Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.14 | ||
Character | \(\chi\) | \(=\) | 690.47 |
Dual form | 690.2.i.f.323.14 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.31559 | − | 1.12660i | 0.759557 | − | 0.650440i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.192443 | − | 2.22777i | 0.0860629 | − | 0.996290i | ||||
\(6\) | 0.133641 | − | 1.72689i | 0.0545587 | − | 0.704999i | ||||
\(7\) | 1.96010 | + | 1.96010i | 0.740849 | + | 0.740849i | 0.972741 | − | 0.231893i | \(-0.0744918\pi\) |
−0.231893 | + | 0.972741i | \(0.574492\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0.461565 | − | 2.96428i | 0.153855 | − | 0.988093i | ||||
\(10\) | −1.43919 | − | 1.71135i | −0.455113 | − | 0.541176i | ||||
\(11\) | − | 2.97195i | − | 0.896078i | −0.894014 | − | 0.448039i | \(-0.852123\pi\) | ||
0.894014 | − | 0.448039i | \(-0.147877\pi\) | |||||||
\(12\) | −1.12660 | − | 1.31559i | −0.325220 | − | 0.379779i | ||||
\(13\) | −1.33263 | + | 1.33263i | −0.369605 | + | 0.369605i | −0.867333 | − | 0.497728i | \(-0.834168\pi\) |
0.497728 | + | 0.867333i | \(0.334168\pi\) | |||||||
\(14\) | 2.77200 | 0.740849 | ||||||||
\(15\) | −2.25662 | − | 3.14764i | −0.582657 | − | 0.812718i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.217329 | + | 0.217329i | −0.0527100 | + | 0.0527100i | −0.732970 | − | 0.680260i | \(-0.761867\pi\) |
0.680260 | + | 0.732970i | \(0.261867\pi\) | |||||||
\(18\) | −1.76969 | − | 2.42244i | −0.417119 | − | 0.570974i | ||||
\(19\) | 6.42606i | 1.47424i | 0.675762 | + | 0.737120i | \(0.263815\pi\) | ||||
−0.675762 | + | 0.737120i | \(0.736185\pi\) | |||||||
\(20\) | −2.22777 | − | 0.192443i | −0.498145 | − | 0.0430315i | ||||
\(21\) | 4.78694 | + | 0.370453i | 1.04459 | + | 0.0808394i | ||||
\(22\) | −2.10149 | − | 2.10149i | −0.448039 | − | 0.448039i | ||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | −1.72689 | − | 0.133641i | −0.352499 | − | 0.0272793i | ||||
\(25\) | −4.92593 | − | 0.857436i | −0.985186 | − | 0.171487i | ||||
\(26\) | 1.88462i | 0.369605i | ||||||||
\(27\) | −2.73231 | − | 4.41978i | −0.525834 | − | 0.850587i | ||||
\(28\) | 1.96010 | − | 1.96010i | 0.370424 | − | 0.370424i | ||||
\(29\) | 1.22002 | 0.226552 | 0.113276 | − | 0.993564i | \(-0.463866\pi\) | ||||
0.113276 | + | 0.993564i | \(0.463866\pi\) | |||||||
\(30\) | −3.82139 | − | 0.630048i | −0.697688 | − | 0.115030i | ||||
\(31\) | 6.33502 | 1.13780 | 0.568902 | − | 0.822405i | \(-0.307368\pi\) | ||||
0.568902 | + | 0.822405i | \(0.307368\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.34819 | − | 3.90988i | −0.582845 | − | 0.680623i | ||||
\(34\) | 0.307349i | 0.0527100i | ||||||||
\(35\) | 4.74387 | − | 3.98945i | 0.801860 | − | 0.674340i | ||||
\(36\) | −2.96428 | − | 0.461565i | −0.494047 | − | 0.0769276i | ||||
\(37\) | 1.43305 | + | 1.43305i | 0.235592 | + | 0.235592i | 0.815022 | − | 0.579430i | \(-0.196725\pi\) |
−0.579430 | + | 0.815022i | \(0.696725\pi\) | |||||||
\(38\) | 4.54391 | + | 4.54391i | 0.737120 | + | 0.737120i | ||||
\(39\) | −0.251863 | + | 3.25453i | −0.0403303 | + | 0.521142i | ||||
\(40\) | −1.71135 | + | 1.43919i | −0.270588 | + | 0.227557i | ||||
\(41\) | 3.04579i | 0.475672i | 0.971305 | + | 0.237836i | \(0.0764380\pi\) | ||||
−0.971305 | + | 0.237836i | \(0.923562\pi\) | |||||||
\(42\) | 3.64682 | − | 3.12292i | 0.562717 | − | 0.481878i | ||||
\(43\) | −1.80190 | + | 1.80190i | −0.274786 | + | 0.274786i | −0.831024 | − | 0.556237i | \(-0.812245\pi\) |
0.556237 | + | 0.831024i | \(0.312245\pi\) | |||||||
\(44\) | −2.97195 | −0.448039 | ||||||||
\(45\) | −6.51491 | − | 1.59872i | −0.971186 | − | 0.238323i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −0.199419 | + | 0.199419i | −0.0290883 | + | 0.0290883i | −0.721501 | − | 0.692413i | \(-0.756548\pi\) |
0.692413 | + | 0.721501i | \(0.256548\pi\) | |||||||
\(48\) | −1.31559 | + | 1.12660i | −0.189889 | + | 0.162610i | ||||
\(49\) | 0.683996i | 0.0977137i | ||||||||
\(50\) | −4.08946 | + | 2.87686i | −0.578337 | + | 0.406850i | ||||
\(51\) | −0.0410744 | + | 0.530758i | −0.00575157 | + | 0.0743210i | ||||
\(52\) | 1.33263 | + | 1.33263i | 0.184803 | + | 0.184803i | ||||
\(53\) | −9.17886 | − | 9.17886i | −1.26081 | − | 1.26081i | −0.950699 | − | 0.310114i | \(-0.899633\pi\) |
−0.310114 | − | 0.950699i | \(-0.600367\pi\) | |||||||
\(54\) | −5.05729 | − | 1.19322i | −0.688211 | − | 0.162377i | ||||
\(55\) | −6.62083 | − | 0.571930i | −0.892753 | − | 0.0771191i | ||||
\(56\) | − | 2.77200i | − | 0.370424i | ||||||
\(57\) | 7.23957 | + | 8.45408i | 0.958905 | + | 1.11977i | ||||
\(58\) | 0.862686 | − | 0.862686i | 0.113276 | − | 0.113276i | ||||
\(59\) | −9.43000 | −1.22768 | −0.613841 | − | 0.789430i | \(-0.710376\pi\) | ||||
−0.613841 | + | 0.789430i | \(0.710376\pi\) | |||||||
\(60\) | −3.14764 | + | 2.25662i | −0.406359 | + | 0.291329i | ||||
\(61\) | 5.57225 | 0.713454 | 0.356727 | − | 0.934209i | \(-0.383893\pi\) | ||||
0.356727 | + | 0.934209i | \(0.383893\pi\) | |||||||
\(62\) | 4.47954 | − | 4.47954i | 0.568902 | − | 0.568902i | ||||
\(63\) | 6.71501 | − | 4.90558i | 0.846011 | − | 0.618044i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 2.71234 | + | 3.22525i | 0.336425 | + | 0.400043i | ||||
\(66\) | −5.13223 | − | 0.397175i | −0.631734 | − | 0.0488888i | ||||
\(67\) | 9.41060 | + | 9.41060i | 1.14969 | + | 1.14969i | 0.986614 | + | 0.163074i | \(0.0521410\pi\) |
0.163074 | + | 0.986614i | \(0.447859\pi\) | |||||||
\(68\) | 0.217329 | + | 0.217329i | 0.0263550 | + | 0.0263550i | ||||
\(69\) | 1.72689 | + | 0.133641i | 0.207893 | + | 0.0160885i | ||||
\(70\) | 0.533451 | − | 6.17539i | 0.0637596 | − | 0.738100i | ||||
\(71\) | 7.64983i | 0.907868i | 0.891035 | + | 0.453934i | \(0.149980\pi\) | ||||
−0.891035 | + | 0.453934i | \(0.850020\pi\) | |||||||
\(72\) | −2.42244 | + | 1.76969i | −0.285487 | + | 0.208560i | ||||
\(73\) | −4.05708 | + | 4.05708i | −0.474845 | + | 0.474845i | −0.903479 | − | 0.428633i | \(-0.858995\pi\) |
0.428633 | + | 0.903479i | \(0.358995\pi\) | |||||||
\(74\) | 2.02664 | 0.235592 | ||||||||
\(75\) | −7.44650 | + | 4.42150i | −0.859848 | + | 0.510550i | ||||
\(76\) | 6.42606 | 0.737120 | ||||||||
\(77\) | 5.82533 | − | 5.82533i | 0.663858 | − | 0.663858i | ||||
\(78\) | 2.12321 | + | 2.47940i | 0.240406 | + | 0.280736i | ||||
\(79\) | − | 14.4298i | − | 1.62348i | −0.584018 | − | 0.811741i | \(-0.698520\pi\) | ||
0.584018 | − | 0.811741i | \(-0.301480\pi\) | |||||||
\(80\) | −0.192443 | + | 2.22777i | −0.0215157 | + | 0.249072i | ||||
\(81\) | −8.57391 | − | 2.73642i | −0.952657 | − | 0.304047i | ||||
\(82\) | 2.15370 | + | 2.15370i | 0.237836 | + | 0.237836i | ||||
\(83\) | 12.1736 | + | 12.1736i | 1.33622 | + | 1.33622i | 0.899688 | + | 0.436533i | \(0.143794\pi\) |
0.436533 | + | 0.899688i | \(0.356206\pi\) | |||||||
\(84\) | 0.370453 | − | 4.78694i | 0.0404197 | − | 0.522297i | ||||
\(85\) | 0.442336 | + | 0.525982i | 0.0479780 | + | 0.0570508i | ||||
\(86\) | 2.54827i | 0.274786i | ||||||||
\(87\) | 1.60505 | − | 1.37447i | 0.172080 | − | 0.147359i | ||||
\(88\) | −2.10149 | + | 2.10149i | −0.224019 | + | 0.224019i | ||||
\(89\) | 2.45643 | 0.260381 | 0.130191 | − | 0.991489i | \(-0.458441\pi\) | ||||
0.130191 | + | 0.991489i | \(0.458441\pi\) | |||||||
\(90\) | −5.73720 | + | 3.47628i | −0.604754 | + | 0.366432i | ||||
\(91\) | −5.22418 | −0.547643 | ||||||||
\(92\) | 0.707107 | − | 0.707107i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | 8.33431 | − | 7.13701i | 0.864227 | − | 0.740073i | ||||
\(94\) | 0.282021i | 0.0290883i | ||||||||
\(95\) | 14.3158 | + | 1.23665i | 1.46877 | + | 0.126877i | ||||
\(96\) | −0.133641 | + | 1.72689i | −0.0136397 | + | 0.176250i | ||||
\(97\) | 8.98748 | + | 8.98748i | 0.912541 | + | 0.912541i | 0.996472 | − | 0.0839309i | \(-0.0267475\pi\) |
−0.0839309 | + | 0.996472i | \(0.526748\pi\) | |||||||
\(98\) | 0.483658 | + | 0.483658i | 0.0488568 | + | 0.0488568i | ||||
\(99\) | −8.80970 | − | 1.37175i | −0.885409 | − | 0.137866i | ||||
\(100\) | −0.857436 | + | 4.92593i | −0.0857436 | + | 0.492593i | ||||
\(101\) | 3.00976i | 0.299482i | 0.988725 | + | 0.149741i | \(0.0478440\pi\) | ||||
−0.988725 | + | 0.149741i | \(0.952156\pi\) | |||||||
\(102\) | 0.346258 | + | 0.404346i | 0.0342847 | + | 0.0400363i | ||||
\(103\) | −1.81831 | + | 1.81831i | −0.179163 | + | 0.179163i | −0.790991 | − | 0.611828i | \(-0.790435\pi\) |
0.611828 | + | 0.790991i | \(0.290435\pi\) | |||||||
\(104\) | 1.88462 | 0.184803 | ||||||||
\(105\) | 1.74649 | − | 10.5929i | 0.170440 | − | 1.03376i | ||||
\(106\) | −12.9809 | −1.26081 | ||||||||
\(107\) | 10.1552 | − | 10.1552i | 0.981744 | − | 0.981744i | −0.0180921 | − | 0.999836i | \(-0.505759\pi\) |
0.999836 | + | 0.0180921i | \(0.00575922\pi\) | |||||||
\(108\) | −4.41978 | + | 2.73231i | −0.425294 | + | 0.262917i | ||||
\(109\) | − | 3.22282i | − | 0.308690i | −0.988017 | − | 0.154345i | \(-0.950673\pi\) | ||
0.988017 | − | 0.154345i | \(-0.0493268\pi\) | |||||||
\(110\) | −5.08605 | + | 4.27722i | −0.484936 | + | 0.407817i | ||||
\(111\) | 3.49978 | + | 0.270842i | 0.332184 | + | 0.0257072i | ||||
\(112\) | −1.96010 | − | 1.96010i | −0.185212 | − | 0.185212i | ||||
\(113\) | 3.72990 | + | 3.72990i | 0.350880 | + | 0.350880i | 0.860437 | − | 0.509557i | \(-0.170191\pi\) |
−0.509557 | + | 0.860437i | \(0.670191\pi\) | |||||||
\(114\) | 11.0971 | + | 0.858785i | 1.03934 | + | 0.0804326i | ||||
\(115\) | 1.71135 | − | 1.43919i | 0.159584 | − | 0.134206i | ||||
\(116\) | − | 1.22002i | − | 0.113276i | ||||||
\(117\) | 3.33519 | + | 4.56539i | 0.308339 | + | 0.422070i | ||||
\(118\) | −6.66802 | + | 6.66802i | −0.613841 | + | 0.613841i | ||||
\(119\) | −0.851973 | −0.0781003 | ||||||||
\(120\) | −0.630048 | + | 3.82139i | −0.0575152 | + | 0.348844i | ||||
