Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(25,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.l (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 129.23 | ||
Character | \(\chi\) | \(=\) | 403.129 |
Dual form | 403.2.l.c.25.12 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.921357i | 0.651498i | 0.945456 | + | 0.325749i | \(0.105616\pi\) | ||||
−0.945456 | + | 0.325749i | \(0.894384\pi\) | |||||||
\(3\) | −0.264605 | + | 0.458309i | −0.152770 | + | 0.264605i | −0.932245 | − | 0.361829i | \(-0.882153\pi\) |
0.779475 | + | 0.626433i | \(0.215486\pi\) | |||||||
\(4\) | 1.15110 | 0.575551 | ||||||||
\(5\) | −2.89414 | + | 1.67093i | −1.29430 | + | 0.747263i | −0.979413 | − | 0.201867i | \(-0.935299\pi\) |
−0.314884 | + | 0.949130i | \(0.601966\pi\) | |||||||
\(6\) | −0.422266 | − | 0.243795i | −0.172389 | − | 0.0995291i | ||||
\(7\) | −0.336375 | − | 0.194206i | −0.127138 | − | 0.0734029i | 0.435082 | − | 0.900391i | \(-0.356719\pi\) |
−0.562220 | + | 0.826988i | \(0.690053\pi\) | |||||||
\(8\) | 2.90329i | 1.02647i | ||||||||
\(9\) | 1.35997 | + | 2.35553i | 0.453323 | + | 0.785178i | ||||
\(10\) | −1.53952 | − | 2.66653i | −0.486840 | − | 0.843232i | ||||
\(11\) | 1.48736 | − | 0.858726i | 0.448455 | − | 0.258916i | −0.258722 | − | 0.965952i | \(-0.583301\pi\) |
0.707178 | + | 0.707036i | \(0.249968\pi\) | |||||||
\(12\) | −0.304587 | + | 0.527560i | −0.0879267 | + | 0.152293i | ||||
\(13\) | −2.58614 | − | 2.51235i | −0.717266 | − | 0.696799i | ||||
\(14\) | 0.178933 | − | 0.309921i | 0.0478218 | − | 0.0828299i | ||||
\(15\) | − | 1.76854i | − | 0.456636i | ||||||
\(16\) | −0.372763 | −0.0931908 | ||||||||
\(17\) | −3.39637 | + | 5.88269i | −0.823741 | + | 1.42676i | 0.0791365 | + | 0.996864i | \(0.474784\pi\) |
−0.902878 | + | 0.429898i | \(0.858550\pi\) | |||||||
\(18\) | −2.17029 | + | 1.25302i | −0.511542 | + | 0.295339i | ||||
\(19\) | −3.04784 | − | 1.75967i | −0.699222 | − | 0.403696i | 0.107836 | − | 0.994169i | \(-0.465608\pi\) |
−0.807057 | + | 0.590473i | \(0.798941\pi\) | |||||||
\(20\) | −3.33144 | + | 1.92341i | −0.744934 | + | 0.430088i | ||||
\(21\) | 0.178013 | − | 0.102776i | 0.0388455 | − | 0.0224275i | ||||
\(22\) | 0.791193 | + | 1.37039i | 0.168683 | + | 0.292167i | ||||
\(23\) | −5.13958 | −1.07168 | −0.535838 | − | 0.844321i | \(-0.680004\pi\) | ||||
−0.535838 | + | 0.844321i | \(0.680004\pi\) | |||||||
\(24\) | −1.33060 | − | 0.768224i | −0.271608 | − | 0.156813i | ||||
\(25\) | 3.08402 | − | 5.34167i | 0.616803 | − | 1.06833i | ||||
\(26\) | 2.31477 | − | 2.38276i | 0.453963 | − | 0.467297i | ||||
\(27\) | −3.02705 | −0.582555 | ||||||||
\(28\) | −0.387201 | − | 0.223551i | −0.0731741 | − | 0.0422471i | ||||
\(29\) | 6.43390 | 1.19474 | 0.597372 | − | 0.801964i | \(-0.296212\pi\) | ||||
0.597372 | + | 0.801964i | \(0.296212\pi\) | |||||||
\(30\) | 1.62946 | 0.297498 | ||||||||
\(31\) | 1.53653 | + | 5.35155i | 0.275969 | + | 0.961167i | ||||
\(32\) | 5.46313i | 0.965754i | ||||||||
\(33\) | 0.908892i | 0.158218i | ||||||||
\(34\) | −5.42006 | − | 3.12927i | −0.929532 | − | 0.536665i | ||||
\(35\) | 1.29802 | 0.219405 | ||||||||
\(36\) | 1.56546 | + | 2.71146i | 0.260910 | + | 0.451910i | ||||
\(37\) | 8.23736 | + | 4.75584i | 1.35421 | + | 0.781855i | 0.988837 | − | 0.149004i | \(-0.0476068\pi\) |
0.365377 | + | 0.930860i | \(0.380940\pi\) | |||||||
\(38\) | 1.62128 | − | 2.80815i | 0.263007 | − | 0.455541i | ||||
\(39\) | 1.83574 | − | 0.520472i | 0.293953 | − | 0.0833423i | ||||
\(40\) | −4.85119 | − | 8.40251i | −0.767041 | − | 1.32855i | ||||
\(41\) | −2.23586 | + | 1.29088i | −0.349183 | + | 0.201601i | −0.664326 | − | 0.747443i | \(-0.731281\pi\) |
0.315142 | + | 0.949044i | \(0.397948\pi\) | |||||||
\(42\) | 0.0946930 | + | 0.164013i | 0.0146115 | + | 0.0253078i | ||||
\(43\) | −0.0134584 | + | 0.0233107i | −0.00205239 | + | 0.00355485i | −0.867050 | − | 0.498222i | \(-0.833987\pi\) |
0.864997 | + | 0.501776i | \(0.167320\pi\) | |||||||
\(44\) | 1.71210 | − | 0.988481i | 0.258109 | − | 0.149019i | ||||
\(45\) | −7.87187 | − | 4.54483i | −1.17347 | − | 0.677503i | ||||
\(46\) | − | 4.73539i | − | 0.698194i | ||||||
\(47\) | − | 8.52072i | − | 1.24287i | −0.783464 | − | 0.621437i | \(-0.786549\pi\) | ||
0.783464 | − | 0.621437i | \(-0.213451\pi\) | |||||||
\(48\) | 0.0986349 | − | 0.170841i | 0.0142367 | − | 0.0246587i | ||||
\(49\) | −3.42457 | − | 5.93153i | −0.489224 | − | 0.847361i | ||||
\(50\) | 4.92159 | + | 2.84148i | 0.696018 | + | 0.401846i | ||||
\(51\) | −1.79739 | − | 3.11317i | −0.251685 | − | 0.435932i | ||||
\(52\) | −2.97691 | − | 2.89196i | −0.412823 | − | 0.401043i | ||||
\(53\) | 5.34839 | + | 9.26368i | 0.734658 | + | 1.27246i | 0.954873 | + | 0.297013i | \(0.0959905\pi\) |
−0.220216 | + | 0.975451i | \(0.570676\pi\) | |||||||
\(54\) | − | 2.78899i | − | 0.379533i | ||||||
\(55\) | −2.86974 | + | 4.97054i | −0.386956 | + | 0.670228i | ||||
\(56\) | 0.563836 | − | 0.976592i | 0.0753457 | − | 0.130503i | ||||
\(57\) | 1.61294 | − | 0.931234i | 0.213640 | − | 0.123345i | ||||
\(58\) | 5.92791i | 0.778373i | ||||||||
\(59\) | 2.19840 | + | 1.26924i | 0.286207 | + | 0.165242i | 0.636230 | − | 0.771499i | \(-0.280493\pi\) |
−0.350023 | + | 0.936741i | \(0.613826\pi\) | |||||||
\(60\) | − | 2.03577i | − | 0.262817i | ||||||
\(61\) | 9.90394 | 1.26807 | 0.634035 | − | 0.773304i | \(-0.281398\pi\) | ||||
0.634035 | + | 0.773304i | \(0.281398\pi\) | |||||||
\(62\) | −4.93069 | + | 1.41569i | −0.626198 | + | 0.179793i | ||||
\(63\) | − | 1.05646i | − | 0.133101i | ||||||
\(64\) | −5.77902 | −0.722377 | ||||||||
\(65\) | 11.6826 | + | 2.94981i | 1.44905 | + | 0.365879i | ||||
\(66\) | −0.837414 | −0.103079 | ||||||||
\(67\) | −1.42755 | + | 0.824195i | −0.174403 | + | 0.100691i | −0.584660 | − | 0.811278i | \(-0.698772\pi\) |
0.410257 | + | 0.911970i | \(0.365439\pi\) | |||||||
\(68\) | −3.90957 | + | 6.77157i | −0.474105 | + | 0.821173i | ||||
\(69\) | 1.35996 | − | 2.35551i | 0.163720 | − | 0.283571i | ||||
\(70\) | 1.19594i | 0.142942i | ||||||||
\(71\) | 13.4306 | − | 7.75418i | 1.59392 | − | 0.920252i | 0.601298 | − | 0.799025i | \(-0.294651\pi\) |
0.992625 | − | 0.121226i | \(-0.0386827\pi\) | |||||||
\(72\) | −6.83880 | + | 3.94838i | −0.805960 | + | 0.465321i | ||||
\(73\) | 0.522668 | − | 0.301763i | 0.0611737 | − | 0.0353187i | −0.469101 | − | 0.883144i | \(-0.655422\pi\) |
0.530275 | + | 0.847826i | \(0.322089\pi\) | |||||||
\(74\) | −4.38183 | + | 7.58955i | −0.509377 | + | 0.882267i | ||||
\(75\) | 1.63209 | + | 2.82686i | 0.188458 | + | 0.326418i | ||||
\(76\) | −3.50837 | − | 2.02556i | −0.402437 | − | 0.232347i | ||||
\(77\) | −0.667079 | −0.0760207 | ||||||||
\(78\) | 0.479541 | + | 1.69137i | 0.0542973 | + | 0.191510i | ||||
\(79\) | −1.05400 | + | 1.82557i | −0.118584 | + | 0.205393i | −0.919207 | − | 0.393775i | \(-0.871169\pi\) |
0.800623 | + | 0.599169i | \(0.204502\pi\) | |||||||
\(80\) | 1.07883 | − | 0.622861i | 0.120617 | − | 0.0696380i | ||||
\(81\) | −3.27894 | + | 5.67928i | −0.364326 | + | 0.631031i | ||||
\(82\) | −1.18936 | − | 2.06003i | −0.131343 | − | 0.227492i | ||||
\(83\) | 14.4287 | − | 8.33039i | 1.58375 | − | 0.914379i | 0.589446 | − | 0.807808i | \(-0.299346\pi\) |
0.994305 | − | 0.106571i | \(-0.0339871\pi\) | |||||||
\(84\) | 0.204911 | − | 0.118305i | 0.0223576 | − | 0.0129082i | ||||
\(85\) | − | 22.7004i | − | 2.46220i | ||||||
\(86\) | −0.0214775 | − | 0.0124000i | −0.00231598 | − | 0.00133713i | ||||
\(87\) | −1.70244 | + | 2.94871i | −0.182521 | + | 0.316135i | ||||
\(88\) | 2.49313 | + | 4.31823i | 0.265769 | + | 0.460325i | ||||
\(89\) | 12.7022i | 1.34643i | 0.739446 | + | 0.673216i | \(0.235088\pi\) | ||||
−0.739446 | + | 0.673216i | \(0.764912\pi\) | |||||||
\(90\) | 4.18741 | − | 7.25280i | 0.441391 | − | 0.764512i | ||||
\(91\) | 0.381999 | + | 1.34733i | 0.0400444 | + | 0.141239i | ||||
\(92\) | −5.91617 | −0.616804 | ||||||||
\(93\) | −2.85924 | − | 0.711841i | −0.296489 | − | 0.0738145i | ||||
\(94\) | 7.85063 | 0.809730 | ||||||||
\(95\) | 11.7611 | 1.20667 | ||||||||
\(96\) | −2.50380 | − | 1.44557i | −0.255543 | − | 0.147538i | ||||
\(97\) | − | 1.89406i | − | 0.192313i | −0.995366 | − | 0.0961564i | \(-0.969345\pi\) | ||
0.995366 | − | 0.0961564i | \(-0.0306549\pi\) | |||||||
\(98\) | 5.46505 | − | 3.15525i | 0.552054 | − | 0.318728i | ||||
\(99\) | 4.04552 | + | 2.33568i | 0.406590 | + | 0.234745i | ||||
\(100\) | 3.55002 | − | 6.14881i | 0.355002 | − | 0.614881i | ||||
\(101\) | 7.21921 | 0.718338 | 0.359169 | − | 0.933272i | \(-0.383060\pi\) | ||||
0.359169 | + | 0.933272i | \(0.383060\pi\) | |||||||
\(102\) | 2.86835 | − | 1.65604i | 0.284009 | − | 0.163972i | ||||
\(103\) | 5.75322 | + | 9.96487i | 0.566882 | + | 0.981868i | 0.996872 | + | 0.0790344i | \(0.0251837\pi\) |
−0.429990 | + | 0.902834i | \(0.641483\pi\) | |||||||
\(104\) | 7.29407 | − | 7.50831i | 0.715242 | − | 0.736251i | ||||
\(105\) | −0.343462 | + | 0.594893i | −0.0335184 | + | 0.0580556i | ||||
\(106\) | −8.53516 | + | 4.92777i | −0.829008 | + | 0.478628i | ||||
\(107\) | −5.39261 | + | 9.34028i | −0.521324 | + | 0.902959i | 0.478369 | + | 0.878159i | \(0.341228\pi\) |
−0.999692 | + | 0.0247999i | \(0.992105\pi\) | |||||||
\(108\) | −3.48444 | −0.335290 | ||||||||
\(109\) | − | 5.01983i | − | 0.480813i | −0.970672 | − | 0.240406i | \(-0.922719\pi\) | ||
0.970672 | − | 0.240406i | \(-0.0772807\pi\) | |||||||
\(110\) | −4.57964 | − | 2.64406i | −0.436652 | − | 0.252101i | ||||
\(111\) | −4.35929 | + | 2.51684i | −0.413765 | + | 0.238888i | ||||
\(112\) | 0.125388 | + | 0.0723928i | 0.0118481 | + | 0.00684048i | ||||
\(113\) | −5.61711 | − | 9.72911i | −0.528413 | − | 0.915238i | −0.999451 | − | 0.0331252i | \(-0.989454\pi\) |
