Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(148,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.f (of order \(3\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 148.9 | ||
Character | \(\chi\) | \(=\) | 441.148 |
Dual form | 441.2.f.h.295.9 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.863305 | + | 1.49529i | 0.610449 | + | 1.05733i | 0.991165 | + | 0.132637i | \(0.0423443\pi\) |
−0.380716 | + | 0.924692i | \(0.624322\pi\) | |||||||
\(3\) | −1.09452 | + | 1.34239i | −0.631924 | + | 0.775030i | ||||
\(4\) | −0.490592 | + | 0.849731i | −0.245296 | + | 0.424865i | ||||
\(5\) | 1.75616 | − | 3.04175i | 0.785377 | − | 1.36031i | −0.143397 | − | 0.989665i | \(-0.545803\pi\) |
0.928774 | − | 0.370647i | \(-0.120864\pi\) | |||||||
\(6\) | −2.95217 | − | 0.477737i | −1.20522 | − | 0.195035i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.75910 | 0.621935 | ||||||||
\(9\) | −0.604030 | − | 2.93856i | −0.201343 | − | 0.979521i | ||||
\(10\) | 6.06439 | 1.91773 | ||||||||
\(11\) | 3.04532 | + | 5.27465i | 0.918199 | + | 1.59037i | 0.802150 | + | 0.597123i | \(0.203690\pi\) |
0.116049 | + | 0.993244i | \(0.462977\pi\) | |||||||
\(12\) | −0.603706 | − | 1.58862i | −0.174275 | − | 0.458595i | ||||
\(13\) | −0.560139 | + | 0.970190i | −0.155355 | + | 0.269082i | −0.933188 | − | 0.359388i | \(-0.882985\pi\) |
0.777833 | + | 0.628471i | \(0.216319\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.16106 | + | 5.68672i | 0.557984 | + | 1.46831i | ||||
\(16\) | 2.49982 | + | 4.32982i | 0.624956 | + | 1.08246i | ||||
\(17\) | −1.20396 | −0.292002 | −0.146001 | − | 0.989284i | \(-0.546640\pi\) | ||||
−0.146001 | + | 0.989284i | \(0.546640\pi\) | |||||||
\(18\) | 3.87254 | − | 3.44008i | 0.912766 | − | 0.810834i | ||||
\(19\) | 2.20537 | 0.505947 | 0.252974 | − | 0.967473i | \(-0.418591\pi\) | ||||
0.252974 | + | 0.967473i | \(0.418591\pi\) | |||||||
\(20\) | 1.72311 | + | 2.98452i | 0.385300 | + | 0.667359i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.25808 | + | 9.10727i | −1.12103 | + | 1.94168i | ||||
\(23\) | 0.636695 | − | 1.10279i | 0.132760 | − | 0.229947i | −0.791980 | − | 0.610548i | \(-0.790949\pi\) |
0.924740 | + | 0.380601i | \(0.124283\pi\) | |||||||
\(24\) | −1.92538 | + | 2.36140i | −0.393016 | + | 0.482018i | ||||
\(25\) | −3.66817 | − | 6.35345i | −0.733633 | − | 1.27069i | ||||
\(26\) | −1.93429 | −0.379345 | ||||||||
\(27\) | 4.60583 | + | 2.40548i | 0.886392 | + | 0.462936i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.10262 | − | 5.37390i | −0.576142 | − | 0.997907i | −0.995917 | − | 0.0902789i | \(-0.971224\pi\) |
0.419774 | − | 0.907628i | \(-0.362109\pi\) | |||||||
\(30\) | −6.63763 | + | 8.14079i | −1.21186 | + | 1.48630i | ||||
\(31\) | −0.0942019 | + | 0.163162i | −0.0169192 | + | 0.0293048i | −0.874361 | − | 0.485276i | \(-0.838719\pi\) |
0.857442 | + | 0.514581i | \(0.172052\pi\) | |||||||
\(32\) | −2.55712 | + | 4.42907i | −0.452040 | + | 0.782956i | ||||
\(33\) | −10.4138 | − | 1.68522i | −1.81281 | − | 0.293360i | ||||
\(34\) | −1.03938 | − | 1.80026i | −0.178252 | − | 0.308742i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.79332 | + | 0.928373i | 0.465553 | + | 0.154729i | ||||
\(37\) | 3.57670 | 0.588006 | 0.294003 | − | 0.955804i | \(-0.405012\pi\) | ||||
0.294003 | + | 0.955804i | \(0.405012\pi\) | |||||||
\(38\) | 1.90391 | + | 3.29767i | 0.308855 | + | 0.534953i | ||||
\(39\) | −0.689288 | − | 1.81382i | −0.110374 | − | 0.290444i | ||||
\(40\) | 3.08925 | − | 5.35074i | 0.488453 | − | 0.846026i | ||||
\(41\) | −1.68320 | + | 2.91538i | −0.262871 | + | 0.455307i | −0.967004 | − | 0.254762i | \(-0.918003\pi\) |
0.704132 | + | 0.710069i | \(0.251336\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90276 | − | 3.29567i | −0.290168 | − | 0.502585i | 0.683681 | − | 0.729781i | \(-0.260378\pi\) |
−0.973849 | + | 0.227195i | \(0.927044\pi\) | |||||||
\(44\) | −5.97604 | −0.900922 | ||||||||
\(45\) | −9.99915 | − | 3.32326i | −1.49058 | − | 0.495403i | ||||
\(46\) | 2.19865 | 0.324173 | ||||||||
\(47\) | −2.86035 | − | 4.95427i | −0.417225 | − | 0.722654i | 0.578434 | − | 0.815729i | \(-0.303664\pi\) |
−0.995659 | + | 0.0930746i | \(0.970331\pi\) | |||||||
\(48\) | −8.54843 | − | 1.38336i | −1.23386 | − | 0.199670i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.33349 | − | 10.9699i | 0.895691 | − | 1.55138i | ||||
\(51\) | 1.31776 | − | 1.61618i | 0.184523 | − | 0.226311i | ||||
\(52\) | −0.549600 | − | 0.951935i | −0.0762158 | − | 0.132010i | ||||
\(53\) | −8.33827 | −1.14535 | −0.572675 | − | 0.819783i | \(-0.694094\pi\) | ||||
−0.572675 | + | 0.819783i | \(0.694094\pi\) | |||||||
\(54\) | 0.379341 | + | 8.96371i | 0.0516218 | + | 1.21981i | ||||
\(55\) | 21.3922 | 2.88453 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.41384 | + | 2.96047i | −0.319720 | + | 0.392124i | ||||
\(58\) | 5.35702 | − | 9.27862i | 0.703411 | − | 1.21834i | ||||
\(59\) | −5.63427 | + | 9.75883i | −0.733519 | + | 1.27049i | 0.221851 | + | 0.975081i | \(0.428790\pi\) |
−0.955370 | + | 0.295411i | \(0.904543\pi\) | |||||||
\(60\) | −5.89238 | − | 0.953538i | −0.760703 | − | 0.123101i | ||||
\(61\) | 6.00109 | + | 10.3942i | 0.768361 | + | 1.33084i | 0.938451 | + | 0.345411i | \(0.112261\pi\) |
−0.170091 | + | 0.985428i | \(0.554406\pi\) | |||||||
\(62\) | −0.325300 | −0.0413131 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.16898 | 0.146123 | ||||||||
\(65\) | 1.96738 | + | 3.40761i | 0.244024 | + | 0.422662i | ||||
\(66\) | −6.47041 | − | 17.0265i | −0.796453 | − | 2.09582i | ||||
\(67\) | 3.95652 | − | 6.85289i | 0.483366 | − | 0.837214i | −0.516452 | − | 0.856316i | \(-0.672748\pi\) |
0.999818 | + | 0.0191025i | \(0.00608088\pi\) | |||||||
\(68\) | 0.590651 | − | 1.02304i | 0.0716270 | − | 0.124062i | ||||
\(69\) | 0.783494 | + | 2.06172i | 0.0943217 | + | 0.248202i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2052 | −1.44850 | −0.724248 | − | 0.689540i | \(-0.757813\pi\) | ||||
−0.724248 | + | 0.689540i | \(0.757813\pi\) | |||||||
\(72\) | −1.06255 | − | 5.16922i | −0.125223 | − | 0.609198i | ||||
\(73\) | 5.31473 | 0.622042 | 0.311021 | − | 0.950403i | \(-0.399329\pi\) | ||||
0.311021 | + | 0.950403i | \(0.399329\pi\) | |||||||
\(74\) | 3.08779 | + | 5.34820i | 0.358948 | + | 0.621716i | ||||
\(75\) | 12.5437 | + | 2.02989i | 1.44842 | + | 0.234392i | ||||
\(76\) | −1.08194 | + | 1.87397i | −0.124107 | + | 0.214959i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.11712 | − | 2.59657i | 0.239717 | − | 0.294003i | ||||
\(79\) | −4.60855 | − | 7.98225i | −0.518503 | − | 0.898073i | −0.999769 | − | 0.0214988i | \(-0.993156\pi\) |
0.481266 | − | 0.876575i | \(-0.340177\pi\) | |||||||
\(80\) | 17.5603 | 1.96330 | ||||||||
\(81\) | −8.27029 | + | 3.54996i | −0.918922 | + | 0.394440i | ||||
\(82\) | −5.81246 | −0.641878 | ||||||||
\(83\) | −0.624950 | − | 1.08245i | −0.0685972 | − | 0.118814i | 0.829687 | − | 0.558229i | \(-0.188519\pi\) |
−0.898284 | + | 0.439415i | \(0.855186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.11433 | + | 3.66213i | −0.229332 | + | 0.397214i | ||||
\(86\) | 3.28532 | − | 5.69034i | 0.354265 | − | 0.613605i | ||||
\(87\) | 10.6098 | + | 1.71693i | 1.13749 | + | 0.184074i | ||||
\(88\) | 5.35702 | + | 9.27862i | 0.571060 | + | 0.989105i | ||||
\(89\) | −5.54131 | −0.587378 | −0.293689 | − | 0.955901i | \(-0.594883\pi\) | ||||
−0.293689 | + | 0.955901i | \(0.594883\pi\) | |||||||
\(90\) | −3.66308 | − | 17.8206i | −0.386122 | − | 1.87846i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.624715 | + | 1.08204i | 0.0651310 | + | 0.112810i | ||||
\(93\) | −0.115922 | − | 0.305041i | −0.0120205 | − | 0.0316313i | ||||
\(94\) | 4.93871 | − | 8.55409i | 0.509389 | − | 0.882287i | ||||
\(95\) | 3.87298 | − | 6.70820i | 0.397359 | − | 0.688246i | ||||
\(96\) | −3.14671 | − | 8.28038i | −0.321159 | − | 0.845113i | ||||
\(97\) | −8.24277 | − | 14.2769i | −0.836926 | − | 1.44960i | −0.892452 | − | 0.451142i | \(-0.851017\pi\) |
0.0555261 | − | 0.998457i | \(-0.482316\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.6604 | − | 12.1349i | 1.37292 | − | 1.21960i | ||||
\(100\) | 7.19829 | 0.719829 | ||||||||
\(101\) | −6.48192 | − | 11.2270i | −0.644975 | − | 1.11713i | −0.984307 | − | 0.176463i | \(-0.943534\pi\) |
0.339332 | − | 0.940667i | \(-0.389799\pi\) | |||||||
\(102\) | 3.55429 | + | 0.575174i | 0.351927 | + | 0.0569507i | ||||
\(103\) | 1.35091 | − | 2.33984i | 0.133109 | − | 0.230552i | −0.791765 | − | 0.610826i | \(-0.790837\pi\) |
0.924873 | + | 0.380275i | \(0.124171\pi\) | |||||||
\(104\) | −0.985340 | + | 1.70666i | −0.0966205 | + | 0.167352i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.19847 | − | 12.4681i | −0.699177 | − | 1.21101i | ||||
\(107\) | −0.178480 | −0.0172544 | −0.00862718 | − | 0.999963i | \(-0.502746\pi\) | ||||
−0.00862718 | + | 0.999963i | \(0.502746\pi\) | |||||||
\(108\) | −4.30360 | + | 2.73360i | −0.414114 | + | 0.263041i | ||||
\(109\) | 9.35853 | 0.896385 | 0.448192 | − | 0.893937i | \(-0.352068\pi\) | ||||
0.448192 | + | 0.893937i | \(0.352068\pi\) | |||||||
\(110\) | 18.4680 | + | 31.9876i | 1.76086 | + | 3.04989i | ||||
\(111\) | −3.91479 | + | 4.80134i | −0.371575 | + | 0.455723i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.21019 | − | 7.29226i | 0.396061 | − | 0.685998i | −0.597175 | − | 0.802111i | \(-0.703710\pi\) |
0.993236 | + | 0.116113i | \(0.0370434\pi\) | |||||||
\(114\) | −6.51064 | − | 1.05359i | −0.609777 | − | 0.0986776i | ||||
\(115\) | −2.23627 | − | 3.87333i | −0.208533 | − | 0.361190i | ||||
