Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 199.5 | ||
Character | \(\chi\) | \(=\) | 375.199 |
Dual form | 375.2.i.d.49.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.18666 | + | 1.63330i | 0.839097 | + | 1.15492i | 0.986161 | + | 0.165791i | \(0.0530177\pi\) |
−0.147064 | + | 0.989127i | \(0.546982\pi\) | |||||||
\(3\) | 0.951057 | + | 0.309017i | 0.549093 | + | 0.178411i | ||||
\(4\) | −0.641469 | + | 1.97424i | −0.320735 | + | 0.987119i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.623865 | + | 1.92006i | 0.254692 | + | 0.783861i | ||||
\(7\) | 1.01887i | 0.385097i | 0.981287 | + | 0.192548i | \(0.0616752\pi\) | ||||
−0.981287 | + | 0.192548i | \(0.938325\pi\) | |||||||
\(8\) | −0.145612 | + | 0.0473123i | −0.0514817 | + | 0.0167274i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.85061 | + | 2.79763i | −1.16100 | + | 0.843517i | −0.989904 | − | 0.141737i | \(-0.954731\pi\) |
−0.171097 | + | 0.985254i | \(0.554731\pi\) | |||||||
\(12\) | −1.22015 | + | 1.67939i | −0.352226 | + | 0.484797i | ||||
\(13\) | 0.0610339 | − | 0.0840060i | 0.0169278 | − | 0.0232991i | −0.800469 | − | 0.599374i | \(-0.795416\pi\) |
0.817397 | + | 0.576075i | \(0.195416\pi\) | |||||||
\(14\) | −1.66412 | + | 1.20905i | −0.444755 | + | 0.323134i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.10871 | + | 2.25861i | 0.777177 | + | 0.564652i | ||||
\(17\) | 5.55204 | − | 1.80397i | 1.34657 | − | 0.437527i | 0.455032 | − | 0.890475i | \(-0.349628\pi\) |
0.891537 | + | 0.452949i | \(0.149628\pi\) | |||||||
\(18\) | 2.01887i | 0.475852i | ||||||||
\(19\) | 0.223853 | + | 0.688949i | 0.0513554 | + | 0.158056i | 0.973445 | − | 0.228920i | \(-0.0735196\pi\) |
−0.922090 | + | 0.386976i | \(0.873520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.314848 | + | 0.969003i | −0.0687055 | + | 0.211454i | ||||
\(22\) | −9.13874 | − | 2.96936i | −1.94839 | − | 0.633069i | ||||
\(23\) | −5.33210 | − | 7.33901i | −1.11182 | − | 1.53029i | −0.818707 | − | 0.574212i | \(-0.805308\pi\) |
−0.293114 | − | 0.956077i | \(-0.594692\pi\) | |||||||
\(24\) | −0.153106 | −0.0312526 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.209634 | 0.0411126 | ||||||||
\(27\) | 0.587785 | + | 0.809017i | 0.113119 | + | 0.155695i | ||||
\(28\) | −2.01149 | − | 0.653574i | −0.380136 | − | 0.123514i | ||||
\(29\) | 1.23251 | − | 3.79326i | 0.228871 | − | 0.704391i | −0.769005 | − | 0.639243i | \(-0.779248\pi\) |
0.997876 | − | 0.0651484i | \(-0.0207521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.329605 | + | 1.01442i | 0.0591988 | + | 0.182195i | 0.976283 | − | 0.216498i | \(-0.0694636\pi\) |
−0.917084 | + | 0.398694i | \(0.869464\pi\) | |||||||
\(32\) | 8.06387i | 1.42550i | ||||||||
\(33\) | −4.52666 | + | 1.47080i | −0.787990 | + | 0.256034i | ||||
\(34\) | 9.53482 | + | 6.92745i | 1.63521 | + | 1.18805i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.67939 | + | 1.22015i | −0.279898 | + | 0.203358i | ||||
\(37\) | 2.36655 | − | 3.25727i | 0.389058 | − | 0.535493i | −0.568898 | − | 0.822408i | \(-0.692630\pi\) |
0.957956 | + | 0.286916i | \(0.0926300\pi\) | |||||||
\(38\) | −0.859623 | + | 1.18317i | −0.139449 | + | 0.191935i | ||||
\(39\) | 0.0840060 | − | 0.0610339i | 0.0134517 | − | 0.00977325i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.83282 | − | 4.23780i | −0.910934 | − | 0.661832i | 0.0303167 | − | 0.999540i | \(-0.490348\pi\) |
−0.941251 | + | 0.337708i | \(0.890348\pi\) | |||||||
\(42\) | −1.95629 | + | 0.635638i | −0.301862 | + | 0.0980810i | ||||
\(43\) | − | 8.62791i | − | 1.31574i | −0.753130 | − | 0.657872i | \(-0.771457\pi\) | ||
0.753130 | − | 0.657872i | \(-0.228543\pi\) | |||||||
\(44\) | −3.05314 | − | 9.39661i | −0.460279 | − | 1.41659i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.65940 | − | 17.4179i | 0.834434 | − | 2.56812i | ||||
\(47\) | −7.79673 | − | 2.53331i | −1.13727 | − | 0.369522i | −0.320936 | − | 0.947101i | \(-0.603997\pi\) |
−0.816335 | + | 0.577579i | \(0.803997\pi\) | |||||||
\(48\) | 2.25861 | + | 3.10871i | 0.326002 | + | 0.448703i | ||||
\(49\) | 5.96190 | 0.851700 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.83776 | 0.817451 | ||||||||
\(52\) | 0.126697 | + | 0.174383i | 0.0175696 | + | 0.0241825i | ||||
\(53\) | 4.15345 | + | 1.34954i | 0.570520 | + | 0.185373i | 0.580049 | − | 0.814581i | \(-0.303033\pi\) |
−0.00952922 | + | 0.999955i | \(0.503033\pi\) | |||||||
\(54\) | −0.623865 | + | 1.92006i | −0.0848973 | + | 0.261287i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.0482051 | − | 0.148360i | −0.00644168 | − | 0.0198254i | ||||
\(57\) | 0.724404i | 0.0959497i | ||||||||
\(58\) | 7.65810 | − | 2.48827i | 1.00556 | − | 0.326726i | ||||
\(59\) | −3.97458 | − | 2.88770i | −0.517446 | − | 0.375947i | 0.298195 | − | 0.954505i | \(-0.403616\pi\) |
−0.815641 | + | 0.578558i | \(0.803616\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.63428 | + | 4.09354i | −0.721396 | + | 0.524125i | −0.886830 | − | 0.462096i | \(-0.847097\pi\) |
0.165434 | + | 0.986221i | \(0.447097\pi\) | |||||||
\(62\) | −1.26572 | + | 1.74212i | −0.160747 | + | 0.221249i | ||||
\(63\) | −0.598877 | + | 0.824283i | −0.0754514 | + | 0.103850i | ||||
\(64\) | −6.95331 | + | 5.05187i | −0.869163 | + | 0.631484i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.77388 | − | 5.64805i | −0.956898 | − | 0.695227i | ||||
\(67\) | 9.43446 | − | 3.06544i | 1.15260 | − | 0.374503i | 0.330480 | − | 0.943813i | \(-0.392790\pi\) |
0.822123 | + | 0.569310i | \(0.192790\pi\) | |||||||
\(68\) | 12.1183i | 1.46955i | ||||||||
\(69\) | −2.80325 | − | 8.62753i | −0.337472 | − | 1.03863i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.33323 | + | 10.2586i | −0.395582 | + | 1.21748i | 0.532925 | + | 0.846162i | \(0.321093\pi\) |
−0.928507 | + | 0.371314i | \(0.878907\pi\) | |||||||
\(72\) | −0.145612 | − | 0.0473123i | −0.0171606 | − | 0.00557581i | ||||
\(73\) | 5.07326 | + | 6.98275i | 0.593781 | + | 0.817269i | 0.995121 | − | 0.0986599i | \(-0.0314556\pi\) |
−0.401341 | + | 0.915929i | \(0.631456\pi\) | |||||||
\(74\) | 8.12840 | 0.944907 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.50375 | −0.172491 | ||||||||
\(77\) | −2.85042 | − | 3.92327i | −0.324836 | − | 0.447098i | ||||
\(78\) | 0.199374 | + | 0.0647804i | 0.0225746 | + | 0.00733493i | ||||
\(79\) | −0.767263 | + | 2.36139i | −0.0863238 | + | 0.265677i | −0.984896 | − | 0.173149i | \(-0.944606\pi\) |
0.898572 | + | 0.438826i | \(0.144606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | − | 14.5556i | − | 1.60740i | ||||||
