Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(199,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.t (of order \(6\), degree \(2\), not 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: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 299.5 | ||
Character | \(\chi\) | \(=\) | 700.299 |
Dual form | 700.2.t.d.199.5 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.790498 | + | 1.17265i | −0.558967 | + | 0.829190i | ||||
\(3\) | 0.573616 | − | 0.331177i | 0.331177 | − | 0.191205i | −0.325186 | − | 0.945650i | \(-0.605427\pi\) |
0.656364 | + | 0.754445i | \(0.272094\pi\) | |||||||
\(4\) | −0.750225 | − | 1.85396i | −0.375113 | − | 0.926979i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0650866 | + | 0.934447i | −0.0265715 | + | 0.381486i | ||||
\(7\) | −2.03775 | − | 1.68748i | −0.770195 | − | 0.637808i | ||||
\(8\) | 2.76710 | + | 0.585797i | 0.978318 | + | 0.207111i | ||||
\(9\) | −1.28064 | + | 2.21814i | −0.426881 | + | 0.739380i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.12892 | − | 1.80648i | 0.943404 | − | 0.544674i | 0.0523781 | − | 0.998627i | \(-0.483320\pi\) |
0.891026 | + | 0.453953i | \(0.149987\pi\) | |||||||
\(12\) | −1.04433 | − | 0.815002i | −0.301472 | − | 0.235271i | ||||
\(13\) | −5.83027 | −1.61703 | −0.808513 | − | 0.588478i | \(-0.799727\pi\) | ||||
−0.808513 | + | 0.588478i | \(0.799727\pi\) | |||||||
\(14\) | 3.58966 | − | 1.05561i | 0.959378 | − | 0.282125i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.87432 | + | 2.78177i | −0.718581 | + | 0.695443i | ||||
\(17\) | −0.684063 | − | 1.18483i | −0.165910 | − | 0.287364i | 0.771068 | − | 0.636752i | \(-0.219723\pi\) |
−0.936978 | + | 0.349389i | \(0.886389\pi\) | |||||||
\(18\) | −1.58876 | − | 3.25518i | −0.374474 | − | 0.767254i | ||||
\(19\) | 2.04788 | − | 3.54704i | 0.469817 | − | 0.813747i | −0.529588 | − | 0.848255i | \(-0.677653\pi\) |
0.999404 | + | 0.0345086i | \(0.0109866\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.72774 | − | 0.293111i | −0.377024 | − | 0.0639622i | ||||
\(22\) | −0.355029 | + | 5.09715i | −0.0756925 | + | 1.08672i | ||||
\(23\) | −1.62259 | + | 2.81042i | −0.338334 | + | 0.586012i | −0.984120 | − | 0.177507i | \(-0.943197\pi\) |
0.645785 | + | 0.763519i | \(0.276530\pi\) | |||||||
\(24\) | 1.78126 | − | 0.580378i | 0.363597 | − | 0.118469i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.60882 | − | 6.83688i | 0.903863 | − | 1.34082i | ||||
\(27\) | 3.68354i | 0.708898i | ||||||||
\(28\) | −1.59975 | + | 5.04389i | −0.302325 | + | 0.953205i | ||||
\(29\) | −5.19327 | −0.964365 | −0.482183 | − | 0.876071i | \(-0.660156\pi\) | ||||
−0.482183 | + | 0.876071i | \(0.660156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.43405 | − | 7.67999i | −0.796378 | − | 1.37937i | −0.921960 | − | 0.387284i | \(-0.873413\pi\) |
0.125582 | − | 0.992083i | \(-0.459920\pi\) | |||||||
\(32\) | −0.989905 | − | 5.56957i | −0.174992 | − | 0.984570i | ||||
\(33\) | 1.19653 | − | 2.07245i | 0.208289 | − | 0.360768i | ||||
\(34\) | 1.93014 | + | 0.134439i | 0.331017 | + | 0.0230562i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.07311 | + | 0.710155i | 0.845518 | + | 0.118359i | ||||
\(37\) | −9.34942 | − | 5.39789i | −1.53704 | − | 0.887408i | −0.999010 | − | 0.0444796i | \(-0.985837\pi\) |
−0.538026 | − | 0.842928i | \(-0.680830\pi\) | |||||||
\(38\) | 2.54059 | + | 5.20538i | 0.412139 | + | 0.844425i | ||||
\(39\) | −3.34434 | + | 1.93085i | −0.535522 | + | 0.309184i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.832730i | 0.130051i | 0.997884 | + | 0.0650253i | \(0.0207128\pi\) | ||||
−0.997884 | + | 0.0650253i | \(0.979287\pi\) | |||||||
\(42\) | 1.70949 | − | 1.79433i | 0.263780 | − | 0.276871i | ||||
\(43\) | −3.10642 | −0.473725 | −0.236862 | − | 0.971543i | \(-0.576119\pi\) | ||||
−0.236862 | + | 0.971543i | \(0.576119\pi\) | |||||||
\(44\) | −5.69653 | − | 4.44561i | −0.858785 | − | 0.670201i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.01298 | − | 4.12437i | −0.296798 | − | 0.608105i | ||||
\(47\) | −5.97212 | − | 3.44801i | −0.871124 | − | 0.502943i | −0.00340208 | − | 0.999994i | \(-0.501083\pi\) |
−0.867721 | + | 0.497051i | \(0.834416\pi\) | |||||||
\(48\) | −0.727497 | + | 2.54758i | −0.105005 | + | 0.367712i | ||||
\(49\) | 1.30481 | + | 6.87732i | 0.186402 | + | 0.982474i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.784778 | − | 0.453092i | −0.109891 | − | 0.0634456i | ||||
\(52\) | 4.37402 | + | 10.8091i | 0.606567 | + | 1.49895i | ||||
\(53\) | 6.42376 | − | 3.70876i | 0.882371 | − | 0.509437i | 0.0109318 | − | 0.999940i | \(-0.496520\pi\) |
0.871440 | + | 0.490503i | \(0.163187\pi\) | |||||||
\(54\) | −4.31952 | − | 2.91183i | −0.587812 | − | 0.396250i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.65012 | − | 5.86314i | −0.621399 | − | 0.783494i | ||||
\(57\) | − | 2.71285i | − | 0.359326i | ||||||
\(58\) | 4.10527 | − | 6.08989i | 0.539048 | − | 0.799642i | ||||
\(59\) | −3.73928 | − | 6.47663i | −0.486813 | − | 0.843185i | 0.513072 | − | 0.858346i | \(-0.328507\pi\) |
−0.999885 | + | 0.0151606i | \(0.995174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.28652 | + | 0.742772i | 0.164722 | + | 0.0951022i | 0.580095 | − | 0.814549i | \(-0.303016\pi\) |
−0.415373 | + | 0.909651i | \(0.636349\pi\) | |||||||
\(62\) | 12.5111 | + | 0.871427i | 1.58891 | + | 0.110671i | ||||
\(63\) | 6.35269 | − | 2.35894i | 0.800364 | − | 0.297199i | ||||
\(64\) | 7.31368 | + | 3.24192i | 0.914210 | + | 0.405240i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.48441 | + | 3.04138i | 0.182718 | + | 0.374368i | ||||
\(67\) | 1.26880 | + | 2.19763i | 0.155009 | + | 0.268484i | 0.933062 | − | 0.359715i | \(-0.117126\pi\) |
−0.778053 | + | 0.628198i | \(0.783793\pi\) | |||||||
\(68\) | −1.68343 | + | 2.15711i | −0.204145 | + | 0.261589i | ||||
\(69\) | 2.14947i | 0.258765i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.52502i | 0.418342i | 0.977879 | + | 0.209171i | \(0.0670766\pi\) | ||||
−0.977879 | + | 0.209171i | \(0.932923\pi\) | |||||||
\(72\) | −4.84305 | + | 5.38762i | −0.570759 | + | 0.634937i | ||||
\(73\) | 2.58492 | + | 4.47721i | 0.302542 | + | 0.524018i | 0.976711 | − | 0.214559i | \(-0.0688314\pi\) |
−0.674169 | + | 0.738577i | \(0.735498\pi\) | |||||||
\(74\) | 13.7206 | − | 6.69660i | 1.59498 | − | 0.778464i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.11244 | − | 1.13561i | −0.930561 | − | 0.130264i | ||||
\(77\) | −9.42434 | − | 1.59884i | −1.07400 | − | 0.182205i | ||||
\(78\) | 0.379472 | − | 5.44808i | 0.0429668 | − | 0.616873i | ||||
\(79\) | 9.82082 | + | 5.67005i | 1.10493 | + | 0.637931i | 0.937511 | − | 0.347955i | \(-0.113124\pi\) |
0.167417 | + | 0.985886i | \(0.446457\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.62202 | − | 4.54148i | −0.291336 | − | 0.504609i | ||||
\(82\) | −0.976503 | − | 0.658272i | −0.107837 | − | 0.0726939i | ||||
\(83\) | − | 6.49145i | − | 0.712529i | −0.934385 | − | 0.356264i | \(-0.884050\pi\) | ||
0.934385 | − | 0.356264i | \(-0.115950\pi\) | |||||||
\(84\) | 0.752777 | + | 3.42306i | 0.0821347 | + | 0.373486i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.45562 | − | 3.64275i | 0.264796 | − | 0.392808i | ||||
\(87\) | −2.97894 | + | 1.71989i | −0.319376 | + | 0.184392i | ||||
\(88\) | 9.71626 | − | 3.16580i | 1.03576 | − | 0.337476i | ||||
\(89\) | −8.13303 | − | 4.69560i | −0.862099 | − | 0.497733i | 0.00261566 | − | 0.999997i | \(-0.499167\pi\) |
−0.864715 | + | 0.502264i | \(0.832501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.8806 | + | 9.83847i | 1.24543 | + | 1.03135i | ||||
\(92\) | 6.42771 | + | 0.899777i | 0.670135 | + | 0.0938083i | ||||
\(93\) | −5.08688 | − | 2.93691i | −0.527485 | − | 0.304544i | ||||
\(94\) | 8.76426 | − | 4.27758i | 0.903965 | − | 0.441199i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.41234 | − | 2.86696i | −0.246208 | − | 0.292608i | ||||
\(97\) | −0.343189 | −0.0348455 | −0.0174228 | − | 0.999848i | \(-0.505546\pi\) | ||||
−0.0174228 | + | 0.999848i | \(0.505546\pi\) | |||||||
\(98\) | −9.09615 | − | 3.90642i | −0.918850 | − | 0.394608i | ||||
\(99\) | 9.25383i | 0.930045i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.92859 | − | 2.26817i | 0.390910 | − | 0.225692i | −0.291645 | − | 0.956527i | \(-0.594202\pi\) |
0.682554 | + | 0.730835i | \(0.260869\pi\) | |||||||
\(102\) | 1.15169 | − | 0.562104i | 0.114034 | − | 0.0556566i | ||||
\(103\) | 5.31577 | + | 3.06906i | 0.523778 | + | 0.302404i | 0.738479 | − | 0.674276i | \(-0.235544\pi\) |
−0.214701 | + | 0.976680i | \(0.568878\pi\) | |||||||
\(104\) | −16.1329 | − | 3.41536i | −1.58196 | − | 0.334903i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.728886 | + | 10.4646i | −0.0707957 | + | 1.01641i | ||||
\(107\) | 3.83398 | − | 6.64066i | 0.370645 | − | 0.641976i | −0.619020 | − | 0.785375i | \(-0.712470\pi\) |
0.989665 | + | 0.143399i | \(0.0458032\pi\) | |||||||
\(108\) | 6.82914 | − | 2.76349i | 0.657134 | − | 0.265917i | ||||
\(109\) | 0.647616 | + | 1.12170i | 0.0620304 | + | 0.107440i | 0.895373 | − | 0.445317i | \(-0.146909\pi\) |
−0.833342 | + | 0.552757i | \(0.813576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.15064 | −0.678709 | ||||||||
\(112\) | 10.5513 | − | 0.818178i | 0.997007 | − | 0.0773105i | ||||
\(113\) | − | 7.10591i | − | 0.668468i | −0.942490 | − | 0.334234i | \(-0.891522\pi\) | ||
0.942490 | − | 0.334234i | \(-0.108478\pi\) | |||||||
\(114\) | 3.18123 | + | 2.14450i | 0.297950 | + | 0.200851i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.89612 | + | 9.62810i | 0.361746 | + | 0.893946i | ||||