\(116\) | 6.08848 | 0.565302 | ||||||||
\(117\) | 3.18930 | + | 1.05998i | 0.294851 | + | 0.0979952i | ||||
\(118\) | −19.4564 | −1.79110 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.80152 | + | 10.0035i | 0.347030 | + | 0.913190i | ||||
\(121\) | −13.0479 | + | 22.5997i | −1.18618 | + | 2.05452i | ||||
\(122\) | −10.3615 | + | 17.9467i | −0.938090 | + | 1.62482i | ||||
\(123\) | −2.07129 | − | 5.45047i | −0.186762 | − | 0.491453i | ||||
\(124\) | −0.0924294 | − | 0.160092i | −0.00830040 | − | 0.0143767i | ||||
\(125\) | −8.20593 | −0.733960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.92438 | −0.880647 | −0.440323 | − | 0.897839i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897839i | \(0.645136\pi\) | |||||||
\(128\) | 6.12343 | + | 10.6061i | 0.541240 | + | 0.937455i | ||||
\(129\) | 6.50670 | + | 1.05295i | 0.572883 | + | 0.0927071i | ||||
\(130\) | −3.39691 | + | 5.88361i | −0.297928 | + | 0.516027i | ||||
\(131\) | −7.62335 | + | 13.2040i | −0.666055 | + | 1.15364i | 0.312943 | + | 0.949772i | \(0.398685\pi\) |
−0.978998 | + | 0.203870i | \(0.934648\pi\) | |||||||
\(132\) | 6.54093 | − | 8.02219i | 0.569314 | − | 0.698242i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.6627 | 1.18028 | ||||||||
\(135\) | 15.4054 | − | 9.78537i | 1.32589 | − | 0.842191i | ||||
\(136\) | −2.11788 | −0.181606 | ||||||||
\(137\) | −3.07350 | − | 5.32346i | −0.262587 | − | 0.454814i | 0.704342 | − | 0.709861i | \(-0.251242\pi\) |
−0.966929 | + | 0.255047i | \(0.917909\pi\) | |||||||
\(138\) | −2.40647 | + | 2.95145i | −0.204853 | + | 0.251244i | ||||
\(139\) | −0.438687 | + | 0.759829i | −0.0372090 | + | 0.0644478i | −0.884030 | − | 0.467430i | \(-0.845180\pi\) |
0.846821 | + | 0.531878i | \(0.178513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.78129 | + | 1.58286i | 0.823733 | + | 0.133301i | ||||
\(142\) | −10.5368 | − | 18.2504i | −0.884233 | − | 1.53154i | ||||
\(143\) | −6.82321 | −0.570586 | ||||||||
\(144\) | 11.2135 | − | 9.96123i | 0.934456 | − | 0.830102i | ||||
\(145\) | −21.7947 | −1.80995 | ||||||||
\(146\) | 4.58824 | + | 7.94706i | 0.379725 | + | 0.657703i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.75470 | + | 3.03923i | −0.144236 | + | 0.249823i | ||||
\(149\) | −2.88776 | + | 5.00175i | −0.236575 | + | 0.409760i | −0.959729 | − | 0.280927i | \(-0.909358\pi\) |
0.723154 | + | 0.690686i | \(0.242692\pi\) | |||||||
\(150\) | 7.79378 | + | 20.5089i | 0.636359 | + | 1.67454i | ||||
\(151\) | 1.01321 | + | 1.75494i | 0.0824541 | + | 0.142815i | 0.904304 | − | 0.426890i | \(-0.140391\pi\) |
−0.821849 | + | 0.569705i | \(0.807058\pi\) | |||||||
\(152\) | 3.87947 | 0.314666 | ||||||||
\(153\) | 0.727226 | + | 3.53790i | 0.0587927 | + | 0.286022i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.330866 | + | 0.573077i | 0.0265758 | + | 0.0460307i | ||||
\(156\) | 1.87942 | + | 0.304138i | 0.150474 | + | 0.0243506i | ||||
\(157\) | −1.52378 | + | 2.63927i | −0.121611 | + | 0.210636i | −0.920403 | − | 0.390971i | \(-0.872139\pi\) |
0.798792 | + | 0.601607i | \(0.205473\pi\) | |||||||
\(158\) | 7.95718 | − | 13.7822i | 0.633039 | − | 1.09646i | ||||
\(159\) | 9.12644 | − | 11.1932i | 0.723774 | − | 0.887680i | ||||
\(160\) | 8.98141 | + | 15.5563i | 0.710043 | + | 1.22983i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.4480 | − | 9.30178i | −0.978008 | − | 0.730817i | ||||
\(163\) | −5.38891 | −0.422092 | −0.211046 | − | 0.977476i | \(-0.567687\pi\) | ||||
−0.211046 | + | 0.977476i | \(0.567687\pi\) | |||||||
\(164\) | −1.65153 | − | 2.86053i | −0.128963 | − | 0.223370i | ||||
\(165\) | −23.4143 | + | 28.7167i | −1.82280 | + | 2.23560i | ||||
\(166\) | 1.07905 | − | 1.86896i | 0.0837502 | − | 0.145060i | ||||
\(167\) | 8.30480 | − | 14.3843i | 0.642645 | − | 1.11309i | −0.342196 | − | 0.939629i | \(-0.611171\pi\) |
0.984840 | − | 0.173464i | \(-0.0554961\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.87249 | + | 10.1714i | 0.451730 | + | 0.782419i | ||||
\(170\) | −7.30126 | −0.559981 | ||||||||
\(171\) | −1.33211 | − | 6.48063i | −0.101869 | − | 0.495586i | ||||
\(172\) | 3.73391 | 0.284708 | ||||||||
\(173\) | −8.82516 | − | 15.2856i | −0.670965 | − | 1.16214i | −0.977631 | − | 0.210328i | \(-0.932547\pi\) |
0.306666 | − | 0.951817i | \(-0.400786\pi\) | |||||||
\(174\) | 6.59216 | + | 17.3469i | 0.499750 | + | 1.31507i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −15.2255 | + | 26.3714i | −1.14767 | + | 1.98782i | ||||
\(177\) | −6.93333 | − | 18.2447i | −0.521141 | − | 1.37135i | ||||
\(178\) | −4.78384 | − | 8.28586i | −0.358564 | − | 0.621051i | ||||
\(179\) | 2.62844 | 0.196459 | 0.0982294 | − | 0.995164i | \(-0.468682\pi\) | ||||
0.0982294 | + | 0.995164i | \(0.468682\pi\) | |||||||
\(180\) | 7.72938 | − | 6.86621i | 0.576114 | − | 0.511777i | ||||
\(181\) | −3.97391 | −0.295378 | −0.147689 | − | 0.989034i | \(-0.547184\pi\) | ||||
−0.147689 | + | 0.989034i | \(0.547184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.5214 | − | 3.32089i | −1.51699 | − | 0.245487i | ||||
\(184\) | 1.12001 | − | 1.93991i | 0.0825681 | − | 0.143012i | ||||
\(185\) | 6.28125 | − | 10.8794i | 0.461806 | − | 0.799872i | ||||
\(186\) | 0.356049 | − | 0.436680i | 0.0261068 | − | 0.0320189i | ||||
\(187\) | −3.66643 | − | 6.35045i | −0.268116 | − | 0.464391i | ||||
\(188\) | 5.61306 | 0.409374 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.3743 | 0.970270 | ||||||||
\(191\) | 9.10295 | + | 15.7668i | 0.658666 | + | 1.14084i | 0.980961 | + | 0.194204i | \(0.0622125\pi\) |
−0.322295 | + | 0.946639i | \(0.604454\pi\) | |||||||
\(192\) | −1.27948 | + | 1.56923i | −0.0923384 | + | 0.113249i | ||||
\(193\) | 0.101193 | − | 0.175271i | 0.00728401 | − | 0.0126163i | −0.862360 | − | 0.506295i | \(-0.831015\pi\) |
0.869644 | + | 0.493679i | \(0.164348\pi\) | |||||||
\(194\) | 14.2321 | − | 24.6506i | 1.02180 | − | 1.76981i | ||||
\(195\) | −6.72770 | − | 1.08871i | −0.481780 | − | 0.0779644i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.63136 | −0.116229 | −0.0581147 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581147 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(198\) | 29.9383 | + | 9.95014i | 2.12762 | + | 0.707125i | ||||
\(199\) | −6.29211 | −0.446036 | −0.223018 | − | 0.974814i | \(-0.571591\pi\) | ||||
−0.223018 | + | 0.974814i | \(0.571591\pi\) | |||||||
\(200\) | −6.45266 | − | 11.1763i | −0.456272 | − | 0.790287i | ||||
\(201\) | 4.86875 | + | 12.8119i | 0.343415 | + | 0.903678i | ||||
\(202\) | 11.1918 | − | 19.3847i | 0.787449 | − | 1.36390i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.726835 | + | 1.91263i | 0.0508886 | + | 0.133911i | ||||
\(205\) | 5.91192 | + | 10.2397i | 0.412906 | + | 0.715174i | ||||
\(206\) | 4.66499 | 0.325025 | ||||||||
\(207\) | −3.62519 | − | 1.20485i | −0.251968 | − | 0.0837429i | ||||
\(208\) | −5.60100 | −0.388359 | ||||||||
\(209\) | 6.71607 | + | 11.6326i | 0.464560 | + | 0.804642i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.14368 | − | 14.1053i | 0.560634 | − | 0.971046i | −0.436807 | − | 0.899555i | \(-0.643891\pi\) |
0.997441 | − | 0.0714912i | \(-0.0227758\pi\) | |||||||
\(212\) | 4.09069 | − | 7.08528i | 0.280950 | − | 0.486619i | ||||
\(213\) | 13.3589 | − | 16.3842i | 0.915339 | − | 1.12263i | ||||
\(214\) | −0.154083 | − | 0.266880i | −0.0105329 | − | 0.0182435i | ||||
\(215\) | −13.3662 | −0.911564 | ||||||||
\(216\) | 8.10210 | + | 4.23148i | 0.551278 | + | 0.287916i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.07927 | + | 13.9937i | 0.547197 | + | 0.947773i | ||||
\(219\) | −5.81711 | + | 7.13445i | −0.393084 | + | 0.482101i | ||||
\(220\) | −10.4949 | + | 18.1776i | −0.707563 | + | 1.22554i | ||||
\(221\) | 0.674383 | − | 1.16807i | 0.0453639 | − | 0.0785726i | ||||
\(222\) | −10.5590 | − | 1.70872i | −0.708677 | − | 0.114682i | ||||
\(223\) | 9.98472 | + | 17.2940i | 0.668626 | + | 1.15809i | 0.978288 | + | 0.207248i | \(0.0664507\pi\) |
−0.309662 | + | 0.950847i | \(0.600216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.4543 | + | 14.6168i | −1.09695 | + | 0.974454i | ||||
\(226\) | 14.5387 | 0.967101 | ||||||||
\(227\) | 1.80642 | + | 3.12880i | 0.119896 | + | 0.207666i | 0.919726 | − | 0.392560i | \(-0.128411\pi\) |
−0.799830 | + | 0.600226i | \(0.795077\pi\) | |||||||
\(228\) | −1.33140 | − | 3.50350i | −0.0881739 | − | 0.232025i | ||||
\(229\) | 6.85733 | − | 11.8772i | 0.453145 | − | 0.784870i | −0.545435 | − | 0.838153i | \(-0.683635\pi\) |
0.998579 | + | 0.0532835i | \(0.0169687\pi\) | |||||||
\(230\) | 3.86117 | − | 6.68774i | 0.254598 | − | 0.440976i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.45781 | − | 9.45321i | −0.358323 | − | 0.620634i | ||||
\(233\) | −25.2542 | −1.65445 | −0.827227 | − | 0.561867i | \(-0.810083\pi\) | ||||
−0.827227 | + | 0.561867i | \(0.810083\pi\) | |||||||
\(234\) | 1.16837 | + | 5.68402i | 0.0763785 | + | 0.371576i | ||||
\(235\) | −20.0929 | −1.31071 | ||||||||
\(236\) | −5.52825 | − | 9.57521i | −0.359859 | − | 0.623293i | ||||
\(237\) | 15.7595 | + | 2.55029i | 1.02369 | + | 0.165659i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.49495 | + | 7.78549i | −0.290754 | + | 0.503601i | −0.973988 | − | 0.226598i | \(-0.927240\pi\) |
0.683234 | + | 0.730200i | \(0.260573\pi\) | |||||||
\(240\) | −19.2202 | + | 23.5728i | −1.24066 | + | 1.52162i | ||||
\(241\) | 4.62862 | + | 8.01701i | 0.298156 | + | 0.516421i | 0.975714 | − | 0.219048i | \(-0.0702952\pi\) |
−0.677558 | + | 0.735469i | \(0.736962\pi\) | |||||||
\(242\) | −45.0575 | −2.89640 | ||||||||
