Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(37,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.t (of order \(18\), degree \(6\), 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: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(204\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 37.16 | ||
Character | \(\chi\) | \(=\) | 648.37 |
Dual form | 648.2.t.a.613.16 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.138542 | + | 1.40741i | −0.0979640 | + | 0.995190i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.96161 | − | 0.389971i | −0.980806 | − | 0.194986i | ||||
\(5\) | −0.608623 | − | 1.67218i | −0.272184 | − | 0.747820i | −0.998190 | − | 0.0601320i | \(-0.980848\pi\) |
0.726006 | − | 0.687688i | \(-0.241374\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.408085 | + | 2.31436i | 0.154242 | + | 0.874748i | 0.959476 | + | 0.281791i | \(0.0909284\pi\) |
−0.805234 | + | 0.592957i | \(0.797960\pi\) | |||||||
\(8\) | 0.820615 | − | 2.70677i | 0.290131 | − | 0.956987i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.43776 | − | 0.624915i | 0.770887 | − | 0.197616i | ||||
\(11\) | 0.860398 | − | 2.36392i | 0.259420 | − | 0.712750i | −0.739784 | − | 0.672845i | \(-0.765072\pi\) |
0.999203 | − | 0.0399051i | \(-0.0127056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.359719 | − | 0.428697i | 0.0997682 | − | 0.118899i | −0.713850 | − | 0.700299i | \(-0.753050\pi\) |
0.813618 | + | 0.581399i | \(0.197495\pi\) | |||||||
\(14\) | −3.31380 | + | 0.253707i | −0.885650 | + | 0.0678060i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.69585 | + | 1.52994i | 0.923961 | + | 0.382486i | ||||
\(17\) | −1.49770 | + | 2.59409i | −0.363245 | + | 0.629158i | −0.988493 | − | 0.151268i | \(-0.951664\pi\) |
0.625248 | + | 0.780426i | \(0.284998\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.64437 | − | 3.83613i | 1.52432 | − | 0.880068i | 0.524737 | − | 0.851264i | \(-0.324164\pi\) |
0.999585 | − | 0.0288032i | \(-0.00916963\pi\) | |||||||
\(20\) | 0.541781 | + | 3.51751i | 0.121146 | + | 0.786539i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.20781 | + | 1.53844i | 0.683908 | + | 0.327996i | ||||
\(23\) | 1.12812 | − | 6.39788i | 0.235229 | − | 1.33405i | −0.606902 | − | 0.794777i | \(-0.707588\pi\) |
0.842131 | − | 0.539273i | \(-0.181301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.40447 | − | 1.17849i | 0.280894 | − | 0.235698i | ||||
\(26\) | 0.553516 | + | 0.565665i | 0.108553 | + | 0.110936i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.102031 | − | 4.69903i | 0.0192820 | − | 0.888033i | ||||
\(29\) | 5.22169 | + | 6.22297i | 0.969643 | + | 1.15558i | 0.987798 | + | 0.155741i | \(0.0497765\pi\) |
−0.0181545 | + | 0.999835i | \(0.505779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.643875 | + | 3.65160i | −0.115643 | + | 0.655846i | 0.870786 | + | 0.491662i | \(0.163610\pi\) |
−0.986430 | + | 0.164184i | \(0.947501\pi\) | |||||||
\(32\) | −2.66529 | + | 4.98961i | −0.471161 | + | 0.882047i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.44345 | − | 2.46726i | −0.590547 | − | 0.423132i | ||||
\(35\) | 3.62166 | − | 2.09096i | 0.612172 | − | 0.353438i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.07450 | + | 2.35241i | 0.669843 | + | 0.386734i | 0.796017 | − | 0.605274i | \(-0.206936\pi\) |
−0.126174 | + | 0.992008i | \(0.540270\pi\) | |||||||
\(38\) | 4.47848 | + | 9.88282i | 0.726506 | + | 1.60320i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.02564 | + | 0.275186i | −0.794623 | + | 0.0435107i | ||||
\(41\) | 5.67863 | + | 4.76494i | 0.886853 | + | 0.744158i | 0.967576 | − | 0.252578i | \(-0.0812785\pi\) |
−0.0807232 | + | 0.996737i | \(0.525723\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.928888 | − | 2.55210i | 0.141654 | − | 0.389191i | −0.848496 | − | 0.529202i | \(-0.822491\pi\) |
0.990150 | + | 0.140011i | \(0.0447136\pi\) | |||||||
\(44\) | −2.60963 | + | 4.30157i | −0.393416 | + | 0.648486i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.84815 | + | 2.47410i | 1.30459 | + | 0.364786i | ||||
\(47\) | −0.0919295 | − | 0.521358i | −0.0134093 | − | 0.0760479i | 0.977369 | − | 0.211543i | \(-0.0678487\pi\) |
−0.990778 | + | 0.135495i | \(0.956738\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.38810 | − | 0.505226i | 0.198300 | − | 0.0721751i | ||||
\(50\) | 1.46404 | + | 2.13994i | 0.207047 | + | 0.302633i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.872809 | + | 0.700657i | −0.121037 | + | 0.0971636i | ||||
\(53\) | − | 6.39371i | − | 0.878244i | −0.898427 | − | 0.439122i | \(-0.855290\pi\) | ||
0.898427 | − | 0.439122i | \(-0.144710\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.47656 | −0.603619 | ||||||||
\(56\) | 6.59933 | + | 0.794612i | 0.881872 | + | 0.106184i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.48170 | + | 6.48692i | −1.24501 | + | 0.851775i | ||||
\(59\) | −2.87131 | − | 7.88886i | −0.373813 | − | 1.02704i | −0.973874 | − | 0.227088i | \(-0.927079\pi\) |
0.600061 | − | 0.799954i | \(-0.295143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.716954 | − | 0.126418i | 0.0917966 | − | 0.0161862i | −0.127561 | − | 0.991831i | \(-0.540715\pi\) |
0.219358 | + | 0.975644i | \(0.429604\pi\) | |||||||
\(62\) | −5.05009 | − | 1.41210i | −0.641363 | − | 0.179336i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.65318 | − | 4.44243i | −0.831648 | − | 0.555304i | ||||
\(65\) | −0.935790 | − | 0.340600i | −0.116070 | − | 0.0422462i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.68574 | − | 4.39249i | 0.450285 | − | 0.536628i | −0.492375 | − | 0.870383i | \(-0.663871\pi\) |
0.942660 | + | 0.333755i | \(0.108316\pi\) | |||||||
\(68\) | 3.94952 | − | 4.50453i | 0.478949 | − | 0.546255i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.44110 | + | 5.38685i | 0.291767 | + | 0.643851i | ||||
\(71\) | −7.38597 | + | 12.7929i | −0.876553 | + | 1.51823i | −0.0214546 | + | 0.999770i | \(0.506830\pi\) |
−0.855099 | + | 0.518465i | \(0.826504\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.98642 | − | 10.3688i | −0.700657 | − | 1.21357i | −0.968236 | − | 0.250038i | \(-0.919557\pi\) |
0.267579 | − | 0.963536i | \(-0.413776\pi\) | |||||||
\(74\) | −3.87530 | + | 5.40859i | −0.450495 | + | 0.628735i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.5296 | + | 4.93388i | −1.66666 | + | 0.565955i | ||||
\(77\) | 5.82210 | + | 1.02659i | 0.663490 | + | 0.116991i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94860 | + | 7.50876i | −1.00680 | + | 0.844802i | −0.987911 | − | 0.155020i | \(-0.950456\pi\) |
−0.0188843 | + | 0.999822i | \(0.506011\pi\) | |||||||
\(80\) | 0.308962 | − | 7.11126i | 0.0345430 | − | 0.795064i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.49296 | + | 7.33203i | −0.827458 | + | 0.809687i | ||||
\(83\) | −4.81848 | − | 5.74244i | −0.528897 | − | 0.630315i | 0.433764 | − | 0.901027i | \(-0.357185\pi\) |
−0.962660 | + | 0.270712i | \(0.912741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.24930 | + | 0.925594i | 0.569367 | + | 0.100395i | ||||
\(86\) | 3.46316 | + | 1.66090i | 0.373442 | + | 0.179099i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.69254 | − | 4.26877i | −0.606826 | − | 0.455052i | ||||
\(89\) | 1.16774 | + | 2.02259i | 0.123780 | + | 0.214394i | 0.921255 | − | 0.388958i | \(-0.127165\pi\) |
−0.797475 | + | 0.603352i | \(0.793832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.13896 | + | 0.657577i | 0.119395 | + | 0.0689328i | ||||
\(92\) | −4.70792 | + | 12.1102i | −0.490834 | + | 1.26258i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.746501 | − | 0.0571526i | 0.0769957 | − | 0.00589484i | ||||
\(95\) | −10.4586 | − | 8.77580i | −1.07303 | − | 0.900378i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8915 | + | 5.05610i | 1.41047 | + | 0.513369i | 0.931268 | − | 0.364336i | \(-0.118704\pi\) |
0.479202 | + | 0.877705i | \(0.340926\pi\) | |||||||
\(98\) | 0.518751 | + | 2.02362i | 0.0524017 | + | 0.204416i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.21460 | + | 1.76404i | −0.321460 | + | 0.176404i | ||||
\(101\) | −12.0747 | + | 2.12910i | −1.20148 | + | 0.211853i | −0.738338 | − | 0.674431i | \(-0.764389\pi\) |
−0.463142 | + | 0.886284i | \(0.653278\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8828 | − | 3.96103i | 1.07232 | − | 0.390292i | 0.255276 | − | 0.966868i | \(-0.417834\pi\) |
0.817043 | + | 0.576576i | \(0.195612\pi\) | |||||||
\(104\) | −0.865191 | − | 1.32547i | −0.0848390 | − | 0.129973i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.99858 | + | 0.885798i | 0.874020 | + | 0.0860363i | ||||
\(107\) | − | 3.95255i | − | 0.382107i | −0.981580 | − | 0.191054i | \(-0.938810\pi\) | ||
0.981580 | − | 0.191054i | \(-0.0611904\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.12938i | − | 0.491305i | −0.969358 | − | 0.245653i | \(-0.920998\pi\) | ||
0.969358 | − | 0.245653i | \(-0.0790023\pi\) | |||||||
\(110\) | 0.620191 | − | 6.30035i | 0.0591329 | − | 0.600715i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.03263 | + | 9.17788i | −0.192065 | + | 0.867228i | ||||