\(121\) | 2.16749 | 0.197044 | ||||||||
\(122\) | 3.94018 | − | 3.94018i | 0.356727 | − | 0.356727i | ||||
\(123\) | 3.43137 | + | 4.00701i | 0.309396 | + | 0.361300i | ||||
\(124\) | − | 6.33502i | − | 0.568902i | ||||||
\(125\) | −2.85813 | + | 10.8088i | −0.255639 | + | 0.966772i | ||||
\(126\) | 1.27946 | − | 8.21699i | 0.113983 | − | 0.732028i | ||||
\(127\) | −9.95020 | − | 9.95020i | −0.882938 | − | 0.882938i | 0.110895 | − | 0.993832i | \(-0.464628\pi\) |
−0.993832 | + | 0.110895i | \(0.964628\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −0.340552 | + | 4.40057i | −0.0299840 | + | 0.387448i | ||||
\(130\) | 4.19851 | + | 0.362682i | 0.368234 | + | 0.0318093i | ||||
\(131\) | 4.14724i | 0.362346i | 0.983451 | + | 0.181173i | \(0.0579894\pi\) | ||||
−0.983451 | + | 0.181173i | \(0.942011\pi\) | |||||||
\(132\) | −3.90988 | + | 3.34819i | −0.340311 | + | 0.291423i | ||||
\(133\) | −12.5957 | + | 12.5957i | −1.09219 | + | 1.09219i | ||||
\(134\) | 13.3086 | 1.14969 | ||||||||
\(135\) | −10.3721 | + | 5.23641i | −0.892686 | + | 0.450679i | ||||
\(136\) | 0.307349 | 0.0263550 | ||||||||
\(137\) | −6.71805 | + | 6.71805i | −0.573962 | + | 0.573962i | −0.933233 | − | 0.359271i | \(-0.883025\pi\) |
0.359271 | + | 0.933233i | \(0.383025\pi\) | |||||||
\(138\) | 1.31559 | − | 1.12660i | 0.111991 | − | 0.0959022i | ||||
\(139\) | − | 21.3303i | − | 1.80921i | −0.426247 | − | 0.904607i | \(-0.640165\pi\) | ||
0.426247 | − | 0.904607i | \(-0.359835\pi\) | |||||||
\(140\) | −3.98945 | − | 4.74387i | −0.337170 | − | 0.400930i | ||||
\(141\) | −0.0376896 | + | 0.487019i | −0.00317404 | + | 0.0410144i | ||||
\(142\) | 5.40925 | + | 5.40925i | 0.453934 | + | 0.453934i | ||||
\(143\) | 3.96052 | + | 3.96052i | 0.331195 | + | 0.331195i | ||||
\(144\) | −0.461565 | + | 2.96428i | −0.0384638 | + | 0.247023i | ||||
\(145\) | 0.234784 | − | 2.71793i | 0.0194978 | − | 0.225712i | ||||
\(146\) | 5.73758i | 0.474845i | ||||||||
\(147\) | 0.770587 | + | 0.899860i | 0.0635569 | + | 0.0742192i | ||||
\(148\) | 1.43305 | − | 1.43305i | 0.117796 | − | 0.117796i | ||||
\(149\) | −2.04707 | −0.167703 | −0.0838514 | − | 0.996478i | \(-0.526722\pi\) | ||||
−0.0838514 | + | 0.996478i | \(0.526722\pi\) | |||||||
\(150\) | −2.13900 | + | 8.39194i | −0.174649 | + | 0.685199i | ||||
\(151\) | −2.64015 | −0.214852 | −0.107426 | − | 0.994213i | \(-0.534261\pi\) | ||||
−0.107426 | + | 0.994213i | \(0.534261\pi\) | |||||||
\(152\) | 4.54391 | − | 4.54391i | 0.368560 | − | 0.368560i | ||||
\(153\) | 0.543912 | + | 0.744535i | 0.0439727 | + | 0.0601921i | ||||
\(154\) | − | 8.23826i | − | 0.663858i | ||||||
\(155\) | 1.21913 | − | 14.1130i | 0.0979227 | − | 1.13358i | ||||
\(156\) | 3.25453 | + | 0.251863i | 0.260571 | + | 0.0201652i | ||||
\(157\) | 0.750993 | + | 0.750993i | 0.0599358 | + | 0.0599358i | 0.736439 | − | 0.676504i | \(-0.236506\pi\) |
−0.676504 | + | 0.736439i | \(0.736506\pi\) | |||||||
\(158\) | −10.2034 | − | 10.2034i | −0.811741 | − | 0.811741i | ||||
\(159\) | −22.4165 | − | 1.73477i | −1.77774 | − | 0.137577i | ||||
\(160\) | 1.43919 | + | 1.71135i | 0.113778 | + | 0.135294i | ||||
\(161\) | 2.77200i | 0.218464i | ||||||||
\(162\) | −7.99761 | + | 4.12773i | −0.628352 | + | 0.324305i | ||||
\(163\) | 6.60415 | − | 6.60415i | 0.517277 | − | 0.517277i | −0.399469 | − | 0.916747i | \(-0.630806\pi\) |
0.916747 | + | 0.399469i | \(0.130806\pi\) | |||||||
\(164\) | 3.04579 | 0.237836 | ||||||||
\(165\) | −9.35465 | + | 6.70657i | −0.728259 | + | 0.522106i | ||||
\(166\) | 17.2160 | 1.33622 | ||||||||
\(167\) | −5.25056 | + | 5.25056i | −0.406300 | + | 0.406300i | −0.880446 | − | 0.474146i | \(-0.842757\pi\) |
0.474146 | + | 0.880446i | \(0.342757\pi\) | |||||||
\(168\) | −3.12292 | − | 3.64682i | −0.240939 | − | 0.281359i | ||||
\(169\) | 9.44819i | 0.726784i | ||||||||
\(170\) | 0.684704 | + | 0.0591471i | 0.0525144 | + | 0.00453638i | ||||
\(171\) | 19.0487 | + | 2.96605i | 1.45669 | + | 0.226819i | ||||
\(172\) | 1.80190 | + | 1.80190i | 0.137393 | + | 0.137393i | ||||
\(173\) | 16.1787 | + | 16.1787i | 1.23004 | + | 1.23004i | 0.963947 | + | 0.266093i | \(0.0857329\pi\) |
0.266093 | + | 0.963947i | \(0.414267\pi\) | |||||||
\(174\) | 0.163045 | − | 2.10684i | 0.0123604 | − | 0.159719i | ||||
\(175\) | −7.97466 | − | 11.3360i | −0.602828 | − | 0.856920i | ||||
\(176\) | 2.97195i | 0.224019i | ||||||||
\(177\) | −12.4060 | + | 10.6238i | −0.932495 | + | 0.798533i | ||||
\(178\) | 1.73696 | − | 1.73696i | 0.130191 | − | 0.130191i | ||||
\(179\) | −12.6087 | −0.942418 | −0.471209 | − | 0.882022i | \(-0.656182\pi\) | ||||
−0.471209 | + | 0.882022i | \(0.656182\pi\) | |||||||
\(180\) | −1.59872 | + | 6.51491i | −0.119161 | + | 0.485593i | ||||
\(181\) | −1.75381 | −0.130360 | −0.0651799 | − | 0.997874i | \(-0.520762\pi\) | ||||
−0.0651799 | + | 0.997874i | \(0.520762\pi\) | |||||||
\(182\) | −3.69405 | + | 3.69405i | −0.273822 | + | 0.273822i | ||||
\(183\) | 7.33081 | − | 6.27767i | 0.541909 | − | 0.464059i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 3.46829 | − | 2.91673i | 0.254994 | − | 0.214442i | ||||
\(186\) | 0.846618 | − | 10.9399i | 0.0620771 | − | 0.802150i | ||||
\(187\) | 0.645891 | + | 0.645891i | 0.0472322 | + | 0.0472322i | ||||
\(188\) | 0.199419 | + | 0.199419i | 0.0145441 | + | 0.0145441i | ||||
\(189\) | 3.30761 | − | 14.0188i | 0.240593 | − | 1.01972i | ||||
\(190\) | 10.9972 | − | 9.24836i | 0.797824 | − | 0.670946i | ||||
\(191\) | 26.9285i | 1.94848i | 0.225520 | + | 0.974238i | \(0.427592\pi\) | ||||
−0.225520 | + | 0.974238i | \(0.572408\pi\) | |||||||
\(192\) | 1.12660 | + | 1.31559i | 0.0813050 | + | 0.0949447i | ||||
\(193\) | −10.9317 | + | 10.9317i | −0.786878 | + | 0.786878i | −0.980981 | − | 0.194103i | \(-0.937820\pi\) |
0.194103 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(194\) | 12.7102 | 0.912541 | ||||||||
\(195\) | 7.20189 | + | 1.18740i | 0.515738 | + | 0.0850317i | ||||
\(196\) | 0.683996 | 0.0488568 | ||||||||
\(197\) | 1.97929 | − | 1.97929i | 0.141019 | − | 0.141019i | −0.633073 | − | 0.774092i | \(-0.718207\pi\) |
0.774092 | + | 0.633073i | \(0.218207\pi\) | |||||||
\(198\) | −7.19938 | + | 5.25943i | −0.511637 | + | 0.373771i | ||||
\(199\) | − | 15.8892i | − | 1.12636i | −0.826336 | − | 0.563178i | \(-0.809579\pi\) | ||
0.826336 | − | 0.563178i | \(-0.190421\pi\) | |||||||
\(200\) | 2.87686 | + | 4.08946i | 0.203425 | + | 0.289168i | ||||
\(201\) | 22.9825 | + | 1.77857i | 1.62106 | + | 0.125451i | ||||
\(202\) | 2.12822 | + | 2.12822i | 0.149741 | + | 0.149741i | ||||
\(203\) | 2.39137 | + | 2.39137i | 0.167841 | + | 0.167841i | ||||
\(204\) | 0.530758 | + | 0.0410744i | 0.0371605 | + | 0.00287579i | ||||
\(205\) | 6.78531 | + | 0.586139i | 0.473907 | + | 0.0409377i | ||||
\(206\) | 2.57147i | 0.179163i | ||||||||
\(207\) | 2.42244 | − | 1.76969i | 0.168371 | − | 0.123002i | ||||
\(208\) | 1.33263 | − | 1.33263i | 0.0924013 | − | 0.0924013i | ||||
\(209\) | 19.0980 | 1.32103 | ||||||||
\(210\) | −6.25536 | − | 8.72527i | −0.431661 | − | 0.602101i | ||||
\(211\) | 11.3907 | 0.784169 | 0.392085 | − | 0.919929i | \(-0.371754\pi\) | ||||
0.392085 | + | 0.919929i | \(0.371754\pi\) | |||||||
\(212\) | −9.17886 | + | 9.17886i | −0.630407 | + | 0.630407i | ||||
\(213\) | 8.61826 | + | 10.0641i | 0.590514 | + | 0.689578i | ||||
\(214\) | − | 14.3617i | − | 0.981744i | ||||||
\(215\) | 3.66745 | + | 4.36097i | 0.250118 | + | 0.297416i | ||||
\(216\) | −1.19322 | + | 5.05729i | −0.0811884 | + | 0.344105i | ||||
\(217\) | 12.4173 | + | 12.4173i | 0.842941 | + | 0.842941i | ||||
\(218\) | −2.27888 | − | 2.27888i | −0.154345 | − | 0.154345i | ||||
\(219\) | −0.766775 | + | 9.90815i | −0.0518138 | + | 0.669531i | ||||
\(220\) | −0.571930 | + | 6.62083i | −0.0385595 | + | 0.446377i | ||||
\(221\) | − | 0.579238i | − | 0.0389638i | ||||||
\(222\) | 2.66623 | − | 2.28320i | 0.178946 | − | 0.153239i | ||||
\(223\) | −10.4680 | + | 10.4680i | −0.700989 | + | 0.700989i | −0.964623 | − | 0.263634i | \(-0.915079\pi\) |
0.263634 | + | 0.964623i | \(0.415079\pi\) | |||||||
\(224\) | −2.77200 | −0.185212 | ||||||||
\(225\) | −4.81532 | + | 14.2061i | −0.321021 | + | 0.947072i | ||||
\(226\) | 5.27488 | 0.350880 | ||||||||
\(227\) | 16.1663 | − | 16.1663i | 1.07299 | − | 1.07299i | 0.0758747 | − | 0.997117i | \(-0.475825\pi\) |
0.997117 | − | 0.0758747i | \(-0.0241749\pi\) | |||||||
\(228\) | 8.45408 | − | 7.23957i | 0.559885 | − | 0.479453i | ||||
\(229\) | − | 16.0298i | − | 1.05928i | −0.848224 | − | 0.529638i | \(-0.822328\pi\) | ||
0.848224 | − | 0.529638i | \(-0.177672\pi\) | |||||||
\(230\) | 0.192443 | − | 2.22777i | 0.0126893 | − | 0.146895i | ||||
\(231\) | 1.10097 | − | 14.2266i | 0.0724384 | − | 0.936038i | ||||
\(232\) | −0.862686 | − | 0.862686i | −0.0566381 | − | 0.0566381i | ||||
\(233\) | 4.14654 | + | 4.14654i | 0.271649 | + | 0.271649i | 0.829764 | − | 0.558115i | \(-0.188475\pi\) |
−0.558115 | + | 0.829764i | \(0.688475\pi\) | |||||||
\(234\) | 5.58655 | + | 0.869877i | 0.365204 | + | 0.0568657i | ||||
\(235\) | 0.405884 | + | 0.482637i | 0.0264769 | + | 0.0314838i | ||||
\(236\) | 9.43000i | 0.613841i | ||||||||
\(237\) | −16.2566 | − | 18.9838i | −1.05598 | − | 1.23313i | ||||
\(238\) | −0.602436 | + | 0.602436i | −0.0390501 | + | 0.0390501i | ||||
\(239\) | −29.7656 | −1.92538 | −0.962690 | − | 0.270608i | \(-0.912775\pi\) | ||||
−0.962690 | + | 0.270608i | \(0.912775\pi\) | |||||||
\(240\) | 2.25662 | + | 3.14764i | 0.145664 | + | 0.203180i | ||||
\(241\) | −18.1553 | −1.16949 | −0.584743 | − | 0.811219i | \(-0.698805\pi\) | ||||
−0.584743 | + | 0.811219i | \(0.698805\pi\) | |||||||
\(242\) | 1.53265 | − | 1.53265i | 0.0985222 | − | 0.0985222i | ||||