\(243\) | 4.28661 | − | 14.9875i | 0.274986 | − | 0.961448i | ||||
\(244\) | −11.7763 | −0.753903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.36188 | − | 7.80259i | 0.405619 | − | 0.497475i | ||||
\(247\) | −1.23532 | + | 2.13963i | −0.0786013 | + | 0.136141i | ||||
\(248\) | −0.165710 | + | 0.287019i | −0.0105226 | + | 0.0182257i | ||||
\(249\) | 2.13709 | + | 0.345836i | 0.135433 | + | 0.0219164i | ||||
\(250\) | −7.08422 | − | 12.2702i | −0.448045 | − | 0.776037i | ||||
\(251\) | −20.6517 | −1.30353 | −0.651763 | − | 0.758422i | \(-0.725970\pi\) | ||||
−0.651763 | + | 0.758422i | \(0.725970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.75576 | 0.487600 | ||||||||
\(254\) | −8.56777 | − | 14.8398i | −0.537590 | − | 0.931133i | ||||
\(255\) | −2.60183 | − | 6.84656i | −0.162933 | − | 0.428748i | ||||
\(256\) | −9.40380 | + | 16.2879i | −0.587738 | + | 1.01799i | ||||
\(257\) | −1.22289 | + | 2.11811i | −0.0762819 | + | 0.132124i | −0.901643 | − | 0.432481i | \(-0.857638\pi\) |
0.825361 | + | 0.564605i | \(0.190972\pi\) | |||||||
\(258\) | 4.04280 | + | 10.6384i | 0.251694 | + | 0.662318i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.86073 | −0.239432 | ||||||||
\(261\) | −13.9174 | + | 12.3632i | −0.861468 | + | 0.765265i | ||||
\(262\) | −26.3251 | −1.62637 | ||||||||
\(263\) | 12.2814 | + | 21.2720i | 0.757302 | + | 1.31169i | 0.944222 | + | 0.329311i | \(0.106816\pi\) |
−0.186919 | + | 0.982375i | \(0.559850\pi\) | |||||||
\(264\) | −18.3189 | − | 2.96447i | −1.12745 | − | 0.182451i | ||||
\(265\) | −14.6433 | + | 25.3629i | −0.899531 | + | 1.55803i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.06510 | − | 7.43861i | 0.371178 | − | 0.455236i | ||||
\(268\) | 3.88207 | + | 6.72395i | 0.237135 | + | 0.410730i | ||||
\(269\) | 29.5703 | 1.80293 | 0.901466 | − | 0.432849i | \(-0.142492\pi\) | ||||
0.901466 | + | 0.432849i | \(0.142492\pi\) | |||||||
\(270\) | 27.9316 | + | 14.5878i | 1.69986 | + | 0.887786i | ||||
\(271\) | 24.7915 | 1.50598 | 0.752989 | − | 0.658034i | \(-0.228612\pi\) | ||||
0.752989 | + | 0.658034i | \(0.228612\pi\) | |||||||
\(272\) | −3.00968 | − | 5.21291i | −0.182488 | − | 0.316079i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.30674 | − | 9.19154i | 0.320592 | − | 0.555281i | ||||
\(275\) | 22.3415 | − | 38.6966i | 1.34724 | − | 2.33349i | ||||
\(276\) | −2.13628 | − | 0.345705i | −0.128589 | − | 0.0208090i | ||||
\(277\) | −0.939249 | − | 1.62683i | −0.0564340 | − | 0.0977466i | 0.836428 | − | 0.548076i | \(-0.184640\pi\) |
−0.892862 | + | 0.450330i | \(0.851306\pi\) | |||||||
\(278\) | −1.51488 | −0.0908567 | ||||||||
\(279\) | 0.536364 | + | 0.178263i | 0.0321113 | + | 0.0106723i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.03965 | + | 10.4610i | 0.360295 | + | 0.624049i | 0.988009 | − | 0.154395i | \(-0.0493427\pi\) |
−0.627714 | + | 0.778444i | \(0.716009\pi\) | |||||||
\(282\) | 6.07740 | + | 15.9923i | 0.361904 | + | 0.952330i | ||||
\(283\) | −13.9859 | + | 24.2244i | −0.831378 | + | 1.43999i | 0.0655680 | + | 0.997848i | \(0.479114\pi\) |
−0.896946 | + | 0.442140i | \(0.854219\pi\) | |||||||
\(284\) | 5.98779 | − | 10.3712i | 0.355310 | − | 0.615415i | ||||
\(285\) | 4.76595 | + | 12.5413i | 0.282311 | + | 0.742885i | ||||
\(286\) | −5.89052 | − | 10.2027i | −0.348314 | − | 0.603297i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 14.5597 | + | 4.83897i | 0.857937 | + | 0.285139i | ||||
\(289\) | −15.5505 | −0.914735 | ||||||||
\(290\) | −18.8155 | − | 32.5894i | −1.10488 | − | 1.91372i | ||||
\(291\) | 28.1871 | + | 4.56139i | 1.65236 | + | 0.267394i | ||||
\(292\) | −2.60736 | + | 4.51609i | −0.152584 | + | 0.264284i | ||||
\(293\) | 4.41163 | − | 7.64117i | 0.257730 | − | 0.446402i | −0.707903 | − | 0.706309i | \(-0.750359\pi\) |
0.965634 | + | 0.259908i | \(0.0836921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.7893 | + | 34.2761i | 1.15218 | + | 1.99563i | ||||
\(296\) | 6.29177 | 0.365702 | ||||||||
\(297\) | 1.33813 | + | 31.6196i | 0.0776463 | + | 1.83475i | ||||
\(298\) | −9.97209 | −0.577668 | ||||||||
\(299\) | 0.713276 | + | 1.23543i | 0.0412498 | + | 0.0714467i | ||||
\(300\) | −7.87871 | + | 9.66293i | −0.454878 | + | 0.557889i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.74942 | + | 3.03009i | −0.100668 | + | 0.174362i | ||||
\(303\) | 22.1657 | + | 3.58697i | 1.27339 | + | 0.206066i | ||||
\(304\) | 5.51304 | + | 9.54887i | 0.316195 | + | 0.547665i | ||||
\(305\) | 42.1554 | 2.41381 | ||||||||
\(306\) | −4.66236 | + | 4.14170i | −0.266530 | + | 0.236765i | ||||
\(307\) | −1.05532 | −0.0602304 | −0.0301152 | − | 0.999546i | \(-0.509587\pi\) | ||||
−0.0301152 | + | 0.999546i | \(0.509587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.66238 | + | 4.37446i | 0.0945696 | + | 0.248855i | ||||
\(310\) | −0.571277 | + | 0.989481i | −0.0324464 | + | 0.0561988i | ||||
\(311\) | 1.53608 | − | 2.66056i | 0.0871029 | − | 0.150867i | −0.819182 | − | 0.573533i | \(-0.805572\pi\) |
0.906285 | + | 0.422666i | \(0.138906\pi\) | |||||||
\(312\) | −1.21253 | − | 3.19069i | −0.0686457 | − | 0.180637i | ||||
\(313\) | 14.0810 | + | 24.3891i | 0.795907 | + | 1.37855i | 0.922262 | + | 0.386566i | \(0.126339\pi\) |
−0.126355 | + | 0.991985i | \(0.540328\pi\) | |||||||
\(314\) | −5.26196 | −0.296949 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.04368 | 0.508747 | ||||||||
\(317\) | −6.42324 | − | 11.1254i | −0.360765 | − | 0.624863i | 0.627322 | − | 0.778760i | \(-0.284151\pi\) |
−0.988087 | + | 0.153897i | \(0.950818\pi\) | |||||||
\(318\) | 24.6160 | + | 3.98350i | 1.38040 | + | 0.223384i | ||||
\(319\) | 18.8969 | − | 32.7305i | 1.05803 | − | 1.83255i | ||||
\(320\) | 2.05291 | − | 3.55575i | 0.114761 | − | 0.198772i | ||||
\(321\) | 0.195351 | − | 0.239591i | 0.0109034 | − | 0.0133726i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.65517 | −0.147738 | ||||||||
\(324\) | 1.04083 | − | 8.76910i | 0.0578240 | − | 0.487172i | ||||
\(325\) | 8.21874 | 0.455893 | ||||||||
\(326\) | −4.65227 | − | 8.05797i | −0.257665 | − | 0.446290i | ||||
\(327\) | −10.2431 | + | 12.5628i | −0.566447 | + | 0.694725i | ||||
\(328\) | −2.96091 | + | 5.12845i | −0.163489 | + | 0.283171i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −63.1535 | − | 10.2199i | −3.47649 | − | 0.562585i | ||||
\(331\) | 10.7780 | + | 18.6681i | 0.592413 | + | 1.02609i | 0.993906 | + | 0.110228i | \(0.0351581\pi\) |
−0.401493 | + | 0.915862i | \(0.631509\pi\) | |||||||
\(332\) | 1.22638 | 0.0673065 | ||||||||
\(333\) | −2.16044 | − | 10.5104i | −0.118391 | − | 0.575964i | ||||
\(334\) | 28.6783 | 1.56921 | ||||||||
\(335\) | −13.8965 | − | 24.0695i | −0.759248 | − | 1.31506i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.30340 | − | 10.9178i | 0.343368 | − | 0.594731i | −0.641688 | − | 0.766966i | \(-0.721766\pi\) |
0.985056 | + | 0.172235i | \(0.0550989\pi\) | |||||||
\(338\) | −10.1395 | + | 17.5621i | −0.551516 | + | 0.955254i | ||||
\(339\) | 5.18091 | + | 13.6333i | 0.281389 | + | 0.740459i | ||||
\(340\) | −2.07455 | − | 3.59323i | −0.112508 | − | 0.194870i | ||||
\(341\) | −1.14750 | −0.0621406 | ||||||||
\(342\) | 8.54039 | − | 7.58665i | 0.461811 | − | 0.410239i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.34714 | − | 5.79741i | −0.180466 | − | 0.312575i | ||||
\(345\) | 7.64718 | + | 1.23751i | 0.411711 | + | 0.0666253i | ||||
\(346\) | 15.2376 | − | 26.3923i | 0.819179 | − | 1.41886i | ||||
\(347\) | −11.5683 | + | 20.0369i | −0.621020 | + | 1.07564i | 0.368276 | + | 0.929716i | \(0.379948\pi\) |
−0.989296 | + | 0.145922i | \(0.953385\pi\) | |||||||
\(348\) | −6.66400 | + | 8.17313i | −0.357228 | + | 0.438126i | ||||
\(349\) | −8.24346 | − | 14.2781i | −0.441262 | − | 0.764289i | 0.556521 | − | 0.830833i | \(-0.312136\pi\) |
−0.997783 | + | 0.0665448i | \(0.978802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.91368 | + | 3.12112i | −0.262273 | + | 0.166593i | ||||
\(352\) | −31.1490 | −1.66025 | ||||||||
\(353\) | −12.2438 | − | 21.2068i | −0.651669 | − | 1.12872i | −0.982718 | − | 0.185110i | \(-0.940736\pi\) |
0.331049 | − | 0.943614i | \(-0.392598\pi\) | |||||||
\(354\) | 21.2955 | − | 26.1181i | 1.13184 | − | 1.38816i | ||||
\(355\) | −21.4343 | + | 37.1253i | −1.13761 | + | 1.97041i | ||||
\(356\) | 2.71852 | − | 4.70862i | 0.144081 | − | 0.249556i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.26915 | + | 3.93028i | 0.119928 | + | 0.207722i | ||||
\(359\) | 20.4777 | 1.08077 | 0.540386 | − | 0.841417i | \(-0.318278\pi\) | ||||
0.540386 | + | 0.841417i | \(0.318278\pi\) | |||||||
\(360\) | −17.5895 | − | 5.84595i | −0.927047 | − | 0.308108i | ||||
\(361\) | −14.1363 | −0.744017 | ||||||||
\(362\) | −3.43070 | − | 5.94214i | −0.180313 | − | 0.312312i | ||||
\(363\) | −16.0564 | − | 42.2514i | −0.842740 | − | 2.21762i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.33349 | − | 16.1661i | 0.488537 | − | 0.846172i | ||||
\(366\) | −12.7506 | − | 33.5524i | −0.666482 | − | 1.75381i | ||||
\(367\) | 11.1269 | + | 19.2724i | 0.580821 | + | 1.00601i | 0.995382 | + | 0.0959900i | \(0.0306017\pi\) |
−0.414561 | + | 0.910021i | \(0.636065\pi\) | |||||||
\(368\) | 6.36650 | 0.331877 | ||||||||
\(369\) | 9.58374 | + | 3.18520i | 0.498910 | + | 0.165815i | ||||
\(370\) | 21.6905 | 1.12764 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.316073 | + | 0.0511487i | 0.0163876 | + | 0.00265194i | ||||
\(373\) | 16.2684 | − | 28.1777i | 0.842347 | − | 1.45899i | −0.0455576 | − | 0.998962i | \(-0.514506\pi\) |
0.887905 | − | 0.460027i | \(-0.152160\pi\) | |||||||