\(113\) | 9.37151 | − | 3.41095i | 0.881597 | − | 0.320875i | 0.138743 | − | 0.990328i | \(-0.455694\pi\) |
0.742854 | + | 0.669453i | \(0.233472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.3850 | + | 2.00748i | −1.06165 | + | 0.187198i | ||||
\(116\) | −7.81615 | − | 14.2434i | −0.725712 | − | 1.32246i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.5007 | − | 2.94818i | 1.05872 | − | 0.271402i | ||||
\(119\) | −6.61485 | − | 2.40761i | −0.606382 | − | 0.220705i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.57864 | + | 3.00283i | 0.325331 | + | 0.272985i | ||||
\(122\) | 0.0785944 | + | 1.02656i | 0.00711560 | + | 0.0929407i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.68705 | − | 6.91192i | 0.241304 | − | 0.620709i | ||||
\(125\) | −10.5309 | − | 6.08000i | −0.941909 | − | 0.543812i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0971 | − | 17.4887i | −0.895973 | − | 1.55187i | −0.832596 | − | 0.553880i | \(-0.813147\pi\) |
−0.0633763 | − | 0.997990i | \(-0.520187\pi\) | |||||||
\(128\) | 7.17407 | − | 8.74830i | 0.634104 | − | 0.773248i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.609010 | − | 1.26985i | 0.0534137 | − | 0.111374i | ||||
\(131\) | 13.3484 | + | 2.35368i | 1.16625 | + | 0.205642i | 0.723060 | − | 0.690785i | \(-0.242735\pi\) |
0.443192 | + | 0.896427i | \(0.353846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.5897 | + | 13.8120i | 1.00495 | + | 1.19765i | ||||
\(134\) | 5.67141 | + | 5.79589i | 0.489935 | + | 0.500689i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.79256 | + | 6.18266i | 0.496708 | + | 0.530159i | ||||
\(137\) | −6.18657 | + | 5.19115i | −0.528555 | + | 0.443510i | −0.867602 | − | 0.497259i | \(-0.834340\pi\) |
0.339047 | + | 0.940769i | \(0.389895\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.8808 | − | 3.32919i | −1.60145 | − | 0.282378i | −0.699633 | − | 0.714502i | \(-0.746653\pi\) |
−0.901814 | + | 0.432124i | \(0.857764\pi\) | |||||||
\(140\) | −7.91970 | + | 2.68932i | −0.669337 | + | 0.227289i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.9816 | − | 12.1674i | −1.42506 | − | 1.02107i | ||||
\(143\) | −0.703905 | − | 1.21920i | −0.0588635 | − | 0.101955i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.22786 | − | 12.5190i | 0.600241 | − | 1.03965i | ||||
\(146\) | 15.4225 | − | 6.98884i | 1.27638 | − | 0.578400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.07521 | − | 6.20346i | −0.581579 | − | 0.509921i | ||||
\(149\) | −0.614187 | + | 0.731960i | −0.0503162 | + | 0.0599645i | −0.790616 | − | 0.612313i | \(-0.790239\pi\) |
0.740299 | + | 0.672277i | \(0.234684\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.04563 | − | 0.380578i | −0.0850921 | − | 0.0309710i | 0.299123 | − | 0.954214i | \(-0.403306\pi\) |
−0.384215 | + | 0.923243i | \(0.625528\pi\) | |||||||
\(152\) | −4.93103 | − | 21.1327i | −0.399960 | − | 1.71409i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.25144 | + | 8.05186i | −0.181426 | + | 0.648837i | ||||
\(155\) | 6.49799 | − | 1.14577i | 0.521931 | − | 0.0920306i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.45899 | + | 6.75603i | 0.196249 | + | 0.539190i | 0.998314 | − | 0.0580471i | \(-0.0184873\pi\) |
−0.802065 | + | 0.597237i | \(0.796265\pi\) | |||||||
\(158\) | −9.32816 | − | 13.6346i | −0.742109 | − | 1.08471i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.96567 | + | 1.42004i | 0.787855 | + | 0.112264i | ||||
\(161\) | 15.2674 | 1.20324 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.783193i | 0.0613444i | 0.999529 | + | 0.0306722i | \(0.00976480\pi\) | ||||
−0.999529 | + | 0.0306722i | \(0.990235\pi\) | |||||||
\(164\) | −9.28109 | − | 11.5615i | −0.724731 | − | 0.902798i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.74953 | − | 5.98601i | 0.679096 | − | 0.464605i | ||||
\(167\) | 13.3409 | − | 4.85570i | 1.03235 | − | 0.375745i | 0.230376 | − | 0.973102i | \(-0.426004\pi\) |
0.801976 | + | 0.597356i | \(0.203782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.20304 | + | 12.4941i | 0.169465 | + | 0.961083i | ||||
\(170\) | −2.02994 | + | 7.25969i | −0.155689 | + | 0.556793i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.81736 | + | 4.64399i | −0.214822 | + | 0.354101i | ||||
\(173\) | −4.11676 | + | 11.3107i | −0.312991 | + | 0.859937i | 0.679058 | + | 0.734085i | \(0.262389\pi\) |
−0.992049 | + | 0.125852i | \(0.959834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.30060 | + | 2.76953i | 0.249502 | + | 0.209357i | ||||
\(176\) | 6.79657 | − | 7.42033i | 0.512311 | − | 0.559329i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00839 | + | 1.36328i | −0.225488 | + | 0.102182i | ||||
\(179\) | 6.41741 | + | 3.70509i | 0.479660 | + | 0.276932i | 0.720275 | − | 0.693689i | \(-0.244016\pi\) |
−0.240615 | + | 0.970621i | \(0.577349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0116 | + | 6.93490i | −0.892815 | + | 0.515467i | −0.874862 | − | 0.484372i | \(-0.839048\pi\) |
−0.0179527 | + | 0.999839i | \(0.505715\pi\) | |||||||
\(182\) | −1.08327 | + | 1.51188i | −0.0802977 | + | 0.112068i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.3918 | − | 8.30375i | −1.20842 | − | 0.612161i | ||||
\(185\) | 1.45382 | − | 8.24501i | 0.106887 | − | 0.606185i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.84361 | + | 5.77239i | 0.354200 | + | 0.422119i | ||||
\(188\) | −0.0229845 | + | 1.05855i | −0.00167632 | + | 0.0772029i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.8001 | − | 13.5037i | 1.00117 | − | 0.979663i | ||||
\(191\) | 6.35332 | − | 5.33107i | 0.459710 | − | 0.385743i | −0.383314 | − | 0.923618i | \(-0.625217\pi\) |
0.843024 | + | 0.537875i | \(0.180773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.66122 | − | 9.42126i | 0.119577 | − | 0.678157i | −0.864804 | − | 0.502109i | \(-0.832558\pi\) |
0.984382 | − | 0.176048i | \(-0.0563314\pi\) | |||||||
\(194\) | −9.04056 | + | 18.8506i | −0.649075 | + | 1.35339i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.91993 | + | 0.449740i | −0.208566 | + | 0.0321243i | ||||
\(197\) | −12.5364 | + | 7.23789i | −0.893181 | + | 0.515678i | −0.874982 | − | 0.484156i | \(-0.839127\pi\) |
−0.0181995 | + | 0.999834i | \(0.505793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2319 | + | 22.9183i | −0.937983 | + | 1.62463i | −0.168758 | + | 0.985658i | \(0.553976\pi\) |
−0.769225 | + | 0.638977i | \(0.779358\pi\) | |||||||
\(200\) | −2.03737 | − | 4.76866i | −0.144064 | − | 0.337195i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.32366 | − | 17.2891i | −0.0931325 | − | 1.21645i | ||||
\(203\) | −12.2713 | + | 14.6244i | −0.861278 | + | 1.02643i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.51167 | − | 12.3957i | 0.315109 | − | 0.865755i | ||||
\(206\) | 4.06707 | + | 15.8654i | 0.283366 | + | 1.10540i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.98535 | − | 1.03405i | 0.137659 | − | 0.0716982i | ||||
\(209\) | −3.35151 | − | 19.0074i | −0.231829 | − | 1.31477i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.13970 | − | 16.8687i | −0.422674 | − | 1.16129i | −0.950170 | − | 0.311731i | \(-0.899091\pi\) |
0.527496 | − | 0.849558i | \(-0.323131\pi\) | |||||||
\(212\) | −2.49336 | + | 12.5420i | −0.171245 | + | 0.861387i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.56286 | + | 0.547594i | 0.380269 | + | 0.0374327i | ||||
\(215\) | −4.83290 | −0.329601 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.71388 | −0.591537 | ||||||||
\(218\) | 7.21915 | + | 0.710634i | 0.488942 | + | 0.0481302i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.78127 | + | 1.74573i | 0.592033 | + | 0.117697i | ||||
\(221\) | 0.573326 | + | 1.57520i | 0.0385661 | + | 0.105959i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.13816 | − | 17.7974i | −0.210147 | − | 1.19180i | −0.889132 | − | 0.457651i | \(-0.848691\pi\) |
0.678985 | − | 0.734152i | \(-0.262420\pi\) | |||||||
\(224\) | −12.6354 | − | 4.13227i | −0.844241 | − | 0.276099i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.50226 | + | 13.6621i | 0.232967 | + | 0.908791i | ||||
\(227\) | 2.07372 | − | 5.69750i | 0.137638 | − | 0.378156i | −0.851655 | − | 0.524103i | \(-0.824401\pi\) |
0.989292 | + | 0.145947i | \(0.0466229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.8939 | + | 17.7498i | −0.984215 | + | 1.17294i | 0.000716763 | 1.00000i | \(0.499772\pi\) | |
−0.984932 | + | 0.172942i | \(0.944673\pi\) | |||||||
\(230\) | −1.24805 | − | 16.3015i | −0.0822940 | − | 1.07489i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 21.1291 | − | 9.02724i | 1.38720 | − | 0.592667i | ||||
\(233\) | −4.63643 | + | 8.03053i | −0.303742 | + | 0.526097i | −0.976981 | − | 0.213328i | \(-0.931570\pi\) |
0.673238 | + | 0.739426i | \(0.264903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.815853 | + | 0.471033i | −0.0532204 | + | 0.0307268i | ||||
\(236\) | 2.55597 | + | 16.5946i | 0.166380 | + | 1.08022i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.30493 | − | 8.97626i | 0.279047 | − | 0.581844i | ||||
