Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 235.7 | ||
Character | \(\chi\) | \(=\) | 429.235 |
Dual form | 429.2.n.d.157.7 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.30744 | + | 0.949910i | 0.924499 | + | 0.671688i | 0.944640 | − | 0.328109i | \(-0.106411\pi\) |
−0.0201407 | + | 0.999797i | \(0.506411\pi\) | |||||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | 0.189034 | + | 0.581786i | 0.0945169 | + | 0.290893i | ||||
\(5\) | 1.69854 | − | 1.23406i | 0.759608 | − | 0.551888i | −0.139182 | − | 0.990267i | \(-0.544447\pi\) |
0.898790 | + | 0.438379i | \(0.144447\pi\) | |||||||
\(6\) | 1.30744 | − | 0.949910i | 0.533760 | − | 0.387799i | ||||
\(7\) | 1.36281 | + | 4.19429i | 0.515093 | + | 1.58529i | 0.783113 | + | 0.621879i | \(0.213630\pi\) |
−0.268021 | + | 0.963413i | \(0.586370\pi\) | |||||||
\(8\) | 0.693300 | − | 2.13376i | 0.245119 | − | 0.754398i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 3.39298 | 1.07295 | ||||||||
\(11\) | −3.28357 | + | 0.467064i | −0.990034 | + | 0.140825i | ||||
\(12\) | 0.611726 | 0.176590 | ||||||||
\(13\) | 0.809017 | + | 0.587785i | 0.224381 | + | 0.163022i | ||||
\(14\) | −2.20241 | + | 6.77832i | −0.588619 | + | 1.81158i | ||||
\(15\) | −0.648783 | − | 1.99675i | −0.167515 | − | 0.515558i | ||||
\(16\) | 3.92312 | − | 2.85031i | 0.980780 | − | 0.712578i | ||||
\(17\) | 5.73404 | − | 4.16602i | 1.39071 | − | 1.01041i | 0.394922 | − | 0.918715i | \(-0.370772\pi\) |
0.995787 | − | 0.0916944i | \(-0.0292283\pi\) | |||||||
\(18\) | −0.499397 | − | 1.53699i | −0.117709 | − | 0.362271i | ||||
\(19\) | 0.292494 | − | 0.900203i | 0.0671027 | − | 0.206521i | −0.911883 | − | 0.410451i | \(-0.865371\pi\) |
0.978986 | + | 0.203930i | \(0.0653714\pi\) | |||||||
\(20\) | 1.03904 | + | 0.754906i | 0.232336 | + | 0.168802i | ||||
\(21\) | 4.41014 | 0.962371 | ||||||||
\(22\) | −4.73674 | − | 2.50844i | −1.00988 | − | 0.534801i | ||||
\(23\) | −4.97977 | −1.03835 | −0.519177 | − | 0.854667i | \(-0.673762\pi\) | ||||
−0.519177 | + | 0.854667i | \(0.673762\pi\) | |||||||
\(24\) | −1.81508 | − | 1.31874i | −0.370502 | − | 0.269186i | ||||
\(25\) | −0.182961 | + | 0.563098i | −0.0365923 | + | 0.112620i | ||||
\(26\) | 0.499397 | + | 1.53699i | 0.0979399 | + | 0.301428i | ||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | −2.18256 | + | 1.58572i | −0.412466 | + | 0.299674i | ||||
\(29\) | 1.54168 | + | 4.74480i | 0.286282 | + | 0.881087i | 0.986011 | + | 0.166678i | \(0.0533041\pi\) |
−0.699729 | + | 0.714409i | \(0.746696\pi\) | |||||||
\(30\) | 1.04849 | − | 3.22691i | 0.191427 | − | 0.589151i | ||||
\(31\) | −6.38023 | − | 4.63551i | −1.14592 | − | 0.832562i | −0.157990 | − | 0.987441i | \(-0.550501\pi\) |
−0.987934 | + | 0.154878i | \(0.950501\pi\) | |||||||
\(32\) | 3.34965 | 0.592140 | ||||||||
\(33\) | −0.570475 | + | 3.26719i | −0.0993070 | + | 0.568746i | ||||
\(34\) | 11.4543 | 1.96439 | ||||||||
\(35\) | 7.49077 | + | 5.44237i | 1.26617 | + | 0.919928i | ||||
\(36\) | 0.189034 | − | 0.581786i | 0.0315056 | − | 0.0969644i | ||||
\(37\) | 2.40088 | + | 7.38914i | 0.394702 | + | 1.21477i | 0.929193 | + | 0.369594i | \(0.120503\pi\) |
−0.534492 | + | 0.845174i | \(0.679497\pi\) | |||||||
\(38\) | 1.23753 | − | 0.899118i | 0.200754 | − | 0.145856i | ||||
\(39\) | 0.809017 | − | 0.587785i | 0.129546 | − | 0.0941210i | ||||
\(40\) | −1.45559 | − | 4.47984i | −0.230149 | − | 0.708325i | ||||
\(41\) | −0.153644 | + | 0.472869i | −0.0239952 | + | 0.0738497i | −0.962337 | − | 0.271859i | \(-0.912362\pi\) |
0.938342 | + | 0.345709i | \(0.112362\pi\) | |||||||
\(42\) | 5.76598 | + | 4.18923i | 0.889711 | + | 0.646413i | ||||
\(43\) | −11.1839 | −1.70553 | −0.852763 | − | 0.522298i | \(-0.825075\pi\) | ||||
−0.852763 | + | 0.522298i | \(0.825075\pi\) | |||||||
\(44\) | −0.892438 | − | 1.82205i | −0.134540 | − | 0.274684i | ||||
\(45\) | −2.09951 | −0.312976 | ||||||||
\(46\) | −6.51075 | − | 4.73034i | −0.959958 | − | 0.697450i | ||||
\(47\) | 0.374620 | − | 1.15296i | 0.0546439 | − | 0.168177i | −0.920010 | − | 0.391895i | \(-0.871820\pi\) |
0.974654 | + | 0.223718i | \(0.0718196\pi\) | |||||||
\(48\) | −1.49850 | − | 4.61190i | −0.216290 | − | 0.665671i | ||||
\(49\) | −10.0717 | + | 7.31752i | −1.43881 | + | 1.04536i | ||||
\(50\) | −0.774103 | + | 0.562419i | −0.109475 | + | 0.0795380i | ||||
\(51\) | −2.19021 | − | 6.74077i | −0.306691 | − | 0.943896i | ||||
\(52\) | −0.189034 | + | 0.581786i | −0.0262143 | + | 0.0806792i | ||||
\(53\) | −0.886832 | − | 0.644321i | −0.121816 | − | 0.0885043i | 0.525209 | − | 0.850973i | \(-0.323987\pi\) |
−0.647025 | + | 0.762469i | \(0.723987\pi\) | |||||||
\(54\) | −1.61608 | −0.219921 | ||||||||
\(55\) | −5.00088 | + | 4.84545i | −0.674319 | + | 0.653360i | ||||
\(56\) | 9.89444 | 1.32220 | ||||||||
\(57\) | −0.765759 | − | 0.556356i | −0.101427 | − | 0.0736912i | ||||
\(58\) | −2.49148 | + | 7.66799i | −0.327147 | + | 1.00686i | ||||
\(59\) | −0.0285215 | − | 0.0877803i | −0.00371319 | − | 0.0114280i | 0.949183 | − | 0.314725i | \(-0.101912\pi\) |
−0.952896 | + | 0.303297i | \(0.901912\pi\) | |||||||
\(60\) | 1.03904 | − | 0.754906i | 0.134139 | − | 0.0974579i | ||||
\(61\) | −7.82276 | + | 5.68357i | −1.00160 | + | 0.727706i | −0.962431 | − | 0.271526i | \(-0.912472\pi\) |
−0.0391708 | + | 0.999233i | \(0.512472\pi\) | |||||||
\(62\) | −3.93845 | − | 12.1213i | −0.500183 | − | 1.53941i | ||||
\(63\) | 1.36281 | − | 4.19429i | 0.171698 | − | 0.528431i | ||||
\(64\) | −3.46678 | − | 2.51876i | −0.433347 | − | 0.314845i | ||||
\(65\) | 2.09951 | 0.260412 | ||||||||
\(66\) | −3.84940 | + | 3.72976i | −0.473829 | + | 0.459101i | ||||
\(67\) | 8.50741 | 1.03935 | 0.519673 | − | 0.854365i | \(-0.326054\pi\) | ||||
0.519673 | + | 0.854365i | \(0.326054\pi\) | |||||||
\(68\) | 3.50766 | + | 2.54847i | 0.425366 | + | 0.309047i | ||||
\(69\) | −1.53883 | + | 4.73604i | −0.185254 | + | 0.570153i | ||||
\(70\) | 4.62397 | + | 14.2311i | 0.552670 | + | 1.70094i | ||||
\(71\) | −13.0623 | + | 9.49035i | −1.55022 | + | 1.12630i | −0.606718 | + | 0.794917i | \(0.707514\pi\) |
−0.943497 | + | 0.331380i | \(0.892486\pi\) | |||||||
\(72\) | −1.81508 | + | 1.31874i | −0.213910 | + | 0.155414i | ||||
\(73\) | −0.962901 | − | 2.96350i | −0.112699 | − | 0.346852i | 0.878761 | − | 0.477262i | \(-0.158371\pi\) |
−0.991460 | + | 0.130410i | \(0.958371\pi\) | |||||||
\(74\) | −3.88002 | + | 11.9415i | −0.451043 | + | 1.38817i | ||||
\(75\) | 0.478999 | + | 0.348013i | 0.0553101 | + | 0.0401851i | ||||
\(76\) | 0.579017 | 0.0664178 | ||||||||
\(77\) | −6.43388 | − | 13.1357i | −0.733209 | − | 1.49696i | ||||
\(78\) | 1.61608 | 0.182985 | ||||||||
\(79\) | −1.97455 | − | 1.43459i | −0.222154 | − | 0.161404i | 0.471142 | − | 0.882057i | \(-0.343842\pi\) |
−0.693296 | + | 0.720653i | \(0.743842\pi\) | |||||||
\(80\) | 3.14611 | − | 9.68272i | 0.351745 | − | 1.08256i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −0.650064 | + | 0.472299i | −0.0717875 | + | 0.0521567i | ||||
\(83\) | 11.1230 | − | 8.08132i | 1.22091 | − | 0.887040i | 0.224731 | − | 0.974421i | \(-0.427850\pi\) |
0.996175 | + | 0.0873803i | \(0.0278495\pi\) | |||||||
\(84\) | 0.833665 | + | 2.56576i | 0.0909603 | + | 0.279947i | ||||
\(85\) | 4.59835 | − | 14.1523i | 0.498762 | − | 1.53503i | ||||
\(86\) | −14.6222 | − | 10.6237i | −1.57676 | − | 1.14558i | ||||
\(87\) | 4.98898 | 0.534874 | ||||||||
\(88\) | −1.27990 | + | 7.33017i | −0.136438 | + | 0.781399i | ||||
\(89\) | 7.34531 | 0.778601 | 0.389301 | − | 0.921111i | \(-0.372717\pi\) | ||||
0.389301 | + | 0.921111i | \(0.372717\pi\) | |||||||
\(90\) | −2.74498 | − | 1.99434i | −0.289346 | − | 0.210222i | ||||
\(91\) | −1.36281 | + | 4.19429i | −0.142861 | + | 0.439681i | ||||
\(92\) | −0.941345 | − | 2.89716i | −0.0981420 | − | 0.302050i | ||||
\(93\) | −6.38023 | + | 4.63551i | −0.661599 | + | 0.480680i | ||||
\(94\) | 1.58500 | − | 1.15157i | 0.163480 | − | 0.118776i | ||||
\(95\) | −0.614092 | − | 1.88998i | −0.0630045 | − | 0.193908i | ||||
\(96\) | 1.03510 | − | 3.18571i | 0.105644 | − | 0.325140i | ||||
\(97\) | 6.01556 | + | 4.37056i | 0.610787 | + | 0.443763i | 0.849691 | − | 0.527280i | \(-0.176788\pi\) |
−0.238904 | + | 0.971043i | \(0.576788\pi\) | |||||||
\(98\) | −20.1191 | −2.03234 | ||||||||
\(99\) | 2.93100 | + | 1.55217i | 0.294577 | + | 0.155999i | ||||
\(100\) | −0.362188 | −0.0362188 | ||||||||
\(101\) | −6.34482 | − | 4.60978i | −0.631333 | − | 0.458690i | 0.225529 | − | 0.974237i | \(-0.427589\pi\) |
−0.856862 | + | 0.515546i | \(0.827589\pi\) | |||||||
\(102\) | 3.53956 | − | 10.8936i | 0.350469 | − | 1.07863i | ||||
\(103\) | −3.60560 | − | 11.0969i | −0.355270 | − | 1.09341i | −0.955852 | − | 0.293847i | \(-0.905064\pi\) |
0.600582 | − | 0.799563i | \(-0.294936\pi\) | |||||||
\(104\) | 1.81508 | − | 1.31874i | 0.177984 | − | 0.129313i | ||||
\(105\) | 7.49077 | − | 5.44237i | 0.731025 | − | 0.531121i | ||||
\(106\) | −0.547432 | − | 1.68482i | −0.0531712 | − | 0.163644i | ||||
\(107\) | 0.413186 | − | 1.27166i | 0.0399442 | − | 0.122936i | −0.929096 | − | 0.369839i | \(-0.879413\pi\) |
0.969040 | + | 0.246903i | \(0.0794129\pi\) | |||||||
\(108\) | −0.494897 | − | 0.359564i | −0.0476215 | − | 0.0345990i | ||||
\(109\) | 3.08747 | 0.295726 | 0.147863 | − | 0.989008i | \(-0.452761\pi\) | ||||
0.147863 | + | 0.989008i | \(0.452761\pi\) | |||||||
\(110\) | −11.1411 | + | 1.58474i | −1.06226 | + | 0.151099i | ||||
\(111\) | 7.76940 | 0.737439 | ||||||||
\(112\) | 17.3015 | + | 12.5703i | 1.63484 | + | 1.18778i | ||||
\(113\) | 1.30386 | − | 4.01288i | 0.122657 | − | 0.377500i | −0.870810 | − | 0.491620i | \(-0.836405\pi\) |
0.993467 | + | 0.114120i | \(0.0364048\pi\) | |||||||
\(114\) | −0.472694 | − | 1.45480i | −0.0442719 | − | 0.136255i | ||||
\(115\) | −8.45832 | + | 6.14533i | −0.788743 | + | 0.573055i | ||||
\(116\) | −2.46903 | + | 1.79385i | −0.229244 | + | 0.166555i | ||||
\(117\) | −0.309017 | − | 0.951057i | −0.0285686 | − | 0.0879252i | ||||
