Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [198,3,Mod(53,198)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(198, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("198.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 198.k (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.39510923433\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 14 x^{14} + 255 x^{12} + 3946 x^{10} + 33929 x^{8} + 477466 x^{6} + 3733455 x^{4} + \cdots + 214358881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 71.1 | ||
Root | \(-2.40294 + 2.28602i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 198.71 |
Dual form | 198.3.k.a.53.1 |
$q$-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 \(\left(\mathbb{Z}/198\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(155\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34500 | + | 0.437016i | −0.672499 | + | 0.218508i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.61803 | − | 1.17557i | 0.404508 | − | 0.293893i | ||||
\(5\) | −2.68314 | − | 0.871805i | −0.536628 | − | 0.174361i | 0.0281501 | − | 0.999604i | \(-0.491038\pi\) |
−0.564778 | + | 0.825243i | \(0.691038\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.80392 | − | 1.31063i | 0.257703 | − | 0.187232i | −0.451431 | − | 0.892306i | \(-0.649086\pi\) |
0.709134 | + | 0.705074i | \(0.249086\pi\) | |||||||
\(8\) | −1.66251 | + | 2.28825i | −0.207813 | + | 0.286031i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.98981 | 0.398981 | ||||||||
\(11\) | −10.9772 | − | 0.707957i | −0.997927 | − | 0.0643598i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.39798 | − | 4.30255i | −0.107537 | − | 0.330966i | 0.882780 | − | 0.469786i | \(-0.155669\pi\) |
−0.990318 | + | 0.138820i | \(0.955669\pi\) | |||||||
\(14\) | −1.85351 | + | 2.55113i | −0.132393 | + | 0.182224i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | − | 3.80423i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −14.0058 | − | 4.55076i | −0.823871 | − | 0.267692i | −0.133409 | − | 0.991061i | \(-0.542592\pi\) |
−0.690461 | + | 0.723369i | \(0.742592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.97019 | − | 6.51722i | −0.472115 | − | 0.343012i | 0.326150 | − | 0.945318i | \(-0.394249\pi\) |
−0.798265 | + | 0.602306i | \(0.794249\pi\) | |||||||
\(20\) | −5.36628 | + | 1.74361i | −0.268314 | + | 0.0871805i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 15.0737 | − | 3.84501i | 0.685167 | − | 0.174773i | ||||
\(23\) | − | 11.0813i | − | 0.481796i | −0.970550 | − | 0.240898i | \(-0.922558\pi\) | ||
0.970550 | − | 0.240898i | \(-0.0774419\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.7862 | − | 10.0163i | −0.551449 | − | 0.400651i | ||||
\(26\) | 3.76057 | + | 5.17598i | 0.144637 | + | 0.199076i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.37807 | − | 4.24128i | 0.0492169 | − | 0.151474i | ||||
\(29\) | −13.3045 | − | 18.3121i | −0.458776 | − | 0.631452i | 0.515478 | − | 0.856903i | \(-0.327614\pi\) |
−0.974254 | + | 0.225451i | \(0.927614\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.11534 | − | 21.8988i | −0.229527 | − | 0.706412i | −0.997800 | − | 0.0662901i | \(-0.978884\pi\) |
0.768273 | − | 0.640122i | \(-0.221116\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 20.8265 | 0.612545 | ||||||||
\(35\) | −5.98279 | + | 1.94393i | −0.170937 | + | 0.0555407i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16.2058 | + | 11.7742i | −0.437994 | + | 0.318221i | −0.784837 | − | 0.619702i | \(-0.787254\pi\) |
0.346843 | + | 0.937923i | \(0.387254\pi\) | |||||||
\(38\) | 14.9130 | + | 4.84553i | 0.392448 | + | 0.127514i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.45565 | − | 4.69030i | 0.161391 | − | 0.117258i | ||||
\(41\) | 23.8256 | − | 32.7931i | 0.581111 | − | 0.799831i | −0.412705 | − | 0.910865i | \(-0.635416\pi\) |
0.993817 | + | 0.111033i | \(0.0354160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −45.6612 | −1.06189 | −0.530944 | − | 0.847407i | \(-0.678163\pi\) | ||||
−0.530944 | + | 0.847407i | \(0.678163\pi\) | |||||||
\(44\) | −18.5937 | + | 11.7590i | −0.422585 | + | 0.267249i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.84271 | + | 14.9043i | 0.105276 | + | 0.324007i | ||||
\(47\) | 6.81426 | − | 9.37903i | 0.144984 | − | 0.199554i | −0.730348 | − | 0.683075i | \(-0.760642\pi\) |
0.875333 | + | 0.483521i | \(0.160642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.6054 | + | 41.8732i | −0.277662 | + | 0.854556i | ||||
\(50\) | 22.9197 | + | 7.44706i | 0.458394 | + | 0.148941i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.31994 | − | 5.31825i | −0.140768 | − | 0.102274i | ||||
\(53\) | 37.2253 | − | 12.0952i | 0.702365 | − | 0.228212i | 0.0640042 | − | 0.997950i | \(-0.479613\pi\) |
0.638361 | + | 0.769737i | \(0.279613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 28.8362 | + | 11.4695i | 0.524294 | + | 0.208537i | ||||
\(56\) | 6.30674i | 0.112620i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 25.8972 | + | 18.8154i | 0.446504 | + | 0.324404i | ||||
\(59\) | 54.7514 | + | 75.3588i | 0.927990 | + | 1.27727i | 0.960639 | + | 0.277801i | \(0.0896057\pi\) |
−0.0326490 | + | 0.999467i | \(0.510394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22.9159 | + | 70.5280i | −0.375671 | + | 1.15620i | 0.567354 | + | 0.823474i | \(0.307967\pi\) |
−0.943025 | + | 0.332723i | \(0.892033\pi\) | |||||||
\(62\) | 19.1402 | + | 26.3443i | 0.308713 | + | 0.424908i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.47214 | − | 7.60845i | −0.0386271 | − | 0.118882i | ||||
\(65\) | 12.7631i | 0.196356i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 87.7093 | 1.30909 | 0.654547 | − | 0.756021i | \(-0.272859\pi\) | ||||
0.654547 | + | 0.756021i | \(0.272859\pi\) | |||||||
\(68\) | −28.0116 | + | 9.10152i | −0.411935 | + | 0.133846i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.19731 | − | 5.22915i | 0.102819 | − | 0.0747021i | ||||
\(71\) | 63.8893 | + | 20.7589i | 0.899850 | + | 0.292379i | 0.722175 | − | 0.691710i | \(-0.243143\pi\) |
0.177675 | + | 0.984089i | \(0.443143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28.8781 | + | 20.9811i | −0.395590 | + | 0.287413i | −0.767742 | − | 0.640759i | \(-0.778620\pi\) |
0.372152 | + | 0.928172i | \(0.378620\pi\) | |||||||
\(74\) | 16.6512 | − | 22.9184i | 0.225017 | − | 0.309709i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.1755 | −0.291783 | ||||||||
\(77\) | −20.7299 | + | 13.1099i | −0.269219 | + | 0.170258i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.84946 | + | 24.1582i | 0.0993603 | + | 0.305800i | 0.988365 | − | 0.152098i | \(-0.0486028\pi\) |
−0.889005 | + | 0.457897i | \(0.848603\pi\) | |||||||
\(80\) | −6.63309 | + | 9.12967i | −0.0829136 | + | 0.114121i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −17.7142 | + | 54.5188i | −0.216027 | + | 0.664863i | ||||
\(83\) | −20.8375 | − | 6.77051i | −0.251054 | − | 0.0815724i | 0.180786 | − | 0.983522i | \(-0.442136\pi\) |
−0.431841 | + | 0.901950i | \(0.642136\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 33.6122 | + | 24.4207i | 0.395437 | + | 0.287302i | ||||
\(86\) | 61.4141 | − | 19.9547i | 0.714118 | − | 0.232031i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 19.8697 | − | 23.9415i | 0.225791 | − | 0.272063i | ||||
\(89\) | − | 34.9908i | − | 0.393155i | −0.980488 | − | 0.196577i | \(-0.937017\pi\) | ||
0.980488 | − | 0.196577i | \(-0.0629827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.16089 | − | 5.92924i | −0.0896801 | − | 0.0651564i | ||||
\(92\) | −13.0269 | − | 17.9299i | −0.141596 | − | 0.194891i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.06638 | + | 15.5927i | −0.0538976 | + | 0.165880i | ||||
\(95\) | 18.3865 | + | 25.3069i | 0.193542 | + | 0.266388i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −33.7192 | − | 103.777i | −0.347621 | − | 1.06987i | −0.960166 | − | 0.279432i | \(-0.909854\pi\) |
0.612545 | − | 0.790436i | \(-0.290146\pi\) | |||||||
\(98\) | − | 62.2652i | − | 0.635359i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −34.0814 | −0.340814 | ||||||||
\(101\) | −171.987 | + | 55.8819i | −1.70284 | + | 0.553286i | −0.989116 | − | 0.147140i | \(-0.952993\pi\) |
−0.713725 | + | 0.700426i | \(0.752993\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 163.062 | − | 118.472i | 1.58313 | − | 1.15021i | 0.670131 | − | 0.742243i | \(-0.266238\pi\) |
0.912997 | − | 0.407967i | \(-0.133762\pi\) | |||||||
\(104\) | 12.1695 | + | 3.95410i | 0.117014 | + | 0.0380202i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −44.7822 | + | 32.5361i | −0.422473 | + | 0.306945i | ||||
\(107\) | 53.7458 | − | 73.9747i | 0.502297 | − | 0.691353i | −0.480300 | − | 0.877104i | \(-0.659472\pi\) |
0.982597 | + | 0.185752i | \(0.0594721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −207.818 | −1.90659 | −0.953295 | − | 0.302040i | \(-0.902332\pi\) | ||||
