Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,3,Mod(11,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.r (of order \(6\), 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: | \(3.43325133094\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.7 | ||
Character | \(\chi\) | \(=\) | 126.11 |
Dual form | 126.3.r.a.23.15 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 2.36405 | + | 1.84696i | 0.788018 | + | 0.615652i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 1.22482 | + | 0.707152i | 0.244965 | + | 0.141430i | 0.617456 | − | 0.786605i | \(-0.288163\pi\) |
−0.372492 | + | 0.928036i | \(0.621496\pi\) | |||||||
\(6\) | 2.61199 | − | 3.34328i | 0.435332 | − | 0.557213i | ||||
\(7\) | 3.10205 | − | 6.27513i | 0.443150 | − | 0.896448i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 2.17750 | + | 8.73261i | 0.241944 | + | 0.970290i | ||||
\(10\) | 1.00006 | − | 1.73216i | 0.100006 | − | 0.173216i | ||||
\(11\) | 15.1176 | − | 8.72813i | 1.37432 | − | 0.793466i | 0.382855 | − | 0.923809i | \(-0.374941\pi\) |
0.991469 | + | 0.130343i | \(0.0416077\pi\) | |||||||
\(12\) | −4.72811 | − | 3.69391i | −0.394009 | − | 0.307826i | ||||
\(13\) | 8.59030 | + | 14.8788i | 0.660793 | + | 1.14453i | 0.980408 | + | 0.196979i | \(0.0631130\pi\) |
−0.319615 | + | 0.947547i | \(0.603554\pi\) | |||||||
\(14\) | −8.87438 | − | 4.38696i | −0.633884 | − | 0.313354i | ||||
\(15\) | 1.58947 | + | 3.93394i | 0.105965 | + | 0.262263i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −20.8700 | − | 12.0493i | −1.22765 | − | 0.708781i | −0.261109 | − | 0.965309i | \(-0.584088\pi\) |
−0.966537 | + | 0.256528i | \(0.917421\pi\) | |||||||
\(18\) | 12.3498 | − | 3.07945i | 0.686099 | − | 0.171080i | ||||
\(19\) | 11.7810 | + | 20.4053i | 0.620051 | + | 1.07396i | 0.989476 | + | 0.144700i | \(0.0462216\pi\) |
−0.369424 | + | 0.929261i | \(0.620445\pi\) | |||||||
\(20\) | −2.44965 | − | 1.41430i | −0.122482 | − | 0.0707152i | ||||
\(21\) | 18.9233 | − | 9.10540i | 0.901110 | − | 0.433591i | ||||
\(22\) | −12.3434 | − | 21.3795i | −0.561065 | − | 0.971794i | ||||
\(23\) | −27.1025 | − | 15.6476i | −1.17837 | − | 0.680331i | −0.222731 | − | 0.974880i | \(-0.571497\pi\) |
−0.955636 | + | 0.294549i | \(0.904831\pi\) | |||||||
\(24\) | −5.22398 | + | 6.68655i | −0.217666 | + | 0.278606i | ||||
\(25\) | −11.4999 | − | 19.9184i | −0.459995 | − | 0.796734i | ||||
\(26\) | 21.0419 | − | 12.1485i | 0.809302 | − | 0.467251i | ||||
\(27\) | −10.9810 | + | 24.6661i | −0.406705 | + | 0.913560i | ||||
\(28\) | −6.20409 | + | 12.5503i | −0.221575 | + | 0.448224i | ||||
\(29\) | −13.7563 | − | 7.94218i | −0.474354 | − | 0.273868i | 0.243707 | − | 0.969849i | \(-0.421637\pi\) |
−0.718061 | + | 0.695981i | \(0.754970\pi\) | |||||||
\(30\) | 5.56344 | − | 2.24785i | 0.185448 | − | 0.0749283i | ||||
\(31\) | −32.1938 | −1.03851 | −0.519255 | − | 0.854619i | \(-0.673791\pi\) | ||||
−0.519255 | + | 0.854619i | \(0.673791\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 51.8592 | + | 7.28773i | 1.57149 | + | 0.220840i | ||||
\(34\) | −17.0403 | + | 29.5146i | −0.501184 | + | 0.868076i | ||||
\(35\) | 8.23694 | − | 5.49231i | 0.235341 | − | 0.156923i | ||||
\(36\) | −4.35500 | − | 17.4652i | −0.120972 | − | 0.485145i | ||||
\(37\) | 15.7030 | + | 27.1985i | 0.424407 | + | 0.735094i | 0.996365 | − | 0.0851890i | \(-0.0271494\pi\) |
−0.571958 | + | 0.820283i | \(0.693816\pi\) | |||||||
\(38\) | 28.8574 | − | 16.6608i | 0.759405 | − | 0.438443i | ||||
\(39\) | −7.17265 | + | 51.0403i | −0.183914 | + | 1.30873i | ||||
\(40\) | −2.00013 | + | 3.46433i | −0.0500032 | + | 0.0866081i | ||||
\(41\) | 8.67466 | − | 5.00832i | 0.211577 | − | 0.122154i | −0.390467 | − | 0.920617i | \(-0.627686\pi\) |
0.602044 | + | 0.798463i | \(0.294353\pi\) | |||||||
\(42\) | −12.8770 | − | 26.7616i | −0.306595 | − | 0.637181i | ||||
\(43\) | −31.6891 | + | 54.8871i | −0.736956 | + | 1.27644i | 0.216904 | + | 0.976193i | \(0.430404\pi\) |
−0.953860 | + | 0.300252i | \(0.902929\pi\) | |||||||
\(44\) | −30.2351 | + | 17.4563i | −0.687162 | + | 0.396733i | ||||
\(45\) | −3.50824 | + | 12.2357i | −0.0779608 | + | 0.271905i | ||||
\(46\) | −22.1291 | + | 38.3287i | −0.481067 | + | 0.833232i | ||||
\(47\) | 4.27193i | 0.0908922i | 0.998967 | + | 0.0454461i | \(0.0144709\pi\) | ||||
−0.998967 | + | 0.0454461i | \(0.985529\pi\) | |||||||
\(48\) | 9.45621 | + | 7.38783i | 0.197004 | + | 0.153913i | ||||
\(49\) | −29.7546 | − | 38.9315i | −0.607237 | − | 0.794521i | ||||
\(50\) | −28.1688 | + | 16.2633i | −0.563376 | + | 0.325265i | ||||
\(51\) | −27.0832 | − | 67.0311i | −0.531044 | − | 1.31434i | ||||
\(52\) | −17.1806 | − | 29.7577i | −0.330396 | − | 0.572263i | ||||
\(53\) | −45.3154 | − | 26.1629i | −0.855008 | − | 0.493639i | 0.00732944 | − | 0.999973i | \(-0.497667\pi\) |
−0.862337 | + | 0.506334i | \(0.831000\pi\) | |||||||
\(54\) | 34.8831 | + | 15.5295i | 0.645984 | + | 0.287584i | ||||
\(55\) | 24.6885 | 0.448881 | ||||||||
\(56\) | 17.7488 | + | 8.77391i | 0.316942 | + | 0.156677i | ||||
\(57\) | −9.83677 | + | 69.9981i | −0.172575 | + | 1.22804i | ||||
\(58\) | −11.2319 | + | 19.4543i | −0.193654 | + | 0.335419i | ||||
\(59\) | 42.1881i | 0.715053i | 0.933903 | + | 0.357527i | \(0.116380\pi\) | ||||
−0.933903 | + | 0.357527i | \(0.883620\pi\) | |||||||
\(60\) | −3.17894 | − | 7.86789i | −0.0529823 | − | 0.131131i | ||||
\(61\) | −12.4785 | −0.204565 | −0.102282 | − | 0.994755i | \(-0.532615\pi\) | ||||
−0.102282 | + | 0.994755i | \(0.532615\pi\) | |||||||
\(62\) | 45.5289i | 0.734338i | ||||||||
\(63\) | 61.5530 | + | 13.4249i | 0.977032 | + | 0.213093i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 24.2986i | 0.373825i | ||||||||
\(66\) | 10.3064 | − | 73.3400i | 0.156158 | − | 1.11121i | ||||
\(67\) | 96.1382 | 1.43490 | 0.717449 | − | 0.696611i | \(-0.245310\pi\) | ||||
0.717449 | + | 0.696611i | \(0.245310\pi\) | |||||||
\(68\) | 41.7399 | + | 24.0986i | 0.613823 | + | 0.354391i | ||||
\(69\) | −35.1712 | − | 87.0489i | −0.509727 | − | 1.26158i | ||||
\(70\) | −7.76730 | − | 11.6488i | −0.110961 | − | 0.166411i | ||||
\(71\) | − | 20.8017i | − | 0.292982i | −0.989212 | − | 0.146491i | \(-0.953202\pi\) | ||
0.989212 | − | 0.146491i | \(-0.0467980\pi\) | |||||||
\(72\) | −24.6996 | + | 6.15889i | −0.343049 | + | 0.0855402i | ||||
\(73\) | 41.6824 | − | 72.1961i | 0.570992 | − | 0.988987i | −0.425472 | − | 0.904971i | \(-0.639892\pi\) |
0.996464 | − | 0.0840158i | \(-0.0267746\pi\) | |||||||
\(74\) | 38.4644 | − | 22.2075i | 0.519790 | − | 0.300101i | ||||
\(75\) | 9.60205 | − | 68.3278i | 0.128027 | − | 0.911038i | ||||
\(76\) | −23.5620 | − | 40.8105i | −0.310026 | − | 0.536980i | ||||
\(77\) | −7.87478 | − | 121.940i | −0.102270 | − | 1.58363i | ||||
\(78\) | 72.1819 | + | 10.1437i | 0.925409 | + | 0.130047i | ||||
\(79\) | −45.1639 | −0.571695 | −0.285848 | − | 0.958275i | \(-0.592275\pi\) | ||||
−0.285848 | + | 0.958275i | \(0.592275\pi\) | |||||||
\(80\) | 4.89930 | + | 2.82861i | 0.0612412 | + | 0.0353576i | ||||
\(81\) | −71.5170 | + | 38.0305i | −0.882926 | + | 0.469512i | ||||
\(82\) | −7.08283 | − | 12.2678i | −0.0863760 | − | 0.149608i | ||||
\(83\) | 3.73381 | + | 2.15572i | 0.0449856 | + | 0.0259725i | 0.522324 | − | 0.852747i | \(-0.325065\pi\) |
−0.477339 | + | 0.878719i | \(0.658398\pi\) | |||||||
\(84\) | −37.8466 | + | 18.2108i | −0.450555 | + | 0.216795i | ||||
\(85\) | −17.0414 | − | 29.5165i | −0.200487 | − | 0.347253i | ||||
\(86\) | 77.6221 | + | 44.8151i | 0.902583 | + | 0.521106i | ||||
\(87\) | −17.8517 | − | 44.1830i | −0.205192 | − | 0.507850i | ||||
\(88\) | 24.6869 | + | 42.7589i | 0.280533 | + | 0.485897i | ||||
\(89\) | 123.803 | − | 71.4779i | 1.39105 | − | 0.803122i | 0.397617 | − | 0.917552i | \(-0.369837\pi\) |
0.993431 | + | 0.114430i | \(0.0365041\pi\) | |||||||
\(90\) | 17.3039 | + | 4.96139i | 0.192266 | + | 0.0551266i | ||||
\(91\) | 120.014 | − | 7.75043i | 1.31884 | − | 0.0851696i | ||||
\(92\) | 54.2049 | + | 31.2952i | 0.589184 | + | 0.340165i | ||||
\(93\) | −76.1079 | − | 59.4606i | −0.818365 | − | 0.639361i | ||||
\(94\) | 6.04143 | 0.0642705 | ||||||||
\(95\) | 33.3238i | 0.350777i | ||||||||
\(96\) | 10.4480 | − | 13.3731i | 0.108833 | − | 0.139303i | ||||
\(97\) | −17.5457 | + | 30.3901i | −0.180884 | + | 0.313300i | −0.942182 | − | 0.335102i | \(-0.891229\pi\) |
0.761298 | + | 0.648402i | \(0.224562\pi\) | |||||||
\(98\) | −55.0575 | + | 42.0794i | −0.561811 | + | 0.429381i | ||||
\(99\) | 109.138 | + | 113.010i | 1.10240 | + | 1.14152i | ||||
\(100\) | 22.9997 | + | 39.8367i | 0.229997 | + | 0.398367i | ||||
\(101\) | −35.9483 | + | 20.7548i | −0.355924 | + | 0.205493i | −0.667291 | − | 0.744797i | \(-0.732546\pi\) |
0.311367 | + | 0.950290i | \(0.399213\pi\) | |||||||
\(102\) | −94.7963 | + | 38.3015i | −0.929375 | + | 0.375504i | ||||
\(103\) | 16.9344 | − | 29.3312i | 0.164412 | − | 0.284769i | −0.772035 | − | 0.635580i | \(-0.780761\pi\) |
0.936446 | + | 0.350811i | \(0.114094\pi\) | |||||||
\(104\) | −42.0837 | + | 24.2970i | −0.404651 | + | 0.233625i | ||||
\(105\) | 29.6166 | + | 2.22915i | 0.282063 | + | 0.0212300i | ||||
\(106\) | −36.9999 | + | 64.0857i | −0.349056 | + | 0.604582i | ||||
\(107\) | −39.7440 | + | 22.9462i | −0.371439 | + | 0.214450i | −0.674087 | − | 0.738652i | \(-0.735463\pi\) |
0.302648 | + | 0.953102i | \(0.402129\pi\) | |||||||
\(108\) | 21.9621 | − | 49.3322i | 0.203353 | − | 0.456780i | ||||
\(109\) | 21.6535 | − | 37.5049i | 0.198656 | − | 0.344082i | −0.749437 | − | 0.662075i | \(-0.769676\pi\) |
0.948093 | + | 0.317994i | \(0.103009\pi\) | |||||||
\(110\) | − | 34.9148i | − | 0.317407i | ||||||
\(111\) | −13.1116 | + | 93.3015i | −0.118122 | + | 0.840554i | ||||
\(112\) | 12.4082 | − | 25.1005i | 0.110787 | − | 0.224112i | ||||
\(113\) | −78.3902 | + | 45.2586i | −0.693719 | + | 0.400519i | −0.805004 | − | 0.593270i | \(-0.797837\pi\) |
0.111285 | + | 0.993789i | \(0.464503\pi\) | |||||||
\(114\) | 98.9922 | + | 13.9113i | 0.868353 | + | 0.122029i | ||||