\(239\) | 1.63200 | − | 9.25552i | 0.105565 | − | 0.598690i | −0.885428 | − | 0.464777i | \(-0.846135\pi\) |
0.990993 | − | 0.133913i | \(-0.0427543\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.4723 | + | 17.1783i | −1.31873 | + | 1.10655i | −0.332163 | + | 0.943222i | \(0.607778\pi\) |
−0.986572 | + | 0.163328i | \(0.947777\pi\) | |||||||
\(242\) | −4.72201 | + | 4.62060i | −0.303543 | + | 0.297023i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.45569 | − | 0.0316075i | −0.0931907 | − | 0.00202347i | ||||
\(245\) | −1.68965 | − | 2.01365i | −0.107948 | − | 0.128647i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.745572 | − | 4.22835i | 0.0474396 | − | 0.269043i | ||||
\(248\) | 9.35565 | + | 4.73938i | 0.594084 | + | 0.300951i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.0160 | − | 13.9789i | 0.633469 | − | 0.884105i | ||||
\(251\) | 0.101849 | − | 0.0588028i | 0.00642868 | − | 0.00371160i | −0.496782 | − | 0.867875i | \(-0.665485\pi\) |
0.503211 | + | 0.864164i | \(0.332152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.1535 | − | 8.17150i | −0.889821 | − | 0.513738i | ||||
\(254\) | 26.0126 | − | 11.7879i | 1.63218 | − | 0.739636i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.3185 | + | 11.3089i | 0.707409 | + | 0.706804i | ||||
\(257\) | 7.73634 | + | 6.49156i | 0.482580 | + | 0.404932i | 0.851358 | − | 0.524585i | \(-0.175779\pi\) |
−0.368778 | + | 0.929517i | \(0.620224\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.78160 | + | 10.3899i | −0.234977 | + | 0.645594i | ||||
\(260\) | 1.70283 | + | 1.03306i | 0.105605 | + | 0.0640674i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.16190 | + | 18.4606i | −0.318903 | + | 1.14050i | ||||
\(263\) | 1.42729 | + | 8.09455i | 0.0880104 | + | 0.499132i | 0.996666 | + | 0.0815860i | \(0.0259985\pi\) |
−0.908656 | + | 0.417546i | \(0.862890\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6914 | + | 3.89136i | −0.656769 | + | 0.239044i | ||||
\(266\) | −21.0448 | + | 14.3979i | −1.29034 | + | 0.882790i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.94293 | + | 7.17903i | −0.546277 | + | 0.438529i | ||||
\(269\) | 16.5496i | 1.00905i | 0.863398 | + | 0.504524i | \(0.168332\pi\) | ||||
−0.863398 | + | 0.504524i | \(0.831668\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.76275 | 0.532299 | 0.266150 | − | 0.963932i | \(-0.414249\pi\) | ||||
0.266150 | + | 0.963932i | \(0.414249\pi\) | |||||||
\(272\) | −9.50406 | + | 7.29595i | −0.576268 | + | 0.442382i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.44898 | − | 9.42624i | −0.389597 | − | 0.569460i | ||||
\(275\) | −1.57746 | − | 4.33403i | −0.0951242 | − | 0.261352i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.89916 | − | 1.04018i | 0.354446 | − | 0.0624985i | 0.00640991 | − | 0.999979i | \(-0.497960\pi\) |
0.348036 | + | 0.937481i | \(0.386849\pi\) | |||||||
\(278\) | 7.30132 | − | 26.1118i | 0.437904 | − | 1.56608i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.68777 | − | 11.5189i | −0.160625 | − | 0.688384i | ||||
\(281\) | −10.4464 | − | 3.80217i | −0.623179 | − | 0.226819i | 0.0110807 | − | 0.999939i | \(-0.496473\pi\) |
−0.634260 | + | 0.773120i | \(0.718695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.16295 | − | 9.72822i | 0.485237 | − | 0.578283i | −0.466763 | − | 0.884383i | \(-0.654580\pi\) |
0.951999 | + | 0.306100i | \(0.0990242\pi\) | |||||||
\(284\) | 19.4773 | − | 22.2143i | 1.15576 | − | 1.31818i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.81343 | − | 0.821773i | 0.107231 | − | 0.0485925i | ||||
\(287\) | −8.71044 | + | 15.0869i | −0.514161 | + | 0.890553i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.01381 | + | 6.95213i | 0.236107 | + | 0.408949i | ||||
\(290\) | 16.6181 | + | 11.9070i | 0.975846 | + | 0.699202i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.69950 | + | 22.6740i | 0.450579 | + | 1.32690i | ||||
\(293\) | 26.3005 | + | 4.63749i | 1.53649 | + | 0.270925i | 0.876890 | − | 0.480691i | \(-0.159614\pi\) |
0.659601 | + | 0.751616i | \(0.270725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.4440 | + | 9.60268i | −0.666297 | + | 0.559089i | ||||
\(296\) | 9.71103 | − | 9.09829i | 0.564442 | − | 0.528828i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.945078 | − | 0.965822i | −0.0547469 | − | 0.0559485i | ||||
\(299\) | −2.33694 | − | 2.78506i | −0.135149 | − | 0.161064i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.28555 | + | 1.10831i | 0.362293 | + | 0.0638821i | ||||
\(302\) | 0.680493 | − | 1.41890i | 0.0391580 | − | 0.0816488i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 30.4256 | − | 4.01222i | 1.74503 | − | 0.230117i | ||||
\(305\) | −0.647748 | − | 1.12193i | −0.0370900 | − | 0.0642417i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.31774 | − | 2.49285i | −0.246426 | − | 0.142274i | 0.371700 | − | 0.928353i | \(-0.378775\pi\) |
−0.618127 | + | 0.786078i | \(0.712108\pi\) | |||||||
\(308\) | −11.0204 | − | 4.28423i | −0.627943 | − | 0.244116i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.712327 | + | 9.30408i | 0.0404574 | + | 0.528436i | ||||
\(311\) | 12.4172 | + | 10.4193i | 0.704116 | + | 0.590824i | 0.922941 | − | 0.384940i | \(-0.125778\pi\) |
−0.218825 | + | 0.975764i | \(0.570222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.8980 | + | 4.69448i | 0.729037 | + | 0.265348i | 0.679757 | − | 0.733437i | \(-0.262085\pi\) |
0.0492798 | + | 0.998785i | \(0.484307\pi\) | |||||||
\(314\) | −9.84919 | + | 2.52482i | −0.555822 | + | 0.142484i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.4819 | − | 11.2396i | 1.15220 | − | 0.632276i | ||||
\(317\) | 5.48493 | − | 0.967141i | 0.308064 | − | 0.0543200i | −0.0174789 | − | 0.999847i | \(-0.505564\pi\) |
0.325543 | + | 0.945527i | \(0.394453\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.2033 | − | 6.98945i | 1.07518 | − | 0.391334i | ||||
\(320\) | −3.37925 | + | 13.8291i | −0.188906 | + | 0.773068i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.11517 | + | 21.4875i | −0.117874 | + | 1.19745i | ||||
\(323\) | 22.9814i | 1.27872i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.02602i | − | 0.0569132i | ||||||
\(326\) | −1.10227 | − | 0.108505i | −0.0610494 | − | 0.00600954i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.5576 | − | 11.4606i | 0.969454 | − | 0.632803i | ||||
\(329\) | 1.16910 | − | 0.425517i | 0.0644545 | − | 0.0234595i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.7828 | + | 4.01723i | −1.25226 | + | 0.220807i | −0.760162 | − | 0.649734i | \(-0.774880\pi\) |
−0.492097 | + | 0.870541i | \(0.663769\pi\) | |||||||
\(332\) | 7.21260 | + | 13.1435i | 0.395843 | + | 0.721344i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.98569 | + | 19.4489i | 0.272805 | + | 1.06420i | ||||
\(335\) | −9.58825 | − | 3.48984i | −0.523862 | − | 0.190670i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.50303 | + | 2.93939i | 0.190822 | + | 0.160119i | 0.733194 | − | 0.680020i | \(-0.238029\pi\) |
−0.542371 | + | 0.840139i | \(0.682473\pi\) | |||||||
\(338\) | −17.8895 | + | 1.36963i | −0.973062 | + | 0.0744982i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.93614 | − | 3.86273i | −0.538863 | − | 0.209486i | ||||
\(341\) | 8.07811 | + | 4.66390i | 0.437454 | + | 0.252564i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.96098 | + | 17.2529i | 0.537842 | + | 0.931570i | ||||
\(344\) | −6.14568 | − | 4.60857i | −0.331353 | − | 0.248478i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.3485 | − | 7.36098i | −0.825138 | − | 0.395729i | ||||
\(347\) | −17.5663 | − | 3.09741i | −0.943008 | − | 0.166278i | −0.319052 | − | 0.947737i | \(-0.603364\pi\) |
−0.623956 | + | 0.781459i | \(0.714476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.1052 | − | 13.2347i | −0.594449 | − | 0.708436i | 0.382006 | − | 0.924160i | \(-0.375233\pi\) |
−0.976454 | + | 0.215724i | \(0.930789\pi\) | |||||||
\(350\) | −4.35514 | + | 4.26160i | −0.232792 | + | 0.227792i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.50185 | + | 10.5936i | 0.506450 | + | 0.564640i | ||||
\(353\) | −21.4608 | + | 18.0078i | −1.14225 | + | 0.958458i | −0.999510 | − | 0.0313029i | \(-0.990034\pi\) |
−0.142736 | + | 0.989761i | \(0.545590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.8872 | + | 4.56461i | 1.37395 | + | 0.242265i | ||||
\(356\) | −1.50190 | − | 4.42291i | −0.0796008 | − | 0.234414i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.10367 | + | 8.51863i | −0.322589 | + | 0.450223i | ||||
\(359\) | 11.9164 | + | 20.6398i | 0.628922 | + | 1.08932i | 0.987768 | + | 0.155928i | \(0.0498369\pi\) |
−0.358846 | + | 0.933397i | \(0.616830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.9317 | − | 34.5228i | 1.04904 | − | 1.81699i | ||||
\(362\) | −8.09614 | − | 17.8660i | −0.425524 | − | 0.939018i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.97776 | − | 1.73407i | −0.103663 | − | 0.0908900i | ||||
\(365\) | −13.6950 | + | 16.3210i | −0.716827 | + | 0.854281i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.313629 | − | 0.114152i | −0.0163713 | − | 0.00595866i | 0.333822 | − | 0.942636i | \(-0.391662\pi\) |