\(374\) | 6.33050 | − | 10.9647i | 0.327342 | − | 0.566974i | ||||
\(375\) | 8.98159 | − | 11.0156i | 0.463807 | − | 0.568841i | ||||
\(376\) | −5.03163 | − | 8.71504i | −0.259487 | − | 0.449444i | ||||
\(377\) | 6.95160 | 0.358026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54440 | 0.0793306 | 0.0396653 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396653 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(380\) | 3.80011 | + | 6.58198i | 0.194941 | + | 0.337648i | ||||
\(381\) | 10.8625 | − | 13.3224i | 0.556502 | − | 0.682528i | ||||
\(382\) | −15.7173 | + | 27.2231i | −0.804165 | + | 1.39285i | ||||
\(383\) | 15.8147 | − | 27.3919i | 0.808093 | − | 1.39966i | −0.106090 | − | 0.994357i | \(-0.533833\pi\) |
0.914183 | − | 0.405302i | \(-0.132834\pi\) | |||||||
\(384\) | −20.9398 | − | 3.38859i | −1.06858 | − | 0.172923i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.349441 | 0.0177861 | ||||||||
\(387\) | −8.53521 | + | 7.58206i | −0.433869 | + | 0.385418i | ||||
\(388\) | 16.1753 | 0.821179 | ||||||||
\(389\) | 2.62313 | + | 4.54340i | 0.132998 | + | 0.230359i | 0.924831 | − | 0.380378i | \(-0.124206\pi\) |
−0.791833 | + | 0.610738i | \(0.790873\pi\) | |||||||
\(390\) | −4.18012 | − | 10.9997i | −0.211668 | − | 0.556993i | ||||
\(391\) | −0.766552 | + | 1.32771i | −0.0387662 | + | 0.0671451i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.38103 | − | 24.6857i | −0.473210 | − | 1.24523i | ||||
\(394\) | −1.40836 | − | 2.43935i | −0.0709521 | − | 0.122893i | ||||
\(395\) | −32.3734 | −1.62888 | ||||||||
\(396\) | 3.60971 | + | 17.5610i | 0.181395 | + | 0.882472i | ||||
\(397\) | −0.0276349 | −0.00138696 | −0.000693478 | − | 1.00000i | \(-0.500221\pi\) | ||||
−0.000693478 | 1.00000i | \(0.500221\pi\) | ||||||||
\(398\) | −5.43201 | − | 9.40851i | −0.272282 | − | 0.471606i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.3395 | − | 31.7650i | 0.916977 | − | 1.58825i | ||||
\(401\) | −6.06885 | + | 10.5115i | −0.303064 | + | 0.524922i | −0.976828 | − | 0.214024i | \(-0.931343\pi\) |
0.673765 | + | 0.738946i | \(0.264676\pi\) | |||||||
\(402\) | −14.9542 | + | 18.3407i | −0.745848 | + | 0.914753i | ||||
\(403\) | −0.105532 | − | 0.182787i | −0.00525694 | − | 0.00910529i | ||||
\(404\) | 12.7199 | 0.632840 | ||||||||
\(405\) | −3.72583 | + | 31.3905i | −0.185138 | + | 1.55980i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.8922 | + | 18.8659i | 0.539907 | + | 0.935146i | ||||
\(408\) | 2.31807 | − | 2.84302i | 0.114762 | − | 0.140750i | ||||
\(409\) | 15.6726 | − | 27.1458i | 0.774963 | − | 1.34227i | −0.159853 | − | 0.987141i | \(-0.551102\pi\) |
0.934816 | − | 0.355134i | \(-0.115565\pi\) | |||||||
\(410\) | −10.2076 | + | 17.6800i | −0.504116 | + | 0.873155i | ||||
\(411\) | 10.5102 | + | 1.70082i | 0.518429 | + | 0.0838951i | ||||
\(412\) | 1.32549 | + | 2.29582i | 0.0653022 | + | 0.113107i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.32805 | − | 6.46086i | −0.0652701 | − | 0.317534i | ||||
\(415\) | −4.39004 | −0.215499 | ||||||||
\(416\) | −2.86469 | − | 4.96179i | −0.140453 | − | 0.243272i | ||||
\(417\) | −0.539833 | − | 1.42054i | −0.0264358 | − | 0.0695642i | ||||
\(418\) | −11.5960 | + | 20.0849i | −0.567181 | + | 0.982385i | ||||
\(419\) | −7.44319 | + | 12.8920i | −0.363623 | + | 0.629814i | −0.988554 | − | 0.150866i | \(-0.951794\pi\) |
0.624931 | + | 0.780680i | \(0.285127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.54213 | − | 7.86721i | −0.221370 | − | 0.383424i | 0.733854 | − | 0.679307i | \(-0.237720\pi\) |
−0.955224 | + | 0.295883i | \(0.904386\pi\) | |||||||
\(422\) | 28.1219 | 1.36895 | ||||||||
\(423\) | −12.8307 | + | 11.3978i | −0.623849 | + | 0.554182i | ||||
\(424\) | −14.6678 | −0.712333 | ||||||||
\(425\) | 4.41631 | + | 7.64927i | 0.214223 | + | 0.371044i | ||||
\(426\) | 36.0320 | + | 5.83089i | 1.74575 | + | 0.282508i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.0875611 | − | 0.151660i | 0.00423243 | − | 0.00733078i | ||||
\(429\) | 7.46818 | − | 9.15943i | 0.360567 | − | 0.442221i | ||||
\(430\) | −11.5391 | − | 19.9863i | −0.556463 | − | 0.963823i | ||||
\(431\) | −16.6355 | −0.801305 | −0.400652 | − | 0.916230i | \(-0.631216\pi\) | ||||
−0.400652 | + | 0.916230i | \(0.631216\pi\) | |||||||
\(432\) | 1.09844 | + | 25.9557i | 0.0528486 | + | 1.24879i | ||||
\(433\) | −19.7423 | −0.948756 | −0.474378 | − | 0.880321i | \(-0.657327\pi\) | ||||
−0.474378 | + | 0.880321i | \(0.657327\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.8549 | − | 29.2571i | 1.14375 | − | 1.40277i | ||||
\(436\) | −4.59122 | + | 7.95223i | −0.219880 | + | 0.380843i | ||||
\(437\) | 1.40415 | − | 2.43206i | 0.0671696 | − | 0.116341i | ||||
\(438\) | −15.6900 | − | 2.53904i | −0.749697 | − | 0.121320i | ||||
\(439\) | −3.36757 | − | 5.83280i | −0.160725 | − | 0.278384i | 0.774404 | − | 0.632692i | \(-0.218050\pi\) |
−0.935129 | + | 0.354307i | \(0.884717\pi\) | |||||||
\(440\) | 37.6310 | 1.79399 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.32879 | 0.110769 | ||||||||
\(443\) | −14.3202 | − | 24.8033i | −0.680372 | − | 1.17844i | −0.974867 | − | 0.222786i | \(-0.928485\pi\) |
0.294496 | − | 0.955653i | \(-0.404848\pi\) | |||||||
\(444\) | −2.15928 | − | 5.68201i | −0.102475 | − | 0.269656i | ||||
\(445\) | −9.73141 | + | 16.8553i | −0.461313 | + | 0.799017i | ||||
\(446\) | −17.2397 | + | 29.8601i | −0.816324 | + | 1.41392i | ||||
\(447\) | −3.55358 | − | 9.35105i | −0.168079 | − | 0.442290i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.66872 | −0.314716 | −0.157358 | − | 0.987542i | \(-0.550298\pi\) | ||||
−0.157358 | + | 0.987542i | \(0.550298\pi\) | |||||||
\(450\) | −36.0615 | − | 11.9852i | −1.69995 | − | 0.564988i | ||||
\(451\) | −20.5035 | −0.965473 | ||||||||
\(452\) | 4.13097 | + | 7.15505i | 0.194305 | + | 0.336545i | ||||
\(453\) | −3.46480 | − | 0.560693i | −0.162790 | − | 0.0263437i | ||||
\(454\) | −3.11898 | + | 5.40223i | −0.146381 | + | 0.253539i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.24617 | + | 5.20776i | −0.198845 | + | 0.243876i | ||||
\(457\) | 14.3287 | + | 24.8180i | 0.670266 | + | 1.16093i | 0.977829 | + | 0.209407i | \(0.0671533\pi\) |
−0.307563 | + | 0.951528i | \(0.599513\pi\) | |||||||
\(458\) | 23.6799 | 1.10649 | ||||||||
\(459\) | −5.54521 | − | 2.89610i | −0.258828 | − | 0.135178i | ||||
\(460\) | 4.38839 | 0.204610 | ||||||||
\(461\) | 10.0087 | + | 17.3355i | 0.466150 | + | 0.807395i | 0.999253 | − | 0.0386554i | \(-0.0123075\pi\) |
−0.533103 | + | 0.846050i | \(0.678974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.95789 | + | 8.58731i | −0.230413 | + | 0.399086i | −0.957930 | − | 0.287003i | \(-0.907341\pi\) |
0.727517 | + | 0.686090i | \(0.240674\pi\) | |||||||
\(464\) | 15.5120 | − | 26.8676i | 0.720127 | − | 1.24730i | ||||
\(465\) | −1.13144 | − | 0.183095i | −0.0524691 | − | 0.00849084i | ||||
\(466\) | −21.8020 | − | 37.7623i | −1.00996 | − | 1.74930i | ||||
\(467\) | 16.0807 | 0.744126 | 0.372063 | − | 0.928207i | \(-0.378651\pi\) | ||||
0.372063 | + | 0.928207i | \(0.378651\pi\) | |||||||
\(468\) | −2.46535 | + | 2.19003i | −0.113961 | + | 0.101234i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17.3463 | − | 30.0446i | −0.800124 | − | 1.38586i | ||||
\(471\) | −1.87511 | − | 4.93426i | −0.0864007 | − | 0.227359i | ||||
\(472\) | −9.91123 | + | 17.1667i | −0.456201 | + | 0.790164i | ||||
\(473\) | 11.5890 | − | 20.0728i | 0.532863 | − | 0.922946i | ||||
\(474\) | 9.79183 | + | 25.7667i | 0.449754 | + | 1.18350i | ||||
\(475\) | −8.08967 | − | 14.0117i | −0.371180 | − | 0.642902i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.03657 | + | 24.5025i | 0.230609 | + | 1.12189i | ||||
\(478\) | −15.5221 | −0.709963 | ||||||||
\(479\) | 4.10128 | + | 7.10362i | 0.187392 | + | 0.324573i | 0.944380 | − | 0.328856i | \(-0.106663\pi\) |
−0.756988 | + | 0.653429i | \(0.773330\pi\) | |||||||
\(480\) | −30.7130 | − | 4.97015i | −1.40185 | − | 0.226855i | ||||
\(481\) | −2.00345 | + | 3.47008i | −0.0913496 | + | 0.158222i | ||||
\(482\) | −7.99183 | + | 13.8423i | −0.364018 | + | 0.630497i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.8024 | − | 22.1745i | −0.581929 | − | 1.00793i | ||||
\(485\) | −57.9023 | −2.62921 | ||||||||
\(486\) | 26.1113 | − | 6.52907i | 1.18443 | − | 0.296165i | ||||
\(487\) | 2.73680 | 0.124016 | 0.0620081 | − | 0.998076i | \(-0.480250\pi\) | ||||
0.0620081 | + | 0.998076i | \(0.480250\pi\) | |||||||
\(488\) | 10.5565 | + | 18.2844i | 0.477871 | + | 0.827696i | ||||
\(489\) | 5.89829 | − | 7.23402i | 0.266730 | − | 0.327134i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.85482 | − | 17.0690i | 0.444742 | − | 0.770315i | −0.553293 | − | 0.832987i | \(-0.686629\pi\) |
0.998034 | + | 0.0626719i | \(0.0199622\pi\) | |||||||
\(492\) | 5.64759 | + | 0.913924i | 0.254613 | + | 0.0412029i | ||||
\(493\) | 3.73542 | + | 6.46993i | 0.168235 | + | 0.291391i | ||||
\(494\) | −4.26582 | −0.191928 | ||||||||
\(495\) | −12.9216 | − | 62.8624i | −0.580781 | − | 2.82545i | ||||
\(496\) | −0.941952 | −0.0422949 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.32784 | + | 3.49413i | 0.0595018 | + | 0.156576i | ||||
\(499\) | 16.5480 | − | 28.6619i | 0.740789 | − | 1.28309i | −0.211347 | − | 0.977411i | \(-0.567785\pi\) |
0.952136 | − | 0.305674i | \(-0.0988817\pi\) | |||||||
\(500\) | 4.02576 | − | 6.97283i | 0.180038 | − | 0.311834i | ||||
\(501\) | 10.2196 | + | 26.8923i | 0.456578 | + | 1.20146i | ||||
\(502\) | −17.8288 | − | 30.8803i | −0.795737 | − | 1.37826i | ||||