\(117\) | 7.46649 | − | 12.9323i | 0.690278 | − | 1.19560i | ||||
\(118\) | 10.5507 | + | 0.734884i | 0.971273 | + | 0.0676516i | ||||
\(119\) | −0.605436 | + | 3.56873i | −0.0555002 | + | 0.327145i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.02675 | − | 1.77837i | 0.0933405 | − | 0.161670i | ||||
\(122\) | −1.88800 | + | 0.921479i | −0.170932 | + | 0.0834268i | ||||
\(123\) | 0.275781 | + | 0.477667i | 0.0248664 | + | 0.0430698i | ||||
\(124\) | −10.9119 | + | 13.9823i | −0.979914 | + | 1.25564i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.25558 | + | 9.31424i | −0.200943 | + | 0.829778i | ||||
\(127\) | 17.0178 | 1.51008 | 0.755041 | − | 0.655677i | \(-0.227617\pi\) | ||||
0.755041 | + | 0.655677i | \(0.227617\pi\) | |||||||
\(128\) | −9.58310 | + | 6.01367i | −0.847034 | + | 0.531539i | ||||
\(129\) | −1.78189 | + | 1.02878i | −0.156887 | + | 0.0905787i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.603066 | + | 1.04454i | −0.0526901 | + | 0.0912619i | −0.891167 | − | 0.453674i | \(-0.850113\pi\) |
0.838477 | + | 0.544936i | \(0.183446\pi\) | |||||||
\(132\) | −4.73991 | − | 0.663512i | −0.412556 | − | 0.0577513i | ||||
\(133\) | −10.1586 | + | 3.77220i | −0.880865 | + | 0.327091i | ||||
\(134\) | −3.58005 | − | 0.249359i | −0.309269 | − | 0.0215414i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.19880 | − | 3.67927i | −0.102796 | − | 0.315495i | ||||
\(137\) | 1.85754 | − | 1.07245i | 0.158701 | − | 0.0916258i | −0.418547 | − | 0.908195i | \(-0.637460\pi\) |
0.577247 | + | 0.816570i | \(0.304127\pi\) | |||||||
\(138\) | −2.52058 | − | 1.69915i | −0.214566 | − | 0.144641i | ||||
\(139\) | 3.39555 | 0.288007 | 0.144004 | − | 0.989577i | \(-0.454002\pi\) | ||||
0.144004 | + | 0.989577i | \(0.454002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.56761 | −0.384662 | ||||||||
\(142\) | −4.13362 | − | 2.78652i | −0.346885 | − | 0.233839i | ||||
\(143\) | −18.2424 | + | 10.5323i | −1.52551 | + | 0.880753i | ||||
\(144\) | −2.48938 | − | 9.93811i | −0.207448 | − | 0.828176i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.29359 | − | 0.508017i | −0.603622 | − | 0.0420438i | ||||
\(147\) | 3.02607 | + | 3.51281i | 0.249586 | + | 0.289732i | ||||
\(148\) | −2.99329 | + | 21.3831i | −0.246047 | + | 1.75768i | ||||
\(149\) | −9.54319 | + | 16.5293i | −0.781808 | + | 1.35413i | 0.149079 | + | 0.988825i | \(0.452369\pi\) |
−0.930887 | + | 0.365307i | \(0.880964\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.31900 | + | 4.80298i | −0.676990 | + | 0.390861i | −0.798720 | − | 0.601703i | \(-0.794489\pi\) |
0.121730 | + | 0.992563i | \(0.461156\pi\) | |||||||
\(152\) | 7.74455 | − | 8.61537i | 0.628166 | − | 0.698799i | ||||
\(153\) | 3.50416 | 0.283295 | ||||||||
\(154\) | 9.32481 | − | 9.78759i | 0.751414 | − | 0.788706i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.08873 | + | 4.75168i | 0.487488 | + | 0.380439i | ||||
\(157\) | 8.23118 | + | 14.2568i | 0.656919 | + | 1.13782i | 0.981409 | + | 0.191928i | \(0.0614742\pi\) |
−0.324490 | + | 0.945889i | \(0.605193\pi\) | |||||||
\(158\) | −14.4123 | + | 7.03424i | −1.14658 | + | 0.559614i | ||||
\(159\) | 2.45651 | − | 4.25481i | 0.194814 | − | 0.337428i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.04896 | − | 2.98881i | 0.634347 | − | 0.235552i | ||||
\(162\) | 7.39828 | + | 0.515309i | 0.581264 | + | 0.0404865i | ||||
\(163\) | 3.57806 | − | 6.19738i | 0.280255 | − | 0.485416i | −0.691192 | − | 0.722671i | \(-0.742914\pi\) |
0.971447 | + | 0.237255i | \(0.0762476\pi\) | |||||||
\(164\) | 1.54385 | − | 0.624735i | 0.120554 | − | 0.0487836i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.61221 | + | 5.13148i | 0.590822 | + | 0.398280i | ||||
\(167\) | 13.7127i | 1.06112i | 0.847646 | + | 0.530562i | \(0.178019\pi\) | ||||
−0.847646 | + | 0.530562i | \(0.821981\pi\) | |||||||
\(168\) | −4.60912 | − | 1.82317i | −0.355601 | − | 0.140661i | ||||
\(169\) | 20.9920 | 1.61477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.24522 | + | 9.08498i | 0.401112 | + | 0.694746i | ||||
\(172\) | 2.33052 | + | 5.75917i | 0.177700 | + | 0.439133i | ||||
\(173\) | 1.96219 | − | 3.39862i | 0.149183 | − | 0.258392i | −0.781743 | − | 0.623601i | \(-0.785669\pi\) |
0.930926 | + | 0.365209i | \(0.119002\pi\) | |||||||
\(174\) | 0.338012 | − | 4.85283i | 0.0256246 | − | 0.367892i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.96830 | + | 13.8963i | −0.299122 | + | 1.04748i | ||||
\(177\) | −4.28982 | − | 2.47673i | −0.322443 | − | 0.186162i | ||||
\(178\) | 11.9355 | − | 5.82534i | 0.894600 | − | 0.436628i | ||||
\(179\) | −17.8002 | + | 10.2769i | −1.33045 | + | 0.768134i | −0.985368 | − | 0.170440i | \(-0.945481\pi\) |
−0.345079 | + | 0.938574i | \(0.612148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0603i | 0.970762i | 0.874303 | + | 0.485381i | \(0.161319\pi\) | ||||
−0.874303 | + | 0.485381i | \(0.838681\pi\) | |||||||
\(182\) | −20.9287 | + | 6.15452i | −1.55134 | + | 0.456203i | ||||
\(183\) | 0.983957 | 0.0727362 | ||||||||
\(184\) | −6.13622 | + | 6.82619i | −0.452368 | + | 0.503234i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.46514 | − | 3.64352i | 0.547371 | − | 0.267156i | ||||
\(187\) | −4.28075 | − | 2.47149i | −0.313039 | − | 0.180733i | ||||
\(188\) | −1.91202 | + | 13.6588i | −0.139449 | + | 0.996174i | ||||
\(189\) | 6.21591 | − | 7.50612i | 0.452141 | − | 0.545990i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8038 | − | 6.23755i | −0.781733 | − | 0.451334i | 0.0553113 | − | 0.998469i | \(-0.482385\pi\) |
−0.837044 | + | 0.547136i | \(0.815718\pi\) | |||||||
\(192\) | 5.26890 | − | 0.562510i | 0.380250 | − | 0.0405956i | ||||
\(193\) | −16.5103 | + | 9.53225i | −1.18844 | + | 0.686147i | −0.957952 | − | 0.286928i | \(-0.907366\pi\) |
−0.230489 | + | 0.973075i | \(0.574033\pi\) | |||||||
\(194\) | 0.271290 | − | 0.402441i | 0.0194775 | − | 0.0288936i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.7714 | − | 7.57860i | 0.840811 | − | 0.541329i | ||||
\(197\) | 1.93188i | 0.137641i | 0.997629 | + | 0.0688203i | \(0.0219235\pi\) | ||||
−0.997629 | + | 0.0688203i | \(0.978076\pi\) | |||||||
\(198\) | −10.8515 | − | 7.31513i | −0.771184 | − | 0.519864i | ||||
\(199\) | −10.2823 | − | 17.8094i | −0.728892 | − | 1.26248i | −0.957352 | − | 0.288924i | \(-0.906702\pi\) |
0.228460 | − | 0.973553i | \(-0.426631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.45561 | + | 0.840398i | 0.102671 | + | 0.0592771i | ||||
\(202\) | −0.445766 | + | 6.39986i | −0.0313640 | + | 0.450293i | ||||
\(203\) | 10.5826 | + | 8.76354i | 0.742750 | + | 0.615080i | ||||
\(204\) | −0.251253 | + | 1.79487i | −0.0175912 | + | 0.125666i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.80105 | + | 3.80746i | −0.543525 | + | 0.265278i | ||||
\(207\) | −4.15593 | − | 7.19828i | −0.288857 | − | 0.500315i | ||||
\(208\) | 16.7581 | − | 16.2185i | 1.16196 | − | 1.12455i | ||||
\(209\) | − | 14.7979i | − | 1.02359i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.98398i | 0.687326i | 0.939093 | + | 0.343663i | \(0.111668\pi\) | ||||
−0.939093 | + | 0.343663i | \(0.888332\pi\) | |||||||
\(212\) | −11.6952 | − | 9.12698i | −0.803227 | − | 0.626843i | ||||
\(213\) | 1.16741 | + | 2.02200i | 0.0799893 | + | 0.138545i | ||||
\(214\) | 4.75642 | + | 9.74536i | 0.325142 | + | 0.666179i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.15781 | + | 10.1927i | −0.146820 | + | 0.693528i | ||||
\(217\) | −3.92439 | + | 23.1322i | −0.266405 | + | 1.57032i | ||||
\(218\) | −1.82731 | − | 0.127277i | −0.123761 | − | 0.00862026i | ||||
\(219\) | 2.96550 | + | 1.71213i | 0.200390 | + | 0.115695i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.98827 | + | 6.90789i | 0.268280 | + | 0.464675i | ||||
\(222\) | 5.65257 | − | 8.38521i | 0.379375 | − | 0.562778i | ||||
\(223\) | − | 16.8179i | − | 1.12621i | −0.826384 | − | 0.563106i | \(-0.809606\pi\) | ||
0.826384 | − | 0.563106i | \(-0.190394\pi\) | |||||||
\(224\) | −7.38137 | + | 13.0198i | −0.493188 | + | 0.869922i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.33276 | + | 5.61721i | 0.554287 | + | 0.373651i | ||||
\(227\) | 17.1766 | − | 9.91692i | 1.14005 | − | 0.658209i | 0.193608 | − | 0.981079i | \(-0.437981\pi\) |
0.946443 | + | 0.322870i | \(0.104648\pi\) | |||||||
\(228\) | −5.02951 | + | 2.03525i | −0.333088 | + | 0.134788i | ||||
\(229\) | −12.0664 | − | 6.96655i | −0.797371 | − | 0.460363i | 0.0451798 | − | 0.998979i | \(-0.485614\pi\) |
−0.842551 | + | 0.538616i | \(0.818947\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.93545 | + | 2.20401i | −0.390524 | + | 0.145013i | ||||
\(232\) | −14.3703 | − | 3.04220i | −0.943455 | − | 0.199730i | ||||
\(233\) | 8.85568 | + | 5.11283i | 0.580155 | + | 0.334953i | 0.761195 | − | 0.648523i | \(-0.224613\pi\) |
−0.181040 | + | 0.983476i | \(0.557946\pi\) | |||||||
\(234\) | 9.26289 | + | 18.9786i | 0.605534 | + | 1.24067i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.20209 | + | 11.7914i | −0.599005 | + | 0.767555i | ||||
\(237\) | 7.51117 | 0.487903 | ||||||||
\(238\) | −3.70628 | − | 3.53104i | −0.240242 | − | 0.228883i | ||||
\(239\) | − | 17.0835i | − | 1.10504i | −0.833501 | − | 0.552518i | \(-0.813667\pi\) | ||
0.833501 | − | 0.552518i | \(-0.186333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.0074 | + | 9.24185i | −1.03112 | + | 0.595320i | −0.917307 | − | 0.398182i | \(-0.869641\pi\) |
−0.113818 | + | 0.993502i | \(0.536308\pi\) | |||||||
\(242\) | 1.27377 | + | 2.60982i | 0.0818813 | + | 0.167765i | ||||