0.471038 | − | 0.882113i | \(-0.343879\pi\) | |||||||
\(114\) | 0.857999 | + | 1.48610i | 0.0803589 | + | 0.139186i | ||||
\(115\) | 14.8746 | − | 8.58787i | 1.38707 | − | 0.800823i | ||||
\(116\) | 7.40607 | 0.687636 | ||||||||
\(117\) | 2.40085 | − | 9.50845i | 0.221958 | − | 0.879057i | ||||
\(118\) | −1.16943 | + | 2.02551i | −0.107655 | + | 0.186463i | ||||
\(119\) | 2.28491 | − | 1.31919i | 0.209457 | − | 0.120930i | ||||
\(120\) | 5.13460 | 0.468722 | ||||||||
\(121\) | −4.02518 | + | 6.97181i | −0.365925 | + | 0.633801i | ||||
\(122\) | 9.12507i | 0.826145i | ||||||||
\(123\) | − | 1.36629i | − | 0.123194i | ||||||
\(124\) | 1.76870 | + | 6.16018i | 0.158834 | + | 0.553200i | ||||
\(125\) | 3.90340i | 0.349131i | ||||||||
\(126\) | 0.973373 | 0.0867149 | ||||||||
\(127\) | 8.40593 | − | 14.5595i | 0.745906 | − | 1.29195i | −0.203865 | − | 0.978999i | \(-0.565350\pi\) |
0.949770 | − | 0.312948i | \(-0.101316\pi\) | |||||||
\(128\) | 5.60172i | 0.495127i | ||||||||
\(129\) | −0.00712234 | − | 0.0123362i | −0.000627087 | − | 0.00108615i | ||||
\(130\) | −2.71783 | + | 10.7638i | −0.238369 | + | 0.944051i | ||||
\(131\) | −4.51417 | + | 7.81877i | −0.394405 | + | 0.683129i | −0.993025 | − | 0.117904i | \(-0.962382\pi\) |
0.598620 | + | 0.801033i | \(0.295716\pi\) | |||||||
\(132\) | 1.04623i | 0.0910624i | ||||||||
\(133\) | 0.683476 | + | 1.18382i | 0.0592649 | + | 0.102650i | ||||
\(134\) | −0.759378 | − | 1.31528i | −0.0656003 | − | 0.113623i | ||||
\(135\) | 8.76068 | − | 5.05798i | 0.753999 | − | 0.435322i | ||||
\(136\) | −17.0791 | − | 9.86065i | −1.46452 | − | 0.845544i | ||||
\(137\) | −14.3387 | + | 8.27844i | −1.22504 | + | 0.707274i | −0.965987 | − | 0.258590i | \(-0.916742\pi\) |
−0.259048 | + | 0.965864i | \(0.583409\pi\) | |||||||
\(138\) | 2.17027 | + | 1.25301i | 0.184746 | + | 0.106663i | ||||
\(139\) | 9.68159 | 0.821182 | 0.410591 | − | 0.911820i | \(-0.365322\pi\) | ||||
0.410591 | + | 0.911820i | \(0.365322\pi\) | |||||||
\(140\) | 1.49415 | 0.126279 | ||||||||
\(141\) | 3.90512 | + | 2.25462i | 0.328871 | + | 0.189874i | ||||
\(142\) | 7.14437 | + | 12.3744i | 0.599542 | + | 1.03844i | ||||
\(143\) | −6.00393 | − | 1.51597i | −0.502074 | − | 0.126772i | ||||
\(144\) | −0.506946 | − | 0.878056i | −0.0422455 | − | 0.0731714i | ||||
\(145\) | −18.6206 | + | 10.7506i | −1.54635 | + | 0.892788i | ||||
\(146\) | 0.278031 | + | 0.481564i | 0.0230100 | + | 0.0398545i | ||||
\(147\) | 3.62463 | 0.298954 | ||||||||
\(148\) | 9.48203 | + | 5.47445i | 0.779418 | + | 0.449997i | ||||
\(149\) | −10.0003 | − | 5.77366i | −0.819255 | − | 0.472997i | 0.0309046 | − | 0.999522i | \(-0.490161\pi\) |
−0.850159 | + | 0.526525i | \(0.823495\pi\) | |||||||
\(150\) | −2.60455 | + | 1.50374i | −0.212661 | + | 0.122780i | ||||
\(151\) | 2.65833i | 0.216332i | 0.994133 | + | 0.108166i | \(0.0344977\pi\) | ||||
−0.994133 | + | 0.108166i | \(0.965502\pi\) | |||||||
\(152\) | 5.10883 | − | 8.84875i | 0.414381 | − | 0.717728i | ||||
\(153\) | −18.4758 | −1.49368 | ||||||||
\(154\) | − | 0.614618i | − | 0.0495273i | ||||||
\(155\) | −13.3890 | − | 12.9207i | −1.07543 | − | 1.03781i | ||||
\(156\) | 2.11312 | − | 0.599116i | 0.169185 | − | 0.0479677i | ||||
\(157\) | 1.35432 | 0.108087 | 0.0540434 | − | 0.998539i | \(-0.482789\pi\) | ||||
0.0540434 | + | 0.998539i | \(0.482789\pi\) | |||||||
\(158\) | −1.68201 | − | 0.971107i | −0.133813 | − | 0.0772571i | ||||
\(159\) | −5.66084 | −0.448934 | ||||||||
\(160\) | −9.12851 | − | 15.8110i | −0.721672 | − | 1.24997i | ||||
\(161\) | 1.72882 | + | 0.998136i | 0.136250 | + | 0.0786642i | ||||
\(162\) | −5.23265 | − | 3.02107i | −0.411116 | − | 0.237358i | ||||
\(163\) | 4.10278i | 0.321355i | 0.987007 | + | 0.160677i | \(0.0513679\pi\) | ||||
−0.987007 | + | 0.160677i | \(0.948632\pi\) | |||||||
\(164\) | −2.57371 | + | 1.48593i | −0.200973 | + | 0.116032i | ||||
\(165\) | −1.51870 | − | 2.63046i | −0.118230 | − | 0.204781i | ||||
\(166\) | 7.67526 | + | 13.2939i | 0.595716 | + | 1.03181i | ||||
\(167\) | 14.3558 | + | 8.28830i | 1.11088 | + | 0.641368i | 0.939058 | − | 0.343759i | \(-0.111700\pi\) |
0.171824 | + | 0.985128i | \(0.445034\pi\) | |||||||
\(168\) | 0.298387 | + | 0.516822i | 0.0230211 | + | 0.0398737i | ||||
\(169\) | 0.376239 | + | 12.9946i | 0.0289415 | + | 0.999581i | ||||
\(170\) | 20.9152 | 1.60412 | ||||||||
\(171\) | − | 9.57238i | − | 0.732018i | ||||||
\(172\) | −0.0154920 | + | 0.0268330i | −0.00118126 | + | 0.00204600i | ||||
\(173\) | −8.61739 | − | 14.9257i | −0.655168 | − | 1.13478i | −0.981852 | − | 0.189650i | \(-0.939265\pi\) |
0.326684 | − | 0.945134i | \(-0.394069\pi\) | |||||||
\(174\) | −2.71682 | − | 1.56855i | −0.205961 | − | 0.118912i | ||||
\(175\) | −2.07477 | + | 1.19787i | −0.156838 | + | 0.0905503i | ||||
\(176\) | −0.554432 | + | 0.320101i | −0.0417919 | + | 0.0241286i | ||||
\(177\) | −1.16341 | + | 0.671697i | −0.0874474 | + | 0.0504878i | ||||
\(178\) | −11.7033 | −0.877198 | ||||||||
\(179\) | −6.46323 | + | 11.1946i | −0.483084 | + | 0.836726i | −0.999811 | − | 0.0194238i | \(-0.993817\pi\) |
0.516727 | + | 0.856150i | \(0.327150\pi\) | |||||||
\(180\) | −9.06132 | − | 5.23155i | −0.675391 | − | 0.389937i | ||||
\(181\) | −0.617119 | − | 1.06888i | −0.0458701 | − | 0.0794493i | 0.842179 | − | 0.539198i | \(-0.181273\pi\) |
−0.888049 | + | 0.459749i | \(0.847939\pi\) | |||||||
\(182\) | −1.24137 | + | 0.351958i | −0.0920168 | + | 0.0260888i | ||||
\(183\) | −2.62063 | + | 4.53906i | −0.193723 | + | 0.335537i | ||||
\(184\) | − | 14.9217i | − | 1.10004i | ||||||
\(185\) | −31.7867 | −2.33701 | ||||||||
\(186\) | 0.655860 | − | 2.63438i | 0.0480900 | − | 0.193162i | ||||
\(187\) | 11.6662i | 0.853118i | ||||||||
\(188\) | − | 9.80821i | − | 0.715337i | ||||||
\(189\) | 1.01822 | + | 0.587870i | 0.0740647 | + | 0.0427613i | ||||
\(190\) | 10.8362i | 0.786141i | ||||||||
\(191\) | −12.0037 | − | 20.7911i | −0.868559 | − | 1.50439i | −0.863469 | − | 0.504402i | \(-0.831713\pi\) |
−0.00509028 | − | 0.999987i | \(-0.501620\pi\) | |||||||
\(192\) | 1.52916 | − | 2.64858i | 0.110357 | − | 0.191145i | ||||
\(193\) | −1.07300 | − | 0.619496i | −0.0772361 | − | 0.0445923i | 0.460885 | − | 0.887460i | \(-0.347532\pi\) |
−0.538121 | + | 0.842868i | \(0.680866\pi\) | |||||||
\(194\) | 1.74511 | 0.125291 | ||||||||
\(195\) | −4.44320 | + | 4.57370i | −0.318184 | + | 0.327530i | ||||
\(196\) | −3.94202 | − | 6.82779i | −0.281573 | − | 0.487699i | ||||
\(197\) | −1.23210 | + | 0.711351i | −0.0877832 | + | 0.0506816i | −0.543249 | − | 0.839572i | \(-0.682806\pi\) |
0.455466 | + | 0.890253i | \(0.349473\pi\) | |||||||
\(198\) | −2.15200 | + | 3.72737i | −0.152936 | + | 0.264892i | ||||
\(199\) | 1.53028 | + | 2.65052i | 0.108479 | + | 0.187890i | 0.915154 | − | 0.403104i | \(-0.132069\pi\) |
−0.806675 | + | 0.590995i | \(0.798735\pi\) | |||||||
\(200\) | 15.5084 | + | 8.95379i | 1.09661 | + | 0.633129i | ||||
\(201\) | − | 0.872344i | − | 0.0615304i | ||||||
\(202\) | 6.65147i | 0.467996i | ||||||||
\(203\) | −2.16420 | − | 1.24950i | −0.151897 | − | 0.0876977i | ||||
\(204\) | −2.06898 | − | 3.58358i | −0.144858 | − | 0.250901i | ||||
\(205\) | 4.31393 | − | 7.47195i | 0.301298 | − | 0.521863i | ||||
\(206\) | −9.18120 | + | 5.30077i | −0.639685 | + | 0.369322i | ||||
\(207\) | −6.98966 | − | 12.1065i | −0.485815 | − | 0.841457i | ||||
\(208\) | 0.964018 | + | 0.936510i | 0.0668426 | + | 0.0649353i | ||||
\(209\) | −6.04430 | −0.418093 | ||||||||
\(210\) | −0.548109 | − | 0.316451i | −0.0378231 | − | 0.0218372i | ||||
\(211\) | 12.5242 | − | 21.6926i | 0.862203 | − | 1.49338i | −0.00759518 | − | 0.999971i | \(-0.502418\pi\) |
0.869798 | − | 0.493408i | \(-0.164249\pi\) | |||||||
\(212\) | 6.15654 | + | 10.6634i | 0.422833 | + | 0.732368i | ||||
\(213\) | 8.20717i | 0.562346i | ||||||||
\(214\) | −8.60573 | − | 4.96852i | −0.588276 | − | 0.339641i | ||||
\(215\) | − | 0.0899525i | − | 0.00613471i | ||||||
\(216\) | − | 8.78839i | − | 0.597974i | ||||||
\(217\) | 0.522454 | − | 2.09853i | 0.0354665 | − | 0.142457i | ||||
\(218\) | 4.62506 | 0.313248 | ||||||||
\(219\) | 0.319391i | 0.0215825i | ||||||||
\(220\) | −3.30337 | + | 5.72160i | −0.222713 | + | 0.385750i | ||||
\(221\) | 23.5628 | − | 6.68060i | 1.58501 | − | 0.449385i | ||||
\(222\) | −2.31890 | − | 4.01646i | −0.155635 | − | 0.269567i | ||||
\(223\) | −18.5559 | − | 10.7133i | −1.24260 | − | 0.717414i | −0.272976 | − | 0.962021i | \(-0.588008\pi\) |
−0.969622 | + | 0.244607i | \(0.921341\pi\) | |||||||
\(224\) | 1.06097 | − | 1.83766i | 0.0708892 | − | 0.122784i | ||||
\(225\) | 16.7767 | 1.11844 | ||||||||
\(226\) | 8.96399 | − | 5.17536i | 0.596275 | − | 0.344260i | ||||
\(227\) | −17.2233 | + | 9.94388i | −1.14315 | + | 0.659998i | −0.947209 | − | 0.320617i | \(-0.896110\pi\) |
−0.195942 | + | 0.980616i | \(0.562776\pi\) | |||||||
\(228\) | 1.85666 | − | 1.07194i | 0.122960 | − | 0.0709913i | ||||
\(229\) | 8.91245 | + | 5.14561i | 0.588951 | + | 0.340031i | 0.764683 | − | 0.644407i | \(-0.222896\pi\) |
−0.175731 | + | 0.984438i | \(0.556229\pi\) | |||||||
\(230\) | 7.91250 | + | 13.7048i | 0.521735 | + | 0.903671i | ||||
\(231\) | 0.176512 | − | 0.305728i | 0.0116137 | − | 0.0201154i | ||||
\(232\) | 18.6795i | 1.22637i | ||||||||
\(233\) | −8.82706 | −0.578280 | −0.289140 | − | 0.957287i | \(-0.593369\pi\) | ||||
−0.289140 | + | 0.957287i | \(0.593369\pi\) | |||||||
\(234\) | 8.76068 | + | 2.21204i | 0.572704 | + | 0.144605i | ||||
\(235\) | 14.2375 | + | 24.6601i | 0.928754 | + | 1.60865i | ||||
\(236\) | 2.53058 | + | 1.46103i | 0.164727 | + | 0.0951049i | ||||
\(237\) | −0.557785 | − | 0.966112i | −0.0362320 | − | 0.0627557i | ||||
\(238\) | 1.21545 | + | 2.10521i | 0.0787856 | + | 0.136461i | ||||