\(243\) | −14.3626 | + | 6.05932i | −0.921362 | + | 0.388706i | ||||
\(244\) | − | 5.57225i | − | 0.356727i | ||||||
\(245\) | 1.52379 | + | 0.131630i | 0.0973512 | + | 0.00840953i | ||||
\(246\) | 5.25973 | + | 0.407041i | 0.335348 | + | 0.0259520i | ||||
\(247\) | −8.56357 | − | 8.56357i | −0.544887 | − | 0.544887i | ||||
\(248\) | −4.47954 | − | 4.47954i | −0.284451 | − | 0.284451i | ||||
\(249\) | 29.7301 | + | 2.30076i | 1.88407 | + | 0.145805i | ||||
\(250\) | 5.62200 | + | 9.66401i | 0.355567 | + | 0.611206i | ||||
\(251\) | − | 19.1213i | − | 1.20693i | −0.797390 | − | 0.603464i | \(-0.793787\pi\) | ||
0.797390 | − | 0.603464i | \(-0.206213\pi\) | |||||||
\(252\) | −4.90558 | − | 6.71501i | −0.309022 | − | 0.423006i | ||||
\(253\) | 2.10149 | − | 2.10149i | 0.132119 | − | 0.132119i | ||||
\(254\) | −14.0717 | −0.882938 | ||||||||
\(255\) | 1.17450 | + | 0.193645i | 0.0735502 | + | 0.0121265i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.0084 | + | 17.0084i | −1.06096 | + | 1.06096i | −0.0629387 | + | 0.998017i | \(0.520047\pi\) |
−0.998017 | + | 0.0629387i | \(0.979953\pi\) | |||||||
\(258\) | 2.87086 | + | 3.35248i | 0.178732 | + | 0.208716i | ||||
\(259\) | 5.61785i | 0.349076i | ||||||||
\(260\) | 3.22525 | − | 2.71234i | 0.200022 | − | 0.168212i | ||||
\(261\) | 0.563120 | − | 3.61649i | 0.0348563 | − | 0.223855i | ||||
\(262\) | 2.93254 | + | 2.93254i | 0.181173 | + | 0.181173i | ||||
\(263\) | −12.3574 | − | 12.3574i | −0.761992 | − | 0.761992i | 0.214690 | − | 0.976682i | \(-0.431126\pi\) |
−0.976682 | + | 0.214690i | \(0.931126\pi\) | |||||||
\(264\) | −0.397175 | + | 5.13223i | −0.0244444 | + | 0.315867i | ||||
\(265\) | −22.2148 | + | 18.6820i | −1.36464 | + | 1.14763i | ||||
\(266\) | 17.8131i | 1.09219i | ||||||||
\(267\) | 3.23166 | − | 2.76740i | 0.197774 | − | 0.169362i | ||||
\(268\) | 9.41060 | − | 9.41060i | 0.574844 | − | 0.574844i | ||||
\(269\) | −20.0999 | −1.22552 | −0.612758 | − | 0.790271i | \(-0.709940\pi\) | ||||
−0.612758 | + | 0.790271i | \(0.709940\pi\) | |||||||
\(270\) | −3.63146 | + | 11.0369i | −0.221004 | + | 0.671682i | ||||
\(271\) | −27.8676 | −1.69284 | −0.846419 | − | 0.532518i | \(-0.821246\pi\) | ||||
−0.846419 | + | 0.532518i | \(0.821246\pi\) | |||||||
\(272\) | 0.217329 | − | 0.217329i | 0.0131775 | − | 0.0131775i | ||||
\(273\) | −6.87289 | + | 5.88554i | −0.415966 | + | 0.356209i | ||||
\(274\) | 9.50076i | 0.573962i | ||||||||
\(275\) | −2.54826 | + | 14.6396i | −0.153666 | + | 0.882804i | ||||
\(276\) | 0.133641 | − | 1.72689i | 0.00804423 | − | 0.103946i | ||||
\(277\) | 7.04930 | + | 7.04930i | 0.423551 | + | 0.423551i | 0.886424 | − | 0.462873i | \(-0.153182\pi\) |
−0.462873 | + | 0.886424i | \(0.653182\pi\) | |||||||
\(278\) | −15.0828 | − | 15.0828i | −0.904607 | − | 0.904607i | ||||
\(279\) | 2.92403 | − | 18.7788i | 0.175057 | − | 1.12426i | ||||
\(280\) | −6.17539 | − | 0.533451i | −0.369050 | − | 0.0318798i | ||||
\(281\) | − | 15.7886i | − | 0.941867i | −0.882169 | − | 0.470934i | \(-0.843917\pi\) | ||
0.882169 | − | 0.470934i | \(-0.156083\pi\) | |||||||
\(282\) | 0.317724 | + | 0.371025i | 0.0189202 | + | 0.0220942i | ||||
\(283\) | 13.2043 | − | 13.2043i | 0.784912 | − | 0.784912i | −0.195743 | − | 0.980655i | \(-0.562712\pi\) |
0.980655 | + | 0.195743i | \(0.0627118\pi\) | |||||||
\(284\) | 7.64983 | 0.453934 | ||||||||
\(285\) | 20.2270 | − | 14.5012i | 1.19814 | − | 0.858977i | ||||
\(286\) | 5.60102 | 0.331195 | ||||||||
\(287\) | −5.97005 | + | 5.97005i | −0.352401 | + | 0.352401i | ||||
\(288\) | 1.76969 | + | 2.42244i | 0.104280 | + | 0.142744i | ||||
\(289\) | 16.9055i | 0.994443i | ||||||||
\(290\) | −1.75585 | − | 2.08788i | −0.103107 | − | 0.122605i | ||||
\(291\) | 21.9491 | + | 1.69860i | 1.28668 | + | 0.0995740i | ||||
\(292\) | 4.05708 | + | 4.05708i | 0.237423 | + | 0.237423i | ||||
\(293\) | −6.93824 | − | 6.93824i | −0.405336 | − | 0.405336i | 0.474772 | − | 0.880109i | \(-0.342530\pi\) |
−0.880109 | + | 0.474772i | \(0.842530\pi\) | |||||||
\(294\) | 1.18118 | + | 0.0914098i | 0.0688880 | + | 0.00533113i | ||||
\(295\) | −1.81473 | + | 21.0079i | −0.105658 | + | 1.22313i | ||||
\(296\) | − | 2.02664i | − | 0.117796i | ||||||
\(297\) | −13.1354 | + | 8.12031i | −0.762192 | + | 0.471188i | ||||
\(298\) | −1.44750 | + | 1.44750i | −0.0838514 | + | 0.0838514i | ||||
\(299\) | −1.88462 | −0.108991 | ||||||||
\(300\) | 4.42150 | + | 7.44650i | 0.255275 | + | 0.429924i | ||||
\(301\) | −7.06380 | −0.407150 | ||||||||
\(302\) | −1.86687 | + | 1.86687i | −0.107426 | + | 0.107426i | ||||
\(303\) | 3.39078 | + | 3.95962i | 0.194795 | + | 0.227474i | ||||
\(304\) | − | 6.42606i | − | 0.368560i | ||||||
\(305\) | 1.07234 | − | 12.4137i | 0.0614019 | − | 0.710807i | ||||
\(306\) | 0.911070 | + | 0.141862i | 0.0520824 | + | 0.00810970i | ||||
\(307\) | −8.38939 | − | 8.38939i | −0.478808 | − | 0.478808i | 0.425943 | − | 0.904750i | \(-0.359943\pi\) |
−0.904750 | + | 0.425943i | \(0.859943\pi\) | |||||||
\(308\) | −5.82533 | − | 5.82533i | −0.331929 | − | 0.331929i | ||||
\(309\) | −0.343654 | + | 4.44065i | −0.0195498 | + | 0.252620i | ||||
\(310\) | −9.11733 | − | 10.8414i | −0.517830 | − | 0.615753i | ||||
\(311\) | − | 22.7094i | − | 1.28773i | −0.765139 | − | 0.643865i | \(-0.777330\pi\) | ||
0.765139 | − | 0.643865i | \(-0.222670\pi\) | |||||||
\(312\) | 2.47940 | − | 2.12321i | 0.140368 | − | 0.120203i | ||||
\(313\) | −19.0911 | + | 19.0911i | −1.07909 | + | 1.07909i | −0.0825035 | + | 0.996591i | \(0.526292\pi\) |
−0.996591 | + | 0.0825035i | \(0.973708\pi\) | |||||||
\(314\) | 1.06206 | 0.0599358 | ||||||||
\(315\) | −9.63625 | − | 15.9035i | −0.542941 | − | 0.896063i | ||||
\(316\) | −14.4298 | −0.811741 | ||||||||
\(317\) | 0.0275450 | − | 0.0275450i | 0.00154708 | − | 0.00154708i | −0.706333 | − | 0.707880i | \(-0.749652\pi\) |
0.707880 | + | 0.706333i | \(0.249652\pi\) | |||||||
\(318\) | −17.0775 | + | 14.6242i | −0.957660 | + | 0.820084i | ||||
\(319\) | − | 3.62585i | − | 0.203009i | ||||||
\(320\) | 2.22777 | + | 0.192443i | 0.124536 | + | 0.0107579i | ||||
\(321\) | 1.91931 | − | 24.8010i | 0.107125 | − | 1.38426i | ||||
\(322\) | 1.96010 | + | 1.96010i | 0.109232 | + | 0.109232i | ||||
\(323\) | −1.39657 | − | 1.39657i | −0.0777072 | − | 0.0777072i | ||||
\(324\) | −2.73642 | + | 8.57391i | −0.152023 | + | 0.476329i | ||||
\(325\) | 7.70709 | − | 5.42180i | 0.427513 | − | 0.300747i | ||||
\(326\) | − | 9.33968i | − | 0.517277i | ||||||
\(327\) | −3.63082 | − | 4.23992i | −0.200785 | − | 0.234468i | ||||
\(328\) | 2.15370 | − | 2.15370i | 0.118918 | − | 0.118918i | ||||
\(329\) | −0.781764 | −0.0431000 | ||||||||
\(330\) | −1.87247 | + | 11.3570i | −0.103076 | + | 0.625182i | ||||
\(331\) | 1.05162 | 0.0578024 | 0.0289012 | − | 0.999582i | \(-0.490799\pi\) | ||||
0.0289012 | + | 0.999582i | \(0.490799\pi\) | |||||||
\(332\) | 12.1736 | − | 12.1736i | 0.668111 | − | 0.668111i | ||||
\(333\) | 4.90941 | − | 3.58652i | 0.269034 | − | 0.196540i | ||||
\(334\) | 7.42541i | 0.406300i | ||||||||
\(335\) | 22.7757 | − | 19.1537i | 1.24437 | − | 1.04648i | ||||
\(336\) | −4.78694 | − | 0.370453i | −0.261149 | − | 0.0202099i | ||||
\(337\) | −10.0242 | − | 10.0242i | −0.546054 | − | 0.546054i | 0.379243 | − | 0.925297i | \(-0.376184\pi\) |
−0.925297 | + | 0.379243i | \(0.876184\pi\) | |||||||
\(338\) | 6.68088 | + | 6.68088i | 0.363392 | + | 0.363392i | ||||
\(339\) | 9.10912 | + | 0.704939i | 0.494740 | + | 0.0382871i | ||||
\(340\) | 0.525982 | − | 0.442336i | 0.0285254 | − | 0.0239890i | ||||
\(341\) | − | 18.8274i | − | 1.01956i | ||||||
\(342\) | 15.5667 | − | 11.3721i | 0.841753 | − | 0.614934i | ||||
\(343\) | 12.3800 | − | 12.3800i | 0.668458 | − | 0.668458i | ||||
\(344\) | 2.54827 | 0.137393 | ||||||||
\(345\) | 0.630048 | − | 3.82139i | 0.0339206 | − | 0.205737i | ||||
\(346\) | 22.8801 | 1.23004 | ||||||||
\(347\) | −18.2887 | + | 18.2887i | −0.981790 | + | 0.981790i | −0.999837 | − | 0.0180467i | \(-0.994255\pi\) |
0.0180467 | + | 0.999837i | \(0.494255\pi\) | |||||||
\(348\) | −1.37447 | − | 1.60505i | −0.0736794 | − | 0.0860398i | ||||
\(349\) | − | 28.7041i | − | 1.53649i | −0.640154 | − | 0.768247i | \(-0.721129\pi\) | ||
0.640154 | − | 0.768247i | \(-0.278871\pi\) | |||||||
\(350\) | −13.6547 | − | 2.37681i | −0.729874 | − | 0.127046i | ||||
\(351\) | 9.53110 | + | 2.24877i | 0.508732 | + | 0.120031i | ||||
\(352\) | 2.10149 | + | 2.10149i | 0.112010 | + | 0.112010i | ||||
\(353\) | −10.4582 | − | 10.4582i | −0.556631 | − | 0.556631i | 0.371715 | − | 0.928347i | \(-0.378770\pi\) |
−0.928347 | + | 0.371715i | \(0.878770\pi\) | |||||||
\(354\) | −1.26023 | + | 16.2846i | −0.0669807 | + | 0.865514i | ||||
\(355\) | 17.0421 | + | 1.47215i | 0.904499 | + | 0.0781337i | ||||
\(356\) | − | 2.45643i | − | 0.130191i | ||||||
\(357\) | −1.12085 | + | 0.959829i | −0.0593216 | + | 0.0507995i | ||||
\(358\) | −8.91569 | + | 8.91569i | −0.471209 | + | 0.471209i | ||||
\(359\) | 10.4419 | 0.551105 | 0.275552 | − | 0.961286i | \(-0.411139\pi\) | ||||
0.275552 | + | 0.961286i | \(0.411139\pi\) | |||||||
\(360\) | 3.47628 | + | 5.73720i | 0.183216 | + | 0.302377i | ||||
\(361\) | −22.2943 | −1.17338 | ||||||||
\(362\) | −1.24013 | + | 1.24013i | −0.0651799 | + | 0.0651799i | ||||
\(363\) | 2.85153 | − | 2.44188i | 0.149667 | − | 0.128166i | ||||
\(364\) | 5.22418i | 0.273822i | ||||||||
\(365\) | 8.25749 | + | 9.81900i | 0.432217 | + | 0.513950i | ||||
\(366\) | 0.744681 | − | 9.62265i | 0.0389251 | − | 0.502984i | ||||
\(367\) | 11.3139 | + | 11.3139i | 0.590580 | + | 0.590580i | 0.937788 | − | 0.347208i | \(-0.112870\pi\) |
−0.347208 | + | 0.937788i | \(0.612870\pi\) | |||||||
\(368\) | −0.707107 | − | 0.707107i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | 9.02856 | + | 1.40583i | 0.470008 | + | 0.0731846i | ||||