\(243\) | −12.5782 | − | 7.26203i | −0.806892 | − | 0.465859i | ||||
\(244\) | 0.411889 | − | 2.94240i | 0.0263685 | − | 0.188368i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.778142 | − | 0.0541995i | −0.0496125 | − | 0.00345564i | ||||
\(247\) | −11.9397 | + | 20.6802i | −0.759706 | + | 1.31585i | ||||
\(248\) | −7.77053 | − | 23.8488i | −0.493429 | − | 1.51440i | ||||
\(249\) | −2.14982 | − | 3.72360i | −0.136239 | − | 0.235973i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.5313 | 1.04344 | 0.521722 | − | 0.853116i | \(-0.325290\pi\) | ||||
0.521722 | + | 0.853116i | \(0.325290\pi\) | |||||||
\(252\) | −9.13933 | − | 10.0079i | −0.575724 | − | 0.630438i | ||||
\(253\) | 11.7247i | 0.737128i | ||||||||
\(254\) | −13.4525 | + | 19.9559i | −0.844086 | + | 1.25215i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.523471 | − | 15.9914i | 0.0327169 | − | 0.999465i | ||||
\(257\) | 3.09749 | − | 5.36502i | 0.193216 | − | 0.334660i | −0.753098 | − | 0.657908i | \(-0.771441\pi\) |
0.946314 | + | 0.323248i | \(0.104775\pi\) | |||||||
\(258\) | 0.202186 | − | 2.90279i | 0.0125876 | − | 0.180720i | ||||
\(259\) | 9.94290 | + | 26.7765i | 0.617822 | + | 1.66381i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.65072 | − | 11.5194i | 0.411669 | − | 0.713032i | ||||
\(262\) | −0.748160 | − | 1.53289i | −0.0462215 | − | 0.0947025i | ||||
\(263\) | 10.5768 | + | 18.3196i | 0.652194 | + | 1.12963i | 0.982589 | + | 0.185790i | \(0.0594844\pi\) |
−0.330396 | + | 0.943842i | \(0.607182\pi\) | |||||||
\(264\) | 4.52496 | − | 5.03376i | 0.278492 | − | 0.309806i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.60691 | − | 14.8945i | 0.221154 | − | 0.913237i | ||||
\(267\) | −6.22031 | −0.380677 | ||||||||
\(268\) | 3.12243 | − | 4.00103i | 0.190733 | − | 0.244402i | ||||
\(269\) | 26.8352 | − | 15.4933i | 1.63617 | − | 0.944642i | 0.654033 | − | 0.756466i | \(-0.273076\pi\) |
0.982135 | − | 0.188177i | \(-0.0602578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5190 | − | 19.9516i | 0.699732 | − | 1.21197i | −0.268827 | − | 0.963188i | \(-0.586636\pi\) |
0.968559 | − | 0.248783i | \(-0.0800306\pi\) | |||||||
\(272\) | 5.26215 | + | 1.50268i | 0.319065 | + | 0.0911134i | ||||
\(273\) | 10.0732 | + | 1.70892i | 0.609657 | + | 0.103428i | ||||
\(274\) | −0.210770 | + | 3.02602i | −0.0127331 | + | 0.182809i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.98502 | − | 1.61258i | 0.239870 | − | 0.0970662i | ||||
\(277\) | 6.01508 | − | 3.47281i | 0.361411 | − | 0.208661i | −0.308288 | − | 0.951293i | \(-0.599756\pi\) |
0.669700 | + | 0.742632i | \(0.266423\pi\) | |||||||
\(278\) | −2.68418 | + | 3.98180i | −0.160986 | + | 0.238813i | ||||
\(279\) | 22.7137 | 1.35984 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.24391 | −0.253170 | −0.126585 | − | 0.991956i | \(-0.540402\pi\) | ||||
−0.126585 | + | 0.991956i | \(0.540402\pi\) | |||||||
\(282\) | 3.61068 | − | 5.35621i | 0.215013 | − | 0.318958i | ||||
\(283\) | −7.38891 | + | 4.26599i | −0.439225 | + | 0.253587i | −0.703269 | − | 0.710924i | \(-0.748277\pi\) |
0.264044 | + | 0.964511i | \(0.414944\pi\) | |||||||
\(284\) | 6.53523 | − | 2.64456i | 0.387795 | − | 0.156926i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.06992 | − | 29.7178i | 0.122397 | − | 1.75725i | ||||
\(287\) | 1.40522 | − | 1.69689i | 0.0829473 | − | 0.100164i | ||||
\(288\) | 13.6218 | + | 4.93688i | 0.802672 | + | 0.290909i | ||||
\(289\) | 7.56412 | − | 13.1014i | 0.444948 | − | 0.770673i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.196859 | + | 0.113656i | −0.0115401 | + | 0.00666265i | ||||
\(292\) | 6.36129 | − | 8.15125i | 0.372267 | − | 0.477016i | ||||
\(293\) | 25.2319 | 1.47406 | 0.737032 | − | 0.675857i | \(-0.236227\pi\) | ||||
0.737032 | + | 0.675857i | \(0.236227\pi\) | |||||||
\(294\) | −6.51141 | + | 0.771656i | −0.379753 | + | 0.0450039i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −22.7087 | − | 20.4134i | −1.31992 | − | 1.18650i | ||||
\(297\) | 6.65425 | + | 11.5255i | 0.386119 | + | 0.668777i | ||||
\(298\) | −11.8392 | − | 24.2572i | −0.685828 | − | 1.40518i | ||||
\(299\) | 9.46017 | − | 16.3855i | 0.547096 | − | 0.947597i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.33009 | + | 5.24203i | 0.364861 | + | 0.302145i | ||||
\(302\) | 0.943933 | − | 13.5520i | 0.0543172 | − | 0.779832i | ||||
\(303\) | 1.50234 | − | 2.60212i | 0.0863070 | − | 0.149488i | ||||
\(304\) | 3.98078 | + | 15.8921i | 0.228313 | + | 0.911474i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.77003 | + | 4.10916i | −0.158352 | + | 0.234905i | ||||
\(307\) | − | 29.2635i | − | 1.67016i | −0.550132 | − | 0.835078i | \(-0.685423\pi\) | ||
0.550132 | − | 0.835078i | \(-0.314577\pi\) | |||||||
\(308\) | 4.10619 | + | 18.6718i | 0.233972 | + | 1.06393i | ||||
\(309\) | 4.06561 | 0.231285 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3730 | − | 19.6987i | −0.644906 | − | 1.11701i | −0.984323 | − | 0.176374i | \(-0.943563\pi\) |
0.339417 | − | 0.940636i | \(-0.389770\pi\) | |||||||
\(312\) | −10.3852 | + | 3.38376i | −0.587946 | + | 0.191568i | ||||
\(313\) | 3.29240 | − | 5.70261i | 0.186098 | − | 0.322331i | −0.757848 | − | 0.652431i | \(-0.773749\pi\) |
0.943946 | + | 0.330100i | \(0.107083\pi\) | |||||||
\(314\) | −23.2250 | − | 1.61768i | −1.31066 | − | 0.0912910i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.14421 | − | 22.4612i | 0.176876 | − | 1.26354i | ||||
\(317\) | 12.2298 | + | 7.06086i | 0.686892 | + | 0.396577i | 0.802447 | − | 0.596724i | \(-0.203531\pi\) |
−0.115555 | + | 0.993301i | \(0.536865\pi\) | |||||||
\(318\) | 3.04754 | + | 6.24405i | 0.170897 | + | 0.350149i | ||||
\(319\) | −16.2493 | + | 9.38153i | −0.909786 | + | 0.525265i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.07891i | − | 0.283477i | ||||||
\(322\) | −2.85785 | + | 11.8013i | −0.159262 | + | 0.657660i | ||||
\(323\) | −5.60352 | −0.311788 | ||||||||
\(324\) | −6.45260 | + | 8.26825i | −0.358478 | + | 0.459347i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.43892 | + | 9.09483i | 0.245849 | + | 0.503716i | ||||
\(327\) | 0.742966 | + | 0.428952i | 0.0410861 | + | 0.0237211i | ||||
\(328\) | −0.487811 | + | 2.30425i | −0.0269349 | + | 0.127231i | ||||
\(329\) | 6.35122 | + | 17.1040i | 0.350154 | + | 0.942974i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.5997 | + | 10.1612i | 0.967368 | + | 0.558510i | 0.898433 | − | 0.439111i | \(-0.144707\pi\) |
0.0689349 | + | 0.997621i | \(0.478040\pi\) | |||||||
\(332\) | −12.0349 | + | 4.87005i | −0.660499 | + | 0.267279i | ||||
\(333\) | 23.9466 | − | 13.8255i | 1.31226 | − | 0.757635i | ||||
\(334\) | −16.0803 | − | 10.8399i | −0.879873 | − | 0.593133i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.78145 | − | 3.96368i | 0.315404 | − | 0.216237i | ||||
\(337\) | 15.7704i | 0.859067i | 0.903051 | + | 0.429533i | \(0.141322\pi\) | ||||
−0.903051 | + | 0.429533i | \(0.858678\pi\) | |||||||
\(338\) | −16.5942 | + | 24.6164i | −0.902604 | + | 1.33895i | ||||
\(339\) | −2.35332 | − | 4.07607i | −0.127815 | − | 0.221381i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.7475 | − | 16.0200i | −1.50261 | − | 0.867534i | ||||
\(342\) | −14.7999 | − | 1.03085i | −0.800285 | − | 0.0557418i | ||||
\(343\) | 8.94647 | − | 16.2161i | 0.483064 | − | 0.875585i | ||||
\(344\) | −8.59578 | − | 1.81973i | −0.463453 | − | 0.0981134i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.43429 | + | 4.98757i | 0.130868 | + | 0.268133i | ||||
\(347\) | −1.52392 | − | 2.63950i | −0.0818082 | − | 0.141696i | 0.822218 | − | 0.569172i | \(-0.192736\pi\) |
−0.904027 | + | 0.427476i | \(0.859403\pi\) | |||||||
\(348\) | 5.42348 | + | 4.23252i | 0.290729 | + | 0.226887i | ||||
\(349\) | − | 8.40462i | − | 0.449889i | −0.974372 | − | 0.224944i | \(-0.927780\pi\) | ||
0.974372 | − | 0.224944i | \(-0.0722201\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 21.4761i | − | 1.14631i | ||||||
\(352\) | −13.1586 | − | 15.6385i | −0.701358 | − | 0.833533i | ||||
\(353\) | −0.216411 | − | 0.374834i | −0.0115184 | − | 0.0199504i | 0.860209 | − | 0.509942i | \(-0.170333\pi\) |
−0.871727 | + | 0.489992i | \(0.837000\pi\) | |||||||
\(354\) | 6.29544 | − | 3.07262i | 0.334599 | − | 0.163308i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.60385 | + | 18.6011i | −0.138004 | + | 0.985854i | ||||
\(357\) | 0.834594 | + | 2.24759i | 0.0441714 | + | 0.118955i | ||||
\(358\) | 2.01973 | − | 28.9973i | 0.106746 | − | 1.53255i | ||||
\(359\) | −23.3662 | − | 13.4905i | −1.23322 | − | 0.712002i | −0.265522 | − | 0.964105i | \(-0.585544\pi\) |
−0.967700 | + | 0.252103i | \(0.918878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.11234 | + | 1.92663i | 0.0585442 | + | 0.101402i | ||||
\(362\) | −15.3151 | − | 10.3241i | −0.804946 | − | 0.542623i | ||||
\(363\) | − | 1.36014i | − | 0.0713888i | ||||||
\(364\) | 9.32699 | − | 29.4072i | 0.488867 | − | 1.54136i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.777816 | + | 1.15384i | −0.0406571 | + | 0.0603121i | ||||
\(367\) | −18.0317 | + | 10.4106i | −0.941248 | + | 0.543430i | −0.890351 | − | 0.455274i | \(-0.849541\pi\) |
−0.0508965 | + | 0.998704i | \(0.516208\pi\) | |||||||
\(368\) | −3.15408 | − | 12.5917i | −0.164418 | − | 0.656390i | ||||
\(369\) | −1.84711 | − | 1.06643i | −0.0961568 | − | 0.0555161i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.3485 | − | 3.28247i | −1.00452 | − | 0.170417i | ||||
\(372\) | −1.62860 | + | 11.6342i | −0.0844392 | + | 0.603206i | ||||