\(239\) | −8.56756 | + | 4.94648i | −0.554190 | + | 0.319961i | −0.750810 | − | 0.660518i | \(-0.770337\pi\) |
0.196621 | + | 0.980480i | \(0.437003\pi\) | |||||||
\(240\) | 0.659248i | 0.0425543i | ||||||||
\(241\) | −3.89676 | − | 2.24979i | −0.251012 | − | 0.144922i | 0.369215 | − | 0.929344i | \(-0.379626\pi\) |
−0.620228 | + | 0.784422i | \(0.712960\pi\) | |||||||
\(242\) | −6.42353 | − | 3.70863i | −0.412920 | − | 0.238400i | ||||
\(243\) | −6.27581 | − | 10.8700i | −0.402594 | − | 0.697312i | ||||
\(244\) | 11.4004 | 0.729838 | ||||||||
\(245\) | 19.8223 | + | 11.4444i | 1.26640 | + | 0.731158i | ||||
\(246\) | 1.25884 | 0.0802607 | ||||||||
\(247\) | 3.46123 | + | 12.2080i | 0.220233 | + | 0.776774i | ||||
\(248\) | −15.5371 | + | 4.46099i | −0.986607 | + | 0.283273i | ||||
\(249\) | 8.81704i | 0.558757i | ||||||||
\(250\) | −3.59643 | −0.227458 | ||||||||
\(251\) | −0.203866 | + | 0.353106i | −0.0128679 | + | 0.0222879i | −0.872388 | − | 0.488815i | \(-0.837429\pi\) |
0.859520 | + | 0.511103i | \(0.170763\pi\) | |||||||
\(252\) | − | 1.21609i | − | 0.0766063i | ||||||
\(253\) | −7.64439 | + | 4.41349i | −0.480599 | + | 0.277474i | ||||
\(254\) | 13.4145 | + | 7.74486i | 0.841700 | + | 0.485956i | ||||
\(255\) | 10.4038 | + | 6.00663i | 0.651511 | + | 0.376150i | ||||
\(256\) | −16.7192 | −1.04495 | ||||||||
\(257\) | 4.56174 | + | 7.90116i | 0.284553 | + | 0.492861i | 0.972501 | − | 0.232900i | \(-0.0748214\pi\) |
−0.687948 | + | 0.725760i | \(0.741488\pi\) | |||||||
\(258\) | 0.0113661 | − | 0.00656221i | 0.000707622 | − | 0.000408546i | ||||
\(259\) | −1.84722 | − | 3.19949i | −0.114781 | − | 0.198806i | ||||
\(260\) | 13.4479 | + | 3.39553i | 0.834000 | + | 0.210582i | ||||
\(261\) | 8.74990 | + | 15.1553i | 0.541605 | + | 0.938087i | ||||
\(262\) | −7.20387 | − | 4.15916i | −0.445057 | − | 0.256954i | ||||
\(263\) | 14.8123 | 0.913367 | 0.456684 | − | 0.889629i | \(-0.349037\pi\) | ||||
0.456684 | + | 0.889629i | \(0.349037\pi\) | |||||||
\(264\) | −2.63878 | −0.162405 | ||||||||
\(265\) | −30.9579 | − | 17.8736i | −1.90173 | − | 1.09796i | ||||
\(266\) | −1.09072 | + | 0.629726i | −0.0668761 | + | 0.0386110i | ||||
\(267\) | −5.82154 | − | 3.36107i | −0.356272 | − | 0.205694i | ||||
\(268\) | −1.64325 | + | 0.948732i | −0.100378 | + | 0.0579530i | ||||
\(269\) | 5.59402 | + | 9.68913i | 0.341074 | + | 0.590757i | 0.984632 | − | 0.174640i | \(-0.0558761\pi\) |
−0.643559 | + | 0.765397i | \(0.722543\pi\) | |||||||
\(270\) | 4.66021 | + | 8.07172i | 0.283611 | + | 0.491229i | ||||
\(271\) | − | 21.4231i | − | 1.30136i | −0.759352 | − | 0.650680i | \(-0.774484\pi\) | ||
0.759352 | − | 0.650680i | \(-0.225516\pi\) | |||||||
\(272\) | 1.26604 | − | 2.19285i | 0.0767651 | − | 0.132961i | ||||
\(273\) | −0.718573 | − | 0.181437i | −0.0434900 | − | 0.0109811i | ||||
\(274\) | −7.62739 | − | 13.2110i | −0.460788 | − | 0.798108i | ||||
\(275\) | − | 10.5933i | − | 0.638800i | ||||||
\(276\) | 1.56545 | − | 2.71144i | 0.0942289 | − | 0.163209i | ||||
\(277\) | −7.73496 | −0.464749 | −0.232374 | − | 0.972626i | \(-0.574649\pi\) | ||||
−0.232374 | + | 0.972626i | \(0.574649\pi\) | |||||||
\(278\) | 8.92020i | 0.534998i | ||||||||
\(279\) | −10.5161 | + | 10.8973i | −0.629584 | + | 0.652403i | ||||
\(280\) | 3.76852i | 0.225212i | ||||||||
\(281\) | − | 22.6650i | − | 1.35208i | −0.736866 | − | 0.676039i | \(-0.763695\pi\) | ||
0.736866 | − | 0.676039i | \(-0.236305\pi\) | |||||||
\(282\) | −2.07731 | + | 3.59801i | −0.123702 | + | 0.214258i | ||||
\(283\) | 13.8479 | 0.823175 | 0.411587 | − | 0.911370i | \(-0.364975\pi\) | ||||
0.411587 | + | 0.911370i | \(0.364975\pi\) | |||||||
\(284\) | 15.4600 | − | 8.92584i | 0.917383 | − | 0.529651i | ||||
\(285\) | −3.11205 | + | 5.39023i | −0.184342 | + | 0.319290i | ||||
\(286\) | 1.39675 | − | 5.53176i | 0.0825915 | − | 0.327100i | ||||
\(287\) | 1.00278 | 0.0591925 | ||||||||
\(288\) | −12.8686 | + | 7.42969i | −0.758289 | + | 0.437798i | ||||
\(289\) | −14.5707 | − | 25.2372i | −0.857099 | − | 1.48454i | ||||
\(290\) | −9.90513 | − | 17.1562i | −0.581649 | − | 1.00745i | ||||
\(291\) | 0.868065 | + | 0.501178i | 0.0508869 | + | 0.0293795i | ||||
\(292\) | 0.601644 | − | 0.347359i | 0.0352086 | − | 0.0203277i | ||||
\(293\) | −24.8644 | − | 14.3555i | −1.45260 | − | 0.838656i | −0.453967 | − | 0.891018i | \(-0.649992\pi\) |
−0.998628 | + | 0.0523623i | \(0.983325\pi\) | |||||||
\(294\) | 3.33958i | 0.194768i | ||||||||
\(295\) | −8.48328 | −0.493916 | ||||||||
\(296\) | −13.8076 | + | 23.9154i | −0.802549 | + | 1.39006i | ||||
\(297\) | −4.50230 | + | 2.59940i | −0.261250 | + | 0.150833i | ||||
\(298\) | 5.31961 | − | 9.21383i | 0.308156 | − | 0.533743i | ||||
\(299\) | 13.2917 | + | 12.9124i | 0.768677 | + | 0.746743i | ||||
\(300\) | 1.87870 | + | 3.25401i | 0.108467 | + | 0.187870i | ||||
\(301\) | 0.00905415 | − | 0.00522742i | 0.000521873 | − | 0.000301303i | ||||
\(302\) | −2.44927 | −0.140940 | ||||||||
\(303\) | −1.91024 | + | 3.30863i | −0.109740 | + | 0.190076i | ||||
\(304\) | 1.13612 | + | 0.655940i | 0.0651610 | + | 0.0376207i | ||||
\(305\) | −28.6634 | + | 16.5488i | −1.64126 | + | 0.947581i | ||||
\(306\) | − | 17.0228i | − | 0.973131i | ||||||
\(307\) | 12.9627 | + | 7.48403i | 0.739821 | + | 0.427136i | 0.822004 | − | 0.569481i | \(-0.192856\pi\) |
−0.0821829 | + | 0.996617i | \(0.526189\pi\) | |||||||
\(308\) | −0.767875 | −0.0437538 | ||||||||
\(309\) | −6.08932 | −0.346409 | ||||||||
\(310\) | 11.9046 | − | 12.3360i | 0.676134 | − | 0.700640i | ||||
\(311\) | 23.3031 | 1.32140 | 0.660698 | − | 0.750651i | \(-0.270260\pi\) | ||||
0.660698 | + | 0.750651i | \(0.270260\pi\) | |||||||
\(312\) | 1.51108 | + | 5.32967i | 0.0855482 | + | 0.301733i | ||||
\(313\) | 5.37275 | − | 9.30588i | 0.303686 | − | 0.526000i | −0.673282 | − | 0.739386i | \(-0.735116\pi\) |
0.976968 | + | 0.213386i | \(0.0684493\pi\) | |||||||
\(314\) | 1.24782i | 0.0704183i | ||||||||
\(315\) | 1.76526 | + | 3.05753i | 0.0994614 | + | 0.172272i | ||||
\(316\) | −1.21326 | + | 2.10142i | −0.0682510 | + | 0.118214i | ||||
\(317\) | 9.81125 | + | 5.66453i | 0.551055 | + | 0.318152i | 0.749547 | − | 0.661951i | \(-0.230271\pi\) |
−0.198492 | + | 0.980102i | \(0.563605\pi\) | |||||||
\(318\) | − | 5.21565i | − | 0.292479i | ||||||
\(319\) | 9.56950 | − | 5.52495i | 0.535789 | − | 0.309338i | ||||
\(320\) | 16.7253 | − | 9.65634i | 0.934971 | − | 0.539806i | ||||
\(321\) | −2.85382 | − | 4.94297i | −0.159285 | − | 0.275889i | ||||
\(322\) | −0.919640 | + | 1.59286i | −0.0512495 | + | 0.0887668i | ||||
\(323\) | 20.7032 | − | 11.9530i | 1.15196 | − | 0.665082i | ||||
\(324\) | −3.77439 | + | 6.53743i | −0.209688 | + | 0.363191i | ||||
\(325\) | −21.3958 | + | 6.06620i | −1.18683 | + | 0.336492i | ||||
\(326\) | −3.78013 | −0.209362 | ||||||||
\(327\) | 2.30063 | + | 1.32827i | 0.127225 | + | 0.0734536i | ||||
\(328\) | −3.74779 | − | 6.49136i | −0.206937 | − | 0.358425i | ||||
\(329\) | −1.65477 | + | 2.86615i | −0.0912307 | + | 0.158016i | ||||
\(330\) | 2.42359 | − | 1.39926i | 0.133414 | − | 0.0770268i | ||||
\(331\) | 1.52114 | − | 0.878228i | 0.0836092 | − | 0.0482718i | −0.457613 | − | 0.889152i | \(-0.651295\pi\) |
0.541222 | + | 0.840880i | \(0.317962\pi\) | |||||||
\(332\) | 16.6088 | − | 9.58912i | 0.911529 | − | 0.526271i | ||||
\(333\) | 25.8712i | 1.41773i | ||||||||
\(334\) | −7.63649 | + | 13.2268i | −0.417850 | + | 0.723737i | ||||
\(335\) | 2.75435 | − | 4.77067i | 0.150486 | − | 0.260649i | ||||
\(336\) | −0.0663565 | + | 0.0383110i | −0.00362005 | + | 0.00209003i | ||||
\(337\) | 3.68645 | 0.200814 | 0.100407 | − | 0.994946i | \(-0.467986\pi\) | ||||
0.100407 | + | 0.994946i | \(0.467986\pi\) | |||||||
\(338\) | −11.9726 | + | 0.346651i | −0.651225 | + | 0.0188553i | ||||
\(339\) | 5.94525 | 0.322902 | ||||||||
\(340\) | − | 26.1305i | − | 1.41712i | ||||||
\(341\) | 6.88088 | + | 6.64021i | 0.372621 | + | 0.359587i | ||||
\(342\) | 8.81958 | 0.476908 | ||||||||
\(343\) | 5.37917i | 0.290448i | ||||||||
\(344\) | −0.0676777 | − | 0.0390737i | −0.00364894 | − | 0.00210672i | ||||
\(345\) | 9.08957i | 0.489366i | ||||||||
\(346\) | 13.7519 | − | 7.93969i | 0.739309 | − | 0.426840i | ||||
\(347\) | 5.42934 | − | 9.40389i | 0.291462 | − | 0.504827i | −0.682693 | − | 0.730705i | \(-0.739192\pi\) |
0.974156 | + | 0.225877i | \(0.0725249\pi\) | |||||||
\(348\) | −1.95968 | + | 3.39427i | −0.105050 | + | 0.181952i | ||||
\(349\) | 24.3630i | 1.30412i | 0.758166 | + | 0.652061i | \(0.226096\pi\) | ||||
−0.758166 | + | 0.652061i | \(0.773904\pi\) | |||||||
\(350\) | −1.10366 | − | 1.91160i | −0.0589933 | − | 0.102179i | ||||
\(351\) | 7.82836 | + | 7.60498i | 0.417847 | + | 0.405924i | ||||
\(352\) | 4.69133 | + | 8.12563i | 0.250049 | + | 0.433097i | ||||
\(353\) | 4.53924 | + | 2.62073i | 0.241599 | + | 0.139487i | 0.615912 | − | 0.787815i | \(-0.288788\pi\) |
−0.374312 | + | 0.927303i | \(0.622121\pi\) | |||||||
\(354\) | −0.618872 | − | 1.07192i | −0.0328927 | − | 0.0569718i | ||||
\(355\) | −25.9134 | + | 44.8833i | −1.37534 | + | 2.38216i | ||||
\(356\) | 14.6215i | 0.774940i | ||||||||
\(357\) | 1.39626i | 0.0738978i | ||||||||
\(358\) | −10.3143 | − | 5.95494i | −0.545125 | − | 0.314728i | ||||
\(359\) | −3.34965 | + | 1.93392i | −0.176788 | + | 0.102069i | −0.585783 | − | 0.810468i | \(-0.699213\pi\) |
0.408995 | + | 0.912537i | \(0.365879\pi\) | |||||||
\(360\) | 13.1949 | − | 22.8543i | 0.695435 | − | 1.20453i | ||||
\(361\) | −3.30713 | − | 5.72812i | −0.174059 | − | 0.301480i | ||||
\(362\) | 0.984822 | − | 0.568587i | 0.0517611 | − | 0.0298843i | ||||
\(363\) | −2.13016 | − | 3.68955i | −0.111805 | − | 0.193651i | ||||
\(364\) | 0.439720 | + | 1.55092i | 0.0230476 | + | 0.0812901i | ||||
