
\(919\) | −8.45347 | + | 11.6352i | −0.278854 | + | 0.383810i | −0.925354 | − | 0.379104i | \(-0.876232\pi\) |
0.646500 | + | 0.762914i | \(0.276232\pi\) | |||||||
\(920\) | 15.6119 | + | 5.07261i | 0.514708 | + | 0.167239i | ||||
\(921\) | 5.39365 | + | 16.5999i | 0.177727 | + | 0.546987i | ||||
\(922\) | 8.33304 | + | 11.4694i | 0.274434 | + | 0.377726i | ||||
\(923\) | −2.58498 | −0.0850857 | ||||||||
\(924\) | 1.61863 | + | 21.0902i | 0.0532492 | + | 0.693816i | ||||
\(925\) | 31.1388i | 1.02384i | ||||||||
\(926\) | 2.48222 | + | 3.41648i | 0.0815707 | + | 0.112272i | ||||
\(927\) | 7.23115 | + | 22.2552i | 0.237502 | + | 0.730956i | ||||
\(928\) | −6.13757 | + | 18.8895i | −0.201476 | + | 0.620078i | ||||
\(929\) | 1.21117 | − | 1.66703i | 0.0397372 | − | 0.0546936i | −0.788686 | − | 0.614796i | \(-0.789238\pi\) |
0.828423 | + | 0.560103i | \(0.189238\pi\) | |||||||
\(930\) | 1.49139 | + | 1.08356i | 0.0489047 | + | 0.0355313i | ||||
\(931\) | 5.64161 | − | 17.3631i | 0.184896 | − | 0.569052i | ||||
\(932\) | 16.1856 | + | 49.8141i | 0.530176 | + | 1.63172i | ||||
\(933\) | −0.923400 | − | 1.27095i | −0.0302308 | − | 0.0416091i | ||||
\(934\) | − | 75.2608i | − | 2.46261i | ||||||
\(935\) | −3.58063 | + | 3.04614i | −0.117099 | + | 0.0996196i | ||||
\(936\) | 1.36302i | 0.0445516i | ||||||||
\(937\) | 24.2559 | − | 17.6229i | 0.792406 | − | 0.575717i | −0.116270 | − | 0.993218i | \(-0.537094\pi\) |
0.908676 | + | 0.417501i | \(0.137094\pi\) | |||||||
\(938\) | 1.66893 | + | 5.13643i | 0.0544925 | + | 0.167711i | ||||
\(939\) | −1.11234 | + | 3.42343i | −0.0362998 | + | 0.111719i | ||||
\(940\) | 2.17736 | − | 2.99688i | 0.0710176 | − | 0.0977473i | ||||
\(941\) | −31.0531 | + | 42.7409i | −1.01230 | + | 1.39331i | −0.0948396 | + | 0.995493i | \(0.530234\pi\) |
−0.917463 | + | 0.397822i | \(0.869766\pi\) | |||||||
\(942\) | 5.37712 | − | 16.5491i | 0.175196 | − | 0.539198i | ||||
\(943\) | −60.4991 | + | 19.6574i | −1.97012 | + | 0.640132i | ||||
\(944\) | −2.92009 | + | 2.12157i | −0.0950407 | + | 0.0690511i | ||||
\(945\) | 5.26355 | 0.171223 | ||||||||
\(946\) | 31.2448 | + | 40.3986i | 1.01586 | + | 1.31347i | ||||
\(947\) | 2.56913 | 0.0834855 | 0.0417428 | − | 0.999128i | \(-0.486709\pi\) | ||||
0.0417428 | + | 0.999128i | \(0.486709\pi\) | |||||||
\(948\) | −14.6625 | + | 10.6529i | −0.476217 | + | 0.345992i | ||||
\(949\) | 1.34067 | − | 0.435611i | 0.0435201 | − | 0.0141405i | ||||
\(950\) | −13.3424 | + | 41.0637i | −0.432885 | + | 1.33228i | ||||
\(951\) | −9.61317 | + | 13.2314i | −0.311728 | + | 0.429057i | ||||
\(952\) | −7.37952 | + | 10.1570i | −0.239171 | + | 0.329191i | ||||
\(953\) | 12.4843 | − | 38.4229i | 0.404408 | − | 1.24464i | −0.516981 | − | 0.855997i | \(-0.672944\pi\) |
0.921389 | − | 0.388642i | \(-0.127056\pi\) | |||||||
\(954\) | −3.68251 | − | 11.3336i | −0.119226 | − | 0.366939i | ||||
\(955\) | −5.66211 | + | 4.11376i | −0.183221 | + | 0.133118i | ||||
\(956\) | − | 27.3602i | − | 0.884891i | ||||||
\(957\) | 17.7164 | − | 7.29812i | 0.572691 | − | 0.235915i | ||||
\(958\) | − | 76.1643i | − | 2.46076i | ||||||
\(959\) | −13.7810 | − | 18.9679i | −0.445011 | − | 0.612505i | ||||
\(960\) | 2.71422 | + | 8.35351i | 0.0876011 | + | 0.269608i | ||||
\(961\) | −9.22077 | + | 28.3786i | −0.297444 | + | 0.915439i | ||||
\(962\) | 2.99776 | + | 2.17800i | 0.0966518 | + | 0.0702216i | ||||
\(963\) | −4.63588 | + | 6.38074i | −0.149389 | + | 0.205616i | ||||