\(373\) | −15.2953 | − | 8.83072i | −0.791958 | − | 0.457237i | 0.0486931 | − | 0.998814i | \(-0.484494\pi\) |
−0.840652 | + | 0.541576i | \(0.817828\pi\) | |||||||
\(374\) | 6.28212 | − | 3.06612i | 0.324841 | − | 0.158545i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.5056 | − | 13.0394i | −0.748071 | − | 0.672457i | ||||
\(377\) | 30.2781 | 1.55940 | ||||||||
\(378\) | 3.88840 | + | 13.2227i | 0.199998 | + | 0.680101i | ||||
\(379\) | − | 15.0551i | − | 0.773331i | −0.922220 | − | 0.386665i | \(-0.873627\pi\) | ||
0.922220 | − | 0.386665i | \(-0.126373\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.76166 | − | 5.63590i | 0.500105 | − | 0.288736i | ||||
\(382\) | 15.8548 | − | 7.73828i | 0.811204 | − | 0.395925i | ||||
\(383\) | −26.2843 | − | 15.1753i | −1.34307 | − | 0.775420i | −0.355811 | − | 0.934558i | \(-0.615795\pi\) |
−0.987256 | + | 0.159138i | \(0.949129\pi\) | |||||||
\(384\) | −3.50542 | + | 6.62324i | −0.178885 | + | 0.337991i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.87338 | − | 26.8961i | 0.0953527 | − | 1.36898i | ||||
\(387\) | 3.97822 | − | 6.89047i | 0.202224 | − | 0.350262i | ||||
\(388\) | 0.257469 | + | 0.636258i | 0.0130710 | + | 0.0323011i | ||||
\(389\) | −3.13909 | − | 5.43706i | −0.159158 | − | 0.275670i | 0.775407 | − | 0.631462i | \(-0.217545\pi\) |
−0.934565 | + | 0.355792i | \(0.884211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.43983 | 0.224532 | ||||||||
\(392\) | −0.418170 | + | 19.7946i | −0.0211208 | + | 0.999777i | ||||
\(393\) | 0.798887i | 0.0402985i | ||||||||
\(394\) | −2.26542 | − | 1.52715i | −0.114130 | − | 0.0769365i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 17.1562 | − | 6.94246i | 0.862132 | − | 0.348872i | ||||
\(397\) | 4.86104 | − | 8.41956i | 0.243968 | − | 0.422566i | −0.717873 | − | 0.696174i | \(-0.754884\pi\) |
0.961841 | + | 0.273609i | \(0.0882173\pi\) | |||||||
\(398\) | 29.0124 | + | 2.02079i | 1.45426 | + | 0.101293i | ||||
\(399\) | −4.57789 | + | 5.52810i | −0.229181 | + | 0.276751i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.49372 | + | 6.05130i | −0.174468 | + | 0.302188i | −0.939977 | − | 0.341238i | \(-0.889154\pi\) |
0.765509 | + | 0.643425i | \(0.222487\pi\) | |||||||
\(402\) | −2.13615 | + | 1.04259i | −0.106542 | + | 0.0519999i | ||||
\(403\) | 25.8517 | + | 44.7764i | 1.28776 | + | 2.23047i | ||||
\(404\) | −7.15243 | − | 5.58181i | −0.355847 | − | 0.277705i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.6421 | + | 5.48209i | −0.925190 | + | 0.272071i | ||||
\(407\) | −39.0048 | −1.93339 | ||||||||
\(408\) | −1.90614 | − | 1.71347i | −0.0943680 | − | 0.0848295i | ||||
\(409\) | −1.94474 | + | 1.12280i | −0.0961611 | + | 0.0555186i | −0.547309 | − | 0.836930i | \(-0.684348\pi\) |
0.451148 | + | 0.892449i | \(0.351015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.710344 | − | 1.23035i | 0.0350387 | − | 0.0606888i | ||||
\(412\) | 1.70189 | − | 12.1577i | 0.0838459 | − | 0.598967i | ||||
\(413\) | −3.30948 | + | 19.5077i | −0.162849 | + | 0.959910i | ||||
\(414\) | 11.7263 | + | 0.816769i | 0.576318 | + | 0.0401420i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.77141 | + | 32.4721i | 0.282967 | + | 1.59207i | ||||
\(417\) | 1.94774 | − | 1.12453i | 0.0953814 | − | 0.0550685i | ||||
\(418\) | 17.3527 | + | 11.6977i | 0.848750 | + | 0.572152i | ||||
\(419\) | 18.3565 | 0.896775 | 0.448388 | − | 0.893839i | \(-0.351998\pi\) | ||||
0.448388 | + | 0.893839i | \(0.351998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.27310 | 0.110784 | 0.0553921 | − | 0.998465i | \(-0.482359\pi\) | ||||
0.0553921 | + | 0.998465i | \(0.482359\pi\) | |||||||
\(422\) | −11.7077 | − | 7.89232i | −0.569924 | − | 0.384192i | ||||
\(423\) | 15.2963 | − | 8.83133i | 0.743732 | − | 0.429394i | ||||
\(424\) | 19.9478 | − | 6.49949i | 0.968749 | − | 0.315643i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.29394 | − | 0.229431i | −0.159592 | − | 0.0111160i | ||||
\(427\) | −1.36818 | − | 3.68456i | −0.0662110 | − | 0.178308i | ||||
\(428\) | −15.1879 | − | 2.12606i | −0.734133 | − | 0.102767i | ||||
\(429\) | −6.97610 | + | 12.0830i | −0.336809 | + | 0.583371i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1379 | + | 6.43048i | −0.536494 | + | 0.309745i | −0.743657 | − | 0.668561i | \(-0.766910\pi\) |
0.207163 | + | 0.978307i | \(0.433577\pi\) | |||||||
\(432\) | −10.2468 | − | 10.5877i | −0.492999 | − | 0.509401i | ||||
\(433\) | −33.6307 | −1.61619 | −0.808094 | − | 0.589054i | \(-0.799501\pi\) | ||||
−0.808094 | + | 0.589054i | \(0.799501\pi\) | |||||||
\(434\) | −24.0238 | − | 22.8879i | −1.15318 | − | 1.09866i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.59373 | − | 2.04218i | 0.0763260 | − | 0.0978029i | ||||
\(437\) | 6.64577 | + | 11.5108i | 0.317910 | + | 0.550637i | ||||
\(438\) | −4.35196 | + | 2.12406i | −0.207945 | + | 0.101492i | ||||
\(439\) | −12.4435 | + | 21.5528i | −0.593896 | + | 1.02866i | 0.399806 | + | 0.916600i | \(0.369078\pi\) |
−0.993702 | + | 0.112058i | \(0.964256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.9258 | − | 5.91313i | −0.805992 | − | 0.281578i | ||||
\(442\) | −11.2533 | − | 0.783818i | −0.535263 | − | 0.0372824i | ||||
\(443\) | 3.97386 | − | 6.88293i | 0.188804 | − | 0.327018i | −0.756048 | − | 0.654516i | \(-0.772872\pi\) |
0.944852 | + | 0.327498i | \(0.106206\pi\) | |||||||
\(444\) | 5.36459 | + | 13.2570i | 0.254592 | + | 0.629149i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.7216 | + | 13.2946i | 0.933845 | + | 0.629515i | ||||
\(447\) | 12.6420i | 0.597944i | ||||||||
\(448\) | −9.43274 | − | 18.9479i | −0.445655 | − | 0.895205i | ||||
\(449\) | −14.3027 | −0.674988 | −0.337494 | − | 0.941328i | \(-0.609579\pi\) | ||||
−0.337494 | + | 0.941328i | \(0.609579\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.50431 | + | 2.60554i | 0.0708352 | + | 0.122690i | ||||
\(452\) | −13.1741 | + | 5.33104i | −0.619656 | + | 0.250751i | ||||
\(453\) | −3.18127 | + | 5.51013i | −0.149469 | + | 0.258888i | ||||
\(454\) | −1.94898 | + | 27.9815i | −0.0914702 | + | 1.31324i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.58918 | − | 7.50673i | 0.0744202 | − | 0.351535i | ||||
\(457\) | −19.2073 | − | 11.0893i | −0.898478 | − | 0.518737i | −0.0217719 | − | 0.999763i | \(-0.506931\pi\) |
−0.876706 | + | 0.481026i | \(0.840264\pi\) | |||||||
\(458\) | 17.7078 | − | 8.64267i | 0.827432 | − | 0.403845i | ||||
\(459\) | 4.36438 | − | 2.51977i | 0.203712 | − | 0.117613i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 32.8587i | − | 1.53038i | −0.643803 | − | 0.765192i | \(-0.722644\pi\) | ||
0.643803 | − | 0.765192i | \(-0.277356\pi\) | |||||||
\(462\) | 2.10743 | − | 8.70248i | 0.0980465 | − | 0.404876i | ||||
\(463\) | −3.31392 | −0.154011 | −0.0770055 | − | 0.997031i | \(-0.524536\pi\) | ||||
−0.0770055 | + | 0.997031i | \(0.524536\pi\) | |||||||
\(464\) | 14.9271 | − | 14.4465i | 0.692974 | − | 0.670661i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.9960 | + | 6.34295i | −0.602027 | + | 0.293832i | ||||
\(467\) | 30.4264 | + | 17.5667i | 1.40797 | + | 0.812890i | 0.995192 | − | 0.0979429i | \(-0.0312263\pi\) |
0.412775 | + | 0.910833i | \(0.364560\pi\) | |||||||
\(468\) | −29.5776 | − | 4.14039i | −1.36722 | − | 0.191390i | ||||
\(469\) | 1.12297 | − | 6.61930i | 0.0518538 | − | 0.305651i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.44307 | + | 5.45196i | 0.435114 | + | 0.251213i | ||||
\(472\) | −6.55298 | − | 20.1119i | −0.301625 | − | 0.925727i | ||||
\(473\) | −9.71973 | + | 5.61169i | −0.446914 | + | 0.258026i | ||||
\(474\) | −5.93757 | + | 8.80799i | −0.272721 | + | 0.404564i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.07049 | − | 1.55490i | 0.324075 | − | 0.0712686i | ||||
\(477\) | 18.9984i | 0.869877i | ||||||||
\(478\) | 20.0329 | + | 13.5044i | 0.916285 | + | 0.617679i | ||||
\(479\) | −11.1633 | − | 19.3354i | −0.510065 | − | 0.883459i | −0.999932 | − | 0.0116615i | \(-0.996288\pi\) |
0.489867 | − | 0.871797i | \(-0.337045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 54.5097 | + | 31.4712i | 2.48543 | + | 1.43496i | ||||
\(482\) | 1.81631 | − | 26.0767i | 0.0827306 | − | 1.18776i | ||||
\(483\) | 3.62719 | − | 4.38007i | 0.165043 | − | 0.199300i | ||||
\(484\) | −4.06732 | − | 0.569361i | −0.184878 | − | 0.0258800i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 18.4589 | − | 9.00923i | 0.837311 | − | 0.408667i | ||||
\(487\) | −3.59259 | − | 6.22255i | −0.162796 | − | 0.281971i | 0.773074 | − | 0.634315i | \(-0.218718\pi\) |
−0.935870 | + | 0.352344i | \(0.885385\pi\) | |||||||
\(488\) | 3.12481 | + | 2.80896i | 0.141454 | + | 0.127156i | ||||
\(489\) | − | 4.73989i | − | 0.214345i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5.80059i | − | 0.261777i | −0.991397 | − | 0.130889i | \(-0.958217\pi\) | ||
0.991397 | − | 0.130889i | \(-0.0417830\pi\) | |||||||
\(492\) | 0.678677 | − | 0.869645i | 0.0305971 | − | 0.0392066i | ||||
\(493\) | 3.55252 | + | 6.15314i | 0.159997 | + | 0.277124i | ||||
\(494\) | −14.8124 | − | 30.3488i | −0.666439 | − | 1.36546i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.1089 | + | 9.74027i | 1.53153 | + | 0.437351i | ||||
\(497\) | 5.94840 | − | 7.18308i | 0.266822 | − | 0.322205i | ||||
\(498\) | 6.06591 | + | 0.422506i | 0.271820 | + | 0.0189329i | ||||
\(499\) | 34.3466 | + | 19.8300i | 1.53757 | + | 0.887715i | 0.998980 | + | 0.0451448i | \(0.0143749\pi\) |
0.538587 | + | 0.842570i | \(0.318958\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.54135 | + | 7.86585i | 0.202892 | + | 0.351420i | ||||
\(502\) | −13.0679 | + | 19.3854i | −0.583250 | + | 0.865213i | ||||