−0.350193 | + | 0.936678i | \(0.613884\pi\) | |||||||
\(368\) | 13.9577 | − | 21.9196i | 0.727598 | − | 1.14264i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.4027 | + | 3.18840i | 0.592799 | + | 0.165757i | ||||
\(371\) | 14.7974 | − | 2.60918i | 0.768242 | − | 0.135462i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.23868 | + | 3.40324i | 0.0641364 | + | 0.176213i | 0.967621 | − | 0.252407i | \(-0.0812221\pi\) |
−0.903485 | + | 0.428620i | \(0.859000\pi\) | |||||||
\(374\) | −8.79516 | + | 6.01723i | −0.454787 | + | 0.311143i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.48663 | − | 0.179003i | −0.0766673 | − | 0.00923136i | ||||
\(377\) | 4.54611 | 0.234137 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.7219i | 1.62944i | 0.579852 | + | 0.814722i | \(0.303110\pi\) | ||||
−0.579852 | + | 0.814722i | \(0.696890\pi\) | |||||||
\(380\) | 17.0934 | + | 21.2933i | 0.876873 | + | 1.09232i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.62280 | + | 9.68031i | 0.338852 | + | 0.495288i | ||||
\(383\) | −15.3087 | + | 5.57190i | −0.782237 | + | 0.284711i | −0.702105 | − | 0.712073i | \(-0.747756\pi\) |
−0.0801320 | + | 0.996784i | \(0.525534\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.82681 | − | 10.3604i | −0.0931031 | − | 0.528014i | ||||
\(386\) | 13.0294 | + | 3.64326i | 0.663181 | + | 0.185437i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.2780 | − | 15.3354i | −1.28330 | − | 0.778536i | ||||
\(389\) | 0.814629 | − | 2.23818i | 0.0413034 | − | 0.113480i | −0.917326 | − | 0.398136i | \(-0.869657\pi\) |
0.958630 | + | 0.284656i | \(0.0918794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.9071 | + | 12.5085i | 0.753883 | + | 0.632583i | ||||
\(392\) | −0.228436 | − | 4.17185i | −0.0115377 | − | 0.210710i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.44987 | − | 18.6466i | −0.425698 | − | 0.939403i | ||||
\(395\) | 18.0023 | + | 10.3936i | 0.905794 | + | 0.522960i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.7658 | + | 8.52506i | −0.741076 | + | 0.427860i | −0.822460 | − | 0.568822i | \(-0.807399\pi\) |
0.0813844 | + | 0.996683i | \(0.474066\pi\) | |||||||
\(398\) | −30.4223 | − | 21.7978i | −1.52493 | − | 1.09263i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.99372 | − | 2.20676i | 0.349686 | − | 0.110338i | ||||
\(401\) | −6.89131 | + | 39.0826i | −0.344136 | + | 1.95169i | −0.0395068 | + | 0.999219i | \(0.512579\pi\) |
−0.304629 | + | 0.952471i | \(0.598532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.33381 | + | 1.58958i | 0.0664420 | + | 0.0791825i | ||||
\(404\) | 24.5162 | + | 0.532325i | 1.21973 | + | 0.0264841i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.8824 | − | 19.2969i | −0.937120 | − | 0.957689i | ||||
\(407\) | 9.06661 | − | 7.60779i | 0.449415 | − | 0.377104i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.68450 | + | 9.55328i | −0.0832932 | + | 0.472379i | 0.914419 | + | 0.404770i | \(0.132648\pi\) |
−0.997712 | + | 0.0676096i | \(0.978463\pi\) | |||||||
\(410\) | 16.8208 | + | 8.06711i | 0.830721 | + | 0.398406i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.8926 | + | 3.52602i | −1.12784 | + | 0.173714i | ||||
\(413\) | 17.0860 | − | 9.86459i | 0.840745 | − | 0.485405i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.66974 | + | 11.5523i | −0.327405 | + | 0.567081i | ||||
\(416\) | 1.18027 | + | 2.93746i | 0.0578677 | + | 0.144021i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 27.2155 | − | 2.08364i | 1.33115 | − | 0.101914i | ||||
\(419\) | −21.3004 | + | 25.3848i | −1.04059 | + | 1.24013i | −0.0704699 | + | 0.997514i | \(0.522450\pi\) |
−0.970122 | + | 0.242616i | \(0.921995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7589 | − | 29.5598i | 0.524355 | − | 1.44065i | −0.341271 | − | 0.939965i | \(-0.610857\pi\) |
0.865627 | − | 0.500690i | \(-0.166920\pi\) | |||||||
\(422\) | 24.5918 | − | 6.30406i | 1.19711 | − | 0.306877i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.3063 | − | 5.24678i | −0.840468 | − | 0.254806i | ||||
\(425\) | 0.953635 | + | 5.40833i | 0.0462581 | + | 0.262343i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.585156 | + | 1.60770i | 0.0283177 | + | 0.0778022i | ||||
\(428\) | −1.54138 | + | 7.75337i | −0.0745054 | + | 0.374773i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.669560 | − | 6.80188i | 0.0322890 | − | 0.328016i | ||||
\(431\) | −9.66850 | −0.465715 | −0.232858 | − | 0.972511i | \(-0.574808\pi\) | ||||
−0.232858 | + | 0.972511i | \(0.574808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0283 | −0.962501 | −0.481250 | − | 0.876583i | \(-0.659817\pi\) | ||||
−0.481250 | + | 0.876583i | \(0.659817\pi\) | |||||||
\(434\) | 1.20724 | − | 12.2640i | 0.0579493 | − | 0.588692i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00031 | + | 10.0619i | −0.0957974 | + | 0.481875i | ||||
\(437\) | −17.0474 | − | 46.8374i | −0.815489 | − | 2.24054i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.0379532 | + | 0.215244i | 0.00181141 | + | 0.0102730i | 0.985700 | − | 0.168509i | \(-0.0538953\pi\) |
−0.983889 | + | 0.178782i | \(0.942784\pi\) | |||||||
\(440\) | −3.67353 | + | 12.1170i | −0.175129 | + | 0.577655i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.29638 | + | 0.588674i | −0.109228 | + | 0.0280004i | ||||
\(443\) | −3.15720 | + | 8.67435i | −0.150003 | + | 0.412131i | −0.991822 | − | 0.127630i | \(-0.959263\pi\) |
0.841819 | + | 0.539761i | \(0.181485\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.67141 | − | 3.18366i | 0.126637 | − | 0.150920i | ||||
\(446\) | 25.4830 | − | 1.95100i | 1.20666 | − | 0.0923824i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.56634 | − | 17.2108i | 0.357476 | − | 0.813133i | ||||
\(449\) | 20.7878 | − | 36.0055i | 0.981036 | − | 1.69920i | 0.322661 | − | 0.946514i | \(-0.395422\pi\) |
0.658375 | − | 0.752690i | \(-0.271244\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.1498 | − | 9.32411i | 0.760466 | − | 0.439055i | ||||
\(452\) | −19.7134 | + | 3.03634i | −0.927242 | + | 0.142818i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.73142 | + | 3.70792i | 0.362854 | + | 0.174021i | ||||
\(455\) | 0.406390 | − | 2.30475i | 0.0190519 | − | 0.108049i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.23132 | − | 1.03320i | 0.0575986 | − | 0.0483309i | −0.613534 | − | 0.789668i | \(-0.710253\pi\) |
0.671132 | + | 0.741337i | \(0.265808\pi\) | |||||||
\(458\) | −22.9179 | − | 23.4209i | −1.07088 | − | 1.09439i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 23.1158 | + | 0.501917i | 1.07778 | + | 0.0234020i | ||||
\(461\) | 16.0349 | + | 19.1096i | 0.746819 | + | 0.890024i | 0.996938 | − | 0.0781909i | \(-0.0249144\pi\) |
−0.250120 | + | 0.968215i | \(0.580470\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.29923 | − | 35.7247i | 0.292750 | − | 1.66027i | −0.383458 | − | 0.923558i | \(-0.625267\pi\) |
0.676208 | − | 0.736711i | \(-0.263622\pi\) | |||||||
\(464\) | 9.77777 | + | 30.9880i | 0.453921 | + | 1.43858i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.6599 | − | 7.63792i | −0.493811 | − | 0.353820i | ||||
\(467\) | −6.88704 | + | 3.97623i | −0.318694 | + | 0.183998i | −0.650810 | − | 0.759240i | \(-0.725571\pi\) |
0.332116 | + | 0.943238i | \(0.392237\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.6699 | + | 6.73763i | 0.538867 | + | 0.311115i | ||||
\(470\) | −0.549907 | − | 1.21350i | −0.0253653 | − | 0.0559745i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.7096 | + | 1.29825i | −1.09132 | + | 0.0597568i | ||||
\(473\) | −5.23375 | − | 4.39164i | −0.240648 | − | 0.201928i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.81097 | − | 13.2180i | 0.220742 | − | 0.606485i | ||||
\(476\) | 12.0369 | + | 7.30239i | 0.551709 | + | 0.334705i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.8002 | + | 3.57917i | 0.585469 | + | 0.163707i | ||||
\(479\) | −2.84409 | − | 16.1296i | −0.129950 | − | 0.736982i | −0.978244 | − | 0.207457i | \(-0.933481\pi\) |
0.848294 | − | 0.529525i | \(-0.177630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.47415 | − | 0.900516i | 0.112811 | − | 0.0410600i | ||||
\(482\) | −21.3406 | − | 31.1928i | −0.972039 | − | 1.42079i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.84888 | − | 7.28596i | −0.265858 | − | 0.331180i | ||||
\(485\) | − | 26.3063i | − | 1.19451i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.24111 | 0.192183 | 0.0960914 | − | 0.995373i | \(-0.469366\pi\) | ||||
0.0960914 | + | 0.995373i | \(0.469366\pi\) | |||||||
\(488\) | 0.246158 | − | 2.04437i | 0.0111431 | − | 0.0925442i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.06812 | − | 2.09906i | 0.138604 | − | 0.0948260i | ||||
\(491\) | −4.31034 | − | 11.8426i | −0.194523 | − | 0.534447i | 0.803635 | − | 0.595123i | \(-0.202897\pi\) |
−0.998158 | + | 0.0606758i | \(0.980674\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.9634 | + | 4.22540i | −1.07926 | + | 0.190302i | ||||
