Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(8,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.n (of order \(4\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.13 | ||
Character | \(\chi\) | \(=\) | 273.8 |
Dual form | 273.2.n.c.239.13 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0762157 | − | 0.0762157i | 0.0538927 | − | 0.0538927i | −0.679647 | − | 0.733539i | \(-0.737867\pi\) |
0.733539 | + | 0.679647i | \(0.237867\pi\) | |||||||
\(3\) | 1.58361 | + | 0.701549i | 0.914299 | + | 0.405040i | ||||
\(4\) | 1.98838i | 0.994191i | ||||||||
\(5\) | 2.41817 | − | 2.41817i | 1.08144 | − | 1.08144i | 0.0850646 | − | 0.996375i | \(-0.472890\pi\) |
0.996375 | − | 0.0850646i | \(-0.0271097\pi\) | |||||||
\(6\) | 0.174165 | − | 0.0672271i | 0.0711027 | − | 0.0274454i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0.303978 | + | 0.303978i | 0.107472 | + | 0.107472i | ||||
\(9\) | 2.01566 | + | 2.22196i | 0.671886 | + | 0.740655i | ||||
\(10\) | − | 0.368606i | − | 0.116563i | ||||||
\(11\) | −3.75644 | − | 3.75644i | −1.13261 | − | 1.13261i | −0.989742 | − | 0.142869i | \(-0.954367\pi\) |
−0.142869 | − | 0.989742i | \(-0.545633\pi\) | |||||||
\(12\) | −1.39495 | + | 3.14883i | −0.402687 | + | 0.908988i | ||||
\(13\) | −3.50109 | + | 0.861588i | −0.971029 | + | 0.238962i | ||||
\(14\) | − | 0.107785i | − | 0.0288068i | ||||||
\(15\) | 5.52592 | − | 2.13298i | 1.42679 | − | 0.550734i | ||||
\(16\) | −3.93043 | −0.982607 | ||||||||
\(17\) | 0.501131 | 0.121542 | 0.0607710 | − | 0.998152i | \(-0.480644\pi\) | ||||
0.0607710 | + | 0.998152i | \(0.480644\pi\) | |||||||
\(18\) | 0.322973 | + | 0.0157237i | 0.0761256 | + | 0.00370612i | ||||
\(19\) | 3.52276 | + | 3.52276i | 0.808176 | + | 0.808176i | 0.984358 | − | 0.176182i | \(-0.0563747\pi\) |
−0.176182 | + | 0.984358i | \(0.556375\pi\) | |||||||
\(20\) | 4.80825 | + | 4.80825i | 1.07516 | + | 1.07516i | ||||
\(21\) | 1.61585 | − | 0.623713i | 0.352608 | − | 0.136105i | ||||
\(22\) | −0.572600 | −0.122079 | ||||||||
\(23\) | −4.77125 | −0.994875 | −0.497438 | − | 0.867500i | \(-0.665726\pi\) | ||||
−0.497438 | + | 0.867500i | \(0.665726\pi\) | |||||||
\(24\) | 0.268128 | + | 0.694638i | 0.0547313 | + | 0.141792i | ||||
\(25\) | − | 6.69513i | − | 1.33903i | ||||||
\(26\) | −0.201172 | + | 0.332505i | −0.0394531 | + | 0.0652096i | ||||
\(27\) | 1.63320 | + | 4.93281i | 0.314310 | + | 0.949320i | ||||
\(28\) | 1.40600 | + | 1.40600i | 0.265709 | + | 0.265709i | ||||
\(29\) | 6.76629i | 1.25647i | 0.778024 | + | 0.628235i | \(0.216222\pi\) | ||||
−0.778024 | + | 0.628235i | \(0.783778\pi\) | |||||||
\(30\) | 0.258595 | − | 0.583729i | 0.0472128 | − | 0.106574i | ||||
\(31\) | −3.11290 | − | 3.11290i | −0.559094 | − | 0.559094i | 0.369956 | − | 0.929049i | \(-0.379373\pi\) |
−0.929049 | + | 0.369956i | \(0.879373\pi\) | |||||||
\(32\) | −0.907516 | + | 0.907516i | −0.160428 | + | 0.160428i | ||||
\(33\) | −3.31342 | − | 8.58408i | −0.576793 | − | 1.49430i | ||||
\(34\) | 0.0381941 | − | 0.0381941i | 0.00655023 | − | 0.00655023i | ||||
\(35\) | − | 3.41981i | − | 0.578054i | ||||||
\(36\) | −4.41811 | + | 4.00790i | −0.736352 | + | 0.667983i | ||||
\(37\) | 2.59939 | − | 2.59939i | 0.427337 | − | 0.427337i | −0.460384 | − | 0.887720i | \(-0.652288\pi\) |
0.887720 | + | 0.460384i | \(0.152288\pi\) | |||||||
\(38\) | 0.536979 | 0.0871095 | ||||||||
\(39\) | −6.14882 | − | 1.09177i | −0.984600 | − | 0.174823i | ||||
\(40\) | 1.47014 | 0.232450 | ||||||||
\(41\) | −1.35341 | + | 1.35341i | −0.211367 | + | 0.211367i | −0.804848 | − | 0.593481i | \(-0.797753\pi\) |
0.593481 | + | 0.804848i | \(0.297753\pi\) | |||||||
\(42\) | 0.0756167 | − | 0.170690i | 0.0116679 | − | 0.0263381i | ||||
\(43\) | − | 5.63601i | − | 0.859484i | −0.902952 | − | 0.429742i | \(-0.858605\pi\) | ||
0.902952 | − | 0.429742i | \(-0.141395\pi\) | |||||||
\(44\) | 7.46925 | − | 7.46925i | 1.12603 | − | 1.12603i | ||||
\(45\) | 10.2473 | + | 0.498883i | 1.52758 | + | 0.0743691i | ||||
\(46\) | −0.363645 | + | 0.363645i | −0.0536165 | + | 0.0536165i | ||||
\(47\) | 4.05418 | + | 4.05418i | 0.591364 | + | 0.591364i | 0.938000 | − | 0.346636i | \(-0.112676\pi\) |
−0.346636 | + | 0.938000i | \(0.612676\pi\) | |||||||
\(48\) | −6.22428 | − | 2.75739i | −0.898397 | − | 0.397995i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −0.510274 | − | 0.510274i | −0.0721636 | − | 0.0721636i | ||||
\(51\) | 0.793597 | + | 0.351568i | 0.111126 | + | 0.0492293i | ||||
\(52\) | −1.71317 | − | 6.96152i | −0.237574 | − | 0.965388i | ||||
\(53\) | 4.05654i | 0.557209i | 0.960406 | + | 0.278604i | \(0.0898718\pi\) | ||||
−0.960406 | + | 0.278604i | \(0.910128\pi\) | |||||||
\(54\) | 0.500434 | + | 0.251482i | 0.0681004 | + | 0.0342224i | ||||
\(55\) | −18.1675 | −2.44970 | ||||||||
\(56\) | 0.429889 | 0.0574463 | ||||||||
\(57\) | 3.10730 | + | 8.05007i | 0.411571 | + | 1.06626i | ||||
\(58\) | 0.515698 | + | 0.515698i | 0.0677145 | + | 0.0677145i | ||||
\(59\) | −9.92175 | − | 9.92175i | −1.29170 | − | 1.29170i | −0.933734 | − | 0.357967i | \(-0.883470\pi\) |
−0.357967 | − | 0.933734i | \(-0.616530\pi\) | |||||||
\(60\) | 4.24119 | + | 10.9876i | 0.547535 | + | 1.41850i | ||||
\(61\) | 0.198691 | 0.0254398 | 0.0127199 | − | 0.999919i | \(-0.495951\pi\) | ||||
0.0127199 | + | 0.999919i | \(0.495951\pi\) | |||||||
\(62\) | −0.474504 | −0.0602621 | ||||||||
\(63\) | 2.99645 | + | 0.145880i | 0.377517 | + | 0.0183792i | ||||
\(64\) | − | 7.72252i | − | 0.965315i | ||||||
\(65\) | −6.38278 | + | 10.5497i | −0.791687 | + | 1.30853i | ||||
\(66\) | −0.906777 | − | 0.401707i | −0.111617 | − | 0.0494467i | ||||
\(67\) | −2.62400 | − | 2.62400i | −0.320573 | − | 0.320573i | 0.528414 | − | 0.848987i | \(-0.322787\pi\) |
−0.848987 | + | 0.528414i | \(0.822787\pi\) | |||||||
\(68\) | 0.996440i | 0.120836i | ||||||||
\(69\) | −7.55582 | − | 3.34727i | −0.909614 | − | 0.402964i | ||||
\(70\) | −0.260644 | − | 0.260644i | −0.0311529 | − | 0.0311529i | ||||
\(71\) | 5.51972 | − | 5.51972i | 0.655071 | − | 0.655071i | −0.299139 | − | 0.954210i | \(-0.596699\pi\) |
0.954210 | + | 0.299139i | \(0.0966994\pi\) | |||||||
\(72\) | −0.0627123 | + | 1.28814i | −0.00739072 | + | 0.151809i | ||||
\(73\) | −5.30667 | + | 5.30667i | −0.621099 | + | 0.621099i | −0.945812 | − | 0.324713i | \(-0.894732\pi\) |
0.324713 | + | 0.945812i | \(0.394732\pi\) | |||||||
\(74\) | − | 0.396228i | − | 0.0460606i | ||||||
\(75\) | 4.69696 | − | 10.6025i | 0.542358 | − | 1.22427i | ||||
\(76\) | −7.00459 | + | 7.00459i | −0.803481 | + | 0.803481i | ||||
\(77\) | −5.31241 | −0.605406 | ||||||||
\(78\) | −0.551847 | + | 0.385427i | −0.0624844 | + | 0.0436411i | ||||
\(79\) | 13.0695 | 1.47043 | 0.735216 | − | 0.677833i | \(-0.237081\pi\) | ||||
0.735216 | + | 0.677833i | \(0.237081\pi\) | |||||||
\(80\) | −9.50446 | + | 9.50446i | −1.06263 | + | 1.06263i | ||||
\(81\) | −0.874246 | + | 8.95744i | −0.0971384 | + | 0.995271i | ||||
\(82\) | 0.206302i | 0.0227823i | ||||||||
\(83\) | −4.32106 | + | 4.32106i | −0.474298 | + | 0.474298i | −0.903302 | − | 0.429004i | \(-0.858864\pi\) |
0.429004 | + | 0.903302i | \(0.358864\pi\) | |||||||
\(84\) | 1.24018 | + | 3.21293i | 0.135315 | + | 0.350560i | ||||
\(85\) | 1.21182 | − | 1.21182i | 0.131440 | − | 0.131440i | ||||
\(86\) | −0.429553 | − | 0.429553i | −0.0463199 | − | 0.0463199i | ||||
\(87\) | −4.74689 | + | 10.7152i | −0.508920 | + | 1.14879i | ||||
\(88\) | − | 2.28375i | − | 0.243448i | ||||||
\(89\) | 1.57446 | + | 1.57446i | 0.166892 | + | 0.166892i | 0.785612 | − | 0.618720i | \(-0.212348\pi\) |
−0.618720 | + | 0.785612i | \(0.712348\pi\) | |||||||
\(90\) | 0.819029 | − | 0.742983i | 0.0863332 | − | 0.0783173i | ||||
\(91\) | −1.86641 | + | 3.08488i | −0.195653 | + | 0.323384i | ||||
\(92\) | − | 9.48708i | − | 0.989096i | ||||||
\(93\) | −2.74578 | − | 7.11349i | −0.284724 | − | 0.737634i | ||||
\(94\) | 0.617985 | 0.0637403 | ||||||||
\(95\) | 17.0373 | 1.74799 | ||||||||
\(96\) | −2.07382 | + | 0.800486i | −0.211658 | + | 0.0816993i | ||||
\(97\) | −4.63648 | − | 4.63648i | −0.470763 | − | 0.470763i | 0.431398 | − | 0.902162i | \(-0.358020\pi\) |
−0.902162 | + | 0.431398i | \(0.858020\pi\) | |||||||
\(98\) | −0.0762157 | − | 0.0762157i | −0.00769895 | − | 0.00769895i | ||||
\(99\) | 0.774976 | − | 15.9184i | 0.0778880 | − | 1.59986i | ||||
\(100\) | 13.3125 | 1.33125 | ||||||||
\(101\) | 15.4221 | 1.53456 | 0.767278 | − | 0.641314i | \(-0.221610\pi\) | ||||
0.767278 | + | 0.641314i | \(0.221610\pi\) | |||||||
\(102\) | 0.0872796 | − | 0.0336896i | 0.00864197 | − | 0.00333577i | ||||
\(103\) | − | 9.63304i | − | 0.949171i | −0.880209 | − | 0.474586i | \(-0.842598\pi\) | ||
0.880209 | − | 0.474586i | \(-0.157402\pi\) | |||||||
\(104\) | −1.32616 | − | 0.802351i | −0.130040 | − | 0.0786770i | ||||
\(105\) | 2.39917 | − | 5.41566i | 0.234135 | − | 0.528514i | ||||
\(106\) | 0.309172 | + | 0.309172i | 0.0300295 | + | 0.0300295i | ||||
\(107\) | − | 13.0585i | − | 1.26241i | −0.775617 | − | 0.631204i | \(-0.782561\pi\) | ||
0.775617 | − | 0.631204i | \(-0.217439\pi\) | |||||||
\(108\) | −9.80832 | + | 3.24744i | −0.943806 | + | 0.312485i | ||||
\(109\) | 10.6979 | + | 10.6979i | 1.02468 | + | 1.02468i | 0.999688 | + | 0.0249883i | \(0.00795486\pi\) |
0.0249883 | + | 0.999688i | \(0.492045\pi\) | |||||||
\(110\) | −1.38465 | + | 1.38465i | −0.132021 | + | 0.132021i | ||||
\(111\) | 5.94002 | − | 2.29282i | 0.563802 | − | 0.217625i | ||||
\(112\) | −2.77923 | + | 2.77923i | −0.262613 | + | 0.262613i | ||||
\(113\) | − | 6.43322i | − | 0.605186i | −0.953120 | − | 0.302593i | \(-0.902148\pi\) | ||
0.953120 | − | 0.302593i | \(-0.0978523\pi\) | |||||||
\(114\) | 0.850367 | + | 0.376717i | 0.0796441 | + | 0.0352828i | ||||