\(83\) | 4.03614 | − | 1.31142i | 0.443024 | − | 0.143947i | −0.0790064 | − | 0.996874i | \(-0.525175\pi\) |
0.522030 | + | 0.852927i | \(0.325175\pi\) | |||||||
\(84\) | −1.71108 | − | 1.24317i | −0.186694 | − | 0.135641i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.0920 | − | 10.2384i | 1.51958 | − | 1.10404i | ||||
\(87\) | 2.34436 | − | 3.22674i | 0.251342 | − | 0.345943i | ||||
\(88\) | 0.428333 | − | 0.589550i | 0.0456605 | − | 0.0628463i | ||||
\(89\) | −14.8659 | + | 10.8007i | −1.57578 | + | 1.14487i | −0.654434 | + | 0.756120i | \(0.727093\pi\) |
−0.921344 | + | 0.388749i | \(0.872907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0855912 | + | 0.0621857i | 0.00897240 | + | 0.00651883i | ||||
\(92\) | 17.9093 | − | 5.81910i | 1.86718 | − | 0.606683i | ||||
\(93\) | 1.06662i | 0.110604i | ||||||||
\(94\) | −5.11443 | − | 15.7406i | −0.527513 | − | 1.62352i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.49187 | + | 7.66920i | −0.254326 | + | 0.782734i | ||||
\(97\) | 6.37090 | + | 2.07003i | 0.646867 | + | 0.210180i | 0.614032 | − | 0.789281i | \(-0.289546\pi\) |
0.0328349 | + | 0.999461i | \(0.489546\pi\) | |||||||
\(98\) | 7.07477 | + | 9.73758i | 0.714659 | + | 0.983644i | ||||
\(99\) | −4.75961 | −0.478359 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.66147 | 0.563337 | 0.281669 | − | 0.959512i | \(-0.409112\pi\) | ||||
0.281669 | + | 0.959512i | \(0.409112\pi\) | |||||||
\(102\) | 6.92745 | + | 9.53482i | 0.685920 | + | 0.944088i | ||||
\(103\) | −0.565393 | − | 0.183707i | −0.0557098 | − | 0.0181012i | 0.281030 | − | 0.959699i | \(-0.409324\pi\) |
−0.336739 | + | 0.941598i | \(0.609324\pi\) | |||||||
\(104\) | −0.00491278 | + | 0.0151200i | −0.000481737 | + | 0.00148263i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.72454 | + | 8.38527i | 0.264631 | + | 0.814450i | ||||
\(107\) | 1.38651i | 0.134039i | 0.997752 | + | 0.0670193i | \(0.0213489\pi\) | ||||
−0.997752 | + | 0.0670193i | \(0.978651\pi\) | |||||||
\(108\) | −1.97424 | + | 0.641469i | −0.189971 | + | 0.0617254i | ||||
\(109\) | −7.16528 | − | 5.20588i | −0.686309 | − | 0.498633i | 0.189136 | − | 0.981951i | \(-0.439431\pi\) |
−0.875445 | + | 0.483318i | \(0.839431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.25727 | − | 2.36655i | 0.309167 | − | 0.224623i | ||||
\(112\) | −2.30123 | + | 3.16737i | −0.217446 | + | 0.299288i | ||||
\(113\) | −3.87373 | + | 5.33173i | −0.364410 | + | 0.501567i | −0.951371 | − | 0.308048i | \(-0.900324\pi\) |
0.586961 | + | 0.809615i | \(0.300324\pi\) | |||||||
\(114\) | −1.18317 | + | 0.859623i | −0.110814 | + | 0.0805111i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.69819 | + | 4.86652i | 0.621911 | + | 0.451845i | ||||
\(117\) | 0.0987550 | − | 0.0320874i | 0.00912990 | − | 0.00296649i | ||||
\(118\) | − | 9.91841i | − | 0.913064i | ||||||
\(119\) | 1.83801 | + | 5.65681i | 0.168490 | + | 0.518559i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.60125 | − | 11.0835i | 0.327387 | − | 1.00759i | ||||
\(122\) | −13.3720 | − | 4.34482i | −1.21064 | − | 0.393361i | ||||
\(123\) | −4.23780 | − | 5.83282i | −0.382109 | − | 0.525928i | ||||
\(124\) | −2.21414 | −0.198836 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.05697 | −0.183249 | ||||||||
\(127\) | 4.28580 | + | 5.89890i | 0.380303 | + | 0.523443i | 0.955665 | − | 0.294457i | \(-0.0951386\pi\) |
−0.575362 | + | 0.817899i | \(0.695139\pi\) | |||||||
\(128\) | −1.16406 | − | 0.378226i | −0.102889 | − | 0.0334308i | ||||
\(129\) | 2.66617 | − | 8.20563i | 0.234743 | − | 0.722465i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.95230 | − | 9.08626i | −0.257944 | − | 0.793870i | −0.993235 | − | 0.116119i | \(-0.962955\pi\) |
0.735291 | − | 0.677751i | \(-0.237045\pi\) | |||||||
\(132\) | − | 9.88018i | − | 0.859959i | ||||||
\(133\) | −0.701950 | + | 0.228077i | −0.0608668 | + | 0.0197768i | ||||
\(134\) | 16.2023 | + | 11.7717i | 1.39967 | + | 1.01692i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.723096 | + | 0.525360i | −0.0620050 | + | 0.0450493i | ||||
\(137\) | −3.64418 | + | 5.01578i | −0.311343 | + | 0.428527i | −0.935799 | − | 0.352533i | \(-0.885320\pi\) |
0.624457 | + | 0.781060i | \(0.285320\pi\) | |||||||
\(138\) | 10.7648 | − | 14.8165i | 0.916363 | − | 1.26127i | ||||
\(139\) | −0.733399 | + | 0.532846i | −0.0622061 | + | 0.0451954i | −0.618454 | − | 0.785821i | \(-0.712241\pi\) |
0.556248 | + | 0.831017i | \(0.312241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.63230 | − | 4.81865i | −0.558540 | − | 0.405803i | ||||
\(142\) | −20.7109 | + | 6.72937i | −1.73802 | + | 0.564716i | ||||
\(143\) | 0.494225i | 0.0413291i | ||||||||
\(144\) | 1.18742 | + | 3.65450i | 0.0989517 | + | 0.304542i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.38468 | + | 16.5723i | −0.445639 | + | 1.37154i | ||||
\(147\) | 5.67011 | + | 1.84233i | 0.467663 | + | 0.151953i | ||||
\(148\) | 4.91257 | + | 6.76157i | 0.403811 | + | 0.555798i | ||||
\(149\) | 4.89808 | 0.401267 | 0.200633 | − | 0.979666i | \(-0.435700\pi\) | ||||
0.200633 | + | 0.979666i | \(0.435700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2626 | −0.835161 | −0.417581 | − | 0.908640i | \(-0.637122\pi\) | ||||
−0.417581 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(152\) | −0.0651916 | − | 0.0897285i | −0.00528773 | − | 0.00727794i | ||||
\(153\) | 5.55204 | + | 1.80397i | 0.448856 | + | 0.145842i | ||||
\(154\) | 3.02539 | − | 9.31119i | 0.243793 | − | 0.750317i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0666083 | + | 0.204999i | 0.00533293 | + | 0.0164131i | ||||
\(157\) | − | 8.89537i | − | 0.709928i | −0.934880 | − | 0.354964i | \(-0.884493\pi\) | ||
0.934880 | − | 0.354964i | \(-0.115507\pi\) | |||||||
\(158\) | −4.76734 | + | 1.54900i | −0.379269 | + | 0.123232i | ||||
\(159\) | 3.53313 | + | 2.56697i | 0.280196 | + | 0.203574i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.47750 | − | 5.43272i | 0.589310 | − | 0.428159i | ||||
\(162\) | −1.18666 | + | 1.63330i | −0.0932330 | + | 0.128324i | ||||
\(163\) | −6.92356 | + | 9.52946i | −0.542295 | + | 0.746405i | −0.988942 | − | 0.148305i | \(-0.952618\pi\) |
0.446647 | + | 0.894710i | \(0.352618\pi\) | |||||||
\(164\) | 12.1080 | − | 8.79697i | 0.945476 | − | 0.686928i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.93148 | + | 5.03602i | 0.537987 | + | 0.390871i | ||||