\(370\) | 0.390012 | − | 4.51489i | 0.0202758 | − | 0.234718i | ||||
\(371\) | − | 35.9830i | − | 1.86814i | ||||||
\(372\) | −7.13701 | − | 8.33431i | −0.370037 | − | 0.432114i | ||||
\(373\) | −20.2494 | + | 20.2494i | −1.04847 | + | 1.04847i | −0.0497082 | + | 0.998764i | \(0.515829\pi\) |
−0.998764 | + | 0.0497082i | \(0.984171\pi\) | |||||||
\(374\) | 0.913428 | 0.0472322 | ||||||||
\(375\) | 8.41706 | + | 17.4400i | 0.434655 | + | 0.900597i | ||||
\(376\) | 0.282021 | 0.0145441 | ||||||||
\(377\) | −1.62584 | + | 1.62584i | −0.0837349 | + | 0.0837349i | ||||
\(378\) | −7.57398 | − | 12.2516i | −0.389563 | − | 0.630157i | ||||
\(379\) | − | 31.4641i | − | 1.61620i | −0.589042 | − | 0.808102i | \(-0.700495\pi\) | ||
0.589042 | − | 0.808102i | \(-0.299505\pi\) | |||||||
\(380\) | 1.23665 | − | 14.3158i | 0.0634387 | − | 0.734385i | ||||
\(381\) | −24.3003 | − | 1.88056i | −1.24494 | − | 0.0963438i | ||||
\(382\) | 19.0413 | + | 19.0413i | 0.974238 | + | 0.974238i | ||||
\(383\) | 5.10098 | + | 5.10098i | 0.260648 | + | 0.260648i | 0.825317 | − | 0.564669i | \(-0.190996\pi\) |
−0.564669 | + | 0.825317i | \(0.690996\pi\) | |||||||
\(384\) | 1.72689 | + | 0.133641i | 0.0881249 | + | 0.00681983i | ||||
\(385\) | −11.8565 | − | 14.0985i | −0.604261 | − | 0.718529i | ||||
\(386\) | 15.4597i | 0.786878i | ||||||||
\(387\) | 4.50963 | + | 6.17302i | 0.229237 | + | 0.313792i | ||||
\(388\) | 8.98748 | − | 8.98748i | 0.456270 | − | 0.456270i | ||||
\(389\) | −18.3647 | −0.931129 | −0.465565 | − | 0.885014i | \(-0.654149\pi\) | ||||
−0.465565 | + | 0.885014i | \(0.654149\pi\) | |||||||
\(390\) | 5.93212 | − | 4.25288i | 0.300385 | − | 0.215353i | ||||
\(391\) | −0.307349 | −0.0155433 | ||||||||
\(392\) | 0.483658 | − | 0.483658i | 0.0244284 | − | 0.0244284i | ||||
\(393\) | 4.67226 | + | 5.45608i | 0.235685 | + | 0.275223i | ||||
\(394\) | − | 2.79914i | − | 0.141019i | ||||||
\(395\) | −32.1463 | − | 2.77691i | −1.61746 | − | 0.139722i | ||||
\(396\) | −1.37175 | + | 8.80970i | −0.0689331 | + | 0.442704i | ||||
\(397\) | −6.90089 | − | 6.90089i | −0.346346 | − | 0.346346i | 0.512401 | − | 0.858746i | \(-0.328756\pi\) |
−0.858746 | + | 0.512401i | \(0.828756\pi\) | |||||||
\(398\) | −11.2354 | − | 11.2354i | −0.563178 | − | 0.563178i | ||||
\(399\) | −2.38055 | + | 30.7612i | −0.119177 | + | 1.53998i | ||||
\(400\) | 4.92593 | + | 0.857436i | 0.246297 | + | 0.0428718i | ||||
\(401\) | 18.3481i | 0.916261i | 0.888885 | + | 0.458131i | \(0.151481\pi\) | ||||
−0.888885 | + | 0.458131i | \(0.848519\pi\) | |||||||
\(402\) | 17.5087 | − | 14.9934i | 0.873254 | − | 0.747803i | ||||
\(403\) | −8.44225 | + | 8.44225i | −0.420538 | + | 0.420538i | ||||
\(404\) | 3.00976 | 0.149741 | ||||||||
\(405\) | −7.74610 | + | 18.5741i | −0.384907 | + | 0.922955i | ||||
\(406\) | 3.38190 | 0.167841 | ||||||||
\(407\) | 4.25896 | − | 4.25896i | 0.211109 | − | 0.211109i | ||||
\(408\) | 0.404346 | − | 0.346258i | 0.0200181 | − | 0.0171423i | ||||
\(409\) | 15.8713i | 0.784783i | 0.919798 | + | 0.392392i | \(0.128352\pi\) | ||||
−0.919798 | + | 0.392392i | \(0.871648\pi\) | |||||||
\(410\) | 5.21240 | − | 4.38348i | 0.257422 | − | 0.216485i | ||||
\(411\) | −1.26969 | + | 16.4067i | −0.0626292 | + | 0.809285i | ||||
\(412\) | 1.81831 | + | 1.81831i | 0.0895816 | + | 0.0895816i | ||||
\(413\) | −18.4838 | − | 18.4838i | −0.909526 | − | 0.909526i | ||||
\(414\) | 0.461565 | − | 2.96428i | 0.0226847 | − | 0.145686i | ||||
\(415\) | 29.4626 | − | 24.7772i | 1.44626 | − | 1.21626i | ||||
\(416\) | − | 1.88462i | − | 0.0924013i | ||||||
\(417\) | −24.0306 | − | 28.0620i | −1.17679 | − | 1.37420i | ||||
\(418\) | 13.5043 | − | 13.5043i | 0.660517 | − | 0.660517i | ||||
\(419\) | 19.9035 | 0.972349 | 0.486175 | − | 0.873862i | \(-0.338392\pi\) | ||||
0.486175 | + | 0.873862i | \(0.338392\pi\) | |||||||
\(420\) | −10.5929 | − | 1.74649i | −0.516881 | − | 0.0852202i | ||||
\(421\) | −9.07200 | −0.442142 | −0.221071 | − | 0.975258i | \(-0.570955\pi\) | ||||
−0.221071 | + | 0.975258i | \(0.570955\pi\) | |||||||
\(422\) | 8.05445 | − | 8.05445i | 0.392085 | − | 0.392085i | ||||
\(423\) | 0.499089 | + | 0.683180i | 0.0242666 | + | 0.0332173i | ||||
\(424\) | 12.9809i | 0.630407i | ||||||||
\(425\) | 1.25689 | − | 0.884201i | 0.0609682 | − | 0.0428901i | ||||
\(426\) | 13.2104 | + | 1.02233i | 0.640046 | + | 0.0495320i | ||||
\(427\) | 10.9222 | + | 10.9222i | 0.528561 | + | 0.528561i | ||||
\(428\) | −10.1552 | − | 10.1552i | −0.490872 | − | 0.490872i | ||||
\(429\) | 9.67232 | + | 0.748525i | 0.466984 | + | 0.0361391i | ||||
\(430\) | 5.67695 | + | 0.490395i | 0.273767 | + | 0.0236489i | ||||
\(431\) | − | 6.60333i | − | 0.318071i | −0.987273 | − | 0.159036i | \(-0.949162\pi\) | ||
0.987273 | − | 0.159036i | \(-0.0508384\pi\) | |||||||
\(432\) | 2.73231 | + | 4.41978i | 0.131458 | + | 0.212647i | ||||
\(433\) | −2.95935 | + | 2.95935i | −0.142217 | + | 0.142217i | −0.774631 | − | 0.632414i | \(-0.782064\pi\) |
0.632414 | + | 0.774631i | \(0.282064\pi\) | |||||||
\(434\) | 17.5607 | 0.842941 | ||||||||
\(435\) | −2.75313 | − | 3.84019i | −0.132002 | − | 0.184123i | ||||
\(436\) | −3.22282 | −0.154345 | ||||||||
\(437\) | −4.54391 | + | 4.54391i | −0.217365 | + | 0.217365i | ||||
\(438\) | 6.46393 | + | 7.54831i | 0.308858 | + | 0.360672i | ||||
\(439\) | − | 11.2528i | − | 0.537068i | −0.963270 | − | 0.268534i | \(-0.913461\pi\) | ||
0.963270 | − | 0.268534i | \(-0.0865392\pi\) | |||||||
\(440\) | 4.27722 | + | 5.08605i | 0.203909 | + | 0.242468i | ||||
\(441\) | 2.02756 | + | 0.315709i | 0.0965503 | + | 0.0150338i | ||||
\(442\) | −0.409583 | − | 0.409583i | −0.0194819 | − | 0.0194819i | ||||
\(443\) | −16.2317 | − | 16.2317i | −0.771194 | − | 0.771194i | 0.207122 | − | 0.978315i | \(-0.433590\pi\) |
−0.978315 | + | 0.207122i | \(0.933590\pi\) | |||||||
\(444\) | 0.270842 | − | 3.49978i | 0.0128536 | − | 0.166092i | ||||
\(445\) | 0.472722 | − | 5.47236i | 0.0224092 | − | 0.259415i | ||||
\(446\) | 14.8040i | 0.700989i | ||||||||
\(447\) | −2.69311 | + | 2.30622i | −0.127380 | + | 0.109081i | ||||
\(448\) | −1.96010 | + | 1.96010i | −0.0926061 | + | 0.0926061i | ||||
\(449\) | −3.47861 | −0.164166 | −0.0820828 | − | 0.996626i | \(-0.526157\pi\) | ||||
−0.0820828 | + | 0.996626i | \(0.526157\pi\) | |||||||
\(450\) | 6.64027 | + | 13.4502i | 0.313025 | + | 0.634047i | ||||
\(451\) | 9.05193 | 0.426239 | ||||||||
\(452\) | 3.72990 | − | 3.72990i | 0.175440 | − | 0.175440i | ||||
\(453\) | −3.47336 | + | 2.97438i | −0.163193 | + | 0.139749i | ||||
\(454\) | − | 22.8625i | − | 1.07299i | ||||||
\(455\) | −1.00535 | + | 11.6383i | −0.0471318 | + | 0.545611i | ||||
\(456\) | 0.858785 | − | 11.0971i | 0.0402163 | − | 0.519669i | ||||
\(457\) | 24.5212 | + | 24.5212i | 1.14705 | + | 1.14705i | 0.987129 | + | 0.159925i | \(0.0511251\pi\) |
0.159925 | + | 0.987129i | \(0.448875\pi\) | |||||||
\(458\) | −11.3347 | − | 11.3347i | −0.529638 | − | 0.529638i | ||||
\(459\) | 1.55436 | + | 0.366736i | 0.0725511 | + | 0.0171178i | ||||
\(460\) | −1.43919 | − | 1.71135i | −0.0671028 | − | 0.0797921i | ||||
\(461\) | − | 7.06441i | − | 0.329022i | −0.986375 | − | 0.164511i | \(-0.947395\pi\) | ||
0.986375 | − | 0.164511i | \(-0.0526047\pi\) | |||||||
\(462\) | −9.28119 | − | 10.8382i | −0.431800 | − | 0.504238i | ||||
\(463\) | 4.91698 | − | 4.91698i | 0.228512 | − | 0.228512i | −0.583559 | − | 0.812071i | \(-0.698340\pi\) |
0.812071 | + | 0.583559i | \(0.198340\pi\) | |||||||
\(464\) | −1.22002 | −0.0566381 | ||||||||
\(465\) | −14.2957 | − | 19.9404i | −0.662950 | − | 0.924714i | ||||
\(466\) | 5.86409 | 0.271649 | ||||||||
\(467\) | 0.279235 | − | 0.279235i | 0.0129214 | − | 0.0129214i | −0.700617 | − | 0.713538i | \(-0.747092\pi\) |
0.713538 | + | 0.700617i | \(0.247092\pi\) | |||||||
\(468\) | 4.56539 | − | 3.33519i | 0.211035 | − | 0.154169i | ||||
\(469\) | 36.8915i | 1.70349i | ||||||||
\(470\) | 0.628279 | + | 0.0542729i | 0.0289804 | + | 0.00250342i | ||||
\(471\) | 1.83407 | + | 0.141935i | 0.0845093 | + | 0.00654003i | ||||
\(472\) | 6.66802 | + | 6.66802i | 0.306920 | + | 0.306920i | ||||
\(473\) | 5.35515 | + | 5.35515i | 0.246230 | + | 0.246230i | ||||
\(474\) | −24.9187 | − | 1.92841i | −1.14455 | − | 0.0885750i | ||||
\(475\) | 5.50994 | − | 31.6544i | 0.252813 | − | 1.45240i | ||||
\(476\) | 0.851973i | 0.0390501i | ||||||||
\(477\) | −31.4454 | + | 22.9721i | −1.43978 | + | 1.05182i | ||||
\(478\) | −21.0475 | + | 21.0475i | −0.962690 | + | 0.962690i | ||||
\(479\) | −19.9714 | −0.912518 | −0.456259 | − | 0.889847i | \(-0.650811\pi\) | ||||
−0.456259 | + | 0.889847i | \(0.650811\pi\) | |||||||
\(480\) | 3.82139 | + | 0.630048i | 0.174422 | + | 0.0287576i | ||||
\(481\) | −3.81946 | −0.174152 | ||||||||
\(482\) | −12.8377 | + | 12.8377i | −0.584743 | + | 0.584743i | ||||
\(483\) | 3.12292 | + | 3.64682i | 0.142098 | + | 0.165936i | ||||
\(484\) | − | 2.16749i | − | 0.0985222i | ||||||
\(485\) | 21.7516 | − | 18.2925i | 0.987691 | − | 0.830619i | ||||
\(486\) | −5.87131 | + | 14.4405i | −0.266328 | + | 0.655034i | ||||
\(487\) | −1.40410 | − | 1.40410i | −0.0636258 | − | 0.0636258i | 0.674578 | − | 0.738204i | \(-0.264326\pi\) |
−0.738204 | + | 0.674578i | \(0.764326\pi\) | |||||||
\(488\) | −3.94018 | − | 3.94018i | −0.178363 | − | 0.178363i | ||||
\(489\) | 1.24816 | − | 16.1286i | 0.0564439 | − | 0.729360i | ||||
\(490\) | 1.17056 | − | 0.984403i | 0.0528803 | − | 0.0444708i | ||||
\(491\) | 6.45884i | 0.291483i | 0.989323 | + | 0.145742i | \(0.0465568\pi\) | ||||
−0.989323 | + | 0.145742i | \(0.953443\pi\) | |||||||
\(492\) | 4.00701 | − | 3.43137i | 0.180650 | − | 0.154698i | ||||
\(493\) | −0.265146 | + | 0.265146i | −0.0119416 | + | 0.0119416i | ||||