\(494\) | 5.84773 | + | 1.63513i | 0.263102 | + | 0.0735679i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.96640 | + | 12.5106i | −0.357702 | + | 0.561744i | ||||
\(497\) | −32.6215 | − | 11.8732i | −1.46327 | − | 0.532588i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.4544 | + | 12.4591i | −0.468003 | + | 0.557744i | −0.947482 | − | 0.319809i | \(-0.896381\pi\) |
0.479479 | + | 0.877553i | \(0.340826\pi\) | |||||||
\(500\) | 18.2865 | + | 16.0333i | 0.817795 | + | 0.717032i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.0686493 | + | 0.151491i | 0.00306397 | + | 0.00676136i | ||||
\(503\) | 17.8227 | − | 30.8698i | 0.794674 | − | 1.37642i | −0.128372 | − | 0.991726i | \(-0.540975\pi\) |
0.923046 | − | 0.384690i | \(-0.125692\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9092 | + | 18.8953i | 0.485452 | + | 0.840828i | ||||
\(506\) | 13.4615 | − | 18.7876i | 0.598437 | − | 0.835213i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.9865 | + | 38.2436i | 0.576183 | + | 1.69679i | ||||
\(509\) | 25.2257 | + | 4.44797i | 1.11811 | + | 0.197153i | 0.702010 | − | 0.712167i | \(-0.252286\pi\) |
0.416099 | + | 0.909319i | \(0.363397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.5542 | − | 18.0861i | 0.953500 | − | 0.800082i | ||||
\(512\) | −17.4843 | + | 14.3631i | −0.772705 | + | 0.634765i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.2081 | + | 9.98886i | −0.450260 | + | 0.440590i | ||||
\(515\) | −13.2471 | − | 15.7873i | −0.583737 | − | 0.695670i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.31155 | − | 0.231261i | −0.0576818 | − | 0.0101709i | ||||
\(518\) | −14.0989 | − | 6.76170i | −0.619470 | − | 0.297092i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.68985 | + | 2.25346i | −0.0741047 | + | 0.0988210i | ||||
\(521\) | −1.83496 | − | 3.17824i | −0.0803909 | − | 0.139241i | 0.823027 | − | 0.568002i | \(-0.192284\pi\) |
−0.903418 | + | 0.428761i | \(0.858950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.27809 | + | 3.62466i | 0.274522 | + | 0.158495i | 0.630941 | − | 0.775831i | \(-0.282669\pi\) |
−0.356419 | + | 0.934326i | \(0.616002\pi\) | |||||||
\(524\) | −25.2665 | − | 9.82248i | −1.10377 | − | 0.429097i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.5901 | + | 0.887346i | −0.505353 | + | 0.0386901i | ||||
\(527\) | −8.50823 | − | 7.13925i | −0.370624 | − | 0.310991i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.0473 | − | 6.56866i | −0.784663 | − | 0.285594i | ||||
\(530\) | −3.99553 | − | 15.5863i | −0.173555 | − | 0.677027i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.3481 | − | 31.6135i | −0.752137 | − | 1.37062i | ||||
\(533\) | 4.08543 | − | 0.720371i | 0.176959 | − | 0.0312027i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.60936 | + | 2.40561i | −0.285747 | + | 0.104004i | ||||
\(536\) | −8.86488 | − | 13.5810i | −0.382905 | − | 0.586609i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −23.2921 | − | 2.29282i | −1.00419 | − | 0.0988503i | ||||
\(539\) | − | 3.71605i | − | 0.160062i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 45.0694i | − | 1.93768i | −0.247679 | − | 0.968842i | \(-0.579668\pi\) | ||
0.247679 | − | 0.968842i | \(-0.420332\pi\) | |||||||
\(542\) | −1.21401 | + | 12.3328i | −0.0521461 | + | 0.529739i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.95169 | − | 14.3869i | −0.383800 | − | 0.616834i | ||||
\(545\) | −8.57723 | + | 3.12186i | −0.367408 | + | 0.133726i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7500 | − | 2.60083i | 0.630666 | − | 0.111203i | 0.150827 | − | 0.988560i | \(-0.451806\pi\) |
0.479839 | + | 0.877357i | \(0.340695\pi\) | |||||||
\(548\) | 14.1601 | − | 7.77044i | 0.604888 | − | 0.331937i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.31830 | − | 1.61969i | 0.269413 | − | 0.0690636i | ||||
\(551\) | 58.5669 | + | 21.3166i | 2.49503 | + | 0.908118i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.0298 | − | 17.6461i | −0.894278 | − | 0.750389i | ||||
\(554\) | 0.646682 | + | 8.44666i | 0.0274749 | + | 0.358864i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 35.7385 | + | 13.8935i | 1.51565 | + | 0.589217i | ||||
\(557\) | −22.1699 | − | 12.7998i | −0.939368 | − | 0.542344i | −0.0496059 | − | 0.998769i | \(-0.515797\pi\) |
−0.889762 | + | 0.456424i | \(0.849130\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.759937 | − | 1.31625i | −0.0321419 | − | 0.0556714i | ||||
\(560\) | 16.5841 | − | 2.18695i | 0.700808 | − | 0.0924155i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.79848 | − | 14.1756i | 0.286777 | − | 0.597962i | ||||
\(563\) | −8.77498 | − | 1.54727i | −0.369821 | − | 0.0652095i | −0.0143510 | − | 0.999897i | \(-0.504568\pi\) |
−0.355470 | + | 0.934688i | \(0.615679\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.4074 | − | 13.5948i | −0.479914 | − | 0.571939i | ||||
\(566\) | 12.5607 | + | 12.8364i | 0.527965 | + | 0.539554i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 28.5663 | + | 30.4901i | 1.19862 | + | 1.27934i | ||||
\(569\) | 16.0670 | − | 13.4818i | 0.673565 | − | 0.565188i | −0.240553 | − | 0.970636i | \(-0.577329\pi\) |
0.914118 | + | 0.405448i | \(0.132884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.19314 | − | 0.210382i | −0.0499312 | − | 0.00880422i | 0.148627 | − | 0.988893i | \(-0.452515\pi\) |
−0.198558 | + | 0.980089i | \(0.563626\pi\) | |||||||
\(572\) | 0.905336 | + | 2.66610i | 0.0378540 | + | 0.111475i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20.0267 | − | 14.3493i | −0.835900 | − | 0.598930i | ||||
\(575\) | −5.95542 | − | 10.3151i | −0.248358 | − | 0.430169i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.95106 | + | 15.5037i | −0.372638 | + | 0.645427i | −0.989970 | − | 0.141275i | \(-0.954880\pi\) |
0.617333 | + | 0.786702i | \(0.288213\pi\) | |||||||
\(578\) | −10.3406 | + | 4.68592i | −0.430111 | + | 0.194909i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.0603 | + | 21.7388i | −0.791437 | + | 0.902655i | ||||
\(581\) | 11.3238 | − | 13.4951i | 0.469788 | − | 0.559872i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.1142 | − | 5.50114i | −0.625968 | − | 0.227834i | ||||
\(584\) | −32.9784 | + | 7.69506i | −1.36466 | + | 0.318424i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.1706 | + | 36.3731i | −0.420143 | + | 1.50256i | ||||
\(587\) | −4.19636 | + | 0.739932i | −0.173202 | + | 0.0305402i | −0.259577 | − | 0.965723i | \(-0.583583\pi\) |
0.0863743 | + | 0.996263i | \(0.472472\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.72984 | + | 26.7325i | 0.400911 | + | 1.10149i | ||||
\(590\) | −11.9294 | − | 17.4368i | −0.491127 | − | 0.717863i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.4597 | + | 14.9279i | 0.470989 | + | 0.613533i | ||||
\(593\) | −14.8627 | −0.610340 | −0.305170 | − | 0.952298i | \(-0.598713\pi\) | ||||
−0.305170 | + | 0.952298i | \(0.598713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.5265i | 0.513537i | ||||||||
\(596\) | 1.49024 | − | 1.19631i | 0.0610426 | − | 0.0490026i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.24349 | − | 2.90319i | 0.173529 | − | 0.118720i | ||||
\(599\) | −4.35844 | + | 1.58634i | −0.178081 | + | 0.0648162i | −0.429522 | − | 0.903057i | \(-0.641318\pi\) |
0.251441 | + | 0.967873i | \(0.419096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.59673 | + | 14.7268i | 0.105923 | + | 0.600718i | 0.990848 | + | 0.134985i | \(0.0430985\pi\) |
−0.884925 | + | 0.465734i | \(0.845790\pi\) | |||||||
\(602\) | −2.43066 | + | 8.69281i | −0.0990665 | + | 0.354292i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.90270 | + | 1.15431i | 0.0774200 | + | 0.0469683i | ||||
\(605\) | 2.84323 | − | 7.81171i | 0.115594 | − | 0.317591i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.7989 | − | 11.5786i | −0.560079 | − | 0.469962i | 0.318258 | − | 0.948004i | \(-0.396902\pi\) |
−0.878337 | + | 0.478042i | \(0.841347\pi\) | |||||||
\(608\) | 1.43162 | + | 43.3772i | 0.0580600 | + | 1.75918i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.66876 | − | 0.756213i | 0.0675662 | − | 0.0306182i | ||||
\(611\) | −0.256573 | − | 0.148133i | −0.0103798 | − | 0.00599281i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.2514 | + | 15.1562i | −1.06028 | + | 0.612155i | −0.925511 | − | 0.378722i | \(-0.876364\pi\) |
−0.134772 | + | 0.990877i | \(0.543030\pi\) | |||||||
\(614\) | 4.10665 | − | 5.73147i | 0.165731 | − | 0.231303i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.55645 | − | 14.9166i | 0.304458 | − | 0.601008i | ||||
\(617\) | 2.22018 | − | 12.5913i | 0.0893810 | − | 0.506905i | −0.906944 | − | 0.421251i | \(-0.861591\pi\) |
0.996325 | − | 0.0856536i | \(-0.0272978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8907 | + | 14.1707i | 0.477926 | + | 0.569570i | 0.950104 | − | 0.311933i | \(-0.100977\pi\) |
−0.472178 | + | 0.881503i | \(0.656532\pi\) | |||||||
\(620\) | −13.1934 | − | 0.286470i | −0.529858 | − | 0.0115049i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.3845 | + | 16.0326i | −0.656960 | + | 0.642850i | ||||