\(115\) | −22.1305 | − | 38.3311i | −0.192439 | − | 0.333314i | ||||
\(116\) | 27.5125 | + | 15.8844i | 0.237177 | + | 0.136934i | ||||
\(117\) | −111.226 | + | 107.414i | −0.950648 | + | 0.918072i | ||||
\(118\) | 59.6630 | 0.505619 | ||||||||
\(119\) | −140.351 | + | 93.5844i | −1.17942 | + | 0.786424i | ||||
\(120\) | −11.1269 | + | 4.49570i | −0.0927239 | + | 0.0374641i | ||||
\(121\) | 91.8604 | − | 159.107i | 0.759177 | − | 1.31493i | ||||
\(122\) | 17.6472i | 0.144649i | ||||||||
\(123\) | 29.7575 | + | 4.18180i | 0.241931 | + | 0.0339983i | ||||
\(124\) | 64.3877 | 0.519255 | ||||||||
\(125\) | − | 67.8863i | − | 0.543090i | ||||||
\(126\) | 18.9856 | − | 87.0491i | 0.150680 | − | 0.690866i | ||||
\(127\) | −135.543 | −1.06727 | −0.533635 | − | 0.845715i | \(-0.679174\pi\) | ||||
−0.533635 | + | 0.845715i | \(0.679174\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | −176.289 | + | 71.2277i | −1.36658 | + | 0.552153i | ||||
\(130\) | 34.3634 | 0.264334 | ||||||||
\(131\) | 192.988 | + | 111.422i | 1.47319 | + | 0.850546i | 0.999545 | − | 0.0301696i | \(-0.00960475\pi\) |
0.473645 | + | 0.880716i | \(0.342938\pi\) | |||||||
\(132\) | −103.718 | − | 14.5755i | −0.785745 | − | 0.110420i | ||||
\(133\) | 164.591 | − | 10.6292i | 1.23753 | − | 0.0799185i | ||||
\(134\) | − | 135.960i | − | 1.01463i | ||||||
\(135\) | −30.8925 | + | 22.4464i | −0.228834 | + | 0.166269i | ||||
\(136\) | 34.0805 | − | 59.0292i | 0.250592 | − | 0.434038i | ||||
\(137\) | −74.8448 | + | 43.2117i | −0.546313 | + | 0.315414i | −0.747633 | − | 0.664112i | \(-0.768810\pi\) |
0.201321 | + | 0.979525i | \(0.435477\pi\) | |||||||
\(138\) | −123.106 | + | 49.7396i | −0.892070 | + | 0.360432i | ||||
\(139\) | 1.61343 | + | 2.79455i | 0.0116074 | + | 0.0201047i | 0.871771 | − | 0.489914i | \(-0.162972\pi\) |
−0.860163 | + | 0.510019i | \(0.829638\pi\) | |||||||
\(140\) | −16.4739 | + | 10.9846i | −0.117671 | + | 0.0784616i | ||||
\(141\) | −7.89008 | + | 10.0991i | −0.0559580 | + | 0.0716247i | ||||
\(142\) | −29.4181 | −0.207170 | ||||||||
\(143\) | 259.729 | + | 149.955i | 1.81629 | + | 1.04863i | ||||
\(144\) | 8.70999 | + | 34.9304i | 0.0604861 | + | 0.242573i | ||||
\(145\) | −11.2327 | − | 19.4555i | −0.0774667 | − | 0.134176i | ||||
\(146\) | −102.101 | − | 58.9478i | −0.699320 | − | 0.403752i | ||||
\(147\) | 1.56337 | − | 146.992i | 0.0106352 | − | 0.999943i | ||||
\(148\) | −31.4061 | − | 54.3969i | −0.212203 | − | 0.367547i | ||||
\(149\) | −169.581 | − | 97.9078i | −1.13813 | − | 0.657100i | −0.192163 | − | 0.981363i | \(-0.561550\pi\) |
−0.945967 | + | 0.324264i | \(0.894884\pi\) | |||||||
\(150\) | −96.6302 | − | 13.5793i | −0.644201 | − | 0.0905290i | ||||
\(151\) | 15.7499 | + | 27.2796i | 0.104304 | + | 0.180659i | 0.913454 | − | 0.406943i | \(-0.133405\pi\) |
−0.809150 | + | 0.587602i | \(0.800072\pi\) | |||||||
\(152\) | −57.7148 | + | 33.3216i | −0.379702 | + | 0.219221i | ||||
\(153\) | 59.7774 | − | 208.487i | 0.390702 | − | 1.36266i | ||||
\(154\) | −172.449 | + | 11.1366i | −1.11980 | + | 0.0723157i | ||||
\(155\) | −39.4318 | − | 22.7659i | −0.254399 | − | 0.146877i | ||||
\(156\) | 14.3453 | − | 102.081i | 0.0919570 | − | 0.654363i | ||||
\(157\) | 89.3761 | 0.569274 | 0.284637 | − | 0.958635i | \(-0.408127\pi\) | ||||
0.284637 | + | 0.958635i | \(0.408127\pi\) | |||||||
\(158\) | 63.8714i | 0.404249i | ||||||||
\(159\) | −58.8064 | − | 145.546i | −0.369851 | − | 0.915384i | ||||
\(160\) | 4.00026 | − | 6.92865i | 0.0250016 | − | 0.0433041i | ||||
\(161\) | −182.264 | + | 121.532i | −1.13207 | + | 0.754857i | ||||
\(162\) | 53.7832 | + | 101.140i | 0.331995 | + | 0.624323i | ||||
\(163\) | 105.258 | + | 182.312i | 0.645755 | + | 1.11848i | 0.984127 | + | 0.177467i | \(0.0567904\pi\) |
−0.338372 | + | 0.941012i | \(0.609876\pi\) | |||||||
\(164\) | −17.3493 | + | 10.0166i | −0.105789 | + | 0.0610770i | ||||
\(165\) | 58.3649 | + | 45.5985i | 0.353726 | + | 0.276355i | ||||
\(166\) | 3.04864 | − | 5.28040i | 0.0183653 | − | 0.0318097i | ||||
\(167\) | 97.8810 | − | 56.5116i | 0.586114 | − | 0.338393i | −0.177446 | − | 0.984131i | \(-0.556783\pi\) |
0.763559 | + | 0.645738i | \(0.223450\pi\) | |||||||
\(168\) | 25.7540 | + | 53.5232i | 0.153297 | + | 0.318590i | ||||
\(169\) | −63.0866 | + | 109.269i | −0.373294 | + | 0.646564i | ||||
\(170\) | −41.7426 | + | 24.1001i | −0.245545 | + | 0.141765i | ||||
\(171\) | −152.538 | + | 147.311i | −0.892036 | + | 0.861468i | ||||
\(172\) | 63.3782 | − | 109.774i | 0.368478 | − | 0.638222i | ||||
\(173\) | 51.8246i | 0.299564i | 0.988719 | + | 0.149782i | \(0.0478572\pi\) | ||||
−0.988719 | + | 0.149782i | \(0.952143\pi\) | |||||||
\(174\) | −62.4842 | + | 25.2461i | −0.359104 | + | 0.145092i | ||||
\(175\) | −160.664 | + | 10.3755i | −0.918077 | + | 0.0592888i | ||||
\(176\) | 60.4702 | − | 34.9125i | 0.343581 | − | 0.198367i | ||||
\(177\) | −77.9197 | + | 99.7350i | −0.440224 | + | 0.563475i | ||||
\(178\) | −101.085 | − | 175.084i | −0.567893 | − | 0.983620i | ||||
\(179\) | 167.471 | + | 96.6894i | 0.935592 | + | 0.540164i | 0.888576 | − | 0.458730i | \(-0.151695\pi\) |
0.0470161 | + | 0.998894i | \(0.485029\pi\) | |||||||
\(180\) | 7.01647 | − | 24.4715i | 0.0389804 | − | 0.135953i | ||||
\(181\) | 175.825 | 0.971411 | 0.485705 | − | 0.874123i | \(-0.338563\pi\) | ||||
0.485705 | + | 0.874123i | \(0.338563\pi\) | |||||||
\(182\) | −10.9608 | − | 169.726i | −0.0602240 | − | 0.932559i | ||||
\(183\) | −29.4997 | − | 23.0472i | −0.161201 | − | 0.125941i | ||||
\(184\) | 44.2581 | − | 76.6573i | 0.240533 | − | 0.416616i | ||||
\(185\) | 44.4178i | 0.240096i | ||||||||
\(186\) | −84.0900 | + | 107.633i | −0.452097 | + | 0.578671i | ||||
\(187\) | −420.671 | −2.24958 | ||||||||
\(188\) | − | 8.54387i | − | 0.0454461i | ||||||
\(189\) | 120.719 | + | 145.423i | 0.638727 | + | 0.769433i | ||||
\(190\) | 47.1270 | 0.248037 | ||||||||
\(191\) | − | 23.2901i | − | 0.121938i | −0.998140 | − | 0.0609690i | \(-0.980581\pi\) | ||
0.998140 | − | 0.0609690i | \(-0.0194191\pi\) | |||||||
\(192\) | −18.9124 | − | 14.7757i | −0.0985022 | − | 0.0769566i | ||||
\(193\) | 84.8341 | 0.439555 | 0.219777 | − | 0.975550i | \(-0.429467\pi\) | ||||
0.219777 | + | 0.975550i | \(0.429467\pi\) | |||||||
\(194\) | 42.9780 | + | 24.8134i | 0.221536 | + | 0.127904i | ||||
\(195\) | −44.8785 | + | 57.4432i | −0.230146 | + | 0.294581i | ||||
\(196\) | 59.5092 | + | 77.8630i | 0.303618 | + | 0.397260i | ||||
\(197\) | − | 153.183i | − | 0.777579i | −0.921327 | − | 0.388789i | \(-0.872893\pi\) | ||
0.921327 | − | 0.388789i | \(-0.127107\pi\) | |||||||
\(198\) | 159.821 | − | 154.344i | 0.807175 | − | 0.779516i | ||||
\(199\) | 0.561812 | − | 0.973087i | 0.00282317 | − | 0.00488988i | −0.864610 | − | 0.502443i | \(-0.832435\pi\) |
0.867434 | + | 0.497553i | \(0.165768\pi\) | |||||||
\(200\) | 56.3376 | − | 32.5265i | 0.281688 | − | 0.162633i | ||||
\(201\) | 227.276 | + | 177.563i | 1.13073 | + | 0.883399i | ||||
\(202\) | 29.3517 | + | 50.8386i | 0.145305 | + | 0.251676i | ||||
\(203\) | −92.5108 | + | 61.6854i | −0.455718 | + | 0.303869i | ||||
\(204\) | 54.1664 | + | 134.062i | 0.265522 | + | 0.657168i | ||||
\(205\) | 14.1666 | 0.0691053 | ||||||||
\(206\) | −41.4806 | − | 23.9488i | −0.201362 | − | 0.116257i | ||||
\(207\) | 77.6290 | − | 270.748i | 0.375019 | − | 1.30796i | ||||
\(208\) | 34.3612 | + | 59.5154i | 0.165198 | + | 0.286132i | ||||
\(209\) | 356.199 | + | 205.652i | 1.70430 | + | 0.983980i | ||||
\(210\) | 3.15249 | − | 41.8842i | 0.0150119 | − | 0.199449i | ||||
\(211\) | −78.9195 | − | 136.693i | −0.374026 | − | 0.647832i | 0.616155 | − | 0.787625i | \(-0.288690\pi\) |
−0.990181 | + | 0.139793i | \(0.955356\pi\) | |||||||
\(212\) | 90.6308 | + | 52.3257i | 0.427504 | + | 0.246820i | ||||
\(213\) | 38.4199 | − | 49.1764i | 0.180375 | − | 0.230875i | ||||
\(214\) | 32.4508 | + | 56.2064i | 0.151639 | + | 0.262647i | ||||
\(215\) | −77.6271 | + | 44.8180i | −0.361056 | + | 0.208456i | ||||
\(216\) | −69.7663 | − | 31.0591i | −0.322992 | − | 0.143792i | ||||
\(217\) | −99.8668 | + | 202.021i | −0.460215 | + | 0.930970i | ||||
\(218\) | −53.0399 | − | 30.6226i | −0.243302 | − | 0.140471i | ||||
\(219\) | 231.883 | − | 93.6897i | 1.05882 | − | 0.427807i | ||||
\(220\) | −49.3769 | −0.224441 | ||||||||
\(221\) | − | 414.028i | − | 1.87343i | ||||||
\(222\) | 131.948 | + | 18.5426i | 0.594361 | + | 0.0835251i | ||||
\(223\) | 52.8284 | − | 91.5014i | 0.236899 | − | 0.410320i | −0.722924 | − | 0.690927i | \(-0.757202\pi\) |
0.959823 | + | 0.280607i | \(0.0905358\pi\) | |||||||
\(224\) | −35.4975 | − | 17.5478i | −0.158471 | − | 0.0783385i | ||||
\(225\) | 148.898 | − | 143.796i | 0.661770 | − | 0.639094i | ||||
\(226\) | 64.0053 | + | 110.860i | 0.283209 | + | 0.490533i | ||||
\(227\) | 52.0479 | − | 30.0498i | 0.229286 | − | 0.132378i | −0.380957 | − | 0.924593i | \(-0.624405\pi\) |
0.610243 | + | 0.792215i | \(0.291072\pi\) | |||||||
\(228\) | 19.6735 | − | 139.996i | 0.0862874 | − | 0.614018i | ||||
\(229\) | −25.5005 | + | 44.1681i | −0.111356 | + | 0.192874i | −0.916317 | − | 0.400453i | \(-0.868853\pi\) |
0.804961 | + | 0.593327i | \(0.202186\pi\) | |||||||
\(230\) | −54.2084 | + | 31.2972i | −0.235689 | + | 0.136075i | ||||
\(231\) | 206.601 | − | 302.817i | 0.894377 | − | 1.31089i | ||||
\(232\) | 22.4639 | − | 38.9086i | 0.0968271 | − | 0.167709i | ||||
\(233\) | 19.7391 | − | 11.3964i | 0.0847171 | − | 0.0489114i | −0.457043 | − | 0.889445i | \(-0.651091\pi\) |
0.541760 | + | 0.840533i | \(0.317758\pi\) | |||||||
\(234\) | 151.907 | + | 157.297i | 0.649175 | + | 0.672209i | ||||
\(235\) | −3.02091 | + | 5.23237i | −0.0128549 | + | 0.0222654i | ||||
\(236\) | − | 84.3763i | − | 0.357527i | ||||||
\(237\) | −106.770 | − | 83.4158i | −0.450506 | − | 0.351965i | ||||
\(238\) | 132.348 | + | 198.486i | 0.556086 | + | 0.833973i | ||||
\(239\) | 350.226 | − | 202.203i | 1.46538 | − | 0.846039i | 0.466131 | − | 0.884716i | \(-0.345648\pi\) |
0.999252 | + | 0.0386769i | \(0.0123143\pi\) | |||||||
\(240\) | 6.35788 | + | 15.7358i | 0.0264912 | + | 0.0655657i | ||||