\(964\) | 11.9526 | − | 36.7863i | 0.384967 | − | 1.18481i | ||||
\(965\) | −1.26334 | − | 3.88815i | −0.0406682 | − | 0.125164i | ||||
\(966\) | 18.5011 | + | 25.4646i | 0.595264 | + | 0.819311i | ||||
\(967\) | 15.0410i | 0.483688i | 0.970315 | + | 0.241844i | \(0.0777521\pi\) | ||||
−0.970315 | + | 0.241844i | \(0.922248\pi\) | |||||||
\(968\) | −34.7843 | − | 17.8940i | −1.11801 | − | 0.575134i | ||||
\(969\) | 10.5468 | 0.338811 | ||||||||
\(970\) | −2.60375 | − | 3.58375i | −0.0836013 | − | 0.115067i | ||||
\(971\) | −11.9572 | − | 36.8005i | −0.383725 | − | 1.18099i | −0.937401 | − | 0.348253i | \(-0.886775\pi\) |
0.553675 | − | 0.832733i | \(-0.313225\pi\) | |||||||
\(972\) | 48.8551 | + | 15.8740i | 1.56703 | + | 0.509158i | ||||
\(973\) | 17.7587 | − | 24.4427i | 0.569317 | − | 0.783597i | ||||
\(974\) | −80.0418 | − | 58.1537i | −2.56470 | − | 1.86337i | ||||
\(975\) | −0.387868 | + | 1.19373i | −0.0124217 | + | 0.0382301i | ||||
\(976\) | −5.24462 | − | 16.1413i | −0.167876 | − | 0.516670i | ||||
\(977\) | −5.74107 | + | 4.17113i | −0.183673 | + | 0.133446i | −0.675822 | − | 0.737064i | \(-0.736211\pi\) |
0.492149 | + | 0.870511i | \(0.336211\pi\) | |||||||
\(978\) | 3.19825 | 0.102269 | ||||||||
\(979\) | −0.116957 | + | 0.0481795i | −0.00373798 | + | 0.00153982i | ||||
\(980\) | − | 10.0523i | − | 0.321108i | ||||||
\(981\) | 12.9992 | + | 17.8918i | 0.415031 | + | 0.571242i | ||||
\(982\) | −15.8455 | − | 48.7675i | −0.505651 | − | 1.55623i | ||||
\(983\) | −14.6319 | − | 4.75419i | −0.466685 | − | 0.151635i | 0.0662294 | − | 0.997804i | \(-0.478903\pi\) |
−0.532914 | + | 0.846169i | \(0.678903\pi\) | |||||||
\(984\) | 28.8851 | + | 20.9863i | 0.920825 | + | 0.669018i | ||||
\(985\) | 5.40748 | + | 3.92877i | 0.172297 | + | 0.125181i | ||||
\(986\) | 25.1010 | + | 8.15582i | 0.799380 | + | 0.259734i | ||||
\(987\) | 2.91091 | − | 0.945813i | 0.0926554 | − | 0.0301056i | ||||
\(988\) | 1.92468 | + | 2.64910i | 0.0612323 | + | 0.0842790i | ||||
\(989\) | 45.3165 | + | 17.0965i | 1.44098 | + | 0.543637i | ||||
\(990\) | −4.18651 | + | 6.80208i | −0.133056 | + | 0.216184i | ||||
\(991\) | − | 27.4412i | − | 0.871699i | −0.900020 | − | 0.435849i | \(-0.856448\pi\) | ||
0.900020 | − | 0.435849i | \(-0.143552\pi\) | |||||||
\(992\) | 3.49369 | − | 2.53831i | 0.110925 | − | 0.0805916i | ||||
\(993\) | 5.00349 | + | 15.3992i | 0.158781 | + | 0.488678i | ||||
\(994\) | −38.4743 | − | 12.5010i | −1.22033 | − | 0.396509i | ||||
\(995\) | −12.5210 | − | 9.09700i | −0.396941 | − | 0.288394i | ||||
\(996\) | 55.9437 | + | 40.6454i | 1.77264 | + | 1.28790i | ||||
\(997\) | 14.3647 | − | 44.2100i | 0.454934 | − | 1.40014i | −0.416278 | − | 0.909237i | \(-0.636666\pi\) |
0.871212 | − | 0.490906i | \(-0.163334\pi\) | |||||||
\(998\) | −86.4544 | + | 28.0907i | −2.73667 | + | 0.889197i | ||||
\(999\) | 29.5692 | − | 21.4833i | 0.935528 | − | 0.679701i |
(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 | 473.2.k.b.85.6 | ✓ | 160 | |
11.7 | odd | 10 | inner | 473.2.k.b.128.35 | yes | 160 | |
43.42 | odd | 2 | inner | 473.2.k.b.85.35 | yes | 160 | |
473.128 | even | 10 | inner | 473.2.k.b.128.6 | yes | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
473.2.k.b.85.6 | ✓ | 160 | 1.1 | even | 1 | trivial | |
473.2.k.b.85.35 | yes | 160 | 43.42 | odd | 2 | inner | |
473.2.k.b.128.6 | yes | 160 | 473.128 | even | 10 | inner | |
473.2.k.b.128.35 | yes | 160 | 11.7 | odd | 10 | inner |