\(167\) | −16.5258 | + | 5.36954i | −1.27880 | + | 0.415508i | −0.868158 | − | 0.496288i | \(-0.834696\pi\) |
−0.410644 | + | 0.911796i | \(0.634696\pi\) | |||||||
\(168\) | − | 0.155995i | − | 0.0120353i | ||||||
\(169\) | 4.01389 | + | 12.3535i | 0.308761 | + | 0.950268i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.223853 | + | 0.688949i | −0.0171185 | + | 0.0526853i | ||||
\(172\) | 17.0336 | + | 5.53454i | 1.29880 | + | 0.422004i | ||||
\(173\) | −7.61744 | − | 10.4845i | −0.579144 | − | 0.797123i | 0.414458 | − | 0.910069i | \(-0.363971\pi\) |
−0.993601 | + | 0.112946i | \(0.963971\pi\) | |||||||
\(174\) | 8.05221 | 0.610436 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −18.2892 | −1.37860 | ||||||||
\(177\) | −2.88770 | − | 3.97458i | −0.217053 | − | 0.298748i | ||||
\(178\) | −35.2815 | − | 11.4636i | −2.64446 | − | 0.859237i | ||||
\(179\) | −0.339600 | + | 1.04518i | −0.0253829 | + | 0.0781206i | −0.962946 | − | 0.269696i | \(-0.913077\pi\) |
0.937563 | + | 0.347817i | \(0.113077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.62898 | − | 14.2465i | −0.344069 | − | 1.05894i | −0.962080 | − | 0.272767i | \(-0.912061\pi\) |
0.618011 | − | 0.786170i | \(-0.287939\pi\) | |||||||
\(182\) | 0.213590i | 0.0158323i | ||||||||
\(183\) | −6.62349 | + | 2.15210i | −0.489623 | + | 0.159088i | ||||
\(184\) | 1.12365 | + | 0.816376i | 0.0828363 | + | 0.0601841i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.74212 | + | 1.26572i | −0.127738 | + | 0.0928073i | ||||
\(187\) | −16.3319 | + | 22.4789i | −1.19431 | + | 1.64382i | ||||
\(188\) | 10.0027 | − | 13.7676i | 0.729524 | − | 1.00410i | ||||
\(189\) | −0.824283 | + | 0.598877i | −0.0599578 | + | 0.0435619i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3072 | + | 7.48861i | 0.745802 | + | 0.541857i | 0.894523 | − | 0.447022i | \(-0.147516\pi\) |
−0.148721 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(192\) | −8.17410 | + | 2.65593i | −0.589915 | + | 0.191675i | ||||
\(193\) | 4.38386i | 0.315557i | 0.987475 | + | 0.157779i | \(0.0504332\pi\) | ||||
−0.987475 | + | 0.157779i | \(0.949567\pi\) | |||||||
\(194\) | 4.17913 | + | 12.8620i | 0.300044 | + | 0.923440i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.82438 | + | 11.7702i | −0.273170 | + | 0.840730i | ||||
\(197\) | 3.06397 | + | 0.995545i | 0.218299 | + | 0.0709296i | 0.416125 | − | 0.909308i | \(-0.363388\pi\) |
−0.197826 | + | 0.980237i | \(0.563388\pi\) | |||||||
\(198\) | −5.64805 | − | 7.77388i | −0.401390 | − | 0.552465i | ||||
\(199\) | 2.70518 | 0.191765 | 0.0958825 | − | 0.995393i | \(-0.469433\pi\) | ||||
0.0958825 | + | 0.995393i | \(0.469433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.91998 | 0.699701 | ||||||||
\(202\) | 6.71825 | + | 9.24688i | 0.472694 | + | 0.650608i | ||||
\(203\) | 3.86484 | + | 1.25576i | 0.271259 | + | 0.0881373i | ||||
\(204\) | −3.74475 | + | 11.5251i | −0.262185 | + | 0.806921i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.370881 | − | 1.14145i | −0.0258405 | − | 0.0795289i | ||||
\(207\) | − | 9.07152i | − | 0.630514i | ||||||
\(208\) | 0.379473 | − | 0.123298i | 0.0263117 | − | 0.00854920i | ||||
\(209\) | −2.78940 | − | 2.02661i | −0.192947 | − | 0.140184i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.3932 | + | 15.5431i | −1.47277 | + | 1.07003i | −0.492970 | + | 0.870046i | \(0.664089\pi\) |
−0.979799 | + | 0.199983i | \(0.935911\pi\) | |||||||
\(212\) | −5.32862 | + | 7.33421i | −0.365971 | + | 0.503716i | ||||
\(213\) | −6.34019 | + | 8.72652i | −0.434423 | + | 0.597931i | ||||
\(214\) | −2.26458 | + | 1.64531i | −0.154804 | + | 0.112471i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.123865 | − | 0.0899934i | −0.00842796 | − | 0.00612327i | ||||
\(217\) | −1.03356 | + | 0.335825i | −0.0701628 | + | 0.0227973i | ||||
\(218\) | − | 17.8807i | − | 1.21103i | ||||||
\(219\) | 2.66717 | + | 8.20871i | 0.180231 | + | 0.554694i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.187319 | − | 0.576508i | 0.0126004 | − | 0.0387802i | ||||
\(222\) | 7.73057 | + | 2.51181i | 0.518842 | + | 0.168582i | ||||
\(223\) | −4.72136 | − | 6.49839i | −0.316165 | − | 0.435164i | 0.621126 | − | 0.783711i | \(-0.286675\pi\) |
−0.937292 | + | 0.348546i | \(0.886675\pi\) | |||||||
\(224\) | −8.21604 | −0.548957 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.3051 | −0.885044 | ||||||||
\(227\) | −9.67356 | − | 13.3145i | −0.642056 | − | 0.883715i | 0.356667 | − | 0.934232i | \(-0.383913\pi\) |
−0.998723 | + | 0.0505168i | \(0.983913\pi\) | |||||||
\(228\) | −1.43015 | − | 0.464683i | −0.0947138 | − | 0.0307744i | ||||
\(229\) | −0.126476 | + | 0.389253i | −0.00835776 | + | 0.0257226i | −0.955148 | − | 0.296127i | \(-0.904305\pi\) |
0.946791 | + | 0.321850i | \(0.104305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.49856 | − | 4.61208i | −0.0985977 | − | 0.303453i | ||||
\(232\) | 0.610658i | 0.0400917i | ||||||||
\(233\) | −17.5604 | + | 5.70571i | −1.15042 | + | 0.373794i | −0.821301 | − | 0.570495i | \(-0.806751\pi\) |
−0.329118 | + | 0.944289i | \(0.606751\pi\) | |||||||
\(234\) | 0.169597 | + | 0.123220i | 0.0110869 | + | 0.00805512i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.25058 | − | 5.99440i | 0.537067 | − | 0.390202i | ||||
\(237\) | −1.45942 | + | 2.00872i | −0.0947995 | + | 0.130480i | ||||
\(238\) | −7.05818 | + | 9.71475i | −0.457514 | + | 0.629714i | ||||
\(239\) | −3.73509 | + | 2.71370i | −0.241603 | + | 0.175535i | −0.701997 | − | 0.712180i | \(-0.747708\pi\) |
0.460394 | + | 0.887715i | \(0.347708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.6251 | + | 17.1646i | 1.52183 | + | 1.10567i | 0.960573 | + | 0.278028i | \(0.0896807\pi\) |
0.561253 | + | 0.827644i | \(0.310319\pi\) | |||||||
\(242\) | 22.3762 | − | 7.27047i | 1.43840 | − | 0.467363i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −4.46742 | − | 13.7493i | −0.285997 | − | 0.880208i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.49792 | − | 13.8432i | 0.286777 | − | 0.882609i | ||||
\(247\) | 0.0715385 | + | 0.0232443i | 0.00455189 | + | 0.00147900i | ||||
\(248\) | −0.0959892 | − | 0.132118i | −0.00609532 | − | 0.00838949i | ||||
\(249\) | 4.24385 | 0.268943 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.389664 | 0.0245954 | 0.0122977 | − | 0.999924i | \(-0.496085\pi\) | ||||
0.0122977 | + | 0.999924i | \(0.496085\pi\) | |||||||
\(252\) | −1.24317 | − | 1.71108i | −0.0783124 | − | 0.107788i | ||||
\(253\) | 41.0637 | + | 13.3424i | 2.58165 | + | 0.838829i | ||||