\(241\) | 151.820 | + | 262.961i | 0.629961 | + | 1.09112i | 0.987559 | + | 0.157248i | \(0.0502623\pi\) |
−0.357599 | + | 0.933875i | \(0.616404\pi\) | |||||||
\(242\) | −225.011 | − | 129.910i | −0.929798 | − | 0.536819i | ||||
\(243\) | −239.311 | − | 42.1827i | −0.984818 | − | 0.173591i | ||||
\(244\) | 24.9569 | 0.102282 | ||||||||
\(245\) | −8.91364 | − | 68.7253i | −0.0363822 | − | 0.280511i | ||||
\(246\) | 5.91395 | − | 42.0835i | 0.0240405 | − | 0.171071i | ||||
\(247\) | −202.404 | + | 350.575i | −0.819451 | + | 1.41933i | ||||
\(248\) | − | 91.0579i | − | 0.367169i | ||||||
\(249\) | 4.84541 | + | 11.9924i | 0.0194595 | + | 0.0481623i | ||||
\(250\) | −96.0057 | −0.384023 | ||||||||
\(251\) | 233.378i | 0.929793i | 0.885365 | + | 0.464897i | \(0.153908\pi\) | ||||
−0.885365 | + | 0.464897i | \(0.846092\pi\) | |||||||
\(252\) | −123.106 | − | 26.8498i | −0.488516 | − | 0.106547i | ||||
\(253\) | −546.297 | −2.15928 | ||||||||
\(254\) | 191.687i | 0.754674i | ||||||||
\(255\) | 14.2290 | − | 101.253i | 0.0558001 | − | 0.397072i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −163.518 | − | 94.4073i | −0.636258 | − | 0.367344i | 0.146914 | − | 0.989149i | \(-0.453066\pi\) |
−0.783172 | + | 0.621806i | \(0.786399\pi\) | |||||||
\(258\) | 100.731 | + | 249.310i | 0.390431 | + | 0.966318i | ||||
\(259\) | 219.386 | − | 14.1678i | 0.847049 | − | 0.0547018i | ||||
\(260\) | − | 48.5972i | − | 0.186912i | ||||||
\(261\) | 39.4018 | − | 137.422i | 0.150965 | − | 0.526522i | ||||
\(262\) | 157.574 | − | 272.926i | 0.601427 | − | 1.04170i | ||||
\(263\) | −154.166 | + | 89.0076i | −0.586181 | + | 0.338432i | −0.763586 | − | 0.645706i | \(-0.776563\pi\) |
0.177405 | + | 0.984138i | \(0.443230\pi\) | |||||||
\(264\) | −20.6128 | + | 146.680i | −0.0780788 | + | 0.555606i | ||||
\(265\) | −37.0023 | − | 64.0898i | −0.139631 | − | 0.241848i | ||||
\(266\) | −15.0319 | − | 232.767i | −0.0565109 | − | 0.875062i | ||||
\(267\) | 424.694 | + | 59.6819i | 1.59061 | + | 0.223528i | ||||
\(268\) | −192.276 | −0.717449 | ||||||||
\(269\) | 446.874 | + | 258.003i | 1.66124 | + | 0.959119i | 0.972123 | + | 0.234472i | \(0.0753362\pi\) |
0.689120 | + | 0.724647i | \(0.257997\pi\) | |||||||
\(270\) | 31.7440 | + | 43.6886i | 0.117570 | + | 0.161810i | ||||
\(271\) | −117.718 | − | 203.894i | −0.434385 | − | 0.752377i | 0.562860 | − | 0.826552i | \(-0.309701\pi\) |
−0.997245 | + | 0.0741751i | \(0.976368\pi\) | |||||||
\(272\) | −83.4799 | − | 48.1971i | −0.306911 | − | 0.177195i | ||||
\(273\) | 298.035 | + | 203.339i | 1.09170 | + | 0.744831i | ||||
\(274\) | 61.1106 | + | 105.847i | 0.223031 | + | 0.386301i | ||||
\(275\) | −347.700 | − | 200.745i | −1.26436 | − | 0.729981i | ||||
\(276\) | 70.3424 | + | 174.098i | 0.254864 | + | 0.630789i | ||||
\(277\) | −254.239 | − | 440.354i | −0.917830 | − | 1.58973i | −0.802705 | − | 0.596376i | \(-0.796607\pi\) |
−0.115125 | − | 0.993351i | \(-0.536727\pi\) | |||||||
\(278\) | 3.95209 | − | 2.28174i | 0.0142161 | − | 0.00820769i | ||||
\(279\) | −70.1020 | − | 281.136i | −0.251262 | − | 1.00766i | ||||
\(280\) | 15.5346 | + | 23.2976i | 0.0554807 | + | 0.0832056i | ||||
\(281\) | −13.5306 | − | 7.81192i | −0.0481517 | − | 0.0278004i | 0.475731 | − | 0.879591i | \(-0.342184\pi\) |
−0.523883 | + | 0.851790i | \(0.675517\pi\) | |||||||
\(282\) | 14.2823 | + | 11.1583i | 0.0506463 | + | 0.0395683i | ||||
\(283\) | −509.979 | −1.80205 | −0.901023 | − | 0.433772i | \(-0.857182\pi\) | ||||
−0.901023 | + | 0.433772i | \(0.857182\pi\) | |||||||
\(284\) | 41.6035i | 0.146491i | ||||||||
\(285\) | −61.5476 | + | 78.7792i | −0.215957 | + | 0.276418i | ||||
\(286\) | 212.068 | − | 367.312i | 0.741496 | − | 1.28431i | ||||
\(287\) | −4.51866 | − | 69.9707i | −0.0157444 | − | 0.243800i | ||||
\(288\) | 49.3991 | − | 12.3178i | 0.171525 | − | 0.0427701i | ||||
\(289\) | 145.870 | + | 252.655i | 0.504742 | + | 0.874239i | ||||
\(290\) | −27.5143 | + | 15.8854i | −0.0948769 | + | 0.0547772i | ||||
\(291\) | −97.6081 | + | 39.4375i | −0.335423 | + | 0.135524i | ||||
\(292\) | −83.3648 | + | 144.392i | −0.285496 | + | 0.494494i | ||||
\(293\) | −378.046 | + | 218.265i | −1.29026 | + | 0.744932i | −0.978700 | − | 0.205294i | \(-0.934185\pi\) |
−0.311560 | + | 0.950226i | \(0.600852\pi\) | |||||||
\(294\) | −207.878 | − | 2.21094i | −0.707067 | − | 0.00752020i | ||||
\(295\) | −29.8334 | + | 51.6730i | −0.101130 | + | 0.175163i | ||||
\(296\) | −76.9289 | + | 44.4149i | −0.259895 | + | 0.150050i | ||||
\(297\) | 49.2824 | + | 468.735i | 0.165934 | + | 1.57823i | ||||
\(298\) | −138.463 | + | 239.824i | −0.464640 | + | 0.804779i | ||||
\(299\) | − | 537.671i | − | 1.79823i | ||||||
\(300\) | −19.2041 | + | 136.656i | −0.0640137 | + | 0.455519i | ||||
\(301\) | 246.123 | + | 369.116i | 0.817684 | + | 1.22630i | ||||
\(302\) | 38.5791 | − | 22.2737i | 0.127745 | − | 0.0737539i | ||||
\(303\) | −123.317 | − | 17.3296i | −0.406986 | − | 0.0571934i | ||||
\(304\) | 47.1239 | + | 81.6210i | 0.155013 | + | 0.268490i | ||||
\(305\) | −15.2839 | − | 8.82417i | −0.0501112 | − | 0.0289317i | ||||
\(306\) | −294.845 | − | 84.5380i | −0.963545 | − | 0.276268i | ||||
\(307\) | −402.350 | −1.31059 | −0.655294 | − | 0.755374i | \(-0.727455\pi\) | ||||
−0.655294 | + | 0.755374i | \(0.727455\pi\) | |||||||
\(308\) | 15.7496 | + | 243.880i | 0.0511349 | + | 0.791817i | ||||
\(309\) | 94.2073 | − | 38.0635i | 0.304878 | − | 0.123183i | ||||
\(310\) | −32.1959 | + | 55.7649i | −0.103858 | + | 0.179887i | ||||
\(311\) | 93.9460i | 0.302077i | 0.988528 | + | 0.151039i | \(0.0482618\pi\) | ||||
−0.988528 | + | 0.151039i | \(0.951738\pi\) | |||||||
\(312\) | −144.364 | − | 20.2873i | −0.462704 | − | 0.0650234i | ||||
\(313\) | 404.222 | 1.29144 | 0.645722 | − | 0.763572i | \(-0.276556\pi\) | ||||
0.645722 | + | 0.763572i | \(0.276556\pi\) | |||||||
\(314\) | − | 126.397i | − | 0.402538i | ||||||
\(315\) | 65.8982 | + | 59.9705i | 0.209201 | + | 0.190382i | ||||
\(316\) | 90.3278 | 0.285848 | ||||||||
\(317\) | − | 116.706i | − | 0.368157i | −0.982912 | − | 0.184078i | \(-0.941070\pi\) | ||
0.982912 | − | 0.184078i | \(-0.0589300\pi\) | |||||||
\(318\) | −205.833 | + | 83.1648i | −0.647274 | + | 0.261524i | ||||
\(319\) | −277.281 | −0.869221 | ||||||||
\(320\) | −9.79859 | − | 5.65722i | −0.0306206 | − | 0.0176788i | ||||
\(321\) | −136.337 | − | 19.1594i | −0.424727 | − | 0.0596865i | ||||
\(322\) | 171.872 | + | 257.760i | 0.533764 | + | 0.800497i | ||||
\(323\) | − | 567.809i | − | 1.75792i | ||||||
\(324\) | 143.034 | − | 76.0610i | 0.441463 | − | 0.234756i | ||||
\(325\) | 197.575 | − | 342.210i | 0.607922 | − | 1.05295i | ||||
\(326\) | 257.828 | − | 148.857i | 0.790885 | − | 0.456617i | ||||
\(327\) | 120.460 | − | 48.6706i | 0.368379 | − | 0.148840i | ||||
\(328\) | 14.1657 | + | 24.5356i | 0.0431880 | + | 0.0748038i | ||||
\(329\) | 26.8070 | + | 13.2517i | 0.0814801 | + | 0.0402788i | ||||
\(330\) | 64.4861 | − | 82.5404i | 0.195412 | − | 0.250122i | ||||
\(331\) | 611.339 | 1.84695 | 0.923474 | − | 0.383662i | \(-0.125337\pi\) | ||||
0.923474 | + | 0.383662i | \(0.125337\pi\) | |||||||
\(332\) | −7.46762 | − | 4.31143i | −0.0224928 | − | 0.0129862i | ||||
\(333\) | −203.320 | + | 196.353i | −0.610571 | + | 0.589649i | ||||
\(334\) | −79.9195 | − | 138.425i | −0.239280 | − | 0.414445i | ||||
\(335\) | 117.752 | + | 67.9844i | 0.351500 | + | 0.202938i | ||||
\(336\) | 75.6932 | − | 36.4216i | 0.225277 | − | 0.108398i | ||||
\(337\) | 3.59903 | + | 6.23370i | 0.0106796 | + | 0.0184976i | 0.871316 | − | 0.490723i | \(-0.163267\pi\) |
−0.860636 | + | 0.509220i | \(0.829934\pi\) | |||||||
\(338\) | 154.530 | + | 89.2180i | 0.457190 | + | 0.263959i | ||||
\(339\) | −268.909 | − | 37.7896i | −0.793243 | − | 0.111474i | ||||
\(340\) | 34.0827 | + | 59.0330i | 0.100243 | + | 0.173626i | ||||
\(341\) | −486.692 | + | 280.992i | −1.42725 | + | 0.824023i | ||||
\(342\) | 208.329 | + | 215.721i | 0.609150 | + | 0.630764i | ||||
\(343\) | −336.601 | + | 65.9467i | −0.981343 | + | 0.192265i | ||||
\(344\) | −155.244 | − | 89.6303i | −0.451291 | − | 0.260553i | ||||
\(345\) | 18.4783 | − | 131.491i | 0.0535603 | − | 0.381133i | ||||
\(346\) | 73.2911 | 0.211824 | ||||||||
\(347\) | 546.466i | 1.57483i | 0.616422 | + | 0.787416i | \(0.288581\pi\) | ||||
−0.616422 | + | 0.787416i | \(0.711419\pi\) | |||||||
\(348\) | 35.7033 | + | 88.3659i | 0.102596 | + | 0.253925i | ||||
\(349\) | −65.1506 | + | 112.844i | −0.186678 | + | 0.323336i | −0.944141 | − | 0.329543i | \(-0.893105\pi\) |
0.757463 | + | 0.652878i | \(0.226439\pi\) | |||||||
\(350\) | 14.6732 | + | 227.213i | 0.0419235 | + | 0.649179i | ||||
\(351\) | −461.334 | + | 48.5042i | −1.31434 | + | 0.138189i | ||||
\(352\) | −49.3737 | − | 85.5178i | −0.140266 | − | 0.242948i | ||||
\(353\) | 19.1736 | − | 11.0699i | 0.0543162 | − | 0.0313595i | −0.472596 | − | 0.881279i | \(-0.656683\pi\) |
0.526912 | + | 0.849920i | \(0.323350\pi\) | |||||||
\(354\) | 141.047 | + | 110.195i | 0.398437 | + | 0.311285i | ||||
\(355\) | 14.7100 | − | 25.4785i | 0.0414366 | − | 0.0717703i | ||||
\(356\) | −247.607 | + | 142.956i | −0.695524 | + | 0.401561i | ||||
\(357\) | −504.643 | − | 37.9828i | −1.41356 | − | 0.106394i | ||||
\(358\) | 136.739 | − | 236.840i | 0.381954 | − | 0.661563i | ||||
\(359\) | 52.1828 | − | 30.1278i | 0.145356 | − | 0.0839214i | −0.425558 | − | 0.904931i | \(-0.639922\pi\) |
0.570914 | + | 0.821010i | \(0.306589\pi\) | |||||||
\(360\) | −34.6079 | − | 9.92279i | −0.0961330 | − | 0.0275633i | ||||
\(361\) | −97.0829 | + | 168.152i | −0.268928 | + | 0.465796i | ||||
\(362\) | − | 248.655i | − | 0.686891i | ||||||
\(363\) | 511.027 | − | 206.475i | 1.40779 | − | 0.568802i | ||||
\(364\) | −240.029 | + | 15.5009i | −0.659419 | + | 0.0425848i | ||||
\(365\) | 102.107 | − | 58.9516i | 0.279746 | − | 0.161511i | ||||
\(366\) | −32.5936 | + | 41.7189i | −0.0890536 | + | 0.113986i | ||||
\(367\) | 3.71386 | + | 6.43260i | 0.0101195 | + | 0.0175275i | 0.871041 | − | 0.491211i | \(-0.163445\pi\) |