\(503\) | − | 8.22384i | − | 0.366683i | −0.983049 | − | 0.183341i | \(-0.941309\pi\) | ||
0.983049 | − | 0.183341i | \(-0.0586914\pi\) | |||||||
\(504\) | 18.9604 | − | 2.80603i | 0.844563 | − | 0.124991i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −13.7490 | − | 9.26839i | −0.611220 | − | 0.412030i | ||||
\(507\) | 12.0414 | − | 6.95209i | 0.534776 | − | 0.308753i | ||||
\(508\) | −12.7672 | − | 31.5502i | −0.566451 | − | 1.39982i | ||||
\(509\) | 28.2081 | + | 16.2860i | 1.25030 | + | 0.721863i | 0.971170 | − | 0.238389i | \(-0.0766194\pi\) |
0.279134 | + | 0.960252i | \(0.409953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.28781 | − | 13.4854i | 0.101207 | − | 0.596560i | ||||
\(512\) | 18.3386 | + | 13.2550i | 0.810459 | + | 0.585796i | ||||
\(513\) | 13.0657 | + | 7.54347i | 0.576864 | + | 0.333052i | ||||
\(514\) | 3.84273 | + | 7.87332i | 0.169496 | + | 0.347277i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.24413 | + | 2.53174i | 0.142815 | + | 0.111454i | ||||
\(517\) | −24.9150 | −1.09576 | ||||||||
\(518\) | −39.2594 | − | 9.50722i | −1.72496 | − | 0.417723i | ||||
\(519\) | − | 2.59934i | − | 0.114098i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.88783 | + | 2.82199i | −0.214140 | + | 0.123634i | −0.603234 | − | 0.797564i | \(-0.706121\pi\) |
0.389094 | + | 0.921198i | \(0.372788\pi\) | |||||||
\(522\) | 8.25085 | + | 16.9050i | 0.361130 | + | 0.739913i | ||||
\(523\) | −2.36780 | − | 1.36705i | −0.103537 | − | 0.0597770i | 0.447338 | − | 0.894365i | \(-0.352372\pi\) |
−0.550874 | + | 0.834588i | \(0.685706\pi\) | |||||||
\(524\) | 2.38897 | + | 0.334418i | 0.104363 | + | 0.0146091i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.8434 | − | 2.07867i | −1.30123 | − | 0.0906342i | ||||
\(527\) | −6.06633 | + | 10.5072i | −0.264254 | + | 0.457701i | ||||
\(528\) | 2.32588 | + | 9.28538i | 0.101221 | + | 0.404094i | ||||
\(529\) | 6.23437 | + | 10.7982i | 0.271060 | + | 0.469489i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.1547 | 0.831245 | ||||||||
\(532\) | 14.6148 | + | 16.0037i | 0.633630 | + | 0.693848i | ||||
\(533\) | − | 4.85504i | − | 0.210295i | ||||||
\(534\) | 4.91714 | − | 7.29426i | 0.212786 | − | 0.315653i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.22354 | + | 6.82433i | 0.0960423 | + | 0.294766i | ||||
\(537\) | −6.80697 | + | 11.7900i | −0.293743 | + | 0.508777i | ||||
\(538\) | −3.04491 | + | 43.7157i | −0.131275 | + | 1.88472i | ||||
\(539\) | 16.5064 | + | 19.1614i | 0.710980 | + | 0.825341i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.1500 | + | 24.5085i | −0.608355 | + | 1.05370i | 0.383157 | + | 0.923683i | \(0.374837\pi\) |
−0.991512 | + | 0.130018i | \(0.958497\pi\) | |||||||
\(542\) | 14.2905 | + | 29.2795i | 0.613828 | + | 1.25766i | ||||
\(543\) | 4.32526 | + | 7.49157i | 0.185615 | + | 0.321494i | ||||
\(544\) | −5.92184 | + | 4.98280i | −0.253897 | + | 0.213636i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.96680 | + | 10.4614i | −0.426540 | + | 0.447708i | ||||
\(547\) | 20.7596 | 0.887616 | 0.443808 | − | 0.896122i | \(-0.353627\pi\) | ||||
0.443808 | + | 0.896122i | \(0.353627\pi\) | |||||||
\(548\) | −3.38186 | − | 2.63922i | −0.144466 | − | 0.112742i | ||||
\(549\) | −3.29514 | + | 1.90245i | −0.140633 | + | 0.0811946i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6352 | + | 18.4207i | −0.453075 | + | 0.784749i | ||||
\(552\) | −1.25915 | + | 5.94779i | −0.0535930 | + | 0.253155i | ||||
\(553\) | −10.4442 | − | 28.1266i | −0.444133 | − | 1.19606i | ||||
\(554\) | −0.682514 | + | 9.79885i | −0.0289973 | + | 0.416313i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.54743 | − | 6.29521i | −0.108035 | − | 0.266977i | ||||
\(557\) | −16.2445 | + | 9.37876i | −0.688301 | + | 0.397391i | −0.802975 | − | 0.596012i | \(-0.796751\pi\) |
0.114674 | + | 0.993403i | \(0.463418\pi\) | |||||||
\(558\) | −17.9552 | + | 26.6353i | −0.760102 | + | 1.12756i | ||||
\(559\) | 18.1113 | 0.766025 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.27401 | −0.138229 | ||||||||
\(562\) | 3.35480 | − | 4.97662i | 0.141514 | − | 0.209926i | ||||
\(563\) | −28.9028 | + | 16.6870i | −1.21811 | + | 0.703274i | −0.964513 | − | 0.264037i | \(-0.914946\pi\) |
−0.253594 | + | 0.967311i | \(0.581613\pi\) | |||||||
\(564\) | 3.42673 | + | 8.46815i | 0.144292 | + | 0.356573i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.838399 | − | 12.0369i | 0.0352405 | − | 0.505948i | ||||
\(567\) | −2.32064 | + | 13.6790i | −0.0974579 | + | 0.574464i | ||||
\(568\) | −2.06494 | + | 9.75407i | −0.0866431 | + | 0.409272i | ||||
\(569\) | 6.51501 | − | 11.2843i | 0.273124 | − | 0.473064i | −0.696536 | − | 0.717521i | \(-0.745277\pi\) |
0.969660 | + | 0.244457i | \(0.0786099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.5406 | + | 16.4779i | −1.19439 | + | 0.689579i | −0.959298 | − | 0.282395i | \(-0.908871\pi\) |
−0.235088 | + | 0.971974i | \(0.575538\pi\) | |||||||
\(572\) | 33.2123 | + | 25.9191i | 1.38868 | + | 1.08373i | ||||
\(573\) | −8.26295 | −0.345190 | ||||||||
\(574\) | 0.879042 | + | 2.98922i | 0.0366905 | + | 0.124768i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −16.5572 | + | 12.0710i | −0.689885 | + | 0.502959i | ||||
\(577\) | −18.1937 | − | 31.5124i | −0.757414 | − | 1.31188i | −0.944165 | − | 0.329473i | \(-0.893129\pi\) |
0.186751 | − | 0.982407i | \(-0.440204\pi\) | |||||||
\(578\) | 9.38400 | + | 19.2267i | 0.390323 | + | 0.799727i | ||||
\(579\) | −6.31373 | + | 10.9357i | −0.262390 | + | 0.454472i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9542 | + | 13.2279i | −0.454457 | + | 0.548786i | ||||
\(582\) | 0.0223370 | − | 0.320692i | 0.000925898 | − | 0.0132931i | ||||
\(583\) | 13.3996 | − | 23.2088i | 0.554955 | − | 0.961210i | ||||
\(584\) | 4.52999 | + | 13.9031i | 0.187452 | + | 0.575316i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.9458 | + | 29.5883i | −0.823953 | + | 1.22228i | ||||
\(587\) | − | 28.4245i | − | 1.17321i | −0.809875 | − | 0.586603i | \(-0.800465\pi\) | ||
0.809875 | − | 0.586603i | \(-0.199535\pi\) | |||||||
\(588\) | 4.24238 | − | 8.24561i | 0.174953 | − | 0.340043i | ||||
\(589\) | −36.3217 | −1.49661 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.639794 | + | 1.10816i | 0.0263176 | + | 0.0455835i | ||||
\(592\) | 41.8890 | − | 10.4927i | 1.72163 | − | 0.431247i | ||||
\(593\) | 3.78574 | − | 6.55710i | 0.155462 | − | 0.269268i | −0.777765 | − | 0.628555i | \(-0.783647\pi\) |
0.933227 | + | 0.359287i | \(0.116980\pi\) | |||||||
\(594\) | −18.7756 | − | 1.30777i | −0.770371 | − | 0.0536583i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 37.8042 | + | 5.29198i | 1.54852 | + | 0.216768i | ||||
\(597\) | −11.7962 | − | 6.81052i | −0.482785 | − | 0.278736i | ||||
\(598\) | 11.7362 | + | 24.0462i | 0.479930 | + | 0.983321i | ||||
\(599\) | −41.0937 | + | 23.7255i | −1.67904 | + | 0.969397i | −0.716772 | + | 0.697307i | \(0.754381\pi\) |
−0.962272 | + | 0.272090i | \(0.912285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3242i | 0.543506i | 0.962367 | + | 0.271753i | \(0.0876034\pi\) | ||||
−0.962367 | + | 0.271753i | \(0.912397\pi\) | |||||||
\(602\) | −11.1510 | + | 3.27918i | −0.454481 | + | 0.133650i | ||||
\(603\) | −6.49954 | −0.264682 | ||||||||
\(604\) | 15.1456 | + | 11.8198i | 0.616267 | + | 0.480939i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.86379 | + | 3.81869i | 0.0757113 | + | 0.155124i | ||||
\(607\) | 13.0610 | + | 7.54080i | 0.530132 | + | 0.306072i | 0.741070 | − | 0.671428i | \(-0.234319\pi\) |
−0.210938 | + | 0.977499i | \(0.567652\pi\) | |||||||
\(608\) | −21.7827 | − | 7.89460i | −0.883405 | − | 0.320168i | ||||
\(609\) | 8.97261 | + | 1.52221i | 0.363588 | + | 0.0616829i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.8191 | + | 20.1028i | 1.40863 | + | 0.813272i | ||||
\(612\) | −2.62891 | − | 6.49657i | −0.106267 | − | 0.262608i | ||||
\(613\) | 4.50739 | − | 2.60234i | 0.182052 | − | 0.105108i | −0.406205 | − | 0.913782i | \(-0.633148\pi\) |
0.588256 | + | 0.808675i | \(0.299815\pi\) | |||||||
\(614\) | 34.3159 | + | 23.1327i | 1.38488 | + | 0.933561i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −25.1415 | − | 9.94491i | −1.01298 | − | 0.400692i | ||||
\(617\) | − | 35.7404i | − | 1.43885i | −0.694569 | − | 0.719426i | \(-0.744405\pi\) | ||
0.694569 | − | 0.719426i | \(-0.255595\pi\) | |||||||
\(618\) | −3.21386 | + | 4.76755i | −0.129280 | + | 0.191779i | ||||
\(619\) | −19.1219 | − | 33.1200i | −0.768573 | − | 1.33121i | −0.938337 | − | 0.345722i | \(-0.887634\pi\) |
0.169764 | − | 0.985485i | \(-0.445699\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.3523 | − | 5.97690i | −0.415423 | − | 0.239845i | ||||
\(622\) | 32.0901 | + | 2.23515i | 1.28670 | + | 0.0896215i | ||||
\(623\) | 8.64929 | + | 23.2928i | 0.346526 | + | 0.933205i | ||||
\(624\) | 4.24151 | − | 14.8531i | 0.169796 | − | 0.594599i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.08454 | + | 8.36874i | 0.163251 | + | 0.334482i | ||||
\(627\) | −4.90071 | − | 8.48828i | −0.195716 | − | 0.338989i | ||||
\(628\) | 20.2563 | − | 25.9561i | 0.808315 | − | 1.03576i | ||||
\(629\) | 14.7700i | 0.588918i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.0334i | − | 0.479042i | −0.970891 | − | 0.239521i | \(-0.923010\pi\) | ||
0.970891 | − | 0.239521i | \(-0.0769904\pi\) | |||||||
\(632\) | 23.8537 | + | 21.4426i | 0.948849 | + | 0.852941i | ||||
\(633\) | 3.30647 | + | 5.72697i | 0.131420 | + | 0.227627i | ||||