\(365\) | −1.00845 | + | 1.74668i | −0.0527846 | + | 0.0914257i | ||||
\(366\) | −4.18210 | − | 2.41454i | −0.218602 | − | 0.126210i | ||||
\(367\) | 10.5358 | + | 18.2485i | 0.549963 | + | 0.952564i | 0.998276 | + | 0.0586874i | \(0.0186915\pi\) |
−0.448313 | + | 0.893876i | \(0.647975\pi\) | |||||||
\(368\) | 1.91584 | 0.0998703 | ||||||||
\(369\) | −6.08141 | − | 3.51110i | −0.316586 | − | 0.182781i | ||||
\(370\) | − | 29.2869i | − | 1.52255i | ||||||
\(371\) | − | 4.15475i | − | 0.215704i | ||||||
\(372\) | −3.29127 | − | 0.819401i | −0.170644 | − | 0.0424840i | ||||
\(373\) | 7.00707 | 0.362812 | 0.181406 | − | 0.983408i | \(-0.441935\pi\) | ||||
0.181406 | + | 0.983408i | \(0.441935\pi\) | |||||||
\(374\) | −10.7487 | −0.555804 | ||||||||
\(375\) | −1.78896 | − | 1.03286i | −0.0923817 | − | 0.0533366i | ||||
\(376\) | 24.7381 | 1.27577 | ||||||||
\(377\) | −16.6390 | − | 16.1642i | −0.856950 | − | 0.832497i | ||||
\(378\) | −0.541638 | + | 0.938145i | −0.0278589 | + | 0.0482530i | ||||
\(379\) | 28.1273 | + | 16.2393i | 1.44480 | + | 0.834157i | 0.998165 | − | 0.0605577i | \(-0.0192879\pi\) |
0.446638 | + | 0.894715i | \(0.352621\pi\) | |||||||
\(380\) | 13.5383 | 0.694498 | ||||||||
\(381\) | 4.44850 | + | 7.70503i | 0.227904 | + | 0.394740i | ||||
\(382\) | 19.1560 | − | 11.0597i | 0.980106 | − | 0.565864i | ||||
\(383\) | 12.4776 | − | 7.20397i | 0.637578 | − | 0.368106i | −0.146103 | − | 0.989269i | \(-0.546673\pi\) |
0.783681 | + | 0.621164i | \(0.213340\pi\) | |||||||
\(384\) | −2.56732 | − | 1.48224i | −0.131013 | − | 0.0756404i | ||||
\(385\) | 1.93062 | − | 1.11464i | 0.0983933 | − | 0.0568074i | ||||
\(386\) | 0.570777 | − | 0.988614i | 0.0290518 | − | 0.0503191i | ||||
\(387\) | −0.0732122 | −0.00372159 | ||||||||
\(388\) | − | 2.18026i | − | 0.110686i | ||||||
\(389\) | 7.09412 | − | 12.2874i | 0.359686 | − | 0.622995i | −0.628222 | − | 0.778034i | \(-0.716217\pi\) |
0.987908 | + | 0.155039i | \(0.0495504\pi\) | |||||||
\(390\) | −4.21401 | − | 4.09377i | −0.213385 | − | 0.207296i | ||||
\(391\) | 17.4559 | − | 30.2345i | 0.882783 | − | 1.52903i | ||||
\(392\) | 17.2209 | − | 9.94251i | 0.869789 | − | 0.502173i | ||||
\(393\) | −2.38894 | − | 4.13777i | −0.120506 | − | 0.208723i | ||||
\(394\) | −0.655408 | − | 1.13520i | −0.0330190 | − | 0.0571905i | ||||
\(395\) | − | 7.04462i | − | 0.354453i | ||||||
\(396\) | 4.65680 | + | 2.68861i | 0.234013 | + | 0.135108i | ||||
\(397\) | 18.6860 | + | 10.7883i | 0.937822 | + | 0.541452i | 0.889277 | − | 0.457369i | \(-0.151208\pi\) |
0.0485448 | + | 0.998821i | \(0.484542\pi\) | |||||||
\(398\) | −2.44208 | + | 1.40993i | −0.122410 | + | 0.0706736i | ||||
\(399\) | −0.723404 | −0.0362155 | ||||||||
\(400\) | −1.14961 | + | 1.99118i | −0.0574804 | + | 0.0995589i | ||||
\(401\) | 18.3217i | 0.914940i | 0.889225 | + | 0.457470i | \(0.151244\pi\) | ||||
−0.889225 | + | 0.457470i | \(0.848756\pi\) | |||||||
\(402\) | 0.803740 | 0.0400869 | ||||||||
\(403\) | 9.47126 | − | 17.7001i | 0.471797 | − | 0.881707i | ||||
\(404\) | 8.31004 | 0.413440 | ||||||||
\(405\) | − | 21.9155i | − | 1.08899i | ||||||
\(406\) | 1.15124 | − | 1.99400i | 0.0571349 | − | 0.0989605i | ||||
\(407\) | 16.3359 | 0.809738 | ||||||||
\(408\) | 9.03845 | − | 5.21835i | 0.447470 | − | 0.258347i | ||||
\(409\) | −31.1134 | − | 17.9633i | −1.53846 | − | 0.888229i | −0.998929 | − | 0.0462613i | \(-0.985269\pi\) |
−0.539528 | − | 0.841968i | \(-0.681397\pi\) | |||||||
\(410\) | 6.88433 | + | 3.97467i | 0.339993 | + | 0.196295i | ||||
\(411\) | − | 8.76205i | − | 0.432200i | ||||||
\(412\) | 6.62254 | + | 11.4706i | 0.326269 | + | 0.565115i | ||||
\(413\) | −0.492990 | − | 0.853883i | −0.0242584 | − | 0.0420169i | ||||
\(414\) | 11.1544 | − | 6.43998i | 0.548207 | − | 0.316508i | ||||
\(415\) | −27.8390 | + | 48.2186i | −1.36656 | + | 2.36696i | ||||
\(416\) | 13.7253 | − | 14.1284i | 0.672937 | − | 0.692703i | ||||
\(417\) | −2.56180 | + | 4.43716i | −0.125452 | + | 0.217289i | ||||
\(418\) | − | 5.56895i | − | 0.272386i | ||||||
\(419\) | 19.8072 | 0.967647 | 0.483824 | − | 0.875165i | \(-0.339248\pi\) | ||||
0.483824 | + | 0.875165i | \(0.339248\pi\) | |||||||
\(420\) | −0.395359 | + | 0.684782i | −0.0192916 | + | 0.0334140i | ||||
\(421\) | 2.64724 | − | 1.52839i | 0.129019 | − | 0.0744889i | −0.434102 | − | 0.900864i | \(-0.642934\pi\) |
0.563120 | + | 0.826375i | \(0.309601\pi\) | |||||||
\(422\) | 19.9866 | + | 11.5393i | 0.972933 | + | 0.561723i | ||||
\(423\) | 20.0709 | − | 11.5879i | 0.975878 | − | 0.563424i | ||||
\(424\) | −26.8951 | + | 15.5279i | −1.30614 | + | 0.754102i | ||||
\(425\) | 20.9489 | + | 36.2846i | 1.01617 | + | 1.76006i | ||||
\(426\) | −7.56173 | −0.366367 | ||||||||
\(427\) | −3.33143 | − | 1.92340i | −0.161219 | − | 0.0930800i | ||||
\(428\) | −6.20744 | + | 10.7516i | −0.300048 | + | 0.519699i | ||||
\(429\) | 2.28345 | − | 2.35052i | 0.110246 | − | 0.113484i | ||||
\(430\) | 0.0828783 | 0.00399675 | ||||||||
\(431\) | −24.6899 | − | 14.2547i | −1.18927 | − | 0.686625i | −0.231129 | − | 0.972923i | \(-0.574242\pi\) |
−0.958141 | + | 0.286298i | \(0.907575\pi\) | |||||||
\(432\) | 1.12837 | 0.0542888 | ||||||||
\(433\) | −9.48475 | −0.455808 | −0.227904 | − | 0.973684i | \(-0.573187\pi\) | ||||
−0.227904 | + | 0.973684i | \(0.573187\pi\) | |||||||
\(434\) | 1.93349 | + | 0.481366i | 0.0928106 | + | 0.0231063i | ||||
\(435\) | − | 11.3786i | − | 0.545564i | ||||||
\(436\) | − | 5.77834i | − | 0.276732i | ||||||
\(437\) | 15.6646 | + | 9.04395i | 0.749339 | + | 0.432631i | ||||
\(438\) | −0.294274 | −0.0140609 | ||||||||
\(439\) | −6.64973 | − | 11.5177i | −0.317374 | − | 0.549709i | 0.662565 | − | 0.749004i | \(-0.269468\pi\) |
−0.979939 | + | 0.199296i | \(0.936135\pi\) | |||||||
\(440\) | −14.4309 | − | 8.33169i | −0.687967 | − | 0.397198i | ||||
\(441\) | 9.31461 | − | 16.1334i | 0.443553 | − | 0.768256i | ||||
\(442\) | 6.15521 | + | 21.7098i | 0.292774 | + | 1.03263i | ||||
\(443\) | −20.4933 | − | 35.4955i | −0.973668 | − | 1.68644i | −0.684262 | − | 0.729236i | \(-0.739876\pi\) |
−0.289406 | − | 0.957207i | \(-0.593458\pi\) | |||||||
\(444\) | −5.01798 | + | 2.89713i | −0.238143 | + | 0.137492i | ||||
\(445\) | −21.2245 | − | 36.7619i | −1.00614 | − | 1.74268i | ||||
\(446\) | 9.87076 | − | 17.0967i | 0.467394 | − | 0.809550i | ||||
\(447\) | 5.29224 | − | 3.05548i | 0.250315 | − | 0.144519i | ||||
\(448\) | 1.94391 | + | 1.12232i | 0.0918413 | + | 0.0530246i | ||||
\(449\) | 15.5080i | 0.731869i | 0.930641 | + | 0.365935i | \(0.119251\pi\) | ||||
−0.930641 | + | 0.365935i | \(0.880749\pi\) | |||||||
\(450\) | 15.4573i | 0.728664i | ||||||||
\(451\) | −2.21702 | + | 3.83999i | −0.104395 | + | 0.180818i | ||||
\(452\) | −6.46586 | − | 11.1992i | −0.304128 | − | 0.526766i | ||||
\(453\) | −1.21834 | − | 0.703406i | −0.0572424 | − | 0.0330489i | ||||
\(454\) | −9.16186 | − | 15.8688i | −0.429987 | − | 0.744760i | ||||
\(455\) | −3.35686 | − | 3.26107i | −0.157372 | − | 0.152881i | ||||
\(456\) | 2.70364 | + | 4.68284i | 0.126610 | + | 0.219294i | ||||
\(457\) | 21.1888i | 0.991170i | 0.868559 | + | 0.495585i | \(0.165046\pi\) | ||||
−0.868559 | + | 0.495585i | \(0.834954\pi\) | |||||||
\(458\) | −4.74094 | + | 8.21155i | −0.221530 | + | 0.383701i | ||||
\(459\) | 10.2810 | − | 17.8072i | 0.479875 | − | 0.831167i | ||||
\(460\) | 17.1222 | − | 9.88551i | 0.798327 | − | 0.460914i | ||||
\(461\) | − | 21.1258i | − | 0.983926i | −0.870616 | − | 0.491963i | \(-0.836280\pi\) | ||
0.870616 | − | 0.491963i | \(-0.163720\pi\) | |||||||
\(462\) | 0.281685 | + | 0.162631i | 0.0131052 | + | 0.00756627i | ||||
\(463\) | 5.56614i | 0.258681i | 0.991600 | + | 0.129340i | \(0.0412860\pi\) | ||||
−0.991600 | + | 0.129340i | \(0.958714\pi\) | |||||||
\(464\) | −2.39832 | −0.111339 | ||||||||
\(465\) | 9.46445 | − | 2.71742i | 0.438904 | − | 0.126017i | ||||
\(466\) | − | 8.13287i | − | 0.376748i | ||||||
\(467\) | −16.1924 | −0.749294 | −0.374647 | − | 0.927167i | \(-0.622236\pi\) | ||||
−0.374647 | + | 0.927167i | \(0.622236\pi\) | |||||||
\(468\) | 2.76362 | − | 10.9452i | 0.127748 | − | 0.505942i | ||||
\(469\) | 0.640254 | 0.0295642 | ||||||||
\(470\) | −22.7208 | + | 13.1178i | −1.04803 | + | 0.605081i | ||||
\(471\) | −0.358361 | + | 0.620699i | −0.0165124 | + | 0.0286003i | ||||
\(472\) | −3.68499 | + | 6.38258i | −0.169615 | + | 0.293782i | ||||
\(473\) | 0.0462285i | 0.00212559i | ||||||||
\(474\) | 0.890134 | − | 0.513919i | 0.0408852 | − | 0.0236051i | ||||
\(475\) | −18.7992 | + | 10.8537i | −0.862564 | + | 0.498002i | ||||
\(476\) | 2.63016 | − | 1.51852i | 0.120553 | − | 0.0696014i | ||||
\(477\) | −14.5473 | + | 25.1966i | −0.666074 | + | 1.15367i | ||||
\(478\) | −4.55748 | − | 7.89378i | −0.208454 | − | 0.361053i | ||||
\(479\) | 14.9827 | + | 8.65028i | 0.684578 | + | 0.395241i | 0.801578 | − | 0.597891i | \(-0.203994\pi\) |
−0.117000 | + | 0.993132i | \(0.537328\pi\) | |||||||
\(480\) | 9.66179 | 0.440998 | ||||||||
\(481\) | −9.35464 | − | 32.9944i | −0.426535 | − | 1.50441i | ||||
\(482\) | 2.07286 | − | 3.59031i | 0.0944164 | − | 0.163534i | ||||
\(483\) | −0.914909 | + | 0.528223i | −0.0416298 | + | 0.0240350i | ||||
\(484\) | −4.63339 | + | 8.02526i | −0.210609 | + | 0.364785i | ||||
\(485\) | 3.16484 | + | 5.48167i | 0.143708 | + | 0.248910i | ||||
\(486\) | 10.0152 | − | 5.78226i | 0.454298 | − | 0.262289i | ||||
\(487\) | −18.3177 | + | 10.5757i | −0.830054 | + | 0.479232i | −0.853871 | − | 0.520485i | \(-0.825751\pi\) |
0.0238175 | + | 0.999716i | \(0.492418\pi\) | |||||||
\(488\) | 28.7540i | 1.30163i | ||||||||
\(489\) | −1.88034 | − | 1.08562i | −0.0850320 | − | 0.0490933i | ||||
\(490\) | −10.5444 | + | 18.2634i | −0.476348 | + | 0.825058i | ||||