\(118\) | 0.0460932 | − | 0.141860i | 0.00424322 | − | 0.0130593i | ||||
\(119\) | 25.2879 | + | 18.3727i | 2.31814 | + | 1.68423i | ||||
\(120\) | −4.71038 | −0.429997 | ||||||||
\(121\) | 10.5637 | − | 3.06728i | 0.960337 | − | 0.278844i | ||||
\(122\) | −15.6267 | −1.41477 | ||||||||
\(123\) | 0.402246 | + | 0.292249i | 0.0362693 | + | 0.0263512i | ||||
\(124\) | 1.49080 | − | 4.58820i | 0.133877 | − | 0.412033i | ||||
\(125\) | 3.62804 | + | 11.1660i | 0.324502 | + | 0.998715i | ||||
\(126\) | 5.76598 | − | 4.18923i | 0.513675 | − | 0.373207i | ||||
\(127\) | −8.47569 | + | 6.15795i | −0.752095 | + | 0.546429i | −0.896476 | − | 0.443093i | \(-0.853881\pi\) |
0.144380 | + | 0.989522i | \(0.453881\pi\) | |||||||
\(128\) | −4.21020 | − | 12.9577i | −0.372133 | − | 1.14531i | ||||
\(129\) | −3.45601 | + | 10.6365i | −0.304285 | + | 0.936492i | ||||
\(130\) | 2.74498 | + | 1.99434i | 0.240750 | + | 0.174915i | ||||
\(131\) | 1.45244 | 0.126901 | 0.0634503 | − | 0.997985i | \(-0.479790\pi\) | ||||
0.0634503 | + | 0.997985i | \(0.479790\pi\) | |||||||
\(132\) | −2.00865 | + | 0.285715i | −0.174830 | + | 0.0248683i | ||||
\(133\) | 4.17433 | 0.361960 | ||||||||
\(134\) | 11.1229 | + | 8.08127i | 0.960874 | + | 0.698116i | ||||
\(135\) | −0.648783 | + | 1.99675i | −0.0558383 | + | 0.171853i | ||||
\(136\) | −4.91388 | − | 15.1234i | −0.421362 | − | 1.29682i | ||||
\(137\) | 15.7711 | − | 11.4584i | 1.34742 | − | 0.978958i | 0.348285 | − | 0.937389i | \(-0.386764\pi\) |
0.999136 | − | 0.0415692i | \(-0.0132357\pi\) | |||||||
\(138\) | −6.51075 | + | 4.73034i | −0.554232 | + | 0.402673i | ||||
\(139\) | 2.99391 | + | 9.21432i | 0.253940 | + | 0.781548i | 0.994037 | + | 0.109047i | \(0.0347799\pi\) |
−0.740096 | + | 0.672501i | \(0.765220\pi\) | |||||||
\(140\) | −1.75028 | + | 5.38682i | −0.147926 | + | 0.455269i | ||||
\(141\) | −0.980767 | − | 0.712569i | −0.0825955 | − | 0.0600092i | ||||
\(142\) | −26.0932 | −2.18969 | ||||||||
\(143\) | −2.93100 | − | 1.55217i | −0.245103 | − | 0.129799i | ||||
\(144\) | −4.84924 | −0.404104 | ||||||||
\(145\) | 8.47395 | + | 6.15669i | 0.703724 | + | 0.511285i | ||||
\(146\) | 1.55613 | − | 4.78927i | 0.128786 | − | 0.396363i | ||||
\(147\) | 3.84705 | + | 11.8400i | 0.317299 | + | 0.976546i | ||||
\(148\) | −3.84505 | + | 2.79360i | −0.316061 | + | 0.229632i | ||||
\(149\) | 4.53248 | − | 3.29304i | 0.371315 | − | 0.269776i | −0.386441 | − | 0.922314i | \(-0.626296\pi\) |
0.757756 | + | 0.652538i | \(0.226296\pi\) | |||||||
\(150\) | 0.295681 | + | 0.910013i | 0.0241423 | + | 0.0743022i | ||||
\(151\) | 1.18800 | − | 3.65628i | 0.0966779 | − | 0.297544i | −0.891009 | − | 0.453985i | \(-0.850002\pi\) |
0.987687 | + | 0.156441i | \(0.0500021\pi\) | |||||||
\(152\) | −1.71803 | − | 1.24822i | −0.139351 | − | 0.101244i | ||||
\(153\) | −7.08766 | −0.573004 | ||||||||
\(154\) | 4.06586 | − | 23.2858i | 0.327637 | − | 1.87642i | ||||
\(155\) | −16.5575 | −1.32993 | ||||||||
\(156\) | 0.494897 | + | 0.359564i | 0.0396235 | + | 0.0287881i | ||||
\(157\) | −2.59264 | + | 7.97932i | −0.206915 | + | 0.636819i | 0.792714 | + | 0.609594i | \(0.208667\pi\) |
−0.999629 | + | 0.0272259i | \(0.991333\pi\) | |||||||
\(158\) | −1.21887 | − | 3.75128i | −0.0969678 | − | 0.298436i | ||||
\(159\) | −0.886832 | + | 0.644321i | −0.0703303 | + | 0.0510980i | ||||
\(160\) | 5.68950 | − | 4.13366i | 0.449794 | − | 0.326795i | ||||
\(161\) | −6.78647 | − | 20.8866i | −0.534849 | − | 1.64609i | ||||
\(162\) | −0.499397 | + | 1.53699i | −0.0392364 | + | 0.120757i | ||||
\(163\) | −14.1203 | − | 10.2590i | −1.10598 | − | 0.803545i | −0.123958 | − | 0.992287i | \(-0.539559\pi\) |
−0.982027 | + | 0.188743i | \(0.939559\pi\) | |||||||
\(164\) | −0.304152 | −0.0237503 | ||||||||
\(165\) | 3.06294 | + | 6.25345i | 0.238449 | + | 0.486830i | ||||
\(166\) | 22.2192 | 1.72454 | ||||||||
\(167\) | 9.69746 | + | 7.04562i | 0.750412 | + | 0.545206i | 0.895954 | − | 0.444146i | \(-0.146493\pi\) |
−0.145543 | + | 0.989352i | \(0.546493\pi\) | |||||||
\(168\) | 3.05755 | − | 9.41017i | 0.235895 | − | 0.726010i | ||||
\(169\) | 0.309017 | + | 0.951057i | 0.0237705 | + | 0.0731582i | ||||
\(170\) | 19.4555 | − | 14.1352i | 1.49217 | − | 1.08412i | ||||
\(171\) | −0.765759 | + | 0.556356i | −0.0585590 | + | 0.0425456i | ||||
\(172\) | −2.11413 | − | 6.50663i | −0.161201 | − | 0.496126i | ||||
\(173\) | 4.64048 | − | 14.2819i | 0.352809 | − | 1.08584i | −0.604459 | − | 0.796636i | \(-0.706611\pi\) |
0.957269 | − | 0.289200i | \(-0.0933891\pi\) | |||||||
\(174\) | 6.52278 | + | 4.73908i | 0.494491 | + | 0.359269i | ||||
\(175\) | −2.61114 | −0.197383 | ||||||||
\(176\) | −11.5506 | + | 11.1916i | −0.870657 | + | 0.843596i | ||||
\(177\) | −0.0922977 | −0.00693752 | ||||||||
\(178\) | 9.60355 | + | 6.97738i | 0.719816 | + | 0.522977i | ||||
\(179\) | 2.94088 | − | 9.05110i | 0.219812 | − | 0.676511i | −0.778965 | − | 0.627067i | \(-0.784255\pi\) |
0.998777 | − | 0.0494439i | \(-0.0157449\pi\) | |||||||
\(180\) | −0.396877 | − | 1.22146i | −0.0295815 | − | 0.0910425i | ||||
\(181\) | −11.4975 | + | 8.35344i | −0.854604 | + | 0.620906i | −0.926412 | − | 0.376512i | \(-0.877123\pi\) |
0.0718074 | + | 0.997419i | \(0.477123\pi\) | |||||||
\(182\) | −5.76598 | + | 4.18923i | −0.427403 | + | 0.310527i | ||||
\(183\) | 2.98803 | + | 9.19621i | 0.220881 | + | 0.679803i | ||||
\(184\) | −3.45248 | + | 10.6256i | −0.254520 | + | 0.783332i | ||||
\(185\) | 13.1966 | + | 9.58790i | 0.970234 | + | 0.704916i | ||||
\(186\) | −12.7451 | −0.934515 | ||||||||
\(187\) | −16.8823 | + | 16.3576i | −1.23456 | + | 1.19619i | ||||
\(188\) | 0.741593 | 0.0540862 | ||||||||
\(189\) | −3.56788 | − | 2.59221i | −0.259525 | − | 0.188556i | ||||
\(190\) | 0.992425 | − | 3.05437i | 0.0719980 | − | 0.221587i | ||||
\(191\) | 3.11863 | + | 9.59816i | 0.225656 | + | 0.694498i | 0.998224 | + | 0.0595665i | \(0.0189719\pi\) |
−0.772568 | + | 0.634932i | \(0.781028\pi\) | |||||||
\(192\) | −3.46678 | + | 2.51876i | −0.250193 | + | 0.181776i | ||||
\(193\) | 7.65399 | − | 5.56095i | 0.550946 | − | 0.400286i | −0.277188 | − | 0.960816i | \(-0.589402\pi\) |
0.828134 | + | 0.560530i | \(0.189402\pi\) | |||||||
\(194\) | 3.71334 | + | 11.4285i | 0.266602 | + | 0.820517i | ||||
\(195\) | 0.648783 | − | 1.99675i | 0.0464603 | − | 0.142990i | ||||
\(196\) | −6.16112 | − | 4.47632i | −0.440080 | − | 0.319737i | ||||
\(197\) | −15.5981 | −1.11132 | −0.555661 | − | 0.831409i | \(-0.687535\pi\) | ||||
−0.555661 | + | 0.831409i | \(0.687535\pi\) | |||||||
\(198\) | 2.35768 | + | 4.81356i | 0.167553 | + | 0.342085i | ||||
\(199\) | 7.17405 | 0.508555 | 0.254277 | − | 0.967131i | \(-0.418162\pi\) | ||||
0.254277 | + | 0.967131i | \(0.418162\pi\) | |||||||
\(200\) | 1.07467 | + | 0.780791i | 0.0759904 | + | 0.0552103i | ||||
\(201\) | 2.62893 | − | 8.09103i | 0.185431 | − | 0.570697i | ||||
\(202\) | −3.91659 | − | 12.0540i | −0.275570 | − | 0.848118i | ||||
\(203\) | −17.8000 | + | 12.9325i | −1.24932 | + | 0.907683i | ||||
\(204\) | 3.50766 | − | 2.54847i | 0.245585 | − | 0.178428i | ||||
\(205\) | 0.322577 | + | 0.992791i | 0.0225298 | + | 0.0693395i | ||||
\(206\) | 5.82695 | − | 17.9335i | 0.405983 | − | 1.24949i | ||||
\(207\) | 4.02872 | + | 2.92704i | 0.280015 | + | 0.203443i | ||||
\(208\) | 4.84924 | 0.336235 | ||||||||
\(209\) | −0.539972 | + | 3.09250i | −0.0373506 | + | 0.213912i | ||||
\(210\) | 14.9635 | 1.03258 | ||||||||
\(211\) | 23.1195 | + | 16.7973i | 1.59161 | + | 1.15637i | 0.901596 | + | 0.432580i | \(0.142397\pi\) |
0.690016 | + | 0.723794i | \(0.257603\pi\) | |||||||
\(212\) | 0.207216 | − | 0.637745i | 0.0142316 | − | 0.0438005i | ||||
\(213\) | 4.98937 | + | 15.3557i | 0.341866 | + | 1.05216i | ||||
\(214\) | 1.74817 | − | 1.27012i | 0.119503 | − | 0.0868238i | ||||
\(215\) | −18.9962 | + | 13.8016i | −1.29553 | + | 0.941259i | ||||
\(216\) | 0.693300 | + | 2.13376i | 0.0471731 | + | 0.145184i | ||||
\(217\) | 10.7476 | − | 33.0779i | 0.729598 | − | 2.24547i | ||||
\(218\) | 4.03668 | + | 2.93282i | 0.273398 | + | 0.198636i | ||||
\(219\) | −3.11601 | −0.210561 | ||||||||
\(220\) | −3.76435 | − | 1.99349i | −0.253792 | − | 0.134401i | ||||
\(221\) | 7.08766 | 0.476768 | ||||||||
\(222\) | 10.1580 | + | 7.38024i | 0.681762 | + | 0.495329i | ||||
\(223\) | 0.0619908 | − | 0.190788i | 0.00415121 | − | 0.0127761i | −0.948959 | − | 0.315398i | \(-0.897862\pi\) |
0.953111 | + | 0.302622i | \(0.0978620\pi\) | |||||||
\(224\) | 4.56493 | + | 14.0494i | 0.305007 | + | 0.938715i | ||||
\(225\) | 0.478999 | − | 0.348013i | 0.0319333 | − | 0.0232009i | ||||
\(226\) | 5.51660 | − | 4.00805i | 0.366959 | − | 0.266611i | ||||
\(227\) | 0.471657 | + | 1.45161i | 0.0313050 | + | 0.0963468i | 0.965488 | − | 0.260447i | \(-0.0838699\pi\) |
−0.934183 | + | 0.356794i | \(0.883870\pi\) | |||||||
\(228\) | 0.178926 | − | 0.550678i | 0.0118497 | − | 0.0364695i | ||||
\(229\) | −22.3704 | − | 16.2531i | −1.47828 | − | 1.07403i | −0.978106 | − | 0.208107i | \(-0.933270\pi\) |
−0.500173 | − | 0.865925i | \(-0.666730\pi\) | |||||||
\(230\) | −16.8963 | −1.11411 | ||||||||
\(231\) | −14.4810 | + | 2.05982i | −0.952780 | + | 0.135526i | ||||
\(232\) | 11.1931 | 0.734863 | ||||||||
\(233\) | 6.66133 | + | 4.83974i | 0.436399 | + | 0.317062i | 0.784202 | − | 0.620505i | \(-0.213072\pi\) |
−0.347804 | + | 0.937567i | \(0.613072\pi\) | |||||||
\(234\) | 0.499397 | − | 1.53699i | 0.0326466 | − | 0.100476i | ||||
\(235\) | −0.786516 | − | 2.42065i | −0.0513067 | − | 0.157906i | ||||
\(236\) | 0.0456778 | − | 0.0331869i | 0.00297337 | − | 0.00216028i | ||||
\(237\) | −1.97455 | + | 1.43459i | −0.128261 | + | 0.0931868i | ||||
\(238\) | 15.6099 | + | 48.0425i | 1.01184 | + | 3.11413i | ||||
\(239\) | 9.18787 | − | 28.2774i | 0.594314 | − | 1.82911i | 0.0362025 | − | 0.999344i | \(-0.488474\pi\) |
0.558111 | − | 0.829766i | \(-0.311526\pi\) | |||||||
\(240\) | −8.23661 | − | 5.98425i | −0.531671 | − | 0.386282i | ||||