−0.860921 | + | 0.508738i | \(0.830112\pi\) | |||||||
\(368\) | −108.410 | − | 62.5904i | −0.294592 | − | 0.170083i | ||||
\(369\) | 62.6248 | + | 64.8468i | 0.169715 | + | 0.175737i | ||||
\(370\) | 62.8162 | 0.169774 | ||||||||
\(371\) | −304.746 | + | 203.202i | −0.821418 | + | 0.547714i | ||||
\(372\) | 152.216 | + | 118.921i | 0.409182 | + | 0.319681i | ||||
\(373\) | 297.356 | − | 515.036i | 0.797201 | − | 1.38079i | −0.124230 | − | 0.992253i | \(-0.539646\pi\) |
0.921432 | − | 0.388540i | \(-0.127020\pi\) | |||||||
\(374\) | 594.918i | 1.59069i | ||||||||
\(375\) | 125.383 | − | 160.487i | 0.334355 | − | 0.427965i | ||||
\(376\) | −12.0829 | −0.0321352 | ||||||||
\(377\) | − | 272.903i | − | 0.723881i | ||||||
\(378\) | 205.659 | − | 170.723i | 0.544072 | − | 0.451648i | ||||
\(379\) | 651.058 | 1.71783 | 0.858915 | − | 0.512118i | \(-0.171139\pi\) | ||||
0.858915 | + | 0.512118i | \(0.171139\pi\) | |||||||
\(380\) | − | 66.6476i | − | 0.175388i | ||||||
\(381\) | −320.432 | − | 250.343i | −0.841028 | − | 0.657068i | ||||
\(382\) | −32.9372 | −0.0862231 | ||||||||
\(383\) | 287.209 | + | 165.820i | 0.749893 | + | 0.432951i | 0.825655 | − | 0.564175i | \(-0.190806\pi\) |
−0.0757623 | + | 0.997126i | \(0.524139\pi\) | |||||||
\(384\) | −20.8959 | + | 26.7462i | −0.0544165 | + | 0.0696516i | ||||
\(385\) | 76.5848 | − | 154.923i | 0.198922 | − | 0.402398i | ||||
\(386\) | − | 119.973i | − | 0.310812i | ||||||
\(387\) | −548.311 | − | 157.212i | −1.41682 | − | 0.406232i | ||||
\(388\) | 35.0914 | − | 60.7801i | 0.0904418 | − | 0.156650i | ||||
\(389\) | 18.0923 | − | 10.4456i | 0.0465098 | − | 0.0268524i | −0.476565 | − | 0.879139i | \(-0.658118\pi\) |
0.523075 | + | 0.852287i | \(0.324785\pi\) | |||||||
\(390\) | 81.2370 | + | 63.4678i | 0.208300 | + | 0.162738i | ||||
\(391\) | 377.085 | + | 653.130i | 0.964412 | + | 1.67041i | ||||
\(392\) | 110.115 | − | 84.1587i | 0.280906 | − | 0.214691i | ||||
\(393\) | 250.443 | + | 619.847i | 0.637259 | + | 1.57722i | ||||
\(394\) | −216.633 | −0.549831 | ||||||||
\(395\) | −55.3178 | − | 31.9378i | −0.140045 | − | 0.0808551i | ||||
\(396\) | −218.276 | − | 226.021i | −0.551201 | − | 0.570759i | ||||
\(397\) | −309.823 | − | 536.629i | −0.780410 | − | 1.35171i | −0.931703 | − | 0.363222i | \(-0.881677\pi\) |
0.151292 | − | 0.988489i | \(-0.451657\pi\) | |||||||
\(398\) | −1.37615 | − | 0.794522i | −0.00345767 | − | 0.00199629i | ||||
\(399\) | 408.733 | + | 278.864i | 1.02439 | + | 0.698908i | ||||
\(400\) | −45.9995 | − | 79.6734i | −0.114999 | − | 0.199184i | ||||
\(401\) | −248.826 | − | 143.660i | −0.620513 | − | 0.358253i | 0.156556 | − | 0.987669i | \(-0.449961\pi\) |
−0.777069 | + | 0.629416i | \(0.783294\pi\) | |||||||
\(402\) | 251.112 | − | 321.417i | 0.624657 | − | 0.799544i | ||||
\(403\) | −276.555 | − | 479.007i | −0.686240 | − | 1.18860i | ||||
\(404\) | 71.8966 | − | 41.5095i | 0.177962 | − | 0.102746i | ||||
\(405\) | −114.489 | − | 3.99277i | −0.282689 | − | 0.00985869i | ||||
\(406\) | 87.2363 | + | 130.830i | 0.214868 | + | 0.322242i | ||||
\(407\) | 474.783 | + | 274.116i | 1.16654 | + | 0.673504i | ||||
\(408\) | 189.593 | − | 76.6029i | 0.464688 | − | 0.187752i | ||||
\(409\) | 441.994 | 1.08067 | 0.540335 | − | 0.841450i | \(-0.318297\pi\) | ||||
0.540335 | + | 0.841450i | \(0.318297\pi\) | |||||||
\(410\) | − | 20.0346i | − | 0.0488648i | ||||||
\(411\) | −256.747 | − | 36.0805i | −0.624689 | − | 0.0877870i | ||||
\(412\) | −33.8688 | + | 58.6624i | −0.0822058 | + | 0.142385i | ||||
\(413\) | 264.736 | + | 130.870i | 0.641008 | + | 0.316875i | ||||
\(414\) | −382.895 | − | 109.784i | −0.924868 | − | 0.265179i | ||||
\(415\) | 3.04884 | + | 5.28074i | 0.00734660 | + | 0.0127247i | ||||
\(416\) | 84.1674 | − | 48.5941i | 0.202326 | − | 0.116813i | ||||
\(417\) | −1.34717 | + | 9.58640i | −0.00323062 | + | 0.0229890i | ||||
\(418\) | 290.835 | − | 503.742i | 0.695779 | − | 1.20512i | ||||
\(419\) | 281.777 | − | 162.684i | 0.672500 | − | 0.388268i | −0.124523 | − | 0.992217i | \(-0.539740\pi\) |
0.797023 | + | 0.603949i | \(0.206407\pi\) | |||||||
\(420\) | −59.2333 | − | 4.45830i | −0.141032 | − | 0.0106150i | ||||
\(421\) | −201.041 | + | 348.214i | −0.477533 | + | 0.827111i | −0.999668 | − | 0.0257517i | \(-0.991802\pi\) |
0.522136 | + | 0.852862i | \(0.325135\pi\) | |||||||
\(422\) | −193.312 | + | 111.609i | −0.458086 | + | 0.264476i | ||||
\(423\) | −37.3051 | + | 9.30213i | −0.0881918 | + | 0.0219908i | ||||
\(424\) | 73.9998 | − | 128.171i | 0.174528 | − | 0.302291i | ||||
\(425\) | 554.261i | 1.30414i | ||||||||
\(426\) | −69.5459 | − | 54.3340i | −0.163253 | − | 0.127545i | ||||
\(427\) | −38.7087 | + | 78.3039i | −0.0906528 | + | 0.183382i | ||||
\(428\) | 79.4879 | − | 45.8924i | 0.185719 | − | 0.107225i | ||||
\(429\) | 337.053 | + | 834.209i | 0.785672 | + | 1.94454i | ||||
\(430\) | 63.3823 | + | 109.781i | 0.147401 | + | 0.255305i | ||||
\(431\) | 148.166 | + | 85.5439i | 0.343774 | + | 0.198478i | 0.661939 | − | 0.749557i | \(-0.269734\pi\) |
−0.318166 | + | 0.948035i | \(0.603067\pi\) | |||||||
\(432\) | −43.9242 | + | 98.6644i | −0.101676 | + | 0.228390i | ||||
\(433\) | −225.192 | −0.520075 | −0.260038 | − | 0.965599i | \(-0.583735\pi\) | ||||
−0.260038 | + | 0.965599i | \(0.583735\pi\) | |||||||
\(434\) | 285.700 | + | 141.233i | 0.658295 | + | 0.325422i | ||||
\(435\) | 9.37894 | − | 66.7402i | 0.0215608 | − | 0.153426i | ||||
\(436\) | −43.3069 | + | 75.0098i | −0.0993278 | + | 0.172041i | ||||
\(437\) | − | 737.377i | − | 1.68736i | ||||||
\(438\) | −132.497 | − | 327.931i | −0.302505 | − | 0.748702i | ||||
\(439\) | −59.3313 | −0.135151 | −0.0675755 | − | 0.997714i | \(-0.521526\pi\) | ||||
−0.0675755 | + | 0.997714i | \(0.521526\pi\) | |||||||
\(440\) | 69.8295i | 0.158703i | ||||||||
\(441\) | 275.183 | − | 344.609i | 0.623998 | − | 0.781426i | ||||
\(442\) | −585.524 | −1.32472 | ||||||||
\(443\) | 306.058i | 0.690875i | 0.938442 | + | 0.345438i | \(0.112270\pi\) | ||||
−0.938442 | + | 0.345438i | \(0.887730\pi\) | |||||||
\(444\) | 26.2231 | − | 186.603i | 0.0590611 | − | 0.420277i | ||||
\(445\) | 202.183 | 0.454344 | ||||||||
\(446\) | −129.403 | − | 74.7106i | −0.290140 | − | 0.167513i | ||||
\(447\) | −220.068 | − | 544.669i | −0.492322 | − | 1.21850i | ||||
\(448\) | −24.8164 | + | 50.2011i | −0.0553937 | + | 0.112056i | ||||
\(449\) | − | 446.116i | − | 0.993578i | −0.867871 | − | 0.496789i | \(-0.834512\pi\) | ||
0.867871 | − | 0.496789i | \(-0.165488\pi\) | |||||||
\(450\) | −203.358 | − | 210.574i | −0.451908 | − | 0.467942i | ||||
\(451\) | 87.4265 | − | 151.427i | 0.193850 | − | 0.335759i | ||||
\(452\) | 156.780 | − | 90.5172i | 0.346859 | − | 0.200259i | ||||
\(453\) | −13.1507 | + | 93.5797i | −0.0290302 | + | 0.206578i | ||||
\(454\) | −42.4969 | − | 73.6068i | −0.0936055 | − | 0.162129i | ||||
\(455\) | 152.477 | + | 75.3755i | 0.335114 | + | 0.165660i | ||||
\(456\) | −197.984 | − | 27.8226i | −0.434176 | − | 0.0610144i | ||||
\(457\) | 317.688 | 0.695160 | 0.347580 | − | 0.937650i | \(-0.387004\pi\) | ||||
0.347580 | + | 0.937650i | \(0.387004\pi\) | |||||||
\(458\) | 62.4632 | + | 36.0631i | 0.136382 | + | 0.0787404i | ||||
\(459\) | 526.383 | − | 382.467i | 1.14680 | − | 0.833262i | ||||
\(460\) | 44.2610 | + | 76.6623i | 0.0962195 | + | 0.166657i | ||||
\(461\) | −66.3830 | − | 38.3263i | −0.143998 | − | 0.0831372i | 0.426270 | − | 0.904596i | \(-0.359827\pi\) |
−0.570268 | + | 0.821459i | \(0.693161\pi\) | |||||||
\(462\) | −428.247 | − | 292.178i | −0.926942 | − | 0.632420i | ||||
\(463\) | 155.730 | + | 269.733i | 0.336350 | + | 0.582576i | 0.983743 | − | 0.179580i | \(-0.0574740\pi\) |
−0.647393 | + | 0.762156i | \(0.724141\pi\) | |||||||
\(464\) | −55.0250 | − | 31.7687i | −0.118588 | − | 0.0684671i | ||||
\(465\) | −51.1711 | − | 126.649i | −0.110045 | − | 0.272363i | ||||
\(466\) | −16.1169 | − | 27.9153i | −0.0345856 | − | 0.0599040i | ||||
\(467\) | 265.027 | − | 153.013i | 0.567510 | − | 0.327652i | −0.188644 | − | 0.982045i | \(-0.560409\pi\) |
0.756154 | + | 0.654394i | \(0.227076\pi\) | |||||||
\(468\) | 222.452 | − | 214.829i | 0.475324 | − | 0.459036i | ||||
\(469\) | 298.225 | − | 603.280i | 0.635875 | − | 1.28631i | ||||
\(470\) | 7.39968 | + | 4.27221i | 0.0157440 | + | 0.00908981i | ||||
\(471\) | 211.290 | + | 165.074i | 0.448598 | + | 0.350475i | ||||
\(472\) | −119.326 | −0.252809 | ||||||||
\(473\) | 1106.35i | 2.33900i | ||||||||
\(474\) | −117.968 | + | 150.995i | −0.248877 | + | 0.318556i | ||||
\(475\) | 270.959 | − | 469.316i | 0.570441 | − | 0.988033i | ||||
\(476\) | 280.701 | − | 187.169i | 0.589708 | − | 0.393212i | ||||
\(477\) | 129.796 | − | 452.692i | 0.272109 | − | 0.949039i | ||||
\(478\) | −285.959 | − | 495.295i | −0.598240 | − | 1.03618i | ||||
\(479\) | −408.566 | + | 235.886i | −0.852956 | + | 0.492454i | −0.861647 | − | 0.507508i | \(-0.830567\pi\) |
0.00869133 | + | 0.999962i | \(0.497233\pi\) | |||||||
\(480\) | 22.2537 | − | 8.99139i | 0.0463620 | − | 0.0187321i | ||||
\(481\) | −269.788 | + | 467.286i | −0.560889 | + | 0.971489i | ||||
\(482\) | 371.883 | − | 214.707i | 0.771541 | − | 0.445449i | ||||
\(483\) | −655.346 | − | 49.3258i | −1.35682 | − | 0.102124i | ||||
\(484\) | −183.721 | + | 318.214i | −0.379588 | + | 0.657466i | ||||
\(485\) | −42.9808 | + | 24.8150i | −0.0886202 | + | 0.0511649i | ||||
\(486\) | −59.6554 | + | 338.436i | −0.122748 | + | 0.696371i | ||||
\(487\) | 195.229 | − | 338.146i | 0.400880 | − | 0.694345i | −0.592952 | − | 0.805238i | \(-0.702038\pi\) |
0.993832 | + | 0.110893i | \(0.0353710\pi\) | |||||||
\(488\) | − | 35.2944i | − | 0.0723246i | ||||||
\(489\) | −87.8873 | + | 625.403i | −0.179729 | + | 1.27894i | ||||
\(490\) | −97.1923 | + | 12.6058i | −0.198352 | + | 0.0257261i | ||||
\(491\) | −498.578 | + | 287.854i | −1.01543 | + | 0.586261i | −0.912778 | − | 0.408456i | \(-0.866067\pi\) |
−0.102656 | + | 0.994717i | \(0.532734\pi\) | |||||||
\(492\) | −59.5150 | − | 8.36359i | −0.120965 | − | 0.0169992i | ||||