−0.953295 | + | 0.302040i | \(0.902332\pi\) | |||||||
\(110\) | −43.7969 | − | 2.82462i | −0.398154 | − | 0.0256783i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.75615 | − | 8.48255i | −0.0246085 | − | 0.0757371i | ||||
\(113\) | 37.3186 | − | 51.3646i | 0.330253 | − | 0.454554i | −0.611310 | − | 0.791391i | \(-0.709357\pi\) |
0.941563 | + | 0.336837i | \(0.109357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.66075 | + | 29.7327i | −0.0840065 | + | 0.258545i | ||||
\(116\) | −43.0543 | − | 13.9892i | −0.371158 | − | 0.120597i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −106.573 | − | 77.4302i | −0.903165 | − | 0.656188i | ||||
\(119\) | −31.2297 | + | 10.1472i | −0.262435 | + | 0.0852702i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119.998 | + | 15.5428i | 0.991716 | + | 0.128453i | ||||
\(122\) | − | 104.875i | − | 0.859628i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −37.2564 | − | 27.0684i | −0.300455 | − | 0.218293i | ||||
\(125\) | 69.7150 | + | 95.9544i | 0.557720 | + | 0.767635i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.3921 | − | 62.7604i | 0.160568 | − | 0.494176i | −0.838115 | − | 0.545494i | \(-0.816342\pi\) |
0.998682 | + | 0.0513177i | \(0.0163421\pi\) | |||||||
\(128\) | 6.65003 | + | 9.15298i | 0.0519534 | + | 0.0715077i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.57769 | − | 17.1664i | −0.0429053 | − | 0.132049i | ||||
\(131\) | 59.5648i | 0.454693i | 0.973814 | + | 0.227347i | \(0.0730050\pi\) | ||||
−0.973814 | + | 0.227347i | \(0.926995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.7232 | −0.185888 | ||||||||
\(134\) | −117.969 | + | 38.3304i | −0.880364 | + | 0.286048i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 33.6980 | − | 24.4830i | 0.247780 | − | 0.180022i | ||||
\(137\) | −180.893 | − | 58.7758i | −1.32039 | − | 0.429020i | −0.437761 | − | 0.899092i | \(-0.644228\pi\) |
−0.882629 | + | 0.470071i | \(0.844228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 189.818 | − | 137.911i | 1.36560 | − | 0.992165i | 0.367531 | − | 0.930011i | \(-0.380203\pi\) |
0.998067 | − | 0.0621540i | \(-0.0197970\pi\) | |||||||
\(140\) | −7.39513 | + | 10.1785i | −0.0528224 | + | 0.0727038i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −95.0029 | −0.669035 | ||||||||
\(143\) | 12.2999 | + | 48.2197i | 0.0860134 | + | 0.337201i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.7333 | + | 60.7329i | 0.136092 | + | 0.418848i | ||||
\(146\) | 29.6718 | − | 40.8397i | 0.203232 | − | 0.279724i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.3801 | + | 38.1021i | −0.0836495 | + | 0.257447i | ||||
\(149\) | −143.042 | − | 46.4770i | −0.960011 | − | 0.311926i | −0.213234 | − | 0.977001i | \(-0.568400\pi\) |
−0.746777 | + | 0.665075i | \(0.768400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 41.1188 | + | 29.8745i | 0.272310 | + | 0.197845i | 0.715556 | − | 0.698555i | \(-0.246173\pi\) |
−0.443246 | + | 0.896400i | \(0.646173\pi\) | |||||||
\(152\) | 29.8260 | − | 9.69106i | 0.196224 | − | 0.0637570i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 22.1524 | − | 26.6921i | 0.143847 | − | 0.173325i | ||||
\(155\) | 64.9607i | 0.419101i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 83.4844 | + | 60.6550i | 0.531748 | + | 0.386338i | 0.821011 | − | 0.570912i | \(-0.193410\pi\) |
−0.289263 | + | 0.957250i | \(0.593410\pi\) | |||||||
\(158\) | −21.1150 | − | 29.0623i | −0.133639 | − | 0.183939i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.93168 | − | 15.1781i | 0.0308230 | − | 0.0948634i | ||||
\(161\) | −14.5235 | − | 19.9898i | −0.0902078 | − | 0.124160i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −83.2710 | − | 256.282i | −0.510865 | − | 1.57228i | −0.790682 | − | 0.612227i | \(-0.790274\pi\) |
0.279817 | − | 0.960053i | \(-0.409726\pi\) | |||||||
\(164\) | − | 81.0690i | − | 0.494323i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 30.9852 | 0.186658 | ||||||||
\(167\) | −201.473 | + | 65.4625i | −1.20642 | + | 0.391991i | −0.842121 | − | 0.539289i | \(-0.818693\pi\) |
−0.364304 | + | 0.931280i | \(0.618693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 120.166 | − | 87.3059i | 0.711043 | − | 0.516603i | ||||
\(170\) | −55.8805 | − | 18.1567i | −0.328709 | − | 0.106804i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −73.8813 | + | 53.6779i | −0.429543 | + | 0.312081i | ||||
\(173\) | 71.0891 | − | 97.8458i | 0.410920 | − | 0.565583i | −0.552523 | − | 0.833498i | \(-0.686335\pi\) |
0.963442 | + | 0.267915i | \(0.0863347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −37.9969 | −0.217125 | ||||||||
\(176\) | −16.2618 | + | 40.8846i | −0.0923965 | + | 0.232299i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.2915 | + | 47.0625i | 0.0859074 | + | 0.264396i | ||||
\(179\) | 27.4907 | − | 37.8377i | 0.153579 | − | 0.211384i | −0.725294 | − | 0.688440i | \(-0.758296\pi\) |
0.878873 | + | 0.477056i | \(0.158296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −87.2836 | + | 268.631i | −0.482230 | + | 1.48415i | 0.353723 | + | 0.935350i | \(0.384916\pi\) |
−0.835953 | + | 0.548801i | \(0.815084\pi\) | |||||||
\(182\) | 13.5675 | + | 4.40836i | 0.0745470 | + | 0.0242218i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 25.3568 | + | 18.4228i | 0.137808 | + | 0.100124i | ||||
\(185\) | 53.7472 | − | 17.4635i | 0.290526 | − | 0.0943975i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 150.523 | + | 59.8701i | 0.804934 | + | 0.320161i | ||||
\(188\) | − | 23.1862i | − | 0.123331i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −35.7894 | − | 26.0025i | −0.188365 | − | 0.136855i | ||||
\(191\) | 210.191 | + | 289.303i | 1.10048 | + | 1.51468i | 0.834750 | + | 0.550628i | \(0.185612\pi\) |
0.265727 | + | 0.964048i | \(0.414388\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4931 | + | 35.3722i | −0.0595499 | + | 0.183276i | −0.976406 | − | 0.215941i | \(-0.930718\pi\) |
0.916856 | + | 0.399217i | \(0.130718\pi\) | |||||||
\(194\) | 90.7046 | + | 124.844i | 0.467549 | + | 0.643526i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 27.2109 | + | 83.7465i | 0.138831 | + | 0.427278i | ||||
\(197\) | − | 129.220i | − | 0.655937i | −0.944689 | − | 0.327969i | \(-0.893636\pi\) | ||
0.944689 | − | 0.327969i | \(-0.106364\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −93.6837 | −0.470772 | −0.235386 | − | 0.971902i | \(-0.575635\pi\) | ||||
−0.235386 | + | 0.971902i | \(0.575635\pi\) | |||||||
\(200\) | 45.8394 | − | 14.8941i | 0.229197 | − | 0.0744706i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 206.901 | − | 150.322i | 1.02426 | − | 0.744169i | ||||
\(203\) | −48.0006 | − | 15.5963i | −0.236456 | − | 0.0768293i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −92.5166 | + | 67.2172i | −0.451300 | + | 0.327889i | ||||
\(206\) | −167.544 | + | 230.605i | −0.813321 | + | 1.11944i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.0959 | −0.0869995 | ||||||||
\(209\) | 93.8536 | + | 77.8914i | 0.449060 | + | 0.372686i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 89.4980 | + | 275.447i | 0.424161 | + | 1.30543i | 0.903795 | + | 0.427965i | \(0.140769\pi\) |
−0.479634 | + | 0.877469i | \(0.659231\pi\) | |||||||
\(212\) | 46.0130 | − | 63.3315i | 0.217043 | − | 0.298734i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −39.9598 | + | 122.984i | −0.186728 | + | 0.574689i | ||||
\(215\) | 122.515 | + | 39.8077i | 0.569839 | + | 0.185152i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −41.5366 | − | 30.1781i | −0.191413 | − | 0.139070i | ||||
\(218\) | 279.515 | − | 90.8199i | 1.28218 | − | 0.416605i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 60.1411 | − | 15.3409i | 0.273369 | − | 0.0697312i | ||||
\(221\) | 66.6226i | 0.301460i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −116.475 | − | 84.6244i | −0.522311 | − | 0.379481i | 0.295163 | − | 0.955447i | \(-0.404626\pi\) |
−0.817474 | + | 0.575966i | \(0.804626\pi\) | |||||||
\(224\) | 7.41402 | + | 10.2045i | 0.0330983 | + | 0.0455559i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.7462 | + | 85.3941i | −0.122771 | + | 0.377850i | ||||
\(227\) | −24.4076 | − | 33.5941i | −0.107522 | − | 0.147992i | 0.751865 | − | 0.659317i | \(-0.229155\pi\) |
−0.859387 | + | 0.511326i | \(0.829155\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −39.1019 | − | 120.343i | −0.170751 | − | 0.525516i | 0.828663 | − | 0.559747i | \(-0.189102\pi\) |
−0.999414 | + | 0.0342310i | \(0.989102\pi\) | |||||||
\(230\) | − | 44.2123i | − | 0.192227i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 64.0214 | 0.275954 | ||||||||
\(233\) | 189.364 | − | 61.5282i | 0.812723 | − | 0.264070i | 0.126972 | − | 0.991906i | \(-0.459474\pi\) |