\(494\) | −12.1107 | −0.544887 | ||||||||
\(495\) | −4.75131 | + | 19.3620i | −0.213556 | + | 0.870258i | ||||
\(496\) | −6.33502 | −0.284451 | ||||||||
\(497\) | −14.9944 | + | 14.9944i | −0.672593 | + | 0.672593i | ||||
\(498\) | 22.6492 | − | 19.3955i | 1.01494 | − | 0.869132i | ||||
\(499\) | 9.53761i | 0.426962i | 0.976947 | + | 0.213481i | \(0.0684802\pi\) | ||||
−0.976947 | + | 0.213481i | \(0.931520\pi\) | |||||||
\(500\) | 10.8088 | + | 2.85813i | 0.483386 | + | 0.127819i | ||||
\(501\) | −0.992338 | + | 12.8228i | −0.0443344 | + | 0.572883i | ||||
\(502\) | −13.5208 | − | 13.5208i | −0.603464 | − | 0.603464i | ||||
\(503\) | 15.2096 | + | 15.2096i | 0.678161 | + | 0.678161i | 0.959584 | − | 0.281423i | \(-0.0908064\pi\) |
−0.281423 | + | 0.959584i | \(0.590806\pi\) | |||||||
\(504\) | −8.21699 | − | 1.27946i | −0.366014 | − | 0.0569917i | ||||
\(505\) | 6.70506 | + | 0.579206i | 0.298371 | + | 0.0257743i | ||||
\(506\) | − | 2.97195i | − | 0.132119i | ||||||
\(507\) | 10.6443 | + | 12.4300i | 0.472730 | + | 0.552034i | ||||
\(508\) | −9.95020 | + | 9.95020i | −0.441469 | + | 0.441469i | ||||
\(509\) | −27.1370 | −1.20282 | −0.601412 | − | 0.798939i | \(-0.705395\pi\) | ||||
−0.601412 | + | 0.798939i | \(0.705395\pi\) | |||||||
\(510\) | 0.967426 | − | 0.693571i | 0.0428384 | − | 0.0307118i | ||||
\(511\) | −15.9046 | −0.703577 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 28.4018 | − | 17.5580i | 1.25397 | − | 0.775205i | ||||
\(514\) | 24.0535i | 1.06096i | ||||||||
\(515\) | 3.70085 | + | 4.40069i | 0.163079 | + | 0.193918i | ||||
\(516\) | 4.40057 | + | 0.340552i | 0.193724 | + | 0.0149920i | ||||
\(517\) | 0.592665 | + | 0.592665i | 0.0260654 | + | 0.0260654i | ||||
\(518\) | 3.97242 | + | 3.97242i | 0.174538 | + | 0.174538i | ||||
\(519\) | 39.5113 | + | 3.05771i | 1.73435 | + | 0.134219i | ||||
\(520\) | 0.362682 | − | 4.19851i | 0.0159047 | − | 0.184117i | ||||
\(521\) | − | 41.9658i | − | 1.83855i | −0.393611 | − | 0.919277i | \(-0.628774\pi\) | ||
0.393611 | − | 0.919277i | \(-0.371226\pi\) | |||||||
\(522\) | −2.15906 | − | 2.95543i | −0.0944994 | − | 0.129356i | ||||
\(523\) | 22.7710 | − | 22.7710i | 0.995704 | − | 0.995704i | −0.00428643 | − | 0.999991i | \(-0.501364\pi\) |
0.999991 | + | 0.00428643i | \(0.00136442\pi\) | |||||||
\(524\) | 4.14724 | 0.181173 | ||||||||
\(525\) | −23.2625 | − | 5.92932i | −1.01526 | − | 0.258777i | ||||
\(526\) | −17.4761 | −0.761992 | ||||||||
\(527\) | −1.37678 | + | 1.37678i | −0.0599736 | + | 0.0599736i | ||||
\(528\) | 3.34819 | + | 3.90988i | 0.145711 | + | 0.170156i | ||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | −2.49807 | + | 28.9184i | −0.108509 | + | 1.25614i | ||||
\(531\) | −4.35256 | + | 27.9532i | −0.188885 | + | 1.21306i | ||||
\(532\) | 12.5957 | + | 12.5957i | 0.546094 | + | 0.546094i | ||||
\(533\) | −4.05891 | − | 4.05891i | −0.175811 | − | 0.175811i | ||||
\(534\) | 0.328279 | − | 4.24198i | 0.0142060 | − | 0.183568i | ||||
\(535\) | −20.6693 | − | 24.5779i | −0.893610 | − | 1.06259i | ||||
\(536\) | − | 13.3086i | − | 0.574844i | ||||||
\(537\) | −16.5879 | + | 14.2049i | −0.715820 | + | 0.612986i | ||||
\(538\) | −14.2128 | + | 14.2128i | −0.612758 | + | 0.612758i | ||||
\(539\) | 2.03280 | 0.0875591 | ||||||||
\(540\) | 5.23641 | + | 10.3721i | 0.225339 | + | 0.446343i | ||||
\(541\) | 8.43337 | 0.362579 | 0.181290 | − | 0.983430i | \(-0.441973\pi\) | ||||
0.181290 | + | 0.983430i | \(0.441973\pi\) | |||||||
\(542\) | −19.7054 | + | 19.7054i | −0.846419 | + | 0.846419i | ||||
\(543\) | −2.30730 | + | 1.97584i | −0.0990157 | + | 0.0847912i | ||||
\(544\) | − | 0.307349i | − | 0.0131775i | ||||||
\(545\) | −7.17971 | − | 0.620208i | −0.307545 | − | 0.0265668i | ||||
\(546\) | −0.698164 | + | 9.02157i | −0.0298787 | + | 0.386088i | ||||
\(547\) | −13.9532 | − | 13.9532i | −0.596597 | − | 0.596597i | 0.342808 | − | 0.939405i | \(-0.388622\pi\) |
−0.939405 | + | 0.342808i | \(0.888622\pi\) | |||||||
\(548\) | 6.71805 | + | 6.71805i | 0.286981 | + | 0.286981i | ||||
\(549\) | 2.57196 | − | 16.5177i | 0.109769 | − | 0.704959i | ||||
\(550\) | 8.54990 | + | 12.1537i | 0.364569 | + | 0.518235i | ||||
\(551\) | 7.83994i | 0.333993i | ||||||||
\(552\) | −1.12660 | − | 1.31559i | −0.0479511 | − | 0.0559953i | ||||
\(553\) | 28.2839 | − | 28.2839i | 1.20275 | − | 1.20275i | ||||
\(554\) | 9.96921 | 0.423551 | ||||||||
\(555\) | 1.27688 | − | 7.74459i | 0.0542006 | − | 0.328739i | ||||
\(556\) | −21.3303 | −0.904607 | ||||||||
\(557\) | 19.9924 | − | 19.9924i | 0.847106 | − | 0.847106i | −0.142665 | − | 0.989771i | \(-0.545567\pi\) |
0.989771 | + | 0.142665i | \(0.0455671\pi\) | |||||||
\(558\) | −11.2110 | − | 15.3462i | −0.474600 | − | 0.649657i | ||||
\(559\) | − | 4.80252i | − | 0.203125i | ||||||
\(560\) | −4.74387 | + | 3.98945i | −0.200465 | + | 0.168585i | ||||
\(561\) | 1.57739 | + | 0.122071i | 0.0665974 | + | 0.00515386i | ||||
\(562\) | −11.1642 | − | 11.1642i | −0.470934 | − | 0.470934i | ||||
\(563\) | 31.0332 | + | 31.0332i | 1.30789 | + | 1.30789i | 0.922935 | + | 0.384957i | \(0.125784\pi\) |
0.384957 | + | 0.922935i | \(0.374216\pi\) | |||||||
\(564\) | 0.487019 | + | 0.0376896i | 0.0205072 | + | 0.00158702i | ||||
\(565\) | 9.02716 | − | 7.59158i | 0.379776 | − | 0.319380i | ||||
\(566\) | − | 18.6737i | − | 0.784912i | ||||||
\(567\) | −11.4421 | − | 22.1694i | −0.480522 | − | 0.931027i | ||||
\(568\) | 5.40925 | − | 5.40925i | 0.226967 | − | 0.226967i | ||||
\(569\) | 30.3632 | 1.27289 | 0.636447 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636447 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(570\) | 4.04873 | − | 24.5565i | 0.169583 | − | 1.02856i | ||||
\(571\) | −13.6437 | −0.570973 | −0.285486 | − | 0.958383i | \(-0.592155\pi\) | ||||
−0.285486 | + | 0.958383i | \(0.592155\pi\) | |||||||
\(572\) | 3.96052 | − | 3.96052i | 0.165598 | − | 0.165598i | ||||
\(573\) | 30.3375 | + | 35.4269i | 1.26737 | + | 1.47998i | ||||
\(574\) | 8.44292i | 0.352401i | ||||||||
\(575\) | −2.87686 | − | 4.08946i | −0.119973 | − | 0.170542i | ||||
\(576\) | 2.96428 | + | 0.461565i | 0.123512 | + | 0.0192319i | ||||
\(577\) | 29.2454 | + | 29.2454i | 1.21750 | + | 1.21750i | 0.968503 | + | 0.249001i | \(0.0801021\pi\) |
0.249001 | + | 0.968503i | \(0.419898\pi\) | |||||||
\(578\) | 11.9540 | + | 11.9540i | 0.497222 | + | 0.497222i | ||||
\(579\) | −2.06605 | + | 26.6972i | −0.0858620 | + | 1.10950i | ||||
\(580\) | −2.71793 | − | 0.234784i | −0.112856 | − | 0.00974888i | ||||
\(581\) | 47.7228i | 1.97988i | ||||||||
\(582\) | 16.7215 | − | 14.3193i | 0.693127 | − | 0.593553i | ||||
\(583\) | −27.2791 | + | 27.2791i | −1.12979 | + | 1.12979i | ||||
\(584\) | 5.73758 | 0.237423 | ||||||||
\(585\) | 10.8125 | − | 6.55147i | 0.447041 | − | 0.270870i | ||||
\(586\) | −9.81215 | −0.405336 | ||||||||
\(587\) | 30.7364 | − | 30.7364i | 1.26863 | − | 1.26863i | 0.321830 | − | 0.946798i | \(-0.395702\pi\) |
0.946798 | − | 0.321830i | \(-0.104298\pi\) | |||||||
\(588\) | 0.899860 | − | 0.770587i | 0.0371096 | − | 0.0317785i | ||||
\(589\) | 40.7093i | 1.67740i | ||||||||
\(590\) | 13.5716 | + | 16.1380i | 0.558734 | + | 0.664392i | ||||
\(591\) | 0.374079 | − | 4.83380i | 0.0153876 | − | 0.198836i | ||||
\(592\) | −1.43305 | − | 1.43305i | −0.0588980 | − | 0.0588980i | ||||
\(593\) | −24.9741 | − | 24.9741i | −1.02557 | − | 1.02557i | −0.999665 | − | 0.0259005i | \(-0.991755\pi\) |
−0.0259005 | − | 0.999665i | \(-0.508245\pi\) | |||||||
\(594\) | −3.54620 | + | 15.0300i | −0.145502 | + | 0.616690i | ||||
\(595\) | −0.163956 | + | 1.89800i | −0.00672154 | + | 0.0778105i | ||||
\(596\) | 2.04707i | 0.0838514i | ||||||||
\(597\) | −17.9007 | − | 20.9037i | −0.732627 | − | 0.855531i | ||||
\(598\) | −1.33263 | + | 1.33263i | −0.0544953 | + | 0.0544953i | ||||
\(599\) | −35.3695 | −1.44516 | −0.722579 | − | 0.691288i | \(-0.757044\pi\) | ||||
−0.722579 | + | 0.691288i | \(0.757044\pi\) | |||||||
\(600\) | 8.39194 | + | 2.13900i | 0.342600 | + | 0.0873244i | ||||
\(601\) | 36.5041 | 1.48903 | 0.744517 | − | 0.667604i | \(-0.232680\pi\) | ||||
0.744517 | + | 0.667604i | \(0.232680\pi\) | |||||||
\(602\) | −4.99486 | + | 4.99486i | −0.203575 | + | 0.203575i | ||||
\(603\) | 32.2393 | − | 23.5521i | 1.31288 | − | 0.959114i | ||||
\(604\) | 2.64015i | 0.107426i | ||||||||
\(605\) | 0.417117 | − | 4.82867i | 0.0169582 | − | 0.196313i | ||||
\(606\) | 5.19752 | + | 0.402227i | 0.211135 | + | 0.0163394i | ||||
\(607\) | 22.0917 | + | 22.0917i | 0.896673 | + | 0.896673i | 0.995140 | − | 0.0984669i | \(-0.0313939\pi\) |
−0.0984669 | + | 0.995140i | \(0.531394\pi\) | |||||||
\(608\) | −4.54391 | − | 4.54391i | −0.184280 | − | 0.184280i | ||||
\(609\) | 5.84017 | + | 0.451961i | 0.236656 | + | 0.0183144i | ||||
\(610\) | −8.01956 | − | 9.53607i | −0.324702 | − | 0.386104i | ||||
\(611\) | − | 0.531504i | − | 0.0215024i | ||||||
\(612\) | 0.744535 | − | 0.543912i | 0.0300960 | − | 0.0219863i | ||||
\(613\) | 16.7926 | − | 16.7926i | 0.678246 | − | 0.678246i | −0.281357 | − | 0.959603i | \(-0.590784\pi\) |
0.959603 | + | 0.281357i | \(0.0907845\pi\) | |||||||
\(614\) | −11.8644 | −0.478808 | ||||||||
\(615\) | 9.58705 | − | 6.87318i | 0.386587 | − | 0.277154i | ||||
\(616\) | −8.23826 | −0.331929 | ||||||||
\(617\) | −26.9980 | + | 26.9980i | −1.08690 | + | 1.08690i | −0.0910505 | + | 0.995846i | \(0.529022\pi\) |
−0.995846 | + | 0.0910505i | \(0.970978\pi\) | |||||||
\(618\) | 2.89701 | + | 3.38301i | 0.116535 | + | 0.136085i | ||||
\(619\) | 31.5835i | 1.26945i | 0.772739 | + | 0.634724i | \(0.218886\pi\) | ||||
−0.772739 | + | 0.634724i | \(0.781114\pi\) | |||||||
\(620\) | −14.1130 | − | 1.21913i | −0.566791 | − | 0.0489614i | ||||