\(493\) | 191.395 | + | 331.506i | 0.388226 | + | 0.672426i | ||||
\(494\) | 495.787 | + | 286.243i | 1.00362 | + | 0.579439i | ||||
\(495\) | 53.7591 | + | 215.595i | 0.108604 | + | 0.435545i | ||||
\(496\) | −128.775 | −0.259628 | ||||||||
\(497\) | −130.534 | − | 64.5280i | −0.262643 | − | 0.129835i | ||||
\(498\) | 16.9598 | − | 6.85244i | 0.0340559 | − | 0.0137599i | ||||
\(499\) | 359.065 | − | 621.919i | 0.719569 | − | 1.24633i | −0.241602 | − | 0.970375i | \(-0.577673\pi\) |
0.961171 | − | 0.275954i | \(-0.0889939\pi\) | |||||||
\(500\) | 135.773i | 0.271545i | ||||||||
\(501\) | 335.770 | + | 47.1855i | 0.670200 | + | 0.0941826i | ||||
\(502\) | 330.046 | 0.657463 | ||||||||
\(503\) | 475.997i | 0.946316i | 0.880978 | + | 0.473158i | \(0.156886\pi\) | ||||
−0.880978 | + | 0.473158i | \(0.843114\pi\) | |||||||
\(504\) | −37.9713 | + | 174.098i | −0.0753399 | + | 0.345433i | ||||
\(505\) | −58.7071 | −0.116252 | ||||||||
\(506\) | 772.581i | 1.52684i | ||||||||
\(507\) | −350.956 | + | 141.800i | −0.692221 | + | 0.279685i | ||||
\(508\) | 271.087 | 0.533635 | ||||||||
\(509\) | 439.257 | + | 253.605i | 0.862981 | + | 0.498242i | 0.865009 | − | 0.501756i | \(-0.167312\pi\) |
−0.00202828 | + | 0.999998i | \(0.500646\pi\) | |||||||
\(510\) | −143.194 | − | 20.1229i | −0.280772 | − | 0.0394566i | ||||
\(511\) | −323.739 | − | 485.518i | −0.633540 | − | 0.950134i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −632.685 | + | 66.5200i | −1.23331 | + | 0.129669i | ||||
\(514\) | −133.512 | + | 231.250i | −0.259751 | + | 0.449902i | ||||
\(515\) | 41.4833 | − | 23.9504i | 0.0805501 | − | 0.0465056i | ||||
\(516\) | 352.578 | − | 142.455i | 0.683290 | − | 0.276076i | ||||
\(517\) | 37.2860 | + | 64.5812i | 0.0721199 | + | 0.124915i | ||||
\(518\) | −20.0362 | − | 310.258i | −0.0386800 | − | 0.598954i | ||||
\(519\) | −95.7178 | + | 122.516i | −0.184427 | + | 0.236062i | ||||
\(520\) | −68.7269 | −0.132167 | ||||||||
\(521\) | −332.558 | − | 192.003i | −0.638308 | − | 0.368527i | 0.145655 | − | 0.989336i | \(-0.453471\pi\) |
−0.783962 | + | 0.620808i | \(0.786805\pi\) | |||||||
\(522\) | −194.344 | − | 55.7225i | −0.372307 | − | 0.106748i | ||||
\(523\) | 182.193 | + | 315.567i | 0.348361 | + | 0.603379i | 0.985959 | − | 0.166990i | \(-0.0534049\pi\) |
−0.637597 | + | 0.770370i | \(0.720072\pi\) | |||||||
\(524\) | −385.976 | − | 222.843i | −0.736595 | − | 0.425273i | ||||
\(525\) | −398.980 | − | 272.210i | −0.759963 | − | 0.518496i | ||||
\(526\) | 125.876 | + | 218.023i | 0.239308 | + | 0.414493i | ||||
\(527\) | 671.884 | + | 387.913i | 1.27492 | + | 0.736077i | ||||
\(528\) | 207.437 | + | 29.1509i | 0.392873 | + | 0.0552100i | ||||
\(529\) | 225.195 | + | 390.050i | 0.425700 | + | 0.737335i | ||||
\(530\) | −90.6367 | + | 52.3291i | −0.171013 | + | 0.0987342i | ||||
\(531\) | −368.413 | + | 91.8646i | −0.693809 | + | 0.173003i | ||||
\(532\) | −329.182 | + | 21.2583i | −0.618763 | + | 0.0399592i | ||||
\(533\) | 149.036 | + | 86.0459i | 0.279617 | + | 0.161437i | ||||
\(534\) | 84.4029 | − | 600.608i | 0.158058 | − | 1.12473i | ||||
\(535\) | −64.9058 | −0.121319 | ||||||||
\(536\) | 271.920i | 0.507313i | ||||||||
\(537\) | 217.329 | + | 537.891i | 0.404710 | + | 1.00166i | ||||
\(538\) | 364.871 | − | 631.976i | 0.678200 | − | 1.17468i | ||||
\(539\) | −789.616 | − | 328.848i | −1.46497 | − | 0.610107i | ||||
\(540\) | 61.7851 | − | 44.8927i | 0.114417 | − | 0.0831347i | ||||
\(541\) | 473.259 | + | 819.709i | 0.874786 | + | 1.51517i | 0.856990 | + | 0.515333i | \(0.172332\pi\) |
0.0177960 | + | 0.999842i | \(0.494335\pi\) | |||||||
\(542\) | −288.350 | + | 166.479i | −0.532011 | + | 0.307157i | ||||
\(543\) | 415.661 | + | 324.742i | 0.765489 | + | 0.598051i | ||||
\(544\) | −68.1610 | + | 118.058i | −0.125296 | + | 0.217019i | ||||
\(545\) | 53.0434 | − | 30.6246i | 0.0973273 | − | 0.0561919i | ||||
\(546\) | 287.564 | − | 421.485i | 0.526675 | − | 0.771950i | ||||
\(547\) | −294.515 | + | 510.116i | −0.538419 | + | 0.932570i | 0.460570 | + | 0.887623i | \(0.347645\pi\) |
−0.998989 | + | 0.0449464i | \(0.985688\pi\) | |||||||
\(548\) | 149.690 | − | 86.4234i | 0.273156 | − | 0.157707i | ||||
\(549\) | −27.1718 | − | 108.969i | −0.0494933 | − | 0.198487i | ||||
\(550\) | −283.896 | + | 491.722i | −0.516174 | + | 0.894040i | ||||
\(551\) | − | 374.267i | − | 0.679250i | ||||||
\(552\) | 246.211 | − | 99.4792i | 0.446035 | − | 0.180216i | ||||
\(553\) | −140.101 | + | 283.410i | −0.253346 | + | 0.512495i | ||||
\(554\) | −622.755 | + | 359.548i | −1.12411 | + | 0.649003i | ||||
\(555\) | −82.0377 | + | 105.006i | −0.147816 | + | 0.189200i | ||||
\(556\) | −3.22687 | − | 5.58910i | −0.00580372 | − | 0.0100523i | ||||
\(557\) | −531.266 | − | 306.727i | −0.953799 | − | 0.550676i | −0.0595401 | − | 0.998226i | \(-0.518963\pi\) |
−0.894259 | + | 0.447550i | \(0.852297\pi\) | |||||||
\(558\) | −397.587 | + | 99.1392i | −0.712521 | + | 0.177669i | ||||
\(559\) | −1088.88 | −1.94790 | ||||||||
\(560\) | 32.9478 | − | 21.9693i | 0.0588353 | − | 0.0392308i | ||||
\(561\) | −994.488 | − | 776.961i | −1.77271 | − | 1.38496i | ||||
\(562\) | −11.0477 | + | 19.1352i | −0.0196579 | + | 0.0340484i | ||||
\(563\) | − | 208.343i | − | 0.370059i | −0.982733 | − | 0.185030i | \(-0.940762\pi\) | ||
0.982733 | − | 0.185030i | \(-0.0592381\pi\) | |||||||
\(564\) | 15.7802 | − | 20.1982i | 0.0279790 | − | 0.0358123i | ||||
\(565\) | −128.019 | −0.226582 | ||||||||
\(566\) | 721.219i | 1.27424i | ||||||||
\(567\) | 16.7973 | + | 566.751i | 0.0296249 | + | 0.999561i | ||||
\(568\) | 58.8362 | 0.103585 | ||||||||
\(569\) | − | 944.539i | − | 1.66000i | −0.557765 | − | 0.829999i | \(-0.688341\pi\) | ||
0.557765 | − | 0.829999i | \(-0.311659\pi\) | |||||||
\(570\) | 111.411 | + | 87.0415i | 0.195457 | + | 0.152704i | ||||
\(571\) | −114.520 | −0.200561 | −0.100280 | − | 0.994959i | \(-0.531974\pi\) | ||||
−0.100280 | + | 0.994959i | \(0.531974\pi\) | |||||||
\(572\) | −519.458 | − | 299.909i | −0.908143 | − | 0.524317i | ||||
\(573\) | 43.0159 | − | 55.0592i | 0.0750714 | − | 0.0960893i | ||||
\(574\) | −98.9535 | + | 6.39035i | −0.172393 | + | 0.0111330i | ||||
\(575\) | 719.782i | 1.25179i | ||||||||
\(576\) | −17.4200 | − | 69.8609i | −0.0302430 | − | 0.121286i | ||||
\(577\) | 493.595 | − | 854.932i | 0.855451 | − | 1.48168i | −0.0207756 | − | 0.999784i | \(-0.506614\pi\) |
0.876226 | − | 0.481900i | \(-0.160053\pi\) | |||||||
\(578\) | 357.308 | − | 206.292i | 0.618180 | − | 0.356907i | ||||
\(579\) | 200.552 | + | 156.685i | 0.346377 | + | 0.270613i | ||||
\(580\) | 22.4653 | + | 38.9111i | 0.0387333 | + | 0.0670881i | ||||
\(581\) | 25.1099 | − | 16.7430i | 0.0432183 | − | 0.0288176i | ||||
\(582\) | 55.7731 | + | 138.039i | 0.0958301 | + | 0.237180i | ||||
\(583\) | −913.411 | −1.56674 | ||||||||
\(584\) | 204.201 | + | 117.896i | 0.349660 | + | 0.201876i | ||||
\(585\) | −212.190 | + | 52.9102i | −0.362719 | + | 0.0904448i | ||||
\(586\) | 308.674 | + | 534.638i | 0.526747 | + | 0.912352i | ||||
\(587\) | −439.957 | − | 254.009i | −0.749501 | − | 0.432725i | 0.0760123 | − | 0.997107i | \(-0.475781\pi\) |
−0.825514 | + | 0.564382i | \(0.809115\pi\) | |||||||
\(588\) | −3.12674 | + | 293.983i | −0.00531759 | + | 0.499972i | ||||
\(589\) | −379.275 | − | 656.923i | −0.643930 | − | 1.11532i | ||||
\(590\) | 73.0767 | + | 42.1909i | 0.123859 | + | 0.0715099i | ||||
\(591\) | 282.922 | − | 362.133i | 0.478718 | − | 0.612746i | ||||
\(592\) | 62.8122 | + | 108.794i | 0.106102 | + | 0.183773i | ||||
\(593\) | 105.925 | − | 61.1560i | 0.178626 | − | 0.103130i | −0.408021 | − | 0.912973i | \(-0.633781\pi\) |
0.586647 | + | 0.809843i | \(0.300448\pi\) | |||||||
\(594\) | 662.892 | − | 69.6959i | 1.11598 | − | 0.117333i | ||||
\(595\) | −238.083 | + | 15.3752i | −0.400140 | + | 0.0258407i | ||||
\(596\) | 339.163 | + | 195.816i | 0.569065 | + | 0.328550i | ||||
\(597\) | 3.12540 | − | 1.26279i | 0.00523518 | − | 0.00211522i | ||||
\(598\) | −760.382 | −1.27154 | ||||||||
\(599\) | − | 934.348i | − | 1.55985i | −0.625875 | − | 0.779923i | \(-0.715258\pi\) | ||
0.625875 | − | 0.779923i | \(-0.284742\pi\) | |||||||
\(600\) | 193.260 | + | 27.1587i | 0.322101 | + | 0.0452645i | ||||
\(601\) | 109.192 | − | 189.127i | 0.181685 | − | 0.314687i | −0.760770 | − | 0.649022i | \(-0.775178\pi\) |
0.942454 | + | 0.334335i | \(0.108512\pi\) | |||||||
\(602\) | 522.009 | − | 348.070i | 0.867124 | − | 0.578190i | ||||
\(603\) | 209.341 | + | 839.538i | 0.347165 | + | 1.39227i | ||||
\(604\) | −31.4997 | − | 54.5591i | −0.0521519 | − | 0.0903297i | ||||
\(605\) | 225.026 | − | 129.919i | 0.371943 | − | 0.214742i | ||||
\(606\) | −24.5078 | + | 174.396i | −0.0404419 | + | 0.287783i | ||||
\(607\) | 532.851 | − | 922.924i | 0.877843 | − | 1.52047i | 0.0241397 | − | 0.999709i | \(-0.492315\pi\) |
0.853703 | − | 0.520760i | \(-0.174351\pi\) | |||||||
\(608\) | 115.430 | − | 66.6433i | 0.189851 | − | 0.109611i | ||||
\(609\) | −332.631 | − | 25.0360i | −0.546192 | − | 0.0411101i | ||||
\(610\) | −12.4793 | + | 21.6147i | −0.0204578 | + | 0.0354339i | ||||
\(611\) | −63.5614 | + | 36.6972i | −0.104029 | + | 0.0600609i | ||||
\(612\) | −119.555 | + | 416.973i | −0.195351 | + | 0.681329i | ||||
\(613\) | −146.885 | + | 254.412i | −0.239616 | + | 0.415027i | −0.960604 | − | 0.277920i | \(-0.910355\pi\) |
0.720988 | + | 0.692947i | \(0.243688\pi\) | |||||||
\(614\) | 569.009i | 0.926725i | ||||||||
\(615\) | 33.4905 | + | 26.1651i | 0.0544562 | + | 0.0425448i | ||||
\(616\) | 344.898 | − | 22.2732i | 0.559899 | − | 0.0361579i | ||||
\(617\) | −103.145 | + | 59.5509i | −0.167172 | + | 0.0965168i | −0.581252 | − | 0.813724i | \(-0.697437\pi\) |
0.414080 | + | 0.910241i | \(0.364103\pi\) | |||||||
\(618\) | −53.8299 | − | 133.229i | −0.0871034 | − | 0.215581i | ||||
\(619\) | 211.746 | + | 366.755i | 0.342077 | + | 0.592495i | 0.984818 | − | 0.173588i | \(-0.0555362\pi\) |
−0.642741 | + | 0.766084i | \(0.722203\pi\) | |||||||
\(620\) | 78.8635 | + | 45.5319i | 0.127199 | + | 0.0734385i | ||||