\(634\) | −17.9475 | + | 8.75966i | −0.712788 | + | 0.347891i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.73118 | − | 1.36221i | −0.385866 | − | 0.0540152i | ||||
\(637\) | −7.60740 | − | 40.0966i | −0.301416 | − | 1.58869i | ||||
\(638\) | 1.84376 | − | 26.4709i | 0.0729952 | − | 1.04799i | ||||
\(639\) | −7.81897 | − | 4.51429i | −0.309314 | − | 0.178582i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.4676 | − | 19.8625i | −0.452944 | − | 0.784522i | 0.545624 | − | 0.838030i | \(-0.316293\pi\) |
−0.998567 | + | 0.0535086i | \(0.982960\pi\) | |||||||
\(642\) | 5.95580 | + | 4.01487i | 0.235057 | + | 0.158454i | ||||
\(643\) | 1.23955i | 0.0488833i | 0.999701 | + | 0.0244416i | \(0.00778079\pi\) | ||||
−0.999701 | + | 0.0244416i | \(0.992219\pi\) | |||||||
\(644\) | −11.5797 | − | 12.6802i | −0.456303 | − | 0.499668i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.42958 | − | 6.57098i | 0.174279 | − | 0.258532i | ||||
\(647\) | 12.2469 | − | 7.07077i | 0.481477 | − | 0.277981i | −0.239555 | − | 0.970883i | \(-0.577002\pi\) |
0.721032 | + | 0.692902i | \(0.243668\pi\) | |||||||
\(648\) | −4.59502 | − | 14.1027i | −0.180509 | − | 0.554006i | ||||
\(649\) | −23.3998 | − | 13.5099i | −0.918523 | − | 0.530309i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.40978 | + | 14.5687i | 0.212026 | + | 0.570992i | ||||
\(652\) | −14.1740 | − | 1.98414i | −0.555098 | − | 0.0777049i | ||||
\(653\) | −14.8017 | − | 8.54579i | −0.579237 | − | 0.334423i | 0.181593 | − | 0.983374i | \(-0.441875\pi\) |
−0.760830 | + | 0.648951i | \(0.775208\pi\) | |||||||
\(654\) | −1.09032 | + | 0.532155i | −0.0426350 | + | 0.0208089i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.31647 | − | 2.39354i | −0.0904428 | − | 0.0934519i | ||||
\(657\) | −13.2414 | −0.516598 | ||||||||
\(658\) | −25.0777 | − | 6.07292i | −0.977629 | − | 0.236747i | ||||
\(659\) | − | 3.45765i | − | 0.134691i | −0.997730 | − | 0.0673455i | \(-0.978547\pi\) | ||
0.997730 | − | 0.0673455i | \(-0.0214530\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.1317 | − | 7.58160i | 0.510765 | − | 0.294890i | −0.222383 | − | 0.974959i | \(-0.571384\pi\) |
0.733148 | + | 0.680069i | \(0.238050\pi\) | |||||||
\(662\) | −25.8281 | + | 12.6059i | −1.00384 | + | 0.489943i | ||||
\(663\) | 4.57547 | + | 2.64165i | 0.177697 | + | 0.102593i | ||||
\(664\) | 3.80267 | − | 17.9625i | 0.147572 | − | 0.697079i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.71715 | + | 39.0100i | −0.105287 | + | 1.51161i | ||||
\(667\) | 8.42657 | − | 14.5952i | 0.326278 | − | 0.565130i | ||||
\(668\) | 25.4229 | − | 10.2876i | 0.983640 | − | 0.398041i | ||||
\(669\) | −5.56972 | − | 9.64704i | −0.215338 | − | 0.372976i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.36721 | 0.207199 | ||||||||
\(672\) | 0.0777937 | + | 9.91291i | 0.00300096 | + | 0.382399i | ||||
\(673\) | 11.2116i | 0.432175i | 0.976374 | + | 0.216087i | \(0.0693296\pi\) | ||||
−0.976374 | + | 0.216087i | \(0.930670\pi\) | |||||||
\(674\) | −18.4932 | − | 12.4664i | −0.712330 | − | 0.480190i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.7488 | − | 38.9184i | −0.605722 | − | 1.49686i | ||||
\(677\) | −1.83818 | + | 3.18383i | −0.0706471 | + | 0.122364i | −0.899185 | − | 0.437568i | \(-0.855840\pi\) |
0.828538 | + | 0.559933i | \(0.189173\pi\) | |||||||
\(678\) | 6.64010 | + | 0.462500i | 0.255011 | + | 0.0177622i | ||||
\(679\) | 0.699331 | + | 0.579125i | 0.0268379 | + | 0.0222248i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.56852 | − | 11.3770i | 0.251706 | − | 0.435968i | ||||
\(682\) | 40.7203 | − | 19.8744i | 1.55926 | − | 0.761029i | ||||
\(683\) | −21.0938 | − | 36.5356i | −0.807133 | − | 1.39800i | −0.914841 | − | 0.403814i | \(-0.867684\pi\) |
0.107708 | − | 0.994183i | \(-0.465649\pi\) | |||||||
\(684\) | 12.9081 | − | 16.5402i | 0.493553 | − | 0.632430i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.9436 | + | 23.3099i | 0.456010 | + | 0.889975i | ||||
\(687\) | −9.22865 | −0.352095 | ||||||||
\(688\) | 8.92886 | − | 8.64136i | 0.340410 | − | 0.329449i | ||||
\(689\) | −37.4523 | + | 21.6231i | −1.42682 | + | 0.823773i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5615 | + | 20.0251i | −0.439820 | + | 0.761790i | −0.997675 | − | 0.0681478i | \(-0.978291\pi\) |
0.557855 | + | 0.829938i | \(0.311624\pi\) | |||||||
\(692\) | −7.77298 | − | 1.08809i | −0.295485 | − | 0.0413631i | ||||
\(693\) | 15.6157 | − | 18.8569i | 0.593190 | − | 0.716316i | ||||
\(694\) | 4.29987 | + | 0.299497i | 0.163221 | + | 0.0113688i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.25053 | + | 3.01406i | −0.350640 | + | 0.114248i | ||||
\(697\) | 0.986645 | − | 0.569640i | 0.0373718 | − | 0.0215766i | ||||
\(698\) | 9.85569 | + | 6.64384i | 0.373043 | + | 0.251473i | ||||
\(699\) | 6.77301 | 0.256179 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3192 | 1.10737 | 0.553686 | − | 0.832725i | \(-0.313221\pi\) | ||||
0.553686 | + | 0.832725i | \(0.313221\pi\) | |||||||
\(702\) | 25.1839 | + | 16.9768i | 0.950506 | + | 0.640747i | ||||
\(703\) | −38.2931 | + | 22.1085i | −1.44425 | + | 0.833839i | ||||
\(704\) | 28.7404 | − | 3.06834i | 1.08319 | − | 0.115642i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.610622 | + | 0.0425314i | 0.0229811 | + | 0.00160069i | ||||
\(707\) | −11.8330 | − | 2.00747i | −0.445025 | − | 0.0754986i | ||||
\(708\) | −1.37342 | + | 9.81126i | −0.0516163 | + | 0.368730i | ||||
\(709\) | 1.67720 | − | 2.90499i | 0.0629884 | − | 0.109099i | −0.832811 | − | 0.553557i | \(-0.813270\pi\) |
0.895800 | + | 0.444458i | \(0.146604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.1539 | + | 14.5226i | −0.943346 | + | 0.544641i | ||||
\(712\) | −19.7542 | − | 17.7575i | −0.740321 | − | 0.665491i | ||||
\(713\) | 28.7786 | 1.07777 | ||||||||
\(714\) | −3.29538 | − | 0.798024i | −0.123327 | − | 0.0298653i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.4071 | + | 25.2908i | 1.21111 | + | 0.945160i | ||||
\(717\) | −5.65765 | − | 9.79934i | −0.211289 | − | 0.365963i | ||||
\(718\) | 34.2906 | − | 16.7362i | 1.27972 | − | 0.624591i | ||||
\(719\) | 15.5142 | − | 26.8714i | 0.578583 | − | 1.00213i | −0.417059 | − | 0.908879i | \(-0.636939\pi\) |
0.995642 | − | 0.0932556i | \(-0.0297274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.65320 | − | 15.2242i | −0.210536 | − | 0.566980i | ||||
\(722\) | −3.13857 | − | 0.218609i | −0.116805 | − | 0.00813579i | ||||
\(723\) | −6.12138 | + | 10.6025i | −0.227657 | + | 0.394313i | ||||
\(724\) | 24.2132 | − | 9.79814i | 0.899876 | − | 0.364145i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.59497 | + | 1.07519i | 0.0591949 | + | 0.0399039i | ||||
\(727\) | 37.9906i | 1.40899i | 0.709707 | + | 0.704497i | \(0.248827\pi\) | ||||
−0.709707 | + | 0.704497i | \(0.751173\pi\) | |||||||
\(728\) | 27.1115 | + | 34.1837i | 1.00482 | + | 1.26693i | ||||
\(729\) | 6.11207 | 0.226373 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.12499 | + | 3.68058i | 0.0785955 | + | 0.136131i | ||||
\(732\) | −0.738189 | − | 1.82421i | −0.0272843 | − | 0.0674249i | ||||
\(733\) | −15.4876 | + | 26.8252i | −0.572046 | + | 0.990813i | 0.424310 | + | 0.905517i | \(0.360517\pi\) |
−0.996356 | + | 0.0852956i | \(0.972817\pi\) | |||||||
\(734\) | 2.04601 | − | 29.3745i | 0.0755195 | − | 1.08423i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.2590 | + | 6.25511i | 0.636176 | + | 0.230566i | ||||
\(737\) | 7.93996 | + | 4.58414i | 0.292472 | + | 0.168859i | ||||
\(738\) | 2.71069 | − | 1.32301i | 0.0997819 | − | 0.0487006i | ||||
\(739\) | −2.53077 | + | 1.46114i | −0.0930957 | + | 0.0537488i | −0.545825 | − | 0.837899i | \(-0.683784\pi\) |
0.452729 | + | 0.891648i | \(0.350450\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.8167i | 0.581039i | ||||||||
\(742\) | 19.1441 | − | 20.0942i | 0.702802 | − | 0.737682i | ||||
\(743\) | 36.6505 | 1.34457 | 0.672287 | − | 0.740290i | \(-0.265312\pi\) | ||||
0.672287 | + | 0.740290i | \(0.265312\pi\) | |||||||
\(744\) | −12.3555 | − | 11.1066i | −0.452974 | − | 0.407188i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22.4462 | − | 10.9553i | 0.821815 | − | 0.401104i | ||||
\(747\) | 14.3989 | + | 8.31323i | 0.526829 | + | 0.304165i | ||||
\(748\) | −1.37052 | + | 9.79051i | −0.0501110 | + | 0.357976i | ||||
\(749\) | −19.0187 | + | 7.06219i | −0.694927 | + | 0.258047i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.3355 | − | 18.0915i | −1.14345 | − | 0.660170i | −0.196166 | − | 0.980571i | \(-0.562849\pi\) |
−0.947282 | + | 0.320401i | \(0.896182\pi\) | |||||||
\(752\) | 26.7574 | − | 6.70241i | 0.975741 | − | 0.244412i | ||||
\(753\) | 9.48259 | − | 5.47478i | 0.345565 | − | 0.199512i | ||||
\(754\) | −23.9348 | + | 35.5057i | −0.871654 | + | 1.29304i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.5794 | − | 5.89276i | −0.675725 | − | 0.214318i | ||||
\(757\) | − | 1.44394i | − | 0.0524807i | −0.999656 | − | 0.0262404i | \(-0.991646\pi\) | ||
0.999656 | − | 0.0262404i | \(-0.00835352\pi\) | |||||||
\(758\) | 17.6544 | + | 11.9011i | 0.641238 | + | 0.432266i | ||||
\(759\) | 3.88297 | + | 6.72550i | 0.140943 | + | 0.244120i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4509 | − | 14.1167i | −0.886343 | − | 0.511730i | −0.0135983 | − | 0.999908i | \(-0.504329\pi\) |
−0.872744 | + | 0.488177i | \(0.837662\pi\) | |||||||
\(762\) | −1.10763 | + | 15.9022i | −0.0401251 | + | 0.576076i | ||||
\(763\) | 0.573178 | − | 3.37859i | 0.0207505 | − | 0.122313i | ||||
\(764\) | −3.45891 | + | 24.7093i | −0.125139 | + | 0.893951i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38.5730 | − | 18.8264i | 1.39370 | − | 0.680224i | ||||