\(254\) | −4.54888 | + | 14.0000i | −0.285422 | + | 0.878438i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.54826 | + | 13.9981i | 0.284266 | + | 0.874882i | ||||
\(257\) | 8.03324i | 0.501100i | 0.968104 | + | 0.250550i | \(0.0806114\pi\) | ||||
−0.968104 | + | 0.250550i | \(0.919389\pi\) | |||||||
\(258\) | 16.5661 | − | 5.38265i | 1.03136 | − | 0.335109i | ||||
\(259\) | 3.31874 | + | 2.41121i | 0.206216 | + | 0.149825i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.22674 | − | 2.34436i | 0.199730 | − | 0.145113i | ||||
\(262\) | 11.3372 | − | 15.6043i | 0.700415 | − | 0.964038i | ||||
\(263\) | 14.2321 | − | 19.5888i | 0.877590 | − | 1.20790i | −0.0994928 | − | 0.995038i | \(-0.531722\pi\) |
0.977083 | − | 0.212860i | \(-0.0682780\pi\) | |||||||
\(264\) | 0.589550 | − | 0.428333i | 0.0362843 | − | 0.0263621i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.20550 | − | 0.875844i | −0.0739137 | − | 0.0537015i | ||||
\(267\) | −17.4759 | + | 5.67825i | −1.06950 | + | 0.347503i | ||||
\(268\) | 20.5923i | 1.25787i | ||||||||
\(269\) | −8.15998 | − | 25.1138i | −0.497523 | − | 1.53122i | −0.812988 | − | 0.582281i | \(-0.802161\pi\) |
0.315465 | − | 0.948937i | \(-0.397839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.21648 | + | 9.89932i | −0.195387 | + | 0.601341i | 0.804584 | + | 0.593838i | \(0.202388\pi\) |
−0.999972 | + | 0.00750242i | \(0.997612\pi\) | |||||||
\(272\) | 21.3341 | + | 6.93188i | 1.29357 | + | 0.420307i | ||||
\(273\) | 0.0621857 | + | 0.0855912i | 0.00376365 | + | 0.00518022i | ||||
\(274\) | −12.5167 | −0.756160 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 18.8310 | 1.13349 | ||||||||
\(277\) | 14.4129 | + | 19.8376i | 0.865987 | + | 1.19193i | 0.980109 | + | 0.198462i | \(0.0635946\pi\) |
−0.114122 | + | 0.993467i | \(0.536405\pi\) | |||||||
\(278\) | −1.74059 | − | 0.565553i | −0.104394 | − | 0.0339196i | ||||
\(279\) | −0.329605 | + | 1.01442i | −0.0197329 | + | 0.0607318i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.45690 | − | 13.7169i | −0.265876 | − | 0.818283i | −0.991490 | − | 0.130181i | \(-0.958444\pi\) |
0.725614 | − | 0.688102i | \(-0.241556\pi\) | |||||||
\(282\) | − | 16.5506i | − | 0.985576i | ||||||
\(283\) | 2.04406 | − | 0.664155i | 0.121507 | − | 0.0394799i | −0.247633 | − | 0.968854i | \(-0.579653\pi\) |
0.369139 | + | 0.929374i | \(0.379653\pi\) | |||||||
\(284\) | −18.1148 | − | 13.1612i | −1.07492 | − | 0.780974i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.807217 | + | 0.586478i | −0.0477317 | + | 0.0346791i | ||||
\(287\) | 4.31776 | − | 5.94289i | 0.254870 | − | 0.350798i | ||||
\(288\) | −4.73982 | + | 6.52381i | −0.279297 | + | 0.384419i | ||||
\(289\) | 13.8176 | − | 10.0391i | 0.812800 | − | 0.590534i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.41941 | + | 3.93743i | 0.317692 | + | 0.230816i | ||||
\(292\) | −17.0400 | + | 5.53662i | −0.997188 | + | 0.324006i | ||||
\(293\) | 9.02970i | 0.527521i | 0.964588 | + | 0.263760i | \(0.0849628\pi\) | ||||
−0.964588 | + | 0.263760i | \(0.915037\pi\) | |||||||
\(294\) | 3.71942 | + | 11.4472i | 0.216921 | + | 0.667615i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.190489 | + | 0.586266i | −0.0110720 | + | 0.0340760i | ||||
\(297\) | −4.52666 | − | 1.47080i | −0.262663 | − | 0.0853445i | ||||
\(298\) | 5.81237 | + | 8.00004i | 0.336702 | + | 0.463430i | ||||
\(299\) | −0.941960 | −0.0544750 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.79072 | 0.506689 | ||||||||
\(302\) | −12.1783 | − | 16.7620i | −0.700781 | − | 0.964543i | ||||
\(303\) | 5.38438 | + | 1.74949i | 0.309324 | + | 0.100506i | ||||
\(304\) | −0.860173 | + | 2.64734i | −0.0493343 | + | 0.151835i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.64198 | + | 11.2089i | 0.208198 | + | 0.640768i | ||||
\(307\) | 5.03454i | 0.287336i | 0.989626 | + | 0.143668i | \(0.0458898\pi\) | ||||
−0.989626 | + | 0.143668i | \(0.954110\pi\) | |||||||
\(308\) | 9.57393 | − | 3.11076i | 0.545525 | − | 0.177252i | ||||
\(309\) | −0.480952 | − | 0.349432i | −0.0273604 | − | 0.0198785i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.95737 | − | 2.87520i | 0.224402 | − | 0.163038i | −0.469904 | − | 0.882718i | \(-0.655711\pi\) |
0.694306 | + | 0.719680i | \(0.255711\pi\) | |||||||
\(312\) | −0.00934465 | + | 0.0128618i | −0.000529037 | + | 0.000728157i | ||||
\(313\) | 1.86494 | − | 2.56686i | 0.105412 | − | 0.145088i | −0.753052 | − | 0.657961i | \(-0.771419\pi\) |
0.858464 | + | 0.512874i | \(0.171419\pi\) | |||||||
\(314\) | 14.5288 | − | 10.5558i | 0.819908 | − | 0.595698i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.16978 | − | 3.02952i | −0.234568 | − | 0.170424i | ||||
\(317\) | 19.0166 | − | 6.17888i | 1.06808 | − | 0.347041i | 0.278341 | − | 0.960482i | \(-0.410215\pi\) |
0.789740 | + | 0.613442i | \(0.210215\pi\) | |||||||
\(318\) | 8.81680i | 0.494422i | ||||||||
\(319\) | 5.86625 | + | 18.0545i | 0.328447 | + | 1.01086i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.428454 | + | 1.31865i | −0.0239140 | + | 0.0735996i | ||||
\(322\) | 17.7465 | + | 5.76620i | 0.988976 | + | 0.321338i | ||||
\(323\) | 2.48569 | + | 3.42125i | 0.138307 | + | 0.190364i | ||||
\(324\) | −2.07584 | −0.115324 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.7804 | −1.31707 | ||||||||
\(327\) | −5.20588 | − | 7.16528i | −0.287886 | − | 0.396241i | ||||
\(328\) | 1.04983 | + | 0.341111i | 0.0579672 | + | 0.0188347i | ||||
\(329\) | 2.58112 | − | 7.94386i | 0.142302 | − | 0.437959i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.85943 | + | 5.72274i | 0.102204 | + | 0.314550i | 0.989064 | − | 0.147487i | \(-0.0471186\pi\) |
−0.886860 | + | 0.462037i | \(0.847119\pi\) | |||||||
\(332\) | 8.80954i | 0.483486i | ||||||||
\(333\) | 3.82916 | − | 1.24417i | 0.209836 | − | 0.0681800i | ||||
\(334\) | −28.3806 | − | 20.6197i | −1.55292 | − | 1.12826i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.16737 | + | 2.30123i | −0.172794 | + | 0.125542i | ||||
\(337\) | 13.4095 | − | 18.4566i | 0.730463 | − | 1.00540i | −0.268648 | − | 0.963238i | \(-0.586577\pi\) |
0.999111 | − | 0.0421575i | \(-0.0134231\pi\) | |||||||
\(338\) | −15.4138 | + | 21.2153i | −0.838401 | + | 1.15396i | ||||
\(339\) | −5.33173 | + | 3.87373i | −0.289580 | + | 0.210392i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.10715 | − | 2.98402i | −0.222415 | − | 0.161594i | ||||
\(342\) | −1.39090 | + | 0.451931i | −0.0752112 | + | 0.0244376i | ||||
\(343\) | 13.2065i | 0.713084i | ||||||||