\(621\) | 683.579 | − | 496.685i | 1.10077 | − | 0.799815i | ||||
\(622\) | 132.860 | 0.213601 | ||||||||
\(623\) | −64.4895 | − | 998.610i | −0.103514 | − | 1.60290i | ||||
\(624\) | −28.6906 | + | 204.161i | −0.0459785 | + | 0.327181i | ||||
\(625\) | −239.491 | + | 414.810i | −0.383185 | + | 0.663696i | ||||
\(626\) | − | 571.657i | − | 0.913189i | ||||||
\(627\) | 462.244 | + | 1144.06i | 0.737231 | + | 1.82465i | ||||
\(628\) | −178.752 | −0.284637 | ||||||||
\(629\) | − | 756.842i | − | 1.20325i | ||||||
\(630\) | 84.8111 | − | 93.1941i | 0.134621 | − | 0.147927i | ||||
\(631\) | 1159.89 | 1.83818 | 0.919091 | − | 0.394046i | \(-0.128925\pi\) | ||||
0.919091 | + | 0.394046i | \(0.128925\pi\) | |||||||
\(632\) | − | 127.743i | − | 0.202125i | ||||||
\(633\) | 65.8954 | − | 468.909i | 0.104100 | − | 0.740773i | ||||
\(634\) | −165.047 | −0.260326 | ||||||||
\(635\) | −166.017 | − | 95.8498i | −0.261444 | − | 0.150945i | ||||
\(636\) | 117.613 | + | 291.092i | 0.184926 | + | 0.457692i | ||||
\(637\) | 323.655 | − | 777.148i | 0.508092 | − | 1.22001i | ||||
\(638\) | 392.135i | 0.614632i | ||||||||
\(639\) | 181.653 | − | 45.2957i | 0.284278 | − | 0.0708853i | ||||
\(640\) | −8.00052 | + | 13.8573i | −0.0125008 | + | 0.0216520i | ||||
\(641\) | −320.420 | + | 184.994i | −0.499875 | + | 0.288603i | −0.728662 | − | 0.684874i | \(-0.759857\pi\) |
0.228787 | + | 0.973476i | \(0.426524\pi\) | |||||||
\(642\) | −27.0955 | + | 192.810i | −0.0422048 | + | 0.300328i | ||||
\(643\) | 223.115 | + | 386.446i | 0.346990 | + | 0.601005i | 0.985713 | − | 0.168432i | \(-0.0538704\pi\) |
−0.638723 | + | 0.769437i | \(0.720537\pi\) | |||||||
\(644\) | 364.528 | − | 243.064i | 0.566037 | − | 0.377428i | ||||
\(645\) | −266.292 | − | 37.4217i | −0.412855 | − | 0.0580182i | ||||
\(646\) | −803.004 | −1.24304 | ||||||||
\(647\) | −287.119 | − | 165.768i | −0.443770 | − | 0.256210i | 0.261426 | − | 0.965224i | \(-0.415807\pi\) |
−0.705195 | + | 0.709013i | \(0.749141\pi\) | |||||||
\(648\) | −107.566 | − | 202.281i | −0.165998 | − | 0.312161i | ||||
\(649\) | 368.223 | + | 637.782i | 0.567370 | + | 0.982714i | ||||
\(650\) | −483.957 | − | 279.413i | −0.744550 | − | 0.429866i | ||||
\(651\) | −609.214 | + | 293.138i | −0.935812 | + | 0.450288i | ||||
\(652\) | −210.516 | − | 364.624i | −0.322877 | − | 0.559240i | ||||
\(653\) | −689.144 | − | 397.877i | −1.05535 | − | 0.609307i | −0.131208 | − | 0.991355i | \(-0.541886\pi\) |
−0.924143 | + | 0.382048i | \(0.875219\pi\) | |||||||
\(654\) | −68.8306 | − | 170.356i | −0.105246 | − | 0.260483i | ||||
\(655\) | 157.584 | + | 272.944i | 0.240586 | + | 0.416708i | ||||
\(656\) | 34.6986 | − | 20.0333i | 0.0528943 | − | 0.0305385i | ||||
\(657\) | 721.224 | + | 206.790i | 1.09775 | + | 0.314748i | ||||
\(658\) | 18.7408 | − | 37.9108i | 0.0284814 | − | 0.0576151i | ||||
\(659\) | −647.026 | − | 373.560i | −0.981830 | − | 0.566860i | −0.0790076 | − | 0.996874i | \(-0.525175\pi\) |
−0.902822 | + | 0.430014i | \(0.858508\pi\) | |||||||
\(660\) | −116.730 | − | 91.1971i | −0.176863 | − | 0.138177i | ||||
\(661\) | −1126.89 | −1.70482 | −0.852411 | − | 0.522872i | \(-0.824861\pi\) | ||||
−0.852411 | + | 0.522872i | \(0.824861\pi\) | |||||||
\(662\) | − | 864.565i | − | 1.30599i | ||||||
\(663\) | 764.692 | − | 978.784i | 1.15338 | − | 1.47630i | ||||
\(664\) | −6.09728 | + | 10.5608i | −0.00918266 | + | 0.0159048i | ||||
\(665\) | 209.111 | + | 103.372i | 0.314453 | + | 0.155447i | ||||
\(666\) | 277.685 | + | 287.538i | 0.416945 | + | 0.431739i | ||||
\(667\) | 248.552 | + | 430.505i | 0.372642 | + | 0.645435i | ||||
\(668\) | −195.762 | + | 113.023i | −0.293057 | + | 0.169196i | ||||
\(669\) | 293.888 | − | 118.743i | 0.439295 | − | 0.177493i | ||||
\(670\) | 96.1444 | − | 166.527i | 0.143499 | − | 0.248548i | ||||
\(671\) | −188.644 | + | 108.913i | −0.281138 | + | 0.162315i | ||||
\(672\) | −51.5079 | − | 107.046i | −0.0766487 | − | 0.159295i | ||||
\(673\) | 264.569 | − | 458.246i | 0.393118 | − | 0.680901i | −0.599741 | − | 0.800194i | \(-0.704730\pi\) |
0.992859 | + | 0.119294i | \(0.0380630\pi\) | |||||||
\(674\) | 8.81578 | − | 5.08979i | 0.0130798 | − | 0.00755162i | ||||
\(675\) | 617.589 | − | 64.9328i | 0.914947 | − | 0.0961967i | ||||
\(676\) | 126.173 | − | 218.539i | 0.186647 | − | 0.323282i | ||||
\(677\) | 188.228i | 0.278032i | 0.990290 | + | 0.139016i | \(0.0443940\pi\) | ||||
−0.990290 | + | 0.139016i | \(0.955606\pi\) | |||||||
\(678\) | −53.4425 | + | 380.295i | −0.0788238 | + | 0.560907i | ||||
\(679\) | 136.274 | + | 204.373i | 0.200698 | + | 0.300991i | ||||
\(680\) | 83.4853 | − | 48.2002i | 0.122772 | − | 0.0708827i | ||||
\(681\) | 178.545 | + | 25.0907i | 0.262180 | + | 0.0368439i | ||||
\(682\) | 397.382 | + | 688.287i | 0.582672 | + | 1.00922i | ||||
\(683\) | 300.248 | + | 173.348i | 0.439601 | + | 0.253804i | 0.703429 | − | 0.710766i | \(-0.251652\pi\) |
−0.263827 | + | 0.964570i | \(0.584985\pi\) | |||||||
\(684\) | 305.076 | − | 294.622i | 0.446018 | − | 0.430734i | ||||
\(685\) | −122.229 | −0.178436 | ||||||||
\(686\) | 93.2628 | + | 476.025i | 0.135952 | + | 0.693914i | ||||
\(687\) | −141.861 | + | 57.3175i | −0.206494 | + | 0.0834316i | ||||
\(688\) | −126.756 | + | 219.548i | −0.184239 | + | 0.319111i | ||||
\(689\) | − | 898.988i | − | 1.30477i | ||||||
\(690\) | −185.956 | − | 26.1323i | −0.269502 | − | 0.0378728i | ||||
\(691\) | 795.908 | 1.15182 | 0.575910 | − | 0.817513i | \(-0.304648\pi\) | ||||
0.575910 | + | 0.817513i | \(0.304648\pi\) | |||||||
\(692\) | − | 103.649i | − | 0.149782i | ||||||
\(693\) | 1047.71 | − | 334.291i | 1.51184 | − | 0.482382i | ||||
\(694\) | 772.820 | 1.11357 | ||||||||
\(695\) | 4.56377i | 0.00656658i | ||||||||
\(696\) | 124.968 | − | 50.4921i | 0.179552 | − | 0.0725462i | ||||
\(697\) | −241.387 | −0.346322 | ||||||||
\(698\) | 159.586 | + | 92.1368i | 0.228633 | + | 0.132001i | ||||
\(699\) | 67.7128 | + | 9.51562i | 0.0968710 | + | 0.0136132i | ||||
\(700\) | 321.327 | − | 20.7511i | 0.459039 | − | 0.0296444i | ||||
\(701\) | 1048.99i | 1.49643i | 0.663459 | + | 0.748213i | \(0.269088\pi\) | ||||
−0.663459 | + | 0.748213i | \(0.730912\pi\) | |||||||
\(702\) | 68.5953 | + | 652.424i | 0.0977141 | + | 0.929379i | ||||
\(703\) | −369.994 | + | 640.849i | −0.526308 | + | 0.911592i | ||||
\(704\) | −120.940 | + | 69.8250i | −0.171790 | + | 0.0991833i | ||||
\(705\) | −16.8055 | + | 6.79011i | −0.0238377 | + | 0.00963136i | ||||
\(706\) | −15.6552 | − | 27.1156i | −0.0221745 | − | 0.0384074i | ||||
\(707\) | 18.7256 | + | 289.963i | 0.0264860 | + | 0.410131i | ||||
\(708\) | 155.839 | − | 199.470i | 0.220112 | − | 0.281737i | ||||
\(709\) | −1020.18 | −1.43890 | −0.719448 | − | 0.694547i | \(-0.755605\pi\) | ||||
−0.719448 | + | 0.694547i | \(0.755605\pi\) | |||||||
\(710\) | −36.0320 | − | 20.8031i | −0.0507493 | − | 0.0293001i | ||||
\(711\) | −98.3443 | − | 394.399i | −0.138318 | − | 0.554710i | ||||
\(712\) | 202.170 | + | 350.169i | 0.283946 | + | 0.491810i | ||||
\(713\) | 872.532 | + | 503.756i | 1.22375 | + | 0.706531i | ||||
\(714\) | −53.7158 | + | 713.672i | −0.0752322 | + | 0.999541i | ||||
\(715\) | 212.081 | + | 367.336i | 0.296617 | + | 0.513756i | ||||
\(716\) | −334.942 | − | 193.379i | −0.467796 | − | 0.270082i | ||||
\(717\) | 1201.41 | + | 168.834i | 1.67561 | + | 0.235472i | ||||
\(718\) | −42.6071 | − | 73.7977i | −0.0593414 | − | 0.102782i | ||||
\(719\) | −836.024 | + | 482.679i | −1.16276 | + | 0.671320i | −0.951964 | − | 0.306210i | \(-0.900939\pi\) |
−0.210796 | + | 0.977530i | \(0.567606\pi\) | |||||||
\(720\) | −14.0329 | + | 48.9429i | −0.0194902 | + | 0.0679763i | ||||
\(721\) | −131.526 | − | 197.252i | −0.182422 | − | 0.273582i | ||||
\(722\) | 237.803 | + | 137.296i | 0.329368 | + | 0.190161i | ||||
\(723\) | −126.766 | + | 902.059i | −0.175333 | + | 1.24766i | ||||
\(724\) | −351.651 | −0.485705 | ||||||||
\(725\) | 365.336i | 0.503912i | ||||||||
\(726\) | −292.000 | − | 722.701i | −0.402203 | − | 0.995455i | ||||
\(727\) | −679.328 | + | 1176.63i | −0.934426 | + | 1.61847i | −0.158773 | + | 0.987315i | \(0.550754\pi\) |
−0.775654 | + | 0.631159i | \(0.782580\pi\) | |||||||
\(728\) | 21.9215 | + | 339.452i | 0.0301120 | + | 0.466280i | ||||
\(729\) | −487.834 | − | 541.719i | −0.669182 | − | 0.743099i | ||||
\(730\) | −83.3702 | − | 144.401i | −0.114206 | − | 0.197810i | ||||
\(731\) | 1322.70 | − | 763.662i | 1.80944 | − | 1.04468i | ||||
\(732\) | 58.9994 | + | 46.0943i | 0.0806003 | + | 0.0629704i | ||||
\(733\) | 106.923 | − | 185.196i | 0.145871 | − | 0.252655i | −0.783827 | − | 0.620980i | \(-0.786735\pi\) |
0.929697 | + | 0.368324i | \(0.120068\pi\) | |||||||
\(734\) | 9.09707 | − | 5.25220i | 0.0123938 | − | 0.00715558i | ||||
\(735\) | 105.860 | − | 178.933i | 0.144028 | − | 0.243447i | ||||
\(736\) | −88.5163 | + | 153.315i | −0.120267 | + | 0.208308i | ||||
\(737\) | 1453.38 | − | 839.106i | 1.97201 | − | 1.13854i | ||||
\(738\) | 91.7073 | − | 88.5648i | 0.124265 | − | 0.120006i | ||||
\(739\) | −23.9766 | + | 41.5286i | −0.0324446 | + | 0.0561957i | −0.881792 | − | 0.471639i | \(-0.843663\pi\) |
0.849347 | + | 0.527835i | \(0.176996\pi\) | |||||||
\(740\) | − | 88.8356i | − | 0.120048i | ||||||
\(741\) | −1125.99 | + | 454.945i | −1.51956 | + | 0.613961i | ||||
\(742\) | 287.371 | + | 430.976i | 0.387292 | + | 0.580830i | ||||
\(743\) | 646.371 | − | 373.182i | 0.869947 | − | 0.502264i | 0.00261651 | − | 0.999997i | \(-0.499167\pi\) |
0.867331 | + | 0.497732i | \(0.165834\pi\) | |||||||
\(744\) | 168.180 | − | 215.266i | 0.226048 | − | 0.289336i | ||||
\(745\) | −138.472 | − | 239.840i | −0.185868 | − | 0.321932i | ||||
\(746\) | −728.371 | − | 420.525i | −0.976368 | − | 0.563707i | ||||
\(747\) | −10.6947 | + | 37.3000i | −0.0143168 | + | 0.0499330i | ||||
\(748\) | 841.341 | 1.12479 | ||||||||
\(749\) | 20.7027 | + | 320.579i | 0.0276405 | + | 0.428009i | ||||
\(750\) | −226.963 | − | 177.318i | −0.302617 | − | 0.236425i | ||||