\(115\) | −11.5377 | + | 11.5377i | −1.07590 | + | 1.07590i | ||||
\(116\) | −13.4540 | −1.24917 | ||||||||
\(117\) | −8.97143 | − | 6.04264i | −0.829409 | − | 0.558642i | ||||
\(118\) | −1.51239 | −0.139226 | ||||||||
\(119\) | 0.354353 | − | 0.354353i | 0.0324835 | − | 0.0324835i | ||||
\(120\) | 2.32813 | + | 1.03138i | 0.212529 | + | 0.0941513i | ||||
\(121\) | 17.2218i | 1.56561i | ||||||||
\(122\) | 0.0151434 | − | 0.0151434i | 0.00137102 | − | 0.00137102i | ||||
\(123\) | −3.09276 | + | 1.19379i | −0.278865 | + | 0.107641i | ||||
\(124\) | 6.18964 | − | 6.18964i | 0.555846 | − | 0.555846i | ||||
\(125\) | −4.09911 | − | 4.09911i | −0.366635 | − | 0.366635i | ||||
\(126\) | 0.239495 | − | 0.217258i | 0.0213359 | − | 0.0193549i | ||||
\(127\) | 9.34163i | 0.828936i | 0.910064 | + | 0.414468i | \(0.136032\pi\) | ||||
−0.910064 | + | 0.414468i | \(0.863968\pi\) | |||||||
\(128\) | −2.40361 | − | 2.40361i | −0.212451 | − | 0.212451i | ||||
\(129\) | 3.95394 | − | 8.92526i | 0.348125 | − | 0.785825i | ||||
\(130\) | 0.317586 | + | 1.29052i | 0.0278542 | + | 0.113186i | ||||
\(131\) | 0.986069i | 0.0861533i | 0.999072 | + | 0.0430766i | \(0.0137160\pi\) | ||||
−0.999072 | + | 0.0430766i | \(0.986284\pi\) | |||||||
\(132\) | 17.0684 | − | 6.58835i | 1.48562 | − | 0.573442i | ||||
\(133\) | 4.98193 | 0.431988 | ||||||||
\(134\) | −0.399980 | −0.0345530 | ||||||||
\(135\) | 15.8778 | + | 7.97902i | 1.36654 | + | 0.686725i | ||||
\(136\) | 0.152333 | + | 0.152333i | 0.0130624 | + | 0.0130624i | ||||
\(137\) | 7.92834 | + | 7.92834i | 0.677363 | + | 0.677363i | 0.959403 | − | 0.282039i | \(-0.0910109\pi\) |
−0.282039 | + | 0.959403i | \(0.591011\pi\) | |||||||
\(138\) | −0.830987 | + | 0.320758i | −0.0707383 | + | 0.0273047i | ||||
\(139\) | 4.55442 | 0.386301 | 0.193150 | − | 0.981169i | \(-0.438129\pi\) | ||||
0.193150 | + | 0.981169i | \(0.438129\pi\) | |||||||
\(140\) | 6.79990 | 0.574696 | ||||||||
\(141\) | 3.57605 | + | 9.26447i | 0.301158 | + | 0.780209i | ||||
\(142\) | − | 0.841379i | − | 0.0706070i | ||||||
\(143\) | 16.3882 | + | 9.91516i | 1.37045 | + | 0.829147i | ||||
\(144\) | −7.92240 | − | 8.73327i | −0.660200 | − | 0.727773i | ||||
\(145\) | 16.3621 | + | 16.3621i | 1.35880 | + | 1.35880i | ||||
\(146\) | 0.808904i | 0.0669454i | ||||||||
\(147\) | 0.701549 | − | 1.58361i | 0.0578628 | − | 0.130614i | ||||
\(148\) | 5.16857 | + | 5.16857i | 0.424854 | + | 0.424854i | ||||
\(149\) | 7.78532 | − | 7.78532i | 0.637798 | − | 0.637798i | −0.312214 | − | 0.950012i | \(-0.601070\pi\) |
0.950012 | + | 0.312214i | \(0.101070\pi\) | |||||||
\(150\) | −0.450094 | − | 1.16606i | −0.0367500 | − | 0.0952083i | ||||
\(151\) | −3.48647 | + | 3.48647i | −0.283725 | + | 0.283725i | −0.834593 | − | 0.550868i | \(-0.814297\pi\) |
0.550868 | + | 0.834593i | \(0.314297\pi\) | |||||||
\(152\) | 2.14168i | 0.173713i | ||||||||
\(153\) | 1.01011 | + | 1.11349i | 0.0816624 | + | 0.0900207i | ||||
\(154\) | −0.404890 | + | 0.404890i | −0.0326269 | + | 0.0326269i | ||||
\(155\) | −15.0551 | −1.20925 | ||||||||
\(156\) | 2.17085 | − | 12.2262i | 0.173807 | − | 0.978881i | ||||
\(157\) | 3.46210 | 0.276306 | 0.138153 | − | 0.990411i | \(-0.455883\pi\) | ||||
0.138153 | + | 0.990411i | \(0.455883\pi\) | |||||||
\(158\) | 0.996100 | − | 0.996100i | 0.0792455 | − | 0.0792455i | ||||
\(159\) | −2.84586 | + | 6.42399i | −0.225691 | + | 0.509455i | ||||
\(160\) | 4.38906i | 0.346986i | ||||||||
\(161\) | −3.37379 | + | 3.37379i | −0.265892 | + | 0.265892i | ||||
\(162\) | 0.616066 | + | 0.749329i | 0.0484028 | + | 0.0588728i | ||||
\(163\) | 10.9583 | − | 10.9583i | 0.858318 | − | 0.858318i | −0.132822 | − | 0.991140i | \(-0.542404\pi\) |
0.991140 | + | 0.132822i | \(0.0424039\pi\) | |||||||
\(164\) | −2.69109 | − | 2.69109i | −0.210139 | − | 0.210139i | ||||
\(165\) | −28.7702 | − | 12.7454i | −2.23976 | − | 0.992226i | ||||
\(166\) | 0.658666i | 0.0511224i | ||||||||
\(167\) | 14.1220 | + | 14.1220i | 1.09280 | + | 1.09280i | 0.995229 | + | 0.0975680i | \(0.0311063\pi\) |
0.0975680 | + | 0.995229i | \(0.468894\pi\) | |||||||
\(168\) | 0.680778 | + | 0.301588i | 0.0525232 | + | 0.0232680i | ||||
\(169\) | 11.5153 | − | 6.03300i | 0.885795 | − | 0.464077i | ||||
\(170\) | − | 0.184720i | − | 0.0141674i | ||||||
\(171\) | −0.726765 | + | 14.9281i | −0.0555771 | + | 1.14158i | ||||
\(172\) | 11.2065 | 0.854491 | ||||||||
\(173\) | −18.6189 | −1.41557 | −0.707786 | − | 0.706427i | \(-0.750306\pi\) | ||||
−0.707786 | + | 0.706427i | \(0.750306\pi\) | |||||||
\(174\) | 0.454879 | + | 1.17845i | 0.0344843 | + | 0.0893383i | ||||
\(175\) | −4.73417 | − | 4.73417i | −0.357870 | − | 0.357870i | ||||
\(176\) | 14.7644 | + | 14.7644i | 1.11291 | + | 1.11291i | ||||
\(177\) | −8.75161 | − | 22.6728i | −0.657812 | − | 1.70419i | ||||
\(178\) | 0.239997 | 0.0179885 | ||||||||
\(179\) | −18.3518 | −1.37168 | −0.685841 | − | 0.727752i | \(-0.740565\pi\) | ||||
−0.685841 | + | 0.727752i | \(0.740565\pi\) | |||||||
\(180\) | −0.991970 | + | 20.3756i | −0.0739371 | + | 1.51870i | ||||
\(181\) | 7.60589i | 0.565342i | 0.959217 | + | 0.282671i | \(0.0912204\pi\) | ||||
−0.959217 | + | 0.282671i | \(0.908780\pi\) | |||||||
\(182\) | 0.0928666 | + | 0.377367i | 0.00688373 | + | 0.0279723i | ||||
\(183\) | 0.314649 | + | 0.139391i | 0.0232595 | + | 0.0103041i | ||||
\(184\) | −1.45035 | − | 1.45035i | −0.106922 | − | 0.106922i | ||||
\(185\) | − | 12.5715i | − | 0.924278i | ||||||
\(186\) | −0.751431 | − | 0.332888i | −0.0550976 | − | 0.0244085i | ||||
\(187\) | −1.88247 | − | 1.88247i | −0.137660 | − | 0.137660i | ||||
\(188\) | −8.06127 | + | 8.06127i | −0.587929 | + | 0.587929i | ||||
\(189\) | 4.64288 | + | 2.33318i | 0.337720 | + | 0.169714i | ||||
\(190\) | 1.29851 | − | 1.29851i | 0.0942037 | − | 0.0942037i | ||||
\(191\) | 9.11788i | 0.659746i | 0.944025 | + | 0.329873i | \(0.107006\pi\) | ||||
−0.944025 | + | 0.329873i | \(0.892994\pi\) | |||||||
\(192\) | 5.41773 | − | 12.2295i | 0.390991 | − | 0.882587i | ||||
\(193\) | 1.65201 | − | 1.65201i | 0.118914 | − | 0.118914i | −0.645145 | − | 0.764060i | \(-0.723203\pi\) |
0.764060 | + | 0.645145i | \(0.223203\pi\) | |||||||
\(194\) | −0.706745 | −0.0507414 | ||||||||
\(195\) | −17.5090 | + | 12.2288i | −1.25385 | + | 0.875725i | ||||
\(196\) | 1.98838 | 0.142027 | ||||||||
\(197\) | 5.88344 | − | 5.88344i | 0.419177 | − | 0.419177i | −0.465743 | − | 0.884920i | \(-0.654213\pi\) |
0.884920 | + | 0.465743i | \(0.154213\pi\) | |||||||
\(198\) | −1.15417 | − | 1.27230i | −0.0820230 | − | 0.0904182i | ||||
\(199\) | 9.84621i | 0.697980i | 0.937127 | + | 0.348990i | \(0.113475\pi\) | ||||
−0.937127 | + | 0.348990i | \(0.886525\pi\) | |||||||
\(200\) | 2.03517 | − | 2.03517i | 0.143908 | − | 0.143908i | ||||
\(201\) | −2.31454 | − | 5.99627i | −0.163255 | − | 0.422944i | ||||
\(202\) | 1.17541 | − | 1.17541i | 0.0827014 | − | 0.0827014i | ||||
\(203\) | 4.78449 | + | 4.78449i | 0.335806 | + | 0.335806i | ||||
\(204\) | −0.699051 | + | 1.57797i | −0.0489434 | + | 0.110480i | ||||
\(205\) | 6.54556i | 0.457161i | ||||||||
\(206\) | −0.734189 | − | 0.734189i | −0.0511534 | − | 0.0511534i | ||||
\(207\) | −9.61722 | − | 10.6016i | −0.668443 | − | 0.736859i | ||||
\(208\) | 13.7608 | − | 3.38641i | 0.954140 | − | 0.234805i | ||||
\(209\) | − | 26.4661i | − | 1.83070i | ||||||
\(210\) | −0.229904 | − | 0.595613i | −0.0158649 | − | 0.0411012i | ||||
\(211\) | −20.9352 | −1.44124 | −0.720620 | − | 0.693330i | \(-0.756143\pi\) | ||||
−0.720620 | + | 0.693330i | \(0.756143\pi\) | |||||||
\(212\) | −8.06595 | −0.553972 | ||||||||
\(213\) | 12.6135 | − | 4.86875i | 0.864260 | − | 0.333601i | ||||
\(214\) | −0.995260 | − | 0.995260i | −0.0680345 | − | 0.0680345i | ||||
\(215\) | −13.6289 | − | 13.6289i | −0.929480 | − | 0.929480i | ||||
\(216\) | −1.00301 | + | 1.99592i | −0.0682460 | + | 0.135805i | ||||
\(217\) | −4.40231 | −0.298848 | ||||||||
\(218\) | 1.63070 | 0.110445 | ||||||||
\(219\) | −12.1266 | + | 4.68082i | −0.819440 | + | 0.316301i | ||||
\(220\) | − | 36.1239i | − | 2.43547i | ||||||
\(221\) | −1.75451 | + | 0.431768i | −0.118021 | + | 0.0290439i | ||||
\(222\) | 0.277974 | − | 0.627472i | 0.0186564 | − | 0.0421132i | ||||
\(223\) | −18.2346 | − | 18.2346i | −1.22108 | − | 1.22108i | −0.967248 | − | 0.253835i | \(-0.918308\pi\) |
−0.253835 | − | 0.967248i | \(-0.581692\pi\) | |||||||
\(224\) | 1.28342i | 0.0857522i | ||||||||
\(225\) | 14.8763 | − | 13.4951i | 0.991755 | − | 0.899672i | ||||
\(226\) | −0.490312 | − | 0.490312i | −0.0326151 | − | 0.0326151i | ||||
\(227\) | −7.91163 | + | 7.91163i | −0.525113 | + | 0.525113i | −0.919111 | − | 0.393998i | \(-0.871092\pi\) |
0.393998 | + | 0.919111i | \(0.371092\pi\) | |||||||
\(228\) | −16.0066 | + | 6.17849i | −1.06006 | + | 0.409181i | ||||
\(229\) | −7.34584 | + | 7.34584i | −0.485427 | + | 0.485427i | −0.906860 | − | 0.421433i | \(-0.861527\pi\) |
0.421433 | + | 0.906860i | \(0.361527\pi\) | |||||||
\(230\) | 1.75871i | 0.115966i | ||||||||
\(231\) | −8.41281 | − | 3.72692i | −0.553522 | − | 0.245213i | ||||
\(232\) | −2.05680 | + | 2.05680i | −0.135036 | + | 0.135036i | ||||
\(233\) | 25.0497 | 1.64106 | 0.820531 | − | 0.571602i | \(-0.193678\pi\) | ||||
0.820531 | + | 0.571602i | \(0.193678\pi\) | |||||||
\(234\) | −1.14431 | + | 0.223220i | −0.0748058 | + | 0.0145923i | ||||
\(235\) | 19.6074 | 1.27905 | ||||||||
\(236\) | 19.7282 | − | 19.7282i | 1.28420 | − | 1.28420i | ||||
\(237\) | 20.6970 | + | 9.16888i | 1.34441 | + | 0.595583i | ||||
\(238\) | − | 0.0540146i | − | 0.00350124i | ||||||
\(239\) | −8.87266 | + | 8.87266i | −0.573924 | + | 0.573924i | −0.933223 | − | 0.359298i | \(-0.883016\pi\) |