\(241\) | 12.8808 | 0.829728 | 0.414864 | − | 0.909884i | \(-0.363829\pi\) | ||||
0.414864 | + | 0.909884i | \(0.363829\pi\) | |||||||
\(242\) | 16.7250 | + | 6.02429i | 1.07513 | + | 0.387256i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.78539 | − | 3.47679i | −0.306353 | − | 0.222578i | ||||
\(245\) | −8.07690 | + | 24.8581i | −0.516014 | + | 1.58813i | ||||
\(246\) | 0.248302 | + | 0.764195i | 0.0158312 | + | 0.0487233i | ||||
\(247\) | 0.765759 | − | 0.556356i | 0.0487241 | − | 0.0354001i | ||||
\(248\) | −14.3145 | + | 10.4001i | −0.908970 | + | 0.660406i | ||||
\(249\) | −4.24860 | − | 13.0759i | −0.269244 | − | 0.828649i | ||||
\(250\) | −5.86322 | + | 18.0451i | −0.370823 | + | 1.14127i | ||||
\(251\) | 10.6204 | + | 7.71616i | 0.670353 | + | 0.487040i | 0.870143 | − | 0.492799i | \(-0.164026\pi\) |
−0.199790 | + | 0.979839i | \(0.564026\pi\) | |||||||
\(252\) | 2.69780 | 0.169945 | ||||||||
\(253\) | 16.3514 | − | 2.32587i | 1.02801 | − | 0.146226i | ||||
\(254\) | −16.9309 | −1.06234 | ||||||||
\(255\) | −12.0386 | − | 8.74659i | −0.753889 | − | 0.547733i | ||||
\(256\) | 4.15565 | − | 12.7898i | 0.259728 | − | 0.799362i | ||||
\(257\) | 8.32381 | + | 25.6181i | 0.519225 | + | 1.59801i | 0.775460 | + | 0.631396i | \(0.217518\pi\) |
−0.256235 | + | 0.966614i | \(0.582482\pi\) | |||||||
\(258\) | −14.6222 | + | 10.6237i | −0.910341 | + | 0.661401i | ||||
\(259\) | −27.7203 | + | 20.1400i | −1.72245 | + | 1.25144i | ||||
\(260\) | 0.396877 | + | 1.22146i | 0.0246133 | + | 0.0757519i | ||||
\(261\) | 1.54168 | − | 4.74480i | 0.0954275 | − | 0.293696i | ||||
\(262\) | 1.89898 | + | 1.37969i | 0.117320 | + | 0.0852376i | ||||
\(263\) | 17.2319 | 1.06256 | 0.531282 | − | 0.847195i | \(-0.321711\pi\) | ||||
0.531282 | + | 0.847195i | \(0.321711\pi\) | |||||||
\(264\) | 6.57589 | + | 3.48240i | 0.404718 | + | 0.214327i | ||||
\(265\) | −2.30145 | −0.141377 | ||||||||
\(266\) | 5.45768 | + | 3.96523i | 0.334632 | + | 0.243124i | ||||
\(267\) | 2.26983 | − | 6.98580i | 0.138911 | − | 0.427524i | ||||
\(268\) | 1.60819 | + | 4.94949i | 0.0982357 | + | 0.302338i | ||||
\(269\) | −1.33811 | + | 0.972196i | −0.0815862 | + | 0.0592759i | −0.627831 | − | 0.778350i | \(-0.716057\pi\) |
0.546244 | + | 0.837626i | \(0.316057\pi\) | |||||||
\(270\) | −2.74498 | + | 1.99434i | −0.167054 | + | 0.121372i | ||||
\(271\) | 0.415173 | + | 1.27777i | 0.0252199 | + | 0.0776190i | 0.962874 | − | 0.269950i | \(-0.0870072\pi\) |
−0.937654 | + | 0.347569i | \(0.887007\pi\) | |||||||
\(272\) | 10.6209 | − | 32.6876i | 0.643984 | − | 1.98198i | ||||
\(273\) | 3.56788 | + | 2.59221i | 0.215938 | + | 0.156888i | ||||
\(274\) | 31.5043 | 1.90324 | ||||||||
\(275\) | 0.337765 | − | 1.93443i | 0.0203680 | − | 0.116650i | ||||
\(276\) | −3.04626 | −0.183363 | ||||||||
\(277\) | −10.5510 | − | 7.66576i | −0.633949 | − | 0.460591i | 0.223817 | − | 0.974631i | \(-0.428148\pi\) |
−0.857766 | + | 0.514040i | \(0.828148\pi\) | |||||||
\(278\) | −4.83841 | + | 14.8911i | −0.290189 | + | 0.893109i | ||||
\(279\) | 2.43703 | + | 7.50042i | 0.145901 | + | 0.449038i | ||||
\(280\) | 16.8061 | − | 12.2103i | 1.00435 | − | 0.729706i | ||||
\(281\) | 18.8714 | − | 13.7109i | 1.12578 | − | 0.817924i | 0.140701 | − | 0.990052i | \(-0.455064\pi\) |
0.985075 | + | 0.172128i | \(0.0550643\pi\) | |||||||
\(282\) | −0.605417 | − | 1.86328i | −0.0360521 | − | 0.110957i | ||||
\(283\) | 3.18956 | − | 9.81645i | 0.189600 | − | 0.583527i | −0.810398 | − | 0.585880i | \(-0.800749\pi\) |
0.999997 | + | 0.00235273i | \(0.000748899\pi\) | |||||||
\(284\) | −7.99058 | − | 5.80549i | −0.474154 | − | 0.344493i | ||||
\(285\) | −1.98724 | −0.117714 | ||||||||
\(286\) | −2.35768 | − | 4.81356i | −0.139412 | − | 0.284632i | ||||
\(287\) | −2.19274 | −0.129433 | ||||||||
\(288\) | −2.70992 | − | 1.96887i | −0.159684 | − | 0.116017i | ||||
\(289\) | 10.2702 | − | 31.6083i | 0.604128 | − | 1.85931i | ||||
\(290\) | 5.23088 | + | 16.0990i | 0.307168 | + | 0.945365i | ||||
\(291\) | 6.01556 | − | 4.37056i | 0.352638 | − | 0.256207i | ||||
\(292\) | 1.54210 | − | 1.12040i | 0.0902448 | − | 0.0655667i | ||||
\(293\) | −0.629549 | − | 1.93755i | −0.0367787 | − | 0.113193i | 0.930982 | − | 0.365066i | \(-0.118954\pi\) |
−0.967760 | + | 0.251873i | \(0.918954\pi\) | |||||||
\(294\) | −6.21715 | + | 19.1344i | −0.362592 | + | 1.11594i | ||||
\(295\) | −0.156771 | − | 0.113901i | −0.00912755 | − | 0.00663156i | ||||
\(296\) | 17.4312 | 1.01317 | ||||||||
\(297\) | 2.38193 | − | 2.30790i | 0.138214 | − | 0.133918i | ||||
\(298\) | 9.05403 | 0.524486 | ||||||||
\(299\) | −4.02872 | − | 2.92704i | −0.232987 | − | 0.169275i | ||||
\(300\) | −0.111922 | + | 0.344461i | −0.00646184 | + | 0.0198875i | ||||
\(301\) | −15.2415 | − | 46.9084i | −0.878504 | − | 2.70376i | ||||
\(302\) | 5.02637 | − | 3.65187i | 0.289235 | − | 0.210142i | ||||
\(303\) | −6.34482 | + | 4.60978i | −0.364500 | + | 0.264825i | ||||
\(304\) | −1.41837 | − | 4.36530i | −0.0813493 | − | 0.250367i | ||||
\(305\) | −6.27338 | + | 19.3075i | −0.359213 | + | 1.10554i | ||||
\(306\) | −9.26669 | − | 6.73264i | −0.529741 | − | 0.384880i | ||||
\(307\) | 26.8345 | 1.53153 | 0.765763 | − | 0.643123i | \(-0.222362\pi\) | ||||
0.765763 | + | 0.643123i | \(0.222362\pi\) | |||||||
\(308\) | 6.42597 | − | 6.22624i | 0.366154 | − | 0.354773i | ||||
\(309\) | −11.6680 | −0.663768 | ||||||||
\(310\) | −21.6480 | − | 15.7282i | −1.22952 | − | 0.893301i | ||||
\(311\) | 4.93791 | − | 15.1973i | 0.280003 | − | 0.861761i | −0.707849 | − | 0.706364i | \(-0.750334\pi\) |
0.987852 | − | 0.155397i | \(-0.0496657\pi\) | |||||||
\(312\) | −0.693300 | − | 2.13376i | −0.0392504 | − | 0.120800i | ||||
\(313\) | −5.37012 | + | 3.90162i | −0.303537 | + | 0.220533i | −0.729118 | − | 0.684387i | \(-0.760070\pi\) |
0.425581 | + | 0.904920i | \(0.360070\pi\) | |||||||
\(314\) | −10.9694 | + | 7.96971i | −0.619037 | + | 0.449757i | ||||
\(315\) | −2.86122 | − | 8.80593i | −0.161212 | − | 0.496158i | ||||
\(316\) | 0.461370 | − | 1.41995i | 0.0259541 | − | 0.0798785i | ||||
\(317\) | −3.78387 | − | 2.74914i | −0.212523 | − | 0.154407i | 0.476431 | − | 0.879212i | \(-0.341930\pi\) |
−0.688955 | + | 0.724805i | \(0.741930\pi\) | |||||||
\(318\) | −1.77153 | −0.0993422 | ||||||||
\(319\) | −7.27834 | − | 14.8598i | −0.407509 | − | 0.831991i | ||||
\(320\) | −8.99675 | −0.502933 | ||||||||
\(321\) | −1.08173 | − | 0.785926i | −0.0603766 | − | 0.0438661i | ||||
\(322\) | 10.9675 | − | 33.7545i | 0.611195 | − | 1.88106i | ||||
\(323\) | −2.07310 | − | 6.38034i | −0.115350 | − | 0.355011i | ||||
\(324\) | −0.494897 | + | 0.359564i | −0.0274943 | + | 0.0199758i | ||||
\(325\) | −0.478999 | + | 0.348013i | −0.0265701 | + | 0.0193043i | ||||
\(326\) | −8.71628 | − | 26.8260i | −0.482750 | − | 1.48575i | ||||
\(327\) | 0.954081 | − | 2.93636i | 0.0527608 | − | 0.162381i | ||||
\(328\) | 0.902466 | + | 0.655680i | 0.0498304 | + | 0.0362039i | ||||
\(329\) | 5.34639 | 0.294756 | ||||||||
\(330\) | −1.93561 | + | 11.0855i | −0.106552 | + | 0.610237i | ||||
\(331\) | 7.33259 | 0.403036 | 0.201518 | − | 0.979485i | \(-0.435413\pi\) | ||||
0.201518 | + | 0.979485i | \(0.435413\pi\) | |||||||
\(332\) | 6.80422 | + | 4.94356i | 0.373430 | + | 0.271313i | ||||
\(333\) | 2.40088 | − | 7.38914i | 0.131567 | − | 0.404923i | ||||
\(334\) | 5.98613 | + | 18.4234i | 0.327547 | + | 1.00808i | ||||
\(335\) | 14.4501 | − | 10.4986i | 0.789495 | − | 0.573602i | ||||
\(336\) | 17.3015 | − | 12.5703i | 0.943874 | − | 0.685765i | ||||
\(337\) | −9.70689 | − | 29.8747i | −0.528768 | − | 1.62738i | −0.756743 | − | 0.653713i | \(-0.773210\pi\) |
0.227975 | − | 0.973667i | \(-0.426790\pi\) | |||||||
\(338\) | −0.499397 | + | 1.53699i | −0.0271636 | + | 0.0836011i | ||||
\(339\) | −3.41356 | − | 2.48010i | −0.185399 | − | 0.134700i | ||||
\(340\) | 9.10284 | 0.493671 | ||||||||
\(341\) | 23.1150 | + | 12.2411i | 1.25175 | + | 0.662891i | ||||
\(342\) | −1.52967 | −0.0827151 | ||||||||
\(343\) | −19.4424 | − | 14.1258i | −1.04979 | − | 0.762719i | ||||
\(344\) | −7.75379 | + | 23.8637i | −0.418056 | + | 1.28664i | ||||
\(345\) | 3.23079 | + | 9.94335i | 0.173940 | + | 0.535332i | ||||
\(346\) | 19.6337 | − | 14.2647i | 1.05551 | − | 0.766876i | ||||
\(347\) | −21.9137 | + | 15.9212i | −1.17639 | + | 0.854695i | −0.991759 | − | 0.128114i | \(-0.959108\pi\) |
−0.184627 | + | 0.982809i | \(0.559108\pi\) | |||||||
\(348\) | 0.943085 | + | 2.90252i | 0.0505547 | + | 0.155591i | ||||
\(349\) | −5.89468 | + | 18.1420i | −0.315535 | + | 0.971117i | 0.659998 | + | 0.751267i | \(0.270557\pi\) |
−0.975534 | + | 0.219850i | \(0.929443\pi\) | |||||||
\(350\) | −3.41390 | − | 2.48034i | −0.182481 | − | 0.132580i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −10.9988 | + | 1.56450i | −0.586239 | + | 0.0833882i | ||||
\(353\) | 0.825609 | 0.0439427 | 0.0219714 | − | 0.999759i | \(-0.493006\pi\) | ||||
0.0219714 | + | 0.999759i | \(0.493006\pi\) | |||||||
\(354\) | −0.120674 | − | 0.0876745i | −0.00641373 | − | 0.00465985i | ||||
\(355\) | −10.4752 | + | 32.2394i | −0.555967 | + | 1.71109i | ||||
\(356\) | 1.38851 | + | 4.27340i | 0.0735910 | + | 0.226490i | ||||
\(357\) | 25.2879 | − | 18.3727i | 1.33838 | − | 0.972388i | ||||
\(358\) | 12.4428 | − | 9.04019i | 0.657620 | − | 0.477789i | ||||
\(359\) | 6.20649 | + | 19.1016i | 0.327566 | + | 1.00814i | 0.970269 | + | 0.242029i | \(0.0778130\pi\) |
−0.642703 | + | 0.766116i | \(0.722187\pi\) | |||||||
\(360\) | −1.45559 | + | 4.47984i | −0.0767162 | + | 0.236108i | ||||
\(361\) | 14.6465 | + | 10.6413i | 0.770869 | + | 0.560069i | ||||
\(362\) | −22.9673 | −1.20714 | ||||||||
\(363\) | 0.347208 | − | 10.9945i | 0.0182237 | − | 0.577063i | ||||
\(364\) | −2.69780 | −0.141403 | ||||||||
\(365\) | −5.29266 | − | 3.84534i | −0.277030 | − | 0.201274i | ||||
\(366\) | −4.82890 | + | 14.8618i | −0.252411 | + | 0.776841i | ||||
\(367\) | 7.70602 | + | 23.7167i | 0.402251 | + | 1.23800i | 0.923169 | + | 0.384395i | \(0.125590\pi\) |