\(623\) | −4.20447 | + | 3.52797i | −0.168448 | + | 0.141345i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.16567 | + | 12.2821i | −0.0866269 | + | 0.491286i | ||||
\(626\) | −8.39398 | + | 17.5024i | −0.335491 | + | 0.699536i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.18894 | − | 14.2117i | −0.0873481 | − | 0.567107i | ||||
\(629\) | −12.2047 | + | 7.04640i | −0.486634 | + | 0.280958i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.30167 | − | 7.45072i | 0.171247 | − | 0.296608i | −0.767609 | − | 0.640918i | \(-0.778554\pi\) |
0.938856 | + | 0.344310i | \(0.111887\pi\) | |||||||
\(632\) | 12.9811 | + | 30.3836i | 0.516361 | + | 1.20859i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.601272 | + | 7.85354i | 0.0238796 | + | 0.311904i | ||||
\(635\) | −23.0989 | + | 27.5281i | −0.916650 | + | 1.09242i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.282736 | − | 0.776812i | 0.0112024 | − | 0.0307784i | ||||
\(638\) | 7.17656 | + | 27.9953i | 0.284123 | + | 1.10835i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.9950 | − | 6.67190i | −0.750843 | − | 0.263730i | ||||
\(641\) | 1.04346 | + | 5.91773i | 0.0412140 | + | 0.233736i | 0.998456 | − | 0.0555530i | \(-0.0176922\pi\) |
−0.957242 | + | 0.289289i | \(0.906581\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.03942 | + | 22.0881i | 0.317044 | + | 0.871070i | 0.991187 | + | 0.132470i | \(0.0422908\pi\) |
−0.674143 | + | 0.738601i | \(0.735487\pi\) | |||||||
\(644\) | −29.9487 | − | 5.95384i | −1.18014 | − | 0.234614i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −32.3443 | − | 3.18389i | −1.27257 | − | 0.125268i | ||||
\(647\) | 10.6875 | 0.420169 | 0.210085 | − | 0.977683i | \(-0.432626\pi\) | ||||
0.210085 | + | 0.977683i | \(0.432626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.1191 | −0.828998 | ||||||||
\(650\) | 1.44403 | + | 0.142146i | 0.0566394 | + | 0.00557544i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.305423 | − | 1.53632i | 0.0119613 | − | 0.0601670i | ||||
\(653\) | −7.40542 | − | 20.3462i | −0.289796 | − | 0.796209i | −0.996094 | − | 0.0882946i | \(-0.971858\pi\) |
0.706298 | − | 0.707915i | \(-0.250364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.18835 | − | 23.7533i | −0.163653 | − | 0.928120i | ||||
\(656\) | 13.6973 | + | 26.2985i | 0.534788 | + | 1.02678i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.436908 | + | 1.70435i | 0.0170324 | + | 0.0664426i | ||||
\(659\) | 6.12164 | − | 16.8191i | 0.238465 | − | 0.655177i | −0.761510 | − | 0.648153i | \(-0.775542\pi\) |
0.999975 | − | 0.00702451i | \(-0.00223599\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6447 | − | 18.6447i | 0.608510 | − | 0.725194i | −0.370539 | − | 0.928817i | \(-0.620827\pi\) |
0.979049 | + | 0.203623i | \(0.0652716\pi\) | |||||||
\(662\) | −2.49751 | − | 32.6214i | −0.0970687 | − | 1.26787i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.4976 | + | 8.33017i | −0.756652 | + | 0.323273i | ||||
\(665\) | 16.0424 | − | 27.7863i | 0.622098 | − | 1.07751i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.7045 | − | 26.3875i | 1.76968 | − | 1.02173i | ||||
\(668\) | −28.0633 | + | 4.32243i | −1.08580 | + | 0.167240i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.24001 | − | 13.0111i | 0.241073 | − | 0.502663i | ||||
\(671\) | 0.318022 | − | 1.80359i | 0.0122771 | − | 0.0696270i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.83345 | − | 6.57304i | 0.301957 | − | 0.253372i | −0.479201 | − | 0.877705i | \(-0.659074\pi\) |
0.781158 | + | 0.624333i | \(0.214629\pi\) | |||||||
\(674\) | −4.62225 | + | 4.52298i | −0.178042 | + | 0.174219i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.550812 | − | 25.3677i | 0.0211851 | − | 0.975679i | ||||
\(677\) | −18.4828 | − | 22.0270i | −0.710352 | − | 0.846565i | 0.283303 | − | 0.959030i | \(-0.408570\pi\) |
−0.993656 | + | 0.112465i | \(0.964125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.03274 | + | 34.2133i | −0.231515 | + | 1.31299i | ||||
\(680\) | 6.81302 | − | 13.4491i | 0.261268 | − | 0.515749i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.68318 | + | 10.7231i | −0.294204 | + | 0.410608i | ||||
\(683\) | 28.1049 | − | 16.2264i | 1.07540 | − | 0.620885i | 0.145751 | − | 0.989321i | \(-0.453440\pi\) |
0.929653 | + | 0.368436i | \(0.120107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.4458 | + | 7.18559i | 0.475530 | + | 0.274547i | ||||
\(686\) | −25.6620 | + | 11.6289i | −0.979778 | + | 0.443995i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.33759 | − | 8.01101i | 0.279743 | − | 0.305417i | ||||
\(689\) | −2.74096 | − | 2.29994i | −0.104422 | − | 0.0876208i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.17035 | + | 25.1953i | −0.348856 | + | 0.958475i | 0.633875 | + | 0.773436i | \(0.281463\pi\) |
−0.982731 | + | 0.185039i | \(0.940759\pi\) | |||||||
\(692\) | 12.4863 | − | 20.5818i | 0.474659 | − | 0.782402i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.79300 | − | 24.2939i | 0.257859 | − | 0.922183i | ||||
\(695\) | 5.92427 | + | 33.5982i | 0.224721 | + | 1.27445i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.8655 | + | 7.59443i | −0.790338 | + | 0.287660i | ||||
\(698\) | 20.1652 | − | 13.7960i | 0.763263 | − | 0.522188i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.39445 | − | 6.71988i | −0.203891 | − | 0.253988i | ||||
\(701\) | − | 26.7362i | − | 1.00981i | −0.863174 | − | 0.504907i | \(-0.831527\pi\) | ||
0.863174 | − | 0.504907i | \(-0.168473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.0966 | 1.36141 | ||||||||
\(704\) | −16.2259 | + | 11.9054i | −0.611538 | + | 0.448700i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.3711 | − | 32.6991i | −0.841949 | − | 1.23065i | ||||
\(707\) | −9.85503 | − | 27.0765i | −0.370636 | − | 1.01832i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.4005 | − | 7.30003i | 1.55483 | − | 0.274158i | 0.670817 | − | 0.741623i | \(-0.265943\pi\) |
0.884012 | + | 0.467464i | \(0.154832\pi\) | |||||||
\(710\) | −10.0108 | + | 35.8016i | −0.375697 | + | 1.34361i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.43294 | − | 1.50104i | 0.241084 | − | 0.0562538i | ||||
\(713\) | 22.6361 | + | 8.23887i | 0.847729 | + | 0.308548i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.61030 | + | 1.91908i | −0.0602219 | + | 0.0717697i | ||||
\(716\) | −11.1436 | − | 9.77056i | −0.416456 | − | 0.365143i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.6995 | + | 13.9118i | −1.14570 | + | 0.519182i | ||||
\(719\) | −7.75793 | + | 13.4371i | −0.289322 | + | 0.501121i | −0.973648 | − | 0.228056i | \(-0.926763\pi\) |
0.684326 | + | 0.729176i | \(0.260097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.6084 | + | 23.5704i | 0.506803 | + | 0.877809i | ||||
\(722\) | 45.8263 | + | 32.8350i | 1.70548 | + | 1.22199i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.2665 | − | 8.91941i | 0.976187 | − | 0.331487i | ||||
\(725\) | 14.6674 | + | 2.58626i | 0.544734 | + | 0.0960512i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.76072 | + | 5.67292i | −0.250741 | + | 0.210397i | −0.759491 | − | 0.650517i | \(-0.774552\pi\) |
0.508750 | + | 0.860914i | \(0.330108\pi\) | |||||||
\(728\) | 2.71455 | − | 2.54327i | 0.100608 | − | 0.0942600i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.0731 | − | 21.5356i | −0.779949 | − | 0.797068i | ||||
\(731\) | 5.22917 | + | 6.23188i | 0.193408 | + | 0.230494i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.4479 | − | 3.07653i | −0.644452 | − | 0.113634i | −0.158136 | − | 0.987417i | \(-0.550549\pi\) |
−0.486316 | + | 0.873783i | \(0.661660\pi\) | |||||||
\(734\) | 0.204109 | − | 0.425590i | 0.00753380 | − | 0.0157088i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.9162 | + | 22.6811i | 1.06586 | + | 0.836035i | ||||
\(737\) | −7.21231 | − | 12.4921i | −0.265669 | − | 0.460152i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.2476 | − | 13.9993i | −0.891961 | − | 0.514974i | −0.0173774 | − | 0.999849i | \(-0.505532\pi\) |
−0.874583 | + | 0.484875i | \(0.838865\pi\) | |||||||
\(740\) | −6.06714 | + | 15.6066i | −0.223033 | + | 0.573709i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.62213 | + | 21.1875i | 0.0595502 | + | 0.777817i | ||||
\(743\) | 0.976314 | + | 0.819225i | 0.0358175 | + | 0.0300544i | 0.660521 | − | 0.750808i | \(-0.270336\pi\) |
−0.624703 | + | 0.780862i | \(0.714780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.59778 | + | 0.581543i | 0.0585379 | + | 0.0213061i | ||||
\(746\) | −4.96137 | + | 1.27184i | −0.181649 | + | 0.0465653i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.25021 | − | 13.2120i | −0.265094 | − | 0.483080i | ||||
\(749\) | 9.14764 | − | 1.61298i | 0.334247 | − | 0.0589368i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.98866 | + | 3.27161i | −0.328001 | + | 0.119383i | −0.500771 | − | 0.865580i | \(-0.666950\pi\) |
0.172771 | + | 0.984962i | \(0.444728\pi\) | |||||||
\(752\) | 0.457892 | − | 2.06751i | 0.0166976 | − | 0.0753942i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.629827 | + | 6.39824i | −0.0229369 | + | 0.233010i | ||||