\(491\) | −6.82944 | − | 11.8289i | −0.308208 | − | 0.533833i | 0.669762 | − | 0.742576i | \(-0.266396\pi\) |
−0.977971 | + | 0.208743i | \(0.933063\pi\) | |||||||
\(492\) | − | 1.57274i | − | 0.0709045i | ||||||
\(493\) | −21.8519 | + | 37.8486i | −0.984160 | + | 1.70462i | ||||
\(494\) | −11.2479 | + | 3.18903i | −0.506067 | + | 0.143481i | ||||
\(495\) | −15.6110 | −0.701664 | ||||||||
\(496\) | −0.572761 | − | 1.99486i | −0.0257177 | − | 0.0895719i | ||||
\(497\) | −6.02363 | −0.270197 | ||||||||
\(498\) | −8.12364 | −0.364029 | ||||||||
\(499\) | 23.8353 | + | 13.7613i | 1.06701 | + | 0.616041i | 0.927364 | − | 0.374160i | \(-0.122069\pi\) |
0.139650 | + | 0.990201i | \(0.455402\pi\) | |||||||
\(500\) | 4.49321i | 0.200943i | ||||||||
\(501\) | −7.59721 | + | 4.38625i | −0.339418 | + | 0.195963i | ||||
\(502\) | −0.325337 | − | 0.187833i | −0.0145205 | − | 0.00838342i | ||||
\(503\) | 0.838225 | − | 1.45185i | 0.0373746 | − | 0.0647347i | −0.846733 | − | 0.532018i | \(-0.821434\pi\) |
0.884108 | + | 0.467283i | \(0.154767\pi\) | |||||||
\(504\) | 3.06720 | 0.136624 | ||||||||
\(505\) | −20.8934 | + | 12.0628i | −0.929743 | + | 0.536787i | ||||
\(506\) | −4.06640 | − | 7.04321i | −0.180773 | − | 0.313109i | ||||
\(507\) | −6.05508 | − | 3.26599i | −0.268915 | − | 0.145048i | ||||
\(508\) | 9.67608 | − | 16.7595i | 0.429307 | − | 0.743581i | ||||
\(509\) | −8.24747 | + | 4.76168i | −0.365563 | + | 0.211058i | −0.671518 | − | 0.740988i | \(-0.734357\pi\) |
0.305956 | + | 0.952046i | \(0.401024\pi\) | |||||||
\(510\) | −5.53426 | + | 9.58561i | −0.245061 | + | 0.424458i | ||||
\(511\) | −0.234416 | −0.0103700 | ||||||||
\(512\) | − | 4.20093i | − | 0.185657i | ||||||
\(513\) | 9.22594 | + | 5.32660i | 0.407335 | + | 0.235175i | ||||
\(514\) | −7.27979 | + | 4.20299i | −0.321098 | + | 0.185386i | ||||
\(515\) | −33.3012 | − | 19.2265i | −1.46743 | − | 0.847219i | ||||
\(516\) | −0.00819853 | − | 0.0142003i | −0.000360920 | − | 0.000625132i | ||||
\(517\) | −7.31697 | − | 12.6734i | −0.321800 | − | 0.557374i | ||||
\(518\) | 2.94787 | − | 1.70195i | 0.129522 | − | 0.0747795i | ||||
\(519\) | 9.12081 | 0.400359 | ||||||||
\(520\) | −8.56415 | + | 33.9180i | −0.375563 | + | 1.48740i | ||||
\(521\) | −9.95759 | + | 17.2471i | −0.436250 | + | 0.755607i | −0.997397 | − | 0.0721092i | \(-0.977027\pi\) |
0.561147 | + | 0.827716i | \(0.310360\pi\) | |||||||
\(522\) | −13.9634 | + | 8.06178i | −0.611162 | + | 0.352854i | ||||
\(523\) | 39.1926 | 1.71377 | 0.856886 | − | 0.515505i | \(-0.172396\pi\) | ||||
0.856886 | + | 0.515505i | \(0.172396\pi\) | |||||||
\(524\) | −5.19626 | + | 9.00019i | −0.227000 | + | 0.393175i | ||||
\(525\) | − | 1.26785i | − | 0.0553334i | ||||||
\(526\) | 13.6474i | 0.595057i | ||||||||
\(527\) | −36.7001 | − | 9.13693i | −1.59868 | − | 0.398011i | ||||
\(528\) | − | 0.338802i | − | 0.0147444i | ||||||
\(529\) | 3.41525 | 0.148489 | ||||||||
\(530\) | 16.4679 | − | 28.5233i | 0.715321 | − | 1.23897i | ||||
\(531\) | 6.90453i | 0.299631i | ||||||||
\(532\) | 0.786750 | + | 1.36269i | 0.0341100 | + | 0.0590802i | ||||
\(533\) | 9.02539 | + | 2.27888i | 0.390933 | + | 0.0987091i | ||||
\(534\) | 3.09674 | − | 5.36372i | 0.134009 | − | 0.232111i | ||||
\(535\) | − | 36.0427i | − | 1.55826i | ||||||
\(536\) | −2.39288 | − | 4.14458i | −0.103357 | − | 0.179019i | ||||
\(537\) | −3.42040 | − | 5.92431i | −0.147601 | − | 0.255653i | ||||
\(538\) | −8.92715 | + | 5.15409i | −0.384877 | + | 0.222209i | ||||
\(539\) | −10.1871 | − | 5.88153i | −0.438790 | − | 0.253336i | ||||
\(540\) | 10.0844 | − | 5.82225i | 0.433965 | − | 0.250550i | ||||
\(541\) | 16.0461 | + | 9.26419i | 0.689874 | + | 0.398299i | 0.803565 | − | 0.595217i | \(-0.202934\pi\) |
−0.113691 | + | 0.993516i | \(0.536267\pi\) | |||||||
\(542\) | 19.7383 | 0.847833 | ||||||||
\(543\) | 0.653171 | 0.0280302 | ||||||||
\(544\) | −32.1379 | − | 18.5548i | −1.37790 | − | 0.795531i | ||||
\(545\) | 8.38779 | + | 14.5281i | 0.359294 | + | 0.622315i | ||||
\(546\) | 0.167168 | − | 0.662063i | 0.00715414 | − | 0.0283337i | ||||
\(547\) | −19.0486 | − | 32.9932i | −0.814460 | − | 1.41069i | −0.909715 | − | 0.415233i | \(-0.863700\pi\) |
0.0952552 | − | 0.995453i | \(-0.469633\pi\) | |||||||
\(548\) | −16.5053 | + | 9.52932i | −0.705070 | + | 0.407072i | ||||
\(549\) | 13.4690 | + | 23.3291i | 0.574845 | + | 0.995661i | ||||
\(550\) | 9.76021 | 0.416177 | ||||||||
\(551\) | −19.6095 | − | 11.3215i | −0.835391 | − | 0.482313i | ||||
\(552\) | 6.83874 | + | 3.94835i | 0.291076 | + | 0.168053i | ||||
\(553\) | 0.709075 | − | 0.409385i | 0.0301529 | − | 0.0174088i | ||||
\(554\) | − | 7.12666i | − | 0.302783i | ||||||
\(555\) | 8.41092 | − | 14.5681i | 0.357024 | − | 0.618383i | ||||
\(556\) | 11.1445 | 0.472632 | ||||||||
\(557\) | − | 4.65769i | − | 0.197353i | −0.995120 | − | 0.0986763i | \(-0.968539\pi\) | ||
0.995120 | − | 0.0986763i | \(-0.0314608\pi\) | |||||||
\(558\) | −10.0403 | − | 9.68911i | −0.425039 | − | 0.410173i | ||||
\(559\) | 0.0933700 | − | 0.0264725i | 0.00394913 | − | 0.00111967i | ||||
\(560\) | −0.483853 | −0.0204465 | ||||||||
\(561\) | −5.34673 | − | 3.08694i | −0.225739 | − | 0.130331i | ||||
\(562\) | 20.8825 | 0.880876 | ||||||||
\(563\) | 10.9845 | + | 19.0258i | 0.462943 | + | 0.801840i | 0.999106 | − | 0.0422741i | \(-0.0134603\pi\) |
−0.536163 | + | 0.844114i | \(0.680127\pi\) | |||||||
\(564\) | 4.49519 | + | 2.59530i | 0.189282 | + | 0.109282i | ||||
\(565\) | 32.5133 | + | 18.7716i | 1.36785 | + | 0.789727i | ||||
\(566\) | 12.7589i | 0.536296i | ||||||||
\(567\) | 2.20590 | − | 1.27358i | 0.0926391 | − | 0.0534852i | ||||
\(568\) | 22.5126 | + | 38.9930i | 0.944609 | + | 1.63611i | ||||
\(569\) | −6.14942 | − | 10.6511i | −0.257797 | − | 0.446518i | 0.707854 | − | 0.706358i | \(-0.249663\pi\) |
−0.965652 | + | 0.259841i | \(0.916330\pi\) | |||||||
\(570\) | −4.96633 | − | 2.86731i | −0.208017 | − | 0.120098i | ||||
\(571\) | 11.4470 | + | 19.8267i | 0.479040 | + | 0.829722i | 0.999711 | − | 0.0240353i | \(-0.00765139\pi\) |
−0.520671 | + | 0.853758i | \(0.674318\pi\) | |||||||
\(572\) | −6.91113 | − | 1.74503i | −0.288969 | − | 0.0729636i | ||||
\(573\) | 12.7050 | 0.530758 | ||||||||
\(574\) | 0.923922i | 0.0385638i | ||||||||
\(575\) | −15.8505 | + | 27.4539i | −0.661013 | + | 1.14491i | ||||
\(576\) | −7.85929 | − | 13.6127i | −0.327470 | − | 0.567195i | ||||
\(577\) | −13.5289 | − | 7.81090i | −0.563214 | − | 0.325172i | 0.191220 | − | 0.981547i | \(-0.438756\pi\) |
−0.754435 | + | 0.656375i | \(0.772089\pi\) | |||||||
\(578\) | 23.2524 | − | 13.4248i | 0.967174 | − | 0.558398i | ||||
\(579\) | 0.567841 | − | 0.327843i | 0.0235987 | − | 0.0136247i | ||||
\(580\) | −21.4342 | + | 12.3750i | −0.890005 | + | 0.513845i | ||||
\(581\) | −6.47124 | −0.268472 | ||||||||
\(582\) | −0.461763 | + | 0.799798i | −0.0191407 | + | 0.0331527i | ||||
\(583\) | 15.9099 | + | 9.18560i | 0.658922 | + | 0.380429i | ||||
\(584\) | 0.876104 | + | 1.51746i | 0.0362535 | + | 0.0627928i | ||||
\(585\) | 8.93958 | + | 31.5304i | 0.369606 | + | 1.30362i | ||||
\(586\) | 13.2265 | − | 22.9090i | 0.546383 | − | 0.946363i | ||||
\(587\) | 15.9702i | 0.659159i | 0.944128 | + | 0.329580i | \(0.106907\pi\) | ||||
−0.944128 | + | 0.329580i | \(0.893093\pi\) | |||||||
\(588\) | 4.17231 | 0.172063 | ||||||||
\(589\) | 4.73387 | − | 19.0144i | 0.195056 | − | 0.783476i | ||||
\(590\) | − | 7.81613i | − | 0.321785i | ||||||
\(591\) | − | 0.752907i | − | 0.0309705i | ||||||
\(592\) | −3.07058 | − | 1.77280i | −0.126200 | − | 0.0728617i | ||||
\(593\) | − | 9.00794i | − | 0.369912i | −0.982747 | − | 0.184956i | \(-0.940786\pi\) | ||
0.982747 | − | 0.184956i | \(-0.0592142\pi\) | |||||||
\(594\) | −2.39498 | − | 4.14822i | −0.0982671 | − | 0.170204i | ||||
\(595\) | −4.40855 | + | 7.63584i | −0.180733 | + | 0.313039i | ||||
\(596\) | −11.5113 | − | 6.64607i | −0.471523 | − | 0.272234i | ||||
\(597\) | −1.61968 | −0.0662890 | ||||||||
\(598\) | −11.8969 | + | 12.2464i | −0.486501 | + | 0.500791i | ||||
\(599\) | −8.82768 | − | 15.2900i | −0.360689 | − | 0.624732i | 0.627385 | − | 0.778709i | \(-0.284125\pi\) |
−0.988074 | + | 0.153977i | \(0.950792\pi\) | |||||||
\(600\) | −8.20721 | + | 4.73843i | −0.335058 | + | 0.193446i | ||||
\(601\) | 12.1027 | − | 20.9626i | 0.493681 | − | 0.855080i | −0.506293 | − | 0.862362i | \(-0.668984\pi\) |
0.999973 | + | 0.00728131i | \(0.00231773\pi\) | |||||||
\(602\) | 0.00481632 | + | 0.00834211i | 0.000196298 | + | 0.000339999i | ||||
\(603\) | −3.88284 | − | 2.24176i | −0.158121 | − | 0.0912915i | ||||
\(604\) | 3.06000i | 0.124510i | ||||||||
\(605\) | − | 26.9032i | − | 1.09377i | ||||||
\(606\) | −3.04843 | − | 1.76001i | −0.123834 | − | 0.0714956i | ||||
\(607\) | 4.10722 | + | 7.11392i | 0.166707 | + | 0.288745i | 0.937260 | − | 0.348631i | \(-0.113353\pi\) |
−0.770553 | + | 0.637376i | \(0.780020\pi\) | |||||||
\(608\) | 9.61330 | − | 16.6507i | 0.389871 | − | 0.675276i | ||||
\(609\) | 1.14531 | − | 0.661248i | 0.0464105 | − | 0.0267951i | ||||
\(610\) | −15.2473 | − | 26.4092i | −0.617347 | − | 1.06928i | ||||
\(611\) | −21.4070 | + | 22.0358i | −0.866034 | + | 0.891472i | ||||
\(612\) | −21.2676 | −0.859690 | ||||||||
\(613\) | 28.3749 | + | 16.3822i | 1.14605 | + | 0.661672i | 0.947922 | − | 0.318504i | \(-0.103180\pi\) |
0.198129 | + | 0.980176i | \(0.436514\pi\) | |||||||
\(614\) | −6.89546 | + | 11.9433i | −0.278278 | + | 0.481992i | ||||
\(615\) | 2.28297 | + | 3.95423i | 0.0920584 | + | 0.159450i | ||||
\(616\) | − | 1.93672i | − | 0.0780328i | ||||||
\(617\) | 19.1584 | + | 11.0611i | 0.771288 | + | 0.445303i | 0.833334 | − | 0.552770i | \(-0.186429\pi\) |
−0.0620459 | + | 0.998073i | \(0.519763\pi\) | |||||||