0.359298 | + | 0.933223i | \(0.383016\pi\) | |||||||
\(240\) | −21.7192 | + | 8.38354i | −1.40197 | + | 0.541155i | ||||
\(241\) | −10.1362 | + | 10.1362i | −0.652931 | + | 0.652931i | −0.953698 | − | 0.300767i | \(-0.902758\pi\) |
0.300767 | + | 0.953698i | \(0.402758\pi\) | |||||||
\(242\) | 1.31257 | + | 1.31257i | 0.0843751 | + | 0.0843751i | ||||
\(243\) | −7.66855 | + | 13.5718i | −0.491938 | + | 0.870630i | ||||
\(244\) | 0.395073i | 0.0252920i | ||||||||
\(245\) | −2.41817 | − | 2.41817i | −0.154491 | − | 0.154491i | ||||
\(246\) | −0.144731 | + | 0.326703i | −0.00922772 | + | 0.0208298i | ||||
\(247\) | −15.3687 | − | 9.29834i | −0.977885 | − | 0.591639i | ||||
\(248\) | − | 1.89251i | − | 0.120174i | ||||||
\(249\) | −9.87432 | + | 3.81145i | −0.625760 | + | 0.241541i | ||||
\(250\) | −0.624833 | −0.0395179 | ||||||||
\(251\) | 20.3901 | 1.28701 | 0.643505 | − | 0.765441i | \(-0.277479\pi\) | ||||
0.643505 | + | 0.765441i | \(0.277479\pi\) | |||||||
\(252\) | −0.290066 | + | 5.95809i | −0.0182724 | + | 0.375324i | ||||
\(253\) | 17.9230 | + | 17.9230i | 1.12681 | + | 1.12681i | ||||
\(254\) | 0.711979 | + | 0.711979i | 0.0446736 | + | 0.0446736i | ||||
\(255\) | 2.76921 | − | 1.06890i | 0.173415 | − | 0.0669373i | ||||
\(256\) | 15.0787 | 0.942416 | ||||||||
\(257\) | −2.53131 | −0.157899 | −0.0789493 | − | 0.996879i | \(-0.525157\pi\) | ||||
−0.0789493 | + | 0.996879i | \(0.525157\pi\) | |||||||
\(258\) | −0.378893 | − | 0.981598i | −0.0235888 | − | 0.0611116i | ||||
\(259\) | − | 3.67609i | − | 0.228421i | ||||||
\(260\) | −20.9769 | − | 12.6914i | −1.30093 | − | 0.787088i | ||||
\(261\) | −15.0345 | + | 13.6385i | −0.930610 | + | 0.844204i | ||||
\(262\) | 0.0751540 | + | 0.0751540i | 0.00464303 | + | 0.00464303i | ||||
\(263\) | − | 13.0477i | − | 0.804558i | −0.915517 | − | 0.402279i | \(-0.868218\pi\) | ||
0.915517 | − | 0.402279i | \(-0.131782\pi\) | |||||||
\(264\) | 1.60216 | − | 3.61657i | 0.0986063 | − | 0.222585i | ||||
\(265\) | 9.80942 | + | 9.80942i | 0.602588 | + | 0.602588i | ||||
\(266\) | 0.379702 | − | 0.379702i | 0.0232810 | − | 0.0232810i | ||||
\(267\) | 1.38877 | + | 3.59789i | 0.0849914 | + | 0.220187i | ||||
\(268\) | 5.21752 | − | 5.21752i | 0.318711 | − | 0.318711i | ||||
\(269\) | 31.5128i | 1.92137i | 0.277637 | + | 0.960686i | \(0.410449\pi\) | ||||
−0.277637 | + | 0.960686i | \(0.589551\pi\) | |||||||
\(270\) | 1.81826 | − | 0.602009i | 0.110656 | − | 0.0366371i | ||||
\(271\) | −16.2599 | + | 16.2599i | −0.987720 | + | 0.987720i | −0.999926 | − | 0.0122053i | \(-0.996115\pi\) |
0.0122053 | + | 0.999926i | \(0.496115\pi\) | |||||||
\(272\) | −1.96966 | −0.119428 | ||||||||
\(273\) | −5.11987 | + | 3.57588i | −0.309869 | + | 0.216422i | ||||
\(274\) | 1.20853 | 0.0730098 | ||||||||
\(275\) | −25.1499 | + | 25.1499i | −1.51659 | + | 1.51659i | ||||
\(276\) | 6.65565 | − | 15.0239i | 0.400623 | − | 0.904330i | ||||
\(277\) | 1.90282i | 0.114329i | 0.998365 | + | 0.0571646i | \(0.0182060\pi\) | ||||
−0.998365 | + | 0.0571646i | \(0.981794\pi\) | |||||||
\(278\) | 0.347118 | − | 0.347118i | 0.0208188 | − | 0.0208188i | ||||
\(279\) | 0.642210 | − | 13.1913i | 0.0384481 | − | 0.789743i | ||||
\(280\) | 1.03955 | − | 1.03955i | 0.0621248 | − | 0.0621248i | ||||
\(281\) | 2.68945 | + | 2.68945i | 0.160439 | + | 0.160439i | 0.782761 | − | 0.622322i | \(-0.213811\pi\) |
−0.622322 | + | 0.782761i | \(0.713811\pi\) | |||||||
\(282\) | 0.978649 | + | 0.433547i | 0.0582777 | + | 0.0258174i | ||||
\(283\) | 13.8911i | 0.825738i | 0.910790 | + | 0.412869i | \(0.135473\pi\) | ||||
−0.910790 | + | 0.412869i | \(0.864527\pi\) | |||||||
\(284\) | 10.9753 | + | 10.9753i | 0.651265 | + | 0.651265i | ||||
\(285\) | 26.9804 | + | 11.9525i | 1.59818 | + | 0.708004i | ||||
\(286\) | 2.00473 | − | 0.493346i | 0.118542 | − | 0.0291721i | ||||
\(287\) | 1.91401i | 0.112980i | ||||||||
\(288\) | −3.84571 | − | 0.187226i | −0.226610 | − | 0.0110324i | ||||
\(289\) | −16.7489 | −0.985228 | ||||||||
\(290\) | 2.49409 | 0.146458 | ||||||||
\(291\) | −4.08967 | − | 10.5951i | −0.239741 | − | 0.621096i | ||||
\(292\) | −10.5517 | − | 10.5517i | −0.617491 | − | 0.617491i | ||||
\(293\) | −11.0121 | − | 11.0121i | −0.643335 | − | 0.643335i | 0.308039 | − | 0.951374i | \(-0.400327\pi\) |
−0.951374 | + | 0.308039i | \(0.900327\pi\) | |||||||
\(294\) | −0.0672271 | − | 0.174165i | −0.00392077 | − | 0.0101575i | ||||
\(295\) | −47.9850 | −2.79380 | ||||||||
\(296\) | 1.58031 | 0.0918537 | ||||||||
\(297\) | 12.3948 | − | 24.6649i | 0.719219 | − | 1.43120i | ||||
\(298\) | − | 1.18673i | − | 0.0687453i | ||||||
\(299\) | 16.7046 | − | 4.11086i | 0.966053 | − | 0.237737i | ||||
\(300\) | 21.0818 | + | 9.33935i | 1.21716 | + | 0.539208i | ||||
\(301\) | −3.98526 | − | 3.98526i | −0.229707 | − | 0.229707i | ||||
\(302\) | 0.531448i | 0.0305814i | ||||||||
\(303\) | 24.4226 | + | 10.8194i | 1.40304 | + | 0.621556i | ||||
\(304\) | −13.8459 | − | 13.8459i | −0.794119 | − | 0.794119i | ||||
\(305\) | 0.480469 | − | 0.480469i | 0.0275116 | − | 0.0275116i | ||||
\(306\) | 0.161852 | + | 0.00787965i | 0.00925246 | + | 0.000450450i | ||||
\(307\) | 10.7862 | − | 10.7862i | 0.615604 | − | 0.615604i | −0.328797 | − | 0.944401i | \(-0.606643\pi\) |
0.944401 | + | 0.328797i | \(0.106643\pi\) | |||||||
\(308\) | − | 10.5631i | − | 0.601889i | ||||||
\(309\) | 6.75805 | − | 15.2550i | 0.384452 | − | 0.867827i | ||||
\(310\) | −1.14743 | + | 1.14743i | −0.0651699 | + | 0.0651699i | ||||
\(311\) | −18.5793 | −1.05353 | −0.526767 | − | 0.850010i | \(-0.676596\pi\) | ||||
−0.526767 | + | 0.850010i | \(0.676596\pi\) | |||||||
\(312\) | −1.53723 | − | 2.20098i | −0.0870286 | − | 0.124606i | ||||
\(313\) | 15.0945 | 0.853193 | 0.426596 | − | 0.904442i | \(-0.359712\pi\) | ||||
0.426596 | + | 0.904442i | \(0.359712\pi\) | |||||||
\(314\) | 0.263866 | − | 0.263866i | 0.0148908 | − | 0.0148908i | ||||
\(315\) | 7.59870 | − | 6.89317i | 0.428138 | − | 0.388386i | ||||
\(316\) | 25.9871i | 1.46189i | ||||||||
\(317\) | 5.43020 | − | 5.43020i | 0.304991 | − | 0.304991i | −0.537972 | − | 0.842963i | \(-0.680809\pi\) |
0.842963 | + | 0.537972i | \(0.180809\pi\) | |||||||
\(318\) | 0.272710 | + | 0.706508i | 0.0152928 | + | 0.0396190i | ||||
\(319\) | 25.4172 | − | 25.4172i | 1.42309 | − | 1.42309i | ||||
\(320\) | −18.6744 | − | 18.6744i | −1.04393 | − | 1.04393i | ||||
\(321\) | 9.16114 | − | 20.6795i | 0.511325 | − | 1.15422i | ||||
\(322\) | 0.514271i | 0.0286592i | ||||||||
\(323\) | 1.76536 | + | 1.76536i | 0.0982274 | + | 0.0982274i | ||||
\(324\) | −17.8108 | − | 1.73833i | −0.989490 | − | 0.0965742i | ||||
\(325\) | 5.76844 | + | 23.4403i | 0.319976 | + | 1.30023i | ||||
\(326\) | − | 1.67038i | − | 0.0925141i | ||||||
\(327\) | 9.43626 | + | 24.4465i | 0.521826 | + | 1.35189i | ||||
\(328\) | −0.822812 | −0.0454322 | ||||||||
\(329\) | 5.73348 | 0.316097 | ||||||||
\(330\) | −3.16414 | + | 1.22135i | −0.174180 | + | 0.0672329i | ||||
\(331\) | −22.0803 | − | 22.0803i | −1.21364 | − | 1.21364i | −0.969819 | − | 0.243826i | \(-0.921597\pi\) |
−0.243826 | − | 0.969819i | \(-0.578403\pi\) | |||||||
\(332\) | −8.59192 | − | 8.59192i | −0.471543 | − | 0.471543i | ||||
\(333\) | 11.0152 | + | 0.536268i | 0.603630 | + | 0.0293873i | ||||
\(334\) | 2.15264 | 0.117787 | ||||||||
\(335\) | −12.6906 | −0.693360 | ||||||||
\(336\) | −6.35100 | + | 2.45146i | −0.346475 | + | 0.133738i | ||||
\(337\) | − | 7.71489i | − | 0.420257i | −0.977674 | − | 0.210128i | \(-0.932612\pi\) | ||
0.977674 | − | 0.210128i | \(-0.0673882\pi\) | |||||||
\(338\) | 0.417840 | − | 1.33746i | 0.0227275 | − | 0.0727482i | ||||
\(339\) | 4.51322 | − | 10.1877i | 0.245124 | − | 0.553321i | ||||
\(340\) | 2.40956 | + | 2.40956i | 0.130677 | + | 0.130677i | ||||
\(341\) | 23.3869i | 1.26647i | ||||||||
\(342\) | 1.08237 | + | 1.19315i | 0.0585277 | + | 0.0645181i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 1.71322 | − | 1.71322i | 0.0923707 | − | 0.0923707i | ||||
\(345\) | −26.3656 | + | 10.1770i | −1.41947 | + | 0.547911i | ||||
\(346\) | −1.41906 | + | 1.41906i | −0.0762889 | + | 0.0762889i | ||||
\(347\) | 4.79422i | 0.257367i | 0.991686 | + | 0.128684i | \(0.0410752\pi\) | ||||
−0.991686 | + | 0.128684i | \(0.958925\pi\) | |||||||
\(348\) | −21.3059 | − | 9.43863i | −1.14212 | − | 0.505963i | ||||
\(349\) | −8.06409 | + | 8.06409i | −0.431661 | + | 0.431661i | −0.889193 | − | 0.457532i | \(-0.848733\pi\) |
0.457532 | + | 0.889193i | \(0.348733\pi\) | |||||||
\(350\) | −0.721636 | −0.0385731 | ||||||||
\(351\) | −9.96806 | − | 15.8631i | −0.532056 | − | 0.846709i | ||||
\(352\) | 6.81806 | 0.363404 | ||||||||
\(353\) | 12.1942 | − | 12.1942i | 0.649030 | − | 0.649030i | −0.303728 | − | 0.952759i | \(-0.598231\pi\) |
0.952759 | + | 0.303728i | \(0.0982315\pi\) | |||||||
\(354\) | −2.39503 | − | 1.06101i | −0.127295 | − | 0.0563922i | ||||
\(355\) | − | 26.6953i | − | 1.41684i | ||||||
\(356\) | −3.13062 | + | 3.13062i | −0.165923 | + | 0.165923i | ||||
\(357\) | 0.809754 | − | 0.312562i | 0.0428567 | − | 0.0165425i | ||||
\(358\) | −1.39870 | + | 1.39870i | −0.0739235 | + | 0.0739235i | ||||
\(359\) | 23.9855 | + | 23.9855i | 1.26591 | + | 1.26591i | 0.948183 | + | 0.317726i | \(0.102919\pi\) |
0.317726 | + | 0.948183i | \(0.397081\pi\) | |||||||
\(360\) | 2.96330 | + | 3.26660i | 0.156180 | + | 0.172165i | ||||
\(361\) | 5.81963i | 0.306296i | ||||||||
\(362\) | 0.579689 | + | 0.579689i | 0.0304678 | + | 0.0304678i | ||||
\(363\) | −12.0819 | + | 27.2726i | −0.634135 | + | 1.43144i | ||||
\(364\) | −6.13393 | − | 3.71114i | −0.321505 | − | 0.194517i | ||||
\(365\) | 25.6649i | 1.34336i | ||||||||
\(366\) | 0.0346050 | − | 0.0133574i | 0.00180883 | − | 0.000698203i | ||||