−0.520918 | + | 0.853607i | \(0.674410\pi\) | |||||||
\(368\) | −19.5362 | + | 14.1939i | −1.01840 | + | 0.739909i | ||||
\(369\) | 0.402246 | − | 0.292249i | 0.0209401 | − | 0.0152139i | ||||
\(370\) | 8.14612 | + | 25.0712i | 0.423497 | + | 1.30339i | ||||
\(371\) | 1.49389 | − | 4.59771i | 0.0775588 | − | 0.238701i | ||||
\(372\) | −3.90296 | − | 2.83566i | −0.202359 | − | 0.147022i | ||||
\(373\) | −23.7393 | −1.22917 | −0.614587 | − | 0.788849i | \(-0.710677\pi\) | ||||
−0.614587 | + | 0.788849i | \(0.710677\pi\) | |||||||
\(374\) | −37.6109 | + | 5.34987i | −1.94481 | + | 0.276635i | ||||
\(375\) | 11.7406 | 0.606282 | ||||||||
\(376\) | −2.20042 | − | 1.59870i | −0.113478 | − | 0.0824465i | ||||
\(377\) | −1.54168 | + | 4.74480i | −0.0794005 | + | 0.244370i | ||||
\(378\) | −2.20241 | − | 6.77832i | −0.113280 | − | 0.348639i | ||||
\(379\) | 18.4708 | − | 13.4198i | 0.948782 | − | 0.689330i | −0.00173686 | − | 0.999998i | \(-0.500553\pi\) |
0.950518 | + | 0.310668i | \(0.100553\pi\) | |||||||
\(380\) | 0.983481 | − | 0.714541i | 0.0504515 | − | 0.0366552i | ||||
\(381\) | 3.23742 | + | 9.96377i | 0.165858 | + | 0.510459i | ||||
\(382\) | −5.03997 | + | 15.5114i | −0.257867 | + | 0.793634i | ||||
\(383\) | 5.59079 | + | 4.06195i | 0.285676 | + | 0.207556i | 0.721389 | − | 0.692530i | \(-0.243504\pi\) |
−0.435713 | + | 0.900085i | \(0.643504\pi\) | |||||||
\(384\) | −13.6245 | −0.695272 | ||||||||
\(385\) | −27.1384 | − | 14.3717i | −1.38310 | − | 0.732451i | ||||
\(386\) | 15.2895 | 0.778217 | ||||||||
\(387\) | 9.04795 | + | 6.57372i | 0.459933 | + | 0.334161i | ||||
\(388\) | −1.40559 | + | 4.32595i | −0.0713578 | + | 0.219617i | ||||
\(389\) | −3.86991 | − | 11.9104i | −0.196212 | − | 0.603880i | −0.999960 | − | 0.00890978i | \(-0.997164\pi\) |
0.803748 | − | 0.594970i | \(-0.202836\pi\) | |||||||
\(390\) | 2.74498 | − | 1.99434i | 0.138997 | − | 0.100987i | ||||
\(391\) | −28.5542 | + | 20.7458i | −1.44405 | + | 1.04916i | ||||
\(392\) | 8.63111 | + | 26.5638i | 0.435937 | + | 1.34168i | ||||
\(393\) | 0.448830 | − | 1.38136i | 0.0226405 | − | 0.0696802i | ||||
\(394\) | −20.3936 | − | 14.8168i | −1.02742 | − | 0.746461i | ||||
\(395\) | −5.12421 | −0.257827 | ||||||||
\(396\) | −0.348975 | + | 1.99863i | −0.0175366 | + | 0.100435i | ||||
\(397\) | 14.6729 | 0.736409 | 0.368205 | − | 0.929745i | \(-0.379973\pi\) | ||||
0.368205 | + | 0.929745i | \(0.379973\pi\) | |||||||
\(398\) | 9.37963 | + | 6.81470i | 0.470158 | + | 0.341590i | ||||
\(399\) | 1.28994 | − | 3.97002i | 0.0645776 | − | 0.198750i | ||||
\(400\) | 0.887225 | + | 2.73060i | 0.0443612 | + | 0.136530i | ||||
\(401\) | −24.3143 | + | 17.6653i | −1.21420 | + | 0.882165i | −0.995605 | − | 0.0936512i | \(-0.970146\pi\) |
−0.218591 | + | 0.975817i | \(0.570146\pi\) | |||||||
\(402\) | 11.1229 | − | 8.08127i | 0.554761 | − | 0.403057i | ||||
\(403\) | −2.43703 | − | 7.50042i | −0.121397 | − | 0.373622i | ||||
\(404\) | 1.48252 | − | 4.56273i | 0.0737582 | − | 0.227004i | ||||
\(405\) | 1.69854 | + | 1.23406i | 0.0844009 | + | 0.0613209i | ||||
\(406\) | −35.5572 | −1.76467 | ||||||||
\(407\) | −11.3347 | − | 23.1414i | −0.561838 | − | 1.14708i | ||||
\(408\) | −15.9016 | −0.787249 | ||||||||
\(409\) | −6.65695 | − | 4.83656i | −0.329165 | − | 0.239153i | 0.410911 | − | 0.911675i | \(-0.365211\pi\) |
−0.740076 | + | 0.672523i | \(0.765211\pi\) | |||||||
\(410\) | −0.521312 | + | 1.60443i | −0.0257458 | + | 0.0792373i | ||||
\(411\) | −6.02404 | − | 18.5401i | −0.297144 | − | 0.914516i | ||||
\(412\) | 5.77444 | − | 4.19538i | 0.284486 | − | 0.206691i | ||||
\(413\) | 0.329307 | − | 0.239255i | 0.0162041 | − | 0.0117730i | ||||
\(414\) | 2.48688 | + | 7.65384i | 0.122224 | + | 0.376166i | ||||
\(415\) | 8.91997 | − | 27.4528i | 0.437864 | − | 1.34761i | ||||
\(416\) | 2.70992 | + | 1.96887i | 0.132865 | + | 0.0965320i | ||||
\(417\) | 9.68851 | 0.474448 | ||||||||
\(418\) | −3.64357 | + | 3.53033i | −0.178213 | + | 0.172674i | ||||
\(419\) | −31.4008 | −1.53403 | −0.767015 | − | 0.641630i | \(-0.778259\pi\) | ||||
−0.767015 | + | 0.641630i | \(0.778259\pi\) | |||||||
\(420\) | 4.58230 | + | 3.32924i | 0.223593 | + | 0.162450i | ||||
\(421\) | −2.30727 | + | 7.10106i | −0.112450 | + | 0.346084i | −0.991407 | − | 0.130817i | \(-0.958240\pi\) |
0.878957 | + | 0.476901i | \(0.158240\pi\) | |||||||
\(422\) | 14.2714 | + | 43.9229i | 0.694721 | + | 2.13813i | ||||
\(423\) | −0.980767 | + | 0.712569i | −0.0476865 | + | 0.0346463i | ||||
\(424\) | −1.98967 | + | 1.44558i | −0.0966267 | + | 0.0702034i | ||||
\(425\) | 1.29677 | + | 3.99105i | 0.0629026 | + | 0.193594i | ||||
\(426\) | −8.06324 | + | 24.8161i | −0.390665 | + | 1.20234i | ||||
\(427\) | −34.4994 | − | 25.0653i | −1.66955 | − | 1.21300i | ||||
\(428\) | 0.817938 | 0.0395365 | ||||||||
\(429\) | −2.38193 | + | 2.30790i | −0.115001 | + | 0.111426i | ||||
\(430\) | −37.9466 | −1.82995 | ||||||||
\(431\) | −26.1632 | − | 19.0087i | −1.26024 | − | 0.915615i | −0.261466 | − | 0.965213i | \(-0.584206\pi\) |
−0.998769 | + | 0.0495977i | \(0.984206\pi\) | |||||||
\(432\) | −1.49850 | + | 4.61190i | −0.0720965 | + | 0.221890i | ||||
\(433\) | 5.68893 | + | 17.5087i | 0.273393 | + | 0.841416i | 0.989640 | + | 0.143570i | \(0.0458581\pi\) |
−0.716248 | + | 0.697846i | \(0.754142\pi\) | |||||||
\(434\) | 45.4729 | − | 33.0380i | 2.18277 | − | 1.58587i | ||||
\(435\) | 8.47395 | − | 6.15669i | 0.406295 | − | 0.295191i | ||||
\(436\) | 0.583636 | + | 1.79625i | 0.0279511 | + | 0.0860246i | ||||
\(437\) | −1.45655 | + | 4.48281i | −0.0696763 | + | 0.214442i | ||||
\(438\) | −4.07400 | − | 2.95993i | −0.194663 | − | 0.141431i | ||||
\(439\) | 4.35766 | 0.207980 | 0.103990 | − | 0.994578i | \(-0.466839\pi\) | ||||
0.103990 | + | 0.994578i | \(0.466839\pi\) | |||||||
\(440\) | 6.87190 | + | 14.0300i | 0.327605 | + | 0.668855i | ||||
\(441\) | 12.4493 | 0.592824 | ||||||||
\(442\) | 9.26669 | + | 6.73264i | 0.440771 | + | 0.320239i | ||||
\(443\) | −3.68705 | + | 11.3476i | −0.175177 | + | 0.539139i | −0.999641 | − | 0.0267746i | \(-0.991476\pi\) |
0.824465 | + | 0.565913i | \(0.191476\pi\) | |||||||
\(444\) | 1.46868 | + | 4.52013i | 0.0697005 | + | 0.214516i | ||||
\(445\) | 12.4763 | − | 9.06454i | 0.591432 | − | 0.429701i | ||||
\(446\) | 0.262281 | − | 0.190558i | 0.0124193 | − | 0.00902318i | ||||
\(447\) | −1.73125 | − | 5.32825i | −0.0818854 | − | 0.252017i | ||||
\(448\) | 5.83987 | − | 17.9733i | 0.275908 | − | 0.849157i | ||||
\(449\) | −17.9031 | − | 13.0074i | −0.844899 | − | 0.613855i | 0.0788355 | − | 0.996888i | \(-0.474880\pi\) |
−0.923735 | + | 0.383032i | \(0.874880\pi\) | |||||||
\(450\) | 0.956844 | 0.0451061 | ||||||||
\(451\) | 0.283642 | − | 1.62446i | 0.0133562 | − | 0.0764929i | ||||
\(452\) | 2.58111 | 0.121405 | ||||||||
\(453\) | −3.11022 | − | 2.25971i | −0.146131 | − | 0.106170i | ||||
\(454\) | −0.762237 | + | 2.34592i | −0.0357735 | + | 0.110100i | ||||
\(455\) | 2.86122 | + | 8.80593i | 0.134136 | + | 0.412829i | ||||
\(456\) | −1.71803 | + | 1.24822i | −0.0804541 | + | 0.0584534i | ||||
\(457\) | 16.6608 | − | 12.1048i | 0.779359 | − | 0.566237i | −0.125428 | − | 0.992103i | \(-0.540030\pi\) |
0.904786 | + | 0.425866i | \(0.140030\pi\) | |||||||
\(458\) | −13.8090 | − | 42.4998i | −0.645253 | − | 1.98588i | ||||
\(459\) | −2.19021 | + | 6.74077i | −0.102230 | + | 0.314632i | ||||
\(460\) | −5.17418 | − | 3.75926i | −0.241247 | − | 0.175276i | ||||
\(461\) | −4.11740 | −0.191766 | −0.0958831 | − | 0.995393i | \(-0.530568\pi\) | ||||
−0.0958831 | + | 0.995393i | \(0.530568\pi\) | |||||||
\(462\) | −20.8897 | − | 11.0626i | −0.971876 | − | 0.514677i | ||||
\(463\) | 13.5247 | 0.628546 | 0.314273 | − | 0.949333i | \(-0.398239\pi\) | ||||
0.314273 | + | 0.949333i | \(0.398239\pi\) | |||||||
\(464\) | 19.5724 | + | 14.2201i | 0.908624 | + | 0.660154i | ||||
\(465\) | −5.11656 | + | 15.7472i | −0.237275 | + | 0.730257i | ||||
\(466\) | 4.11197 | + | 12.6553i | 0.190483 | + | 0.586247i | ||||
\(467\) | −12.2634 | + | 8.90988i | −0.567482 | + | 0.412300i | −0.834190 | − | 0.551478i | \(-0.814064\pi\) |
0.266708 | + | 0.963778i | \(0.414064\pi\) | |||||||
\(468\) | 0.494897 | − | 0.359564i | 0.0228766 | − | 0.0166208i | ||||
\(469\) | 11.5940 | + | 35.6825i | 0.535359 | + | 1.64767i | ||||
\(470\) | 1.27108 | − | 3.91197i | 0.0586304 | − | 0.180446i | ||||
\(471\) | 6.78762 | + | 4.93149i | 0.312757 | + | 0.227231i | ||||
\(472\) | −0.207076 | −0.00953144 | ||||||||
\(473\) | 36.7231 | − | 5.22359i | 1.68853 | − | 0.240181i | ||||
\(474\) | −3.94433 | −0.181169 | ||||||||
\(475\) | 0.453387 | + | 0.329405i | 0.0208028 | + | 0.0151141i | ||||
\(476\) | −5.90873 | + | 18.1852i | −0.270826 | + | 0.833518i | ||||
\(477\) | 0.338740 | + | 1.04253i | 0.0155098 | + | 0.0477343i | ||||
\(478\) | 38.8735 | − | 28.2433i | 1.77803 | − | 1.29182i | ||||
\(479\) | −0.383924 | + | 0.278937i | −0.0175419 | + | 0.0127450i | −0.596522 | − | 0.802597i | \(-0.703451\pi\) |
0.578980 | + | 0.815342i | \(0.303451\pi\) | |||||||
\(480\) | −2.17320 | − | 6.68841i | −0.0991923 | − | 0.305283i | ||||
\(481\) | −2.40088 | + | 7.38914i | −0.109471 | + | 0.336916i | ||||
\(482\) | 16.8409 | + | 12.2356i | 0.767082 | + | 0.557318i | ||||
\(483\) | −21.9615 | −0.999282 | ||||||||
\(484\) | 3.78140 | + | 5.56600i | 0.171882 | + | 0.253000i | ||||
\(485\) | 15.6112 | 0.708866 | ||||||||
\(486\) | 1.30744 | + | 0.949910i | 0.0593066 | + | 0.0430888i | ||||
\(487\) | 4.46306 | − | 13.7359i | 0.202240 | − | 0.622432i | −0.797575 | − | 0.603220i | \(-0.793884\pi\) |
0.999815 | − | 0.0192121i | \(-0.00611578\pi\) | |||||||
\(488\) | 6.70384 | + | 20.6323i | 0.303469 | + | 0.933980i | ||||
\(489\) | −14.1203 | + | 10.2590i | −0.638540 | + | 0.463927i | ||||
\(490\) | −34.1730 | + | 24.8282i | −1.54378 | + | 1.12162i | ||||
\(491\) | −8.31046 | − | 25.5770i | −0.375046 | − | 1.15427i | −0.943448 | − | 0.331521i | \(-0.892438\pi\) |
0.568402 | − | 0.822751i | \(-0.307562\pi\) | |||||||