\(618\) | − | 5.61044i | − | 0.225685i | ||||||
\(619\) | 19.7208i | 0.792645i | 0.918111 | + | 0.396323i | \(0.129714\pi\) | ||||
−0.918111 | + | 0.396323i | \(0.870286\pi\) | |||||||
\(620\) | −15.4121 | − | 14.8730i | −0.618964 | − | 0.597315i | ||||
\(621\) | 15.5577 | 0.624310 | ||||||||
\(622\) | 21.4705i | 0.860887i | ||||||||
\(623\) | 2.46685 | − | 4.27270i | 0.0988321 | − | 0.171182i | ||||
\(624\) | −0.684294 | + | 0.194013i | −0.0273937 | + | 0.00776673i | ||||
\(625\) | 8.89777 | + | 15.4114i | 0.355911 | + | 0.616455i | ||||
\(626\) | 8.57404 | + | 4.95023i | 0.342688 | + | 0.197851i | ||||
\(627\) | 1.59935 | − | 2.77015i | 0.0638719 | − | 0.110629i | ||||
\(628\) | 1.55896 | 0.0622094 | ||||||||
\(629\) | −55.9543 | + | 32.3052i | −2.23104 | + | 1.28809i | ||||
\(630\) | −2.81707 | + | 1.62644i | −0.112235 | + | 0.0647989i | ||||
\(631\) | −17.9143 | + | 10.3428i | −0.713156 | + | 0.411741i | −0.812228 | − | 0.583340i | \(-0.801746\pi\) |
0.0990727 | + | 0.995080i | \(0.468412\pi\) | |||||||
\(632\) | −5.30017 | − | 3.06006i | −0.210830 | − | 0.121722i | ||||
\(633\) | 6.62794 | + | 11.4799i | 0.263437 | + | 0.456286i | ||||
\(634\) | −5.21905 | + | 9.03967i | −0.207275 | + | 0.359011i | ||||
\(635\) | 56.1829i | 2.22955i | ||||||||
\(636\) | −6.51620 | −0.258384 | ||||||||
\(637\) | −6.04563 | + | 23.9435i | −0.239537 | + | 0.948674i | ||||
\(638\) | 5.09046 | + | 8.81693i | 0.201533 | + | 0.349066i | ||||
\(639\) | 36.5305 | + | 21.0909i | 1.44512 | + | 0.834342i | ||||
\(640\) | −9.36009 | − | 16.2121i | −0.369990 | − | 0.640841i | ||||
\(641\) | −13.7787 | − | 23.8653i | −0.544224 | − | 0.942624i | −0.998655 | − | 0.0518422i | \(-0.983491\pi\) |
0.454431 | − | 0.890782i | \(-0.349843\pi\) | |||||||
\(642\) | 4.55424 | − | 2.62939i | 0.179741 | − | 0.103774i | ||||
\(643\) | − | 1.24221i | − | 0.0489881i | −0.999700 | − | 0.0244940i | \(-0.992203\pi\) | ||
0.999700 | − | 0.0244940i | \(-0.00779748\pi\) | |||||||
\(644\) | 1.99005 | + | 1.14896i | 0.0784190 | + | 0.0452752i | ||||
\(645\) | 0.0412260 | + | 0.0238019i | 0.00162327 | + | 0.000937197i | ||||
\(646\) | 11.0130 | + | 19.0750i | 0.433299 | + | 0.750496i | ||||
\(647\) | −25.4546 | −1.00072 | −0.500362 | − | 0.865816i | \(-0.666800\pi\) | ||||
−0.500362 | + | 0.865816i | \(0.666800\pi\) | |||||||
\(648\) | −16.4886 | − | 9.51970i | −0.647733 | − | 0.373969i | ||||
\(649\) | 4.35974 | 0.171135 | ||||||||
\(650\) | −5.58913 | − | 19.7132i | −0.219224 | − | 0.773215i | ||||
\(651\) | 0.823530 | + | 0.794726i | 0.0322767 | + | 0.0311478i | ||||
\(652\) | 4.72272i | 0.184956i | ||||||||
\(653\) | 43.7442 | 1.71184 | 0.855921 | − | 0.517107i | \(-0.172991\pi\) | ||||
0.855921 | + | 0.517107i | \(0.172991\pi\) | |||||||
\(654\) | −1.22381 | + | 2.11971i | −0.0478549 | + | 0.0828870i | ||||
\(655\) | − | 30.1714i | − | 1.17890i | ||||||
\(656\) | 0.833448 | − | 0.481191i | 0.0325407 | − | 0.0187874i | ||||
\(657\) | 1.42163 | + | 0.820776i | 0.0554629 | + | 0.0320215i | ||||
\(658\) | −2.64075 | − | 1.52464i | −0.102947 | − | 0.0594366i | ||||
\(659\) | −20.2139 | −0.787420 | −0.393710 | − | 0.919235i | \(-0.628809\pi\) | ||||
−0.393710 | + | 0.919235i | \(0.628809\pi\) | |||||||
\(660\) | −1.74817 | − | 3.02792i | −0.0680475 | − | 0.117862i | ||||
\(661\) | 14.7989 | − | 8.54414i | 0.575610 | − | 0.332328i | −0.183777 | − | 0.982968i | \(-0.558832\pi\) |
0.759387 | + | 0.650640i | \(0.225499\pi\) | |||||||
\(662\) | 0.809162 | + | 1.40151i | 0.0314490 | + | 0.0544712i | ||||
\(663\) | −3.17306 | + | 12.5668i | −0.123232 | + | 0.488053i | ||||
\(664\) | 24.1855 | + | 41.8906i | 0.938580 | + | 1.62567i | ||||
\(665\) | −3.95615 | − | 2.28408i | −0.153413 | − | 0.0885729i | ||||
\(666\) | −23.8366 | −0.923649 | ||||||||
\(667\) | −33.0675 | −1.28038 | ||||||||
\(668\) | 16.5249 | + | 9.54068i | 0.639369 | + | 0.369140i | ||||
\(669\) | 9.81998 | − | 5.66957i | 0.379663 | − | 0.219198i | ||||
\(670\) | 4.39549 | + | 2.53774i | 0.169812 | + | 0.0980413i | ||||
\(671\) | 14.7307 | − | 8.50477i | 0.568672 | − | 0.328323i | ||||
\(672\) | 0.561477 | + | 0.972506i | 0.0216594 | + | 0.0375152i | ||||
\(673\) | 11.1009 | + | 19.2272i | 0.427907 | + | 0.741156i | 0.996687 | − | 0.0813336i | \(-0.0259179\pi\) |
−0.568780 | + | 0.822489i | \(0.692585\pi\) | |||||||
\(674\) | 3.39653i | 0.130830i | ||||||||
\(675\) | −9.33546 | + | 16.1695i | −0.359322 | + | 0.622364i | ||||
\(676\) | 0.433089 | + | 14.9580i | 0.0166573 | + | 0.575310i | ||||
\(677\) | 2.21818 | + | 3.84200i | 0.0852515 | + | 0.147660i | 0.905498 | − | 0.424350i | \(-0.139497\pi\) |
−0.820247 | + | 0.572010i | \(0.806164\pi\) | |||||||
\(678\) | 5.47770i | 0.210370i | ||||||||
\(679\) | −0.367838 | + | 0.637114i | −0.0141163 | + | 0.0244502i | ||||
\(680\) | 65.9058 | 2.52737 | ||||||||
\(681\) | − | 10.5248i | − | 0.403311i | ||||||
\(682\) | −6.11800 | + | 6.33975i | −0.234270 | + | 0.242762i | ||||
\(683\) | − | 43.5287i | − | 1.66558i | −0.553590 | − | 0.832789i | \(-0.686743\pi\) | ||
0.553590 | − | 0.832789i | \(-0.313257\pi\) | |||||||
\(684\) | − | 11.0188i | − | 0.421314i | ||||||
\(685\) | 27.6654 | − | 47.9178i | 1.05704 | − | 1.83085i | ||||
\(686\) | −4.95613 | −0.189226 | ||||||||
\(687\) | −4.71656 | + | 2.72310i | −0.179948 | + | 0.103893i | ||||
\(688\) | 0.00501681 | − | 0.00868937i | 0.000191264 | − | 0.000331279i | ||||
\(689\) | 9.44189 | − | 37.3942i | 0.359707 | − | 1.42460i | ||||
\(690\) | −8.37474 | −0.318821 | ||||||||
\(691\) | 23.4368 | − | 13.5312i | 0.891577 | − | 0.514752i | 0.0171191 | − | 0.999853i | \(-0.494551\pi\) |
0.874458 | + | 0.485101i | \(0.161217\pi\) | |||||||
\(692\) | −9.91948 | − | 17.1811i | −0.377082 | − | 0.653126i | ||||
\(693\) | −0.907206 | − | 1.57133i | −0.0344619 | − | 0.0596898i | ||||
\(694\) | 8.66434 | + | 5.00236i | 0.328894 | + | 0.189887i | ||||
\(695\) | −28.0199 | + | 16.1773i | −1.06285 | + | 0.613639i | ||||
\(696\) | −8.56096 | − | 4.94267i | −0.324502 | − | 0.187352i | ||||
\(697\) | − | 17.5372i | − | 0.664269i | ||||||
\(698\) | −22.4470 | −0.849633 | ||||||||
\(699\) | 2.33568 | − | 4.04552i | 0.0883436 | − | 0.153016i | ||||
\(700\) | −2.38827 | + | 1.37887i | −0.0902681 | + | 0.0521163i | ||||
\(701\) | −15.3204 | + | 26.5358i | −0.578644 | + | 1.00224i | 0.416991 | + | 0.908911i | \(0.363085\pi\) |
−0.995635 | + | 0.0933308i | \(0.970249\pi\) | |||||||
\(702\) | −7.00691 | + | 7.21272i | −0.264459 | + | 0.272226i | ||||
\(703\) | −16.7374 | − | 28.9900i | −0.631263 | − | 1.09338i | ||||
\(704\) | −8.59547 | + | 4.96260i | −0.323954 | + | 0.187035i | ||||
\(705\) | −15.0693 | −0.567542 | ||||||||
\(706\) | −2.41463 | + | 4.18226i | −0.0908757 | + | 0.157401i | ||||
\(707\) | −2.42836 | − | 1.40201i | −0.0913278 | − | 0.0527281i | ||||
\(708\) | −1.33921 | + | 0.773191i | −0.0503304 | + | 0.0290583i | ||||
\(709\) | 4.56728i | 0.171528i | 0.996315 | + | 0.0857638i | \(0.0273331\pi\) | ||||
−0.996315 | + | 0.0857638i | \(0.972667\pi\) | |||||||
\(710\) | −41.3535 | − | 23.8755i | −1.55197 | − | 0.896031i | ||||
\(711\) | −5.73361 | −0.215027 | ||||||||
\(712\) | −36.8782 | −1.38207 | ||||||||
\(713\) | −7.89711 | − | 27.5047i | −0.295749 | − | 1.03006i | ||||
\(714\) | −1.28645 | −0.0481442 | ||||||||
\(715\) | 19.9093 | − | 5.64473i | 0.744565 | − | 0.211101i | ||||
\(716\) | −7.43983 | + | 12.8862i | −0.278039 | + | 0.481578i | ||||
\(717\) | − | 5.23545i | − | 0.195522i | ||||||
\(718\) | −1.78183 | − | 3.08623i | −0.0664974 | − | 0.115177i | ||||
\(719\) | −10.1438 | + | 17.5695i | −0.378299 | + | 0.655233i | −0.990815 | − | 0.135225i | \(-0.956824\pi\) |
0.612516 | + | 0.790458i | \(0.290157\pi\) | |||||||
\(720\) | 2.93434 | + | 1.69414i | 0.109356 | + | 0.0631370i | ||||
\(721\) | − | 4.46924i | − | 0.166443i | ||||||
\(722\) | 5.27764 | − | 3.04705i | 0.196413 | − | 0.113399i | ||||
\(723\) | 2.06220 | − | 1.19061i | 0.0766941 | − | 0.0442794i | ||||
\(724\) | −0.710367 | − | 1.23039i | −0.0264006 | − | 0.0457271i | ||||
\(725\) | 19.8422 | − | 34.3678i | 0.736922 | − | 1.27639i | ||||
\(726\) | 3.39939 | − | 1.96264i | 0.126163 | − | 0.0728404i | ||||
\(727\) | 4.81063 | − | 8.33226i | 0.178417 | − | 0.309026i | −0.762922 | − | 0.646491i | \(-0.776236\pi\) |
0.941338 | + | 0.337464i | \(0.109569\pi\) | |||||||
\(728\) | −3.91170 | + | 1.10905i | −0.144977 | + | 0.0411043i | ||||
\(729\) | −13.0312 | −0.482636 | ||||||||
\(730\) | −1.60932 | − | 0.929142i | −0.0595636 | − | 0.0343891i | ||||
\(731\) | −0.0914197 | − | 0.158344i | −0.00338128 | − | 0.00585655i | ||||
\(732\) | −3.01661 | + | 5.22492i | −0.111497 | + | 0.193119i | ||||
\(733\) | −40.9888 | + | 23.6649i | −1.51396 | + | 0.874083i | −0.514089 | + | 0.857737i | \(0.671870\pi\) |
−0.999866 | + | 0.0163462i | \(0.994797\pi\) | |||||||
\(734\) | −16.8134 | + | 9.70721i | −0.620593 | + | 0.358300i | ||||
\(735\) | −10.4902 | + | 6.05650i | −0.386936 | + | 0.223397i | ||||
\(736\) | − | 28.0782i | − | 1.03498i | ||||||
\(737\) | −1.41552 | + | 2.45175i | −0.0521412 | + | 0.0903112i | ||||
\(738\) | 3.23498 | − | 5.60315i | 0.119081 | − | 0.206255i | ||||
\(739\) | 8.17341 | − | 4.71892i | 0.300664 | − | 0.173588i | −0.342077 | − | 0.939672i | \(-0.611130\pi\) |
0.642741 | + | 0.766083i | \(0.277797\pi\) | |||||||
\(740\) | −36.5897 | −1.34507 | ||||||||
\(741\) | −6.51088 | − | 1.64397i | −0.239183 | − | 0.0603928i | ||||
\(742\) | 3.82801 | 0.140531 | ||||||||
\(743\) | 10.0321i | 0.368044i | 0.982922 | + | 0.184022i | \(0.0589117\pi\) | ||||
−0.982922 | + | 0.184022i | \(0.941088\pi\) | |||||||
\(744\) | 2.06668 | − | 8.30119i | 0.0757682 | − | 0.304336i | ||||
\(745\) | 38.5896 | 1.41381 | ||||||||
\(746\) | 6.45601i | 0.236371i | ||||||||