\(367\) | −2.28417 | −0.119233 | −0.0596165 | − | 0.998221i | \(-0.518988\pi\) | ||||
−0.0596165 | + | 0.998221i | \(0.518988\pi\) | |||||||
\(368\) | 18.7531 | 0.977572 | ||||||||
\(369\) | −5.73524 | − | 0.279216i | −0.298564 | − | 0.0145354i | ||||
\(370\) | −0.958149 | − | 0.958149i | −0.0498118 | − | 0.0498118i | ||||
\(371\) | 2.86841 | + | 2.86841i | 0.148920 | + | 0.148920i | ||||
\(372\) | 14.1443 | − | 5.45966i | 0.733349 | − | 0.283070i | ||||
\(373\) | 11.8342 | 0.612749 | 0.306375 | − | 0.951911i | \(-0.400884\pi\) | ||||
0.306375 | + | 0.951911i | \(0.400884\pi\) | |||||||
\(374\) | −0.286948 | −0.0148377 | ||||||||
\(375\) | −3.61567 | − | 9.36712i | −0.186713 | − | 0.483716i | ||||
\(376\) | 2.46476i | 0.127110i | ||||||||
\(377\) | −5.82976 | − | 23.6894i | −0.300248 | − | 1.22007i | ||||
\(378\) | 0.531685 | − | 0.176036i | 0.0273469 | − | 0.00905429i | ||||
\(379\) | −19.4424 | − | 19.4424i | −0.998690 | − | 0.998690i | 0.00130884 | − | 0.999999i | \(-0.499583\pi\) |
−0.999999 | + | 0.00130884i | \(0.999583\pi\) | |||||||
\(380\) | 33.8766i | 1.73783i | ||||||||
\(381\) | −6.55361 | + | 14.7935i | −0.335752 | + | 0.757895i | ||||
\(382\) | 0.694926 | + | 0.694926i | 0.0355555 | + | 0.0355555i | ||||
\(383\) | −2.79878 | + | 2.79878i | −0.143011 | + | 0.143011i | −0.774988 | − | 0.631976i | \(-0.782244\pi\) |
0.631976 | + | 0.774988i | \(0.282244\pi\) | |||||||
\(384\) | −2.12014 | − | 5.49264i | −0.108193 | − | 0.280295i | ||||
\(385\) | −12.8463 | + | 12.8463i | −0.654710 | + | 0.654710i | ||||
\(386\) | − | 0.251819i | − | 0.0128172i | ||||||
\(387\) | 12.5230 | − | 11.3603i | 0.636581 | − | 0.577475i | ||||
\(388\) | 9.21909 | − | 9.21909i | 0.468029 | − | 0.468029i | ||||
\(389\) | 0.726856 | 0.0368530 | 0.0184265 | − | 0.999830i | \(-0.494134\pi\) | ||||
0.0184265 | + | 0.999830i | \(0.494134\pi\) | |||||||
\(390\) | −0.402432 | + | 2.26649i | −0.0203779 | + | 0.114768i | ||||
\(391\) | −2.39102 | −0.120919 | ||||||||
\(392\) | 0.303978 | − | 0.303978i | 0.0153532 | − | 0.0153532i | ||||
\(393\) | −0.691776 | + | 1.56155i | −0.0348955 | + | 0.0787699i | ||||
\(394\) | − | 0.896821i | − | 0.0451812i | ||||||
\(395\) | 31.6043 | − | 31.6043i | 1.59018 | − | 1.59018i | ||||
\(396\) | 31.6518 | + | 1.54095i | 1.59057 | + | 0.0774356i | ||||
\(397\) | 24.2351 | − | 24.2351i | 1.21632 | − | 1.21632i | 0.247413 | − | 0.968910i | \(-0.420420\pi\) |
0.968910 | − | 0.247413i | \(-0.0795805\pi\) | |||||||
\(398\) | 0.750436 | + | 0.750436i | 0.0376160 | + | 0.0376160i | ||||
\(399\) | 7.88945 | + | 3.49507i | 0.394966 | + | 0.174972i | ||||
\(400\) | 26.3147i | 1.31574i | ||||||||
\(401\) | −1.28813 | − | 1.28813i | −0.0643260 | − | 0.0643260i | 0.674212 | − | 0.738538i | \(-0.264483\pi\) |
−0.738538 | + | 0.674212i | \(0.764483\pi\) | |||||||
\(402\) | −0.633414 | − | 0.280606i | −0.0315918 | − | 0.0139953i | ||||
\(403\) | 13.5806 | + | 8.21653i | 0.676498 | + | 0.409294i | ||||
\(404\) | 30.6650i | 1.52564i | ||||||||
\(405\) | 19.5466 | + | 23.7747i | 0.971276 | + | 1.18138i | ||||
\(406\) | 0.729307 | 0.0361949 | ||||||||
\(407\) | −19.5289 | −0.968012 | ||||||||
\(408\) | 0.134367 | + | 0.348104i | 0.00665216 | + | 0.0172337i | ||||
\(409\) | 16.8469 | + | 16.8469i | 0.833026 | + | 0.833026i | 0.987930 | − | 0.154903i | \(-0.0495066\pi\) |
−0.154903 | + | 0.987930i | \(0.549507\pi\) | |||||||
\(410\) | 0.498874 | + | 0.498874i | 0.0246376 | + | 0.0246376i | ||||
\(411\) | 6.99330 | + | 18.1175i | 0.344954 | + | 0.893672i | ||||
\(412\) | 19.1542 | 0.943658 | ||||||||
\(413\) | −14.0315 | −0.690444 | ||||||||
\(414\) | −1.54099 | − | 0.0750220i | −0.0757355 | − | 0.00368713i | ||||
\(415\) | 20.8981i | 1.02585i | ||||||||
\(416\) | 2.39539 | − | 3.95920i | 0.117444 | − | 0.194116i | ||||
\(417\) | 7.21243 | + | 3.19515i | 0.353194 | + | 0.156467i | ||||
\(418\) | −2.01713 | − | 2.01713i | −0.0986611 | − | 0.0986611i | ||||
\(419\) | 11.4113i | 0.557480i | 0.960367 | + | 0.278740i | \(0.0899168\pi\) | ||||
−0.960367 | + | 0.278740i | \(0.910083\pi\) | |||||||
\(420\) | 10.7684 | + | 4.77046i | 0.525444 | + | 0.232775i | ||||
\(421\) | −4.62592 | − | 4.62592i | −0.225454 | − | 0.225454i | 0.585337 | − | 0.810790i | \(-0.300962\pi\) |
−0.810790 | + | 0.585337i | \(0.800962\pi\) | |||||||
\(422\) | −1.59559 | + | 1.59559i | −0.0776723 | + | 0.0776723i | ||||
\(423\) | −0.836402 | + | 17.1801i | −0.0406672 | + | 0.835325i | ||||
\(424\) | −1.23310 | + | 1.23310i | −0.0598845 | + | 0.0598845i | ||||
\(425\) | − | 3.35513i | − | 0.162748i | ||||||
\(426\) | 0.590269 | − | 1.33242i | 0.0285986 | − | 0.0645559i | ||||
\(427\) | 0.140496 | − | 0.140496i | 0.00679906 | − | 0.00679906i | ||||
\(428\) | 25.9652 | 1.25508 | ||||||||
\(429\) | 18.9966 | + | 27.1989i | 0.917162 | + | 1.31317i | ||||
\(430\) | −2.07747 | −0.100184 | ||||||||
\(431\) | 13.4869 | − | 13.4869i | 0.649642 | − | 0.649642i | −0.303264 | − | 0.952907i | \(-0.598076\pi\) |
0.952907 | + | 0.303264i | \(0.0980764\pi\) | |||||||
\(432\) | −6.41920 | − | 19.3881i | −0.308844 | − | 0.932809i | ||||
\(433\) | − | 15.1964i | − | 0.730291i | −0.930950 | − | 0.365145i | \(-0.881019\pi\) | ||
0.930950 | − | 0.365145i | \(-0.118981\pi\) | |||||||
\(434\) | −0.335525 | + | 0.335525i | −0.0161057 | + | 0.0161057i | ||||
\(435\) | 14.4324 | + | 37.3900i | 0.691980 | + | 1.79271i | ||||
\(436\) | −21.2716 | + | 21.2716i | −1.01872 | + | 1.01872i | ||||
\(437\) | −16.8080 | − | 16.8080i | −0.804034 | − | 0.804034i | ||||
\(438\) | −0.567486 | + | 1.28099i | −0.0271155 | + | 0.0612081i | ||||
\(439\) | 16.7674i | 0.800264i | 0.916458 | + | 0.400132i | \(0.131036\pi\) | ||||
−0.916458 | + | 0.400132i | \(0.868964\pi\) | |||||||
\(440\) | −5.52250 | − | 5.52250i | −0.263275 | − | 0.263275i | ||||
\(441\) | 2.22196 | − | 2.01566i | 0.105808 | − | 0.0959837i | ||||
\(442\) | −0.100813 | + | 0.166629i | −0.00479521 | + | 0.00792571i | ||||
\(443\) | − | 39.9481i | − | 1.89799i | −0.315290 | − | 0.948995i | \(-0.602102\pi\) | ||
0.315290 | − | 0.948995i | \(-0.397898\pi\) | |||||||
\(444\) | 4.55901 | + | 11.8110i | 0.216361 | + | 0.560527i | ||||
\(445\) | 7.61462 | 0.360967 | ||||||||
\(446\) | −2.77953 | −0.131615 | ||||||||
\(447\) | 17.7907 | − | 6.86715i | 0.841472 | − | 0.324805i | ||||
\(448\) | −5.46065 | − | 5.46065i | −0.257991 | − | 0.257991i | ||||
\(449\) | −14.9022 | − | 14.9022i | −0.703279 | − | 0.703279i | 0.261834 | − | 0.965113i | \(-0.415673\pi\) |
−0.965113 | + | 0.261834i | \(0.915673\pi\) | |||||||
\(450\) | 0.105272 | − | 2.16235i | 0.00496259 | − | 0.101934i | ||||
\(451\) | 10.1680 | 0.478793 | ||||||||
\(452\) | 12.7917 | 0.601671 | ||||||||
\(453\) | −7.96715 | + | 3.07529i | −0.374329 | + | 0.144490i | ||||
\(454\) | 1.20598i | 0.0565995i | ||||||||
\(455\) | 2.94647 | + | 11.9731i | 0.138133 | + | 0.561307i | ||||
\(456\) | −1.50249 | + | 3.39159i | −0.0703606 | + | 0.158826i | ||||
\(457\) | −11.6398 | − | 11.6398i | −0.544485 | − | 0.544485i | 0.380355 | − | 0.924841i | \(-0.375802\pi\) |
−0.924841 | + | 0.380355i | \(0.875802\pi\) | |||||||
\(458\) | 1.11974i | 0.0523219i | ||||||||
\(459\) | 0.818449 | + | 2.47198i | 0.0382019 | + | 0.115382i | ||||
\(460\) | −22.9414 | − | 22.9414i | −1.06965 | − | 1.06965i | ||||
\(461\) | −3.58435 | + | 3.58435i | −0.166940 | + | 0.166940i | −0.785633 | − | 0.618693i | \(-0.787663\pi\) |
0.618693 | + | 0.785633i | \(0.287663\pi\) | |||||||
\(462\) | −0.925238 | + | 0.357138i | −0.0430460 | + | 0.0166156i | ||||
\(463\) | 11.1773 | − | 11.1773i | 0.519453 | − | 0.519453i | −0.397953 | − | 0.917406i | \(-0.630279\pi\) |
0.917406 | + | 0.397953i | \(0.130279\pi\) | |||||||
\(464\) | − | 26.5944i | − | 1.23462i | ||||||
\(465\) | −23.8414 | − | 10.5619i | −1.10562 | − | 0.489795i | ||||
\(466\) | 1.90918 | − | 1.90918i | 0.0884412 | − | 0.0884412i | ||||
\(467\) | 8.54855 | 0.395580 | 0.197790 | − | 0.980244i | \(-0.436624\pi\) | ||||
0.197790 | + | 0.980244i | \(0.436624\pi\) | |||||||
\(468\) | 12.0151 | − | 17.8386i | 0.555397 | − | 0.824591i | ||||
\(469\) | −3.71090 | −0.171353 | ||||||||
\(470\) | 1.49440 | − | 1.49440i | 0.0689313 | − | 0.0689313i | ||||
\(471\) | 5.48263 | + | 2.42883i | 0.252626 | + | 0.111915i | ||||
\(472\) | − | 6.03198i | − | 0.277644i | ||||||
\(473\) | −21.1714 | + | 21.1714i | −0.973460 | + | 0.973460i | ||||
\(474\) | 2.27625 | − | 0.878624i | 0.104552 | − | 0.0403565i | ||||
\(475\) | 23.5853 | − | 23.5853i | 1.08217 | − | 1.08217i | ||||
\(476\) | 0.704589 | + | 0.704589i | 0.0322948 | + | 0.0322948i | ||||
\(477\) | −9.01348 | + | 8.17660i | −0.412699 | + | 0.374381i | ||||
\(478\) | 1.35247i | 0.0618606i | ||||||||
\(479\) | −8.43892 | − | 8.43892i | −0.385584 | − | 0.385584i | 0.487525 | − | 0.873109i | \(-0.337900\pi\) |
−0.873109 | + | 0.487525i | \(0.837900\pi\) | |||||||
\(480\) | −3.07914 | + | 6.95057i | −0.140543 | + | 0.317249i | ||||
\(481\) | −6.86110 | + | 11.3403i | −0.312839 | + | 0.517073i | ||||
\(482\) | 1.54508i | 0.0703764i | ||||||||
\(483\) | −7.70965 | + | 2.97589i | −0.350801 | + | 0.135408i | ||||
\(484\) | −34.2434 | −1.55652 | ||||||||
\(485\) | −22.4236 | −1.01820 | ||||||||
\(486\) | 0.449920 | + | 1.61885i | 0.0204088 | + | 0.0734324i | ||||
\(487\) | 19.8189 | + | 19.8189i | 0.898079 | + | 0.898079i | 0.995266 | − | 0.0971868i | \(-0.0309844\pi\) |
−0.0971868 | + | 0.995266i | \(0.530984\pi\) | |||||||
\(488\) | 0.0603975 | + | 0.0603975i | 0.00273407 | + | 0.00273407i | ||||
\(489\) | 25.0414 | − | 9.66589i | 1.13241 | − | 0.437107i | ||||
\(490\) | −0.368606 | −0.0166519 | ||||||||
\(491\) | 19.7592 | 0.891722 | 0.445861 | − | 0.895102i | \(-0.352898\pi\) | ||||