\(621\) | 1.19322 | − | 5.05729i | 0.0478823 | − | 0.202942i | ||||
\(622\) | −16.0579 | − | 16.0579i | −0.643865 | − | 0.643865i | ||||
\(623\) | 4.81485 | + | 4.81485i | 0.192903 | + | 0.192903i | ||||
\(624\) | 0.251863 | − | 3.25453i | 0.0100826 | − | 0.130286i | ||||
\(625\) | 23.5296 | + | 8.44734i | 0.941184 | + | 0.337894i | ||||
\(626\) | 26.9989i | 1.07909i | ||||||||
\(627\) | 25.1251 | − | 21.5157i | 1.00340 | − | 0.859254i | ||||
\(628\) | 0.750993 | − | 0.750993i | 0.0299679 | − | 0.0299679i | ||||
\(629\) | −0.622887 | −0.0248361 | ||||||||
\(630\) | −18.0594 | − | 4.43164i | −0.719502 | − | 0.176561i | ||||
\(631\) | −27.4404 | −1.09239 | −0.546193 | − | 0.837659i | \(-0.683924\pi\) | ||||
−0.546193 | + | 0.837659i | \(0.683924\pi\) | |||||||
\(632\) | −10.2034 | + | 10.2034i | −0.405870 | + | 0.405870i | ||||
\(633\) | 14.9855 | − | 12.8327i | 0.595622 | − | 0.510055i | ||||
\(634\) | − | 0.0389545i | − | 0.00154708i | ||||||
\(635\) | −24.0816 | + | 20.2519i | −0.955650 | + | 0.803673i | ||||
\(636\) | −1.73477 | + | 22.4165i | −0.0687883 | + | 0.888872i | ||||
\(637\) | −0.911514 | − | 0.911514i | −0.0361155 | − | 0.0361155i | ||||
\(638\) | −2.56386 | − | 2.56386i | −0.101504 | − | 0.101504i | ||||
\(639\) | 22.6762 | + | 3.53090i | 0.897058 | + | 0.139680i | ||||
\(640\) | 1.71135 | − | 1.43919i | 0.0676470 | − | 0.0568892i | ||||
\(641\) | 1.78898i | 0.0706606i | 0.999376 | + | 0.0353303i | \(0.0112483\pi\) | ||||
−0.999376 | + | 0.0353303i | \(0.988752\pi\) | |||||||
\(642\) | −16.1798 | − | 18.8941i | −0.638566 | − | 0.745691i | ||||
\(643\) | 24.6839 | − | 24.6839i | 0.973437 | − | 0.973437i | −0.0262188 | − | 0.999656i | \(-0.508347\pi\) |
0.999656 | + | 0.0262188i | \(0.00834667\pi\) | |||||||
\(644\) | 2.77200 | 0.109232 | ||||||||
\(645\) | 9.73792 | + | 1.60553i | 0.383430 | + | 0.0632177i | ||||
\(646\) | −1.97505 | −0.0777072 | ||||||||
\(647\) | −2.36727 | + | 2.36727i | −0.0930671 | + | 0.0930671i | −0.752108 | − | 0.659040i | \(-0.770963\pi\) |
0.659040 | + | 0.752108i | \(0.270963\pi\) | |||||||
\(648\) | 4.12773 | + | 7.99761i | 0.162153 | + | 0.314176i | ||||
\(649\) | 28.0255i | 1.10010i | ||||||||
\(650\) | 1.61594 | − | 9.28353i | 0.0633826 | − | 0.364130i | ||||
\(651\) | 30.3254 | + | 2.34683i | 1.18854 | + | 0.0919794i | ||||
\(652\) | −6.60415 | − | 6.60415i | −0.258639 | − | 0.258639i | ||||
\(653\) | −2.10868 | − | 2.10868i | −0.0825189 | − | 0.0825189i | 0.664643 | − | 0.747161i | \(-0.268584\pi\) |
−0.747161 | + | 0.664643i | \(0.768584\pi\) | |||||||
\(654\) | −5.56545 | − | 0.430701i | −0.217626 | − | 0.0168417i | ||||
\(655\) | 9.23911 | + | 0.798106i | 0.361002 | + | 0.0311846i | ||||
\(656\) | − | 3.04579i | − | 0.118918i | ||||||
\(657\) | 10.1537 | + | 13.8989i | 0.396134 | + | 0.542249i | ||||
\(658\) | −0.552791 | + | 0.552791i | −0.0215500 | + | 0.0215500i | ||||
\(659\) | −40.8784 | −1.59240 | −0.796199 | − | 0.605035i | \(-0.793159\pi\) | ||||
−0.796199 | + | 0.605035i | \(0.793159\pi\) | |||||||
\(660\) | 6.70657 | + | 9.35465i | 0.261053 | + | 0.364129i | ||||
\(661\) | 17.8125 | 0.692828 | 0.346414 | − | 0.938082i | \(-0.387399\pi\) | ||||
0.346414 | + | 0.938082i | \(0.387399\pi\) | |||||||
\(662\) | 0.743610 | − | 0.743610i | 0.0289012 | − | 0.0289012i | ||||
\(663\) | −0.652567 | − | 0.762041i | −0.0253436 | − | 0.0295952i | ||||
\(664\) | − | 17.2160i | − | 0.668111i | ||||||
\(665\) | 25.6365 | + | 30.4844i | 0.994140 | + | 1.18213i | ||||
\(666\) | 0.935427 | − | 6.00753i | 0.0362471 | − | 0.232787i | ||||
\(667\) | 0.862686 | + | 0.862686i | 0.0334033 | + | 0.0334033i | ||||
\(668\) | 5.25056 | + | 5.25056i | 0.203150 | + | 0.203150i | ||||
\(669\) | −1.97842 | + | 25.5648i | −0.0764900 | + | 0.988392i | ||||
\(670\) | 2.56114 | − | 29.6485i | 0.0989455 | − | 1.14542i | ||||
\(671\) | − | 16.5605i | − | 0.639310i | ||||||
\(672\) | −3.64682 | + | 3.12292i | −0.140679 | + | 0.120469i | ||||
\(673\) | 13.7420 | − | 13.7420i | 0.529714 | − | 0.529714i | −0.390773 | − | 0.920487i | \(-0.627792\pi\) |
0.920487 | + | 0.390773i | \(0.127792\pi\) | |||||||
\(674\) | −14.1764 | −0.546054 | ||||||||
\(675\) | 9.66951 | + | 24.1143i | 0.372179 | + | 0.928161i | ||||
\(676\) | 9.44819 | 0.363392 | ||||||||
\(677\) | −1.91031 | + | 1.91031i | −0.0734192 | + | 0.0734192i | −0.742863 | − | 0.669444i | \(-0.766533\pi\) |
0.669444 | + | 0.742863i | \(0.266533\pi\) | |||||||
\(678\) | 6.93959 | − | 5.94265i | 0.266513 | − | 0.228226i | ||||
\(679\) | 35.2328i | 1.35211i | ||||||||
\(680\) | 0.0591471 | − | 0.684704i | 0.00226819 | − | 0.0262572i | ||||
\(681\) | 3.05537 | − | 39.4810i | 0.117082 | − | 1.51292i | ||||
\(682\) | −13.3130 | − | 13.3130i | −0.509780 | − | 0.509780i | ||||
\(683\) | 33.5563 | + | 33.5563i | 1.28400 | + | 1.28400i | 0.938374 | + | 0.345623i | \(0.112332\pi\) |
0.345623 | + | 0.938374i | \(0.387668\pi\) | |||||||
\(684\) | 2.96605 | − | 19.0487i | 0.113410 | − | 0.728344i | ||||
\(685\) | 13.6735 | + | 16.2591i | 0.522436 | + | 0.621229i | ||||
\(686\) | − | 17.5080i | − | 0.668458i | ||||||
\(687\) | −18.0590 | − | 21.0886i | −0.688996 | − | 0.804581i | ||||
\(688\) | 1.80190 | − | 1.80190i | 0.0686966 | − | 0.0686966i | ||||
\(689\) | 24.4641 | 0.932006 | ||||||||
\(690\) | −2.25662 | − | 3.14764i | −0.0859081 | − | 0.119829i | ||||
\(691\) | −27.4000 | −1.04234 | −0.521172 | − | 0.853451i | \(-0.674505\pi\) | ||||
−0.521172 | + | 0.853451i | \(0.674505\pi\) | |||||||
\(692\) | 16.1787 | − | 16.1787i | 0.615020 | − | 0.615020i | ||||
\(693\) | −14.5791 | − | 19.9567i | −0.553816 | − | 0.758092i | ||||
\(694\) | 25.8642i | 0.981790i | ||||||||
\(695\) | −47.5191 | − | 4.10486i | −1.80250 | − | 0.155706i | ||||
\(696\) | −2.10684 | − | 0.163045i | −0.0798596 | − | 0.00618020i | ||||
\(697\) | −0.661937 | − | 0.661937i | −0.0250727 | − | 0.0250727i | ||||
\(698\) | −20.2968 | − | 20.2968i | −0.768247 | − | 0.768247i | ||||
\(699\) | 10.1266 | + | 0.783682i | 0.383024 | + | 0.0296416i | ||||
\(700\) | −11.3360 | + | 7.97466i | −0.428460 | + | 0.301414i | ||||
\(701\) | 17.7628i | 0.670893i | 0.942059 | + | 0.335446i | \(0.108887\pi\) | ||||
−0.942059 | + | 0.335446i | \(0.891113\pi\) | |||||||
\(702\) | 8.32963 | − | 5.14938i | 0.314381 | − | 0.194351i | ||||
\(703\) | −9.20888 | + | 9.20888i | −0.347319 | + | 0.347319i | ||||
\(704\) | 2.97195 | 0.112010 | ||||||||
\(705\) | 1.07771 | + | 0.177687i | 0.0405891 | + | 0.00669208i | ||||
\(706\) | −14.7901 | −0.556631 | ||||||||
\(707\) | −5.89944 | + | 5.89944i | −0.221871 | + | 0.221871i | ||||
\(708\) | 10.6238 | + | 12.4060i | 0.399267 | + | 0.466247i | ||||
\(709\) | 25.1030i | 0.942763i | 0.881929 | + | 0.471382i | \(0.156245\pi\) | ||||
−0.881929 | + | 0.471382i | \(0.843755\pi\) | |||||||
\(710\) | 13.0915 | − | 11.0096i | 0.491316 | − | 0.413183i | ||||
\(711\) | −42.7740 | − | 6.66031i | −1.60415 | − | 0.249781i | ||||
\(712\) | −1.73696 | − | 1.73696i | −0.0650953 | − | 0.0650953i | ||||
\(713\) | 4.47954 | + | 4.47954i | 0.167760 | + | 0.167760i | ||||
\(714\) | −0.113858 | + | 1.47126i | −0.00426104 | + | 0.0550606i | ||||
\(715\) | 9.58530 | − | 8.06095i | 0.358470 | − | 0.301463i | ||||
\(716\) | 12.6087i | 0.471209i | ||||||||
\(717\) | −39.1594 | + | 33.5338i | −1.46244 | + | 1.25234i | ||||
\(718\) | 7.38357 | − | 7.38357i | 0.275552 | − | 0.275552i | ||||
\(719\) | −7.11858 | −0.265478 | −0.132739 | − | 0.991151i | \(-0.542377\pi\) | ||||
−0.132739 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(720\) | 6.51491 | + | 1.59872i | 0.242797 | + | 0.0595806i | ||||
\(721\) | −7.12813 | −0.265466 | ||||||||
\(722\) | −15.7644 | + | 15.7644i | −0.586692 | + | 0.586692i | ||||
\(723\) | −23.8850 | + | 20.4537i | −0.888292 | + | 0.760681i | ||||
\(724\) | 1.75381i | 0.0651799i | ||||||||
\(725\) | −6.00975 | − | 1.04609i | −0.223196 | − | 0.0388508i | ||||
\(726\) | 0.289665 | − | 3.74301i | 0.0107505 | − | 0.138916i | ||||
\(727\) | −21.0233 | − | 21.0233i | −0.779711 | − | 0.779711i | 0.200070 | − | 0.979782i | \(-0.435883\pi\) |
−0.979782 | + | 0.200070i | \(0.935883\pi\) | |||||||
\(728\) | 3.69405 | + | 3.69405i | 0.136911 | + | 0.136911i | ||||
\(729\) | −12.0689 | + | 24.1524i | −0.446998 | + | 0.894535i | ||||
\(730\) | 12.7820 | + | 1.10415i | 0.473083 | + | 0.0408666i | ||||
\(731\) | − | 0.783208i | − | 0.0289680i | ||||||
\(732\) | −6.27767 | − | 7.33081i | −0.232030 | − | 0.270955i | ||||
\(733\) | −8.70985 | + | 8.70985i | −0.321706 | + | 0.321706i | −0.849421 | − | 0.527715i | \(-0.823049\pi\) |
0.527715 | + | 0.849421i | \(0.323049\pi\) | |||||||
\(734\) | 16.0003 | 0.590580 | ||||||||
\(735\) | 2.15298 | − | 1.54352i | 0.0794137 | − | 0.0569336i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 27.9679 | − | 27.9679i | 1.03021 | − | 1.03021i | ||||
\(738\) | 7.37823 | − | 5.39009i | 0.271596 | − | 0.198412i | ||||
\(739\) | − | 13.3134i | − | 0.489743i | −0.969556 | − | 0.244871i | \(-0.921254\pi\) | ||
0.969556 | − | 0.244871i | \(-0.0787458\pi\) | |||||||
\(740\) | −2.91673 | − | 3.46829i | −0.107221 | − | 0.127497i | ||||
\(741\) | −20.9138 | − | 1.61849i | −0.768289 | − | 0.0594566i | ||||
\(742\) | −25.4438 | − | 25.4438i | −0.934072 | − | 0.934072i | ||||
\(743\) | 31.8345 | + | 31.8345i | 1.16789 | + | 1.16789i | 0.982702 | + | 0.185193i | \(0.0592909\pi\) |
0.185193 | + | 0.982702i | \(0.440709\pi\) | |||||||
\(744\) | −10.9399 | − | 0.846618i | −0.401075 | − | 0.0310385i | ||||
\(745\) | −0.393944 | + | 4.56041i | −0.0144330 | + | 0.167081i | ||||
\(746\) | 28.6369i | 1.04847i | ||||||||
\(747\) | 41.7047 | − | 30.4669i | 1.52590 | − | 1.11473i | ||||
\(748\) | 0.645891 | − | 0.645891i | 0.0236161 | − | 0.0236161i | ||||
\(749\) | 39.8106 | 1.45465 | ||||||||