\(344\) | 0.408206 | + | 1.25633i | 0.0220090 | + | 0.0677368i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.08502 | − | 24.8831i | 0.434654 | − | 1.33773i | ||||
\(347\) | 9.31149 | + | 3.02549i | 0.499867 | + | 0.162417i | 0.548089 | − | 0.836420i | \(-0.315356\pi\) |
−0.0482222 | + | 0.998837i | \(0.515356\pi\) | |||||||
\(348\) | 4.86652 | + | 6.69819i | 0.260873 | + | 0.359061i | ||||
\(349\) | 1.28648 | 0.0688639 | 0.0344320 | − | 0.999407i | \(-0.489038\pi\) | ||||
0.0344320 | + | 0.999407i | \(0.489038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.103837 | 0.00554242 | ||||||||
\(352\) | −22.5597 | − | 31.0508i | −1.20244 | − | 1.65501i | ||||
\(353\) | −1.10724 | − | 0.359765i | −0.0589326 | − | 0.0191484i | 0.279402 | − | 0.960174i | \(-0.409864\pi\) |
−0.338335 | + | 0.941026i | \(0.609864\pi\) | |||||||
\(354\) | 3.06496 | − | 9.43297i | 0.162901 | − | 0.501357i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.7871 | − | 36.2770i | −0.624716 | − | 1.92268i | ||||
\(357\) | 5.94793i | 0.314798i | ||||||||
\(358\) | −2.11009 | + | 0.685609i | −0.111522 | + | 0.0362356i | ||||
\(359\) | 15.4121 | + | 11.1975i | 0.813418 | + | 0.590983i | 0.914820 | − | 0.403863i | \(-0.132333\pi\) |
−0.101402 | + | 0.994846i | \(0.532333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.9468 | − | 10.8595i | 0.786673 | − | 0.571551i | ||||
\(362\) | 17.7758 | − | 24.4663i | 0.934277 | − | 1.28592i | ||||
\(363\) | 6.84999 | − | 9.42821i | 0.359531 | − | 0.494853i | ||||
\(364\) | −0.177673 | + | 0.129087i | −0.00931262 | + | 0.00676602i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11.3749 | − | 8.26433i | −0.594575 | − | 0.431984i | ||||
\(367\) | −15.9487 | + | 5.18204i | −0.832514 | + | 0.270500i | −0.694104 | − | 0.719875i | \(-0.744199\pi\) |
−0.138410 | + | 0.990375i | \(0.544199\pi\) | |||||||
\(368\) | − | 34.8580i | − | 1.81710i | ||||||
\(369\) | −2.22794 | − | 6.85690i | −0.115982 | − | 0.356956i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.37500 | + | 4.23183i | −0.0713866 | + | 0.219705i | ||||
\(372\) | −2.10577 | − | 0.684207i | −0.109179 | − | 0.0354745i | ||||
\(373\) | −10.0229 | − | 13.7954i | −0.518967 | − | 0.714297i | 0.466432 | − | 0.884557i | \(-0.345539\pi\) |
−0.985399 | + | 0.170260i | \(0.945539\pi\) | |||||||
\(374\) | −56.0953 | −2.90062 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.25516 | 0.0647298 | ||||||||
\(377\) | −0.243432 | − | 0.335056i | −0.0125374 | − | 0.0172562i | ||||
\(378\) | −1.95629 | − | 0.635638i | −0.100621 | − | 0.0326937i | ||||
\(379\) | −0.514857 | + | 1.58457i | −0.0264464 | + | 0.0813938i | −0.963409 | − | 0.268037i | \(-0.913625\pi\) |
0.936962 | + | 0.349431i | \(0.113625\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.25318 | + | 6.93457i | 0.115434 | + | 0.355269i | ||||
\(382\) | 25.7212i | 1.31601i | ||||||||
\(383\) | 2.90416 | − | 0.943618i | 0.148396 | − | 0.0482166i | −0.233877 | − | 0.972266i | \(-0.575141\pi\) |
0.382273 | + | 0.924049i | \(0.375141\pi\) | |||||||
\(384\) | −0.990210 | − | 0.719429i | −0.0505314 | − | 0.0367132i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.16016 | + | 5.20216i | −0.364443 | + | 0.264783i | ||||
\(387\) | 5.07136 | − | 6.98013i | 0.257792 | − | 0.354820i | ||||
\(388\) | −8.17347 | + | 11.2498i | −0.414945 | + | 0.571123i | ||||
\(389\) | 22.8730 | − | 16.6182i | 1.15971 | − | 0.842575i | 0.169965 | − | 0.985450i | \(-0.445635\pi\) |
0.989741 | + | 0.142875i | \(0.0456347\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.8434 | − | 31.1276i | −2.16669 | − | 1.57419i | ||||
\(392\) | −0.868127 | + | 0.282071i | −0.0438470 | + | 0.0142468i | ||||
\(393\) | − | 9.55386i | − | 0.481928i | ||||||
\(394\) | 2.00988 | + | 6.18576i | 0.101256 | + | 0.311634i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.05314 | − | 9.39661i | 0.153426 | − | 0.472197i | ||||
\(397\) | −19.4760 | − | 6.32814i | −0.977472 | − | 0.317600i | −0.223644 | − | 0.974671i | \(-0.571795\pi\) |
−0.753829 | + | 0.657071i | \(0.771795\pi\) | |||||||
\(398\) | 3.21013 | + | 4.41837i | 0.160909 | + | 0.221473i | ||||
\(399\) | −0.738074 | −0.0369499 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.5952 | 1.27816 | 0.639081 | − | 0.769139i | \(-0.279315\pi\) | ||||
0.639081 | + | 0.769139i | \(0.279315\pi\) | |||||||
\(402\) | 11.7717 | + | 16.2023i | 0.587117 | + | 0.808097i | ||||
\(403\) | 0.105335 | + | 0.0342253i | 0.00524709 | + | 0.00170488i | ||||
\(404\) | −3.63166 | + | 11.1771i | −0.180682 | + | 0.556081i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.53522 | + | 7.80262i | 0.125821 | + | 0.387237i | ||||
\(407\) | 19.1632i | 0.949885i | ||||||||
\(408\) | −0.850050 | + | 0.276198i | −0.0420838 | + | 0.0136738i | ||||
\(409\) | −9.74072 | − | 7.07705i | −0.481648 | − | 0.349938i | 0.320316 | − | 0.947311i | \(-0.396211\pi\) |
−0.801963 | + | 0.597373i | \(0.796211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.01578 | + | 3.64418i | −0.247410 | + | 0.179754i | ||||
\(412\) | 0.725364 | − | 0.998377i | 0.0357361 | − | 0.0491865i | ||||
\(413\) | 2.94219 | − | 4.04958i | 0.144776 | − | 0.199267i | ||||
\(414\) | 14.8165 | − | 10.7648i | 0.728192 | − | 0.529062i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.677414 | + | 0.492170i | 0.0332129 | + | 0.0241306i | ||||
\(417\) | −0.862162 | + | 0.280134i | −0.0422203 | + | 0.0137182i | ||||
\(418\) | − | 6.96083i | − | 0.340465i | ||||||
\(419\) | 10.6934 | + | 32.9108i | 0.522405 | + | 1.60780i | 0.769390 | + | 0.638779i | \(0.220560\pi\) |
−0.246985 | + | 0.969019i | \(0.579440\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.62056 | + | 14.2206i | −0.225193 | + | 0.693071i | 0.773079 | + | 0.634309i | \(0.218715\pi\) |
−0.998272 | + | 0.0587622i | \(0.981285\pi\) | |||||||
\(422\) | −50.7730 | − | 16.4972i | −2.47159 | − | 0.803069i | ||||
\(423\) | −4.81865 | − | 6.63230i | −0.234291 | − | 0.322473i | ||||
\(424\) | −0.668643 | −0.0324722 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −21.7767 | −1.05508 | ||||||||
\(427\) | −4.17079 | − | 5.74060i | −0.201839 | − | 0.277807i | ||||
\(428\) | −2.73729 | − | 0.889401i | −0.132312 | − | 0.0429908i | ||||
\(429\) | −0.152724 | + | 0.470035i | −0.00737357 | + | 0.0226935i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.48670 | + | 4.57560i | 0.0716119 | + | 0.220399i | 0.980456 | − | 0.196736i | \(-0.0630342\pi\) |
−0.908845 | + | 0.417135i | \(0.863034\pi\) | |||||||
\(432\) | 3.84257i | 0.184876i | ||||||||