0.445861 | + | 0.895102i | \(0.352898\pi\) | |||||||
\(492\) | −2.37372 | − | 6.14959i | −0.107015 | − | 0.277245i | ||||
\(493\) | 3.39080i | 0.152714i | ||||||||
\(494\) | −1.88001 | + | 0.462655i | −0.0845859 | + | 0.0208158i | ||||
\(495\) | −36.6194 | − | 40.3675i | −1.64592 | − | 1.81438i | ||||
\(496\) | 12.2350 | + | 12.2350i | 0.549370 | + | 0.549370i | ||||
\(497\) | − | 7.80607i | − | 0.350150i | ||||||
\(498\) | −0.462086 | + | 1.04307i | −0.0207066 | + | 0.0467411i | ||||
\(499\) | 4.18799 | + | 4.18799i | 0.187480 | + | 0.187480i | 0.794606 | − | 0.607126i | \(-0.207678\pi\) |
−0.607126 | + | 0.794606i | \(0.707678\pi\) | |||||||
\(500\) | 8.15059 | − | 8.15059i | 0.364506 | − | 0.364506i | ||||
\(501\) | 12.4565 | + | 32.2712i | 0.556517 | + | 1.44177i | ||||
\(502\) | 1.55405 | − | 1.55405i | 0.0693605 | − | 0.0693605i | ||||
\(503\) | − | 5.88524i | − | 0.262410i | −0.991355 | − | 0.131205i | \(-0.958115\pi\) | ||
0.991355 | − | 0.131205i | \(-0.0418846\pi\) | |||||||
\(504\) | 0.866509 | + | 0.955198i | 0.0385974 | + | 0.0425479i | ||||
\(505\) | 37.2933 | − | 37.2933i | 1.65953 | − | 1.65953i | ||||
\(506\) | 2.73202 | 0.121453 | ||||||||
\(507\) | 22.4683 | − | 1.47537i | 0.997851 | − | 0.0655236i | ||||
\(508\) | −18.5747 | −0.824121 | ||||||||
\(509\) | 25.8430 | − | 25.8430i | 1.14547 | − | 1.14547i | 0.158038 | − | 0.987433i | \(-0.449483\pi\) |
0.987433 | − | 0.158038i | \(-0.0505170\pi\) | |||||||
\(510\) | 0.129590 | − | 0.292524i | 0.00573834 | − | 0.0129532i | ||||
\(511\) | 7.50477i | 0.331991i | ||||||||
\(512\) | 5.95645 | − | 5.95645i | 0.263240 | − | 0.263240i | ||||
\(513\) | −11.6237 | + | 23.1305i | −0.513200 | + | 1.02124i | ||||
\(514\) | −0.192926 | + | 0.192926i | −0.00850958 | + | 0.00850958i | ||||
\(515\) | −23.2944 | − | 23.2944i | −1.02647 | − | 1.02647i | ||||
\(516\) | 17.7468 | + | 7.86194i | 0.781261 | + | 0.346103i | ||||
\(517\) | − | 30.4586i | − | 1.33957i | ||||||
\(518\) | −0.280176 | − | 0.280176i | −0.0123102 | − | 0.0123102i | ||||
\(519\) | −29.4852 | − | 13.0621i | −1.29426 | − | 0.573363i | ||||
\(520\) | −5.14710 | + | 1.26666i | −0.225715 | + | 0.0555465i | ||||
\(521\) | 37.6849i | 1.65100i | 0.564399 | + | 0.825502i | \(0.309108\pi\) | ||||
−0.564399 | + | 0.825502i | \(0.690892\pi\) | |||||||
\(522\) | −0.106391 | + | 2.18533i | −0.00465663 | + | 0.0956494i | ||||
\(523\) | −5.99895 | −0.262316 | −0.131158 | − | 0.991361i | \(-0.541870\pi\) | ||||
−0.131158 | + | 0.991361i | \(0.541870\pi\) | |||||||
\(524\) | −1.96068 | −0.0856528 | ||||||||
\(525\) | −4.17584 | − | 10.8183i | −0.182249 | − | 0.472151i | ||||
\(526\) | −0.994443 | − | 0.994443i | −0.0433598 | − | 0.0433598i | ||||
\(527\) | −1.55997 | − | 1.55997i | −0.0679534 | − | 0.0679534i | ||||
\(528\) | 13.0232 | + | 33.7391i | 0.566761 | + | 1.46831i | ||||
\(529\) | −0.235131 | −0.0102231 | ||||||||
\(530\) | 1.49526 | 0.0649501 | ||||||||
\(531\) | 2.04691 | − | 42.0446i | 0.0888285 | − | 1.82458i | ||||
\(532\) | 9.90598i | 0.429479i | ||||||||
\(533\) | 3.57233 | − | 5.90450i | 0.154735 | − | 0.255752i | ||||
\(534\) | 0.380062 | + | 0.168369i | 0.0164469 | + | 0.00728606i | ||||
\(535\) | −31.5776 | − | 31.5776i | −1.36522 | − | 1.36522i | ||||
\(536\) | − | 1.59527i | − | 0.0689054i | ||||||
\(537\) | −29.0622 | − | 12.8747i | −1.25413 | − | 0.555585i | ||||
\(538\) | 2.40177 | + | 2.40177i | 0.103548 | + | 0.103548i | ||||
\(539\) | −3.75644 | + | 3.75644i | −0.161802 | + | 0.161802i | ||||
\(540\) | −15.8653 | + | 31.5711i | −0.682736 | + | 1.35860i | ||||
\(541\) | −7.87500 | + | 7.87500i | −0.338573 | + | 0.338573i | −0.855830 | − | 0.517257i | \(-0.826953\pi\) |
0.517257 | + | 0.855830i | \(0.326953\pi\) | |||||||
\(542\) | 2.47852i | 0.106462i | ||||||||
\(543\) | −5.33591 | + | 12.0448i | −0.228986 | + | 0.516891i | ||||
\(544\) | −0.454784 | + | 0.454784i | −0.0194987 | + | 0.0194987i | ||||
\(545\) | 51.7389 | 2.21625 | ||||||||
\(546\) | −0.117677 | + | 0.662753i | −0.00503609 | + | 0.0283632i | ||||
\(547\) | −43.8530 | −1.87502 | −0.937510 | − | 0.347959i | \(-0.886875\pi\) | ||||
−0.937510 | + | 0.347959i | \(0.886875\pi\) | |||||||
\(548\) | −15.7646 | + | 15.7646i | −0.673429 | + | 0.673429i | ||||
\(549\) | 0.400493 | + | 0.441484i | 0.0170926 | + | 0.0188421i | ||||
\(550\) | 3.83363i | 0.163467i | ||||||||
\(551\) | −23.8360 | + | 23.8360i | −1.01545 | + | 1.01545i | ||||
\(552\) | −1.27930 | − | 3.31429i | −0.0544508 | − | 0.141066i | ||||
\(553\) | 9.24152 | − | 9.24152i | 0.392989 | − | 0.392989i | ||||
\(554\) | 0.145025 | + | 0.145025i | 0.00616151 | + | 0.00616151i | ||||
\(555\) | 8.81955 | − | 19.9084i | 0.374369 | − | 0.845066i | ||||
\(556\) | 9.05592i | 0.384057i | ||||||||
\(557\) | −22.1841 | − | 22.1841i | −0.939971 | − | 0.939971i | 0.0583261 | − | 0.998298i | \(-0.481424\pi\) |
−0.998298 | + | 0.0583261i | \(0.981424\pi\) | |||||||
\(558\) | −0.956439 | − | 1.05433i | −0.0404893 | − | 0.0446334i | ||||
\(559\) | 4.85592 | + | 19.7322i | 0.205384 | + | 0.834584i | ||||
\(560\) | 13.4413i | 0.568000i | ||||||||
\(561\) | −1.66046 | − | 4.30175i | −0.0701046 | − | 0.181620i | ||||
\(562\) | 0.409957 | 0.0172930 | ||||||||
\(563\) | −21.3528 | −0.899912 | −0.449956 | − | 0.893051i | \(-0.648560\pi\) | ||||
−0.449956 | + | 0.893051i | \(0.648560\pi\) | |||||||
\(564\) | −18.4213 | + | 7.11055i | −0.775677 | + | 0.299408i | ||||
\(565\) | −15.5566 | − | 15.5566i | −0.654473 | − | 0.654473i | ||||
\(566\) | 1.05872 | + | 1.05872i | 0.0445012 | + | 0.0445012i | ||||
\(567\) | 5.71568 | + | 6.95205i | 0.240036 | + | 0.291959i | ||||
\(568\) | 3.35574 | 0.140804 | ||||||||
\(569\) | 0.257521 | 0.0107959 | 0.00539793 | − | 0.999985i | \(-0.498282\pi\) | ||||
0.00539793 | + | 0.999985i | \(0.498282\pi\) | |||||||
\(570\) | 2.96730 | − | 1.14537i | 0.124287 | − | 0.0479741i | ||||
\(571\) | − | 19.1071i | − | 0.799608i | −0.916601 | − | 0.399804i | \(-0.869078\pi\) | ||
0.916601 | − | 0.399804i | \(-0.130922\pi\) | |||||||
\(572\) | −19.7151 | + | 32.5860i | −0.824331 | + | 1.36249i | ||||
\(573\) | −6.39664 | + | 14.4392i | −0.267223 | + | 0.603205i | ||||
\(574\) | 0.145878 | + | 0.145878i | 0.00608882 | + | 0.00608882i | ||||
\(575\) | 31.9441i | 1.33216i | ||||||||
\(576\) | 17.1592 | − | 15.5660i | 0.714965 | − | 0.648582i | ||||
\(577\) | −1.97056 | − | 1.97056i | −0.0820354 | − | 0.0820354i | 0.664898 | − | 0.746934i | \(-0.268475\pi\) |
−0.746934 | + | 0.664898i | \(0.768475\pi\) | |||||||
\(578\) | −1.27653 | + | 1.27653i | −0.0530965 | + | 0.0530965i | ||||
\(579\) | 3.77511 | − | 1.45718i | 0.156888 | − | 0.0605583i | ||||
\(580\) | −32.5341 | + | 32.5341i | −1.35090 | + | 1.35090i | ||||
\(581\) | 6.11090i | 0.253523i | ||||||||
\(582\) | −1.11921 | − | 0.495817i | −0.0463928 | − | 0.0205523i | ||||
\(583\) | 15.2382 | − | 15.2382i | 0.631100 | − | 0.631100i | ||||
\(584\) | −3.22622 | −0.133502 | ||||||||
\(585\) | −36.3066 | + | 7.08232i | −1.50109 | + | 0.292818i | ||||
\(586\) | −1.67859 | −0.0693421 | ||||||||
\(587\) | −13.5995 | + | 13.5995i | −0.561312 | + | 0.561312i | −0.929680 | − | 0.368368i | \(-0.879917\pi\) |
0.368368 | + | 0.929680i | \(0.379917\pi\) | |||||||
\(588\) | 3.14883 | + | 1.39495i | 0.129855 | + | 0.0575267i | ||||
\(589\) | − | 21.9320i | − | 0.903692i | ||||||
\(590\) | −3.65721 | + | 3.65721i | −0.150565 | + | 0.150565i | ||||
\(591\) | 13.4446 | − | 5.18956i | 0.553037 | − | 0.213470i | ||||
\(592\) | −10.2167 | + | 10.2167i | −0.419904 | + | 0.419904i | ||||
\(593\) | 7.34318 | + | 7.34318i | 0.301548 | + | 0.301548i | 0.841619 | − | 0.540071i | \(-0.181603\pi\) |
−0.540071 | + | 0.841619i | \(0.681603\pi\) | |||||||
\(594\) | −0.935174 | − | 2.82453i | −0.0383706 | − | 0.115892i | ||||
\(595\) | − | 1.71377i | − | 0.0702579i | ||||||
\(596\) | 15.4802 | + | 15.4802i | 0.634094 | + | 0.634094i | ||||
\(597\) | −6.90760 | + | 15.5926i | −0.282709 | + | 0.638162i | ||||
\(598\) | 0.959843 | − | 1.58647i | 0.0392509 | − | 0.0648754i | ||||
\(599\) | − | 6.49210i | − | 0.265260i | −0.991166 | − | 0.132630i | \(-0.957658\pi\) | ||
0.991166 | − | 0.132630i | \(-0.0423422\pi\) | |||||||
\(600\) | 4.65069 | − | 1.79515i | 0.189863 | − | 0.0732866i | ||||
\(601\) | 18.1602 | 0.740770 | 0.370385 | − | 0.928878i | \(-0.379226\pi\) | ||||
0.370385 | + | 0.928878i | \(0.379226\pi\) | |||||||
\(602\) | −0.607479 | −0.0247590 | ||||||||
\(603\) | 0.541347 | − | 11.1195i | 0.0220453 | − | 0.452822i | ||||
\(604\) | −6.93244 | − | 6.93244i | −0.282077 | − | 0.282077i | ||||
\(605\) | 41.6452 | + | 41.6452i | 1.69312 | + | 1.69312i | ||||
\(606\) | 2.68600 | − | 1.03678i | 0.109111 | − | 0.0421165i | ||||
\(607\) | −5.36955 | −0.217943 | −0.108972 | − | 0.994045i | \(-0.534756\pi\) | ||||
−0.108972 | + | 0.994045i | \(0.534756\pi\) | |||||||
\(608\) | −6.39391 | −0.259307 | ||||||||
\(609\) | 4.22023 | + | 10.9333i | 0.171012 | + | 0.443041i | ||||
\(610\) | − | 0.0732386i | − | 0.00296534i | ||||||
\(611\) | −17.6871 | − | 10.7010i | −0.715544 | − | 0.432918i | ||||
\(612\) | −2.21405 | + | 2.00848i | −0.0894978 | + | 0.0811881i | ||||
\(613\) | −33.3385 | − | 33.3385i | −1.34653 | − | 1.34653i | −0.889398 | − | 0.457133i | \(-0.848876\pi\) |
−0.457133 | − | 0.889398i | \(-0.651124\pi\) | |||||||
\(614\) | − | 1.64416i | − | 0.0663530i | ||||||
\(615\) | −4.59203 | + | 10.3656i | −0.185168 | + | 0.417982i | ||||
\(616\) | −1.61485 | − | 1.61485i | −0.0650643 | − | 0.0650643i | ||||
\(617\) | 24.3339 | − | 24.3339i | 0.979648 | − | 0.979648i | −0.0201491 | − | 0.999797i | \(-0.506414\pi\) |
0.999797 | + | 0.0201491i | \(0.00641408\pi\) | |||||||
\(618\) | −0.647602 | − | 1.67774i | −0.0260504 | − | 0.0674886i | ||||