\(750\) | 18.2837 | + | 6.38017i | 0.667626 | + | 0.232971i | ||||
\(751\) | 1.87068 | 0.0682622 | 0.0341311 | − | 0.999417i | \(-0.489134\pi\) | ||||
0.0341311 | + | 0.999417i | \(0.489134\pi\) | |||||||
\(752\) | 0.199419 | − | 0.199419i | 0.00727207 | − | 0.00727207i | ||||
\(753\) | −21.5420 | − | 25.1559i | −0.785035 | − | 0.916732i | ||||
\(754\) | 2.29928i | 0.0837349i | ||||||||
\(755\) | −0.508077 | + | 5.88165i | −0.0184908 | + | 0.214055i | ||||
\(756\) | −14.0188 | − | 3.30761i | −0.509860 | − | 0.120297i | ||||
\(757\) | −4.50446 | − | 4.50446i | −0.163717 | − | 0.163717i | 0.620494 | − | 0.784211i | \(-0.286932\pi\) |
−0.784211 | + | 0.620494i | \(0.786932\pi\) | |||||||
\(758\) | −22.2485 | − | 22.2485i | −0.808102 | − | 0.808102i | ||||
\(759\) | 0.397175 | − | 5.13223i | 0.0144165 | − | 0.186288i | ||||
\(760\) | −9.24836 | − | 10.9972i | −0.335473 | − | 0.398912i | ||||
\(761\) | 29.5482i | 1.07112i | 0.844497 | + | 0.535561i | \(0.179900\pi\) | ||||
−0.844497 | + | 0.535561i | \(0.820100\pi\) | |||||||
\(762\) | −18.5126 | + | 15.8531i | −0.670642 | + | 0.574298i | ||||
\(763\) | 6.31706 | − | 6.31706i | 0.228693 | − | 0.228693i | ||||
\(764\) | 26.9285 | 0.974238 | ||||||||
\(765\) | 1.76333 | − | 1.06843i | 0.0637532 | − | 0.0386292i | ||||
\(766\) | 7.21387 | 0.260648 | ||||||||
\(767\) | 12.5667 | − | 12.5667i | 0.453757 | − | 0.453757i | ||||
\(768\) | 1.31559 | − | 1.12660i | 0.0474723 | − | 0.0406525i | ||||
\(769\) | 14.7558i | 0.532107i | 0.963958 | + | 0.266054i | \(0.0857199\pi\) | ||||
−0.963958 | + | 0.266054i | \(0.914280\pi\) | |||||||
\(770\) | −18.3530 | − | 1.58539i | −0.661395 | − | 0.0571336i | ||||
\(771\) | −3.21454 | + | 41.5378i | −0.115769 | + | 1.49595i | ||||
\(772\) | 10.9317 | + | 10.9317i | 0.393439 | + | 0.393439i | ||||
\(773\) | −9.22983 | − | 9.22983i | −0.331974 | − | 0.331974i | 0.521362 | − | 0.853336i | \(-0.325424\pi\) |
−0.853336 | + | 0.521362i | \(0.825424\pi\) | |||||||
\(774\) | 7.55377 | + | 1.17619i | 0.271515 | + | 0.0422773i | ||||
\(775\) | −31.2059 | − | 5.43188i | −1.12095 | − | 0.195119i | ||||
\(776\) | − | 12.7102i | − | 0.456270i | ||||||
\(777\) | 6.32905 | + | 7.39080i | 0.227053 | + | 0.265144i | ||||
\(778\) | −12.9858 | + | 12.9858i | −0.465565 | + | 0.465565i | ||||
\(779\) | −19.5724 | −0.701254 | ||||||||
\(780\) | 1.18740 | − | 7.20189i | 0.0425159 | − | 0.257869i | ||||
\(781\) | 22.7349 | 0.813520 | ||||||||
\(782\) | −0.217329 | + | 0.217329i | −0.00777166 | + | 0.00777166i | ||||
\(783\) | −3.33348 | − | 5.39223i | −0.119129 | − | 0.192703i | ||||
\(784\) | − | 0.683996i | − | 0.0244284i | ||||||
\(785\) | 1.81756 | − | 1.52852i | 0.0648716 | − | 0.0545551i | ||||
\(786\) | 7.16182 | + | 0.554241i | 0.255454 | + | 0.0197691i | ||||
\(787\) | 21.4398 | + | 21.4398i | 0.764246 | + | 0.764246i | 0.977087 | − | 0.212841i | \(-0.0682716\pi\) |
−0.212841 | + | 0.977087i | \(0.568272\pi\) | |||||||
\(788\) | −1.97929 | − | 1.97929i | −0.0705093 | − | 0.0705093i | ||||
\(789\) | −30.1792 | − | 2.33552i | −1.07441 | − | 0.0831466i | ||||
\(790\) | −24.6945 | + | 20.7673i | −0.878590 | + | 0.738868i | ||||
\(791\) | 14.6220i | 0.519898i | ||||||||
\(792\) | 5.25943 | + | 7.19938i | 0.186886 | + | 0.255819i | ||||
\(793\) | −7.42575 | + | 7.42575i | −0.263696 | + | 0.263696i | ||||
\(794\) | −9.75933 | −0.346346 | ||||||||
\(795\) | −8.17857 | + | 49.6050i | −0.290064 | + | 1.75931i | ||||
\(796\) | −15.8892 | −0.563178 | ||||||||
\(797\) | 18.1902 | − | 18.1902i | 0.644331 | − | 0.644331i | −0.307286 | − | 0.951617i | \(-0.599421\pi\) |
0.951617 | + | 0.307286i | \(0.0994208\pi\) | |||||||
\(798\) | 20.0681 | + | 23.4347i | 0.710404 | + | 0.829580i | ||||
\(799\) | − | 0.0866791i | − | 0.00306649i | ||||||
\(800\) | 4.08946 | − | 2.87686i | 0.144584 | − | 0.101712i | ||||
\(801\) | 1.13380 | − | 7.28155i | 0.0400610 | − | 0.257281i | ||||
\(802\) | 12.9741 | + | 12.9741i | 0.458131 | + | 0.458131i | ||||
\(803\) | 12.0575 | + | 12.0575i | 0.425498 | + | 0.425498i | ||||
\(804\) | 1.77857 | − | 22.9825i | 0.0627254 | − | 0.810529i | ||||
\(805\) | 6.17539 | + | 0.533451i | 0.217654 | + | 0.0188017i | ||||
\(806\) | 11.9391i | 0.420538i | ||||||||
\(807\) | −26.4433 | + | 22.6445i | −0.930849 | + | 0.797124i | ||||
\(808\) | 2.12822 | − | 2.12822i | 0.0748706 | − | 0.0748706i | ||||
\(809\) | 37.6524 | 1.32379 | 0.661893 | − | 0.749598i | \(-0.269753\pi\) | ||||
0.661893 | + | 0.749598i | \(0.269753\pi\) | |||||||
\(810\) | 7.65656 | + | 18.6112i | 0.269024 | + | 0.653931i | ||||
\(811\) | 34.7632 | 1.22070 | 0.610350 | − | 0.792132i | \(-0.291029\pi\) | ||||
0.610350 | + | 0.792132i | \(0.291029\pi\) | |||||||
\(812\) | 2.39137 | − | 2.39137i | 0.0839205 | − | 0.0839205i | ||||
\(813\) | −36.6624 | + | 31.3955i | −1.28581 | + | 1.10109i | ||||
\(814\) | − | 6.02308i | − | 0.211109i | ||||||
\(815\) | −13.4416 | − | 15.9835i | −0.470839 | − | 0.559876i | ||||
\(816\) | 0.0410744 | − | 0.530758i | 0.00143789 | − | 0.0185802i | ||||
\(817\) | −11.5791 | − | 11.5791i | −0.405101 | − | 0.405101i | ||||
\(818\) | 11.2227 | + | 11.2227i | 0.392392 | + | 0.392392i | ||||
\(819\) | −2.41130 | + | 15.4859i | −0.0842577 | + | 0.541122i | ||||
\(820\) | 0.586139 | − | 6.78531i | 0.0204689 | − | 0.236953i | ||||
\(821\) | − | 22.5188i | − | 0.785913i | −0.919557 | − | 0.392957i | \(-0.871452\pi\) | ||
0.919557 | − | 0.392957i | \(-0.128548\pi\) | |||||||
\(822\) | 10.7035 | + | 12.4991i | 0.373328 | + | 0.435957i | ||||
\(823\) | 20.6173 | − | 20.6173i | 0.718674 | − | 0.718674i | −0.249660 | − | 0.968334i | \(-0.580319\pi\) |
0.968334 | + | 0.249660i | \(0.0803188\pi\) | |||||||
\(824\) | 2.57147 | 0.0895816 | ||||||||
\(825\) | 13.1405 | + | 22.1307i | 0.457493 | + | 0.770491i | ||||
\(826\) | −26.1400 | −0.909526 | ||||||||
\(827\) | −7.61157 | + | 7.61157i | −0.264680 | + | 0.264680i | −0.826952 | − | 0.562272i | \(-0.809927\pi\) |
0.562272 | + | 0.826952i | \(0.309927\pi\) | |||||||
\(828\) | −1.76969 | − | 2.42244i | −0.0615009 | − | 0.0841856i | ||||
\(829\) | − | 42.8945i | − | 1.48979i | −0.667184 | − | 0.744893i | \(-0.732500\pi\) | ||
0.667184 | − | 0.744893i | \(-0.267500\pi\) | |||||||
\(830\) | 3.31309 | − | 38.3533i | 0.114999 | − | 1.33126i | ||||
\(831\) | 17.2157 | + | 1.33229i | 0.597206 | + | 0.0462168i | ||||
\(832\) | −1.33263 | − | 1.33263i | −0.0462006 | − | 0.0462006i | ||||
\(833\) | −0.148652 | − | 0.148652i | −0.00515049 | − | 0.00515049i | ||||
\(834\) | −36.8350 | − | 2.85060i | −1.27549 | − | 0.0987083i | ||||
\(835\) | 10.6866 | + | 12.7075i | 0.369826 | + | 0.439760i | ||||
\(836\) | − | 19.0980i | − | 0.660517i | ||||||
\(837\) | −17.3093 | − | 27.9994i | −0.598296 | − | 0.967802i | ||||
\(838\) | 14.0739 | − | 14.0739i | 0.486175 | − | 0.486175i | ||||
\(839\) | 41.0356 | 1.41671 | 0.708353 | − | 0.705858i | \(-0.249438\pi\) | ||||
0.708353 | + | 0.705858i | \(0.249438\pi\) | |||||||
\(840\) | −8.72527 | + | 6.25536i | −0.301051 | + | 0.215830i | ||||
\(841\) | −27.5115 | −0.948674 | ||||||||
\(842\) | −6.41487 | + | 6.41487i | −0.221071 | + | 0.221071i | ||||
\(843\) | −17.7873 | − | 20.7713i | −0.612628 | − | 0.715402i | ||||
\(844\) | − | 11.3907i | − | 0.392085i | ||||||
\(845\) | 21.0484 | + | 1.81823i | 0.724087 | + | 0.0625492i | ||||
\(846\) | 0.835990 | + | 0.130171i | 0.0287419 | + | 0.00447538i | ||||
\(847\) | 4.24850 | + | 4.24850i | 0.145980 | + | 0.145980i | ||||
\(848\) | 9.17886 | + | 9.17886i | 0.315203 | + | 0.315203i | ||||
\(849\) | 2.49556 | − | 32.2473i | 0.0856475 | − | 1.10672i | ||||
\(850\) | 0.263532 | − | 1.51398i | 0.00903909 | − | 0.0519292i | ||||
\(851\) | 2.02664i | 0.0694723i | ||||||||
\(852\) | 10.0641 | − | 8.61826i | 0.344789 | − | 0.295257i | ||||
\(853\) | −7.35122 | + | 7.35122i | −0.251701 | + | 0.251701i | −0.821668 | − | 0.569967i | \(-0.806956\pi\) |
0.569967 | + | 0.821668i | \(0.306956\pi\) | |||||||
\(854\) | 15.4463 | 0.528561 | ||||||||
\(855\) | 10.2735 | − | 41.8653i | 0.351345 | − | 1.43176i | ||||
\(856\) | −14.3617 | −0.490872 | ||||||||
\(857\) | 6.84555 | − | 6.84555i | 0.233839 | − | 0.233839i | −0.580454 | − | 0.814293i | \(-0.697125\pi\) |
0.814293 | + | 0.580454i | \(0.197125\pi\) | |||||||
\(858\) | 7.36865 | − | 6.31008i | 0.251562 | − | 0.215423i | ||||
\(859\) | 28.4706i | 0.971403i | 0.874125 | + | 0.485702i | \(0.161436\pi\) | ||||
−0.874125 | + | 0.485702i | \(0.838564\pi\) | |||||||
\(860\) | 4.36097 | − | 3.66745i | 0.148708 | − | 0.125059i | ||||
\(861\) | −1.12832 | + | 14.5800i | −0.0384530 | + | 0.496884i | ||||
\(862\) | −4.66926 | − | 4.66926i | −0.159036 | − | 0.159036i | ||||
\(863\) | 25.7598 | + | 25.7598i | 0.876873 | + | 0.876873i | 0.993210 | − | 0.116337i | \(-0.0371152\pi\) |
−0.116337 | + | 0.993210i | \(0.537115\pi\) | |||||||
\(864\) | 5.05729 | + | 1.19322i | 0.172053 | + | 0.0405942i | ||||
\(865\) | 39.1558 | − | 32.9289i | 1.33134 | − | 1.11962i | ||||
\(866\) | 4.18515i | 0.142217i | ||||||||
\(867\) | 19.0457 | + | 22.2408i | 0.646826 | + | 0.755337i | ||||
\(868\) | 12.4173 | − | 12.4173i | 0.421470 | − | 0.421470i | ||||
\(869\) | −42.8848 | −1.45477 | ||||||||
\(870\) | −4.66218 | − | 0.768672i | −0.158063 | − | 0.0260604i | ||||
\(871\) | −25.0817 | −0.849861 | ||||||||
\(872\) | −2.27888 | + | 2.27888i | −0.0771726 | + | 0.0771726i | ||||
\(873\) | 30.7897 | − | 22.4931i | 1.04207 | − | 0.761276i | ||||
\(874\) | 6.42606i | 0.217365i | ||||||||
\(875\) | −26.7887 | + | 15.5842i | −0.905622 | + | 0.526842i | ||||
\(876\) | 9.90815 | + | 0.766775i | 0.334765 | + | 0.0259069i | ||||
\(877\) | 15.9225 | + | 15.9225i | 0.537663 | + | 0.537663i | 0.922842 | − | 0.385179i | \(-0.125860\pi\) |
−0.385179 | + | 0.922842i | \(0.625860\pi\) | |||||||