\(767\) | 21.8010 | + | 37.7605i | 0.787189 | + | 1.36345i | ||||
\(768\) | −4.99573 | − | 9.34630i | −0.180268 | − | 0.337256i | ||||
\(769\) | 38.3866i | 1.38426i | 0.721774 | + | 0.692129i | \(0.243327\pi\) | ||||
−0.721774 | + | 0.692129i | \(0.756673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 4.10328i | − | 0.147776i | ||||||
\(772\) | 30.0589 | + | 23.4582i | 1.08184 | + | 0.844278i | ||||
\(773\) | −9.54086 | − | 16.5252i | −0.343161 | − | 0.594372i | 0.641857 | − | 0.766824i | \(-0.278164\pi\) |
−0.985018 | + | 0.172452i | \(0.944831\pi\) | |||||||
\(774\) | 4.93535 | + | 10.1120i | 0.177398 | + | 0.363467i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.949638 | − | 0.201039i | −0.0340900 | − | 0.00721688i | ||||
\(777\) | 14.5712 | + | 12.0666i | 0.522738 | + | 0.432886i | ||||
\(778\) | 8.85722 | + | 0.616928i | 0.317547 | + | 0.0221179i | ||||
\(779\) | 2.95373 | + | 1.70533i | 0.105828 | + | 0.0611000i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.36787 | + | 11.0295i | 0.227860 | + | 0.394666i | ||||
\(782\) | −3.50967 | + | 5.20637i | −0.125506 | + | 0.186179i | ||||
\(783\) | − | 19.1296i | − | 0.683637i | ||||||
\(784\) | −22.8816 | − | 16.1379i | −0.817199 | − | 0.576355i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.936816 | − | 0.631519i | −0.0334151 | − | 0.0225255i | ||||
\(787\) | −4.41858 | + | 2.55107i | −0.157505 | + | 0.0909358i | −0.576681 | − | 0.816969i | \(-0.695652\pi\) |
0.419176 | + | 0.907905i | \(0.362319\pi\) | |||||||
\(788\) | 3.58162 | − | 1.44934i | 0.127590 | − | 0.0516308i | ||||
\(789\) | 12.1340 | + | 7.00559i | 0.431983 | + | 0.249406i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.9911 | + | 14.4800i | −0.426354 | + | 0.514851i | ||||
\(792\) | −5.42087 | + | 25.6063i | −0.192622 | + | 0.909879i | ||||
\(793\) | −7.50075 | − | 4.33056i | −0.266359 | − | 0.153783i | ||||
\(794\) | 6.03058 | + | 12.3560i | 0.214017 | + | 0.438496i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.3039 | + | 32.4240i | −0.896874 | + | 1.14924i | ||||
\(797\) | −25.6101 | −0.907155 | −0.453578 | − | 0.891217i | \(-0.649852\pi\) | ||||
−0.453578 | + | 0.891217i | \(0.649852\pi\) | |||||||
\(798\) | −2.86373 | − | 9.73822i | −0.101375 | − | 0.344729i | ||||
\(799\) | 9.43461i | 0.333772i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.8310 | − | 12.0268i | 0.736027 | − | 0.424946i | ||||
\(802\) | −4.33429 | − | 8.88046i | −0.153049 | − | 0.313580i | ||||
\(803\) | 16.1760 | + | 9.33922i | 0.570839 | + | 0.329574i | ||||
\(804\) | 0.466026 | − | 3.32913i | 0.0164355 | − | 0.117409i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −72.9429 | − | 5.08065i | −2.56930 | − | 0.178958i | ||||
\(807\) | 10.2621 | − | 17.7744i | 0.361241 | − | 0.625688i | ||||
\(808\) | 12.1995 | − | 3.97491i | 0.429177 | − | 0.139837i | ||||
\(809\) | 25.2381 | + | 43.7136i | 0.887323 | + | 1.53689i | 0.843028 | + | 0.537870i | \(0.180771\pi\) |
0.0442955 | + | 0.999018i | \(0.485896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.15050 | −0.110629 | −0.0553145 | − | 0.998469i | \(-0.517616\pi\) | ||||
−0.0553145 | + | 0.998469i | \(0.517616\pi\) | |||||||
\(812\) | 8.30794 | − | 26.1942i | 0.291552 | − | 0.919238i | ||||
\(813\) | − | 15.2594i | − | 0.535170i | ||||||
\(814\) | 30.8332 | − | 45.7390i | 1.08070 | − | 1.60315i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.51611 | − | 0.880743i | 0.123088 | − | 0.0308322i | ||||
\(817\) | −6.36159 | + | 11.0186i | −0.222564 | + | 0.385492i | ||||
\(818\) | 0.220664 | − | 3.16807i | 0.00771533 | − | 0.110769i | ||||
\(819\) | −37.0379 | + | 13.7533i | −1.29421 | + | 0.480578i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.7416 | − | 30.7294i | 0.619187 | − | 1.07246i | −0.370448 | − | 0.928853i | \(-0.620796\pi\) |
0.989634 | − | 0.143609i | \(-0.0458709\pi\) | |||||||
\(822\) | 0.881249 | + | 1.80558i | 0.0307371 | + | 0.0629767i | ||||
\(823\) | −4.20565 | − | 7.28440i | −0.146600 | − | 0.253918i | 0.783369 | − | 0.621557i | \(-0.213500\pi\) |
−0.929969 | + | 0.367639i | \(0.880166\pi\) | |||||||
\(824\) | 12.9114 | + | 11.6064i | 0.449790 | + | 0.404327i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.2596 | − | 19.3017i | −0.704921 | − | 0.671591i | ||||
\(827\) | 4.33435 | 0.150720 | 0.0753601 | − | 0.997156i | \(-0.475989\pi\) | ||||
0.0753601 | + | 0.997156i | \(0.475989\pi\) | |||||||
\(828\) | −10.2274 | + | 13.1053i | −0.355428 | + | 0.455439i | ||||
\(829\) | −20.9404 | + | 12.0899i | −0.727289 | + | 0.419900i | −0.817429 | − | 0.576029i | \(-0.804602\pi\) |
0.0901408 | + | 0.995929i | \(0.471268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.30023 | − | 3.98412i | 0.0797942 | − | 0.138208i | ||||
\(832\) | −42.6407 | − | 18.9013i | −1.47830 | − | 0.655283i | ||||
\(833\) | 7.25589 | − | 6.25050i | 0.251402 | − | 0.216567i | ||||
\(834\) | −0.221005 | + | 3.17296i | −0.00765277 | + | 0.109871i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −27.4346 | + | 11.1017i | −0.948846 | + | 0.383961i | ||||
\(837\) | 28.2896 | − | 16.3330i | 0.977831 | − | 0.564551i | ||||
\(838\) | −14.5108 | + | 21.5258i | −0.501267 | + | 0.743597i | ||||
\(839\) | 18.3056 | 0.631979 | 0.315989 | − | 0.948763i | \(-0.397664\pi\) | ||||
0.315989 | + | 0.948763i | \(0.397664\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.02999 | −0.0699998 | ||||||||
\(842\) | −1.79688 | + | 2.66556i | −0.0619246 | + | 0.0918611i | ||||
\(843\) | −2.43437 | + | 1.40549i | −0.0838442 | + | 0.0484075i | ||||
\(844\) | 18.5099 | − | 7.49024i | 0.637137 | − | 0.257825i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.73563 | + | 24.9184i | −0.0596722 | + | 0.856712i | ||||
\(847\) | −5.09322 | + | 1.89126i | −0.175005 | + | 0.0649845i | ||||
\(848\) | −8.14704 | + | 28.5296i | −0.279770 | + | 0.979711i | ||||
\(849\) | −2.82560 | + | 4.89408i | −0.0969743 | + | 0.167964i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.3407 | − | 17.5172i | 1.04006 | − | 0.600481i | ||||
\(852\) | 2.87290 | − | 3.68128i | 0.0984238 | − | 0.126119i | ||||
\(853\) | −16.9533 | −0.580469 | −0.290234 | − | 0.956956i | \(-0.593733\pi\) | ||||
−0.290234 | + | 0.956956i | \(0.593733\pi\) | |||||||
\(854\) | 5.40225 | + | 1.30823i | 0.184861 | + | 0.0447668i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.4991 | − | 16.1294i | 0.495569 | − | 0.551292i | ||||
\(857\) | −25.2872 | − | 43.7988i | −0.863795 | − | 1.49614i | −0.868238 | − | 0.496147i | \(-0.834748\pi\) |
0.00444284 | − | 0.999990i | \(-0.498586\pi\) | |||||||
\(858\) | −8.65451 | − | 17.7321i | −0.295460 | − | 0.605364i | ||||
\(859\) | 2.51925 | − | 4.36346i | 0.0859555 | − | 0.148879i | −0.819842 | − | 0.572589i | \(-0.805939\pi\) |
0.905798 | + | 0.423710i | \(0.139272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.244083 | − | 1.43874i | 0.00831832 | − | 0.0490321i | ||||
\(862\) | 1.26379 | − | 18.1442i | 0.0430448 | − | 0.617993i | ||||
\(863\) | −5.87084 | + | 10.1686i | −0.199846 | + | 0.346143i | −0.948478 | − | 0.316842i | \(-0.897377\pi\) |
0.748633 | + | 0.662985i | \(0.230711\pi\) | |||||||
\(864\) | 20.5157 | − | 3.64636i | 0.697960 | − | 0.124052i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.5850 | − | 39.4371i | 0.903395 | − | 1.34013i | ||||
\(867\) | − | 10.0203i | − | 0.340306i | ||||||
\(868\) | 45.8304 | − | 10.0787i | 1.55559 | − | 0.342095i | ||||
\(869\) | 40.9714 | 1.38986 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.39747 | − | 12.8128i | −0.250654 | − | 0.434145i | ||||
\(872\) | 1.13493 | + | 3.48324i | 0.0384335 | + | 0.117957i | ||||
\(873\) | 0.439502 | − | 0.761240i | 0.0148749 | − | 0.0257641i | ||||
\(874\) | −18.7517 | − | 1.30610i | −0.634284 | − | 0.0441795i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.949429 | − | 6.78241i | 0.0320782 | − | 0.229156i | ||||
\(877\) | 20.9426 | + | 12.0912i | 0.707180 | + | 0.408290i | 0.810016 | − | 0.586408i | \(-0.199458\pi\) |
−0.102836 | + | 0.994698i | \(0.532792\pi\) | |||||||
\(878\) | −15.4373 | − | 31.6293i | −0.520985 | − | 1.06744i | ||||
\(879\) | 14.4734 | − | 8.35624i | 0.488177 | − | 0.281849i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 19.6285i | − | 0.661301i | −0.943753 | − | 0.330651i | \(-0.892732\pi\) | ||
0.943753 | − | 0.330651i | \(-0.107268\pi\) | |||||||
\(882\) | 20.3139 | − | 15.1738i | 0.684004 | − | 0.510928i | ||||
\(883\) | −11.2418 | −0.378315 | −0.189158 | − | 0.981947i | \(-0.560576\pi\) | ||||
−0.189158 | + | 0.981947i | \(0.560576\pi\) | |||||||
\(884\) | 9.81483 | − | 12.5766i | 0.330108 | − | 0.422995i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.92995 | + | 10.1009i | 0.165625 | + | 0.339346i | ||||
\(887\) | −36.2085 | − | 20.9050i | −1.21576 | − | 0.701920i | −0.251753 | − | 0.967792i | \(-0.581007\pi\) |
−0.964009 | + | 0.265871i | \(0.914340\pi\) | |||||||
\(888\) | −19.7865 | − | 4.18882i | −0.663993 | − | 0.140568i | ||||
\(889\) | −34.6779 | − | 28.7172i | −1.16306 | − | 0.963143i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.4082 | − | 9.47327i | −0.549695 | − | 0.317366i | ||||
\(892\) | −31.1798 | + | 12.6173i | −1.04398 | + | 0.422457i | ||||
\(893\) | −24.4604 | + | 14.1222i | −0.818537 | + | 0.472583i | ||||
\(894\) | −14.8246 | − | 9.99344i | −0.495809 | − | 0.334231i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.6759 | + | 3.91696i | 0.991401 | + | 0.130856i | ||||
\(897\) | − | 12.5320i | − | 0.418430i | ||||||
\(898\) | 11.3063 | − | 16.7721i | 0.377296 | − | 0.559693i | ||||