\(503\) | 12.1860 | 0.543346 | 0.271673 | − | 0.962390i | \(-0.412423\pi\) | ||||
0.271673 | + | 0.962390i | \(0.412423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.5331 | −2.02619 | ||||||||
\(506\) | 6.69559 | + | 11.5971i | 0.297655 | + | 0.515554i | ||||
\(507\) | −20.0816 | − | 3.24972i | −0.891857 | − | 0.144325i | ||||
\(508\) | 4.86882 | − | 8.43305i | 0.216019 | − | 0.374156i | ||||
\(509\) | −6.81965 | + | 11.8120i | −0.302276 | + | 0.523557i | −0.976651 | − | 0.214832i | \(-0.931080\pi\) |
0.674375 | + | 0.738389i | \(0.264413\pi\) | |||||||
\(510\) | 7.99142 | − | 9.80116i | 0.353866 | − | 0.434002i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.97968 | −0.352656 | ||||||||
\(513\) | 10.1576 | + | 5.30499i | 0.448468 | + | 0.234221i | ||||
\(514\) | −4.22292 | −0.186265 | ||||||||
\(515\) | −4.74481 | − | 8.21826i | −0.209081 | − | 0.362140i | ||||
\(516\) | −4.08686 | + | 5.01237i | −0.179914 | + | 0.220657i | ||||
\(517\) | 17.4214 | − | 30.1747i | 0.766190 | − | 1.32708i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.1787 | + | 4.88368i | 1.32470 | + | 0.214370i | ||||
\(520\) | 3.46082 | + | 5.99432i | 0.151767 | + | 0.262868i | ||||
\(521\) | −35.5490 | −1.55743 | −0.778714 | − | 0.627379i | \(-0.784128\pi\) | ||||
−0.778714 | + | 0.627379i | \(0.784128\pi\) | |||||||
\(522\) | −30.5016 | − | 10.1374i | −1.33502 | − | 0.443700i | ||||
\(523\) | 26.7187 | 1.16833 | 0.584163 | − | 0.811636i | \(-0.301423\pi\) | ||||
0.584163 | + | 0.811636i | \(0.301423\pi\) | |||||||
\(524\) | −7.47991 | − | 12.9556i | −0.326761 | − | 0.565967i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2052 | + | 36.7284i | −0.924589 | + | 1.60143i | ||||
\(527\) | 0.113415 | − | 0.196440i | 0.00494043 | − | 0.00855708i | ||||
\(528\) | −18.7360 | − | 49.3027i | −0.815380 | − | 2.14563i | ||||
\(529\) | 10.6892 | + | 18.5143i | 0.464750 | + | 0.804970i | ||||
\(530\) | −50.5665 | −2.19647 | ||||||||
\(531\) | 32.0802 | + | 10.6620i | 1.39216 | + | 0.462692i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.88565 | − | 3.26604i | −0.0816766 | − | 0.141468i | ||||
\(534\) | 16.3589 | + | 2.64729i | 0.707919 | + | 0.114559i | ||||
\(535\) | −0.313440 | + | 0.542893i | −0.0135512 | + | 0.0234713i | ||||
\(536\) | 6.95990 | − | 12.0549i | 0.300622 | − | 0.520693i | ||||
\(537\) | −2.87689 | + | 3.52840i | −0.124147 | + | 0.152262i | ||||
\(538\) | 25.5282 | + | 44.2161i | 1.10060 | + | 1.90629i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.757146 | + | 17.8911i | 0.0325824 | + | 0.769910i | ||||
\(541\) | 37.5855 | 1.61593 | 0.807963 | − | 0.589233i | \(-0.200570\pi\) | ||||
0.807963 | + | 0.589233i | \(0.200570\pi\) | |||||||
\(542\) | 21.4026 | + | 37.0705i | 0.919322 | + | 1.59231i | ||||
\(543\) | 4.34954 | − | 5.33454i | 0.186657 | − | 0.228927i | ||||
\(544\) | 3.07866 | − | 5.33240i | 0.131997 | − | 0.228625i | ||||
\(545\) | 16.4350 | − | 28.4663i | 0.704000 | − | 1.21936i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.13381 | − | 15.8202i | −0.390533 | − | 0.676424i | 0.601986 | − | 0.798506i | \(-0.294376\pi\) |
−0.992520 | + | 0.122082i | \(0.961043\pi\) | |||||||
\(548\) | 6.03134 | 0.257646 | ||||||||
\(549\) | 26.9191 | − | 23.9130i | 1.14888 | − | 1.02058i | ||||
\(550\) | 77.1501 | 3.28969 | ||||||||
\(551\) | −6.84243 | − | 11.8514i | −0.291498 | − | 0.504889i | ||||
\(552\) | 1.37824 | + | 3.62677i | 0.0586619 | + | 0.154366i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.62172 | − | 2.80890i | 0.0689002 | − | 0.119339i | ||||
\(555\) | 7.72949 | + | 20.3397i | 0.328098 | + | 0.863373i | ||||
\(556\) | −0.430433 | − | 0.745532i | −0.0182544 | − | 0.0316176i | ||||
\(557\) | −3.89272 | −0.164940 | −0.0824698 | − | 0.996594i | \(-0.526281\pi\) | ||||
−0.0824698 | + | 0.996594i | \(0.526281\pi\) | |||||||
\(558\) | 0.196491 | + | 0.955914i | 0.00831813 | + | 0.0404671i | ||||
\(559\) | 4.26324 | 0.180316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.5378 | + | 2.02893i | 0.529346 | + | 0.0856617i | ||||
\(562\) | −10.4281 | + | 18.0620i | −0.439884 | + | 0.761901i | ||||
\(563\) | 1.66428 | − | 2.88261i | 0.0701409 | − | 0.121488i | −0.828822 | − | 0.559512i | \(-0.810988\pi\) |
0.898963 | + | 0.438025i | \(0.144322\pi\) | |||||||
\(564\) | −6.14363 | + | 7.53492i | −0.258694 | + | 0.317277i | ||||
\(565\) | −14.7875 | − | 25.6127i | −0.622115 | − | 1.07753i | ||||
\(566\) | −48.2965 | −2.03006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.4702 | −0.900870 | ||||||||
\(569\) | 18.3122 | + | 31.7177i | 0.767688 | + | 1.32967i | 0.938814 | + | 0.344425i | \(0.111926\pi\) |
−0.171126 | + | 0.985249i | \(0.554741\pi\) | |||||||
\(570\) | −14.6385 | + | 17.9535i | −0.613137 | + | 0.751989i | ||||
\(571\) | 11.2912 | − | 19.5569i | 0.472522 | − | 0.818432i | −0.526984 | − | 0.849875i | \(-0.676677\pi\) |
0.999506 | + | 0.0314435i | \(0.0100104\pi\) | |||||||
\(572\) | 3.34742 | − | 5.79789i | 0.139962 | − | 0.242422i | ||||
\(573\) | −31.1286 | − | 5.03740i | −1.30042 | − | 0.210441i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.34201 | −0.389589 | ||||||||
\(576\) | −0.706100 | − | 3.43512i | −0.0294208 | − | 0.143130i | ||||
\(577\) | −22.5449 | −0.938557 | −0.469279 | − | 0.883050i | \(-0.655486\pi\) | ||||
−0.469279 | + | 0.883050i | \(0.655486\pi\) | |||||||
\(578\) | −13.4248 | − | 23.2525i | −0.558399 | − | 0.967175i | ||||
\(579\) | 0.124524 | + | 0.327678i | 0.00517505 | + | 0.0136179i | ||||
\(580\) | 10.6923 | − | 18.5197i | 0.443975 | − | 0.768987i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.5135 | + | 46.0857i | 0.725957 | + | 1.91031i | ||||
\(583\) | −25.3927 | − | 43.9814i | −1.05166 | − | 1.82152i | ||||
\(584\) | 9.34913 | 0.386870 | ||||||||
\(585\) | 8.82511 | − | 7.83958i | 0.364873 | − | 0.324127i | ||||
\(586\) | 15.2343 | 0.629325 | ||||||||
\(587\) | 12.1198 | + | 20.9921i | 0.500237 | + | 0.866436i | 1.00000 | 0.000273884i | \(8.71801e-5\pi\) | |
−0.499763 | + | 0.866162i | \(0.666579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.207750 | + | 0.359834i | −0.00856020 | + | 0.0148267i | ||||
\(590\) | −34.1684 | + | 59.1814i | −1.40669 | + | 2.43646i | ||||
\(591\) | 1.78556 | − | 2.18992i | 0.0734482 | − | 0.0900813i | ||||
\(592\) | 8.94112 | + | 15.4865i | 0.367478 | + | 0.636490i | ||||
\(593\) | 45.7326 | 1.87801 | 0.939007 | − | 0.343898i | \(-0.111747\pi\) | ||||
0.939007 | + | 0.343898i | \(0.111747\pi\) | |||||||
\(594\) | −46.1252 | + | 29.2983i | −1.89254 | + | 1.20212i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.83343 | − | 4.90764i | −0.116062 | − | 0.201025i | ||||
\(597\) | 6.88687 | − | 8.44647i | 0.281861 | − | 0.345691i | ||||
\(598\) | −1.23155 | + | 2.13311i | −0.0503618 | + | 0.0872292i | ||||
\(599\) | 15.0834 | − | 26.1252i | 0.616290 | − | 1.06745i | −0.373866 | − | 0.927483i | \(-0.621968\pi\) |
0.990157 | − | 0.139963i | \(-0.0446985\pi\) | |||||||
\(600\) | 22.0656 | + | 3.57078i | 0.900825 | + | 0.145777i | ||||
\(601\) | −7.36933 | − | 12.7641i | −0.300601 | − | 0.520657i | 0.675671 | − | 0.737203i | \(-0.263854\pi\) |
−0.976272 | + | 0.216547i | \(0.930521\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.5275 | − | 7.48712i | −0.917391 | − | 0.304899i | ||||
\(604\) | −1.98830 | −0.0809027 | ||||||||
\(605\) | 45.8285 | + | 79.3772i | 1.86319 | + | 3.22714i | ||||
\(606\) | 13.7722 | + | 36.2407i | 0.559457 | + | 1.47218i | ||||
\(607\) | −3.03918 | + | 5.26401i | −0.123356 | + | 0.213660i | −0.921089 | − | 0.389351i | \(-0.872699\pi\) |
0.797733 | + | 0.603011i | \(0.206033\pi\) | |||||||
\(608\) | −5.63941 | + | 9.76774i | −0.228708 | + | 0.396134i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.3930 | + | 63.0345i | 1.47351 | + | 2.55219i | ||||
\(611\) | 6.40877 | 0.259271 | ||||||||
\(612\) | −3.36303 | − | 1.11772i | −0.135943 | − | 0.0451811i | ||||
\(613\) | 11.7734 | 0.475522 | 0.237761 | − | 0.971324i | \(-0.423587\pi\) | ||||
0.237761 | + | 0.971324i | \(0.423587\pi\) | |||||||
\(614\) | −0.911065 | − | 1.57801i | −0.0367676 | − | 0.0636833i | ||||
\(615\) | −20.2165 | − | 3.27154i | −0.815207 | − | 0.131921i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.0319 | + | 27.7680i | −0.645418 | + | 1.11790i | 0.338786 | + | 0.940863i | \(0.389984\pi\) |
−0.984205 | + | 0.177034i | \(0.943350\pi\) | |||||||
\(618\) | −5.10594 | + | 6.26224i | −0.205391 | + | 0.251904i | ||||
\(619\) | −6.27588 | − | 10.8701i | −0.252249 | − | 0.436908i | 0.711896 | − | 0.702285i | \(-0.247837\pi\) |
−0.964145 | + | 0.265377i | \(0.914504\pi\) | |||||||
\(620\) | −0.649282 | −0.0260758 | ||||||||
\(621\) | 5.58524 | − | 3.54769i | 0.224128 | − | 0.142364i | ||||
\(622\) | 5.30441 | 0.212688 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.13043 | − | 7.51873i | 0.245414 | − | 0.300990i | ||||
\(625\) | 3.92995 | − | 6.80687i | 0.157198 | − | 0.272275i | ||||
\(626\) | −24.3125 | + | 42.1104i | −0.971721 | + | 1.68307i | ||||
\(627\) | −22.9664 | − | 3.71655i | −0.917188 | − | 0.148425i | ||||
\(628\) | −1.49511 | − | 2.58961i | −0.0596614 | − | 0.103337i | ||||
\(629\) | −4.30619 | −0.171699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4642 | 1.33219 | 0.666095 | − | 0.745867i | \(-0.267964\pi\) | ||||
0.666095 | + | 0.745867i | \(0.267964\pi\) | |||||||
\(632\) | −8.10690 | − | 14.0416i | −0.322475 | − | 0.558543i | ||||
\(633\) | 10.0213 | + | 26.3706i | 0.398312 | + | 1.04814i | ||||
\(634\) | 11.0904 | − | 19.2092i | 0.440457 | − | 0.762894i | ||||
\(635\) | −17.4288 | + | 30.1875i | −0.691639 | + | 1.19795i | ||||