\(878\) | −7.95695 | − | 7.95695i | −0.268534 | − | 0.268534i | ||||
\(879\) | −16.9445 | − | 1.31130i | −0.571523 | − | 0.0442292i | ||||
\(880\) | 6.62083 | + | 0.571930i | 0.223188 | + | 0.0192798i | ||||
\(881\) | 23.1667i | 0.780505i | 0.920708 | + | 0.390253i | \(0.127612\pi\) | ||||
−0.920708 | + | 0.390253i | \(0.872388\pi\) | |||||||
\(882\) | 1.65694 | − | 1.21046i | 0.0557920 | − | 0.0407583i | ||||
\(883\) | −19.6995 | + | 19.6995i | −0.662940 | + | 0.662940i | −0.956072 | − | 0.293132i | \(-0.905302\pi\) |
0.293132 | + | 0.956072i | \(0.405302\pi\) | |||||||
\(884\) | −0.579238 | −0.0194819 | ||||||||
\(885\) | 21.2799 | + | 29.6823i | 0.715317 | + | 0.997759i | ||||
\(886\) | −22.9552 | −0.771194 | ||||||||
\(887\) | 5.93272 | − | 5.93272i | 0.199201 | − | 0.199201i | −0.600456 | − | 0.799658i | \(-0.705014\pi\) |
0.799658 | + | 0.600456i | \(0.205014\pi\) | |||||||
\(888\) | −2.28320 | − | 2.66623i | −0.0766193 | − | 0.0894729i | ||||
\(889\) | − | 39.0068i | − | 1.30825i | ||||||
\(890\) | −3.53528 | − | 4.20381i | −0.118503 | − | 0.140912i | ||||
\(891\) | −8.13251 | + | 25.4813i | −0.272449 | + | 0.853655i | ||||
\(892\) | 10.4680 | + | 10.4680i | 0.350494 | + | 0.350494i | ||||
\(893\) | −1.28148 | − | 1.28148i | −0.0428831 | − | 0.0428831i | ||||
\(894\) | −0.273573 | + | 3.53507i | −0.00914964 | + | 0.118230i | ||||
\(895\) | −2.42645 | + | 28.0893i | −0.0811072 | + | 0.938921i | ||||
\(896\) | 2.77200i | 0.0926061i | ||||||||
\(897\) | −2.47940 | + | 2.12321i | −0.0827846 | + | 0.0708919i | ||||
\(898\) | −2.45975 | + | 2.45975i | −0.0820828 | + | 0.0820828i | ||||
\(899\) | 7.72887 | 0.257772 | ||||||||
\(900\) | 14.2061 | + | 4.81532i | 0.473536 | + | 0.160511i | ||||
\(901\) | 3.98966 | 0.132915 | ||||||||
\(902\) | 6.40068 | − | 6.40068i | 0.213119 | − | 0.213119i | ||||
\(903\) | −9.29307 | + | 7.95804i | −0.309254 | + | 0.264827i | ||||
\(904\) | − | 5.27488i | − | 0.175440i | ||||||
\(905\) | −0.337508 | + | 3.90709i | −0.0112191 | + | 0.129876i | ||||
\(906\) | −0.352832 | + | 4.55924i | −0.0117221 | + | 0.151471i | ||||
\(907\) | −28.2405 | − | 28.2405i | −0.937710 | − | 0.937710i | 0.0604604 | − | 0.998171i | \(-0.480743\pi\) |
−0.998171 | + | 0.0604604i | \(0.980743\pi\) | |||||||
\(908\) | −16.1663 | − | 16.1663i | −0.536496 | − | 0.536496i | ||||
\(909\) | 8.92177 | + | 1.38920i | 0.295917 | + | 0.0460769i | ||||
\(910\) | 7.51862 | + | 8.94040i | 0.249240 | + | 0.296371i | ||||
\(911\) | 0.663646i | 0.0219876i | 0.999940 | + | 0.0109938i | \(0.00349950\pi\) | ||||
−0.999940 | + | 0.0109938i | \(0.996501\pi\) | |||||||
\(912\) | −7.23957 | − | 8.45408i | −0.239726 | − | 0.279943i | ||||
\(913\) | 36.1792 | − | 36.1792i | 1.19736 | − | 1.19736i | ||||
\(914\) | 34.6782 | 1.14705 | ||||||||
\(915\) | −12.5745 | − | 17.5395i | −0.415699 | − | 0.579837i | ||||
\(916\) | −16.0298 | −0.529638 | ||||||||
\(917\) | −8.12901 | + | 8.12901i | −0.268444 | + | 0.268444i | ||||
\(918\) | 1.35842 | − | 0.839775i | 0.0448344 | − | 0.0277167i | ||||
\(919\) | − | 12.5913i | − | 0.415350i | −0.978198 | − | 0.207675i | \(-0.933410\pi\) | ||
0.978198 | − | 0.207675i | \(-0.0665897\pi\) | |||||||
\(920\) | −2.22777 | − | 0.192443i | −0.0734475 | − | 0.00634464i | ||||
\(921\) | −20.4885 | − | 1.58557i | −0.675117 | − | 0.0522462i | ||||
\(922\) | −4.99529 | − | 4.99529i | −0.164511 | − | 0.164511i | ||||
\(923\) | −10.1944 | − | 10.1944i | −0.335553 | − | 0.335553i | ||||
\(924\) | −14.2266 | − | 1.10097i | −0.468019 | − | 0.0362192i | ||||
\(925\) | −5.83036 | − | 8.28786i | −0.191701 | − | 0.272503i | ||||
\(926\) | − | 6.95367i | − | 0.228512i | ||||||
\(927\) | 4.55070 | + | 6.22924i | 0.149465 | + | 0.204595i | ||||
\(928\) | −0.862686 | + | 0.862686i | −0.0283191 | + | 0.0283191i | ||||
\(929\) | −5.22216 | −0.171334 | −0.0856668 | − | 0.996324i | \(-0.527302\pi\) | ||||
−0.0856668 | + | 0.996324i | \(0.527302\pi\) | |||||||
\(930\) | −24.2086 | − | 3.99137i | −0.793832 | − | 0.130882i | ||||
\(931\) | −4.39540 | −0.144053 | ||||||||
\(932\) | 4.14654 | − | 4.14654i | 0.135824 | − | 0.135824i | ||||
\(933\) | −25.5843 | − | 29.8763i | −0.837591 | − | 0.978105i | ||||
\(934\) | − | 0.394898i | − | 0.0129214i | ||||||
\(935\) | 1.56320 | − | 1.31460i | 0.0511219 | − | 0.0429921i | ||||
\(936\) | 0.869877 | − | 5.58655i | 0.0284328 | − | 0.182602i | ||||
\(937\) | −5.96477 | − | 5.96477i | −0.194861 | − | 0.194861i | 0.602932 | − | 0.797793i | \(-0.293999\pi\) |
−0.797793 | + | 0.602932i | \(0.793999\pi\) | |||||||
\(938\) | 26.0862 | + | 26.0862i | 0.851745 | + | 0.851745i | ||||
\(939\) | −3.60816 | + | 46.6241i | −0.117748 | + | 1.52152i | ||||
\(940\) | 0.482637 | − | 0.405884i | 0.0157419 | − | 0.0132385i | ||||
\(941\) | − | 9.07148i | − | 0.295722i | −0.989008 | − | 0.147861i | \(-0.952761\pi\) | ||
0.989008 | − | 0.147861i | \(-0.0472388\pi\) | |||||||
\(942\) | 1.39724 | − | 1.19652i | 0.0455247 | − | 0.0389846i | ||||
\(943\) | −2.15370 | + | 2.15370i | −0.0701340 | + | 0.0701340i | ||||
\(944\) | 9.43000 | 0.306920 | ||||||||
\(945\) | −30.5942 | − | 10.0664i | −0.995230 | − | 0.327461i | ||||
\(946\) | 7.57333 | 0.246230 | ||||||||
\(947\) | 0.282615 | − | 0.282615i | 0.00918377 | − | 0.00918377i | −0.702500 | − | 0.711684i | \(-0.747933\pi\) |
0.711684 | + | 0.702500i | \(0.247933\pi\) | |||||||
\(948\) | −18.9838 | + | 16.2566i | −0.616564 | + | 0.527989i | ||||
\(949\) | − | 10.8132i | − | 0.351011i | ||||||
\(950\) | −18.4869 | − | 26.2791i | −0.599794 | − | 0.852607i | ||||
\(951\) | 0.00520591 | − | 0.0672700i | 0.000168813 | − | 0.00218138i | ||||
\(952\) | 0.602436 | + | 0.602436i | 0.0195251 | + | 0.0195251i | ||||
\(953\) | 11.5078 | + | 11.5078i | 0.372773 | + | 0.372773i | 0.868486 | − | 0.495713i | \(-0.165093\pi\) |
−0.495713 | + | 0.868486i | \(0.665093\pi\) | |||||||
\(954\) | −5.99152 | + | 38.4789i | −0.193983 | + | 1.24580i | ||||
\(955\) | 59.9905 | + | 5.18219i | 1.94125 | + | 0.167692i | ||||
\(956\) | 29.7656i | 0.962690i | ||||||||
\(957\) | −4.08487 | − | 4.77014i | −0.132045 | − | 0.154197i | ||||
\(958\) | −14.1219 | + | 14.1219i | −0.456259 | + | 0.456259i | ||||
\(959\) | −26.3361 | −0.850438 | ||||||||
\(960\) | 3.14764 | − | 2.25662i | 0.101590 | − | 0.0728321i | ||||
\(961\) | 9.13253 | 0.294598 | ||||||||
\(962\) | −2.70076 | + | 2.70076i | −0.0870761 | + | 0.0870761i | ||||
\(963\) | −25.4157 | − | 34.7903i | −0.819009 | − | 1.12110i | ||||
\(964\) | 18.1553i | 0.584743i | ||||||||
\(965\) | 22.2495 | + | 26.4570i | 0.716238 | + | 0.851680i | ||||
\(966\) | 4.78694 | + | 0.370453i | 0.154017 | + | 0.0119191i | ||||
\(967\) | −40.1895 | − | 40.1895i | −1.29241 | − | 1.29241i | −0.933294 | − | 0.359113i | \(-0.883079\pi\) |
−0.359113 | − | 0.933294i | \(-0.616921\pi\) | |||||||
\(968\) | −1.53265 | − | 1.53265i | −0.0492611 | − | 0.0492611i | ||||
\(969\) | −3.41068 | − | 0.263947i | −0.109567 | − | 0.00847920i | ||||
\(970\) | 2.44599 | − | 28.3155i | 0.0785359 | − | 0.909155i | ||||
\(971\) | 20.3254i | 0.652272i | 0.945323 | + | 0.326136i | \(0.105747\pi\) | ||||
−0.945323 | + | 0.326136i | \(0.894253\pi\) | |||||||
\(972\) | 6.05932 | + | 14.3626i | 0.194353 | + | 0.460681i | ||||
\(973\) | 41.8096 | − | 41.8096i | 1.34035 | − | 1.34035i | ||||
\(974\) | −1.98570 | −0.0636258 | ||||||||
\(975\) | 4.03121 | − | 15.8157i | 0.129102 | − | 0.506506i | ||||
\(976\) | −5.57225 | −0.178363 | ||||||||
\(977\) | −31.6440 | + | 31.6440i | −1.01238 | + | 1.01238i | −0.0124590 | + | 0.999922i | \(0.503966\pi\) |
−0.999922 | + | 0.0124590i | \(0.996034\pi\) | |||||||
\(978\) | −10.5220 | − | 12.2872i | −0.336458 | − | 0.392902i | ||||
\(979\) | − | 7.30040i | − | 0.233322i | ||||||
\(980\) | 0.131630 | − | 1.52379i | 0.00420476 | − | 0.0486756i | ||||
\(981\) | −9.55335 | − | 1.48754i | −0.305015 | − | 0.0474936i | ||||
\(982\) | 4.56709 | + | 4.56709i | 0.145742 | + | 0.145742i | ||||
\(983\) | −14.9031 | − | 14.9031i | −0.475336 | − | 0.475336i | 0.428301 | − | 0.903636i | \(-0.359112\pi\) |
−0.903636 | + | 0.428301i | \(0.859112\pi\) | |||||||
\(984\) | 0.407041 | − | 5.25973i | 0.0129760 | − | 0.167674i | ||||
\(985\) | −4.02851 | − | 4.79031i | −0.128359 | − | 0.152632i | ||||
\(986\) | 0.374973i | 0.0119416i | ||||||||
\(987\) | −1.02848 | + | 0.880732i | −0.0327370 | + | 0.0280340i | ||||
\(988\) | −8.56357 | + | 8.56357i | −0.272443 | + | 0.272443i | ||||
\(989\) | −2.54827 | −0.0810301 | ||||||||
\(990\) | 10.3313 | + | 17.0507i | 0.328351 | + | 0.541907i | ||||
\(991\) | −30.3099 | −0.962827 | −0.481414 | − | 0.876494i | \(-0.659876\pi\) | ||||
−0.481414 | + | 0.876494i | \(0.659876\pi\) | |||||||
\(992\) | −4.47954 | + | 4.47954i | −0.142225 | + | 0.142225i | ||||
\(993\) | 1.38351 | − | 1.18475i | 0.0439043 | − | 0.0375970i | ||||
\(994\) | 21.2053i | 0.672593i | ||||||||
\(995\) | −35.3975 | − | 3.05776i | −1.12218 | − | 0.0969374i | ||||
\(996\) | 2.30076 | − | 29.7301i | 0.0729024 | − | 0.942034i | ||||
\(997\) | 19.3131 | + | 19.3131i | 0.611651 | + | 0.611651i | 0.943376 | − | 0.331725i | \(-0.107631\pi\) |
−0.331725 | + | 0.943376i | \(0.607631\pi\) | |||||||
\(998\) | 6.74411 | + | 6.74411i | 0.213481 | + | 0.213481i | ||||
\(999\) | 2.41823 | − | 10.2493i | 0.0765094 | − | 0.324274i |
(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 | 690.2.i.f.47.14 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.47.7 | ✓ | 32 | |
5.3 | odd | 4 | inner | 690.2.i.f.323.7 | yes | 32 | |
15.8 | even | 4 | inner | 690.2.i.f.323.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.7 | ✓ | 32 | 3.2 | odd | 2 | inner | |
690.2.i.f.47.14 | yes | 32 | 1.1 | even | 1 | trivial | |
690.2.i.f.323.7 | yes | 32 | 5.3 | odd | 4 | inner | |
690.2.i.f.323.14 | yes | 32 | 15.8 | even | 4 | inner |