0.685751 | + | 0.727837i | \(0.259474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.4603 | + | 19.2245i | −0.112597 | + | 0.0818066i | ||||
\(236\) | 177.179 | + | 57.5690i | 0.750759 | + | 0.243937i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 37.5694 | − | 27.2958i | 0.157855 | − | 0.114688i | ||||
\(239\) | 144.854 | − | 199.374i | 0.606084 | − | 0.834203i | −0.390164 | − | 0.920745i | \(-0.627582\pi\) |
0.996248 | + | 0.0865424i | \(0.0275818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −439.621 | −1.82415 | −0.912076 | − | 0.410021i | \(-0.865521\pi\) | ||||
−0.912076 | + | 0.410021i | \(0.865521\pi\) | |||||||
\(242\) | −168.189 | + | 31.5359i | −0.694995 | + | 0.130314i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 45.8319 | + | 141.056i | 0.187836 | + | 0.578098i | ||||
\(245\) | 73.0106 | − | 100.491i | 0.298003 | − | 0.410165i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.5005 | + | 47.7057i | −0.0627551 | + | 0.193140i | ||||
\(248\) | 61.9391 | + | 20.1252i | 0.249754 | + | 0.0811501i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −135.700 | − | 98.5918i | −0.542800 | − | 0.394367i | ||||
\(251\) | 153.228 | − | 49.7869i | 0.610471 | − | 0.198354i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
0.597905 | + | 0.801567i | \(0.296000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.84509 | + | 121.642i | −0.0310083 | + | 0.480797i | ||||
\(254\) | 93.3242i | 0.367418i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 63.6815 | + | 87.6500i | 0.247788 | + | 0.341051i | 0.914735 | − | 0.404054i | \(-0.132399\pi\) |
−0.666947 | + | 0.745105i | \(0.732399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.8024 | + | 42.4795i | −0.0532912 | + | 0.164013i | ||||
\(260\) | 15.0040 | + | 20.6512i | 0.0577075 | + | 0.0794276i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −26.0308 | − | 80.1145i | −0.0993541 | − | 0.305780i | ||||
\(263\) | − | 263.126i | − | 1.00048i | −0.865887 | − | 0.500240i | \(-0.833245\pi\) | ||
0.865887 | − | 0.500240i | \(-0.166755\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −110.426 | −0.416700 | ||||||||
\(266\) | 33.2526 | − | 10.8044i | 0.125010 | − | 0.0406181i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 141.917 | − | 103.108i | 0.529540 | − | 0.384733i | ||||
\(269\) | −302.144 | − | 98.1724i | −1.12321 | − | 0.364953i | −0.312218 | − | 0.950010i | \(-0.601072\pi\) |
−0.810992 | + | 0.585057i | \(0.801072\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −35.1264 | + | 25.5208i | −0.129618 | + | 0.0941729i | −0.650705 | − | 0.759331i | \(-0.725527\pi\) |
0.521087 | + | 0.853503i | \(0.325527\pi\) | |||||||
\(272\) | −34.6242 | + | 47.6562i | −0.127295 | + | 0.175207i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 268.987 | 0.981704 | ||||||||
\(275\) | 144.243 | + | 119.711i | 0.524520 | + | 0.435312i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 109.009 | + | 335.496i | 0.393535 | + | 1.21118i | 0.930096 | + | 0.367316i | \(0.119723\pi\) |
−0.536561 | + | 0.843862i | \(0.680277\pi\) | |||||||
\(278\) | −195.036 | + | 268.443i | −0.701567 | + | 0.965624i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.49825 | − | 16.9219i | 0.0196366 | − | 0.0604353i | ||||
\(281\) | 170.582 | + | 55.4255i | 0.607054 | + | 0.197244i | 0.596384 | − | 0.802699i | \(-0.296604\pi\) |
0.0106699 | + | 0.999943i | \(0.496604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −167.826 | − | 121.933i | −0.593026 | − | 0.430859i | 0.250370 | − | 0.968150i | \(-0.419448\pi\) |
−0.843397 | + | 0.537291i | \(0.819448\pi\) | |||||||
\(284\) | 127.779 | − | 41.5178i | 0.449925 | − | 0.146189i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −37.6161 | − | 59.4801i | −0.131525 | − | 0.207972i | ||||
\(287\) | − | 90.3826i | − | 0.314922i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −58.3528 | − | 42.3958i | −0.201913 | − | 0.146698i | ||||
\(290\) | −53.0825 | − | 73.0618i | −0.183043 | − | 0.251937i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.0609 | + | 67.8964i | −0.0755509 | + | 0.232522i | ||||
\(293\) | −230.223 | − | 316.875i | −0.785745 | − | 1.08149i | −0.994625 | − | 0.103544i | \(-0.966982\pi\) |
0.208880 | − | 0.977941i | \(-0.433018\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −81.2075 | − | 249.931i | −0.275280 | − | 0.847223i | ||||
\(296\) | − | 56.6575i | − | 0.191411i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 212.702 | 0.713764 | ||||||||
\(299\) | −47.6779 | + | 15.4915i | −0.159458 | + | 0.0518110i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −82.3692 | + | 59.8447i | −0.273652 | + | 0.198820i | ||||
\(302\) | −68.3603 | − | 22.2116i | −0.226358 | − | 0.0735483i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −35.8808 | + | 26.0689i | −0.118029 | + | 0.0857530i | ||||
\(305\) | 122.973 | − | 169.258i | 0.403191 | − | 0.554945i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 82.4090 | 0.268433 | 0.134217 | − | 0.990952i | \(-0.457148\pi\) | ||||
0.134217 | + | 0.990952i | \(0.457148\pi\) | |||||||
\(308\) | −18.1300 | + | 45.5817i | −0.0588637 | + | 0.147992i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −28.3889 | − | 87.3720i | −0.0915770 | − | 0.281845i | ||||
\(311\) | −210.988 | + | 290.400i | −0.678418 | + | 0.933762i | −0.999914 | − | 0.0131491i | \(-0.995814\pi\) |
0.321496 | + | 0.946911i | \(0.395814\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 130.603 | − | 401.956i | 0.417264 | − | 1.28421i | −0.492947 | − | 0.870059i | \(-0.664080\pi\) |
0.910211 | − | 0.414146i | \(-0.135920\pi\) | |||||||
\(314\) | −138.794 | − | 45.0968i | −0.442018 | − | 0.143620i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 41.1003 | + | 29.8611i | 0.130064 | + | 0.0944973i | ||||
\(317\) | −356.602 | + | 115.867i | −1.12493 | + | 0.365511i | −0.811646 | − | 0.584150i | \(-0.801428\pi\) |
−0.313281 | + | 0.949661i | \(0.601428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 133.082 | + | 210.434i | 0.417185 | + | 0.659669i | ||||
\(320\) | 22.5698i | 0.0705305i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 28.2699 | + | 20.5393i | 0.0877946 | + | 0.0637865i | ||||
\(323\) | 95.9764 | + | 132.100i | 0.297140 | + | 0.408979i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.8226 | + | 73.3185i | −0.0733004 | + | 0.225596i | ||||
\(326\) | 223.999 | + | 308.307i | 0.687112 | + | 0.945729i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 35.4284 | + | 109.038i | 0.108014 | + | 0.332431i | ||||
\(329\) | − | 25.8500i | − | 0.0785714i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −166.263 | −0.502305 | −0.251152 | − | 0.967948i | \(-0.580810\pi\) | ||||
−0.251152 | + | 0.967948i | \(0.580810\pi\) | |||||||
\(332\) | −41.6750 | + | 13.5410i | −0.125527 | + | 0.0407862i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 242.372 | − | 176.094i | 0.725666 | − | 0.527227i | ||||
\(335\) | −235.336 | − | 76.4655i | −0.702497 | − | 0.228255i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 508.288 | − | 369.293i | 1.50827 | − | 1.09583i | 0.541339 | − | 0.840805i | \(-0.317918\pi\) |
0.966936 | − | 0.255021i | \(-0.0820823\pi\) | |||||||
\(338\) | −123.469 | + | 169.941i | −0.365293 | + | 0.502783i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 83.0939 | 0.244394 | ||||||||
\(341\) | 62.6031 | + | 245.425i | 0.183587 | + | 0.719720i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 64.0998 | + | 197.279i | 0.186880 | + | 0.575157i | ||||
\(344\) | 75.9121 | − | 104.484i | 0.220675 | − | 0.303733i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −52.8545 | + | 162.669i | −0.152759 | + | 0.470143i | ||||
\(347\) | −541.504 | − | 175.945i | −1.56053 | − | 0.507047i | −0.603580 | − | 0.797302i | \(-0.706260\pi\) |
−0.956949 | + | 0.290256i | \(0.906260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 72.1627 | + | 52.4293i | 0.206770 | + | 0.150227i | 0.686351 | − | 0.727270i | \(-0.259211\pi\) |
−0.479581 | + | 0.877498i | \(0.659211\pi\) | |||||||
\(350\) | 51.1057 | − | 16.6052i | 0.146016 | − | 0.0474435i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.00481 | − | 62.0964i | 0.0113773 | − | 0.176410i | ||||
\(353\) | 490.203i | 1.38868i | 0.719649 | + | 0.694338i | \(0.244303\pi\) | ||||
−0.719649 | + | 0.694338i | \(0.755697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −153.326 | − | 111.398i | −0.431905 | − | 0.313798i | ||||
\(356\) | −41.1341 | − | 56.6162i | −0.115545 | − | 0.159034i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.4392 | + | 62.9055i | −0.0570928 | + | 0.175714i | ||||
\(359\) | −281.600 | − | 387.589i | −0.784401 | − | 1.07964i | −0.994783 | − | 0.102016i | \(-0.967471\pi\) |
0.210382 | − | 0.977619i | \(-0.432529\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −73.5650 | − | 226.410i | −0.203781 | − | 0.627174i | ||||