\(751\) | 538.756 | − | 933.153i | 0.717385 | − | 1.24255i | −0.244647 | − | 0.969612i | \(-0.578672\pi\) |
0.962032 | − | 0.272935i | \(-0.0879945\pi\) | |||||||
\(752\) | 17.0877i | 0.0227230i | ||||||||
\(753\) | −431.039 | + | 551.718i | −0.572429 | + | 0.732694i | ||||
\(754\) | −385.943 | −0.511861 | ||||||||
\(755\) | 44.5502i | 0.0590069i | ||||||||
\(756\) | −241.439 | − | 290.846i | −0.319364 | − | 0.384717i | ||||
\(757\) | 50.0542 | 0.0661217 | 0.0330609 | − | 0.999453i | \(-0.489474\pi\) | ||||
0.0330609 | + | 0.999453i | \(0.489474\pi\) | |||||||
\(758\) | − | 920.734i | − | 1.21469i | ||||||
\(759\) | −1291.48 | − | 1008.99i | −1.70155 | − | 1.32936i | ||||
\(760\) | −94.2539 | −0.124018 | ||||||||
\(761\) | 13.0930 | + | 7.55923i | 0.0172050 | + | 0.00993329i | 0.508578 | − | 0.861016i | \(-0.330171\pi\) |
−0.491373 | + | 0.870949i | \(0.663505\pi\) | |||||||
\(762\) | −354.038 | + | 453.159i | −0.464617 | + | 0.594697i | ||||
\(763\) | −168.178 | − | 252.220i | −0.220417 | − | 0.330564i | ||||
\(764\) | 46.5803i | 0.0609690i | ||||||||
\(765\) | 220.649 | − | 213.088i | 0.288430 | − | 0.278546i | ||||
\(766\) | 234.505 | − | 406.175i | 0.306142 | − | 0.530254i | ||||
\(767\) | −627.711 | + | 362.409i | −0.818397 | + | 0.472502i | ||||
\(768\) | 37.8249 | + | 29.5513i | 0.0492511 | + | 0.0384783i | ||||
\(769\) | −268.317 | − | 464.739i | −0.348917 | − | 0.604342i | 0.637140 | − | 0.770748i | \(-0.280117\pi\) |
−0.986057 | + | 0.166406i | \(0.946784\pi\) | |||||||
\(770\) | −219.095 | − | 108.307i | −0.284539 | − | 0.140659i | ||||
\(771\) | −212.200 | − | 525.195i | −0.275227 | − | 0.681187i | ||||
\(772\) | −169.668 | −0.219777 | ||||||||
\(773\) | −965.601 | − | 557.490i | −1.24916 | − | 0.721203i | −0.278219 | − | 0.960518i | \(-0.589744\pi\) |
−0.970942 | + | 0.239315i | \(0.923077\pi\) | |||||||
\(774\) | −222.331 | + | 775.429i | −0.287250 | + | 1.00185i | ||||
\(775\) | 370.225 | + | 641.248i | 0.477709 | + | 0.827417i | ||||
\(776\) | −85.9561 | − | 49.6267i | −0.110768 | − | 0.0639520i | ||||
\(777\) | 544.807 | + | 371.702i | 0.701167 | + | 0.478382i | ||||
\(778\) | −14.7723 | − | 25.5864i | −0.0189875 | − | 0.0328874i | ||||
\(779\) | 204.392 | + | 118.006i | 0.262377 | + | 0.151484i | ||||
\(780\) | 89.7570 | − | 114.886i | 0.115073 | − | 0.147290i | ||||
\(781\) | −181.560 | − | 314.471i | −0.232471 | − | 0.402652i | ||||
\(782\) | 923.666 | − | 533.279i | 1.18116 | − | 0.681942i | ||||
\(783\) | 346.961 | − | 252.100i | 0.443117 | − | 0.321967i | ||||
\(784\) | −119.018 | − | 155.726i | −0.151809 | − | 0.198630i | ||||
\(785\) | 109.470 | + | 63.2025i | 0.139452 | + | 0.0805127i | ||||
\(786\) | 876.596 | − | 354.179i | 1.11526 | − | 0.450610i | ||||
\(787\) | −512.099 | −0.650698 | −0.325349 | − | 0.945594i | \(-0.605482\pi\) | ||||
−0.325349 | + | 0.945594i | \(0.605482\pi\) | |||||||
\(788\) | 306.366i | 0.388789i | ||||||||
\(789\) | −528.849 | − | 74.3187i | −0.670278 | − | 0.0941935i | ||||
\(790\) | −45.1668 | + | 78.2312i | −0.0571732 | + | 0.0990269i | ||||
\(791\) | 40.8337 | + | 632.303i | 0.0516229 | + | 0.799372i | ||||
\(792\) | −319.641 | + | 308.688i | −0.403588 | + | 0.389758i | ||||
\(793\) | −107.194 | − | 185.665i | −0.135175 | − | 0.234130i | ||||
\(794\) | −758.908 | + | 438.156i | −0.955804 | + | 0.551834i | ||||
\(795\) | 30.8958 | − | 219.853i | 0.0388626 | − | 0.276545i | ||||
\(796\) | −1.12362 | + | 1.94617i | −0.00141159 | + | 0.00244494i | ||||
\(797\) | −205.675 | + | 118.747i | −0.258061 | + | 0.148992i | −0.623450 | − | 0.781863i | \(-0.714269\pi\) |
0.365388 | + | 0.930855i | \(0.380936\pi\) | |||||||
\(798\) | 394.374 | − | 578.036i | 0.494203 | − | 0.724356i | ||||
\(799\) | 51.4737 | − | 89.1551i | 0.0644227 | − | 0.111583i | ||||
\(800\) | −112.675 | + | 65.0531i | −0.140844 | + | 0.0813164i | ||||
\(801\) | 893.770 | + | 925.483i | 1.11582 | + | 1.15541i | ||||
\(802\) | −203.165 | + | 351.892i | −0.253323 | + | 0.438769i | ||||
\(803\) | − | 1455.24i | − | 1.81225i | ||||||
\(804\) | −454.552 | − | 355.126i | −0.565363 | − | 0.441699i | ||||
\(805\) | −309.183 | + | 19.9668i | −0.384078 | + | 0.0248035i | ||||
\(806\) | −677.418 | + | 391.107i | −0.840469 | + | 0.485245i | ||||
\(807\) | 579.914 | + | 1435.29i | 0.718605 | + | 1.77855i | ||||
\(808\) | −58.7033 | − | 101.677i | −0.0726526 | − | 0.125838i | ||||
\(809\) | 227.210 | + | 131.180i | 0.280853 | + | 0.162150i | 0.633809 | − | 0.773489i | \(-0.281490\pi\) |
−0.352957 | + | 0.935640i | \(0.614824\pi\) | |||||||
\(810\) | −5.64663 | + | 161.912i | −0.00697115 | + | 0.199891i | ||||
\(811\) | 241.274 | 0.297502 | 0.148751 | − | 0.988875i | \(-0.452475\pi\) | ||||
0.148751 | + | 0.988875i | \(0.452475\pi\) | |||||||
\(812\) | 185.022 | − | 123.371i | 0.227859 | − | 0.151934i | ||||
\(813\) | 98.2913 | − | 699.438i | 0.120900 | − | 0.860317i | ||||
\(814\) | 387.659 | − | 671.445i | 0.476240 | − | 0.824871i | ||||
\(815\) | 297.734i | 0.365317i | ||||||||
\(816\) | −108.333 | − | 268.124i | −0.132761 | − | 0.328584i | ||||
\(817\) | −1493.31 | −1.82780 | ||||||||
\(818\) | − | 625.074i | − | 0.764150i | ||||||
\(819\) | 329.012 | + | 1031.16i | 0.401724 | + | 1.25905i | ||||
\(820\) | −28.3332 | −0.0345526 | ||||||||
\(821\) | 928.640i | 1.13111i | 0.824711 | + | 0.565554i | \(0.191338\pi\) | ||||
−0.824711 | + | 0.565554i | \(0.808662\pi\) | |||||||
\(822\) | −51.0255 | + | 363.096i | −0.0620748 | + | 0.441722i | ||||
\(823\) | −133.546 | −0.162268 | −0.0811339 | − | 0.996703i | \(-0.525854\pi\) | ||||
−0.0811339 | + | 0.996703i | \(0.525854\pi\) | |||||||
\(824\) | 82.9612 | + | 47.8977i | 0.100681 | + | 0.0581283i | ||||
\(825\) | −451.215 | − | 1116.76i | −0.546927 | − | 1.35365i | ||||
\(826\) | 185.078 | − | 374.394i | 0.224065 | − | 0.453261i | ||||
\(827\) | 880.144i | 1.06426i | 0.846662 | + | 0.532130i | \(0.178608\pi\) | ||||
−0.846662 | + | 0.532130i | \(0.821392\pi\) | |||||||
\(828\) | −155.258 | + | 541.496i | −0.187510 | + | 0.653980i | ||||
\(829\) | −268.250 | + | 464.622i | −0.323582 | + | 0.560461i | −0.981224 | − | 0.192870i | \(-0.938221\pi\) |
0.657642 | + | 0.753330i | \(0.271554\pi\) | |||||||
\(830\) | 7.46810 | − | 4.31171i | 0.00899771 | − | 0.00519483i | ||||
\(831\) | 212.282 | − | 1510.59i | 0.255453 | − | 1.81780i | ||||
\(832\) | −68.7224 | − | 119.031i | −0.0825991 | − | 0.143066i | ||||
\(833\) | 151.881 | + | 1171.02i | 0.182330 | + | 1.40579i | ||||
\(834\) | 13.5572 | + | 1.90518i | 0.0162557 | + | 0.00228439i | ||||
\(835\) | 159.849 | 0.191436 | ||||||||
\(836\) | −712.399 | − | 411.303i | −0.852151 | − | 0.491990i | ||||
\(837\) | 353.522 | − | 794.096i | 0.422368 | − | 0.948741i | ||||
\(838\) | −230.070 | − | 398.493i | −0.274547 | − | 0.475529i | ||||
\(839\) | 1336.23 | + | 771.471i | 1.59264 | + | 0.919513i | 0.992852 | + | 0.119356i | \(0.0380830\pi\) |
0.599791 | + | 0.800157i | \(0.295250\pi\) | |||||||
\(840\) | −6.30498 | + | 83.7685i | −0.00750593 | + | 0.0997244i | ||||
\(841\) | −294.344 | − | 509.818i | −0.349992 | − | 0.606204i | ||||
\(842\) | 492.448 | + | 284.315i | 0.584856 | + | 0.337666i | ||||
\(843\) | −17.5589 | − | 43.4583i | −0.0208290 | − | 0.0515520i | ||||
\(844\) | 157.839 | + | 273.385i | 0.187013 | + | 0.323916i | ||||
\(845\) | −154.540 | + | 89.2237i | −0.182888 | + | 0.105590i | ||||
\(846\) | 13.1552 | + | 52.7574i | 0.0155499 | + | 0.0623610i | ||||
\(847\) | −713.462 | − | 1069.99i | −0.842340 | − | 1.26327i | ||||
\(848\) | −181.262 | − | 104.651i | −0.213752 | − | 0.123410i | ||||
\(849\) | −1205.62 | − | 941.909i | −1.42004 | − | 1.10943i | ||||
\(850\) | 783.843 | 0.922168 | ||||||||
\(851\) | − | 982.860i | − | 1.15495i | ||||||
\(852\) | −76.8398 | + | 98.3528i | −0.0901876 | + | 0.115438i | ||||
\(853\) | −470.293 | + | 814.571i | −0.551340 | + | 0.954948i | 0.446839 | + | 0.894615i | \(0.352550\pi\) |
−0.998178 | + | 0.0603337i | \(0.980784\pi\) | |||||||
\(854\) | 110.739 | + | 54.7424i | 0.129670 | + | 0.0641012i | ||||
\(855\) | −291.004 | + | 72.5625i | −0.340355 | + | 0.0848684i | ||||
\(856\) | −64.9016 | − | 112.413i | −0.0758196 | − | 0.131323i | ||||
\(857\) | −553.341 | + | 319.471i | −0.645672 | + | 0.372779i | −0.786796 | − | 0.617213i | \(-0.788262\pi\) |
0.141124 | + | 0.989992i | \(0.454928\pi\) | |||||||
\(858\) | 1179.75 | − | 476.665i | 1.37500 | − | 0.555554i | ||||
\(859\) | −149.147 | + | 258.330i | −0.173628 | + | 0.300733i | −0.939686 | − | 0.342039i | \(-0.888882\pi\) |
0.766057 | + | 0.642772i | \(0.222216\pi\) | |||||||
\(860\) | 155.254 | − | 89.6361i | 0.180528 | − | 0.104228i | ||||
\(861\) | 118.551 | − | 173.760i | 0.137689 | − | 0.201812i | ||||
\(862\) | 120.977 | − | 209.539i | 0.140345 | − | 0.243085i | ||||
\(863\) | −949.481 | + | 548.183i | −1.10021 | + | 0.635207i | −0.936276 | − | 0.351265i | \(-0.885752\pi\) |
−0.163934 | + | 0.986471i | \(0.552418\pi\) | |||||||
\(864\) | 139.533 | + | 62.1181i | 0.161496 | + | 0.0718960i | ||||
\(865\) | −36.6479 | + | 63.4760i | −0.0423675 | + | 0.0733827i | ||||
\(866\) | 318.470i | 0.367749i | ||||||||
\(867\) | −121.798 | + | 866.707i | −0.140482 | + | 0.999662i | ||||
\(868\) | 199.734 | − | 404.041i | 0.230108 | − | 0.465485i | ||||
\(869\) | −682.768 | + | 394.196i | −0.785694 | + | 0.453621i | ||||
\(870\) | −94.3849 | − | 13.2638i | −0.108488 | − | 0.0152458i | ||||
\(871\) | 825.856 | + | 1430.43i | 0.948170 | + | 1.64228i | ||||
\(872\) | 106.080 | + | 61.2452i | 0.121651 | + | 0.0702354i | ||||
\(873\) | −303.590 | − | 87.0455i | −0.347755 | − | 0.0997085i | ||||
\(874\) | −1042.81 | −1.19314 | ||||||||
\(875\) | −425.995 | − | 210.586i | −0.486852 | − | 0.240670i | ||||
\(876\) | −463.765 | + | 187.379i | −0.529412 | + | 0.213903i | ||||
\(877\) | −91.0649 | + | 157.729i | −0.103837 | + | 0.179851i | −0.913262 | − | 0.407372i | \(-0.866445\pi\) |
0.809426 | + | 0.587223i | \(0.199779\pi\) | |||||||
\(878\) | 83.9072i | 0.0955662i | ||||||||
\(879\) | −1296.85 | − | 182.245i | −1.47537 | − | 0.207332i | ||||
\(880\) | 98.7539 | 0.112220 | ||||||||