\(636\) | 5.03386 | + | 13.2463i | 0.199606 | + | 0.525251i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 65.2553 | 2.58348 | ||||||||
\(639\) | 7.37233 | + | 35.8659i | 0.291645 | + | 1.41883i | ||||
\(640\) | 43.0148 | 1.70031 | ||||||||
\(641\) | 9.49183 | + | 16.4403i | 0.374905 | + | 0.649354i | 0.990313 | − | 0.138855i | \(-0.0443421\pi\) |
−0.615408 | + | 0.788209i | \(0.711009\pi\) | |||||||
\(642\) | 0.526905 | + | 0.0852667i | 0.0207953 | + | 0.00336521i | ||||
\(643\) | −4.81347 | + | 8.33718i | −0.189825 | + | 0.328786i | −0.945192 | − | 0.326516i | \(-0.894125\pi\) |
0.755367 | + | 0.655302i | \(0.227459\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.6296 | − | 17.9426i | 0.576039 | − | 0.706490i | ||||
\(646\) | −2.29222 | − | 3.97025i | −0.0901864 | − | 0.156207i | ||||
\(647\) | 7.81214 | 0.307127 | 0.153564 | − | 0.988139i | \(-0.450925\pi\) | ||||
0.153564 | + | 0.988139i | \(0.450925\pi\) | |||||||
\(648\) | −14.5483 | + | 6.24473i | −0.571510 | + | 0.245316i | ||||
\(649\) | −68.6326 | −2.69406 | ||||||||
\(650\) | 7.09528 | + | 12.2894i | 0.278300 | + | 0.482029i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.64376 | − | 4.57912i | 0.103537 | − | 0.179332i | ||||
\(653\) | −15.8714 | + | 27.4901i | −0.621097 | + | 1.07577i | 0.368185 | + | 0.929753i | \(0.379979\pi\) |
−0.989282 | + | 0.146019i | \(0.953354\pi\) | |||||||
\(654\) | −27.6280 | − | 4.47092i | −1.08034 | − | 0.174827i | ||||
\(655\) | 26.7756 | + | 46.3767i | 1.04621 | + | 1.81209i | ||||
\(656\) | −16.8308 | −0.657132 | ||||||||
\(657\) | −3.21026 | − | 15.6177i | −0.125244 | − | 0.609303i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.10685 | + | 5.38122i | 0.121026 | + | 0.209623i | 0.920172 | − | 0.391513i | \(-0.128048\pi\) |
−0.799147 | + | 0.601136i | \(0.794715\pi\) | |||||||
\(660\) | −12.9146 | − | 33.9841i | −0.502700 | − | 1.32283i | ||||
\(661\) | 13.7631 | − | 23.8384i | 0.535324 | − | 0.927208i | −0.463824 | − | 0.885927i | \(-0.653523\pi\) |
0.999148 | − | 0.0412802i | \(-0.0131436\pi\) | |||||||
\(662\) | −18.6094 | + | 32.2325i | −0.723276 | + | 1.25275i | ||||
\(663\) | 0.829873 | + | 2.18376i | 0.0322296 | + | 0.0848103i | ||||
\(664\) | −1.09935 | − | 1.90413i | −0.0426630 | − | 0.0738945i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.8509 | − | 12.3041i | 0.536712 | − | 0.476775i | ||||
\(667\) | −7.90169 | −0.305955 | ||||||||
\(668\) | 8.14854 | + | 14.1137i | 0.315276 | + | 0.546075i | ||||
\(669\) | −34.1439 | − | 5.52536i | −1.32008 | − | 0.213623i | ||||
\(670\) | 23.9939 | − | 41.5586i | 0.926965 | − | 1.60555i | ||||
\(671\) | −36.5505 | + | 63.3073i | −1.41102 | + | 2.44395i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.10894 | − | 14.0451i | −0.312577 | − | 0.541399i | 0.666343 | − | 0.745646i | \(-0.267859\pi\) |
−0.978919 | + | 0.204247i | \(0.934526\pi\) | |||||||
\(674\) | 21.7670 | 0.838434 | ||||||||
\(675\) | −1.61181 | − | 38.0866i | −0.0620387 | − | 1.46595i | ||||
\(676\) | −11.5240 | −0.443230 | ||||||||
\(677\) | −10.2545 | − | 17.7613i | −0.394112 | − | 0.682623i | 0.598875 | − | 0.800842i | \(-0.295615\pi\) |
−0.992987 | + | 0.118220i | \(0.962281\pi\) | |||||||
\(678\) | −15.9130 | + | 19.5167i | −0.611135 | + | 0.749532i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.71932 | + | 6.44205i | −0.142629 | + | 0.247041i | ||||
\(681\) | −6.17725 | − | 0.999637i | −0.236713 | − | 0.0383062i | ||||
\(682\) | −0.990642 | − | 1.71584i | −0.0379337 | − | 0.0657030i | ||||
\(683\) | −0.112308 | −0.00429736 | −0.00214868 | − | 0.999998i | \(-0.500684\pi\) | ||||
−0.00214868 | + | 0.999998i | \(0.500684\pi\) | |||||||
\(684\) | 6.16031 | + | 2.04741i | 0.235545 | + | 0.0782846i | ||||
\(685\) | −21.5902 | −0.824918 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.43839 | + | 22.2052i | 0.321945 | + | 0.847179i | ||||
\(688\) | 9.51311 | − | 16.4772i | 0.362684 | − | 0.628187i | ||||
\(689\) | 4.67059 | − | 8.08970i | 0.177935 | − | 0.308193i | ||||
\(690\) | 4.75142 | + | 12.5031i | 0.180883 | + | 0.475985i | ||||
\(691\) | 9.43351 | + | 16.3393i | 0.358868 | + | 0.621577i | 0.987772 | − | 0.155906i | \(-0.0498296\pi\) |
−0.628904 | + | 0.777483i | \(0.716496\pi\) | |||||||
\(692\) | 17.3182 | 0.658340 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.9480 | −1.51640 | ||||||||
\(695\) | 1.54081 | + | 2.66876i | 0.0584461 | + | 0.101232i | ||||
\(696\) | 18.6636 | + | 3.02025i | 0.707443 | + | 0.114482i | ||||
\(697\) | 2.02650 | − | 3.51000i | 0.0767590 | − | 0.132951i | ||||
\(698\) | 14.2332 | − | 24.6527i | 0.538736 | − | 0.933118i | ||||
\(699\) | 27.6413 | − | 33.9010i | 1.04549 | − | 1.28225i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.16006 | −0.119354 | −0.0596770 | − | 0.998218i | \(-0.519007\pi\) | ||||
−0.0596770 | + | 0.998218i | \(0.519007\pi\) | |||||||
\(702\) | −8.90898 | − | 4.65289i | −0.336248 | − | 0.175612i | ||||
\(703\) | 7.88796 | 0.297500 | ||||||||
\(704\) | 3.55992 | + | 6.16596i | 0.134170 | + | 0.232388i | ||||
\(705\) | 21.9921 | − | 26.9725i | 0.828272 | − | 1.01584i | ||||
\(706\) | 21.1402 | − | 36.6159i | 0.795622 | − | 1.37806i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.9045 | + | 3.05923i | 0.710475 | + | 0.114973i | ||||
\(709\) | 10.7606 | + | 18.6378i | 0.404121 | + | 0.699959i | 0.994219 | − | 0.107373i | \(-0.0342440\pi\) |
−0.590097 | + | 0.807332i | \(0.700911\pi\) | |||||||
\(710\) | −74.0174 | −2.77782 | ||||||||
\(711\) | −20.6726 | + | 18.3640i | −0.775284 | + | 0.688705i | ||||
\(712\) | −9.74771 | −0.365311 | ||||||||
\(713\) | 0.119956 | + | 0.207769i | 0.00449237 | + | 0.00778102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.9826 | + | 20.7545i | −0.448125 | + | 0.776175i | ||||
\(716\) | −1.28949 | + | 2.23347i | −0.0481906 | + | 0.0834685i | ||||
\(717\) | −5.53133 | − | 14.5554i | −0.206571 | − | 0.543581i | ||||
\(718\) | 17.6785 | + | 30.6201i | 0.659757 | + | 1.14273i | ||||
\(719\) | 18.8302 | 0.702246 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(720\) | −10.6070 | − | 51.6021i | −0.395298 | − | 1.92310i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.2040 | − | 21.1379i | −0.454185 | − | 0.786671i | ||||
\(723\) | −15.8281 | − | 2.56139i | −0.588654 | − | 0.0952592i | ||||
\(724\) | 1.94957 | − | 3.37675i | 0.0724551 | − | 0.125496i | ||||
\(725\) | −22.7618 | + | 39.4247i | −0.845354 | + | 1.46420i | ||||
\(726\) | 49.3165 | − | 60.4847i | 1.83031 | − | 2.24480i | ||||
\(727\) | 19.5426 | + | 33.8489i | 0.724797 | + | 1.25538i | 0.959058 | + | 0.283211i | \(0.0913996\pi\) |
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.4273 | + | 22.1585i | 0.571381 | + | 0.820685i | ||||
\(730\) | 32.2306 | 1.19291 | ||||||||
\(731\) | 2.29084 | + | 3.96784i | 0.0847296 | + | 0.146756i | ||||
\(732\) | 12.8895 | − | 15.8085i | 0.476410 | − | 0.584298i | ||||
\(733\) | 9.29924 | − | 16.1068i | 0.343475 | − | 0.594917i | −0.641600 | − | 0.767039i | \(-0.721729\pi\) |
0.985076 | + | 0.172123i | \(0.0550625\pi\) | |||||||
\(734\) | −19.2119 | + | 33.2759i | −0.709123 | + | 1.22824i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.25621 | + | 5.63993i | 0.120026 | + | 0.207890i | ||||
\(737\) | 48.1954 | 1.77530 | ||||||||
\(738\) | 3.51090 | + | 17.0803i | 0.129238 | + | 0.628733i | ||||
\(739\) | 5.50136 | 0.202371 | 0.101185 | − | 0.994868i | \(-0.467736\pi\) | ||||
0.101185 | + | 0.994868i | \(0.467736\pi\) | |||||||
\(740\) | 6.16306 | + | 10.6747i | 0.226559 | + | 0.392411i | ||||
\(741\) | −1.52014 | − | 4.00016i | −0.0558436 | − | 0.146949i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2326 | − | 17.7234i | 0.375399 | − | 0.650210i | −0.614988 | − | 0.788537i | \(-0.710839\pi\) |
0.990387 | + | 0.138327i | \(0.0441725\pi\) | |||||||
\(744\) | −0.203917 | − | 0.536597i | −0.00747597 | − | 0.0196726i | ||||
\(745\) | 10.1427 | + | 17.5677i | 0.371601 | + | 0.643631i | ||||
\(746\) | 56.1785 | 2.05684 | ||||||||
\(747\) | −2.80334 | + | 2.49028i | −0.102569 | + | 0.0911147i | ||||
\(748\) | 7.19489 | 0.263071 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 24.2253 | + | 3.92027i | 0.884583 | + | 0.143148i | ||||
\(751\) | −19.0230 | + | 32.9488i | −0.694159 | + | 1.20232i | 0.276305 | + | 0.961070i | \(0.410890\pi\) |
−0.970463 | + | 0.241248i | \(0.922443\pi\) | |||||||
\(752\) | 14.3007 | − | 24.7696i | 0.521494 | − | 0.903254i | ||||
\(753\) | 22.6039 | − | 27.7227i | 0.823730 | − | 1.01027i | ||||
\(754\) | 6.00135 | + | 10.3946i | 0.218556 | + | 0.378551i | ||||
\(755\) | 7.11744 | 0.259030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.0780 | −1.85646 | −0.928230 | − | 0.372006i | \(-0.878670\pi\) | ||||
−0.928230 | + | 0.372006i | \(0.878670\pi\) | |||||||
\(758\) | 1.33329 | + | 2.30933i | 0.0484273 | + | 0.0838786i | ||||
\(759\) | −8.48887 | + | 10.4113i | −0.308126 | + | 0.377905i | ||||
\(760\) | 6.81295 | − | 11.8004i | 0.247132 | − | 0.428045i | ||||
\(761\) | −20.0375 | + | 34.7059i | −0.726357 | + | 1.25809i | 0.232055 | + | 0.972703i | \(0.425455\pi\) |
−0.958413 | + | 0.285385i | \(0.907878\pi\) | |||||||
\(762\) | 29.2985 | + | 4.74124i | 1.06137 | + | 0.171757i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.8633 | −0.646273 | ||||||||
\(765\) | 12.0385 | + | 4.00106i | 0.435254 | + | 0.144659i | ||||
\(766\) | 54.6116 | 1.97320 | ||||||||
\(767\) | −6.31195 | − | 10.9326i | −0.227911 | − | 0.394754i | ||||
\(768\) | −11.5720 | − | 30.4511i | −0.417568 | − | 1.09881i | ||||
\(769\) | −22.4828 | + | 38.9414i | −0.810751 | + | 1.40426i | 0.101587 | + | 0.994827i | \(0.467608\pi\) |