\(362\) | − | 399.453i | − | 1.10346i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −20.1748 | −0.0554254 | ||||||||
\(365\) | 95.7754 | − | 31.1193i | 0.262398 | − | 0.0852584i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.71416 | + | 2.69850i | −0.0101203 | + | 0.00735285i | −0.592834 | − | 0.805325i | \(-0.701991\pi\) |
0.582714 | + | 0.812678i | \(0.301991\pi\) | |||||||
\(368\) | −42.1558 | − | 13.6973i | −0.114554 | − | 0.0372208i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −64.6580 | + | 46.9768i | −0.174751 | + | 0.126964i | ||||
\(371\) | 51.2993 | − | 70.6074i | 0.138273 | − | 0.190316i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −127.560 | −0.341984 | −0.170992 | − | 0.985272i | \(-0.554697\pi\) | ||||
−0.170992 | + | 0.985272i | \(0.554697\pi\) | |||||||
\(374\) | −228.617 | − | 14.7443i | −0.611275 | − | 0.0394232i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.1328 | + | 31.1854i | 0.0269488 | + | 0.0829399i | ||||
\(377\) | −60.1893 | + | 82.8434i | −0.159653 | + | 0.219744i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 97.6391 | − | 300.502i | 0.257623 | − | 0.792882i | −0.735678 | − | 0.677331i | \(-0.763137\pi\) |
0.993302 | − | 0.115551i | \(-0.0368635\pi\) | |||||||
\(380\) | 59.5001 | + | 19.3327i | 0.156579 | + | 0.0508757i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −409.137 | − | 297.255i | −1.07104 | − | 0.778155i | ||||
\(383\) | −269.358 | + | 87.5199i | −0.703286 | + | 0.228511i | −0.638762 | − | 0.769405i | \(-0.720553\pi\) |
−0.0645242 | + | 0.997916i | \(0.520553\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 67.0505 | − | 17.1033i | 0.174157 | − | 0.0444241i | ||||
\(386\) | − | 52.5982i | − | 0.136265i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −176.556 | − | 128.276i | −0.455042 | − | 0.330607i | ||||
\(389\) | −173.179 | − | 238.360i | −0.445189 | − | 0.612750i | 0.526166 | − | 0.850382i | \(-0.323629\pi\) |
−0.971355 | + | 0.237632i | \(0.923629\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50.4284 | + | 155.203i | −0.128973 | + | 0.396938i | ||||
\(392\) | −73.1971 | − | 100.747i | −0.186727 | − | 0.257008i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 56.4711 | + | 173.800i | 0.143328 | + | 0.441117i | ||||
\(395\) | − | 71.6630i | − | 0.181425i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 354.576 | 0.893138 | 0.446569 | − | 0.894749i | \(-0.352646\pi\) | ||||
0.446569 | + | 0.894749i | \(0.352646\pi\) | |||||||
\(398\) | 126.004 | − | 40.9413i | 0.316594 | − | 0.102867i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −55.1449 | + | 40.0651i | −0.137862 | + | 0.100163i | ||||
\(401\) | −38.8054 | − | 12.6086i | −0.0967715 | − | 0.0314430i | 0.260231 | − | 0.965546i | \(-0.416201\pi\) |
−0.357003 | + | 0.934103i | \(0.616201\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −84.2735 | + | 61.2283i | −0.209115 | + | 0.151931i | ||||
\(404\) | −212.588 | + | 292.602i | −0.526207 | + | 0.724261i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 71.3765 | 0.175804 | ||||||||
\(407\) | 186.230 | − | 117.775i | 0.457567 | − | 0.289373i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −147.530 | − | 454.050i | −0.360708 | − | 1.11015i | −0.952625 | − | 0.304147i | \(-0.901629\pi\) |
0.591917 | − | 0.805999i | \(-0.298371\pi\) | |||||||
\(410\) | 95.0595 | − | 130.838i | 0.231852 | − | 0.319118i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 124.568 | − | 383.382i | 0.302350 | − | 0.930539i | ||||
\(413\) | 197.534 | + | 64.1828i | 0.478292 | + | 0.155406i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 50.0074 | + | 36.3325i | 0.120500 | + | 0.0875482i | ||||
\(416\) | 24.3389 | − | 7.90819i | 0.0585070 | − | 0.0190101i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −160.273 | − | 63.7481i | −0.383427 | − | 0.152507i | ||||
\(419\) | 75.9631i | 0.181296i | 0.995883 | + | 0.0906481i | \(0.0288938\pi\) | ||||
−0.995883 | + | 0.0906481i | \(0.971106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 225.960 | + | 164.170i | 0.536722 | + | 0.389951i | 0.822866 | − | 0.568235i | \(-0.192374\pi\) |
−0.286144 | + | 0.958187i | \(0.592374\pi\) | |||||||
\(422\) | −240.749 | − | 331.363i | −0.570496 | − | 0.785220i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −34.2105 | + | 105.289i | −0.0806852 | + | 0.248323i | ||||
\(425\) | 147.505 | + | 203.024i | 0.347072 | + | 0.477703i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 51.0973 | + | 157.261i | 0.119666 | + | 0.368293i | ||||
\(428\) | − | 182.876i | − | 0.427279i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −182.179 | −0.423673 | ||||||||
\(431\) | 565.456 | − | 183.728i | 1.31196 | − | 0.426282i | 0.432235 | − | 0.901761i | \(-0.357725\pi\) |
0.879727 | + | 0.475479i | \(0.157725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 127.561 | − | 92.6786i | 0.294598 | − | 0.214038i | −0.430661 | − | 0.902514i | \(-0.641720\pi\) |
0.725260 | + | 0.688475i | \(0.241720\pi\) | |||||||
\(434\) | 69.0550 | + | 22.4373i | 0.159113 | + | 0.0516989i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −336.257 | + | 244.305i | −0.771232 | + | 0.560333i | ||||
\(437\) | −72.2194 | + | 99.4014i | −0.165262 | + | 0.227463i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 265.463 | 0.604699 | 0.302349 | − | 0.953197i | \(-0.402229\pi\) | ||||
0.302349 | + | 0.953197i | \(0.402229\pi\) | |||||||
\(440\) | −74.1854 | + | 46.9160i | −0.168603 | + | 0.106627i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −29.1151 | − | 89.6072i | −0.0658714 | − | 0.202731i | ||||
\(443\) | 35.1370 | − | 48.3619i | 0.0793160 | − | 0.109169i | −0.767515 | − | 0.641030i | \(-0.778507\pi\) |
0.846831 | + | 0.531861i | \(0.178507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.5051 | + | 93.8852i | −0.0685509 | + | 0.210978i | ||||
\(446\) | 193.641 | + | 62.9179i | 0.434173 | + | 0.141071i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.4314 | − | 10.4850i | −0.0322129 | − | 0.0234040i | ||||
\(449\) | 264.409 | − | 85.9116i | 0.588884 | − | 0.191340i | 0.000607294 | − | 1.00000i | \(-0.499807\pi\) |
0.588276 | + | 0.808660i | \(0.299807\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −284.754 | + | 343.109i | −0.631384 | + | 0.760773i | ||||
\(452\) | − | 126.980i | − | 0.280930i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 47.5093 | + | 34.5175i | 0.104646 | + | 0.0760297i | ||||
\(455\) | 16.7277 | + | 23.0237i | 0.0367642 | + | 0.0506015i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 101.783 | − | 313.255i | 0.222720 | − | 0.685460i | −0.775795 | − | 0.630984i | \(-0.782651\pi\) |
0.998515 | − | 0.0544760i | \(-0.0173488\pi\) | |||||||
\(458\) | 105.184 | + | 144.773i | 0.229659 | + | 0.316099i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 19.3215 | + | 59.4654i | 0.0420032 | + | 0.129273i | ||||
\(461\) | 628.919i | 1.36425i | 0.731236 | + | 0.682124i | \(0.238944\pi\) | ||||
−0.731236 | + | 0.682124i | \(0.761056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −509.930 | −1.10136 | −0.550680 | − | 0.834716i | \(-0.685632\pi\) | ||||
−0.550680 | + | 0.834716i | \(0.685632\pi\) | |||||||
\(464\) | −86.1086 | + | 27.9784i | −0.185579 | + | 0.0602983i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −227.806 | + | 165.511i | −0.488854 | + | 0.355173i | ||||
\(467\) | 210.460 | + | 68.3826i | 0.450664 | + | 0.146430i | 0.525550 | − | 0.850762i | \(-0.323859\pi\) |
−0.0748865 | + | 0.997192i | \(0.523859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 158.221 | − | 114.954i | 0.337358 | − | 0.245105i | ||||
\(470\) | 27.1876 | − | 37.4205i | 0.0578460 | − | 0.0796182i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −263.464 | −0.558187 | ||||||||
\(473\) | 501.232 | + | 32.3262i | 1.05969 | + | 0.0683428i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 58.3867 | + | 179.696i | 0.122919 | + | 0.378307i | ||||
\(476\) | −38.6021 | + | 53.1312i | −0.0810968 | + | 0.111620i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −107.698 | + | 331.462i | −0.225310 | + | 0.693434i | ||||
\(479\) | −245.892 | − | 79.8953i | −0.513345 | − | 0.166796i | 0.0408778 | − | 0.999164i | \(-0.486985\pi\) |
−0.554223 | + | 0.832368i | \(0.686985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 73.3145 | + | 53.2661i | 0.152421 | + | 0.110740i | ||||
\(482\) | 591.288 | − | 192.121i | 1.22674 | − | 0.398592i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 212.432 | − | 115.917i | 0.438909 | − | 0.239498i | ||||
\(485\) | 307.845i | 0.634733i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 361.333 | + | 262.523i | 0.741956 | + | 0.539063i | 0.893323 | − | 0.449415i | \(-0.148368\pi\) |
−0.151367 | + | 0.988478i | \(0.548368\pi\) | |||||||
\(488\) | −123.287 | − | 169.691i | −0.252638 | − | 0.347727i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −54.2831 | + | 167.066i | −0.110782 | + | 0.340952i | ||||