\(747\) | 39.2450 | + | 22.6581i | 1.43590 | + | 0.829018i | ||||
\(748\) | 13.4290i | 0.491013i | ||||||||
\(749\) | 3.62787 | − | 2.09455i | 0.132560 | − | 0.0765334i | ||||
\(750\) | 0.951632 | − | 1.64827i | 0.0347487 | − | 0.0601865i | ||||
\(751\) | −2.93092 | + | 5.07650i | −0.106951 | + | 0.185244i | −0.914534 | − | 0.404510i | \(-0.867442\pi\) |
0.807583 | + | 0.589754i | \(0.200775\pi\) | |||||||
\(752\) | 3.17621i | 0.115824i | ||||||||
\(753\) | −0.107888 | − | 0.186867i | −0.00393165 | − | 0.00680982i | ||||
\(754\) | 14.8930 | − | 15.3304i | 0.542370 | − | 0.558301i | ||||
\(755\) | −4.44188 | − | 7.69356i | −0.161657 | − | 0.279997i | ||||
\(756\) | 1.17208 | + | 0.676698i | 0.0426280 | + | 0.0246113i | ||||
\(757\) | 8.29928 | + | 14.3748i | 0.301642 | + | 0.522460i | 0.976508 | − | 0.215481i | \(-0.0691318\pi\) |
−0.674866 | + | 0.737941i | \(0.735798\pi\) | |||||||
\(758\) | −14.9622 | + | 25.9153i | −0.543451 | + | 0.941286i | ||||
\(759\) | − | 4.67132i | − | 0.169558i | ||||||
\(760\) | 34.1460i | 1.23861i | ||||||||
\(761\) | 14.5945 | + | 8.42614i | 0.529050 | + | 0.305447i | 0.740630 | − | 0.671914i | \(-0.234527\pi\) |
−0.211580 | + | 0.977361i | \(0.567861\pi\) | |||||||
\(762\) | −7.09908 | + | 4.09866i | −0.257173 | + | 0.148479i | ||||
\(763\) | −0.974881 | + | 1.68854i | −0.0352931 | + | 0.0611294i | ||||
\(764\) | −13.8175 | − | 23.9326i | −0.499900 | − | 0.865852i | ||||
\(765\) | 53.4716 | − | 30.8718i | 1.93327 | − | 1.11617i | ||||
\(766\) | 6.63743 | + | 11.4964i | 0.239820 | + | 0.415381i | ||||
\(767\) | −2.49658 | − | 8.80558i | −0.0901463 | − | 0.317951i | ||||
\(768\) | 4.42399 | − | 7.66257i | 0.159637 | − | 0.276499i | ||||
\(769\) | −7.22585 | − | 4.17185i | −0.260571 | − | 0.150441i | 0.364024 | − | 0.931390i | \(-0.381403\pi\) |
−0.624595 | + | 0.780949i | \(0.714736\pi\) | |||||||
\(770\) | 1.02698 | + | 1.77879i | 0.0370099 | + | 0.0641030i | ||||
\(771\) | −4.82823 | −0.173884 | ||||||||
\(772\) | −1.23513 | − | 0.713102i | −0.0444533 | − | 0.0256651i | ||||
\(773\) | − | 37.6289i | − | 1.35342i | −0.736251 | − | 0.676709i | \(-0.763406\pi\) | ||
0.736251 | − | 0.676709i | \(-0.236594\pi\) | |||||||
\(774\) | − | 0.0674546i | − | 0.00242461i | ||||||
\(775\) | 33.3249 | + | 8.29663i | 1.19707 | + | 0.298024i | ||||
\(776\) | 5.49901 | 0.197403 | ||||||||
\(777\) | 1.95514 | 0.0701402 | ||||||||
\(778\) | 11.3211 | + | 6.53622i | 0.405880 | + | 0.234335i | ||||
\(779\) | 9.08607 | 0.325542 | ||||||||
\(780\) | −5.11457 | + | 5.26480i | −0.183131 | + | 0.188510i | ||||
\(781\) | 13.3174 | − | 23.0665i | 0.476535 | − | 0.825383i | ||||
\(782\) | 27.8568 | + | 16.0831i | 0.996157 | + | 0.575131i | ||||
\(783\) | −19.4757 | −0.696005 | ||||||||
\(784\) | 1.27655 | + | 2.21105i | 0.0455912 | + | 0.0789662i | ||||
\(785\) | −3.91960 | + | 2.26298i | −0.139896 | + | 0.0807693i | ||||
\(786\) | 3.81236 | − | 2.20107i | 0.135982 | − | 0.0785094i | ||||
\(787\) | −39.6702 | − | 22.9036i | −1.41409 | − | 0.816425i | −0.418319 | − | 0.908300i | \(-0.637381\pi\) |
−0.995771 | + | 0.0918750i | \(0.970714\pi\) | |||||||
\(788\) | −1.41827 | + | 0.818837i | −0.0505237 | + | 0.0291698i | ||||
\(789\) | −3.91941 | + | 6.78862i | −0.139535 | + | 0.241681i | ||||
\(790\) | 6.49061 | 0.230925 | ||||||||
\(791\) | 4.36350i | 0.155148i | ||||||||
\(792\) | −6.78116 | + | 11.7453i | −0.240958 | + | 0.417351i | ||||
\(793\) | −25.6130 | − | 24.8821i | −0.909544 | − | 0.883590i | ||||
\(794\) | −9.93992 | + | 17.2164i | −0.352754 | + | 0.610989i | ||||
\(795\) | 16.3832 | − | 9.45886i | 0.581053 | − | 0.335471i | ||||
\(796\) | 1.76151 | + | 3.05102i | 0.0624349 | + | 0.108140i | ||||
\(797\) | −12.7555 | − | 22.0932i | −0.451824 | − | 0.782582i | 0.546676 | − | 0.837345i | \(-0.315893\pi\) |
−0.998499 | + | 0.0547627i | \(0.982560\pi\) | |||||||
\(798\) | − | 0.666514i | − | 0.0235943i | ||||||
\(799\) | 50.1247 | + | 28.9395i | 1.77329 | + | 1.02381i | ||||
\(800\) | 29.1823 | + | 16.8484i | 1.03175 | + | 0.595680i | ||||
\(801\) | −29.9205 | + | 17.2746i | −1.05719 | + | 0.610368i | ||||
\(802\) | −16.8808 | −0.596081 | ||||||||
\(803\) | 0.518263 | − | 0.897658i | 0.0182891 | − | 0.0316777i | ||||
\(804\) | − | 1.00416i | − | 0.0354139i | ||||||
\(805\) | −6.67126 | −0.235131 | ||||||||
\(806\) | 16.3082 | + | 8.72642i | 0.574430 | + | 0.307375i | ||||
\(807\) | −5.92082 | −0.208423 | ||||||||
\(808\) | 20.9595i | 0.737351i | ||||||||
\(809\) | 2.50873 | − | 4.34525i | 0.0882022 | − | 0.152771i | −0.818549 | − | 0.574437i | \(-0.805221\pi\) |
0.906751 | + | 0.421666i | \(0.138554\pi\) | |||||||
\(810\) | 20.1920 | 0.709474 | ||||||||
\(811\) | 17.3151 | − | 9.99687i | 0.608015 | − | 0.351037i | −0.164173 | − | 0.986432i | \(-0.552496\pi\) |
0.772188 | + | 0.635394i | \(0.219162\pi\) | |||||||
\(812\) | −2.49121 | − | 1.43830i | −0.0874244 | − | 0.0504745i | ||||
\(813\) | 9.81839 | + | 5.66865i | 0.344346 | + | 0.198808i | ||||
\(814\) | 15.0512i | 0.527543i | ||||||||
\(815\) | −6.85547 | − | 11.8740i | −0.240136 | − | 0.415929i | ||||
\(816\) | 0.670002 | + | 1.16048i | 0.0234547 | + | 0.0406248i | ||||
\(817\) | 0.0820383 | − | 0.0473648i | 0.00287016 | − | 0.00165708i | ||||
\(818\) | 16.5506 | − | 28.6665i | 0.578679 | − | 1.00230i | ||||
\(819\) | −2.65418 | + | 2.73214i | −0.0927446 | + | 0.0954688i | ||||
\(820\) | 4.96577 | − | 8.60097i | 0.173412 | − | 0.300359i | ||||
\(821\) | − | 55.0809i | − | 1.92234i | −0.275961 | − | 0.961169i | \(-0.588996\pi\) | ||
0.275961 | − | 0.961169i | \(-0.411004\pi\) | |||||||
\(822\) | 8.07298 | 0.281578 | ||||||||
\(823\) | 7.76866 | − | 13.4557i | 0.270798 | − | 0.469037i | −0.698268 | − | 0.715836i | \(-0.746046\pi\) |
0.969067 | + | 0.246800i | \(0.0793790\pi\) | |||||||
\(824\) | −28.9309 | + | 16.7033i | −1.00786 | + | 0.581886i | ||||
\(825\) | 4.85501 | + | 2.80304i | 0.169030 | + | 0.0975893i | ||||
\(826\) | 0.786731 | − | 0.454220i | 0.0273739 | − | 0.0158043i | ||||
\(827\) | 37.8451 | − | 21.8499i | 1.31600 | − | 0.759795i | 0.332920 | − | 0.942955i | \(-0.391966\pi\) |
0.983083 | + | 0.183160i | \(0.0586328\pi\) | |||||||
\(828\) | −8.04581 | − | 13.9358i | −0.279611 | − | 0.484301i | ||||
\(829\) | 3.66182 | 0.127180 | 0.0635901 | − | 0.997976i | \(-0.479745\pi\) | ||||
0.0635901 | + | 0.997976i | \(0.479745\pi\) | |||||||
\(830\) | −44.4265 | − | 25.6497i | −1.54207 | − | 0.890312i | ||||
\(831\) | 2.04671 | − | 3.54500i | 0.0709995 | − | 0.122975i | ||||
\(832\) | 14.9454 | + | 14.5189i | 0.518137 | + | 0.503352i | ||||
\(833\) | 46.5244 | 1.61198 | ||||||||
\(834\) | −4.08821 | − | 2.36033i | −0.141563 | − | 0.0817315i | ||||
\(835\) | −55.3967 | −1.91708 | ||||||||
\(836\) | −6.95760 | −0.240634 | ||||||||
\(837\) | −4.65114 | − | 16.1994i | −0.160767 | − | 0.559933i | ||||
\(838\) | 18.2495i | 0.630420i | ||||||||
\(839\) | 4.45862i | 0.153929i | 0.997034 | + | 0.0769643i | \(0.0245227\pi\) | ||||
−0.997034 | + | 0.0769643i | \(0.975477\pi\) | |||||||
\(840\) | −1.72715 | − | 0.997169i | −0.0595922 | − | 0.0344056i | ||||
\(841\) | 12.3950 | 0.427414 | ||||||||
\(842\) | 1.40819 | + | 2.43905i | 0.0485294 | + | 0.0840554i | ||||
\(843\) | 10.3876 | + | 5.99726i | 0.357766 | + | 0.206557i | ||||
\(844\) | 14.4166 | − | 24.9704i | 0.496241 | − | 0.859515i | ||||
\(845\) | −22.8019 | − | 36.9793i | −0.784409 | − | 1.27213i | ||||
\(846\) | 10.6766 | + | 18.4924i | 0.367069 | + | 0.635783i | ||||
\(847\) | 2.70794 | − | 1.56343i | 0.0930457 | − | 0.0537200i | ||||
\(848\) | −1.99368 | − | 3.45316i | −0.0684633 | − | 0.118582i | ||||
\(849\) | −3.66423 | + | 6.34664i | −0.125756 | + | 0.217816i | ||||
\(850\) | −33.4311 | + | 19.3014i | −1.14668 | + | 0.662034i | ||||
\(851\) | −42.3365 | − | 24.4430i | −1.45128 | − | 0.837896i | ||||
\(852\) | 9.44728i | 0.323659i | ||||||||
\(853\) | − | 20.4210i | − | 0.699203i | −0.936899 | − | 0.349601i | \(-0.886317\pi\) | ||
0.936899 | − | 0.349601i | \(-0.113683\pi\) | |||||||
\(854\) | 1.77214 | − | 3.06944i | 0.0606414 | − | 0.105034i | ||||
\(855\) | 15.9948 | + | 27.7038i | 0.547010 | + | 0.947449i | ||||
\(856\) | −27.1175 | − | 15.6563i | −0.926858 | − | 0.535122i | ||||
\(857\) | 12.3972 | + | 21.4726i | 0.423481 | + | 0.733491i | 0.996277 | − | 0.0862068i | \(-0.0274746\pi\) |
−0.572796 | + | 0.819698i | \(0.694141\pi\) | |||||||
\(858\) | 2.16567 | + | 2.10387i | 0.0739348 | + | 0.0718251i | ||||
\(859\) | 19.0481 | + | 32.9923i | 0.649913 | + | 1.12568i | 0.983143 | + | 0.182837i | \(0.0585280\pi\) |
−0.333230 | + | 0.942845i | \(0.608139\pi\) | |||||||
\(860\) | − | 0.103544i | − | 0.00353084i | ||||||
\(861\) | −0.265341 | + | 0.459585i | −0.00904281 | + | 0.0156626i | ||||
\(862\) | 13.1337 | − | 22.7482i | 0.447335 | − | 0.774806i | ||||
\(863\) | 17.6592 | − | 10.1955i | 0.601125 | − | 0.347060i | −0.168359 | − | 0.985726i | \(-0.553847\pi\) |
0.769484 | + | 0.638666i | \(0.220513\pi\) | |||||||
\(864\) | − | 16.5371i | − | 0.562605i | ||||||
\(865\) | 49.8798 | + | 28.7981i | 1.69596 | + | 0.979165i | ||||
\(866\) | − | 8.73884i | − | 0.296958i | ||||||
\(867\) | 15.4219 | 0.523755 | ||||||||
\(868\) | 0.601397 | − | 2.41562i | 0.0204127 | − | 0.0819914i | ||||
\(869\) | 3.62038i | 0.122813i | ||||||||
\(870\) | 10.4838 | 0.355434 | ||||||||
\(871\) | 5.76250 | + | 1.45501i | 0.195255 | + | 0.0493011i | ||||
\(872\) | 14.5740 | 0.493539 | ||||||||
\(873\) | 4.46153 | − | 2.57586i | 0.151000 | − | 0.0871798i | ||||
\(874\) | −8.33271 | + | 14.4327i | −0.281858 | + | 0.488193i | ||||
\(875\) | 0.758064 | − | 1.31301i | 0.0256272 | − | 0.0443877i | ||||
\(876\) | 0.367652i | 0.0124218i | ||||||||
\(877\) | 34.2446 | − | 19.7711i | 1.15636 | − | 0.667624i | 0.205930 | − | 0.978567i | \(-0.433978\pi\) |