\(492\) | −0.0939883 | + | 0.289266i | −0.00423732 | + | 0.0130411i | ||||
\(493\) | 28.6070 | + | 20.7842i | 1.28839 | + | 0.936073i | ||||
\(494\) | 1.52967 | 0.0688232 | ||||||||
\(495\) | 6.89388 | − | 0.980604i | 0.309857 | − | 0.0440749i | ||||
\(496\) | −38.2431 | −1.71717 | ||||||||
\(497\) | −57.6067 | − | 41.8537i | −2.58401 | − | 1.87740i | ||||
\(498\) | 6.86610 | − | 21.1317i | 0.307677 | − | 0.946933i | ||||
\(499\) | −4.35334 | − | 13.3982i | −0.194882 | − | 0.599786i | −0.999978 | − | 0.00664097i | \(-0.997886\pi\) |
0.805096 | − | 0.593145i | \(-0.202114\pi\) | |||||||
\(500\) | −5.81038 | + | 4.22149i | −0.259848 | + | 0.188791i | ||||
\(501\) | 9.69746 | − | 7.04562i | 0.433250 | − | 0.314775i | ||||
\(502\) | 6.55585 | + | 20.1768i | 0.292602 | + | 0.900536i | ||||
\(503\) | 3.59302 | − | 11.0582i | 0.160205 | − | 0.493060i | −0.838446 | − | 0.544984i | \(-0.816536\pi\) |
0.998651 | + | 0.0519248i | \(0.0165356\pi\) | |||||||
\(504\) | −8.00477 | − | 5.81580i | −0.356561 | − | 0.259056i | ||||
\(505\) | −16.4656 | −0.732712 | ||||||||
\(506\) | 23.5879 | + | 12.4915i | 1.04861 | + | 0.555313i | ||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −5.18480 | − | 3.76698i | −0.230038 | − | 0.167133i | ||||
\(509\) | −3.40327 | + | 10.4742i | −0.150847 | + | 0.464261i | −0.997717 | − | 0.0675407i | \(-0.978485\pi\) |
0.846869 | + | 0.531802i | \(0.178485\pi\) | |||||||
\(510\) | −7.43133 | − | 22.8713i | −0.329065 | − | 1.01276i | ||||
\(511\) | 11.1175 | − | 8.07737i | 0.491811 | − | 0.357322i | ||||
\(512\) | −4.46249 | + | 3.24219i | −0.197216 | + | 0.143286i | ||||
\(513\) | 0.292494 | + | 0.900203i | 0.0129139 | + | 0.0397449i | ||||
\(514\) | −13.4520 | + | 41.4009i | −0.593341 | + | 1.82612i | ||||
\(515\) | −19.8185 | − | 14.3990i | −0.873306 | − | 0.634494i | ||||
\(516\) | −6.84147 | −0.301179 | ||||||||
\(517\) | −0.691585 | + | 3.96080i | −0.0304159 | + | 0.174196i | ||||
\(518\) | −55.3737 | −2.43298 | ||||||||
\(519\) | −12.1489 | − | 8.82672i | −0.533279 | − | 0.387450i | ||||
\(520\) | 1.45559 | − | 4.47984i | 0.0638317 | − | 0.196454i | ||||
\(521\) | −10.7307 | − | 33.0257i | −0.470120 | − | 1.44688i | −0.852427 | − | 0.522846i | \(-0.824870\pi\) |
0.382307 | − | 0.924035i | \(-0.375130\pi\) | |||||||
\(522\) | 6.52278 | − | 4.73908i | 0.285494 | − | 0.207424i | ||||
\(523\) | −32.6239 | + | 23.7027i | −1.42654 | + | 1.03645i | −0.435898 | + | 0.899996i | \(0.643569\pi\) |
−0.990647 | + | 0.136449i | \(0.956431\pi\) | |||||||
\(524\) | 0.274561 | + | 0.845012i | 0.0119943 | + | 0.0369145i | ||||
\(525\) | −0.806885 | + | 2.48334i | −0.0352154 | + | 0.108382i | ||||
\(526\) | 22.5296 | + | 16.3687i | 0.982339 | + | 0.713711i | ||||
\(527\) | −55.8962 | −2.43488 | ||||||||
\(528\) | 7.07449 | + | 14.4436i | 0.307877 | + | 0.628578i | ||||
\(529\) | 1.79813 | 0.0781795 | ||||||||
\(530\) | −3.00900 | − | 2.18617i | −0.130703 | − | 0.0949610i | ||||
\(531\) | −0.0285215 | + | 0.0877803i | −0.00123773 | + | 0.00380934i | ||||
\(532\) | 0.789088 | + | 2.42856i | 0.0342113 | + | 0.105292i | ||||
\(533\) | −0.402246 | + | 0.292249i | −0.0174232 | + | 0.0126587i | ||||
\(534\) | 9.60355 | − | 6.97738i | 0.415586 | − | 0.301941i | ||||
\(535\) | −0.867486 | − | 2.66985i | −0.0375047 | − | 0.115428i | ||||
\(536\) | 5.89819 | − | 18.1528i | 0.254763 | − | 0.784080i | ||||
\(537\) | −7.69933 | − | 5.59389i | −0.332251 | − | 0.241394i | ||||
\(538\) | −2.67300 | −0.115241 | ||||||||
\(539\) | 29.6534 | − | 28.7317i | 1.27726 | − | 1.23756i | ||||
\(540\) | −1.28432 | −0.0552684 | ||||||||
\(541\) | −3.06411 | − | 2.22621i | −0.131736 | − | 0.0957120i | 0.519966 | − | 0.854187i | \(-0.325945\pi\) |
−0.651702 | + | 0.758475i | \(0.725945\pi\) | |||||||
\(542\) | −0.670954 | + | 2.06498i | −0.0288199 | + | 0.0886986i | ||||
\(543\) | 4.39166 | + | 13.5162i | 0.188464 | + | 0.580034i | ||||
\(544\) | 19.2070 | − | 13.9547i | 0.823494 | − | 0.598304i | ||||
\(545\) | 5.24418 | − | 3.81012i | 0.224636 | − | 0.163208i | ||||
\(546\) | 2.20241 | + | 6.77832i | 0.0942545 | + | 0.290085i | ||||
\(547\) | −11.9571 | + | 36.8000i | −0.511247 | + | 1.57346i | 0.278762 | + | 0.960360i | \(0.410076\pi\) |
−0.790009 | + | 0.613096i | \(0.789924\pi\) | |||||||
\(548\) | 9.64762 | + | 7.00941i | 0.412126 | + | 0.299427i | ||||
\(549\) | 9.66946 | 0.412683 | ||||||||
\(550\) | 2.27914 | − | 2.20830i | 0.0971828 | − | 0.0941622i | ||||
\(551\) | 4.72221 | 0.201173 | ||||||||
\(552\) | 9.03870 | + | 6.56700i | 0.384713 | + | 0.279510i | ||||
\(553\) | 3.32617 | − | 10.2369i | 0.141443 | − | 0.435317i | ||||
\(554\) | −6.51302 | − | 20.0450i | −0.276712 | − | 0.851632i | ||||
\(555\) | 13.1966 | − | 9.58790i | 0.560165 | − | 0.406984i | ||||
\(556\) | −4.79481 | + | 3.48363i | −0.203345 | + | 0.147739i | ||||
\(557\) | 4.36248 | + | 13.4263i | 0.184844 | + | 0.568892i | 0.999946 | − | 0.0104264i | \(-0.00331889\pi\) |
−0.815102 | + | 0.579318i | \(0.803319\pi\) | |||||||
\(558\) | −3.93845 | + | 12.1213i | −0.166728 | + | 0.513135i | ||||
\(559\) | −9.04795 | − | 6.57372i | −0.382687 | − | 0.278039i | ||||
\(560\) | 44.8997 | 1.89736 | ||||||||
\(561\) | 10.3401 | + | 21.1108i | 0.436559 | + | 0.891300i | ||||
\(562\) | 37.6974 | 1.59017 | ||||||||
\(563\) | −16.1663 | − | 11.7455i | −0.681329 | − | 0.495014i | 0.192469 | − | 0.981303i | \(-0.438350\pi\) |
−0.873798 | + | 0.486289i | \(0.838350\pi\) | |||||||
\(564\) | 0.229165 | − | 0.705297i | 0.00964958 | − | 0.0296983i | ||||
\(565\) | −2.73747 | − | 8.42507i | −0.115166 | − | 0.354445i | ||||
\(566\) | 13.4949 | − | 9.80462i | 0.567233 | − | 0.412119i | ||||
\(567\) | −3.56788 | + | 2.59221i | −0.149837 | + | 0.108863i | ||||
\(568\) | 11.1940 | + | 34.4516i | 0.469689 | + | 1.44556i | ||||
\(569\) | 0.624122 | − | 1.92085i | 0.0261646 | − | 0.0805263i | −0.937122 | − | 0.349003i | \(-0.886520\pi\) |
0.963286 | + | 0.268477i | \(0.0865203\pi\) | |||||||
\(570\) | −2.59820 | − | 1.88770i | −0.108827 | − | 0.0790672i | ||||
\(571\) | 25.0318 | 1.04755 | 0.523774 | − | 0.851857i | \(-0.324524\pi\) | ||||
0.523774 | + | 0.851857i | \(0.324524\pi\) | |||||||
\(572\) | 0.348975 | − | 1.99863i | 0.0145914 | − | 0.0835668i | ||||
\(573\) | 10.0921 | 0.421604 | ||||||||
\(574\) | −2.86687 | − | 2.08290i | −0.119661 | − | 0.0869387i | ||||
\(575\) | 0.911106 | − | 2.80410i | 0.0379958 | − | 0.116939i | ||||
\(576\) | 1.32419 | + | 4.07544i | 0.0551746 | + | 0.169810i | ||||
\(577\) | −20.0401 | + | 14.5600i | −0.834279 | + | 0.606139i | −0.920767 | − | 0.390114i | \(-0.872436\pi\) |
0.0864876 | + | 0.996253i | \(0.472436\pi\) | |||||||
\(578\) | 43.4527 | − | 31.5702i | 1.80739 | − | 1.31315i | ||||
\(579\) | −2.92357 | − | 8.99781i | −0.121499 | − | 0.373936i | ||||
\(580\) | −1.98001 | + | 6.09385i | −0.0822155 | + | 0.253033i | ||||
\(581\) | 49.0539 | + | 35.6397i | 2.03510 | + | 1.47859i | ||||
\(582\) | 12.0166 | 0.498105 | ||||||||
\(583\) | 3.21292 | + | 1.70147i | 0.133065 | + | 0.0704676i | ||||
\(584\) | −6.99098 | −0.289289 | ||||||||
\(585\) | −1.69854 | − | 1.23406i | −0.0702258 | − | 0.0510220i | ||||
\(586\) | 1.01740 | − | 3.13125i | 0.0420286 | − | 0.129351i | ||||
\(587\) | −13.1771 | − | 40.5550i | −0.543878 | − | 1.67389i | −0.723642 | − | 0.690176i | \(-0.757533\pi\) |
0.179763 | − | 0.983710i | \(-0.442467\pi\) | |||||||
\(588\) | −6.16112 | + | 4.47632i | −0.254080 | + | 0.184600i | ||||
\(589\) | −6.03908 | + | 4.38765i | −0.248836 | + | 0.180790i | ||||
\(590\) | −0.0967729 | − | 0.297837i | −0.00398408 | − | 0.0122617i | ||||
\(591\) | −4.82009 | + | 14.8347i | −0.198272 | + | 0.610219i | ||||
\(592\) | 30.4803 | + | 22.1452i | 1.25273 | + | 0.910164i | ||||
\(593\) | −22.8548 | −0.938534 | −0.469267 | − | 0.883056i | \(-0.655482\pi\) | ||||
−0.469267 | + | 0.883056i | \(0.655482\pi\) | |||||||
\(594\) | 5.30653 | − | 0.754815i | 0.217729 | − | 0.0309704i | ||||
\(595\) | 65.6254 | 2.69038 | ||||||||
\(596\) | 2.77264 | + | 2.01444i | 0.113572 | + | 0.0825146i | ||||
\(597\) | 2.21690 | − | 6.82292i | 0.0907318 | − | 0.279244i | ||||
\(598\) | −2.48688 | − | 7.65384i | −0.101696 | − | 0.312989i | ||||
\(599\) | 18.6876 | − | 13.5774i | 0.763556 | − | 0.554756i | −0.136443 | − | 0.990648i | \(-0.543567\pi\) |
0.899999 | + | 0.435892i | \(0.143567\pi\) | |||||||
\(600\) | 1.07467 | − | 0.780791i | 0.0438731 | − | 0.0318757i | ||||
\(601\) | −4.12736 | − | 12.7027i | −0.168359 | − | 0.518154i | 0.830910 | − | 0.556408i | \(-0.187821\pi\) |
−0.999268 | + | 0.0382532i | \(0.987821\pi\) | |||||||
\(602\) | 24.6315 | − | 75.8079i | 1.00390 | − | 3.08970i | ||||
\(603\) | −6.88264 | − | 5.00053i | −0.280283 | − | 0.203637i | ||||
\(604\) | 2.35175 | 0.0956912 | ||||||||
\(605\) | 14.1576 | − | 18.2461i | 0.575589 | − | 0.741810i | ||||
\(606\) | −12.6743 | −0.514860 | ||||||||
\(607\) | 6.14272 | + | 4.46294i | 0.249325 | + | 0.181145i | 0.705428 | − | 0.708782i | \(-0.250755\pi\) |
−0.456103 | + | 0.889927i | \(0.650755\pi\) | |||||||
\(608\) | 0.979752 | − | 3.01537i | 0.0397342 | − | 0.122289i | ||||
\(609\) | 6.79901 | + | 20.9252i | 0.275510 | + | 0.847932i | ||||
\(610\) | −26.5424 | + | 19.2842i | −1.07467 | + | 0.780795i | ||||
\(611\) | 0.980767 | − | 0.712569i | 0.0396776 | − | 0.0288275i | ||||
\(612\) | −1.33981 | − | 4.12350i | −0.0541585 | − | 0.166683i | ||||
\(613\) | −8.22487 | + | 25.3135i | −0.332199 | + | 1.02240i | 0.635886 | + | 0.771783i | \(0.280635\pi\) |
−0.968085 | + | 0.250621i | \(0.919365\pi\) | |||||||
\(614\) | 35.0845 | + | 25.4904i | 1.41589 | + | 1.02871i | ||||
\(615\) | 1.04388 | 0.0420934 | ||||||||
\(616\) | −32.4891 | + | 4.62134i | −1.30902 | + | 0.186199i | ||||
\(617\) | −21.5936 | −0.869326 | −0.434663 | − | 0.900593i | \(-0.643133\pi\) | ||||
−0.434663 | + | 0.900593i | \(0.643133\pi\) | |||||||
\(618\) | −15.2552 | − | 11.0835i | −0.613653 | − | 0.445845i | ||||
\(619\) | 4.13104 | − | 12.7140i | 0.166041 | − | 0.511020i | −0.833071 | − | 0.553166i | \(-0.813419\pi\) |