\(491\) | 261.208 | + | 359.522i | 0.531992 | + | 0.732224i | 0.987432 | − | 0.158042i | \(-0.0505183\pi\) |
−0.455441 | + | 0.890266i | \(0.650518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 103.006 | + | 317.021i | 0.208938 | + | 0.643045i | ||||
\(494\) | − | 70.9380i | − | 0.143599i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −92.1030 | −0.185691 | ||||||||
\(497\) | 142.459 | − | 46.2876i | 0.286637 | − | 0.0931340i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −608.499 | + | 442.100i | −1.21944 | + | 0.885973i | −0.996053 | − | 0.0887576i | \(-0.971710\pi\) |
−0.223384 | + | 0.974731i | \(0.571710\pi\) | |||||||
\(500\) | 225.602 | + | 73.3026i | 0.451205 | + | 0.146605i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −184.334 | + | 133.926i | −0.367199 | + | 0.266786i | ||||
\(503\) | 196.115 | − | 269.929i | 0.389890 | − | 0.536638i | −0.568280 | − | 0.822835i | \(-0.692391\pi\) |
0.958171 | + | 0.286197i | \(0.0923911\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 510.183 | 1.01026 | ||||||||
\(506\) | −42.6077 | − | 167.036i | −0.0842050 | − | 0.330111i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −40.7842 | − | 125.521i | −0.0802838 | − | 0.247088i | ||||
\(509\) | 208.025 | − | 286.322i | 0.408693 | − | 0.562518i | −0.554206 | − | 0.832380i | \(-0.686978\pi\) |
0.962899 | + | 0.269862i | \(0.0869780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.5953 | + | 75.6967i | −0.0481318 | + | 0.148134i | ||||
\(512\) | 21.5200 | + | 6.99226i | 0.0420312 | + | 0.0136568i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −123.956 | − | 90.0592i | −0.241159 | − | 0.175212i | ||||
\(515\) | −540.803 | + | 175.718i | −1.05010 | + | 0.341199i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −81.4414 | + | 98.1312i | −0.157527 | + | 0.189809i | ||||
\(518\) | − | 63.1666i | − | 0.121943i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −29.2052 | − | 21.2188i | −0.0561638 | − | 0.0408054i | ||||
\(521\) | 460.803 | + | 634.240i | 0.884458 | + | 1.21735i | 0.975166 | + | 0.221474i | \(0.0710869\pi\) |
−0.0907083 | + | 0.995878i | \(0.528913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 129.129 | − | 397.420i | 0.246902 | − | 0.759885i | −0.748416 | − | 0.663229i | \(-0.769185\pi\) |
0.995318 | − | 0.0966555i | \(-0.0308145\pi\) | |||||||
\(524\) | 70.0226 | + | 96.3779i | 0.133631 | + | 0.183927i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 114.990 | + | 353.904i | 0.218613 | + | 0.672821i | ||||
\(527\) | 339.090i | 0.643435i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 406.205 | 0.767873 | ||||||||
\(530\) | 148.522 | − | 48.2577i | 0.280230 | − | 0.0910523i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −40.0029 | + | 29.0638i | −0.0751935 | + | 0.0546313i | ||||
\(533\) | −174.402 | − | 56.6666i | −0.327208 | − | 0.106316i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −208.699 | + | 151.629i | −0.390092 | + | 0.283418i | ||||
\(536\) | −145.817 | + | 200.700i | −0.272047 | + | 0.374441i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 449.285 | 0.835103 | ||||||||
\(539\) | 178.994 | − | 450.019i | 0.332085 | − | 0.834914i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.8020 | − | 36.3229i | −0.0218152 | − | 0.0671404i | 0.939556 | − | 0.342395i | \(-0.111238\pi\) |
−0.961371 | + | 0.275254i | \(0.911238\pi\) | |||||||
\(542\) | 36.0919 | − | 49.6763i | 0.0665903 | − | 0.0916536i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 25.7430 | − | 79.2288i | 0.0473217 | − | 0.145641i | ||||
\(545\) | 557.606 | + | 181.177i | 1.02313 | + | 0.332435i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 741.060 | + | 538.411i | 1.35477 | + | 0.984299i | 0.998758 | + | 0.0498175i | \(0.0158640\pi\) |
0.356013 | + | 0.934481i | \(0.384136\pi\) | |||||||
\(548\) | −361.787 | + | 117.552i | −0.660195 | + | 0.214510i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −246.322 | − | 97.9740i | −0.447858 | − | 0.178135i | ||||
\(551\) | 250.972i | 0.455484i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45.8221 | + | 33.2917i | 0.0828610 | + | 0.0602021i | ||||
\(554\) | −293.234 | − | 403.603i | −0.529304 | − | 0.728524i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 145.008 | − | 446.289i | 0.260806 | − | 0.802678i | ||||
\(557\) | −456.163 | − | 627.854i | −0.818964 | − | 1.12721i | −0.989878 | − | 0.141921i | \(-0.954672\pi\) |
0.170914 | − | 0.985286i | \(-0.445328\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 63.8336 | + | 196.460i | 0.114192 | + | 0.351448i | ||||
\(560\) | 25.1627i | 0.0449334i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −253.654 | −0.451342 | ||||||||
\(563\) | −371.042 | + | 120.559i | −0.659045 | + | 0.214137i | −0.619398 | − | 0.785077i | \(-0.712623\pi\) |
−0.0396470 | + | 0.999214i | \(0.512623\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −144.911 | + | 105.284i | −0.256480 | + | 0.186343i | ||||
\(566\) | 279.013 | + | 90.6567i | 0.492955 | + | 0.160171i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −153.718 | + | 111.683i | −0.270630 | + | 0.196624i | ||||
\(569\) | −61.3644 | + | 84.4609i | −0.107846 | + | 0.148437i | −0.859528 | − | 0.511088i | \(-0.829243\pi\) |
0.751682 | + | 0.659525i | \(0.229243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −66.1095 | −0.115778 | −0.0578892 | − | 0.998323i | \(-0.518437\pi\) | ||||
−0.0578892 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(572\) | 76.5873 | + | 63.5616i | 0.133894 | + | 0.111122i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 39.4986 | + | 121.564i | 0.0688130 | + | 0.211785i | ||||
\(575\) | −110.993 | + | 152.769i | −0.193032 | + | 0.265686i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 297.125 | − | 914.456i | 0.514948 | − | 1.58485i | −0.268429 | − | 0.963299i | \(-0.586505\pi\) |
0.783377 | − | 0.621547i | \(-0.213495\pi\) | |||||||
\(578\) | 97.0120 | + | 31.5211i | 0.167841 | + | 0.0545348i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 103.325 | + | 75.0700i | 0.178147 | + | 0.129431i | ||||
\(581\) | −46.4628 | + | 15.0967i | −0.0799704 | + | 0.0259840i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −417.193 | + | 106.418i | −0.715596 | + | 0.182535i | ||||
\(584\) | − | 100.961i | − | 0.172879i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 448.129 | + | 325.585i | 0.764726 | + | 0.555606i | ||||
\(587\) | −387.993 | − | 534.026i | −0.660976 | − | 0.909755i | 0.338537 | − | 0.940953i | \(-0.390068\pi\) |
−0.999513 | + | 0.0311975i | \(0.990068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −78.8933 | + | 242.809i | −0.133944 | + | 0.412239i | ||||
\(590\) | 218.448 | + | 300.667i | 0.370250 | + | 0.509606i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24.7602 | + | 76.2042i | 0.0418247 | + | 0.128723i | ||||
\(593\) | 883.670i | 1.49017i | 0.666970 | + | 0.745084i | \(0.267591\pi\) | ||||
−0.666970 | + | 0.745084i | \(0.732409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 92.6401 | 0.155698 | ||||||||
\(596\) | −286.083 | + | 92.9541i | −0.480005 | + | 0.155963i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 57.3566 | − | 41.6720i | 0.0959141 | − | 0.0696857i | ||||
\(599\) | 223.184 | + | 72.5169i | 0.372595 | + | 0.121063i | 0.489328 | − | 0.872100i | \(-0.337242\pi\) |
−0.116733 | + | 0.993163i | \(0.537242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 126.159 | − | 91.6602i | 0.209916 | − | 0.152513i | −0.477860 | − | 0.878436i | \(-0.658587\pi\) |
0.687776 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(602\) | 84.6332 | − | 116.488i | 0.140587 | − | 0.193501i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 101.651 | 0.168297 | ||||||||
\(605\) | −308.420 | − | 146.318i | −0.509786 | − | 0.241848i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −322.483 | − | 992.500i | −0.531273 | − | 1.63509i | −0.751567 | − | 0.659657i | \(-0.770702\pi\) |
0.220293 | − | 0.975434i | \(-0.429298\pi\) | |||||||
\(608\) | 36.8670 | − | 50.7431i | 0.0606365 | − | 0.0834590i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −91.4302 | + | 281.393i | −0.149886 | + | 0.461301i | ||||
\(611\) | −49.8800 | − | 16.2070i | −0.0816367 | − | 0.0265254i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 667.207 | + | 484.754i | 1.08843 | + | 0.790790i | 0.979133 | − | 0.203219i | \(-0.0651403\pi\) |
0.109296 | + | 0.994009i | \(0.465140\pi\) | |||||||
\(614\) | −110.840 | + | 36.0141i | −0.180521 | + | 0.0586548i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.46490 | − | 69.2303i | 0.00724822 | − | 0.112387i | ||||
\(617\) | − | 513.392i | − | 0.832078i | −0.909347 | − | 0.416039i | \(-0.863418\pi\) | ||
0.909347 | − | 0.416039i | \(-0.136582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −657.376 | − | 477.612i | −1.06200 | − | 0.771586i | −0.0875403 | − | 0.996161i | \(-0.527901\pi\) |