−0.912339 | + | 0.409436i | \(0.865726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.50485 | − | 3.95993i | −0.0541958 | − | 0.142613i | ||||
\(772\) | 0.0992886 | + | 0.171973i | 0.00357348 | + | 0.00618944i | ||||
\(773\) | 24.3561 | 0.876029 | 0.438014 | − | 0.898968i | \(-0.355682\pi\) | ||||
0.438014 | + | 0.898968i | \(0.355682\pi\) | |||||||
\(774\) | −18.7059 | − | 6.21698i | −0.672368 | − | 0.223465i | ||||
\(775\) | 1.38219 | 0.0496498 | ||||||||
\(776\) | −14.4998 | − | 25.1145i | −0.520514 | − | 0.901556i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.52913 | + | 7.84468i | −0.162377 | + | 0.281245i | ||||
\(779\) | −3.71208 | + | 6.42951i | −0.132999 | + | 0.230361i | ||||
\(780\) | 4.22567 | − | 5.18261i | 0.151303 | − | 0.185567i | ||||
\(781\) | −37.1689 | − | 64.3784i | −1.33001 | − | 2.30364i | ||||
\(782\) | −2.64707 | −0.0946592 | ||||||||
\(783\) | −1.36331 | − | 32.2145i | −0.0487207 | − | 1.15125i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.35200 | + | 9.26993i | 0.191021 | + | 0.330858i | ||||
\(786\) | 28.8135 | − | 35.3386i | 1.02774 | − | 1.26049i | ||||
\(787\) | 20.7617 | − | 35.9603i | 0.740073 | − | 1.28184i | −0.212388 | − | 0.977185i | \(-0.568124\pi\) |
0.952461 | − | 0.304659i | \(-0.0985426\pi\) | |||||||
\(788\) | 0.800331 | − | 1.38621i | 0.0285106 | − | 0.0493818i | ||||
\(789\) | −41.9976 | − | 6.79628i | −1.49515 | − | 0.241954i | ||||
\(790\) | −27.9481 | − | 48.4075i | −0.994349 | − | 1.72226i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 24.0300 | − | 21.3465i | 0.853869 | − | 0.758515i | ||||
\(793\) | −13.4458 | −0.477474 | ||||||||
\(794\) | −0.0238574 | − | 0.0413222i | −0.000846666 | − | 0.00146647i | ||||
\(795\) | −18.0195 | − | 47.4174i | −0.639087 | − | 1.68172i | ||||
\(796\) | 3.08686 | − | 5.34659i | 0.109411 | − | 0.189505i | ||||
\(797\) | 17.3018 | − | 29.9676i | 0.612861 | − | 1.06151i | −0.377895 | − | 0.925848i | \(-0.623352\pi\) |
0.990756 | − | 0.135657i | \(-0.0433146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.44373 | + | 5.96472i | 0.121831 | + | 0.211017i | ||||
\(800\) | 37.5198 | 1.32653 | ||||||||
\(801\) | 3.34712 | + | 16.2835i | 0.118265 | + | 0.575349i | ||||
\(802\) | −20.9571 | −0.740020 | ||||||||
\(803\) | 16.1851 | + | 28.0333i | 0.571158 | + | 0.989275i | ||||
\(804\) | −13.2752 | − | 2.14827i | −0.468180 | − | 0.0757635i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.182213 | − | 0.315603i | 0.00641819 | − | 0.0111166i | ||||
\(807\) | −32.3654 | + | 39.6949i | −1.13932 | + | 1.39733i | ||||
\(808\) | −11.4023 | − | 19.7494i | −0.401133 | − | 0.694782i | ||||
\(809\) | −11.2519 | −0.395597 | −0.197799 | − | 0.980243i | \(-0.563379\pi\) | ||||
−0.197799 | + | 0.980243i | \(0.563379\pi\) | |||||||
\(810\) | −50.1543 | + | 21.5284i | −1.76224 | + | 0.756430i | ||||
\(811\) | 29.6803 | 1.04222 | 0.521108 | − | 0.853491i | \(-0.325519\pi\) | ||||
0.521108 | + | 0.853491i | \(0.325519\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.1349 | + | 33.2799i | −0.951664 | + | 1.16718i | ||||
\(814\) | −18.8066 | + | 32.5740i | −0.659171 | + | 1.14172i | ||||
\(815\) | −9.46376 | + | 16.3917i | −0.331501 | + | 0.574177i | ||||
\(816\) | 10.2919 | + | 1.66550i | 0.360290 | + | 0.0583041i | ||||
\(817\) | −4.19629 | − | 7.26819i | −0.146810 | − | 0.254282i | ||||
\(818\) | 54.1211 | 1.89230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.6014 | −0.405137 | ||||||||
\(821\) | −17.3215 | − | 30.0018i | −0.604526 | − | 1.04707i | −0.992126 | − | 0.125242i | \(-0.960029\pi\) |
0.387600 | − | 0.921828i | \(-0.373304\pi\) | |||||||
\(822\) | 6.53029 | + | 17.1841i | 0.227770 | + | 0.599364i | ||||
\(823\) | −18.1935 | + | 31.5121i | −0.634186 | + | 1.09844i | 0.352501 | + | 0.935811i | \(0.385331\pi\) |
−0.986687 | + | 0.162631i | \(0.948002\pi\) | |||||||
\(824\) | 2.37638 | − | 4.11601i | 0.0827851 | − | 0.143388i | ||||
\(825\) | 27.4927 | + | 72.3454i | 0.957171 | + | 2.51874i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.3576 | −0.846997 | −0.423498 | − | 0.905897i | \(-0.639198\pi\) | ||||
−0.423498 | + | 0.905897i | \(0.639198\pi\) | |||||||
\(828\) | 2.80229 | − | 2.48935i | 0.0973863 | − | 0.0865108i | ||||
\(829\) | −39.1702 | −1.36044 | −0.680219 | − | 0.733009i | \(-0.738115\pi\) | ||||
−0.680219 | + | 0.733009i | \(0.738115\pi\) | |||||||
\(830\) | −3.78994 | − | 6.56438i | −0.131551 | − | 0.227853i | ||||
\(831\) | 3.21187 | + | 0.519763i | 0.111419 | + | 0.0180304i | ||||
\(832\) | −0.654792 | + | 1.13413i | −0.0227008 | + | 0.0393190i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.65808 | − | 2.03357i | 0.0574146 | − | 0.0704167i | ||||
\(835\) | −29.1690 | − | 50.5223i | −1.00944 | − | 1.74839i | ||||
\(836\) | −13.1794 | −0.455819 | ||||||||
\(837\) | −0.826362 | + | 0.524897i | −0.0285633 | + | 0.0181431i | ||||
\(838\) | −25.7030 | −0.887894 | ||||||||
\(839\) | 17.1739 | + | 29.7460i | 0.592907 | + | 1.02695i | 0.993839 | + | 0.110838i | \(0.0353534\pi\) |
−0.400931 | + | 0.916108i | \(0.631313\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.75250 | + | 8.23157i | −0.163879 | + | 0.283847i | ||||
\(842\) | 7.84250 | − | 13.5836i | 0.270270 | − | 0.468122i | ||||
\(843\) | −20.6533 | − | 3.34223i | −0.711336 | − | 0.115112i | ||||
\(844\) | 7.99045 | + | 13.8399i | 0.275043 | + | 0.476388i | ||||
\(845\) | 41.2520 | 1.41911 | ||||||||
\(846\) | −28.1199 | − | 9.34577i | −0.966781 | − | 0.321314i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.8442 | − | 36.1032i | −0.715793 | − | 1.23979i | ||||
\(849\) | −17.2106 | − | 45.2888i | −0.590667 | − | 1.55431i | ||||
\(850\) | −7.62525 | + | 13.2073i | −0.261544 | + | 0.453007i | ||||
\(851\) | 2.27727 | − | 3.94434i | 0.0780637 | − | 0.135210i | ||||
\(852\) | 7.36837 | + | 19.3895i | 0.252436 | + | 0.664272i | ||||
\(853\) | 16.3371 | + | 28.2967i | 0.559373 | + | 0.968862i | 0.997549 | + | 0.0699730i | \(0.0222913\pi\) |
−0.438176 | + | 0.898889i | \(0.644375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0518 | − | 7.32904i | −0.754157 | − | 0.250648i | ||||
\(856\) | −0.313965 | −0.0107311 | ||||||||
\(857\) | −28.8340 | − | 49.9419i | −0.984950 | − | 1.70598i | −0.642159 | − | 0.766571i | \(-0.721961\pi\) |
−0.342791 | − | 0.939412i | \(-0.611372\pi\) | |||||||
\(858\) | 20.1433 | + | 3.25970i | 0.687681 | + | 0.111284i | ||||
\(859\) | 14.9884 | − | 25.9607i | 0.511397 | − | 0.885766i | −0.488515 | − | 0.872555i | \(-0.662461\pi\) |
0.999913 | − | 0.0132108i | \(-0.00420525\pi\) | |||||||
\(860\) | 6.55733 | − | 11.3576i | 0.223603 | − | 0.387292i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.3615 | − | 24.8749i | −0.489156 | − | 0.847243i | ||||
\(863\) | −23.1776 | −0.788974 | −0.394487 | − | 0.918901i | \(-0.629078\pi\) | ||||
−0.394487 | + | 0.918901i | \(0.629078\pi\) | |||||||
\(864\) | −22.4317 | + | 14.2484i | −0.763143 | + | 0.484740i | ||||
\(865\) | −61.9934 | −2.10784 | ||||||||
\(866\) | −17.0437 | − | 29.5205i | −0.579167 | − | 1.00315i | ||||
\(867\) | 17.0204 | − | 20.8748i | 0.578043 | − | 0.708947i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.0690 | − | 48.6170i | 0.952177 | − | 1.64922i | ||||
\(870\) | 64.3418 | + | 10.4122i | 2.18139 | + | 0.353005i | ||||
\(871\) | 4.43240 | + | 7.67715i | 0.150186 | + | 0.260130i | ||||
\(872\) | 16.4626 | 0.557493 | ||||||||
\(873\) | −36.9747 | + | 32.8456i | −1.25140 | + | 1.11165i | ||||
\(874\) | 4.84884 | 0.164014 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.20853 | − | 8.44308i | −0.108406 | − | 0.285265i | ||||
\(877\) | 0.369978 | − | 0.640820i | 0.0124933 | − | 0.0216390i | −0.859711 | − | 0.510780i | \(-0.829357\pi\) |
0.872204 | + | 0.489141i | \(0.162690\pi\) | |||||||
\(878\) | 5.81448 | − | 10.0710i | 0.196229 | − | 0.339879i | ||||
\(879\) | 5.42880 | + | 14.2856i | 0.183109 | + | 0.481841i | ||||
\(880\) | 53.4768 | + | 92.6245i | 1.80270 | + | 3.12237i | ||||
\(881\) | 18.0285 | 0.607395 | 0.303697 | − | 0.952769i | \(-0.401779\pi\) | ||||
0.303697 | + | 0.952769i | \(0.401779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0928 | 1.45019 | 0.725095 | − | 0.688649i | \(-0.241796\pi\) | ||||
0.725095 | + | 0.688649i | \(0.241796\pi\) | |||||||
\(884\) | 0.661694 | + | 1.14609i | 0.0222552 | + | 0.0385471i | ||||
\(885\) | −67.6718 | − | 10.9510i | −2.27476 | − | 0.368115i | ||||
\(886\) | 24.7254 | − | 42.8256i | 0.830664 | − | 1.43875i | ||||
\(887\) | −15.4763 | + | 26.8058i | −0.519645 | + | 0.900051i | 0.480094 | + | 0.877217i | \(0.340602\pi\) |
−0.999739 | + | 0.0228344i | \(0.992731\pi\) | |||||||
\(888\) | −6.88650 | + | 8.44602i | −0.231096 | + | 0.283430i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −33.6047 | −1.12643 | ||||||||
\(891\) | −43.9105 | − | 32.8121i | −1.47106 | − | 1.09925i | ||||
\(892\) | −19.5937 | −0.656046 | ||||||||
\(893\) | −6.30813 | − | 10.9260i | −0.211094 | − | 0.365625i | ||||
\(894\) | 10.9147 | − | 13.3864i | 0.365042 | − | 0.447710i | ||||
\(895\) | 4.61595 | − | 7.99506i | 0.154294 | − | 0.267245i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.43913 | − | 0.394713i | −0.0814401 | − | 0.0131791i | ||||
\(898\) | −5.75714 | − | 9.97165i | −0.192118 | − | 0.332758i | ||||
\(899\) | 1.16909 | 0.0389913 | ||||||||
\(900\) | −4.34799 | − | 21.1526i | −0.144933 | − | 0.705088i | ||||
\(901\) | 10.0389 | 0.334444 | ||||||||
\(902\) | −17.7008 | − | 30.6587i | −0.589372 | − | 1.02082i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.40614 | − | 12.8278i | 0.246324 | − | 0.426646i | ||||