0.950429 | + | 0.310943i | \(0.100645\pi\) | |||||||
\(878\) | 10.6119 | − | 6.12678i | 0.358134 | − | 0.206769i | ||||
\(879\) | 13.1585 | − | 7.59706i | 0.443825 | − | 0.256242i | ||||
\(880\) | 1.06973 | − | 1.85283i | 0.0360607 | − | 0.0624590i | ||||
\(881\) | 23.5855 | + | 40.8512i | 0.794614 | + | 1.37631i | 0.923084 | + | 0.384599i | \(0.125660\pi\) |
−0.128470 | + | 0.991713i | \(0.541006\pi\) | |||||||
\(882\) | 14.8646 | + | 8.58208i | 0.500517 | + | 0.288974i | ||||
\(883\) | 31.8717 | 1.07257 | 0.536285 | − | 0.844037i | \(-0.319827\pi\) | ||||
0.536285 | + | 0.844037i | \(0.319827\pi\) | |||||||
\(884\) | 27.1232 | − | 7.69004i | 0.912252 | − | 0.258644i | ||||
\(885\) | 2.24472 | − | 3.88796i | 0.0754553 | − | 0.130692i | ||||
\(886\) | 32.7040 | − | 18.8817i | 1.09871 | − | 0.634343i | ||||
\(887\) | 27.6379 | − | 47.8702i | 0.927989 | − | 1.60732i | 0.141306 | − | 0.989966i | \(-0.454870\pi\) |
0.786683 | − | 0.617357i | \(-0.211797\pi\) | |||||||
\(888\) | −7.30710 | − | 12.6563i | −0.245210 | − | 0.424717i | ||||
\(889\) | −5.65508 | + | 3.26496i | −0.189665 | + | 0.109503i | ||||
\(890\) | 33.8709 | − | 19.5554i | 1.13535 | − | 0.655497i | ||||
\(891\) | 11.2628i | 0.377319i | ||||||||
\(892\) | −21.3598 | − | 12.3321i | −0.715178 | − | 0.412908i | ||||
\(893\) | −14.9936 | + | 25.9698i | −0.501743 | + | 0.869045i | ||||
\(894\) | 2.81519 | + | 4.87605i | 0.0941539 | + | 0.163079i | ||||
\(895\) | − | 43.1984i | − | 1.44396i | ||||||
\(896\) | 1.08789 | − | 1.88428i | 0.0363438 | − | 0.0629492i | ||||
\(897\) | −9.43490 | + | 2.67501i | −0.315022 | + | 0.0893159i | ||||
\(898\) | −14.2884 | −0.476811 | ||||||||
\(899\) | 9.88586 | + | 34.4313i | 0.329712 | + | 1.14835i | ||||
\(900\) | 19.3116 | 0.643721 | ||||||||
\(901\) | −72.6605 | −2.42067 | ||||||||
\(902\) | −3.53800 | − | 2.04267i | −0.117803 | − | 0.0680134i | ||||
\(903\) | 0.00553280i | 0.000184120i | ||||||||
\(904\) | 28.2464 | − | 16.3081i | 0.939462 | − | 0.542399i | ||||
\(905\) | 3.57205 | + | 2.06233i | 0.118739 | + | 0.0685540i | ||||
\(906\) | 0.648088 | − | 1.12252i | 0.0215313 | − | 0.0372933i | ||||
\(907\) | 10.7677 | 0.357535 | 0.178768 | − | 0.983891i | \(-0.442789\pi\) | ||||
0.178768 | + | 0.983891i | \(0.442789\pi\) | |||||||
\(908\) | −19.8258 | + | 11.4464i | −0.657941 | + | 0.379862i | ||||
\(909\) | 9.81790 | + | 17.0051i | 0.325639 | + | 0.564024i | ||||
\(910\) | 3.00461 | − | 3.09286i | 0.0996018 | − | 0.102527i | ||||
\(911\) | −10.6815 | + | 18.5008i | −0.353893 | + | 0.612960i | −0.986928 | − | 0.161163i | \(-0.948476\pi\) |
0.633035 | + | 0.774123i | \(0.281809\pi\) | |||||||
\(912\) | −0.601246 | + | 0.347130i | −0.0199092 | + | 0.0114946i | ||||
\(913\) | 14.3070 | − | 24.7805i | 0.473494 | − | 0.820116i | ||||
\(914\) | −19.5224 | −0.645745 | ||||||||
\(915\) | − | 17.5156i | − | 0.579047i | ||||||
\(916\) | 10.2591 | + | 5.92311i | 0.338971 | + | 0.195705i | ||||
\(917\) | 3.03690 | − | 1.75336i | 0.100287 | − | 0.0579009i | ||||
\(918\) | 16.4068 | + | 9.47244i | 0.541504 | + | 0.312637i | ||||
\(919\) | 0.476889 | + | 0.825996i | 0.0157311 | + | 0.0272471i | 0.873784 | − | 0.486315i | \(-0.161659\pi\) |
−0.858053 | + | 0.513562i | \(0.828326\pi\) | |||||||
\(920\) | 24.9331 | + | 43.1854i | 0.822019 | + | 1.42378i | ||||
\(921\) | −6.86000 | + | 3.96062i | −0.226045 | + | 0.130507i | ||||
\(922\) | 19.4644 | 0.641025 | ||||||||
\(923\) | −54.2147 | − | 13.6890i | −1.78450 | − | 0.450579i | ||||
\(924\) | 0.203183 | − | 0.351924i | 0.00668425 | − | 0.0115775i | ||||
\(925\) | 50.8083 | − | 29.3342i | 1.67057 | − | 0.964502i | ||||
\(926\) | −5.12840 | −0.168530 | ||||||||
\(927\) | −15.6484 | + | 27.1038i | −0.513961 | + | 0.890206i | ||||
\(928\) | 35.1492i | 1.15383i | ||||||||
\(929\) | − | 8.40497i | − | 0.275758i | −0.990449 | − | 0.137879i | \(-0.955971\pi\) | ||
0.990449 | − | 0.137879i | \(-0.0440285\pi\) | |||||||
\(930\) | 2.50371 | + | 8.72014i | 0.0821000 | + | 0.285945i | ||||
\(931\) | 24.1044i | 0.789991i | ||||||||
\(932\) | −10.1608 | −0.332829 | ||||||||
\(933\) | −6.16611 | + | 10.6800i | −0.201869 | + | 0.349648i | ||||
\(934\) | − | 14.9190i | − | 0.488164i | ||||||
\(935\) | −19.4934 | − | 33.7636i | −0.637503 | − | 1.10419i | ||||
\(936\) | 27.6058 | + | 6.97036i | 0.902323 | + | 0.227833i | ||||
\(937\) | −9.87366 | + | 17.1017i | −0.322558 | + | 0.558687i | −0.981015 | − | 0.193931i | \(-0.937876\pi\) |
0.658457 | + | 0.752619i | \(0.271210\pi\) | |||||||
\(938\) | 0.589903i | 0.0192610i | ||||||||
\(939\) | 2.84331 | + | 4.92476i | 0.0927880 | + | 0.160714i | ||||
\(940\) | 16.3888 | + | 28.3863i | 0.534545 | + | 0.925859i | ||||
\(941\) | 4.69039 | − | 2.70800i | 0.152902 | − | 0.0882782i | −0.421597 | − | 0.906783i | \(-0.638530\pi\) |
0.574499 | + | 0.818505i | \(0.305197\pi\) | |||||||
\(942\) | −0.571885 | − | 0.330178i | −0.0186330 | − | 0.0107578i | ||||
\(943\) | 11.4914 | − | 6.63456i | 0.374211 | − | 0.216051i | ||||
\(944\) | −0.819481 | − | 0.473128i | −0.0266718 | − | 0.0153990i | ||||
\(945\) | −3.92916 | −0.127816 | ||||||||
\(946\) | −0.0425929 | −0.00138482 | ||||||||
\(947\) | −37.2271 | − | 21.4931i | −1.20972 | − | 0.698431i | −0.247020 | − | 0.969010i | \(-0.579451\pi\) |
−0.962698 | + | 0.270580i | \(0.912785\pi\) | |||||||
\(948\) | −0.642067 | − | 1.11209i | −0.0208534 | − | 0.0361191i | ||||
\(949\) | −2.10983 | − | 0.532723i | −0.0684878 | − | 0.0172929i | ||||
\(950\) | −10.0001 | − | 17.3207i | −0.324447 | − | 0.561959i | ||||
\(951\) | −5.19221 | + | 2.99772i | −0.168369 | + | 0.0972078i | ||||
\(952\) | 3.82999 | + | 6.63374i | 0.124131 | + | 0.215001i | ||||
\(953\) | 0.870073 | 0.0281844 | 0.0140922 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140922 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(954\) | −23.2151 | − | 13.4032i | −0.751616 | − | 0.433946i | ||||
\(955\) | 69.4809 | + | 40.1148i | 2.24835 | + | 1.29808i | ||||
\(956\) | −9.86213 | + | 5.69390i | −0.318964 | + | 0.184154i | ||||
\(957\) | 5.84772i | 0.189030i | ||||||||
\(958\) | −7.97000 | + | 13.8044i | −0.257499 | + | 0.446001i | ||||
\(959\) | 6.43088 | 0.207664 | ||||||||
\(960\) | 10.2205i | 0.329864i | ||||||||
\(961\) | −26.2782 | + | 16.4456i | −0.847683 | + | 0.530504i | ||||
\(962\) | 30.3996 | − | 8.61897i | 0.980122 | − | 0.277887i | ||||
\(963\) | −29.3351 | −0.945312 | ||||||||
\(964\) | −4.48556 | − | 2.58974i | −0.144470 | − | 0.0834100i | ||||
\(965\) | 4.14054 | 0.133289 | ||||||||
\(966\) | −0.486682 | − | 0.842958i | −0.0156587 | − | 0.0271217i | ||||
\(967\) | −20.6969 | − | 11.9493i | −0.665567 | − | 0.384265i | 0.128828 | − | 0.991667i | \(-0.458878\pi\) |
−0.794395 | + | 0.607402i | \(0.792212\pi\) | |||||||
\(968\) | −20.2412 | − | 11.6863i | −0.650577 | − | 0.375611i | ||||
\(969\) | 12.6513i | 0.406417i | ||||||||
\(970\) | −5.05057 | + | 2.91595i | −0.162164 | + | 0.0936255i | ||||
\(971\) | −18.0930 | − | 31.3379i | −0.580631 | − | 1.00568i | −0.995405 | − | 0.0957579i | \(-0.969473\pi\) |
0.414774 | − | 0.909925i | \(-0.363861\pi\) | |||||||
\(972\) | −7.22410 | − | 12.5125i | −0.231713 | − | 0.401339i | ||||
\(973\) | −3.25664 | − | 1.88022i | −0.104403 | − | 0.0602772i | ||||
\(974\) | −9.74401 | − | 16.8771i | −0.312218 | − | 0.540778i | ||||
\(975\) | 2.88125 | − | 11.4110i | 0.0922737 | − | 0.365446i | ||||
\(976\) | −3.69182 | −0.118172 | ||||||||
\(977\) | 42.1760i | 1.34933i | 0.738123 | + | 0.674666i | \(0.235712\pi\) | ||||
−0.738123 | + | 0.674666i | \(0.764288\pi\) | |||||||
\(978\) | 1.00024 | − | 1.73247i | 0.0319842 | − | 0.0553982i | ||||
\(979\) | 10.9077 | + | 18.8927i | 0.348612 | + | 0.603814i | ||||
\(980\) | 22.8175 | + | 13.1737i | 0.728879 | + | 0.420818i | ||||
\(981\) | 11.8244 | − | 6.82682i | 0.377524 | − | 0.217963i | ||||
\(982\) | 10.8987 | − | 6.29236i | 0.347791 | − | 0.200797i | ||||
\(983\) | −43.5851 | + | 25.1639i | −1.39015 | + | 0.802604i | −0.993331 | − | 0.115293i | \(-0.963219\pi\) |
−0.396819 | + | 0.917897i | \(0.629886\pi\) | |||||||
\(984\) | 3.96673 | 0.126455 | ||||||||
\(985\) | 2.37723 | − | 4.11749i | 0.0757450 | − | 0.131194i | ||||
\(986\) | −34.8721 | − | 20.1334i | −1.11055 | − | 0.641178i | ||||
\(987\) | −0.875722 | − | 1.51680i | −0.0278746 | − | 0.0482801i | ||||
\(988\) | 3.98423 | + | 14.0526i | 0.126755 | + | 0.447073i | ||||
\(989\) | 0.0691707 | − | 0.119807i | 0.00219950 | − | 0.00380965i | ||||
\(990\) | − | 14.3833i | − | 0.457133i | ||||||
\(991\) | −16.3695 | −0.519995 | −0.259997 | − | 0.965609i | \(-0.583722\pi\) | ||||
−0.259997 | + | 0.965609i | \(0.583722\pi\) | |||||||
\(992\) | −29.2362 | + | 8.39426i | −0.928251 | + | 0.266518i | ||||
\(993\) | 0.929533i | 0.0294979i | ||||||||
\(994\) | − | 5.54991i | − | 0.176033i | ||||||
\(995\) | −8.85767 | − | 5.11398i | −0.280807 | − | 0.162124i | ||||
\(996\) | 10.1493i | 0.321593i | ||||||||
\(997\) | −6.78633 | − | 11.7543i | −0.214925 | − | 0.372262i | 0.738324 | − | 0.674446i | \(-0.235617\pi\) |
−0.953249 | + | 0.302184i | \(0.902284\pi\) | |||||||
\(998\) | −12.6791 | + | 21.9608i | −0.401349 | + | 0.695158i | ||||
\(999\) | −24.9349 | − | 14.3961i | −0.788904 | − | 0.455474i |
(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 | 403.2.l.c.129.23 | yes | 68 | |
13.12 | even | 2 | inner | 403.2.l.c.129.12 | yes | 68 | |
31.25 | even | 3 | inner | 403.2.l.c.25.23 | yes | 68 | |
403.25 | even | 6 | inner | 403.2.l.c.25.12 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.l.c.25.12 | ✓ | 68 | 403.25 | even | 6 | inner | |
403.2.l.c.25.23 | yes | 68 | 31.25 | even | 3 | inner | |
403.2.l.c.129.12 | yes | 68 | 13.12 | even | 2 | inner | |
403.2.l.c.129.23 | yes | 68 | 1.1 | even | 1 | trivial |