−0.974457 | + | 0.224575i | \(0.927901\pi\) | |||||||
\(620\) | 76.3659 | + | 105.109i | 0.123171 | + | 0.169530i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 156.869 | − | 482.792i | 0.252200 | − | 0.776193i | ||||
\(623\) | −45.8598 | − | 63.1206i | −0.0736112 | − | 0.101317i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 28.2452 | + | 86.9298i | 0.0451923 | + | 0.139088i | ||||
\(626\) | 597.706i | 0.954802i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 206.385 | 0.328638 | ||||||||
\(629\) | 280.557 | − | 91.1584i | 0.446036 | − | 0.144926i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −483.503 | + | 351.286i | −0.766249 | + | 0.556713i | −0.900821 | − | 0.434191i | \(-0.857034\pi\) |
0.134572 | + | 0.990904i | \(0.457034\pi\) | |||||||
\(632\) | −68.3296 | − | 22.2016i | −0.108116 | − | 0.0351292i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 428.992 | − | 311.681i | 0.676644 | − | 0.491611i | ||||
\(635\) | −109.430 | + | 150.617i | −0.172330 | + | 0.237192i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 199.182 | 0.312688 | ||||||||
\(638\) | −270.958 | − | 224.875i | −0.424699 | − | 0.352468i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.86335 | − | 30.3563i | −0.0154115 | − | 0.0474317i | ||||
\(641\) | 479.564 | − | 660.063i | 0.748150 | − | 1.02974i | −0.249958 | − | 0.968257i | \(-0.580417\pi\) |
0.998108 | − | 0.0614833i | \(-0.0195831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −143.098 | + | 440.409i | −0.222547 | + | 0.684928i | 0.775985 | + | 0.630752i | \(0.217253\pi\) |
−0.998531 | + | 0.0541765i | \(0.982747\pi\) | |||||||
\(644\) | −46.9989 | − | 15.2709i | −0.0729796 | − | 0.0237125i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −186.818 | − | 135.731i | −0.289192 | − | 0.210110i | ||||
\(647\) | −945.308 | + | 307.149i | −1.46106 | + | 0.474728i | −0.928395 | − | 0.371596i | \(-0.878811\pi\) |
−0.532668 | + | 0.846324i | \(0.678811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −547.666 | − | 865.990i | −0.843861 | − | 1.33435i | ||||
\(650\) | − | 109.024i | − | 0.167729i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −436.013 | − | 316.782i | −0.668731 | − | 0.485862i | ||||
\(653\) | −359.048 | − | 494.187i | −0.549843 | − | 0.756794i | 0.440148 | − | 0.897925i | \(-0.354926\pi\) |
−0.989991 | + | 0.141131i | \(0.954926\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 51.9289 | − | 159.821i | 0.0792808 | − | 0.244001i | ||||
\(656\) | −95.3023 | − | 131.172i | −0.145278 | − | 0.199958i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.2969 | + | 34.7682i | 0.0171685 | + | 0.0528391i | ||||
\(659\) | − | 249.471i | − | 0.378560i | −0.981923 | − | 0.189280i | \(-0.939385\pi\) | ||
0.981923 | − | 0.189280i | \(-0.0606154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1210.43 | −1.83121 | −0.915604 | − | 0.402081i | \(-0.868287\pi\) | ||||
−0.915604 | + | 0.402081i | \(0.868287\pi\) | |||||||
\(662\) | 223.623 | − | 72.6595i | 0.337799 | − | 0.109758i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 50.1351 | − | 36.4253i | 0.0755047 | − | 0.0548573i | ||||
\(665\) | 66.3358 | + | 21.5538i | 0.0997530 | + | 0.0324117i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −202.922 | + | 147.431i | −0.304231 | + | 0.221037i | ||||
\(668\) | −249.034 | + | 342.766i | −0.372806 | + | 0.513123i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 349.943 | 0.522304 | ||||||||
\(671\) | 301.484 | − | 757.976i | 0.449305 | − | 1.12962i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −346.565 | − | 1066.62i | −0.514955 | − | 1.58487i | −0.783364 | − | 0.621563i | \(-0.786498\pi\) |
0.268409 | − | 0.963305i | \(-0.413502\pi\) | |||||||
\(674\) | −522.259 | + | 718.828i | −0.774866 | + | 1.06651i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 91.7989 | − | 282.528i | 0.135797 | − | 0.417941i | ||||
\(677\) | −227.144 | − | 73.8036i | −0.335516 | − | 0.109016i | 0.136414 | − | 0.990652i | \(-0.456442\pi\) |
−0.471930 | + | 0.881636i | \(0.656442\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −196.840 | − | 143.013i | −0.289897 | − | 0.210622i | ||||
\(680\) | −111.761 | + | 36.3133i | −0.164354 | + | 0.0534020i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −191.455 | − | 302.737i | −0.280726 | − | 0.443895i | ||||
\(683\) | − | 1328.40i | − | 1.94494i | −0.233023 | − | 0.972471i | \(-0.574862\pi\) | ||
0.233023 | − | 0.972471i | \(-0.425138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 434.121 | + | 315.408i | 0.633754 | + | 0.460449i | ||||
\(686\) | −172.428 | − | 237.327i | −0.251353 | − | 0.345958i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −56.4403 | + | 173.705i | −0.0820354 | + | 0.252479i | ||||
\(689\) | −104.081 | − | 143.255i | −0.151061 | − | 0.207917i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6560 | − | 38.9513i | −0.0183155 | − | 0.0563694i | 0.941481 | − | 0.337066i | \(-0.109435\pi\) |
−0.959797 | + | 0.280697i | \(0.909435\pi\) | |||||||
\(692\) | − | 241.888i | − | 0.349549i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 805.212 | 1.16025 | ||||||||
\(695\) | −629.540 | + | 204.550i | −0.905814 | + | 0.294317i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −482.930 | + | 350.869i | −0.692869 | + | 0.503399i | ||||
\(698\) | −119.971 | − | 38.9810i | −0.171878 | − | 0.0558466i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −61.4802 | + | 44.6680i | −0.0878289 | + | 0.0638114i | ||||
\(701\) | −136.416 | + | 187.761i | −0.194602 | + | 0.267847i | −0.895156 | − | 0.445752i | \(-0.852936\pi\) |
0.700554 | + | 0.713599i | \(0.252936\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 222.104 | 0.315938 | ||||||||
\(704\) | 21.7507 | + | 85.2696i | 0.0308958 | + | 0.121122i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −214.226 | − | 659.321i | −0.303437 | − | 0.933883i | ||||
\(707\) | −237.011 | + | 326.217i | −0.335234 | + | 0.461410i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 66.5049 | − | 204.681i | 0.0938010 | − | 0.288690i | −0.893138 | − | 0.449782i | \(-0.851502\pi\) |
0.986939 | + | 0.161092i | \(0.0515017\pi\) | |||||||
\(710\) | 254.906 | + | 82.8241i | 0.359023 | + | 0.116654i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 80.0675 | + | 58.1724i | 0.112454 | + | 0.0817028i | ||||
\(713\) | −242.667 | + | 78.8473i | −0.340347 | + | 0.110585i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.03575 | − | 140.103i | 0.0126374 | − | 0.195949i | ||||
\(716\) | − | 93.5399i | − | 0.130642i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 548.134 | + | 398.242i | 0.763417 | + | 0.554655i | ||||
\(719\) | 89.7795 | + | 123.571i | 0.124867 | + | 0.171865i | 0.866874 | − | 0.498528i | \(-0.166126\pi\) |
−0.742007 | + | 0.670393i | \(0.766126\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 138.879 | − | 427.427i | 0.192621 | − | 0.592825i | ||||
\(722\) | 197.890 | + | 272.372i | 0.274085 | + | 0.377246i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 174.567 | + | 537.263i | 0.241115 | + | 0.742076i | ||||
\(725\) | 385.716i | 0.532023i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 610.733 | 0.840073 | 0.420037 | − | 0.907507i | \(-0.362017\pi\) | ||||
0.420037 | + | 0.907507i | \(0.362017\pi\) | |||||||
\(728\) | 27.1351 | − | 8.81673i | 0.0372735 | − | 0.0121109i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −115.218 | + | 83.7108i | −0.157833 | + | 0.114672i | ||||
\(731\) | 639.521 | + | 207.793i | 0.874858 | + | 0.284259i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 180.227 | − | 130.943i | 0.245876 | − | 0.178640i | −0.458021 | − | 0.888941i | \(-0.651442\pi\) |
0.703897 | + | 0.710302i | \(0.251442\pi\) | |||||||
\(734\) | 3.81625 | − | 5.25262i | 0.00519925 | − | 0.00715616i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 62.6853 | 0.0851703 | ||||||||
\(737\) | −962.802 | − | 62.0944i | −1.30638 | − | 0.0842530i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −99.1503 | − | 305.153i | −0.134168 | − | 0.412927i | 0.861291 | − | 0.508111i | \(-0.169656\pi\) |
−0.995460 | + | 0.0951838i | \(0.969656\pi\) | |||||||
\(740\) | 66.4352 | − | 91.4402i | 0.0897773 | − | 0.123568i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −38.1408 | + | 117.385i | −0.0514027 | + | 0.158201i | ||||
\(743\) | −263.302 | − | 85.5519i | −0.354377 | − | 0.115144i | 0.126418 | − | 0.991977i | \(-0.459652\pi\) |
−0.480795 | + | 0.876833i | \(0.659652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 343.282 | + | 249.409i | 0.460781 | + | 0.334777i | ||||
\(746\) | 171.568 | − | 55.7457i | 0.229983 | − | 0.0747262i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 313.932 | − | 80.0782i | 0.419696 | − | 0.107056i | ||||