\(905\) | −6.97880 | + | 12.0876i | −0.231983 | + | 0.401807i | ||||
\(906\) | −2.15278 | − | 5.66492i | −0.0715214 | − | 0.188205i | ||||
\(907\) | 21.4042 | + | 37.0731i | 0.710714 | + | 1.23099i | 0.964590 | + | 0.263755i | \(0.0849611\pi\) |
−0.253876 | + | 0.967237i | \(0.581706\pi\) | |||||||
\(908\) | −3.54485 | −0.117640 | ||||||||
\(909\) | −29.0760 | + | 25.8290i | −0.964391 | + | 0.856694i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.04869 | + | 5.28049i | 0.101008 | + | 0.174950i | 0.912100 | − | 0.409968i | \(-0.134460\pi\) |
−0.811092 | + | 0.584918i | \(0.801127\pi\) | |||||||
\(912\) | −18.8525 | − | 3.05081i | −0.624268 | − | 0.101023i | ||||
\(913\) | 3.80635 | − | 6.59278i | 0.125972 | − | 0.218189i | ||||
\(914\) | −24.7400 | + | 42.8509i | −0.818327 | + | 1.41738i | ||||
\(915\) | −46.1401 | + | 56.5890i | −1.52535 | + | 1.87078i | ||||
\(916\) | 6.72830 | + | 11.6538i | 0.222309 | + | 0.385051i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.456710 | − | 10.7919i | −0.0150737 | − | 0.356186i | ||||
\(919\) | 24.8613 | 0.820100 | 0.410050 | − | 0.912063i | \(-0.365511\pi\) | ||||
0.410050 | + | 0.912063i | \(0.365511\pi\) | |||||||
\(920\) | −3.93382 | − | 6.81357i | −0.129694 | − | 0.224637i | ||||
\(921\) | 1.15508 | − | 1.41666i | 0.0380611 | − | 0.0466804i | ||||
\(922\) | −17.2811 | + | 29.9317i | −0.569121 | + | 0.985747i | ||||
\(923\) | 6.83664 | − | 11.8414i | 0.225031 | − | 0.389764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1199 | − | 22.7244i | −0.431381 | − | 0.747174i | ||||
\(926\) | −17.1207 | −0.562621 | ||||||||
\(927\) | −7.69176 | − | 2.55639i | −0.252631 | − | 0.0839630i | ||||
\(928\) | 31.7351 | 1.04176 | ||||||||
\(929\) | −20.9201 | − | 36.2347i | −0.686366 | − | 1.18882i | −0.973005 | − | 0.230783i | \(-0.925871\pi\) |
0.286639 | − | 0.958039i | \(-0.407462\pi\) | |||||||
\(930\) | −0.702994 | − | 1.84989i | −0.0230521 | − | 0.0606603i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.3895 | − | 21.4592i | 0.405831 | − | 0.702920i | ||||
\(933\) | 1.89024 | + | 4.97407i | 0.0618838 | + | 0.162844i | ||||
\(934\) | 13.8826 | + | 24.0453i | 0.454251 | + | 0.786786i | ||||
\(935\) | −25.7553 | −0.842288 | ||||||||
\(936\) | 5.61030 | + | 1.86461i | 0.183378 | + | 0.0609467i | ||||
\(937\) | 29.2537 | 0.955676 | 0.477838 | − | 0.878448i | \(-0.341421\pi\) | ||||
0.477838 | + | 0.878448i | \(0.341421\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.1517 | − | 7.79218i | −1.57137 | − | 0.254288i | ||||
\(940\) | 9.85740 | − | 17.0735i | 0.321513 | − | 0.556877i | ||||
\(941\) | −1.67869 | + | 2.90757i | −0.0547236 | + | 0.0947841i | −0.892090 | − | 0.451859i | \(-0.850761\pi\) |
0.837366 | + | 0.546643i | \(0.184094\pi\) | |||||||
\(942\) | 5.75934 | − | 7.06360i | 0.187649 | − | 0.230145i | ||||
\(943\) | 2.14337 | + | 3.71242i | 0.0697976 | + | 0.120893i | ||||
\(944\) | −56.3387 | −1.83367 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0194 | 1.30114 | ||||||||
\(947\) | −2.63300 | − | 4.56050i | −0.0855612 | − | 0.148196i | 0.820069 | − | 0.572265i | \(-0.193935\pi\) |
−0.905630 | + | 0.424068i | \(0.860602\pi\) | |||||||
\(948\) | −9.89854 | + | 12.1402i | −0.321490 | + | 0.394294i | ||||
\(949\) | −2.97699 | + | 5.15630i | −0.0966372 | + | 0.167381i | ||||
\(950\) | 13.9677 | − | 24.1928i | 0.453173 | − | 0.784918i | ||||
\(951\) | 21.9650 | + | 3.55450i | 0.712264 | + | 0.115263i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.2520 | 1.82218 | 0.911090 | − | 0.412208i | \(-0.135242\pi\) | ||||
0.911090 | + | 0.412208i | \(0.135242\pi\) | |||||||
\(954\) | −32.2902 | + | 28.6843i | −1.04544 | + | 0.928688i | ||||
\(955\) | 63.9448 | 2.06921 | ||||||||
\(956\) | −4.41038 | − | 7.63900i | −0.142642 | − | 0.247063i | ||||
\(957\) | 23.2539 | + | 61.1914i | 0.751693 | + | 1.97804i | ||||
\(958\) | −7.08131 | + | 12.2652i | −0.228787 | + | 0.396270i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.52624 | + | 6.64767i | 0.0815341 | + | 0.214553i | ||||
\(961\) | 15.4823 | + | 26.8160i | 0.499427 | + | 0.865034i | ||||
\(962\) | −6.91836 | −0.223057 | ||||||||
\(963\) | 0.107808 | + | 0.524476i | 0.00347405 | + | 0.0169010i | ||||
\(964\) | −9.08306 | −0.292546 | ||||||||
\(965\) | −0.355420 | − | 0.615606i | −0.0114414 | − | 0.0198171i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.88641 | + | 11.9276i | −0.221452 | + | 0.383566i | −0.955249 | − | 0.295803i | \(-0.904413\pi\) |
0.733797 | + | 0.679369i | \(0.237746\pi\) | |||||||
\(968\) | −22.9526 | + | 39.7551i | −0.737725 | + | 1.27778i | ||||
\(969\) | 2.90615 | − | 3.56428i | 0.0933591 | − | 0.114501i | ||||
\(970\) | −49.9874 | − | 86.5807i | −1.60500 | − | 2.77994i | ||||
\(971\) | −51.3254 | −1.64711 | −0.823555 | − | 0.567236i | \(-0.808013\pi\) | ||||
−0.823555 | + | 0.567236i | \(0.808013\pi\) | |||||||
\(972\) | 10.6324 | + | 10.9952i | 0.341033 | + | 0.352671i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.36269 | + | 4.09230i | 0.0757055 | + | 0.131126i | ||||
\(975\) | −8.99561 | + | 11.0328i | −0.288090 | + | 0.353331i | ||||
\(976\) | −30.0033 | + | 51.9673i | −0.960383 | + | 1.66343i | ||||
\(977\) | −8.84252 | + | 15.3157i | −0.282897 | + | 0.489992i | −0.972097 | − | 0.234579i | \(-0.924629\pi\) |
0.689200 | + | 0.724571i | \(0.257962\pi\) | |||||||
\(978\) | 15.9090 | + | 2.57448i | 0.508713 | + | 0.0823228i | ||||
\(979\) | −16.8751 | − | 29.2285i | −0.539329 | − | 0.934146i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.65284 | − | 27.5006i | −0.180481 | − | 0.878027i | ||||
\(982\) | 34.0309 | 1.08597 | ||||||||
\(983\) | 8.00207 | + | 13.8600i | 0.255226 | + | 0.442065i | 0.964957 | − | 0.262408i | \(-0.0845166\pi\) |
−0.709731 | + | 0.704473i | \(0.751183\pi\) | |||||||
\(984\) | −3.64359 | − | 9.58792i | −0.116154 | − | 0.305652i | ||||
\(985\) | −2.86492 | + | 4.96218i | −0.0912839 | + | 0.158108i | ||||
\(986\) | −6.44961 | + | 11.1711i | −0.205397 | + | 0.355759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.21207 | − | 2.09937i | −0.0385612 | − | 0.0667899i | ||||
\(989\) | −4.84590 | −0.154091 | ||||||||
\(990\) | 82.8422 | − | 73.5909i | 2.63290 | − | 2.33887i | ||||
\(991\) | −10.8664 | −0.345182 | −0.172591 | − | 0.984994i | \(-0.555214\pi\) | ||||
−0.172591 | + | 0.984994i | \(0.555214\pi\) | |||||||
\(992\) | −0.481771 | − | 0.834453i | −0.0152963 | − | 0.0264939i | ||||
\(993\) | −36.8567 | − | 5.96435i | −1.16961 | − | 0.189273i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.0499 | + | 19.1390i | −0.350306 | + | 0.606748i | ||||
\(996\) | −1.34231 | + | 1.64629i | −0.0425326 | + | 0.0521645i | ||||
\(997\) | −20.5187 | − | 35.5395i | −0.649835 | − | 1.12555i | −0.983162 | − | 0.182736i | \(-0.941505\pi\) |
0.333327 | − | 0.942811i | \(-0.391829\pi\) | |||||||
\(998\) | 57.1438 | 1.80886 | ||||||||
\(999\) | 16.4737 | + | 8.60370i | 0.521204 | + | 0.272209i |
(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 | 441.2.f.h.148.9 | ✓ | 24 | |
3.2 | odd | 2 | 1323.2.f.h.442.3 | 24 | |||
7.2 | even | 3 | 441.2.g.h.67.9 | 24 | |||
7.3 | odd | 6 | 441.2.h.h.373.3 | 24 | |||
7.4 | even | 3 | 441.2.h.h.373.4 | 24 | |||
7.5 | odd | 6 | 441.2.g.h.67.10 | 24 | |||
7.6 | odd | 2 | inner | 441.2.f.h.148.10 | yes | 24 | |
9.2 | odd | 6 | 1323.2.f.h.883.3 | 24 | |||
9.4 | even | 3 | 3969.2.a.bh.1.3 | 12 | |||
9.5 | odd | 6 | 3969.2.a.bi.1.10 | 12 | |||
9.7 | even | 3 | inner | 441.2.f.h.295.9 | yes | 24 | |
21.2 | odd | 6 | 1323.2.g.h.361.4 | 24 | |||
21.5 | even | 6 | 1323.2.g.h.361.3 | 24 | |||
21.11 | odd | 6 | 1323.2.h.h.226.10 | 24 | |||
21.17 | even | 6 | 1323.2.h.h.226.9 | 24 | |||
21.20 | even | 2 | 1323.2.f.h.442.4 | 24 | |||
63.2 | odd | 6 | 1323.2.h.h.802.10 | 24 | |||
63.11 | odd | 6 | 1323.2.g.h.667.4 | 24 | |||
63.13 | odd | 6 | 3969.2.a.bh.1.4 | 12 | |||
63.16 | even | 3 | 441.2.h.h.214.4 | 24 | |||
63.20 | even | 6 | 1323.2.f.h.883.4 | 24 | |||
63.25 | even | 3 | 441.2.g.h.79.9 | 24 | |||
63.34 | odd | 6 | inner | 441.2.f.h.295.10 | yes | 24 | |
63.38 | even | 6 | 1323.2.g.h.667.3 | 24 | |||
63.41 | even | 6 | 3969.2.a.bi.1.9 | 12 | |||
63.47 | even | 6 | 1323.2.h.h.802.9 | 24 | |||
63.52 | odd | 6 | 441.2.g.h.79.10 | 24 | |||
63.61 | odd | 6 | 441.2.h.h.214.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
441.2.f.h.148.10 | yes | 24 | 7.6 | odd | 2 | inner | |
441.2.f.h.295.9 | yes | 24 | 9.7 | even | 3 | inner | |
441.2.f.h.295.10 | yes | 24 | 63.34 | odd | 6 | inner | |
441.2.g.h.67.9 | 24 | 7.2 | even | 3 | |||
441.2.g.h.67.10 | 24 | 7.5 | odd | 6 | |||
441.2.g.h.79.9 | 24 | 63.25 | even | 3 | |||
441.2.g.h.79.10 | 24 | 63.52 | odd | 6 | |||
441.2.h.h.214.3 | 24 | 63.61 | odd | 6 | |||
441.2.h.h.214.4 | 24 | 63.16 | even | 3 | |||
441.2.h.h.373.3 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.373.4 | 24 | 7.4 | even | 3 | |||
1323.2.f.h.442.3 | 24 | 3.2 | odd | 2 | |||
1323.2.f.h.442.4 | 24 | 21.20 | even | 2 | |||
1323.2.f.h.883.3 | 24 | 9.2 | odd | 6 | |||
1323.2.f.h.883.4 | 24 | 63.20 | even | 6 | |||
1323.2.g.h.361.3 | 24 | 21.5 | even | 6 | |||
1323.2.g.h.361.4 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.667.3 | 24 | 63.38 | even | 6 | |||
1323.2.g.h.667.4 | 24 | 63.11 | odd | 6 | |||
1323.2.h.h.226.9 | 24 | 21.17 | even | 6 | |||
1323.2.h.h.226.10 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.802.9 | 24 | 63.47 | even | 6 | |||
1323.2.h.h.802.10 | 24 | 63.2 | odd | 6 | |||
3969.2.a.bh.1.3 | 12 | 9.4 | even | 3 | |||
3969.2.a.bh.1.4 | 12 | 63.13 | odd | 6 | |||
3969.2.a.bi.1.9 | 12 | 63.41 | even | 6 | |||
3969.2.a.bi.1.10 | 12 | 9.5 | odd | 6 |