\(619\) | −1.81623 | + | 1.81623i | −0.0730002 | + | 0.0730002i | −0.742664 | − | 0.669664i | \(-0.766438\pi\) |
0.669664 | + | 0.742664i | \(0.266438\pi\) | |||||||
\(620\) | − | 29.9353i | − | 1.20223i | ||||||
\(621\) | −7.79244 | − | 23.5357i | −0.312700 | − | 0.944455i | ||||
\(622\) | −1.41603 | + | 1.41603i | −0.0567777 | + | 0.0567777i | ||||
\(623\) | 2.22662 | 0.0892075 | ||||||||
\(624\) | 24.1675 | + | 4.29111i | 0.967475 | + | 0.171782i | ||||
\(625\) | 13.6509 | 0.546037 | ||||||||
\(626\) | 1.15044 | − | 1.15044i | 0.0459808 | − | 0.0459808i | ||||
\(627\) | 18.5673 | − | 41.9120i | 0.741505 | − | 1.67380i | ||||
\(628\) | 6.88398i | 0.274701i | ||||||||
\(629\) | 1.30263 | − | 1.30263i | 0.0519394 | − | 0.0519394i | ||||
\(630\) | 0.0537723 | − | 1.10451i | 0.00214234 | − | 0.0440047i | ||||
\(631\) | −11.6645 | + | 11.6645i | −0.464356 | + | 0.464356i | −0.900080 | − | 0.435725i | \(-0.856492\pi\) |
0.435725 | + | 0.900080i | \(0.356492\pi\) | |||||||
\(632\) | 3.97283 | + | 3.97283i | 0.158031 | + | 0.158031i | ||||
\(633\) | −33.1533 | − | 14.6871i | −1.31772 | − | 0.583759i | ||||
\(634\) | − | 0.827734i | − | 0.0328735i | ||||||
\(635\) | 22.5897 | + | 22.5897i | 0.896444 | + | 0.896444i | ||||
\(636\) | −12.7733 | − | 5.65866i | −0.506496 | − | 0.224380i | ||||
\(637\) | 0.861588 | + | 3.50109i | 0.0341374 | + | 0.138718i | ||||
\(638\) | − | 3.87438i | − | 0.153388i | ||||||
\(639\) | 23.3905 | + | 1.13875i | 0.925314 | + | 0.0450483i | ||||
\(640\) | −11.6247 | −0.459506 | ||||||||
\(641\) | −32.9439 | −1.30121 | −0.650603 | − | 0.759418i | \(-0.725484\pi\) | ||||
−0.650603 | + | 0.759418i | \(0.725484\pi\) | |||||||
\(642\) | −0.877882 | − | 2.27433i | −0.0346473 | − | 0.0897606i | ||||
\(643\) | −10.4149 | − | 10.4149i | −0.410724 | − | 0.410724i | 0.471267 | − | 0.881991i | \(-0.343797\pi\) |
−0.881991 | + | 0.471267i | \(0.843797\pi\) | |||||||
\(644\) | −6.70838 | − | 6.70838i | −0.264347 | − | 0.264347i | ||||
\(645\) | −12.0215 | − | 31.1441i | −0.473347 | − | 1.22630i | ||||
\(646\) | 0.269097 | 0.0105875 | ||||||||
\(647\) | −6.47112 | −0.254406 | −0.127203 | − | 0.991877i | \(-0.540600\pi\) | ||||
−0.127203 | + | 0.991877i | \(0.540600\pi\) | |||||||
\(648\) | −2.98861 | + | 2.45711i | −0.117404 | + | 0.0965243i | ||||
\(649\) | 74.5410i | 2.92599i | ||||||||
\(650\) | 2.22616 | + | 1.34687i | 0.0873173 | + | 0.0528286i | ||||
\(651\) | −6.97155 | − | 3.08844i | −0.273237 | − | 0.121045i | ||||
\(652\) | 21.7892 | + | 21.7892i | 0.853332 | + | 0.853332i | ||||
\(653\) | − | 21.2554i | − | 0.831789i | −0.909413 | − | 0.415894i | \(-0.863469\pi\) | ||
0.909413 | − | 0.415894i | \(-0.136531\pi\) | |||||||
\(654\) | 2.58240 | + | 1.14402i | 0.100980 | + | 0.0447346i | ||||
\(655\) | 2.38449 | + | 2.38449i | 0.0931696 | + | 0.0931696i | ||||
\(656\) | 5.31948 | − | 5.31948i | 0.207691 | − | 0.207691i | ||||
\(657\) | −22.4877 | − | 1.09480i | −0.877328 | − | 0.0427121i | ||||
\(658\) | 0.436982 | − | 0.436982i | 0.0170353 | − | 0.0170353i | ||||
\(659\) | 7.13030i | 0.277757i | 0.990309 | + | 0.138878i | \(0.0443497\pi\) | ||||
−0.990309 | + | 0.138878i | \(0.955650\pi\) | |||||||
\(660\) | 25.3427 | − | 57.2062i | 0.986462 | − | 2.22675i | ||||
\(661\) | 2.74264 | − | 2.74264i | 0.106676 | − | 0.106676i | −0.651754 | − | 0.758430i | \(-0.725967\pi\) |
0.758430 | + | 0.651754i | \(0.225967\pi\) | |||||||
\(662\) | −3.36574 | −0.130813 | ||||||||
\(663\) | −3.08137 | − | 0.547118i | −0.119670 | − | 0.0212483i | ||||
\(664\) | −2.62701 | −0.101948 | ||||||||
\(665\) | 12.0472 | − | 12.0472i | 0.467169 | − | 0.467169i | ||||
\(666\) | 0.880405 | − | 0.798661i | 0.0341150 | − | 0.0309475i | ||||
\(667\) | − | 32.2837i | − | 1.25003i | ||||||
\(668\) | −28.0800 | + | 28.0800i | −1.08645 | + | 1.08645i | ||||
\(669\) | −16.0841 | − | 41.6691i | −0.621848 | − | 1.61102i | ||||
\(670\) | −0.967222 | + | 0.967222i | −0.0373670 | + | 0.0373670i | ||||
\(671\) | −0.746371 | − | 0.746371i | −0.0288133 | − | 0.0288133i | ||||
\(672\) | −0.900383 | + | 2.03244i | −0.0347330 | + | 0.0784031i | ||||
\(673\) | 27.9879i | 1.07885i | 0.842033 | + | 0.539427i | \(0.181359\pi\) | ||||
−0.842033 | + | 0.539427i | \(0.818641\pi\) | |||||||
\(674\) | −0.587996 | − | 0.587996i | −0.0226488 | − | 0.0226488i | ||||
\(675\) | 33.0258 | − | 10.9345i | 1.27116 | − | 0.420870i | ||||
\(676\) | 11.9959 | + | 22.8969i | 0.461382 | + | 0.880649i | ||||
\(677\) | − | 0.255809i | − | 0.00983153i | −0.999988 | − | 0.00491576i | \(-0.998435\pi\) | ||
0.999988 | − | 0.00491576i | \(-0.00156474\pi\) | |||||||
\(678\) | −0.432487 | − | 1.12044i | −0.0166096 | − | 0.0430304i | ||||
\(679\) | −6.55697 | −0.251633 | ||||||||
\(680\) | 0.736733 | 0.0282524 | ||||||||
\(681\) | −18.0793 | + | 6.97856i | −0.692802 | + | 0.267419i | ||||
\(682\) | 1.78245 | + | 1.78245i | 0.0682535 | + | 0.0682535i | ||||
\(683\) | 2.86120 | + | 2.86120i | 0.109481 | + | 0.109481i | 0.759725 | − | 0.650244i | \(-0.225334\pi\) |
−0.650244 | + | 0.759725i | \(0.725334\pi\) | |||||||
\(684\) | −29.6828 | − | 1.44509i | −1.13495 | − | 0.0552543i | ||||
\(685\) | 38.3442 | 1.46506 | ||||||||
\(686\) | −0.107785 | −0.00411526 | ||||||||
\(687\) | −16.7864 | + | 6.47950i | −0.640442 | + | 0.247208i | ||||
\(688\) | 22.1519i | 0.844535i | ||||||||
\(689\) | −3.49507 | − | 14.2023i | −0.133151 | − | 0.541066i | ||||
\(690\) | −1.23382 | + | 2.78512i | −0.0469708 | + | 0.106028i | ||||
\(691\) | 10.8229 | + | 10.8229i | 0.411723 | + | 0.411723i | 0.882338 | − | 0.470616i | \(-0.155968\pi\) |
−0.470616 | + | 0.882338i | \(0.655968\pi\) | |||||||
\(692\) | − | 37.0216i | − | 1.40735i | ||||||
\(693\) | −10.7080 | − | 11.8040i | −0.406764 | − | 0.448397i | ||||
\(694\) | 0.365395 | + | 0.365395i | 0.0138702 | + | 0.0138702i | ||||
\(695\) | 11.0134 | − | 11.0134i | 0.417761 | − | 0.417761i | ||||
\(696\) | −4.70012 | + | 1.81423i | −0.178158 | + | 0.0687682i | ||||
\(697\) | −0.678235 | + | 0.678235i | −0.0256900 | + | 0.0256900i | ||||
\(698\) | 1.22922i | 0.0465267i | ||||||||
\(699\) | 39.6691 | + | 17.5736i | 1.50042 | + | 0.664695i | ||||
\(700\) | 9.41334 | − | 9.41334i | 0.355791 | − | 0.355791i | ||||
\(701\) | −25.3131 | −0.956063 | −0.478031 | − | 0.878343i | \(-0.658650\pi\) | ||||
−0.478031 | + | 0.878343i | \(0.658650\pi\) | |||||||
\(702\) | −1.96874 | − | 0.449295i | −0.0743053 | − | 0.0169575i | ||||
\(703\) | 18.3140 | 0.690726 | ||||||||
\(704\) | −29.0092 | + | 29.0092i | −1.09333 | + | 1.09333i | ||||
\(705\) | 31.0506 | + | 13.7556i | 1.16943 | + | 0.518065i | ||||
\(706\) | − | 1.85878i | − | 0.0699560i | ||||||
\(707\) | 10.9051 | − | 10.9051i | 0.410128 | − | 0.410128i | ||||
\(708\) | 45.0822 | − | 17.4016i | 1.69429 | − | 0.653990i | ||||
\(709\) | 15.2862 | − | 15.2862i | 0.574087 | − | 0.574087i | −0.359181 | − | 0.933268i | \(-0.616944\pi\) |
0.933268 | + | 0.359181i | \(0.116944\pi\) | |||||||
\(710\) | −2.03460 | − | 2.03460i | −0.0763572 | − | 0.0763572i | ||||
\(711\) | 26.3436 | + | 29.0399i | 0.987963 | + | 1.08908i | ||||
\(712\) | 0.957198i | 0.0358725i | ||||||||
\(713\) | 14.8525 | + | 14.8525i | 0.556229 | + | 0.556229i | ||||
\(714\) | 0.0378939 | − | 0.0855381i | 0.00141814 | − | 0.00320118i | ||||
\(715\) | 63.6060 | − | 15.6529i | 2.37873 | − | 0.585384i | ||||
\(716\) | − | 36.4905i | − | 1.36371i | ||||||
\(717\) | −20.2755 | + | 7.82625i | −0.757201 | + | 0.292277i | ||||
\(718\) | 3.65615 | 0.136446 | ||||||||
\(719\) | 5.98364 | 0.223152 | 0.111576 | − | 0.993756i | \(-0.464410\pi\) | ||||
0.111576 | + | 0.993756i | \(0.464410\pi\) | |||||||
\(720\) | −40.2763 | − | 1.96082i | −1.50101 | − | 0.0730756i | ||||
\(721\) | −6.81159 | − | 6.81159i | −0.253677 | − | 0.253677i | ||||
\(722\) | 0.443548 | + | 0.443548i | 0.0165071 | + | 0.0165071i | ||||
\(723\) | −23.1629 | + | 8.94079i | −0.861437 | + | 0.332512i | ||||
\(724\) | −15.1234 | −0.562058 | ||||||||
\(725\) | 45.3012 | 1.68244 | ||||||||
\(726\) | 1.15777 | + | 2.99943i | 0.0429688 | + | 0.111319i | ||||
\(727\) | 32.6607i | 1.21132i | 0.795724 | + | 0.605660i | \(0.207091\pi\) | ||||
−0.795724 | + | 0.605660i | \(0.792909\pi\) | |||||||
\(728\) | −1.50508 | + | 0.370387i | −0.0557821 | + | 0.0137275i | ||||
\(729\) | −21.6653 | + | 16.1126i | −0.802418 | + | 0.596763i | ||||
\(730\) | 1.95607 | + | 1.95607i | 0.0723974 | + | 0.0723974i | ||||
\(731\) | − | 2.82438i | − | 0.104463i | ||||||
\(732\) | −0.277163 | + | 0.625643i | −0.0102442 | + | 0.0231244i | ||||
\(733\) | 4.27208 | + | 4.27208i | 0.157793 | + | 0.157793i | 0.781588 | − | 0.623795i | \(-0.214410\pi\) |
−0.623795 | + | 0.781588i | \(0.714410\pi\) | |||||||
\(734\) | −0.174090 | + | 0.174090i | −0.00642578 | + | 0.00642578i | ||||
\(735\) | −2.13298 | − | 5.52592i | −0.0786763 | − | 0.203827i | ||||
\(736\) | 4.32999 | − | 4.32999i | 0.159605 | − | 0.159605i | ||||
\(737\) | 19.7138i | 0.726168i | ||||||||
\(738\) | −0.458396 | + | 0.415835i | −0.0168738 | + | 0.0153071i | ||||
\(739\) | 29.0152 | − | 29.0152i | 1.06734 | − | 1.06734i | 0.0697770 | − | 0.997563i | \(-0.477771\pi\) |
0.997563 | − | 0.0697770i | \(-0.0222288\pi\) | |||||||
\(740\) | 24.9970 | 0.918909 | ||||||||
\(741\) | −17.8148 | − | 25.5068i | −0.654442 | − | 0.937017i | ||||
\(742\) | 0.437235 | 0.0160514 | ||||||||
\(743\) | −17.8103 | + | 17.8103i | −0.653395 | + | 0.653395i | −0.953809 | − | 0.300414i | \(-0.902875\pi\) |
0.300414 | + | 0.953809i | \(0.402875\pi\) | |||||||
\(744\) | 1.32769 | − | 2.99700i | 0.0486753 | − | 0.109875i | ||||
\(745\) | − | 37.6525i | − | 1.37948i | ||||||
\(746\) | 0.901949 | − | 0.901949i | 0.0330227 | − | 0.0330227i | ||||
\(747\) | −18.3110 | − | 0.891460i | −0.669965 | − | 0.0326168i | ||||