\(749\) | − | 203.885i | − | 0.272210i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −433.264 | − | 314.785i | −0.576916 | − | 0.419154i | 0.260695 | − | 0.965421i | \(-0.416048\pi\) |
−0.837611 | + | 0.546267i | \(0.816048\pi\) | |||||||
\(752\) | −27.2570 | − | 37.5161i | −0.0362461 | − | 0.0498884i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 44.7505 | − | 137.728i | 0.0593508 | − | 0.182663i | ||||
\(755\) | −84.2827 | − | 116.005i | −0.111633 | − | 0.153649i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 209.813 | + | 645.737i | 0.277163 | + | 0.853021i | 0.988639 | + | 0.150310i | \(0.0480272\pi\) |
−0.711476 | + | 0.702711i | \(0.751973\pi\) | |||||||
\(758\) | 446.845i | 0.589505i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −88.4762 | −0.116416 | ||||||||
\(761\) | 534.529 | − | 173.679i | 0.702404 | − | 0.228225i | 0.0640263 | − | 0.997948i | \(-0.479606\pi\) |
0.638378 | + | 0.769723i | \(0.279606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −374.888 | + | 272.372i | −0.491334 | + | 0.356975i | ||||
\(764\) | 680.193 | + | 221.008i | 0.890305 | + | 0.289278i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 324.039 | − | 235.428i | 0.423027 | − | 0.307347i | ||||
\(767\) | 247.694 | − | 340.921i | 0.322938 | − | 0.444487i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −113.242 | −0.147258 | −0.0736291 | − | 0.997286i | \(-0.523458\pi\) | ||||
−0.0736291 | + | 0.997286i | \(0.523458\pi\) | |||||||
\(770\) | −82.7082 | + | 52.3060i | −0.107413 | + | 0.0679299i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.9863 | + | 70.7444i | 0.0297749 | + | 0.0916378i | ||||
\(773\) | −629.282 | + | 866.132i | −0.814077 | + | 1.12048i | 0.176604 | + | 0.984282i | \(0.443489\pi\) |
−0.990681 | + | 0.136199i | \(0.956511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −121.251 | + | 373.171i | −0.156452 | + | 0.481511i | ||||
\(776\) | 293.526 | + | 95.3724i | 0.378255 | + | 0.122903i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 337.092 | + | 244.911i | 0.433280 | + | 0.314796i | ||||
\(779\) | −427.440 | + | 138.884i | −0.548703 | + | 0.178284i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −686.629 | − | 273.105i | −0.879167 | − | 0.349687i | ||||
\(782\) | − | 230.785i | − | 0.295122i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 142.478 | + | 103.516i | 0.181732 | + | 0.132036i | ||||
\(785\) | −171.121 | − | 235.528i | −0.217989 | − | 0.300036i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 64.3376 | − | 198.011i | 0.0817505 | − | 0.251602i | −0.901824 | − | 0.432103i | \(-0.857772\pi\) |
0.983575 | + | 0.180501i | \(0.0577718\pi\) | |||||||
\(788\) | −151.907 | − | 209.082i | −0.192775 | − | 0.265332i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 31.3179 | + | 96.3865i | 0.0396429 | + | 0.122008i | ||||
\(791\) | − | 141.569i | − | 0.178974i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 335.487 | 0.423060 | ||||||||
\(794\) | −476.903 | + | 154.955i | −0.600634 | + | 0.195158i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −151.583 | + | 110.132i | −0.190431 | + | 0.138356i | ||||
\(797\) | 250.710 | + | 81.4605i | 0.314567 | + | 0.102209i | 0.462045 | − | 0.886856i | \(-0.347116\pi\) |
−0.147479 | + | 0.989065i | \(0.547116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −138.121 | + | 100.351i | −0.172867 | + | 0.125595i | ||||
\(800\) | 56.6606 | − | 77.9866i | 0.0708258 | − | 0.0974833i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 57.7033 | 0.0719492 | ||||||||
\(803\) | 331.854 | − | 209.870i | 0.413267 | − | 0.261357i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.5412 | + | 66.2971i | 0.0267593 | + | 0.0823567i | ||||
\(806\) | 86.5899 | − | 119.181i | 0.107432 | − | 0.147867i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 158.058 | − | 486.452i | 0.195616 | − | 0.602045i | ||||
\(809\) | 920.341 | + | 299.037i | 1.13763 | + | 0.369638i | 0.816470 | − | 0.577388i | \(-0.195928\pi\) |
0.321158 | + | 0.947026i | \(0.395928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 354.977 | + | 257.906i | 0.437703 | + | 0.318010i | 0.784721 | − | 0.619849i | \(-0.212806\pi\) |
−0.347019 | + | 0.937858i | \(0.612806\pi\) | |||||||
\(812\) | −96.0012 | + | 31.1927i | −0.118228 | + | 0.0384146i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −199.009 | + | 239.792i | −0.244483 | + | 0.294585i | ||||
\(815\) | 760.236i | 0.932805i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 409.589 | + | 297.584i | 0.501333 | + | 0.364240i | ||||
\(818\) | 396.854 | + | 546.223i | 0.485152 | + | 0.667754i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −70.6764 | + | 217.519i | −0.0861907 | + | 0.265268i | ||||
\(821\) | 162.007 | + | 222.984i | 0.197329 | + | 0.271600i | 0.896202 | − | 0.443645i | \(-0.146315\pi\) |
−0.698874 | + | 0.715245i | \(0.746315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 374.035 | + | 1151.16i | 0.454477 | + | 1.39874i | 0.871748 | + | 0.489955i | \(0.162987\pi\) |
−0.417271 | + | 0.908782i | \(0.637013\pi\) | |||||||
\(824\) | 570.086i | 0.691852i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −293.732 | −0.355608 | ||||||||
\(827\) | 1037.13 | − | 336.983i | 1.25408 | − | 0.407476i | 0.394701 | − | 0.918810i | \(-0.370848\pi\) |
0.859382 | + | 0.511333i | \(0.170848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1038.92 | + | 754.823i | −1.25323 | + | 0.910522i | −0.998404 | − | 0.0564665i | \(-0.982017\pi\) |
−0.254821 | + | 0.966988i | \(0.582017\pi\) | |||||||
\(830\) | −83.1377 | − | 27.0131i | −0.100166 | − | 0.0325459i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −29.2798 | + | 21.2730i | −0.0351920 | + | 0.0255685i | ||||
\(833\) | 381.110 | − | 524.553i | 0.457515 | − | 0.629716i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 597.651 | 0.715750 | ||||||||
\(836\) | 243.425 | + | 15.6993i | 0.291178 | + | 0.0187791i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.1971 | − | 102.170i | −0.0396147 | − | 0.121921i | ||||
\(839\) | 311.504 | − | 428.748i | 0.371280 | − | 0.511023i | −0.581968 | − | 0.813211i | \(-0.697717\pi\) |
0.953248 | + | 0.302189i | \(0.0977173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 101.561 | − | 312.571i | 0.120762 | − | 0.371666i | ||||
\(842\) | −375.660 | − | 122.059i | −0.446152 | − | 0.144964i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 468.618 | + | 340.471i | 0.555234 | + | 0.403401i | ||||
\(845\) | −398.537 | + | 129.492i | −0.471641 | + | 0.153246i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 236.837 | − | 129.234i | 0.279619 | − | 0.152579i | ||||
\(848\) | − | 156.564i | − | 0.184628i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −287.119 | − | 208.604i | −0.337787 | − | 0.245417i | ||||
\(851\) | 130.473 | + | 179.581i | 0.153318 | + | 0.211024i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −377.749 | + | 1162.59i | −0.442847 | + | 1.36294i | 0.441980 | + | 0.897025i | \(0.354276\pi\) |
−0.884828 | + | 0.465919i | \(0.845724\pi\) | |||||||
\(854\) | −137.451 | − | 189.186i | −0.160950 | − | 0.221529i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 79.9196 | + | 245.967i | 0.0933640 | + | 0.287345i | ||||
\(857\) | 1479.73i | 1.72664i | 0.504653 | + | 0.863322i | \(0.331620\pi\) | ||||
−0.504653 | + | 0.863322i | \(0.668380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 95.9499 | 0.111700 | 0.0558498 | − | 0.998439i | \(-0.482213\pi\) | ||||
0.0558498 | + | 0.998439i | \(0.482213\pi\) | |||||||
\(860\) | 245.031 | − | 79.6153i | 0.284920 | − | 0.0925760i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −680.244 | + | 494.226i | −0.789147 | + | 0.573349i | ||||
\(863\) | 1214.69 | + | 394.678i | 1.40752 | + | 0.457332i | 0.911616 | − | 0.411043i | \(-0.134835\pi\) |
0.495908 | + | 0.868375i | \(0.334835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −276.045 | + | 200.558i | −0.319127 | + | 0.231859i | ||||
\(866\) | −131.067 | + | 180.399i | −0.151348 | + | 0.208313i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −102.684 | −0.118300 | ||||||||
\(869\) | −69.0621 | − | 270.746i | −0.0794731 | − | 0.311560i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −122.616 | − | 377.374i | −0.140776 | − | 0.433265i | ||||
\(872\) | 345.500 | − | 475.539i | 0.396215 | − | 0.545343i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 53.6948 | − | 165.256i | 0.0614357 | − | 0.189080i | ||||
\(875\) | 251.521 | + | 81.7240i | 0.287452 | + | 0.0933989i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −265.285 | − | 192.741i | −0.302491 | − | 0.219773i | 0.426177 | − | 0.904640i | \(-0.359860\pi\) |
−0.728668 | + | 0.684867i | \(0.759860\pi\) | |||||||
\(878\) | −357.047 | + | 116.011i | −0.406659 | + | 0.132131i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 79.2761 | − | 95.5222i | 0.0900865 | − | 0.108548i | ||||