\(433\) | 9.83725 | − | 3.19632i | 0.472748 | − | 0.153605i | −0.0629466 | − | 0.998017i | \(-0.520050\pi\) |
0.535695 | + | 0.844412i | \(0.320050\pi\) | |||||||
\(434\) | −1.77499 | − | 1.28961i | −0.0852024 | − | 0.0619032i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.8739 | − | 10.8066i | 0.712333 | − | 0.517540i | ||||
\(437\) | 3.86260 | − | 5.31641i | 0.184773 | − | 0.254318i | ||||
\(438\) | −10.2423 | + | 14.0973i | −0.489394 | + | 0.673593i | ||||
\(439\) | 24.8886 | − | 18.0826i | 1.18787 | − | 0.863037i | 0.194831 | − | 0.980837i | \(-0.437584\pi\) |
0.993037 | + | 0.117800i | \(0.0375840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.82328 | + | 3.50432i | 0.229680 | + | 0.166872i | ||||
\(442\) | 1.16390 | − | 0.378173i | 0.0553609 | − | 0.0179878i | ||||
\(443\) | 17.7545i | 0.843543i | 0.906702 | + | 0.421772i | \(0.138592\pi\) | ||||
−0.906702 | + | 0.421772i | \(0.861408\pi\) | |||||||
\(444\) | 2.58269 | + | 7.94870i | 0.122569 | + | 0.377229i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.01117 | − | 15.4228i | 0.237286 | − | 0.730290i | ||||
\(447\) | 4.65836 | + | 1.51359i | 0.220333 | + | 0.0715904i | ||||
\(448\) | −5.14720 | − | 7.08452i | −0.243183 | − | 0.334712i | ||||
\(449\) | 37.2184 | 1.75645 | 0.878223 | − | 0.478251i | \(-0.158729\pi\) | ||||
0.878223 | + | 0.478251i | \(0.158729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.3157 | 1.61586 | ||||||||
\(452\) | −8.04124 | − | 11.0678i | −0.378228 | − | 0.520586i | ||||
\(453\) | −9.76034 | − | 3.17133i | −0.458581 | − | 0.149002i | ||||
\(454\) | 10.2673 | − | 31.5996i | 0.481870 | − | 1.48304i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.0342732 | − | 0.105482i | −0.00160499 | − | 0.00493966i | ||||
\(457\) | − | 27.6987i | − | 1.29569i | −0.761772 | − | 0.647846i | \(-0.775670\pi\) | ||
0.761772 | − | 0.647846i | \(-0.224330\pi\) | |||||||
\(458\) | −0.785851 | + | 0.255338i | −0.0367204 | + | 0.0119312i | ||||
\(459\) | 4.72285 | + | 3.43135i | 0.220444 | + | 0.160162i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.94246 | + | 5.77053i | −0.369917 | + | 0.268760i | −0.757177 | − | 0.653210i | \(-0.773422\pi\) |
0.387259 | + | 0.921971i | \(0.373422\pi\) | |||||||
\(462\) | 5.75463 | − | 7.92057i | 0.267730 | − | 0.368498i | ||||
\(463\) | 2.19086 | − | 3.01546i | 0.101818 | − | 0.140140i | −0.755068 | − | 0.655647i | \(-0.772396\pi\) |
0.856886 | + | 0.515506i | \(0.172396\pi\) | |||||||
\(464\) | 12.3990 | − | 9.00840i | 0.575609 | − | 0.418204i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.1574 | − | 21.9106i | −1.39701 | − | 1.01499i | ||||
\(467\) | 6.75179 | − | 2.19379i | 0.312436 | − | 0.101516i | −0.148602 | − | 0.988897i | \(-0.547477\pi\) |
0.461038 | + | 0.887381i | \(0.347477\pi\) | |||||||
\(468\) | 0.215549i | 0.00996376i | ||||||||
\(469\) | 3.12329 | + | 9.61249i | 0.144220 | + | 0.443864i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.74882 | − | 8.46000i | 0.126659 | − | 0.389816i | ||||
\(472\) | 0.715372 | + | 0.232438i | 0.0329277 | + | 0.0106988i | ||||
\(473\) | 24.1377 | + | 33.2227i | 1.10985 | + | 1.52758i | ||||
\(474\) | −5.01268 | −0.230240 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.3469 | −0.565920 | ||||||||
\(477\) | 2.56697 | + | 3.53313i | 0.117534 | + | 0.161771i | ||||
\(478\) | −8.86457 | − | 2.88027i | −0.405456 | − | 0.131741i | ||||
\(479\) | 8.79003 | − | 27.0529i | 0.401627 | − | 1.23608i | −0.522053 | − | 0.852913i | \(-0.674834\pi\) |
0.923679 | − | 0.383166i | \(-0.125166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.129191 | − | 0.397609i | −0.00589060 | − | 0.0181294i | ||||
\(482\) | 58.9555i | 2.68535i | ||||||||
\(483\) | 8.79033 | − | 2.85615i | 0.399974 | − | 0.129959i | ||||
\(484\) | 19.5714 | + | 14.2195i | 0.889610 | + | 0.646340i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.63330 | + | 1.18666i | −0.0740880 | + | 0.0538281i | ||||
\(487\) | −8.66301 | + | 11.9236i | −0.392558 | + | 0.540310i | −0.958857 | − | 0.283890i | \(-0.908375\pi\) |
0.566298 | + | 0.824200i | \(0.308375\pi\) | |||||||
\(488\) | 0.626746 | − | 0.862641i | 0.0283714 | − | 0.0390499i | ||||
\(489\) | −9.52946 | + | 6.92356i | −0.430937 | + | 0.313094i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.9772 | + | 16.6939i | 1.03695 | + | 0.753387i | 0.969687 | − | 0.244349i | \(-0.0785742\pi\) |
0.0672603 | + | 0.997735i | \(0.478574\pi\) | |||||||
\(492\) | 14.2338 | − | 4.62484i | 0.641709 | − | 0.208504i | ||||
\(493\) | − | 23.2838i | − | 1.04865i | ||||||
\(494\) | 0.0469272 | + | 0.144427i | 0.00211135 | + | 0.00649808i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.26653 | + | 3.89799i | −0.0568690 | + | 0.175025i | ||||
\(497\) | −10.4522 | − | 3.39613i | −0.468846 | − | 0.152337i | ||||
\(498\) | 5.03602 | + | 6.93148i | 0.225669 | + | 0.310607i | ||||
\(499\) | −26.3842 | −1.18112 | −0.590559 | − | 0.806995i | \(-0.701093\pi\) | ||||
−0.590559 | + | 0.806995i | \(0.701093\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3762 | −0.776312 | ||||||||
\(502\) | 0.462400 | + | 0.636439i | 0.0206379 | + | 0.0284057i | ||||
\(503\) | −15.8438 | − | 5.14796i | −0.706440 | − | 0.229536i | −0.0663060 | − | 0.997799i | \(-0.521121\pi\) |
−0.640134 | + | 0.768263i | \(0.721121\pi\) | |||||||
\(504\) | 0.0482051 | − | 0.148360i | 0.00214723 | − | 0.00660848i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.9366 | + | 82.9022i | 1.19748 | + | 3.68545i | ||||
\(507\) | 12.9892i | 0.576871i | ||||||||
\(508\) | −14.3950 | + | 4.67723i | −0.638677 | + | 0.207519i | ||||
\(509\) | −25.7073 | − | 18.6774i | −1.13946 | − | 0.827863i | −0.152413 | − | 0.988317i | \(-0.548704\pi\) |
−0.987043 | + | 0.160454i | \(0.948704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.11452 | + | 5.16900i | −0.314728 | + | 0.228663i | ||||
\(512\) | −18.9047 | + | 26.0201i | −0.835479 | + | 1.14994i | ||||
\(513\) | −0.425794 | + | 0.586055i | −0.0187993 | + | 0.0258750i | ||||
\(514\) | −13.1207 | + | 9.53274i | −0.578729 | + | 0.420471i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.4896 | + | 10.5273i | 0.637869 | + | 0.463439i | ||||
\(517\) | 37.1094 | − | 12.0576i | 1.63207 | − | 0.530292i | ||||
\(518\) | 8.28179i | 0.363881i | ||||||||
\(519\) | −4.00473 | − | 12.3253i | −0.175788 | − | 0.541020i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.183050 | + | 0.563371i | −0.00801958 | + | 0.0246817i | −0.954986 | − | 0.296650i | \(-0.904130\pi\) |