\(899\) | 23.0272 | + | 39.8842i | 0.768000 | + | 1.33021i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.78851 | − | 5.07405i | −0.292788 | − | 0.169041i | ||||
\(902\) | −4.24455 | − | 0.295644i | −0.141328 | − | 0.00984385i | ||||
\(903\) | 5.36708 | + | 0.910527i | 0.178605 | + | 0.0303005i | ||||
\(904\) | 4.16262 | − | 19.6628i | 0.138447 | − | 0.653974i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.94667 | − | 8.08627i | −0.131119 | − | 0.268648i | ||||
\(907\) | −10.9044 | − | 18.8870i | −0.362076 | − | 0.627133i | 0.626227 | − | 0.779641i | \(-0.284598\pi\) |
−0.988302 | + | 0.152508i | \(0.951265\pi\) | |||||||
\(908\) | −31.2719 | − | 24.4048i | −1.03779 | − | 0.809901i | ||||
\(909\) | 11.6189i | 0.385374i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.40991i | 0.0798440i | 0.999203 | + | 0.0399220i | \(0.0127109\pi\) | ||||
−0.999203 | + | 0.0399220i | \(0.987289\pi\) | |||||||
\(912\) | 7.54654 | + | 7.79761i | 0.249891 | + | 0.258205i | ||||
\(913\) | −11.7267 | − | 20.3112i | −0.388096 | − | 0.672202i | ||||
\(914\) | 28.1872 | − | 13.7574i | 0.932350 | − | 0.455053i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.86316 | + | 27.5971i | −0.127642 | + | 0.911835i | ||||
\(917\) | 2.99154 | − | 1.11085i | 0.0987893 | − | 0.0366833i | ||||
\(918\) | −0.495214 | + | 7.10977i | −0.0163445 | + | 0.234657i | ||||
\(919\) | 13.1661 | + | 7.60145i | 0.434310 | + | 0.250749i | 0.701181 | − | 0.712983i | \(-0.252657\pi\) |
−0.266871 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.69140 | − | 16.7860i | −0.319343 | − | 0.553118i | ||||
\(922\) | 38.5318 | + | 25.9748i | 1.26898 | + | 0.855433i | ||||
\(923\) | − | 20.5518i | − | 0.676470i | ||||||
\(924\) | 8.53906 | + | 9.35058i | 0.280914 | + | 0.307611i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.61965 | − | 3.88607i | 0.0860870 | − | 0.127704i | ||||
\(927\) | −13.6152 | + | 7.86074i | −0.447182 | + | 0.258181i | ||||
\(928\) | 5.14084 | + | 28.9242i | 0.168756 | + | 0.949485i | ||||
\(929\) | −18.0735 | − | 10.4347i | −0.592971 | − | 0.342352i | 0.173300 | − | 0.984869i | \(-0.444557\pi\) |
−0.766272 | + | 0.642517i | \(0.777890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.0662 | + | 9.45573i | 0.887059 | + | 0.309899i | ||||
\(932\) | 2.83522 | − | 20.2538i | 0.0928706 | − | 0.663437i | ||||
\(933\) | −13.0475 | − | 7.53299i | −0.427157 | − | 0.246619i | ||||
\(934\) | −44.6517 | + | 21.7932i | −1.46105 | + | 0.713094i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 28.2363 | − | 31.4112i | 0.922931 | − | 1.02671i | ||||
\(937\) | −10.9083 | −0.356358 | −0.178179 | − | 0.983998i | \(-0.557021\pi\) | ||||
−0.178179 | + | 0.983998i | \(0.557021\pi\) | |||||||
\(938\) | 6.87443 | + | 6.54939i | 0.224458 | + | 0.213845i | ||||
\(939\) | − | 4.36148i | − | 0.142331i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.7569 | + | 24.6857i | −1.39383 | + | 0.804730i | −0.993737 | − | 0.111743i | \(-0.964357\pi\) |
−0.400097 | + | 0.916473i | \(0.631023\pi\) | |||||||
\(942\) | −13.8580 | + | 6.76367i | −0.451517 | + | 0.220372i | ||||
\(943\) | −2.34032 | − | 1.35118i | −0.0762113 | − | 0.0440006i | ||||
\(944\) | 28.7644 | + | 8.21408i | 0.936202 | + | 0.267346i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.10287 | − | 15.8339i | 0.0358574 | − | 0.514804i | ||||
\(947\) | −7.27929 | + | 12.6081i | −0.236545 | + | 0.409708i | −0.959721 | − | 0.280956i | \(-0.909349\pi\) |
0.723175 | + | 0.690664i | \(0.242682\pi\) | |||||||
\(948\) | −5.63507 | − | 13.9254i | −0.183019 | − | 0.452276i | ||||
\(949\) | −15.0708 | − | 26.1034i | −0.489218 | − | 0.847351i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.35358 | 0.303311 | ||||||||
\(952\) | −3.76585 | + | 9.52036i | −0.122052 | + | 0.308557i | ||||
\(953\) | 9.87954i | 0.320030i | 0.987115 | + | 0.160015i | \(0.0511542\pi\) | ||||
−0.987115 | + | 0.160015i | \(0.948846\pi\) | |||||||
\(954\) | −22.2785 | − | 15.0182i | −0.721293 | − | 0.486232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −31.6720 | + | 12.8164i | −1.02435 | + | 0.414513i | ||||
\(957\) | −6.21390 | + | 10.7628i | −0.200867 | + | 0.347912i | ||||
\(958\) | 31.4983 | + | 2.19394i | 1.01766 | + | 0.0708829i | ||||
\(959\) | −5.59494 | − | 0.949183i | −0.180670 | − | 0.0306507i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.8215 | + | 41.2601i | −0.768437 | + | 1.33097i | ||||
\(962\) | −79.9945 | + | 39.0430i | −2.57913 | + | 1.25880i | ||||
\(963\) | 9.81993 | + | 17.0086i | 0.316443 | + | 0.548095i | ||||
\(964\) | 29.1431 | + | 22.7435i | 0.938637 | + | 0.732519i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.26901 | + | 7.71586i | 0.0730042 | + | 0.248254i | ||||
\(967\) | 15.5047 | 0.498597 | 0.249298 | − | 0.968427i | \(-0.419800\pi\) | ||||
0.249298 | + | 0.968427i | \(0.419800\pi\) | |||||||
\(968\) | 3.88287 | − | 4.31948i | 0.124800 | − | 0.138833i | ||||
\(969\) | −3.21427 | + | 1.85576i | −0.103257 | + | 0.0596156i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5173 | − | 28.6089i | 0.530067 | − | 0.918102i | −0.469318 | − | 0.883029i | \(-0.655500\pi\) |
0.999385 | − | 0.0350732i | \(-0.0111664\pi\) | |||||||
\(972\) | −4.02701 | + | 28.7676i | −0.129166 | + | 0.922721i | ||||
\(973\) | −6.91927 | − | 5.72993i | −0.221822 | − | 0.183693i | ||||
\(974\) | 10.1368 | + | 0.706056i | 0.324805 | + | 0.0226235i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.76409 | + | 1.44384i | −0.184504 | + | 0.0462161i | ||||
\(977\) | −44.1430 | + | 25.4860i | −1.41226 | + | 0.815369i | −0.995601 | − | 0.0936930i | \(-0.970133\pi\) |
−0.416660 | + | 0.909062i | \(0.636799\pi\) | |||||||
\(978\) | 5.55824 | + | 3.74687i | 0.177733 | + | 0.119812i | ||||
\(979\) | −33.9301 | −1.08441 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.31746 | −0.105918 | ||||||||
\(982\) | 6.80208 | + | 4.58536i | 0.217063 | + | 0.146325i | ||||
\(983\) | 21.2423 | − | 12.2642i | 0.677523 | − | 0.391168i | −0.121398 | − | 0.992604i | \(-0.538738\pi\) |
0.798921 | + | 0.601436i | \(0.205404\pi\) | |||||||
\(984\) | 0.483298 | + | 1.48330i | 0.0154070 | + | 0.0472860i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.0238 | − | 0.698180i | −0.319221 | − | 0.0222346i | ||||
\(987\) | 9.30762 | + | 7.70775i | 0.296265 | + | 0.245340i | ||||
\(988\) | 47.2977 | + | 6.62093i | 1.50474 | + | 0.210640i | ||||
\(989\) | 5.04046 | − | 8.73034i | 0.160277 | − | 0.277609i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.8274 | − | 26.4585i | 1.45576 | − | 0.840481i | 0.456957 | − | 0.889489i | \(-0.348939\pi\) |
0.998798 | + | 0.0490078i | \(0.0156059\pi\) | |||||||
\(992\) | −38.3850 | + | 32.2982i | −1.21872 | + | 1.02547i | ||||
\(993\) | 13.4606 | 0.427160 | ||||||||
\(994\) | 3.72106 | + | 12.6536i | 0.118025 | + | 0.401348i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.29054 | + | 6.77921i | −0.167637 | + | 0.214808i | ||||
\(997\) | 8.51148 | + | 14.7423i | 0.269561 | + | 0.466894i | 0.968749 | − | 0.248045i | \(-0.0797880\pi\) |
−0.699187 | + | 0.714939i | \(0.746455\pi\) | |||||||
\(998\) | −50.4047 | + | 24.6011i | −1.59553 | + | 0.778733i | ||||
\(999\) | 19.8834 | − | 34.4390i | 0.629082 | − | 1.08960i |
(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 | 700.2.t.d.299.5 | 32 | ||
4.3 | odd | 2 | inner | 700.2.t.d.299.10 | 32 | ||
5.2 | odd | 4 | 700.2.p.c.551.3 | 32 | |||
5.3 | odd | 4 | 140.2.o.a.131.14 | yes | 32 | ||
5.4 | even | 2 | 700.2.t.c.299.12 | 32 | |||
7.3 | odd | 6 | 700.2.t.c.199.7 | 32 | |||
20.3 | even | 4 | 140.2.o.a.131.2 | yes | 32 | ||
20.7 | even | 4 | 700.2.p.c.551.15 | 32 | |||
20.19 | odd | 2 | 700.2.t.c.299.7 | 32 | |||
28.3 | even | 6 | 700.2.t.c.199.12 | 32 | |||
35.3 | even | 12 | 140.2.o.a.31.2 | ✓ | 32 | ||
35.13 | even | 4 | 980.2.o.f.411.14 | 32 | |||
35.17 | even | 12 | 700.2.p.c.451.15 | 32 | |||
35.18 | odd | 12 | 980.2.o.f.31.2 | 32 | |||
35.23 | odd | 12 | 980.2.g.a.391.17 | 32 | |||
35.24 | odd | 6 | inner | 700.2.t.d.199.10 | 32 | ||
35.33 | even | 12 | 980.2.g.a.391.18 | 32 | |||
140.3 | odd | 12 | 140.2.o.a.31.14 | yes | 32 | ||
140.23 | even | 12 | 980.2.g.a.391.20 | 32 | |||
140.59 | even | 6 | inner | 700.2.t.d.199.5 | 32 | ||
140.83 | odd | 4 | 980.2.o.f.411.2 | 32 | |||
140.87 | odd | 12 | 700.2.p.c.451.3 | 32 | |||
140.103 | odd | 12 | 980.2.g.a.391.19 | 32 | |||
140.123 | even | 12 | 980.2.o.f.31.14 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.o.a.31.2 | ✓ | 32 | 35.3 | even | 12 | ||
140.2.o.a.31.14 | yes | 32 | 140.3 | odd | 12 | ||
140.2.o.a.131.2 | yes | 32 | 20.3 | even | 4 | ||
140.2.o.a.131.14 | yes | 32 | 5.3 | odd | 4 | ||
700.2.p.c.451.3 | 32 | 140.87 | odd | 12 | |||
700.2.p.c.451.15 | 32 | 35.17 | even | 12 | |||
700.2.p.c.551.3 | 32 | 5.2 | odd | 4 | |||
700.2.p.c.551.15 | 32 | 20.7 | even | 4 | |||
700.2.t.c.199.7 | 32 | 7.3 | odd | 6 | |||
700.2.t.c.199.12 | 32 | 28.3 | even | 6 | |||
700.2.t.c.299.7 | 32 | 20.19 | odd | 2 | |||
700.2.t.c.299.12 | 32 | 5.4 | even | 2 | |||
700.2.t.d.199.5 | 32 | 140.59 | even | 6 | inner | ||
700.2.t.d.199.10 | 32 | 35.24 | odd | 6 | inner | ||
700.2.t.d.299.5 | 32 | 1.1 | even | 1 | trivial | ||
700.2.t.d.299.10 | 32 | 4.3 | odd | 2 | inner | ||
980.2.g.a.391.17 | 32 | 35.23 | odd | 12 | |||
980.2.g.a.391.18 | 32 | 35.33 | even | 12 | |||
980.2.g.a.391.19 | 32 | 140.103 | odd | 12 | |||
980.2.g.a.391.20 | 32 | 140.23 | even | 12 | |||
980.2.o.f.31.2 | 32 | 35.18 | odd | 12 | |||
980.2.o.f.31.14 | 32 | 140.123 | even | 12 | |||
980.2.o.f.411.2 | 32 | 140.83 | odd | 4 | |||
980.2.o.f.411.14 | 32 | 35.13 | even | 4 |