\(755\) | 1.98011i | 0.0720634i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.24463i | − | 0.190619i | −0.995448 | − | 0.0953096i | \(-0.969616\pi\) | ||
0.995448 | − | 0.0953096i | \(-0.0303841\pi\) | |||||||
\(758\) | −44.6457 | − | 4.39481i | −1.62161 | − | 0.159627i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −32.3365 | + | 21.1074i | −1.17297 | + | 0.765647i | ||||
\(761\) | −27.2099 | + | 9.90361i | −0.986360 | + | 0.359006i | −0.784310 | − | 0.620370i | \(-0.786983\pi\) |
−0.202050 | + | 0.979375i | \(0.564760\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.8713 | − | 2.09322i | 0.429768 | − | 0.0757797i | ||||
\(764\) | −14.5417 | + | 7.97988i | −0.526101 | + | 0.288702i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.72107 | − | 22.3176i | −0.206711 | − | 0.806366i | ||||
\(767\) | −4.41479 | − | 1.60685i | −0.159409 | − | 0.0580201i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0584 | − | 26.0611i | −1.11999 | − | 0.939786i | −0.121389 | − | 0.992605i | \(-0.538735\pi\) |
−0.998604 | + | 0.0528190i | \(0.983179\pi\) | |||||||
\(770\) | 14.8344 | − | 1.13573i | 0.534595 | − | 0.0409289i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.93269 | + | 17.8330i | −0.249513 | + | 0.641825i | ||||
\(773\) | 8.73768 | + | 5.04470i | 0.314273 | + | 0.181445i | 0.648837 | − | 0.760928i | \(-0.275256\pi\) |
−0.334564 | + | 0.942373i | \(0.608589\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.39906 | + | 5.88735i | 0.122098 | + | 0.211480i | ||||
\(776\) | 25.0853 | − | 33.4520i | 0.900509 | − | 1.20086i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.03717 | + | 1.45660i | 0.108888 | + | 0.0522216i | ||||
\(779\) | 56.0098 | + | 9.87604i | 2.00676 | + | 0.353846i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.8865 | + | 28.4668i | 0.854726 | + | 1.01862i | ||||
\(782\) | −19.6699 | + | 19.2474i | −0.703393 | + | 0.688286i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.90316 | + | 0.256473i | 0.210827 | + | 0.00915977i | ||||
\(785\) | 9.80068 | − | 8.22375i | 0.349801 | − | 0.293518i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | − | 2.46858i | −0.499046 | − | 0.0879952i | −0.0815410 | − | 0.996670i | \(-0.525984\pi\) |
−0.417505 | + | 0.908675i | \(0.637095\pi\) | |||||||
\(788\) | 27.4141 | − | 9.30910i | 0.976587 | − | 0.331623i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.1222 | + | 23.8967i | −0.609180 | + | 0.850206i | ||||
\(791\) | 11.7186 | + | 20.2971i | 0.416664 | + | 0.721683i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.203707 | − | 0.352831i | 0.00723385 | − | 0.0125294i | ||||
\(794\) | −9.95258 | − | 21.9627i | −0.353204 | − | 0.779426i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34.8933 | − | 39.7968i | 1.23676 | − | 1.41056i | ||||
\(797\) | −14.0727 | + | 16.7712i | −0.498482 | + | 0.594068i | −0.955354 | − | 0.295465i | \(-0.904525\pi\) |
0.456871 | + | 0.889533i | \(0.348970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.49013 | + | 0.542363i | 0.0527170 | + | 0.0191874i | ||||
\(800\) | 2.13689 | + | 10.1488i | 0.0755504 | + | 0.358813i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −54.0505 | − | 15.1135i | −1.90859 | − | 0.533676i | ||||
\(803\) | −29.6617 | + | 5.23016i | −1.04674 | + | 0.184568i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.29208 | − | 25.5298i | −0.327503 | − | 0.899806i | ||||
\(806\) | −2.42198 | + | 1.65700i | −0.0853105 | + | 0.0583654i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.14572 | + | 34.4306i | −0.145846 | + | 1.21127i | ||||
\(809\) | −40.9197 | −1.43866 | −0.719331 | − | 0.694668i | \(-0.755551\pi\) | ||||
−0.719331 | + | 0.694668i | \(0.755551\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0286i | 0.668185i | 0.942540 | + | 0.334093i | \(0.108430\pi\) | ||||
−0.942540 | + | 0.334093i | \(0.891570\pi\) | |||||||
\(812\) | 29.7747 | − | 23.9019i | 1.04489 | − | 0.838793i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.45118 | + | 13.8144i | 0.331264 | + | 0.484196i | ||||
\(815\) | 1.30964 | − | 0.476669i | 0.0458746 | − | 0.0166970i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.61830 | − | 20.5204i | −0.126588 | − | 0.717918i | ||||
\(818\) | −13.2120 | − | 3.69432i | −0.461947 | − | 0.129169i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.6841 | + | 22.5562i | −0.477871 | + | 0.787696i | ||||
\(821\) | −4.35542 | + | 11.9664i | −0.152005 | + | 0.417631i | −0.992200 | − | 0.124653i | \(-0.960218\pi\) |
0.840195 | + | 0.542284i | \(0.182440\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.3183 | + | 9.49719i | 0.394531 | + | 0.331051i | 0.818375 | − | 0.574684i | \(-0.194875\pi\) |
−0.423844 | + | 0.905735i | \(0.639320\pi\) | |||||||
\(824\) | −1.79096 | − | 32.7078i | −0.0623912 | − | 1.13943i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.5164 | + | 25.4136i | 0.400707 | + | 0.884253i | ||||
\(827\) | −18.0361 | − | 10.4132i | −0.627178 | − | 0.362101i | 0.152481 | − | 0.988306i | \(-0.451274\pi\) |
−0.779658 | + | 0.626205i | \(0.784607\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.5499 | − | 6.66836i | 0.401146 | − | 0.231602i | −0.285832 | − | 0.958280i | \(-0.592270\pi\) |
0.686978 | + | 0.726678i | \(0.258937\pi\) | |||||||
\(830\) | −15.3348 | − | 10.9875i | −0.532280 | − | 0.381383i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.29773 | + | 1.25417i | −0.148997 | + | 0.0434805i | ||||
\(833\) | −0.768348 | + | 4.35752i | −0.0266217 | + | 0.150979i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.2392 | − | 19.3531i | −0.561980 | − | 0.669742i | ||||
\(836\) | −0.837956 | + | 38.5921i | −0.0289813 | + | 1.33473i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32.7759 | − | 33.4953i | −1.13222 | − | 1.15708i | ||||
\(839\) | 9.48780 | − | 7.96121i | 0.327555 | − | 0.274852i | −0.464148 | − | 0.885758i | \(-0.653639\pi\) |
0.791703 | + | 0.610906i | \(0.209195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.42348 | + | 36.4294i | −0.221499 | + | 1.25619i | ||||
\(842\) | 40.1122 | + | 19.2374i | 1.38236 | + | 0.662966i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.46541 | + | 35.4841i | 0.188127 | + | 1.22141i | ||||
\(845\) | 19.5515 | − | 11.2881i | 0.672592 | − | 0.388321i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.48927 | + | 9.50769i | −0.188613 | + | 0.326688i | ||||
\(848\) | 9.78202 | − | 23.6302i | 0.335916 | − | 0.811464i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.74386 | + | 0.592875i | −0.265612 | + | 0.0203355i | ||||
\(851\) | 19.6470 | − | 23.4143i | 0.673489 | − | 0.802633i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.85840 | + | 24.3382i | −0.303306 | + | 0.833326i | 0.690614 | + | 0.723223i | \(0.257340\pi\) |
−0.993920 | + | 0.110103i | \(0.964882\pi\) | |||||||
\(854\) | −2.34377 | + | 0.600821i | −0.0802021 | + | 0.0205597i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.6986 | − | 3.24352i | −0.365672 | − | 0.110861i | ||||
\(857\) | −0.658395 | − | 3.73394i | −0.0224903 | − | 0.127549i | 0.971495 | − | 0.237058i | \(-0.0761832\pi\) |
−0.993986 | + | 0.109509i | \(0.965072\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7084 | − | 34.9159i | −0.433603 | − | 1.19132i | −0.943585 | − | 0.331130i | \(-0.892570\pi\) |
0.509982 | − | 0.860185i | \(-0.329652\pi\) | |||||||
\(860\) | 9.48028 | + | 1.88469i | 0.323275 | + | 0.0642674i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.33949 | − | 13.6076i | 0.0456233 | − | 0.463475i | ||||
\(863\) | −14.8041 | −0.503936 | −0.251968 | − | 0.967736i | \(-0.581078\pi\) | ||||
−0.251968 | + | 0.967736i | \(0.581078\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.4190 | 0.728269 | ||||||||
\(866\) | 2.77477 | − | 28.1881i | 0.0942904 | − | 0.957871i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17.0933 | + | 3.39816i | 0.580183 | + | 0.115341i | ||||
\(869\) | 10.0508 | + | 27.6143i | 0.340950 | + | 0.936752i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.557216 | − | 3.16013i | −0.0188805 | − | 0.107077i | ||||
\(872\) | −13.8840 | − | 4.20925i | −0.470173 | − | 0.142543i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 68.2813 | − | 17.5038i | 2.30965 | − | 0.592075i | ||||
\(875\) | 9.77385 | − | 26.8534i | 0.330416 | − | 0.907811i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8616 | − | 24.8619i | 0.704447 | − | 0.839527i | −0.288575 | − | 0.957457i | \(-0.593182\pi\) |
0.993022 | + | 0.117931i | \(0.0376260\pi\) | |||||||
\(878\) | −0.308194 | + | 0.0235956i | −0.0104011 | + | 0.000796311i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16.5447 | − | 6.84888i | −0.557720 | − | 0.230876i | ||||
\(881\) | −9.60040 | + | 16.6284i | −0.323446 | + | 0.560224i | −0.981197 | − | 0.193011i | \(-0.938175\pi\) |
0.657751 | + | 0.753235i | \(0.271508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.82855 | + | 1.63307i | −0.0951884 | + | 0.0549571i | −0.546839 | − | 0.837238i | \(-0.684169\pi\) |
0.451650 | + | 0.892195i | \(0.350836\pi\) | |||||||