\(881\) | − | 768.903i | − | 0.872761i | −0.899762 | − | 0.436381i | \(-0.856260\pi\) | ||
0.899762 | − | 0.436381i | \(-0.143740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 564.755 | + | 410.318i | 0.639586 | + | 0.464687i | 0.859708 | − | 0.510786i | \(-0.170645\pi\) |
−0.220122 | + | 0.975472i | \(0.570645\pi\) | |||||||
\(884\) | 78.3196 | + | 107.798i | 0.0885968 | + | 0.121943i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.1242 | + | 80.4021i | −0.0294856 | + | 0.0907472i | ||||
\(887\) | 491.752 | + | 676.839i | 0.554399 | + | 0.763065i | 0.990601 | − | 0.136784i | \(-0.0436766\pi\) |
−0.436202 | + | 0.899849i | \(0.643677\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.4697 | − | 139.941i | −0.0511470 | − | 0.157414i | ||||
\(890\) | − | 139.607i | − | 0.156861i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −287.943 | −0.322806 | ||||||||
\(893\) | −122.250 | + | 39.7216i | −0.136899 | + | 0.0444811i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −106.749 | + | 77.5573i | −0.119272 | + | 0.0866563i | ||||
\(896\) | 23.9923 | + | 7.79556i | 0.0267771 | + | 0.00870040i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −318.084 | + | 231.102i | −0.354214 | + | 0.257352i | ||||
\(899\) | −306.346 | + | 421.650i | −0.340763 | + | 0.469021i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −576.413 | −0.639748 | ||||||||
\(902\) | 233.049 | − | 585.922i | 0.258370 | − | 0.649581i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 55.4925 | + | 170.788i | 0.0613855 | + | 0.188925i | ||||
\(905\) | 468.389 | − | 644.682i | 0.517556 | − | 0.712355i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.9257 | + | 104.413i | −0.0374043 | + | 0.115119i | −0.968015 | − | 0.250891i | \(-0.919276\pi\) |
0.930611 | + | 0.366010i | \(0.119276\pi\) | |||||||
\(908\) | −78.9845 | − | 25.6636i | −0.0869874 | − | 0.0282639i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −32.5604 | − | 23.6565i | −0.0357807 | − | 0.0259962i | ||||
\(911\) | 961.698 | − | 312.475i | 1.05565 | − | 0.343002i | 0.270767 | − | 0.962645i | \(-0.412723\pi\) |
0.784884 | + | 0.619643i | \(0.212723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 223.944 | + | 89.0733i | 0.245284 | + | 0.0975611i | ||||
\(914\) | 465.808i | 0.509637i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −204.740 | − | 148.752i | −0.223515 | − | 0.162393i | ||||
\(917\) | 78.0672 | + | 107.450i | 0.0851332 | + | 0.117176i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 229.979 | − | 707.803i | 0.250249 | − | 0.770188i | −0.744479 | − | 0.667645i | \(-0.767302\pi\) |
0.994729 | − | 0.102542i | \(-0.0326977\pi\) | |||||||
\(920\) | −51.9747 | − | 71.5370i | −0.0564942 | − | 0.0777576i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −274.848 | − | 845.894i | −0.298099 | − | 0.917455i | ||||
\(923\) | − | 303.908i | − | 0.329261i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 341.350 | 0.369027 | ||||||||
\(926\) | 685.854 | − | 222.847i | 0.740663 | − | 0.240656i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 103.589 | − | 75.2617i | 0.111626 | − | 0.0811010i | ||||
\(929\) | 172.202 | + | 55.9519i | 0.185363 | + | 0.0602281i | 0.400228 | − | 0.916416i | \(-0.368931\pi\) |
−0.214865 | + | 0.976644i | \(0.568931\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 394.941 | − | 286.941i | 0.424211 | − | 0.308207i | ||||
\(932\) | 234.067 | − | 322.166i | 0.251145 | − | 0.345672i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −312.952 | −0.335067 | ||||||||
\(935\) | −351.679 | − | 291.866i | −0.376127 | − | 0.312157i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 249.812 | + | 768.843i | 0.266609 | + | 0.820537i | 0.991318 | + | 0.131483i | \(0.0419738\pi\) |
−0.724710 | + | 0.689054i | \(0.758026\pi\) | |||||||
\(938\) | −162.570 | + | 223.758i | −0.173315 | + | 0.238548i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −20.2139 | + | 62.2119i | −0.0215041 | + | 0.0661829i | ||||
\(941\) | −124.609 | − | 40.4881i | −0.132422 | − | 0.0430266i | 0.242056 | − | 0.970262i | \(-0.422178\pi\) |
−0.374478 | + | 0.927236i | \(0.622178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −363.390 | − | 264.018i | −0.385356 | − | 0.279977i | ||||
\(944\) | 354.358 | − | 115.138i | 0.375380 | − | 0.121968i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −688.282 | + | 175.568i | −0.727571 | + | 0.185589i | ||||
\(947\) | 816.092i | 0.861765i | 0.902408 | + | 0.430883i | \(0.141798\pi\) | ||||
−0.902408 | + | 0.430883i | \(0.858202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 130.644 | + | 94.9181i | 0.137664 | + | 0.100019i | ||||
\(950\) | −157.060 | − | 216.174i | −0.165326 | − | 0.227552i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28.7005 | − | 88.3310i | 0.0301476 | − | 0.0927847i | ||||
\(953\) | −588.175 | − | 809.554i | −0.617183 | − | 0.849480i | 0.379961 | − | 0.925003i | \(-0.375937\pi\) |
−0.997144 | + | 0.0755229i | \(0.975937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −311.756 | − | 959.487i | −0.326446 | − | 1.00470i | ||||
\(956\) | − | 492.881i | − | 0.515566i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 365.640 | 0.381670 | ||||||||
\(959\) | −403.351 | + | 131.057i | −0.420595 | + | 0.136660i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 348.537 | − | 253.227i | 0.362682 | − | 0.263504i | ||||
\(962\) | −121.886 | − | 39.6032i | −0.126701 | − | 0.0411675i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −711.321 | + | 516.805i | −0.737885 | + | 0.536105i | ||||
\(965\) | 61.6754 | − | 84.8889i | 0.0639123 | − | 0.0879677i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1675.29 | 1.73247 | 0.866233 | − | 0.499640i | \(-0.166534\pi\) | ||||
0.866233 | + | 0.499640i | \(0.166534\pi\) | |||||||
\(968\) | −235.063 | + | 248.744i | −0.242833 | + | 0.256967i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −134.533 | − | 414.051i | −0.138694 | − | 0.426857i | ||||
\(971\) | −828.699 | + | 1140.61i | −0.853449 | + | 1.17467i | 0.129644 | + | 0.991561i | \(0.458617\pi\) |
−0.983092 | + | 0.183111i | \(0.941383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 161.667 | − | 497.561i | 0.166154 | − | 0.511368i | ||||
\(974\) | −600.718 | − | 195.185i | −0.616754 | − | 0.200395i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 239.979 | + | 174.355i | 0.245880 | + | 0.178642i | ||||
\(977\) | 621.149 | − | 201.824i | 0.635772 | − | 0.206575i | 0.0266416 | − | 0.999645i | \(-0.491519\pi\) |
0.609130 | + | 0.793070i | \(0.291519\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.7720 | + | 384.100i | −0.0253033 | + | 0.392340i | ||||
\(980\) | − | 248.426i | − | 0.253496i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −508.441 | − | 369.404i | −0.517760 | − | 0.376175i | ||||
\(983\) | −376.857 | − | 518.699i | −0.383374 | − | 0.527669i | 0.573100 | − | 0.819485i | \(-0.305741\pi\) |
−0.956475 | + | 0.291816i | \(0.905741\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −112.654 | + | 346.715i | −0.114370 | + | 0.351995i | ||||
\(986\) | −277.087 | − | 381.377i | −0.281021 | − | 0.386792i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 31.0010 | + | 95.4114i | 0.0313776 | + | 0.0965702i | ||||
\(989\) | 505.986i | 0.511613i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 435.813 | 0.439771 | 0.219886 | − | 0.975526i | \(-0.429432\pi\) | ||||
0.219886 | + | 0.975526i | \(0.429432\pi\) | |||||||
\(992\) | 123.878 | − | 40.2505i | 0.124877 | − | 0.0405751i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −171.378 | + | 124.513i | −0.172412 | + | 0.125265i | ||||
\(995\) | 251.367 | + | 81.6739i | 0.252630 | + | 0.0820843i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −341.582 | + | 248.174i | −0.342610 | + | 0.248921i | −0.745762 | − | 0.666212i | \(-0.767915\pi\) |
0.403152 | + | 0.915133i | \(0.367915\pi\) | |||||||
\(998\) | 625.225 | − | 860.548i | 0.626477 | − | 0.862272i | ||||
\(999\) | 0 | 0 |
(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 | 198.3.k.a.71.1 | yes | 16 | |
3.2 | odd | 2 | inner | 198.3.k.a.71.4 | yes | 16 | |
11.3 | even | 5 | 2178.3.c.p.485.6 | 8 | |||
11.8 | odd | 10 | 2178.3.c.m.485.2 | 8 | |||
11.9 | even | 5 | inner | 198.3.k.a.53.4 | yes | 16 | |
33.8 | even | 10 | 2178.3.c.m.485.7 | 8 | |||
33.14 | odd | 10 | 2178.3.c.p.485.3 | 8 | |||
33.20 | odd | 10 | inner | 198.3.k.a.53.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
198.3.k.a.53.1 | ✓ | 16 | 33.20 | odd | 10 | inner | |
198.3.k.a.53.4 | yes | 16 | 11.9 | even | 5 | inner | |
198.3.k.a.71.1 | yes | 16 | 1.1 | even | 1 | trivial | |
198.3.k.a.71.4 | yes | 16 | 3.2 | odd | 2 | inner | |
2178.3.c.m.485.2 | 8 | 11.8 | odd | 10 | |||
2178.3.c.m.485.7 | 8 | 33.8 | even | 10 | |||
2178.3.c.p.485.3 | 8 | 33.14 | odd | 10 | |||
2178.3.c.p.485.6 | 8 | 11.3 | even | 5 |