\(748\) | 3.74307 | − | 3.74307i | 0.136860 | − | 0.136860i | ||||
\(749\) | −9.23372 | − | 9.23372i | −0.337393 | − | 0.337393i | ||||
\(750\) | −0.989493 | − | 0.438351i | −0.0361312 | − | 0.0160063i | ||||
\(751\) | 42.7282i | 1.55917i | 0.626294 | + | 0.779587i | \(0.284571\pi\) | ||||
−0.626294 | + | 0.779587i | \(0.715429\pi\) | |||||||
\(752\) | −15.9347 | − | 15.9347i | −0.581078 | − | 0.581078i | ||||
\(753\) | 32.2900 | + | 14.3046i | 1.17671 | + | 0.521290i | ||||
\(754\) | −2.24983 | − | 1.36119i | −0.0819339 | − | 0.0495716i | ||||
\(755\) | 16.8618i | 0.613663i | ||||||||
\(756\) | −4.63924 | + | 9.23181i | −0.168728 | + | 0.335758i | ||||
\(757\) | 37.7081 | 1.37052 | 0.685262 | − | 0.728297i | \(-0.259688\pi\) | ||||
0.685262 | + | 0.728297i | \(0.259688\pi\) | |||||||
\(758\) | −2.96364 | −0.107644 | ||||||||
\(759\) | 15.8092 | + | 40.9568i | 0.573837 | + | 1.48664i | ||||
\(760\) | 5.17895 | + | 5.17895i | 0.187860 | + | 0.187860i | ||||
\(761\) | −7.63106 | − | 7.63106i | −0.276626 | − | 0.276626i | 0.555135 | − | 0.831760i | \(-0.312667\pi\) |
−0.831760 | + | 0.555135i | \(0.812667\pi\) | |||||||
\(762\) | 0.628011 | + | 1.62699i | 0.0227504 | + | 0.0589396i | ||||
\(763\) | 15.1292 | 0.547712 | ||||||||
\(764\) | −18.1298 | −0.655914 | ||||||||
\(765\) | 5.13524 | + | 0.250006i | 0.185665 | + | 0.00903898i | ||||
\(766\) | 0.426623i | 0.0154145i | ||||||||
\(767\) | 43.2854 | + | 26.1885i | 1.56295 | + | 0.945613i | ||||
\(768\) | 23.8788 | + | 10.5784i | 0.861651 | + | 0.381716i | ||||
\(769\) | −3.70390 | − | 3.70390i | −0.133566 | − | 0.133566i | 0.637163 | − | 0.770729i | \(-0.280108\pi\) |
−0.770729 | + | 0.637163i | \(0.780108\pi\) | |||||||
\(770\) | 1.95819i | 0.0705681i | ||||||||
\(771\) | −4.00861 | − | 1.77584i | −0.144367 | − | 0.0639552i | ||||
\(772\) | 3.28483 | + | 3.28483i | 0.118224 | + | 0.118224i | ||||
\(773\) | 0.164003 | − | 0.164003i | 0.00589878 | − | 0.00589878i | −0.704151 | − | 0.710050i | \(-0.748672\pi\) |
0.710050 | + | 0.704151i | \(0.248672\pi\) | |||||||
\(774\) | 0.0886192 | − | 1.82028i | 0.00318535 | − | 0.0654287i | ||||
\(775\) | −20.8413 | + | 20.8413i | −0.748641 | + | 0.748641i | ||||
\(776\) | − | 2.81877i | − | 0.101188i | ||||||
\(777\) | 2.57896 | − | 5.82150i | 0.0925195 | − | 0.208845i | ||||
\(778\) | 0.0553978 | − | 0.0553978i | 0.00198611 | − | 0.00198611i | ||||
\(779\) | −9.53546 | −0.341643 | ||||||||
\(780\) | −24.3156 | − | 34.8146i | −0.870639 | − | 1.24656i | ||||
\(781\) | −41.4691 | −1.48388 | ||||||||
\(782\) | −0.182234 | + | 0.182234i | −0.00651666 | + | 0.00651666i | ||||
\(783\) | −33.3769 | + | 11.0507i | −1.19279 | + | 0.394921i | ||||
\(784\) | 3.93043i | 0.140372i | ||||||||
\(785\) | 8.37196 | − | 8.37196i | 0.298808 | − | 0.298808i | ||||
\(786\) | 0.0662906 | + | 0.171739i | 0.00236451 | + | 0.00612573i | ||||
\(787\) | 0.0454837 | − | 0.0454837i | 0.00162132 | − | 0.00162132i | −0.706296 | − | 0.707917i | \(-0.749635\pi\) |
0.707917 | + | 0.706296i | \(0.249635\pi\) | |||||||
\(788\) | 11.6985 | + | 11.6985i | 0.416743 | + | 0.416743i | ||||
\(789\) | 9.15363 | − | 20.6626i | 0.325878 | − | 0.735607i | ||||
\(790\) | − | 4.81749i | − | 0.171398i | ||||||
\(791\) | −4.54897 | − | 4.54897i | −0.161743 | − | 0.161743i | ||||
\(792\) | 5.07441 | − | 4.60326i | 0.180311 | − | 0.163570i | ||||
\(793\) | −0.695635 | + | 0.171190i | −0.0247027 | + | 0.00607912i | ||||
\(794\) | − | 3.69419i | − | 0.131102i | ||||||
\(795\) | 8.65253 | + | 22.4161i | 0.306874 | + | 0.795017i | ||||
\(796\) | −19.5780 | −0.693925 | ||||||||
\(797\) | −42.6814 | −1.51185 | −0.755927 | − | 0.654656i | \(-0.772813\pi\) | ||||
−0.755927 | + | 0.654656i | \(0.772813\pi\) | |||||||
\(798\) | 0.867679 | − | 0.334921i | 0.0307155 | − | 0.0118561i | ||||
\(799\) | 2.03168 | + | 2.03168i | 0.0718756 | + | 0.0718756i | ||||
\(800\) | 6.07593 | + | 6.07593i | 0.214817 | + | 0.214817i | ||||
\(801\) | −0.324819 | + | 6.67195i | −0.0114769 | + | 0.235742i | ||||
\(802\) | −0.196351 | −0.00693340 | ||||||||
\(803\) | 39.8685 | 1.40693 | ||||||||
\(804\) | 11.9229 | − | 4.60218i | 0.420487 | − | 0.162306i | ||||
\(805\) | 16.3168i | 0.575092i | ||||||||
\(806\) | 1.66129 | − | 0.408827i | 0.0585163 | − | 0.0144003i | ||||
\(807\) | −22.1078 | + | 49.9041i | −0.778232 | + | 1.75671i | ||||
\(808\) | 4.68797 | + | 4.68797i | 0.164922 | + | 0.164922i | ||||
\(809\) | 10.1993i | 0.358588i | 0.983796 | + | 0.179294i | \(0.0573813\pi\) | ||||
−0.983796 | + | 0.179294i | \(0.942619\pi\) | |||||||
\(810\) | 3.30176 | + | 0.322252i | 0.116012 | + | 0.0113228i | ||||
\(811\) | −0.875146 | − | 0.875146i | −0.0307305 | − | 0.0307305i | 0.691575 | − | 0.722305i | \(-0.256917\pi\) |
−0.722305 | + | 0.691575i | \(0.756917\pi\) | |||||||
\(812\) | −9.51340 | + | 9.51340i | −0.333855 | + | 0.333855i | ||||
\(813\) | −37.1566 | + | 14.3423i | −1.30314 | + | 0.503006i | ||||
\(814\) | −1.48841 | + | 1.48841i | −0.0521687 | + | 0.0521687i | ||||
\(815\) | − | 52.9980i | − | 1.85644i | ||||||
\(816\) | −3.11918 | − | 1.38181i | −0.109193 | − | 0.0483731i | ||||
\(817\) | 19.8543 | − | 19.8543i | 0.694614 | − | 0.694614i | ||||
\(818\) | 2.56800 | 0.0897880 | ||||||||
\(819\) | −10.6165 | + | 2.07097i | −0.370972 | + | 0.0723654i | ||||
\(820\) | −13.0151 | −0.454506 | ||||||||
\(821\) | 6.81319 | − | 6.81319i | 0.237782 | − | 0.237782i | −0.578149 | − | 0.815931i | \(-0.696225\pi\) |
0.815931 | + | 0.578149i | \(0.196225\pi\) | |||||||
\(822\) | 1.91384 | + | 0.847842i | 0.0667528 | + | 0.0295719i | ||||
\(823\) | 4.17913i | 0.145675i | 0.997344 | + | 0.0728376i | \(0.0232055\pi\) | ||||
−0.997344 | + | 0.0728376i | \(0.976795\pi\) | |||||||
\(824\) | 2.92823 | − | 2.92823i | 0.102010 | − | 0.102010i | ||||
\(825\) | −57.4715 | + | 22.1838i | −2.00090 | + | 0.772340i | ||||
\(826\) | −1.06942 | + | 1.06942i | −0.0372098 | + | 0.0372098i | ||||
\(827\) | 10.0858 | + | 10.0858i | 0.350718 | + | 0.350718i | 0.860377 | − | 0.509659i | \(-0.170228\pi\) |
−0.509659 | + | 0.860377i | \(0.670228\pi\) | |||||||
\(828\) | 21.0799 | − | 19.1227i | 0.732579 | − | 0.664560i | ||||
\(829\) | 52.7813i | 1.83317i | 0.399839 | + | 0.916585i | \(0.369066\pi\) | ||||
−0.399839 | + | 0.916585i | \(0.630934\pi\) | |||||||
\(830\) | 1.59277 | + | 1.59277i | 0.0552858 | + | 0.0552858i | ||||
\(831\) | −1.33492 | + | 3.01333i | −0.0463078 | + | 0.104531i | ||||
\(832\) | 6.65364 | + | 27.0373i | 0.230673 | + | 0.937349i | ||||
\(833\) | − | 0.501131i | − | 0.0173632i | ||||||
\(834\) | 0.793221 | − | 0.306180i | 0.0274670 | − | 0.0106022i | ||||
\(835\) | 68.2991 | 2.36359 | ||||||||
\(836\) | 52.6247 | 1.82006 | ||||||||
\(837\) | 10.2714 | − | 20.4394i | 0.355030 | − | 0.706488i | ||||
\(838\) | 0.869723 | + | 0.869723i | 0.0300441 | + | 0.0300441i | ||||
\(839\) | 0.873967 | + | 0.873967i | 0.0301727 | + | 0.0301727i | 0.722032 | − | 0.691859i | \(-0.243208\pi\) |
−0.691859 | + | 0.722032i | \(0.743208\pi\) | |||||||
\(840\) | 2.37553 | − | 0.916946i | 0.0819636 | − | 0.0316376i | ||||
\(841\) | −16.7827 | −0.578715 | ||||||||
\(842\) | −0.705136 | −0.0243006 | ||||||||
\(843\) | 2.37227 | + | 6.14583i | 0.0817052 | + | 0.211674i | ||||
\(844\) | − | 41.6272i | − | 1.43287i | ||||||
\(845\) | 13.2572 | − | 42.4349i | 0.456062 | − | 1.45981i | ||||
\(846\) | 1.24565 | + | 1.37314i | 0.0428262 | + | 0.0472096i | ||||
\(847\) | 12.1776 | + | 12.1776i | 0.418428 | + | 0.418428i | ||||
\(848\) | − | 15.9439i | − | 0.547517i | ||||||
\(849\) | −9.74526 | + | 21.9981i | −0.334456 | + | 0.754971i | ||||
\(850\) | −0.255714 | − | 0.255714i | −0.00877092 | − | 0.00877092i | ||||
\(851\) | −12.4023 | + | 12.4023i | −0.425147 | + | 0.425147i | ||||
\(852\) | 9.68093 | + | 25.0804i | 0.331663 | + | 0.859240i | ||||
\(853\) | −8.36431 | + | 8.36431i | −0.286388 | + | 0.286388i | −0.835650 | − | 0.549262i | \(-0.814909\pi\) |
0.549262 | + | 0.835650i | \(0.314909\pi\) | |||||||
\(854\) | − | 0.0214160i | − | 0.000732839i | ||||||
\(855\) | 34.3413 | + | 37.8562i | 1.17445 | + | 1.29465i | ||||
\(856\) | 3.96948 | − | 3.96948i | 0.135674 | − | 0.135674i | ||||
\(857\) | −36.9543 | −1.26234 | −0.631168 | − | 0.775646i | \(-0.717424\pi\) | ||||
−0.631168 | + | 0.775646i | \(0.717424\pi\) | |||||||
\(858\) | 3.52082 | + | 0.625147i | 0.120199 | + | 0.0213422i | ||||
\(859\) | 38.8763 | 1.32644 | 0.663220 | − | 0.748424i | \(-0.269189\pi\) | ||||
0.663220 | + | 0.748424i | \(0.269189\pi\) | |||||||
\(860\) | 27.0994 | − | 27.0994i | 0.924081 | − | 0.924081i | ||||
\(861\) | −1.34277 | + | 3.03105i | −0.0457615 | + | 0.103298i | ||||
\(862\) | − | 2.05583i | − | 0.0700219i | ||||||
\(863\) | −2.77181 | + | 2.77181i | −0.0943535 | + | 0.0943535i | −0.752708 | − | 0.658355i | \(-0.771253\pi\) |
0.658355 | + | 0.752708i | \(0.271253\pi\) | |||||||
\(864\) | −5.95876 | − | 2.99445i | −0.202721 | − | 0.101873i | ||||
\(865\) | −45.0238 | + | 45.0238i | −1.53086 | + | 1.53086i | ||||
\(866\) | −1.15820 | − | 1.15820i | −0.0393573 | − | 0.0393573i | ||||
\(867\) | −26.5237 | − | 11.7502i | −0.900793 | − | 0.399056i | ||||
\(868\) | − | 8.75348i | − | 0.297112i | ||||||
\(869\) | −49.0948 | − | 49.0948i | −1.66543 | − | 1.66543i | ||||
\(870\) | 3.94968 | + | 1.74973i | 0.133907 | + | 0.0593214i | ||||
\(871\) | 11.4477 | + | 6.92607i | 0.387890 | + | 0.234681i | ||||
\(872\) | 6.50386i | 0.220249i | ||||||||
\(873\) | 0.956532 | − | 19.6476i | 0.0323737 | − | 0.664972i | ||||
\(874\) | −2.56206 | −0.0866631 | ||||||||
\(875\) | −5.79701 | −0.195975 | ||||||||
\(876\) | −9.30727 | − | 24.1123i | −0.314463 | − | 0.814680i | ||||
\(877\) | −4.98129 | − | 4.98129i | −0.168206 | − | 0.168206i | 0.617984 | − | 0.786190i | \(-0.287950\pi\) |