0.999111 | + | 0.0421460i | \(0.0134195\pi\) | |||||||
\(620\) | −3.12994 | − | 9.63295i | −0.125701 | − | 0.386869i | ||||
\(621\) | 4.02872 | − | 2.92704i | 0.161667 | − | 0.117458i | ||||
\(622\) | 20.8921 | − | 15.1790i | 0.837697 | − | 0.608622i | ||||
\(623\) | 10.0102 | + | 30.8084i | 0.401052 | + | 1.23431i | ||||
\(624\) | 1.49850 | − | 4.61190i | 0.0599880 | − | 0.184624i | ||||
\(625\) | 17.5468 | + | 12.7485i | 0.701873 | + | 0.509941i | ||||
\(626\) | −10.7273 | −0.428749 | ||||||||
\(627\) | 2.77428 | + | 1.46918i | 0.110794 | + | 0.0586733i | ||||
\(628\) | −5.13236 | −0.204803 | ||||||||
\(629\) | 44.5501 | + | 32.3675i | 1.77633 | + | 1.29058i | ||||
\(630\) | 4.62397 | − | 14.2311i | 0.184223 | − | 0.566982i | ||||
\(631\) | 11.5516 | + | 35.5522i | 0.459862 | + | 1.41531i | 0.865330 | + | 0.501202i | \(0.167109\pi\) |
−0.405468 | + | 0.914109i | \(0.632891\pi\) | |||||||
\(632\) | −4.43003 | + | 3.21860i | −0.176217 | + | 0.128029i | ||||
\(633\) | 23.1195 | − | 16.7973i | 0.918918 | − | 0.667633i | ||||
\(634\) | −2.33574 | − | 7.18867i | −0.0927641 | − | 0.285498i | ||||
\(635\) | −6.79699 | + | 20.9190i | −0.269730 | + | 0.830145i | ||||
\(636\) | −0.542498 | − | 0.394148i | −0.0215115 | − | 0.0156290i | ||||
\(637\) | −12.4493 | −0.493259 | ||||||||
\(638\) | 4.59952 | − | 26.3421i | 0.182097 | − | 1.04289i | ||||
\(639\) | 16.1459 | 0.638724 | ||||||||
\(640\) | −23.1417 | − | 16.8134i | −0.914756 | − | 0.664609i | ||||
\(641\) | 7.27351 | − | 22.3856i | 0.287286 | − | 0.884177i | −0.698418 | − | 0.715691i | \(-0.746112\pi\) |
0.985704 | − | 0.168486i | \(-0.0538879\pi\) | |||||||
\(642\) | −0.667743 | − | 2.05510i | −0.0263537 | − | 0.0811084i | ||||
\(643\) | −32.1590 | + | 23.3649i | −1.26823 | + | 0.921421i | −0.999131 | − | 0.0416919i | \(-0.986725\pi\) |
−0.269097 | + | 0.963113i | \(0.586725\pi\) | |||||||
\(644\) | 10.8687 | − | 7.89655i | 0.428285 | − | 0.311168i | ||||
\(645\) | 7.25591 | + | 22.3314i | 0.285701 | + | 0.879298i | ||||
\(646\) | 3.35030 | − | 10.3112i | 0.131816 | − | 0.405687i | ||||
\(647\) | 10.4115 | + | 7.56442i | 0.409320 | + | 0.297388i | 0.773326 | − | 0.634008i | \(-0.218591\pi\) |
−0.364007 | + | 0.931396i | \(0.618591\pi\) | |||||||
\(648\) | 2.24357 | 0.0881356 | ||||||||
\(649\) | 0.134652 | + | 0.274912i | 0.00528554 | + | 0.0107912i | ||||
\(650\) | −0.956844 | −0.0375305 | ||||||||
\(651\) | −28.1377 | − | 20.4432i | −1.10280 | − | 0.801234i | ||||
\(652\) | 3.29932 | − | 10.1543i | 0.129211 | − | 0.397672i | ||||
\(653\) | 11.0056 | + | 33.8718i | 0.430683 | + | 1.32551i | 0.897446 | + | 0.441123i | \(0.145420\pi\) |
−0.466764 | + | 0.884382i | \(0.654580\pi\) | |||||||
\(654\) | 4.03668 | − | 2.93282i | 0.157847 | − | 0.114682i | ||||
\(655\) | 2.46703 | − | 1.79240i | 0.0963948 | − | 0.0700349i | ||||
\(656\) | 0.745059 | + | 2.29306i | 0.0290897 | + | 0.0895288i | ||||
\(657\) | −0.962901 | + | 2.96350i | −0.0375663 | + | 0.115617i | ||||
\(658\) | 6.99008 | + | 5.07859i | 0.272502 | + | 0.197984i | ||||
\(659\) | 27.4165 | 1.06800 | 0.533998 | − | 0.845486i | \(-0.320689\pi\) | ||||
0.533998 | + | 0.845486i | \(0.320689\pi\) | |||||||
\(660\) | −3.05917 | + | 2.96409i | −0.119078 | + | 0.115377i | ||||
\(661\) | 2.93350 | 0.114100 | 0.0570499 | − | 0.998371i | \(-0.481831\pi\) | ||||
0.0570499 | + | 0.998371i | \(0.481831\pi\) | |||||||
\(662\) | 9.58692 | + | 6.96530i | 0.372606 | + | 0.270714i | ||||
\(663\) | 2.19021 | − | 6.74077i | 0.0850606 | − | 0.261790i | ||||
\(664\) | −9.53202 | − | 29.3366i | −0.369914 | − | 1.13848i | ||||
\(665\) | 7.09024 | − | 5.15136i | 0.274948 | − | 0.199761i | ||||
\(666\) | 10.1580 | − | 7.38024i | 0.393615 | − | 0.285978i | ||||
\(667\) | −7.67721 | − | 23.6280i | −0.297263 | − | 0.914880i | ||||
\(668\) | −2.26589 | + | 6.97371i | −0.0876701 | + | 0.269821i | ||||
\(669\) | −0.162294 | − | 0.117913i | −0.00627465 | − | 0.00455880i | ||||
\(670\) | 28.8654 | 1.11517 | ||||||||
\(671\) | 23.0320 | − | 22.3161i | 0.889141 | − | 0.861505i | ||||
\(672\) | 14.7724 | 0.569858 | ||||||||
\(673\) | 2.21758 | + | 1.61116i | 0.0854813 | + | 0.0621058i | 0.629705 | − | 0.776834i | \(-0.283176\pi\) |
−0.544224 | + | 0.838940i | \(0.683176\pi\) | |||||||
\(674\) | 15.6871 | − | 48.2801i | 0.604246 | − | 1.85968i | ||||
\(675\) | −0.182961 | − | 0.563098i | −0.00704219 | − | 0.0216736i | ||||
\(676\) | −0.494897 | + | 0.359564i | −0.0190345 | + | 0.0138294i | ||||
\(677\) | 18.7138 | − | 13.5964i | 0.719230 | − | 0.522551i | −0.166908 | − | 0.985972i | \(-0.553378\pi\) |
0.886138 | + | 0.463421i | \(0.153378\pi\) | |||||||
\(678\) | −2.10715 | − | 6.48515i | −0.0809248 | − | 0.249061i | ||||
\(679\) | −10.1333 | + | 31.1872i | −0.388882 | + | 1.19686i | ||||
\(680\) | −27.0095 | − | 19.6236i | −1.03577 | − | 0.752529i | ||||
\(681\) | 1.52631 | 0.0584885 | ||||||||
\(682\) | 18.5936 | + | 37.9617i | 0.711986 | + | 1.45363i | ||||
\(683\) | 10.6098 | 0.405971 | 0.202986 | − | 0.979182i | \(-0.434936\pi\) | ||||
0.202986 | + | 0.979182i | \(0.434936\pi\) | |||||||
\(684\) | −0.468435 | − | 0.340338i | −0.0179110 | − | 0.0130131i | ||||
\(685\) | 12.6475 | − | 38.9250i | 0.483237 | − | 1.48725i | ||||
\(686\) | −12.0016 | − | 36.9371i | −0.458223 | − | 1.41027i | ||||
\(687\) | −22.3704 | + | 16.2531i | −0.853485 | + | 0.620093i | ||||
\(688\) | −43.8757 | + | 31.8776i | −1.67275 | + | 1.21532i | ||||
\(689\) | −0.338740 | − | 1.04253i | −0.0129050 | − | 0.0397174i | ||||
\(690\) | −5.22123 | + | 16.0693i | −0.198769 | + | 0.611747i | ||||
\(691\) | 0.460311 | + | 0.334435i | 0.0175110 | + | 0.0127225i | 0.596506 | − | 0.802608i | \(-0.296555\pi\) |
−0.578995 | + | 0.815331i | \(0.696555\pi\) | |||||||
\(692\) | 9.18624 | 0.349208 | ||||||||
\(693\) | −2.51587 | + | 14.4088i | −0.0955702 | + | 0.547344i | ||||
\(694\) | −43.7745 | −1.66166 | ||||||||
\(695\) | 16.4563 | + | 11.9562i | 0.624222 | + | 0.453524i | ||||
\(696\) | 3.45886 | − | 10.6453i | 0.131108 | − | 0.403508i | ||||
\(697\) | 1.08898 | + | 3.35153i | 0.0412480 | + | 0.126948i | ||||
\(698\) | −24.9402 | + | 18.1201i | −0.944000 | + | 0.685856i | ||||
\(699\) | 6.66133 | − | 4.83974i | 0.251955 | − | 0.183056i | ||||
\(700\) | −0.493593 | − | 1.51912i | −0.0186561 | − | 0.0574174i | ||||
\(701\) | 3.33374 | − | 10.2602i | 0.125914 | − | 0.387523i | −0.868153 | − | 0.496297i | \(-0.834693\pi\) |
0.994066 | + | 0.108774i | \(0.0346926\pi\) | |||||||
\(702\) | −1.30744 | − | 0.949910i | −0.0493461 | − | 0.0358520i | ||||
\(703\) | 7.35397 | 0.277360 | ||||||||
\(704\) | 12.5598 | + | 6.65133i | 0.473367 | + | 0.250681i | ||||
\(705\) | −2.54522 | −0.0958586 | ||||||||
\(706\) | 1.07943 | + | 0.784255i | 0.0406250 | + | 0.0295158i | ||||
\(707\) | 10.6880 | − | 32.8943i | 0.401963 | − | 1.23712i | ||||
\(708\) | −0.0174474 | − | 0.0536975i | −0.000655713 | − | 0.00201808i | ||||
\(709\) | −25.6535 | + | 18.6384i | −0.963439 | + | 0.699979i | −0.953947 | − | 0.299976i | \(-0.903021\pi\) |
−0.00949199 | + | 0.999955i | \(0.503021\pi\) | |||||||
\(710\) | −44.3202 | + | 32.2005i | −1.66331 | + | 1.20846i | ||||
\(711\) | 0.754210 | + | 2.32122i | 0.0282851 | + | 0.0870525i | ||||
\(712\) | 5.09250 | − | 15.6731i | 0.190850 | − | 0.587375i | ||||
\(713\) | 31.7721 | + | 23.0838i | 1.18987 | + | 0.864495i | ||||
\(714\) | 50.5148 | 1.89047 | ||||||||
\(715\) | −6.89388 | + | 0.980604i | −0.257816 | + | 0.0366725i | ||||
\(716\) | 5.82173 | 0.217568 | ||||||||
\(717\) | −24.0542 | − | 17.4764i | −0.898319 | − | 0.652667i | ||||
\(718\) | −10.0302 | + | 30.8698i | −0.374324 | + | 1.15205i | ||||
\(719\) | 12.4350 | + | 38.2709i | 0.463746 | + | 1.42726i | 0.860553 | + | 0.509361i | \(0.170118\pi\) |
−0.396807 | + | 0.917902i | \(0.629882\pi\) | |||||||
\(720\) | −8.23661 | + | 5.98425i | −0.306960 | + | 0.223020i | ||||
\(721\) | 41.6299 | − | 30.2459i | 1.55038 | − | 1.12642i | ||||
\(722\) | 9.04113 | + | 27.8257i | 0.336476 | + | 1.03557i | ||||
\(723\) | 3.98040 | − | 12.2504i | 0.148033 | − | 0.455597i | ||||
\(724\) | −7.03334 | − | 5.11002i | −0.261392 | − | 0.189912i | ||||
\(725\) | −2.95385 | −0.109703 | ||||||||
\(726\) | 10.8978 | − | 14.0448i | 0.404454 | − | 0.521253i | ||||
\(727\) | 28.7502 | 1.06628 | 0.533142 | − | 0.846026i | \(-0.321011\pi\) | ||||
0.533142 | + | 0.846026i | \(0.321011\pi\) | |||||||
\(728\) | 8.00477 | + | 5.81580i | 0.296676 | + | 0.215548i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −3.26710 | − | 10.0551i | −0.120921 | − | 0.372156i | ||||
\(731\) | −64.1288 | + | 46.5923i | −2.37189 | + | 1.72328i | ||||
\(732\) | −4.78539 | + | 3.47679i | −0.176873 | + | 0.128506i | ||||
\(733\) | 3.74810 | + | 11.5355i | 0.138439 | + | 0.426072i | 0.996109 | − | 0.0881288i | \(-0.0280887\pi\) |
−0.857670 | + | 0.514201i | \(0.828089\pi\) | |||||||
\(734\) | −12.4536 | + | 38.3282i | −0.459670 | + | 1.41472i | ||||
\(735\) | 21.1456 | + | 15.3632i | 0.779967 | + | 0.566679i | ||||
\(736\) | −16.6805 | −0.614851 | ||||||||
\(737\) | −27.9347 | + | 3.97351i | −1.02899 | + | 0.146366i | ||||
\(738\) | 0.803523 | 0.0295781 | ||||||||
\(739\) | 21.1216 | + | 15.3457i | 0.776969 | + | 0.564501i | 0.904068 | − | 0.427389i | \(-0.140567\pi\) |
−0.127099 | + | 0.991890i | \(0.540567\pi\) | |||||||
\(740\) | −3.08350 | + | 9.49004i | −0.113352 | + | 0.348861i | ||||
\(741\) | −0.292494 | − | 0.900203i | −0.0107450 | − | 0.0330698i | ||||
\(742\) | 6.32058 | − | 4.59217i | 0.232036 | − | 0.168584i | ||||
\(743\) | −30.4945 | + | 22.1556i | −1.11874 | + | 0.812810i | −0.984017 | − | 0.178074i | \(-0.943013\pi\) |
−0.134719 | + | 0.990884i | \(0.543013\pi\) | |||||||
\(744\) | 5.46765 | + | 16.8277i | 0.200454 | + | 0.616933i | ||||
\(745\) | 3.63478 | − | 11.1867i | 0.133168 | − | 0.409849i | ||||
\(746\) | −31.0377 | − | 22.5502i | −1.13637 | − | 0.825621i | ||||
\(747\) | −13.7488 | −0.503041 | ||||||||
\(748\) | −12.7080 | − | 6.72977i | −0.464649 | − | 0.246065i | ||||