\(881\) | − | 447.835i | − | 0.508325i | −0.967161 | − | 0.254163i | \(-0.918200\pi\) | ||
0.967161 | − | 0.254163i | \(-0.0817999\pi\) | |||||||
\(882\) | −487.350 | − | 389.168i | −0.552551 | − | 0.441233i | ||||
\(883\) | 576.635 | 0.653040 | 0.326520 | − | 0.945190i | \(-0.394124\pi\) | ||||
0.326520 | + | 0.945190i | \(0.394124\pi\) | |||||||
\(884\) | 828.056i | 0.936715i | ||||||||
\(885\) | −165.966 | + | 67.0567i | −0.187532 | + | 0.0757703i | ||||
\(886\) | 432.831 | 0.488523 | ||||||||
\(887\) | 1412.61 | + | 815.571i | 1.59257 | + | 0.919471i | 0.992864 | + | 0.119252i | \(0.0380495\pi\) |
0.599707 | + | 0.800220i | \(0.295284\pi\) | |||||||
\(888\) | −263.896 | − | 37.0851i | −0.297181 | − | 0.0417625i | ||||
\(889\) | −420.462 | + | 850.553i | −0.472961 | + | 0.956752i | ||||
\(890\) | − | 285.930i | − | 0.321270i | ||||||
\(891\) | −749.228 | + | 1199.14i | −0.840884 | + | 1.34583i | ||||
\(892\) | −105.657 | + | 183.003i | −0.118449 | + | 0.205160i | ||||
\(893\) | −87.1699 | + | 50.3275i | −0.0976146 | + | 0.0563578i | ||||
\(894\) | −770.278 | + | 311.223i | −0.861609 | + | 0.348124i | ||||
\(895\) | 136.748 | + | 236.855i | 0.152791 | + | 0.264642i | ||||
\(896\) | 70.9950 | + | 35.0957i | 0.0792355 | + | 0.0391693i | ||||
\(897\) | 993.055 | − | 1271.08i | 1.10708 | − | 1.41704i | ||||
\(898\) | −630.904 | −0.702566 | ||||||||
\(899\) | 442.867 | + | 255.689i | 0.492621 | + | 0.284415i | ||||
\(900\) | −297.797 | + | 287.592i | −0.330885 | + | 0.319547i | ||||
\(901\) | 630.488 | + | 1092.04i | 0.699764 | + | 1.21203i | ||||
\(902\) | −214.150 | − | 123.640i | −0.237417 | − | 0.137073i | ||||
\(903\) | −99.8931 | + | 1327.19i | −0.110624 | + | 1.46975i | ||||
\(904\) | −128.011 | − | 221.721i | −0.141605 | − | 0.245267i | ||||
\(905\) | 215.355 | + | 124.335i | 0.237961 | + | 0.137387i | ||||
\(906\) | 132.342 | + | 18.5979i | 0.146072 | + | 0.0205274i | ||||
\(907\) | 477.583 | + | 827.199i | 0.526553 | + | 0.912016i | 0.999521 | + | 0.0309368i | \(0.00984906\pi\) |
−0.472969 | + | 0.881079i | \(0.656818\pi\) | |||||||
\(908\) | −104.096 | + | 60.0997i | −0.114643 | + | 0.0661891i | ||||
\(909\) | −259.521 | − | 268.729i | −0.285501 | − | 0.295632i | ||||
\(910\) | 106.597 | − | 215.635i | 0.117140 | − | 0.236962i | ||||
\(911\) | 198.257 | + | 114.464i | 0.217625 | + | 0.125646i | 0.604850 | − | 0.796339i | \(-0.293233\pi\) |
−0.387225 | + | 0.921985i | \(0.626566\pi\) | |||||||
\(912\) | −39.3471 | + | 279.992i | −0.0431437 | + | 0.307009i | ||||
\(913\) | 75.2614 | 0.0824331 | ||||||||
\(914\) | − | 449.279i | − | 0.491552i | ||||||
\(915\) | −19.8341 | − | 49.0895i | −0.0216766 | − | 0.0536497i | ||||
\(916\) | 51.0009 | − | 88.3362i | 0.0556779 | − | 0.0964369i | ||||
\(917\) | 1297.84 | − | 865.389i | 1.41531 | − | 0.943718i | ||||
\(918\) | −540.890 | − | 744.418i | −0.589205 | − | 0.810913i | ||||
\(919\) | −431.028 | − | 746.563i | −0.469019 | − | 0.812364i | 0.530354 | − | 0.847776i | \(-0.322059\pi\) |
−0.999373 | + | 0.0354120i | \(0.988726\pi\) | |||||||
\(920\) | 108.417 | − | 62.5945i | 0.117844 | − | 0.0680375i | ||||
\(921\) | −951.178 | − | 743.124i | −1.03277 | − | 0.806866i | ||||
\(922\) | −54.2015 | + | 93.8798i | −0.0587869 | + | 0.101822i | ||||
\(923\) | 309.506 | − | 178.693i | 0.335326 | − | 0.193600i | ||||
\(924\) | −413.202 | + | 605.633i | −0.447189 | + | 0.655447i | ||||
\(925\) | 361.166 | − | 625.558i | 0.390450 | − | 0.676279i | ||||
\(926\) | 381.460 | − | 220.236i | 0.411943 | − | 0.237836i | ||||
\(927\) | 293.013 | + | 84.0128i | 0.316087 | + | 0.0906287i | ||||
\(928\) | −44.9278 | + | 77.8172i | −0.0484135 | + | 0.0838547i | ||||
\(929\) | 1396.41i | 1.50313i | 0.659658 | + | 0.751566i | \(0.270701\pi\) | ||||
−0.659658 | + | 0.751566i | \(0.729299\pi\) | |||||||
\(930\) | −179.108 | + | 72.3668i | −0.192590 | + | 0.0778138i | ||||
\(931\) | 443.869 | − | 1065.80i | 0.476766 | − | 1.14479i | ||||
\(932\) | −39.4781 | + | 22.7927i | −0.0423585 | + | 0.0244557i | ||||
\(933\) | −173.514 | + | 222.093i | −0.185975 | + | 0.238042i | ||||
\(934\) | −216.394 | − | 374.805i | −0.231685 | − | 0.401290i | ||||
\(935\) | −515.248 | − | 297.478i | −0.551067 | − | 0.318159i | ||||
\(936\) | −303.814 | − | 314.594i | −0.324588 | − | 0.336105i | ||||
\(937\) | −744.918 | −0.795003 | −0.397501 | − | 0.917602i | \(-0.630123\pi\) | ||||
−0.397501 | + | 0.917602i | \(0.630123\pi\) | |||||||
\(938\) | −853.167 | − | 421.754i | −0.909560 | − | 0.449631i | ||||
\(939\) | 955.603 | + | 746.581i | 1.01768 | + | 0.795081i | ||||
\(940\) | 6.04182 | − | 10.4647i | 0.00642746 | − | 0.0111327i | ||||
\(941\) | 1615.42i | 1.71671i | 0.513056 | + | 0.858355i | \(0.328513\pi\) | ||||
−0.513056 | + | 0.858355i | \(0.671487\pi\) | |||||||
\(942\) | 233.450 | − | 298.809i | 0.247823 | − | 0.317207i | ||||
\(943\) | −313.473 | −0.332421 | ||||||||
\(944\) | 168.753i | 0.178763i | ||||||||
\(945\) | 45.0239 | + | 263.484i | 0.0476443 | + | 0.278820i | ||||
\(946\) | 1564.61 | 1.65392 | ||||||||
\(947\) | − | 685.435i | − | 0.723796i | −0.932218 | − | 0.361898i | \(-0.882129\pi\) | ||
0.932218 | − | 0.361898i | \(-0.117871\pi\) | |||||||
\(948\) | 213.540 | + | 166.832i | 0.225253 | + | 0.175983i | ||||
\(949\) | 1432.26 | 1.50923 | ||||||||
\(950\) | −663.712 | − | 383.195i | −0.698645 | − | 0.403363i | ||||
\(951\) | 215.550 | − | 275.898i | 0.226657 | − | 0.290114i | ||||
\(952\) | −264.697 | − | 396.971i | −0.278043 | − | 0.416987i | ||||
\(953\) | 988.352i | 1.03710i | 0.855049 | + | 0.518548i | \(0.173527\pi\) | ||||
−0.855049 | + | 0.518548i | \(0.826473\pi\) | |||||||
\(954\) | −640.203 | − | 183.559i | −0.671072 | − | 0.192410i | ||||
\(955\) | 16.4697 | − | 28.5263i | 0.0172457 | − | 0.0298705i | ||||
\(956\) | −700.453 | + | 404.407i | −0.732691 | + | 0.423019i | ||||
\(957\) | −655.508 | − | 512.127i | −0.684962 | − | 0.535138i | ||||
\(958\) | 333.593 | + | 577.799i | 0.348218 | + | 0.603131i | ||||
\(959\) | 38.9869 | + | 603.706i | 0.0406537 | + | 0.629516i | ||||
\(960\) | −12.7158 | − | 31.4715i | −0.0132456 | − | 0.0327829i | ||||
\(961\) | 75.4424 | 0.0785040 | ||||||||
\(962\) | 660.842 | + | 381.538i | 0.686946 | + | 0.396609i | ||||
\(963\) | −286.923 | − | 297.103i | −0.297947 | − | 0.308518i | ||||
\(964\) | −303.641 | − | 525.922i | −0.314980 | − | 0.545562i | ||||
\(965\) | 103.907 | + | 59.9906i | 0.107675 | + | 0.0621664i | ||||
\(966\) | −69.7572 | + | 926.799i | −0.0722124 | + | 0.959419i | ||||
\(967\) | −252.350 | − | 437.083i | −0.260962 | − | 0.451999i | 0.705536 | − | 0.708674i | \(-0.250706\pi\) |
−0.966498 | + | 0.256675i | \(0.917373\pi\) | |||||||
\(968\) | 450.022 | + | 259.820i | 0.464899 | + | 0.268410i | ||||
\(969\) | 1048.72 | − | 1342.33i | 1.08227 | − | 1.38528i | ||||
\(970\) | 35.0937 | + | 60.7840i | 0.0361790 | + | 0.0626640i | ||||
\(971\) | −1011.31 | + | 583.878i | −1.04151 | + | 0.601316i | −0.920261 | − | 0.391306i | \(-0.872024\pi\) |
−0.121250 | + | 0.992622i | \(0.538690\pi\) | |||||||
\(972\) | 478.621 | + | 84.3655i | 0.492409 | + | 0.0867957i | ||||
\(973\) | 22.5411 | − | 1.45569i | 0.0231666 | − | 0.00149608i | ||||
\(974\) | −478.211 | − | 276.095i | −0.490976 | − | 0.283465i | ||||
\(975\) | 1099.12 | − | 444.090i | 1.12731 | − | 0.455476i | ||||
\(976\) | −49.9138 | −0.0511412 | ||||||||
\(977\) | − | 294.617i | − | 0.301552i | −0.988568 | − | 0.150776i | \(-0.951823\pi\) | ||
0.988568 | − | 0.150776i | \(-0.0481773\pi\) | |||||||
\(978\) | 884.453 | + | 124.291i | 0.904349 | + | 0.127087i | ||||
\(979\) | 1247.74 | − | 2161.14i | 1.27450 | − | 2.20750i | ||||
\(980\) | 17.8273 | + | 137.451i | 0.0181911 | + | 0.140256i | ||||
\(981\) | 374.666 | + | 107.424i | 0.381923 | + | 0.109505i | ||||
\(982\) | 407.087 | + | 705.096i | 0.414549 | + | 0.718020i | ||||
\(983\) | −539.646 | + | 311.565i | −0.548978 | + | 0.316953i | −0.748710 | − | 0.662898i | \(-0.769326\pi\) |
0.199731 | + | 0.979851i | \(0.435993\pi\) | |||||||
\(984\) | −11.8279 | + | 84.1670i | −0.0120202 | + | 0.0855355i | ||||
\(985\) | 108.324 | − | 187.622i | 0.109973 | − | 0.190479i | ||||
\(986\) | 468.821 | − | 270.674i | 0.475477 | − | 0.274517i | ||||
\(987\) | 38.8977 | + | 80.8391i | 0.0394100 | + | 0.0819039i | ||||
\(988\) | 404.809 | − | 701.149i | 0.409725 | − | 0.709665i | ||||
\(989\) | 1717.70 | − | 991.717i | 1.73681 | − | 1.00275i | ||||
\(990\) | 304.897 | − | 76.0268i | 0.307977 | − | 0.0767948i | ||||
\(991\) | 272.200 | − | 471.464i | 0.274672 | − | 0.475746i | −0.695380 | − | 0.718642i | \(-0.744764\pi\) |
0.970052 | + | 0.242896i | \(0.0780974\pi\) | |||||||
\(992\) | 182.116i | 0.183584i | ||||||||
\(993\) | 1445.24 | + | 1129.12i | 1.45543 | + | 1.13708i | ||||
\(994\) | −91.2563 | + | 184.602i | −0.0918072 | + | 0.185717i | ||||
\(995\) | 1.37624 | − | 0.794573i | 0.00138316 | − | 0.000798566i | ||||
\(996\) | −9.69082 | − | 23.9848i | −0.00972974 | − | 0.0240811i | ||||
\(997\) | 523.979 | + | 907.559i | 0.525556 | + | 0.910290i | 0.999557 | + | 0.0297653i | \(0.00947600\pi\) |
−0.474001 | + | 0.880524i | \(0.657191\pi\) | |||||||
\(998\) | −879.526 | − | 507.794i | −0.881288 | − | 0.508812i | ||||
\(999\) | −843.316 | + | 88.6655i | −0.844160 | + | 0.0887543i |
(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 | 126.3.r.a.11.7 | yes | 32 | |
3.2 | odd | 2 | 378.3.r.a.305.12 | 32 | |||
7.2 | even | 3 | 126.3.i.a.65.1 | ✓ | 32 | ||
9.4 | even | 3 | 378.3.i.a.179.12 | 32 | |||
9.5 | odd | 6 | 126.3.i.a.95.1 | yes | 32 | ||
21.2 | odd | 6 | 378.3.i.a.359.13 | 32 | |||
63.23 | odd | 6 | inner | 126.3.r.a.23.15 | yes | 32 | |
63.58 | even | 3 | 378.3.r.a.233.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.i.a.65.1 | ✓ | 32 | 7.2 | even | 3 | ||
126.3.i.a.95.1 | yes | 32 | 9.5 | odd | 6 | ||
126.3.r.a.11.7 | yes | 32 | 1.1 | even | 1 | trivial | |
126.3.r.a.23.15 | yes | 32 | 63.23 | odd | 6 | inner | |
378.3.i.a.179.12 | 32 | 9.4 | even | 3 | |||
378.3.i.a.359.13 | 32 | 21.2 | odd | 6 | |||
378.3.r.a.233.4 | 32 | 63.58 | even | 3 | |||
378.3.r.a.305.12 | 32 | 3.2 | odd | 2 |