0.946967 | + | 0.321332i | \(0.104130\pi\) | |||||||
\(522\) | 7.65810 | + | 2.48827i | 0.335186 | + | 0.108909i | ||||
\(523\) | −10.1274 | − | 13.9392i | −0.442840 | − | 0.609518i | 0.528000 | − | 0.849244i | \(-0.322942\pi\) |
−0.970840 | + | 0.239727i | \(0.922942\pi\) | |||||||
\(524\) | 19.8323 | 0.866376 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 48.8832 | 2.13141 | ||||||||
\(527\) | 3.65997 | + | 5.03751i | 0.159431 | + | 0.219437i | ||||
\(528\) | −17.3940 | − | 5.65166i | −0.756978 | − | 0.245957i | ||||
\(529\) | −18.3224 | + | 56.3904i | −0.796625 | + | 2.45176i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.51815 | − | 4.67240i | −0.0658823 | − | 0.202765i | ||||
\(532\) | − | 1.53212i | − | 0.0664259i | ||||||
\(533\) | −0.712001 | + | 0.231343i | −0.0308402 | + | 0.0100206i | ||||
\(534\) | −30.0122 | − | 21.8052i | −1.29876 | − | 0.943601i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.22874 | + | 0.892732i | −0.0530735 | + | 0.0385602i | ||||
\(537\) | −0.645959 | + | 0.889086i | −0.0278752 | + | 0.0383669i | ||||
\(538\) | 31.3353 | − | 43.1293i | 1.35096 | − | 1.85944i | ||||
\(539\) | −22.9569 | + | 16.6792i | −0.988826 | + | 0.718424i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9726 | − | 8.69863i | −0.514744 | − | 0.373983i | 0.299876 | − | 0.953978i | \(-0.403055\pi\) |
−0.814620 | + | 0.579995i | \(0.803055\pi\) | |||||||
\(542\) | −19.9854 | + | 6.49366i | −0.858448 | + | 0.278927i | ||||
\(543\) | − | 14.9797i | − | 0.642840i | ||||||
\(544\) | 14.5470 | + | 44.7710i | 0.623696 | + | 1.91954i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.0660028 | + | 0.203136i | −0.00282466 | + | 0.00869341i | ||||
\(547\) | 6.18953 | + | 2.01110i | 0.264645 | + | 0.0859884i | 0.438334 | − | 0.898812i | \(-0.355569\pi\) |
−0.173689 | + | 0.984801i | \(0.555569\pi\) | |||||||
\(548\) | −7.56472 | − | 10.4119i | −0.323149 | − | 0.444776i | ||||
\(549\) | −6.96435 | −0.297231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.88927 | 0.123087 | ||||||||
\(552\) | 0.816376 | + | 1.12365i | 0.0347473 | + | 0.0478255i | ||||
\(553\) | −2.40595 | − | 0.781741i | −0.102311 | − | 0.0332430i | ||||
\(554\) | −15.2976 | + | 47.0812i | −0.649933 | + | 2.00029i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.581512 | − | 1.78971i | −0.0246616 | − | 0.0759006i | ||||
\(557\) | − | 6.67224i | − | 0.282712i | −0.989959 | − | 0.141356i | \(-0.954854\pi\) | ||
0.989959 | − | 0.141356i | \(-0.0451462\pi\) | |||||||
\(558\) | −2.04798 | + | 0.665430i | −0.0866981 | + | 0.0281699i | ||||
\(559\) | −0.724796 | − | 0.526595i | −0.0306556 | − | 0.0222726i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.4789 | + | 16.3319i | −0.949061 | + | 0.689534i | ||||
\(562\) | 17.1150 | − | 23.5568i | 0.721953 | − | 0.993684i | ||||
\(563\) | −11.7947 | + | 16.2340i | −0.497087 | + | 0.684181i | −0.981675 | − | 0.190561i | \(-0.938969\pi\) |
0.484589 | + | 0.874742i | \(0.338969\pi\) | |||||||
\(564\) | 13.7676 | − | 10.0027i | 0.579719 | − | 0.421191i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.51037 | + | 2.55043i | 0.147552 | + | 0.107203i | ||||
\(567\) | −0.969003 | + | 0.314848i | −0.0406943 | + | 0.0132224i | ||||
\(568\) | − | 1.65149i | − | 0.0692949i | ||||||
\(569\) | 6.67287 | + | 20.5370i | 0.279741 | + | 0.860955i | 0.987926 | + | 0.154927i | \(0.0495144\pi\) |
−0.708185 | + | 0.706027i | \(0.750486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.13758 | + | 25.0449i | −0.340547 | + | 1.04810i | 0.623377 | + | 0.781921i | \(0.285760\pi\) |
−0.963925 | + | 0.266176i | \(0.914240\pi\) | |||||||
\(572\) | −0.975717 | − | 0.317030i | −0.0407968 | − | 0.0132557i | ||||
\(573\) | 7.48861 | + | 10.3072i | 0.312841 | + | 0.430589i | ||||
\(574\) | 14.8303 | 0.619003 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.59476 | −0.358115 | ||||||||
\(577\) | 5.39728 | + | 7.42872i | 0.224692 | + | 0.309262i | 0.906448 | − | 0.422318i | \(-0.138783\pi\) |
−0.681756 | + | 0.731580i | \(0.738783\pi\) | |||||||
\(578\) | 32.7937 | + | 10.6553i | 1.36404 | + | 0.443202i | ||||
\(579\) | −1.35469 | + | 4.16930i | −0.0562989 | + | 0.173270i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.33617 | + | 4.11230i | 0.0554336 | + | 0.170607i | ||||
\(582\) | 13.5239i | 0.560585i | ||||||||
\(583\) | −19.7688 | + | 6.42327i | −0.818740 | + | 0.266025i | ||||
\(584\) | −1.06910 | − | 0.776746i | −0.0442397 | − | 0.0321420i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.7482 | + | 10.7152i | −0.609243 | + | 0.442641i | ||||
\(587\) | 23.4980 | − | 32.3422i | 0.969865 | − | 1.33491i | 0.0277503 | − | 0.999615i | \(-0.491166\pi\) |
0.942115 | − | 0.335290i | \(-0.108834\pi\) | |||||||
\(588\) | −7.27440 | + | 10.0123i | −0.299991 | + | 0.412902i | ||||
\(589\) | −0.625101 | + | 0.454163i | −0.0257568 | + | 0.0187134i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.60637 | + | 1.89364i | 0.107212 | + | 0.0778939i | ||||
\(592\) | 14.7138 | − | 4.78081i | 0.604734 | − | 0.196490i | ||||
\(593\) | 41.6331i | 1.70967i | 0.518902 | + | 0.854834i | \(0.326341\pi\) | ||||
−0.518902 | + | 0.854834i | \(0.673659\pi\) | |||||||
\(594\) | −2.96936 | − | 9.13874i | −0.121834 | − | 0.374967i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.14197 | + | 9.66999i | −0.128700 | + | 0.396098i | ||||
\(597\) | 2.57278 | + | 0.835946i | 0.105297 | + | 0.0342130i | ||||
\(598\) | −1.11779 | − | 1.53850i | −0.0457098 | − | 0.0629141i | ||||
\(599\) | −39.0726 | −1.59646 | −0.798232 | − | 0.602350i | \(-0.794231\pi\) | ||||
−0.798232 | + | 0.602350i | \(0.794231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.46965 | 0.223112 | 0.111556 | − | 0.993758i | \(-0.464417\pi\) | ||||
0.111556 | + | 0.993758i | \(0.464417\pi\) | |||||||
\(602\) | 10.4316 | + | 14.3579i | 0.425161 | + | 0.585184i | ||||
\(603\) | 9.43446 | + | 3.06544i | 0.384201 | + | 0.124834i | ||||
\(604\) | 6.58316 | − | 20.2609i | 0.267865 | − | 0.824404i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.53199 | + | 10.8704i | 0.143477 | + | 0.441578i | ||||
\(607\) | 42.3108i | 1.71734i | 0.512527 | + | 0.858671i | \(0.328709\pi\) | ||||
−0.512527 | + | 0.858671i | \(0.671291\pi\) | |||||||
\(608\) | −5.55560 | + | 1.80512i | −0.225309 | + | 0.0732074i | ||||
\(609\) | 3.28763 | + | 2.38860i | 0.133222 | + | 0.0967911i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.688679 | + | 0.500355i | −0.0278610 | + | 0.0202422i | ||||
\(612\) | −7.12293 | + | 9.80387i | −0.287927 | + | 0.396298i | ||||