\(884\) | −0.510361 | − | 3.31351i | −0.0171653 | − | 0.111446i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.7710 | − | 5.64525i | −0.395453 | − | 0.189656i | ||||
\(887\) | −4.93246 | + | 27.9734i | −0.165616 | + | 0.939255i | 0.782811 | + | 0.622259i | \(0.213785\pi\) |
−0.948427 | + | 0.316995i | \(0.897326\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.3547 | − | 30.5052i | 1.21930 | − | 1.02311i | ||||
\(890\) | 4.11062 | + | 4.20084i | 0.137788 | + | 0.140812i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.784614 | + | 36.1354i | −0.0262708 | + | 1.20990i | ||||
\(893\) | −2.61081 | − | 3.11144i | −0.0873674 | − | 0.104120i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.28979 | − | 12.9861i | 0.0765393 | − | 0.434076i | ||||
\(896\) | 23.1744 | + | 13.0334i | 0.774202 | + | 0.435414i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 47.7946 | + | 34.2452i | 1.59493 | + | 1.14278i | ||||
\(899\) | −26.0859 | + | 15.0607i | −0.870013 | + | 0.502302i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.5858 | + | 9.57584i | 0.552555 | + | 0.319018i | ||||
\(902\) | 10.8854 | + | 24.0212i | 0.362445 | + | 0.799819i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.54225 | − | 28.1656i | −0.0512944 | − | 0.936773i | ||||
\(905\) | 18.9069 | + | 15.8648i | 0.628487 | + | 0.527363i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.87326 | − | 10.6417i | 0.128609 | − | 0.353351i | −0.858630 | − | 0.512596i | \(-0.828684\pi\) |
0.987239 | + | 0.159245i | \(0.0509059\pi\) | |||||||
\(908\) | −6.28969 | + | 10.3676i | −0.208731 | + | 0.344061i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.18743 | + | 0.891263i | 0.105662 | + | 0.0295451i | ||||
\(911\) | 1.07530 | + | 6.09830i | 0.0356261 | + | 0.202046i | 0.997426 | − | 0.0717092i | \(-0.0228454\pi\) |
−0.961799 | + | 0.273755i | \(0.911734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.7205 | + | 6.44973i | −0.586463 | + | 0.213455i | ||||
\(914\) | 1.28354 | + | 1.87611i | 0.0424559 | + | 0.0620562i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.1379 | − | 29.0101i | 1.19403 | − | 0.958521i | ||||
\(917\) | 31.8535i | 1.05190i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.3693 | 1.26569 | 0.632844 | − | 0.774279i | \(-0.281887\pi\) | ||||
0.632844 | + | 0.774279i | \(0.281887\pi\) | |||||||
\(920\) | −3.90891 | + | 32.4639i | −0.128873 | + | 1.07030i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.1166 | + | 19.9202i | −0.958904 | + | 0.656036i | ||||
\(923\) | 2.82739 | + | 7.76819i | 0.0930646 | + | 0.255693i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.49480 | − | 1.49786i | 0.279307 | − | 0.0492494i | ||||
\(926\) | 49.4067 | + | 13.8150i | 1.62360 | + | 0.453989i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −44.9675 | + | 9.46820i | −1.47613 | + | 0.310809i | ||||
\(929\) | 24.3789 | + | 8.87320i | 0.799846 | + | 0.291120i | 0.709423 | − | 0.704783i | \(-0.248956\pi\) |
0.0904233 | + | 0.995903i | \(0.471178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.28491 | − | 8.68182i | 0.238753 | − | 0.284535i | ||||
\(932\) | 12.2265 | − | 13.9447i | 0.400494 | − | 0.456774i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.64205 | − | 10.2438i | −0.151893 | − | 0.335186i | ||||
\(935\) | 6.70452 | − | 11.6126i | 0.219261 | − | 0.379772i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.82408 | + | 17.0158i | 0.320939 | + | 0.555882i | 0.980682 | − | 0.195609i | \(-0.0626684\pi\) |
−0.659743 | + | 0.751491i | \(0.729335\pi\) | |||||||
\(938\) | −11.0994 | + | 15.4909i | −0.362408 | + | 0.505797i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.78408 | − | 0.605825i | 0.0581901 | − | 0.0197598i | ||||
\(941\) | −13.6658 | − | 2.40964i | −0.445491 | − | 0.0785520i | −0.0535973 | − | 0.998563i | \(-0.517069\pi\) |
−0.391894 | + | 0.920011i | \(0.628180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.8917 | − | 30.9558i | 1.20136 | − | 1.00806i | ||||
\(944\) | 1.45760 | − | 33.5490i | 0.0474407 | − | 1.09193i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.90594 | − | 6.75761i | 0.224531 | − | 0.219709i | ||||
\(947\) | 22.0765 | + | 26.3098i | 0.717391 | + | 0.854953i | 0.994375 | − | 0.105921i | \(-0.0337792\pi\) |
−0.276984 | + | 0.960875i | \(0.589335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.59849 | − | 1.16349i | −0.214196 | − | 0.0377685i | ||||
\(950\) | 17.9367 | + | 8.60227i | 0.581943 | + | 0.279094i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.9451 | + | 15.9291i | −0.387142 | + | 0.516266i | ||||
\(953\) | −7.72473 | − | 13.3796i | −0.250228 | − | 0.433408i | 0.713360 | − | 0.700798i | \(-0.247172\pi\) |
−0.963589 | + | 0.267389i | \(0.913839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.7813 | − | 7.37926i | −0.413592 | − | 0.238787i | ||||
\(956\) | −6.81073 | + | 17.5193i | −0.220275 | + | 0.566615i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.0951 | − | 1.76817i | 0.746168 | − | 0.0571271i | ||||
\(959\) | −14.5389 | − | 12.1996i | −0.469484 | − | 0.393944i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.2109 | + | 5.90028i | 0.522932 | + | 0.190332i | ||||
\(962\) | 0.924623 | + | 3.60690i | 0.0298110 | + | 0.116291i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46.8577 | − | 25.7135i | 1.50918 | − | 0.828177i | ||||
\(965\) | −16.7651 | + | 2.95613i | −0.539687 | + | 0.0951613i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.1303 | + | 8.41874i | −0.743820 | + | 0.270728i | −0.686003 | − | 0.727599i | \(-0.740636\pi\) |
−0.0578171 | + | 0.998327i | \(0.518414\pi\) | |||||||
\(968\) | 11.0647 | − | 7.22237i | 0.355632 | − | 0.232136i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 37.0238 | + | 3.64453i | 1.18876 | + | 0.117019i | ||||
\(971\) | 14.5202i | 0.465977i | 0.972480 | + | 0.232988i | \(0.0748504\pi\) | ||||
−0.972480 | + | 0.232988i | \(0.925150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 45.0556i | − | 1.44442i | ||||||
\(974\) | −0.587571 | + | 5.96898i | −0.0188270 | + | 0.191258i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.84316 | + | 0.629677i | 0.0910075 | + | 0.0201555i | ||||
\(977\) | −1.09977 | + | 0.400283i | −0.0351847 | + | 0.0128062i | −0.359553 | − | 0.933125i | \(-0.617071\pi\) |
0.324368 | + | 0.945931i | \(0.394848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.78596 | − | 1.02022i | 0.184920 | − | 0.0326064i | ||||
\(980\) | 2.52918 | + | 4.60892i | 0.0807917 | + | 0.147226i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.2645 | − | 4.42573i | 0.550933 | − | 0.141231i | ||||
\(983\) | 10.8380 | + | 3.94472i | 0.345679 | + | 0.125817i | 0.509025 | − | 0.860752i | \(-0.330006\pi\) |
−0.163345 | + | 0.986569i | \(0.552228\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.7330 | + | 16.5579i | 0.628745 | + | 0.527579i | ||||
\(986\) | −2.62693 | − | 34.3118i | −0.0836586 | − | 1.09271i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.11146 | + | 8.00363i | −0.0989886 | + | 0.254629i | ||||
\(989\) | −15.2801 | − | 8.82198i | −0.485879 | − | 0.280523i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.8387 | − | 49.9500i | −0.916091 | − | 1.58672i | −0.805297 | − | 0.592872i | \(-0.797994\pi\) |
−0.110794 | − | 0.993843i | \(-0.535339\pi\) | |||||||
\(992\) | −16.5039 | − | 12.9453i | −0.524001 | − | 0.411012i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.2300 | − | 44.2669i | 0.673374 | − | 1.40406i | ||||
\(995\) | 46.3767 | + | 8.17746i | 1.47024 | + | 0.259243i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.71942 | − | 2.04913i | −0.0544547 | − | 0.0648966i | 0.738130 | − | 0.674659i | \(-0.235709\pi\) |
−0.792584 | + | 0.609762i | \(0.791265\pi\) | |||||||
\(998\) | −16.0867 | − | 16.4397i | −0.509214 | − | 0.520391i | ||||
\(999\) | 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 | 648.2.t.a.37.16 | 204 | ||
3.2 | odd | 2 | 216.2.t.a.157.19 | ✓ | 204 | ||
8.5 | even | 2 | inner | 648.2.t.a.37.1 | 204 | ||
12.11 | even | 2 | 864.2.bf.a.49.17 | 204 | |||
24.5 | odd | 2 | 216.2.t.a.157.34 | yes | 204 | ||
24.11 | even | 2 | 864.2.bf.a.49.18 | 204 | |||
27.11 | odd | 18 | 216.2.t.a.205.34 | yes | 204 | ||
27.16 | even | 9 | inner | 648.2.t.a.613.1 | 204 | ||
108.11 | even | 18 | 864.2.bf.a.529.18 | 204 | |||
216.11 | even | 18 | 864.2.bf.a.529.17 | 204 | |||
216.173 | odd | 18 | 216.2.t.a.205.19 | yes | 204 | ||
216.205 | even | 18 | inner | 648.2.t.a.613.16 | 204 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.t.a.157.19 | ✓ | 204 | 3.2 | odd | 2 | ||
216.2.t.a.157.34 | yes | 204 | 24.5 | odd | 2 | ||
216.2.t.a.205.19 | yes | 204 | 216.173 | odd | 18 | ||
216.2.t.a.205.34 | yes | 204 | 27.11 | odd | 18 | ||
648.2.t.a.37.1 | 204 | 8.5 | even | 2 | inner | ||
648.2.t.a.37.16 | 204 | 1.1 | even | 1 | trivial | ||
648.2.t.a.613.1 | 204 | 27.16 | even | 9 | inner | ||
648.2.t.a.613.16 | 204 | 216.205 | even | 18 | inner | ||
864.2.bf.a.49.17 | 204 | 12.11 | even | 2 | |||
864.2.bf.a.49.18 | 204 | 24.11 | even | 2 | |||
864.2.bf.a.529.17 | 204 | 216.11 | even | 18 | |||
864.2.bf.a.529.18 | 204 | 108.11 | even | 18 |