\(749\) | 5.89678 | 0.215464 | ||||||||
\(750\) | 15.3501 | + | 11.1525i | 0.560507 | + | 0.407232i | ||||
\(751\) | −7.21031 | + | 22.1910i | −0.263108 | + | 0.809763i | 0.729015 | + | 0.684497i | \(0.239978\pi\) |
−0.992123 | + | 0.125265i | \(0.960022\pi\) | |||||||
\(752\) | −1.81662 | − | 5.59099i | −0.0662454 | − | 0.203882i | ||||
\(753\) | 10.6204 | − | 7.71616i | 0.387028 | − | 0.281193i | ||||
\(754\) | −6.52278 | + | 4.73908i | −0.237546 | + | 0.172587i | ||||
\(755\) | −2.49421 | − | 7.67638i | −0.0907735 | − | 0.279372i | ||||
\(756\) | 0.833665 | − | 2.56576i | 0.0303201 | − | 0.0933157i | ||||
\(757\) | −31.4875 | − | 22.8770i | −1.14443 | − | 0.831480i | −0.156703 | − | 0.987646i | \(-0.550087\pi\) |
−0.987731 | + | 0.156166i | \(0.950087\pi\) | |||||||
\(758\) | 36.8971 | 1.34016 | ||||||||
\(759\) | 2.84084 | − | 16.2699i | 0.103116 | − | 0.590559i | ||||
\(760\) | −4.45852 | −0.161727 | ||||||||
\(761\) | 3.01413 | + | 2.18989i | 0.109262 | + | 0.0793835i | 0.641075 | − | 0.767479i | \(-0.278489\pi\) |
−0.531813 | + | 0.846862i | \(0.678489\pi\) | |||||||
\(762\) | −5.23195 | + | 16.1023i | −0.189533 | + | 0.583324i | ||||
\(763\) | 4.20763 | + | 12.9497i | 0.152326 | + | 0.468812i | ||||
\(764\) | −4.99455 | + | 3.62875i | −0.180696 | + | 0.131284i | ||||
\(765\) | −12.0386 | + | 8.74659i | −0.435258 | + | 0.316234i | ||||
\(766\) | 3.45113 | + | 10.6215i | 0.124694 | + | 0.383770i | ||||
\(767\) | 0.0285215 | − | 0.0877803i | 0.00102985 | − | 0.00316956i | ||||
\(768\) | −10.8796 | − | 7.90452i | −0.392585 | − | 0.285230i | ||||
\(769\) | 52.0029 | 1.87527 | 0.937636 | − | 0.347618i | \(-0.113009\pi\) | ||||
0.937636 | + | 0.347618i | \(0.113009\pi\) | |||||||
\(770\) | −21.8300 | − | 44.5692i | −0.786699 | − | 1.60616i | ||||
\(771\) | 26.9364 | 0.970092 | ||||||||
\(772\) | 4.68215 | + | 3.40178i | 0.168514 | + | 0.122433i | ||||
\(773\) | −3.93228 | + | 12.1023i | −0.141434 | + | 0.435290i | −0.996535 | − | 0.0831717i | \(-0.973495\pi\) |
0.855101 | + | 0.518461i | \(0.173495\pi\) | |||||||
\(774\) | 5.58520 | + | 17.1895i | 0.200756 | + | 0.617863i | ||||
\(775\) | 3.77758 | − | 2.74457i | 0.135695 | − | 0.0985880i | ||||
\(776\) | 13.4963 | − | 9.80564i | 0.484489 | − | 0.352002i | ||||
\(777\) | 10.5882 | + | 32.5871i | 0.379850 | + | 1.16906i | ||||
\(778\) | 6.25411 | − | 19.2482i | 0.224221 | − | 0.690080i | ||||
\(779\) | 0.380738 | + | 0.276622i | 0.0136414 | + | 0.00991102i | ||||
\(780\) | 1.28432 | 0.0459861 | ||||||||
\(781\) | 38.4586 | − | 37.2632i | 1.37616 | − | 1.33338i | ||||
\(782\) | −57.0396 | −2.03973 | ||||||||
\(783\) | −4.03617 | − | 2.93245i | −0.144241 | − | 0.104797i | ||||
\(784\) | −18.6553 | + | 57.4150i | −0.666260 | + | 2.05054i | ||||
\(785\) | 5.44326 | + | 16.7526i | 0.194278 | + | 0.597927i | ||||
\(786\) | 1.89898 | − | 1.37969i | 0.0677345 | − | 0.0492120i | ||||
\(787\) | 24.3861 | − | 17.7176i | 0.869272 | − | 0.631563i | −0.0611194 | − | 0.998130i | \(-0.519467\pi\) |
0.930392 | + | 0.366567i | \(0.119467\pi\) | |||||||
\(788\) | −2.94858 | − | 9.07478i | −0.105039 | − | 0.323276i | ||||
\(789\) | 5.32495 | − | 16.3885i | 0.189573 | − | 0.583446i | ||||
\(790\) | −6.69959 | − | 4.86754i | −0.238361 | − | 0.173179i | ||||
\(791\) | 18.6081 | 0.661628 | ||||||||
\(792\) | 5.34402 | − | 5.17792i | 0.189892 | − | 0.183990i | ||||
\(793\) | −9.66946 | −0.343373 | ||||||||
\(794\) | 19.1839 | + | 13.9379i | 0.680810 | + | 0.494637i | ||||
\(795\) | −0.711186 | + | 2.18880i | −0.0252232 | + | 0.0776289i | ||||
\(796\) | 1.35614 | + | 4.17376i | 0.0480670 | + | 0.147935i | ||||
\(797\) | −15.1658 | + | 11.0186i | −0.537202 | + | 0.390300i | −0.823045 | − | 0.567977i | \(-0.807726\pi\) |
0.285843 | + | 0.958276i | \(0.407726\pi\) | |||||||
\(798\) | 5.45768 | − | 3.96523i | 0.193200 | − | 0.140368i | ||||
\(799\) | −2.65518 | − | 8.17180i | −0.0939335 | − | 0.289098i | ||||
\(800\) | −0.612857 | + | 1.88618i | −0.0216678 | + | 0.0666865i | ||||
\(801\) | −5.94248 | − | 4.31746i | −0.209967 | − | 0.152550i | ||||
\(802\) | −48.5699 | −1.71506 | ||||||||
\(803\) | 4.54590 | + | 9.28114i | 0.160421 | + | 0.327524i | ||||
\(804\) | 5.20420 | 0.183538 | ||||||||
\(805\) | −37.3024 | − | 27.1017i | −1.31474 | − | 0.955211i | ||||
\(806\) | 3.93845 | − | 12.1213i | 0.138726 | − | 0.426955i | ||||
\(807\) | 0.511114 | + | 1.57305i | 0.0179921 | + | 0.0553739i | ||||
\(808\) | −14.2350 | + | 10.3424i | −0.500787 | + | 0.363843i | ||||
\(809\) | −10.0588 | + | 7.30814i | −0.353648 | + | 0.256940i | −0.750398 | − | 0.660986i | \(-0.770138\pi\) |
0.396750 | + | 0.917927i | \(0.370138\pi\) | |||||||
\(810\) | 1.04849 | + | 3.22691i | 0.0368401 | + | 0.113382i | ||||
\(811\) | −8.36700 | + | 25.7510i | −0.293805 | + | 0.904239i | 0.689815 | + | 0.723985i | \(0.257692\pi\) |
−0.983620 | + | 0.180253i | \(0.942308\pi\) | |||||||
\(812\) | −10.8888 | − | 7.91114i | −0.382120 | − | 0.277627i | ||||
\(813\) | 1.34353 | 0.0471195 | ||||||||
\(814\) | 7.16289 | − | 41.0229i | 0.251059 | − | 1.43785i | ||||
\(815\) | −36.6439 | −1.28358 | ||||||||
\(816\) | −27.8058 | − | 20.2021i | −0.973396 | − | 0.707214i | ||||
\(817\) | −3.27121 | + | 10.0678i | −0.114445 | + | 0.352226i | ||||
\(818\) | −4.10926 | − | 12.6470i | −0.143677 | − | 0.442193i | ||||
\(819\) | 3.56788 | − | 2.59221i | 0.124672 | − | 0.0905793i | ||||
\(820\) | −0.516614 | + | 0.375342i | −0.0180409 | + | 0.0131075i | ||||
\(821\) | −9.34055 | − | 28.7473i | −0.325987 | − | 1.00329i | −0.970993 | − | 0.239108i | \(-0.923145\pi\) |
0.645006 | − | 0.764178i | \(-0.276855\pi\) | |||||||
\(822\) | 9.73536 | − | 29.9623i | 0.339560 | − | 1.04506i | ||||
\(823\) | 23.8304 | + | 17.3138i | 0.830674 | + | 0.603520i | 0.919750 | − | 0.392505i | \(-0.128391\pi\) |
−0.0890759 | + | 0.996025i | \(0.528391\pi\) | |||||||
\(824\) | −26.1779 | −0.911949 | ||||||||
\(825\) | −1.73537 | − | 0.919004i | −0.0604180 | − | 0.0319956i | ||||
\(826\) | 0.657819 | 0.0228885 | ||||||||
\(827\) | −35.6492 | − | 25.9007i | −1.23964 | − | 0.900654i | −0.242069 | − | 0.970259i | \(-0.577826\pi\) |
−0.997575 | + | 0.0696051i | \(0.977826\pi\) | |||||||
\(828\) | −0.941345 | + | 2.89716i | −0.0327140 | + | 0.100683i | ||||
\(829\) | −10.5238 | − | 32.3888i | −0.365505 | − | 1.12491i | −0.949664 | − | 0.313270i | \(-0.898576\pi\) |
0.584159 | − | 0.811639i | \(-0.301424\pi\) | |||||||
\(830\) | 37.7400 | − | 27.4197i | 1.30998 | − | 0.951753i | ||||
\(831\) | −10.5510 | + | 7.66576i | −0.366011 | + | 0.265922i | ||||
\(832\) | −1.32419 | − | 4.07544i | −0.0459081 | − | 0.141291i | ||||
\(833\) | −27.2666 | + | 83.9179i | −0.944731 | + | 2.90758i | ||||
\(834\) | 12.6671 | + | 9.20321i | 0.438627 | + | 0.318681i | ||||
\(835\) | 25.1662 | 0.870912 | ||||||||
\(836\) | −1.90124 | + | 0.270438i | −0.0657559 | + | 0.00935330i | ||||
\(837\) | 7.88640 | 0.272594 | ||||||||
\(838\) | −41.0546 | − | 29.8279i | −1.41821 | − | 1.03039i | ||||
\(839\) | 0.667628 | − | 2.05475i | 0.0230491 | − | 0.0709378i | −0.938870 | − | 0.344271i | \(-0.888126\pi\) |
0.961919 | + | 0.273333i | \(0.0881261\pi\) | |||||||
\(840\) | −6.41934 | − | 19.7567i | −0.221488 | − | 0.681671i | ||||
\(841\) | 3.32516 | − | 2.41587i | 0.114661 | − | 0.0833058i | ||||
\(842\) | −9.76198 | + | 7.09250i | −0.336420 | + | 0.244424i | ||||
\(843\) | −7.20825 | − | 22.1847i | −0.248265 | − | 0.764082i | ||||
\(844\) | −5.40207 | + | 16.6259i | −0.185947 | + | 0.572286i | ||||
\(845\) | 1.69854 | + | 1.23406i | 0.0584314 | + | 0.0424529i | ||||
\(846\) | −1.95917 | −0.0673577 | ||||||||
\(847\) | 27.2613 | + | 40.1271i | 0.936711 | + | 1.37878i | ||||
\(848\) | −5.31566 | −0.182541 | ||||||||
\(849\) | −8.35037 | − | 6.06690i | −0.286584 | − | 0.208215i | ||||
\(850\) | −2.09569 | + | 6.44986i | −0.0718815 | + | 0.221228i | ||||
\(851\) | −11.9558 | − | 36.7962i | −0.409840 | − | 1.26136i | ||||
\(852\) | −7.99058 | + | 5.80549i | −0.273753 | + | 0.198893i | ||||
\(853\) | 32.8705 | − | 23.8818i | 1.12547 | − | 0.817699i | 0.140437 | − | 0.990090i | \(-0.455149\pi\) |
0.985029 | + | 0.172391i | \(0.0551492\pi\) | |||||||
\(854\) | −21.2961 | − | 65.5427i | −0.728738 | − | 2.24283i | ||||
\(855\) | −0.614092 | + | 1.88998i | −0.0210015 | + | 0.0646360i | ||||
\(856\) | −2.42694 | − | 1.76328i | −0.0829512 | − | 0.0602676i | ||||
\(857\) | 6.55009 | 0.223747 | 0.111873 | − | 0.993722i | \(-0.464315\pi\) | ||||
0.111873 | + | 0.993722i | \(0.464315\pi\) | |||||||
\(858\) | −5.30653 | + | 0.754815i | −0.181162 | + | 0.0257690i | ||||
\(859\) | −17.9430 | −0.612207 | −0.306103 | − | 0.951998i | \(-0.599025\pi\) | ||||
−0.306103 | + | 0.951998i | \(0.599025\pi\) | |||||||
\(860\) | −11.6205 | − | 8.44278i | −0.396255 | − | 0.287896i | ||||
\(861\) | −0.677593 | + | 2.08542i | −0.0230923 | + | 0.0710708i | ||||
\(862\) | −16.1502 | − | 49.7053i | −0.550079 | − | 1.69297i | ||||
\(863\) | 11.0397 | − | 8.02079i | 0.375795 | − | 0.273031i | −0.383815 | − | 0.923410i | \(-0.625390\pi\) |
0.759610 | + | 0.650379i | \(0.225390\pi\) | |||||||
\(864\) | −2.70992 | + | 1.96887i | −0.0921935 | + | 0.0669825i | ||||
\(865\) | −9.74272 | − | 29.9850i | −0.331262 | − | 1.01952i | ||||
\(866\) | −9.19379 | + | 28.2956i | −0.312418 | + | 0.961523i | ||||
\(867\) | −26.8877 | − | 19.5350i | −0.913153 | − | 0.663444i | ||||
\(868\) | 21.2759 | 0.722151 | ||||||||
\(869\) | 7.15362 | + | 3.78835i | 0.242670 | + | 0.128511i | ||||
\(870\) | 16.9275 | 0.573895 | ||||||||
\(871\) | 6.88264 | + | 5.00053i | 0.233209 | + | 0.169436i | ||||
\(872\) | 2.14054 | − | 6.58791i | 0.0724879 | − | 0.223095i | ||||
\(873\) | −2.29774 | − | 7.07171i | −0.0777667 | − | 0.239341i | ||||
\(874\) | −6.16262 | + | 4.47740i | −0.208454 | + | 0.151450i | ||||
\(875\) | −41.8890 | + | 30.4341i | −1.41611 | + | 1.02886i | ||||
\(876\) | −0.589031 | − | 1.81285i | −0.0199015 | − | 0.0612506i | ||||
\(877\) | −14.0168 | + | 43.1392i | −0.473313 | + | 1.45671i | 0.374906 | + | 0.927063i | \(0.377675\pi\) |