−0.786190 | + | 0.617984i | \(0.787950\pi\) | |||||||
\(878\) | 1.27794 | + | 1.27794i | 0.0431283 | + | 0.0431283i | ||||
\(879\) | −9.71339 | − | 25.1645i | −0.327625 | − | 0.848777i | ||||
\(880\) | 71.4059 | 2.40709 | ||||||||
\(881\) | −24.6836 | −0.831610 | −0.415805 | − | 0.909454i | \(-0.636500\pi\) | ||||
−0.415805 | + | 0.909454i | \(0.636500\pi\) | |||||||
\(882\) | 0.0157237 | − | 0.322973i | 0.000529446 | − | 0.0108751i | ||||
\(883\) | − | 42.4570i | − | 1.42879i | −0.699741 | − | 0.714397i | \(-0.746701\pi\) | ||
0.699741 | − | 0.714397i | \(-0.253299\pi\) | |||||||
\(884\) | −0.858521 | − | 3.48863i | −0.0288752 | − | 0.117335i | ||||
\(885\) | −75.9897 | − | 33.6638i | −2.55436 | − | 1.13160i | ||||
\(886\) | −3.04467 | − | 3.04467i | −0.102288 | − | 0.102288i | ||||
\(887\) | − | 32.9418i | − | 1.10608i | −0.833155 | − | 0.553039i | \(-0.813468\pi\) | ||
0.833155 | − | 0.553039i | \(-0.186532\pi\) | |||||||
\(888\) | 2.50260 | + | 1.10867i | 0.0839817 | + | 0.0372044i | ||||
\(889\) | 6.60553 | + | 6.60553i | 0.221542 | + | 0.221542i | ||||
\(890\) | 0.580354 | − | 0.580354i | 0.0194535 | − | 0.0194535i | ||||
\(891\) | 36.9322 | − | 30.3641i | 1.23727 | − | 1.01723i | ||||
\(892\) | 36.2575 | − | 36.2575i | 1.21399 | − | 1.21399i | ||||
\(893\) | 28.5638i | 0.955852i | ||||||||
\(894\) | 0.832548 | − | 1.87932i | 0.0278446 | − | 0.0628538i | ||||
\(895\) | −44.3779 | + | 44.3779i | −1.48339 | + | 1.48339i | ||||
\(896\) | −3.39922 | −0.113560 | ||||||||
\(897\) | 29.3376 | + | 5.20910i | 0.979554 | + | 0.173927i | ||||
\(898\) | −2.27157 | −0.0758031 | ||||||||
\(899\) | 21.0628 | − | 21.0628i | 0.702484 | − | 0.702484i | ||||
\(900\) | 26.8334 | + | 29.5798i | 0.894446 | + | 0.985994i | ||||
\(901\) | 2.03286i | 0.0677243i | ||||||||
\(902\) | 0.774963 | − | 0.774963i | 0.0258034 | − | 0.0258034i | ||||
\(903\) | −3.51525 | − | 9.10697i | −0.116980 | − | 0.303061i | ||||
\(904\) | 1.95555 | − | 1.95555i | 0.0650407 | − | 0.0650407i | ||||
\(905\) | 18.3924 | + | 18.3924i | 0.611383 | + | 0.611383i | ||||
\(906\) | −0.372837 | + | 0.841608i | −0.0123867 | + | 0.0279605i | ||||
\(907\) | 37.1213i | 1.23259i | 0.787514 | + | 0.616297i | \(0.211368\pi\) | ||||
−0.787514 | + | 0.616297i | \(0.788632\pi\) | |||||||
\(908\) | −15.7313 | − | 15.7313i | −0.522063 | − | 0.522063i | ||||
\(909\) | 31.0857 | + | 34.2674i | 1.03105 | + | 1.13658i | ||||
\(910\) | 1.13711 | + | 0.687971i | 0.0376947 | + | 0.0228060i | ||||
\(911\) | − | 5.99621i | − | 0.198663i | −0.995054 | − | 0.0993316i | \(-0.968330\pi\) | ||
0.995054 | − | 0.0993316i | \(-0.0316705\pi\) | |||||||
\(912\) | −12.2130 | − | 31.6402i | −0.404413 | − | 1.04771i | ||||
\(913\) | 32.4637 | 1.07439 | ||||||||
\(914\) | −1.77427 | −0.0586875 | ||||||||
\(915\) | 1.09795 | − | 0.423804i | 0.0362971 | − | 0.0140105i | ||||
\(916\) | −14.6063 | − | 14.6063i | −0.482607 | − | 0.482607i | ||||
\(917\) | 0.697256 | + | 0.697256i | 0.0230254 | + | 0.0230254i | ||||
\(918\) | 0.250783 | + | 0.126025i | 0.00827707 | + | 0.00415946i | ||||
\(919\) | −8.82388 | −0.291073 | −0.145536 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145536 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(920\) | −7.01442 | −0.231258 | ||||||||
\(921\) | 24.6483 | − | 9.51416i | 0.812190 | − | 0.313502i | ||||
\(922\) | 0.546368i | 0.0179937i | ||||||||
\(923\) | −14.5693 | + | 24.0808i | −0.479556 | + | 0.792629i | ||||
\(924\) | 7.41054 | − | 16.7279i | 0.243789 | − | 0.550307i | ||||
\(925\) | −17.4032 | − | 17.4032i | −0.572214 | − | 0.572214i | ||||
\(926\) | − | 1.70377i | − | 0.0559894i | ||||||
\(927\) | 21.4043 | − | 19.4169i | 0.703008 | − | 0.637735i | ||||
\(928\) | −6.14052 | − | 6.14052i | −0.201572 | − | 0.201572i | ||||
\(929\) | −30.5160 | + | 30.5160i | −1.00120 | + | 1.00120i | −0.00119660 | + | 0.999999i | \(0.500381\pi\) |
−0.999999 | + | 0.00119660i | \(0.999619\pi\) | |||||||
\(930\) | −2.62207 | + | 1.01211i | −0.0859811 | + | 0.0331884i | ||||
\(931\) | 3.52276 | − | 3.52276i | 0.115454 | − | 0.115454i | ||||
\(932\) | 49.8084i | 1.63153i | ||||||||
\(933\) | −29.4224 | − | 13.0343i | −0.963245 | − | 0.426723i | ||||
\(934\) | 0.651534 | − | 0.651534i | 0.0213188 | − | 0.0213188i | ||||
\(935\) | −9.10428 | −0.297742 | ||||||||
\(936\) | −0.890286 | − | 4.56394i | −0.0290999 | − | 0.149177i | ||||
\(937\) | −48.0385 | −1.56935 | −0.784675 | − | 0.619908i | \(-0.787170\pi\) | ||||
−0.784675 | + | 0.619908i | \(0.787170\pi\) | |||||||
\(938\) | −0.282829 | + | 0.282829i | −0.00923469 | + | 0.00923469i | ||||
\(939\) | 23.9039 | + | 10.5895i | 0.780074 | + | 0.345577i | ||||
\(940\) | 38.9871i | 1.27162i | ||||||||
\(941\) | −21.9053 | + | 21.9053i | −0.714093 | + | 0.714093i | −0.967389 | − | 0.253296i | \(-0.918485\pi\) |
0.253296 | + | 0.967389i | \(0.418485\pi\) | |||||||
\(942\) | 0.602978 | − | 0.232747i | 0.0196461 | − | 0.00758331i | ||||
\(943\) | 6.45746 | − | 6.45746i | 0.210284 | − | 0.210284i | ||||
\(944\) | 38.9967 | + | 38.9967i | 1.26924 | + | 1.26924i | ||||
\(945\) | 16.8693 | − | 5.58526i | 0.548758 | − | 0.181688i | ||||
\(946\) | 3.22718i | 0.104925i | ||||||||
\(947\) | 22.3201 | + | 22.3201i | 0.725306 | + | 0.725306i | 0.969681 | − | 0.244375i | \(-0.0785826\pi\) |
−0.244375 | + | 0.969681i | \(0.578583\pi\) | |||||||
\(948\) | −18.2312 | + | 41.1535i | −0.592123 | + | 1.33661i | ||||
\(949\) | 14.0070 | − | 23.1513i | 0.454686 | − | 0.751524i | ||||
\(950\) | − | 3.59514i | − | 0.116642i | ||||||
\(951\) | 12.4089 | − | 4.78978i | 0.402386 | − | 0.155319i | ||||
\(952\) | 0.215431 | 0.00698215 | ||||||||
\(953\) | 8.90539 | 0.288474 | 0.144237 | − | 0.989543i | \(-0.453927\pi\) | ||||
0.144237 | + | 0.989543i | \(0.453927\pi\) | |||||||
\(954\) | −0.0637840 | + | 1.31015i | −0.00206508 | + | 0.0424178i | ||||
\(955\) | 22.0486 | + | 22.0486i | 0.713476 | + | 0.713476i | ||||
\(956\) | −17.6422 | − | 17.6422i | −0.570591 | − | 0.570591i | ||||
\(957\) | 58.0824 | − | 22.4196i | 1.87754 | − | 0.724723i | ||||
\(958\) | −1.28636 | −0.0415603 | ||||||||
\(959\) | 11.2124 | 0.362066 | ||||||||
\(960\) | −16.4720 | − | 42.6740i | −0.531632 | − | 1.37730i | ||||
\(961\) | − | 11.6197i | − | 0.374828i | ||||||
\(962\) | 0.341386 | + | 1.38723i | 0.0110067 | + | 0.0447262i | ||||
\(963\) | 29.0154 | − | 26.3214i | 0.935008 | − | 0.848194i | ||||
\(964\) | −20.1547 | − | 20.1547i | −0.649138 | − | 0.649138i | ||||
\(965\) | − | 7.98970i | − | 0.257198i | ||||||
\(966\) | −0.360786 | + | 0.814406i | −0.0116081 | + | 0.0262031i | ||||
\(967\) | 28.2133 | + | 28.2133i | 0.907278 | + | 0.907278i | 0.996052 | − | 0.0887740i | \(-0.0282949\pi\) |
−0.0887740 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(968\) | −5.23503 | + | 5.23503i | −0.168260 | + | 0.168260i | ||||
\(969\) | 1.55716 | + | 4.03414i | 0.0500232 | + | 0.129595i | ||||
\(970\) | −1.70903 | + | 1.70903i | −0.0548737 | + | 0.0548737i | ||||
\(971\) | − | 50.5527i | − | 1.62231i | −0.584828 | − | 0.811157i | \(-0.698838\pi\) | ||
0.584828 | − | 0.811157i | \(-0.301162\pi\) | |||||||
\(972\) | −26.9859 | − | 15.2480i | −0.865573 | − | 0.489080i | ||||
\(973\) | 3.22046 | − | 3.22046i | 0.103243 | − | 0.103243i | ||||
\(974\) | 3.02102 | 0.0967998 | ||||||||
\(975\) | −7.30952 | + | 41.1672i | −0.234092 | + | 1.31840i | ||||
\(976\) | −0.780940 | −0.0249973 | ||||||||
\(977\) | −8.22638 | + | 8.22638i | −0.263185 | + | 0.263185i | −0.826347 | − | 0.563162i | \(-0.809585\pi\) |
0.563162 | + | 0.826347i | \(0.309585\pi\) | |||||||
\(978\) | 1.17186 | − | 2.64524i | 0.0374718 | − | 0.0845855i | ||||
\(979\) | − | 11.8287i | − | 0.378047i | ||||||
\(980\) | 4.80825 | − | 4.80825i | 0.153594 | − | 0.153594i | ||||
\(981\) | −2.20705 | + | 45.3338i | −0.0704655 | + | 1.44740i | ||||
\(982\) | 1.50596 | − | 1.50596i | 0.0480573 | − | 0.0480573i | ||||
\(983\) | 6.08660 | + | 6.08660i | 0.194132 | + | 0.194132i | 0.797479 | − | 0.603347i | \(-0.206166\pi\) |
−0.603347 | + | 0.797479i | \(0.706166\pi\) | |||||||
\(984\) | −1.30302 | − | 0.577243i | −0.0415386 | − | 0.0184018i | ||||
\(985\) | − | 28.4543i | − | 0.906631i | ||||||
\(986\) | 0.258432 | + | 0.258432i | 0.00823016 | + | 0.00823016i | ||||
\(987\) | 9.07962 | + | 4.02232i | 0.289007 | + | 0.128032i | ||||
\(988\) | 18.4887 | − | 30.5588i | 0.588202 | − | 0.972205i | ||||
\(989\) | 26.8908i | 0.855079i | ||||||||
\(990\) | −5.86761 | − | 0.285661i | −0.186485 | − | 0.00907889i | ||||
\(991\) | −51.0667 | −1.62219 | −0.811094 | − | 0.584916i | \(-0.801128\pi\) | ||||
−0.811094 | + | 0.584916i | \(0.801128\pi\) | |||||||
\(992\) | 5.65002 | 0.179388 | ||||||||
\(993\) | −19.4763 | − | 50.4571i | −0.618060 | − | 1.60121i | ||||
\(994\) | −0.594945 | − | 0.594945i | −0.0188705 | − | 0.0188705i | ||||
\(995\) | 23.8098 | + | 23.8098i | 0.754823 | + | 0.754823i | ||||
\(996\) | −7.57862 | − | 19.6339i | −0.240138 | − | 0.622125i | ||||
\(997\) | −27.4732 | −0.870086 | −0.435043 | − | 0.900410i | \(-0.643267\pi\) | ||||
−0.435043 | + | 0.900410i | \(0.643267\pi\) | |||||||
\(998\) | 0.638381 | 0.0202076 | ||||||||
\(999\) | 17.0676 | + | 8.57696i | 0.539996 | + | 0.271363i |
(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 | 273.2.n.c.8.13 | yes | 48 | |
3.2 | odd | 2 | inner | 273.2.n.c.8.12 | ✓ | 48 | |
13.5 | odd | 4 | inner | 273.2.n.c.239.12 | yes | 48 | |
39.5 | even | 4 | inner | 273.2.n.c.239.13 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.n.c.8.12 | ✓ | 48 | 3.2 | odd | 2 | inner | |
273.2.n.c.8.13 | yes | 48 | 1.1 | even | 1 | trivial | |
273.2.n.c.239.12 | yes | 48 | 13.5 | odd | 4 | inner | |
273.2.n.c.239.13 | yes | 48 | 39.5 | even | 4 | inner |