−0.848219 | + | 0.529645i | \(0.822325\pi\) | |||||||
\(878\) | 5.69738 | + | 4.13939i | 0.192277 | + | 0.139698i | ||||
\(879\) | −2.03726 | −0.0687152 | ||||||||
\(880\) | −5.80802 | + | 33.2634i | −0.195788 | + | 1.12131i | ||||
\(881\) | −0.648468 | −0.0218474 | −0.0109237 | − | 0.999940i | \(-0.503477\pi\) | ||||
−0.0109237 | + | 0.999940i | \(0.503477\pi\) | |||||||
\(882\) | 16.2767 | + | 11.8257i | 0.548065 | + | 0.398193i | ||||
\(883\) | −16.6313 | + | 51.1859i | −0.559688 | + | 1.72254i | 0.123541 | + | 0.992340i | \(0.460575\pi\) |
−0.683229 | + | 0.730204i | \(0.739425\pi\) | |||||||
\(884\) | 1.33981 | + | 4.12350i | 0.0450626 | + | 0.138688i | ||||
\(885\) | −0.156771 | + | 0.113901i | −0.00526980 | + | 0.00382873i | ||||
\(886\) | −15.5997 | + | 11.3339i | −0.524084 | + | 0.380769i | ||||
\(887\) | 0.227875 | + | 0.701327i | 0.00765129 | + | 0.0235483i | 0.954809 | − | 0.297219i | \(-0.0960592\pi\) |
−0.947158 | + | 0.320767i | \(0.896059\pi\) | |||||||
\(888\) | 5.38653 | − | 16.5780i | 0.180760 | − | 0.556322i | ||||
\(889\) | −37.3789 | − | 27.1574i | −1.25365 | − | 0.910829i | ||||
\(890\) | 24.9225 | 0.835403 | ||||||||
\(891\) | −1.45888 | − | 2.97853i | −0.0488745 | − | 0.0997846i | ||||
\(892\) | 0.122716 | 0.00410884 | ||||||||
\(893\) | −0.928326 | − | 0.674468i | −0.0310652 | − | 0.0225702i | ||||
\(894\) | 2.79785 | − | 8.61089i | 0.0935741 | − | 0.287991i | ||||
\(895\) | −6.17440 | − | 19.0028i | −0.206387 | − | 0.635195i | ||||
\(896\) | 48.6105 | − | 35.3176i | 1.62396 | − | 1.17988i | ||||
\(897\) | −4.02872 | + | 2.92704i | −0.134515 | + | 0.0977309i | ||||
\(898\) | −11.0514 | − | 34.0127i | −0.368790 | − | 1.13502i | ||||
\(899\) | 12.1583 | − | 37.4194i | 0.405502 | − | 1.24801i | ||||
\(900\) | 0.293016 | + | 0.212889i | 0.00976721 | + | 0.00709630i | ||||
\(901\) | −7.76939 | −0.258836 | ||||||||
\(902\) | 1.91394 | − | 1.85445i | 0.0637271 | − | 0.0617464i | ||||
\(903\) | −49.3224 | −1.64135 | ||||||||
\(904\) | −7.65855 | − | 5.56426i | −0.254720 | − | 0.185065i | ||||
\(905\) | −9.22032 | + | 28.3772i | −0.306494 | + | 0.943291i | ||||
\(906\) | −1.91990 | − | 5.90886i | −0.0637845 | − | 0.196309i | ||||
\(907\) | −17.5533 | + | 12.7532i | −0.582848 | + | 0.423464i | −0.839750 | − | 0.542974i | \(-0.817298\pi\) |
0.256902 | + | 0.966438i | \(0.417298\pi\) | |||||||
\(908\) | −0.755368 | + | 0.548807i | −0.0250678 | + | 0.0182128i | ||||
\(909\) | 2.42351 | + | 7.45878i | 0.0803826 | + | 0.247392i | ||||
\(910\) | −4.62397 | + | 14.2311i | −0.153283 | + | 0.471757i | ||||
\(911\) | −6.16070 | − | 4.47601i | −0.204113 | − | 0.148297i | 0.481033 | − | 0.876702i | \(-0.340262\pi\) |
−0.685146 | + | 0.728406i | \(0.740262\pi\) | |||||||
\(912\) | −4.58995 | −0.151989 | ||||||||
\(913\) | −32.7486 | + | 31.7308i | −1.08382 | + | 1.05014i | ||||
\(914\) | 33.2814 | 1.10085 | ||||||||
\(915\) | 16.4239 | + | 11.9327i | 0.542958 | + | 0.394482i | ||||
\(916\) | 5.22704 | − | 16.0872i | 0.172706 | − | 0.531535i | ||||
\(917\) | 1.97940 | + | 6.09197i | 0.0653656 | + | 0.201175i | ||||
\(918\) | −9.26669 | + | 6.73264i | −0.305846 | + | 0.222210i | ||||
\(919\) | 12.3268 | − | 8.95593i | 0.406623 | − | 0.295429i | −0.365610 | − | 0.930768i | \(-0.619140\pi\) |
0.772233 | + | 0.635339i | \(0.219140\pi\) | |||||||
\(920\) | 7.24850 | + | 22.3086i | 0.238976 | + | 0.735492i | ||||
\(921\) | 8.29232 | − | 25.5211i | 0.273241 | − | 0.840950i | ||||
\(922\) | −5.38325 | − | 3.91116i | −0.177288 | − | 0.128807i | ||||
\(923\) | −16.1459 | −0.531450 | ||||||||
\(924\) | −3.93577 | − | 8.03547i | −0.129477 | − | 0.264348i | ||||
\(925\) | −4.60008 | −0.151250 | ||||||||
\(926\) | 17.6827 | + | 12.8472i | 0.581090 | + | 0.422187i | ||||
\(927\) | −3.60560 | + | 11.0969i | −0.118423 | + | 0.364470i | ||||
\(928\) | 5.16408 | + | 15.8934i | 0.169519 | + | 0.521727i | ||||
\(929\) | −34.1610 | + | 24.8194i | −1.12079 | + | 0.814298i | −0.984328 | − | 0.176348i | \(-0.943572\pi\) |
−0.136457 | + | 0.990646i | \(0.543572\pi\) | |||||||
\(930\) | −21.6480 | + | 15.7282i | −0.709865 | + | 0.515747i | ||||
\(931\) | 3.64134 | + | 11.2069i | 0.119340 | + | 0.367291i | ||||
\(932\) | −1.55648 | + | 4.79035i | −0.0509841 | + | 0.156913i | ||||
\(933\) | −12.9276 | − | 9.39246i | −0.423231 | − | 0.307495i | ||||
\(934\) | −24.4972 | −0.801574 | ||||||||
\(935\) | −8.48901 | + | 48.6178i | −0.277620 | + | 1.58997i | ||||
\(936\) | −2.24357 | −0.0733333 | ||||||||
\(937\) | 10.3811 | + | 7.54231i | 0.339136 | + | 0.246396i | 0.744297 | − | 0.667849i | \(-0.232785\pi\) |
−0.405161 | + | 0.914245i | \(0.632785\pi\) | |||||||
\(938\) | −18.7368 | + | 57.6660i | −0.611778 | + | 1.88286i | ||||
\(939\) | 2.05120 | + | 6.31296i | 0.0669385 | + | 0.206016i | ||||
\(940\) | 1.25962 | − | 0.915169i | 0.0410843 | − | 0.0298495i | ||||
\(941\) | 23.6940 | − | 17.2147i | 0.772402 | − | 0.561183i | −0.130287 | − | 0.991476i | \(-0.541590\pi\) |
0.902689 | + | 0.430293i | \(0.141590\pi\) | |||||||
\(942\) | 4.18992 | + | 12.8953i | 0.136515 | + | 0.420150i | ||||
\(943\) | 0.765114 | − | 2.35478i | 0.0249155 | − | 0.0766821i | ||||
\(944\) | −0.362095 | − | 0.263077i | −0.0117852 | − | 0.00856244i | ||||
\(945\) | −9.25911 | −0.301199 | ||||||||
\(946\) | 52.9751 | + | 28.0541i | 1.72237 | + | 0.912118i | ||||
\(947\) | −5.04354 | −0.163893 | −0.0819466 | − | 0.996637i | \(-0.526114\pi\) | ||||
−0.0819466 | + | 0.996637i | \(0.526114\pi\) | |||||||
\(948\) | −1.20788 | − | 0.877578i | −0.0392302 | − | 0.0285024i | ||||
\(949\) | 0.962901 | − | 2.96350i | 0.0312571 | − | 0.0961994i | ||||
\(950\) | 0.279871 | + | 0.861354i | 0.00908021 | + | 0.0279460i | ||||
\(951\) | −3.78387 | + | 2.74914i | −0.122700 | + | 0.0891470i | ||||
\(952\) | 56.7351 | − | 41.2205i | 1.83879 | − | 1.33596i | ||||
\(953\) | −4.58297 | − | 14.1049i | −0.148457 | − | 0.456904i | 0.848982 | − | 0.528421i | \(-0.177216\pi\) |
−0.997439 | + | 0.0715175i | \(0.977216\pi\) | |||||||
\(954\) | −0.547432 | + | 1.68482i | −0.0177237 | + | 0.0545481i | ||||
\(955\) | 17.1418 | + | 12.4542i | 0.554696 | + | 0.403010i | ||||
\(956\) | 18.1882 | 0.588248 | ||||||||
\(957\) | −16.3817 | + | 2.33017i | −0.529544 | + | 0.0753238i | ||||
\(958\) | −0.766922 | −0.0247781 | ||||||||
\(959\) | 69.5529 | + | 50.5332i | 2.24598 | + | 1.63180i | ||||
\(960\) | −2.78015 | + | 8.55641i | −0.0897289 | + | 0.276157i | ||||
\(961\) | 9.63990 | + | 29.6686i | 0.310964 | + | 0.957050i | ||||
\(962\) | −10.1580 | + | 7.38024i | −0.327508 | + | 0.237948i | ||||
\(963\) | −1.08173 | + | 0.785926i | −0.0348584 | + | 0.0253261i | ||||
\(964\) | 2.43491 | + | 7.49389i | 0.0784233 | + | 0.241362i | ||||
\(965\) | 6.13804 | − | 18.8909i | 0.197591 | − | 0.608121i | ||||
\(966\) | −28.7133 | − | 20.8614i | −0.923835 | − | 0.671205i | ||||
\(967\) | 27.0278 | 0.869156 | 0.434578 | − | 0.900634i | \(-0.356898\pi\) | ||||
0.434578 | + | 0.900634i | \(0.356898\pi\) | |||||||
\(968\) | 0.778984 | − | 24.6669i | 0.0250375 | − | 0.792825i | ||||
\(969\) | −6.70868 | −0.215514 | ||||||||
\(970\) | 20.4106 | + | 14.8292i | 0.655346 | + | 0.476137i | ||||
\(971\) | 4.08660 | − | 12.5773i | 0.131145 | − | 0.403624i | −0.863825 | − | 0.503792i | \(-0.831938\pi\) |
0.994971 | + | 0.100168i | \(0.0319379\pi\) | |||||||
\(972\) | 0.189034 | + | 0.581786i | 0.00606326 | + | 0.0186608i | ||||
\(973\) | −34.5674 | + | 25.1147i | −1.10818 | + | 0.805139i | ||||
\(974\) | 18.8830 | − | 13.7193i | 0.605051 | − | 0.439595i | ||||
\(975\) | 0.182961 | + | 0.563098i | 0.00585946 | + | 0.0180336i | ||||
\(976\) | −14.4897 | + | 44.5946i | −0.463803 | + | 1.42744i | ||||
\(977\) | −20.3209 | − | 14.7640i | −0.650124 | − | 0.472343i | 0.213190 | − | 0.977011i | \(-0.431615\pi\) |
−0.863313 | + | 0.504668i | \(0.831615\pi\) | |||||||
\(978\) | −28.2065 | −0.901944 | ||||||||
\(979\) | −24.1189 | + | 3.43073i | −0.770842 | + | 0.109647i | ||||
\(980\) | −15.9889 | −0.510747 | ||||||||
\(981\) | −2.49782 | − | 1.81477i | −0.0797491 | − | 0.0579411i | ||||
\(982\) | 13.4304 | − | 41.3345i | 0.428581 | − | 1.31904i | ||||
\(983\) | −1.52431 | − | 4.69134i | −0.0486179 | − | 0.149630i | 0.923800 | − | 0.382875i | \(-0.125066\pi\) |
−0.972418 | + | 0.233244i | \(0.925066\pi\) | |||||||
\(984\) | 0.902466 | − | 0.655680i | 0.0287696 | − | 0.0209023i | ||||
\(985\) | −26.4940 | + | 19.2490i | −0.844169 | + | 0.613325i | ||||
\(986\) | 17.6588 | + | 54.3481i | 0.562370 | + | 1.73080i | ||||
\(987\) | 1.65212 | − | 5.08472i | 0.0525877 | − | 0.161848i | ||||
\(988\) | 0.468435 | + | 0.340338i | 0.0149029 | + | 0.0108276i | ||||
\(989\) | 55.6932 | 1.77094 | ||||||||
\(990\) | 9.94481 | + | 5.26649i | 0.316067 | + | 0.167380i | ||||
\(991\) | 9.74941 | 0.309700 | 0.154850 | − | 0.987938i | \(-0.450511\pi\) | ||||
0.154850 | + | 0.987938i | \(0.450511\pi\) | |||||||
\(992\) | −21.3715 | − | 15.5273i | −0.678547 | − | 0.492994i | ||||
\(993\) | 2.26590 | − | 6.97371i | 0.0719060 | − | 0.221304i | ||||
\(994\) | −35.5600 | − | 109.442i | −1.12789 | − | 3.47130i | ||||
\(995\) | 12.1854 | − | 8.85319i | 0.386302 | − | 0.280665i | ||||
\(996\) | 6.80422 | − | 4.94356i | 0.215600 | − | 0.156643i | ||||
\(997\) | 1.45918 | + | 4.49089i | 0.0462126 | + | 0.142228i | 0.971500 | − | 0.237038i | \(-0.0761766\pi\) |
−0.925288 | + | 0.379266i | \(0.876177\pi\) | |||||||
\(998\) | 7.03536 | − | 21.6526i | 0.222700 | − | 0.685402i | ||||
\(999\) | −6.28558 | − | 4.56674i | −0.198867 | − | 0.144485i |
(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 | 429.2.n.d.235.7 | yes | 36 | |
11.3 | even | 5 | inner | 429.2.n.d.157.7 | ✓ | 36 | |
11.5 | even | 5 | 4719.2.a.bq.1.5 | 18 | |||
11.6 | odd | 10 | 4719.2.a.br.1.14 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.d.157.7 | ✓ | 36 | 11.3 | even | 5 | inner | |
429.2.n.d.235.7 | yes | 36 | 1.1 | even | 1 | trivial | |
4719.2.a.bq.1.5 | 18 | 11.5 | even | 5 | |||
4719.2.a.br.1.14 | 18 | 11.6 | odd | 10 |