\(613\) | 19.9885 | − | 27.5118i | 0.807327 | − | 1.11119i | −0.184403 | − | 0.982851i | \(-0.559035\pi\) |
0.991730 | − | 0.128340i | \(-0.0409647\pi\) | |||||||
\(614\) | −8.22292 | + | 5.97430i | −0.331850 | + | 0.241103i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.600675 | + | 0.436416i | 0.0242019 | + | 0.0175837i | ||||
\(617\) | −22.1760 | + | 7.20543i | −0.892773 | + | 0.290080i | −0.719251 | − | 0.694750i | \(-0.755515\pi\) |
−0.173522 | + | 0.984830i | \(0.555515\pi\) | |||||||
\(618\) | − | 1.20020i | − | 0.0482790i | ||||||
\(619\) | −10.9082 | − | 33.5721i | −0.438439 | − | 1.34938i | −0.889521 | − | 0.456893i | \(-0.848962\pi\) |
0.451083 | − | 0.892482i | \(-0.351038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.80325 | − | 8.62753i | 0.112491 | − | 0.346211i | ||||
\(622\) | 9.39213 | + | 3.05169i | 0.376590 | + | 0.122362i | ||||
\(623\) | −11.0045 | − | 15.1464i | −0.440885 | − | 0.606827i | ||||
\(624\) | 0.399002 | 0.0159729 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.40551 | 0.256016 | ||||||||
\(627\) | −2.02661 | − | 2.78940i | −0.0809352 | − | 0.111398i | ||||
\(628\) | 17.5616 | + | 5.70610i | 0.700783 | + | 0.227698i | ||||
\(629\) | 7.26316 | − | 22.3537i | 0.289601 | − | 0.891301i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.08290 | − | 3.33282i | −0.0431095 | − | 0.132677i | 0.927185 | − | 0.374603i | \(-0.122221\pi\) |
−0.970295 | + | 0.241926i | \(0.922221\pi\) | |||||||
\(632\) | − | 0.380149i | − | 0.0151215i | ||||||
\(633\) | −25.1492 | + | 8.17148i | −0.999592 | + | 0.324787i | ||||
\(634\) | 32.6583 | + | 23.7276i | 1.29703 | + | 0.942345i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.33421 | + | 5.32862i | −0.290820 | + | 0.211293i | ||||
\(637\) | 0.363878 | − | 0.500836i | 0.0144174 | − | 0.0198438i | ||||
\(638\) | −22.5271 | + | 31.0059i | −0.891856 | + | 1.22753i | ||||
\(639\) | −8.72652 | + | 6.34019i | −0.345216 | + | 0.250814i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.51448 | + | 5.45959i | 0.296804 | + | 0.215641i | 0.726214 | − | 0.687469i | \(-0.241278\pi\) |
−0.429409 | + | 0.903110i | \(0.641278\pi\) | |||||||
\(642\) | −2.66218 | + | 0.864993i | −0.105068 | + | 0.0341386i | ||||
\(643\) | 0.0291680i | 0.00115028i | 1.00000 | 0.000575138i | \(0.000183072\pi\) | |||||
−1.00000 | 0.000575138i | \(0.999817\pi\) | ||||||||
\(644\) | 5.92891 | + | 18.2473i | 0.233632 | + | 0.719044i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.63826 | + | 8.11974i | −0.103801 | + | 0.319467i | ||||
\(647\) | −0.802787 | − | 0.260841i | −0.0315608 | − | 0.0102547i | 0.293194 | − | 0.956053i | \(-0.405282\pi\) |
−0.324755 | + | 0.945798i | \(0.605282\pi\) | |||||||
\(648\) | −0.0899934 | − | 0.123865i | −0.00353527 | − | 0.00486589i | ||||
\(649\) | 23.3833 | 0.917874 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.08675 | −0.0425932 | ||||||||
\(652\) | −14.3722 | − | 19.7816i | −0.562858 | − | 0.774708i | ||||
\(653\) | −36.2077 | − | 11.7646i | −1.41692 | − | 0.460385i | −0.502297 | − | 0.864695i | \(-0.667511\pi\) |
−0.914622 | + | 0.404311i | \(0.867511\pi\) | |||||||
\(654\) | 5.52543 | − | 17.0055i | 0.216061 | − | 0.664969i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.56103 | − | 26.3481i | −0.334252 | − | 1.02872i | ||||
\(657\) | 8.63115i | 0.336733i | ||||||||
\(658\) | 16.0376 | − | 5.21094i | 0.625212 | − | 0.203144i | ||||
\(659\) | 30.6086 | + | 22.2385i | 1.19234 | + | 0.866287i | 0.993510 | − | 0.113746i | \(-0.0362851\pi\) |
0.198832 | + | 0.980034i | \(0.436285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.0165 | − | 10.9101i | 0.584074 | − | 0.424355i | −0.256116 | − | 0.966646i | \(-0.582443\pi\) |
0.840191 | + | 0.542291i | \(0.182443\pi\) | |||||||
\(662\) | −7.14044 | + | 9.82797i | −0.277521 | + | 0.381975i | ||||
\(663\) | 0.356302 | − | 0.490407i | 0.0138376 | − | 0.0190458i | ||||
\(664\) | −0.525665 | + | 0.381918i | −0.0203998 | + | 0.0148213i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.57601 | + | 4.77775i | 0.254815 | + | 0.185134i | ||||
\(667\) | −34.4106 | + | 11.1807i | −1.33239 | + | 0.432918i | ||||
\(668\) | − | 36.0702i | − | 1.39560i | ||||||
\(669\) | −2.48216 | − | 7.63932i | −0.0959660 | − | 0.295353i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.2432 | − | 31.5253i | 0.395433 | − | 1.21702i | ||||
\(672\) | −7.81392 | − | 2.53890i | −0.301428 | − | 0.0979400i | ||||
\(673\) | 10.6746 | + | 14.6923i | 0.411475 | + | 0.566347i | 0.963578 | − | 0.267429i | \(-0.0861742\pi\) |
−0.552102 | + | 0.833776i | \(0.686174\pi\) | |||||||
\(674\) | 46.0578 | 1.77408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.9635 | −1.03706 | ||||||||
\(677\) | 3.31695 | + | 4.56538i | 0.127481 | + | 0.175462i | 0.867986 | − | 0.496588i | \(-0.165414\pi\) |
−0.740506 | + | 0.672050i | \(0.765414\pi\) | |||||||
\(678\) | −12.6539 | − | 4.11151i | −0.485971 | − | 0.157902i | ||||
\(679\) | −2.10909 | + | 6.49112i | −0.0809396 | + | 0.249106i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.08569 | − | 15.6521i | −0.194884 | − | 0.599791i | ||||
\(682\) | − | 10.2492i | − | 0.392464i | ||||||
\(683\) | 28.9567 | − | 9.40859i | 1.10800 | − | 0.360010i | 0.302821 | − | 0.953047i | \(-0.402071\pi\) |
0.805175 | + | 0.593038i | \(0.202071\pi\) | |||||||
\(684\) | −1.21656 | − | 0.883879i | −0.0465162 | − | 0.0337960i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −21.5702 | + | 15.6717i | −0.823553 | + | 0.598346i | ||||
\(687\) | −0.240572 | + | 0.331118i | −0.00917838 | + | 0.0126330i | ||||
\(688\) | 19.4871 | − | 26.8216i | 0.742937 | − | 1.02257i | ||||
\(689\) | 0.366871 | − | 0.266547i | 0.0139767 | − | 0.0101546i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.46294 | + | 5.42214i | 0.283904 | + | 0.206268i | 0.720618 | − | 0.693332i | \(-0.243858\pi\) |
−0.436715 | + | 0.899600i | \(0.643858\pi\) | |||||||
\(692\) | 25.5853 | − | 8.31316i | 0.972607 | − | 0.316019i | ||||
\(693\) | − | 4.84943i | − | 0.184215i | ||||||
\(694\) | 6.10806 | + | 18.7987i | 0.231859 | + | 0.713588i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.188704 | + | 0.580771i | −0.00715280 | + | 0.0220141i | ||||
\(697\) | −40.0290 | − | 13.0062i | −1.51620 | − | 0.492645i | ||||
\(698\) | 1.52662 | + | 2.10121i | 0.0577835 | + | 0.0795322i | ||||
\(699\) | −18.4641 | −0.698375 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9822 | −0.754717 | −0.377358 | − | 0.926067i | \(-0.623168\pi\) | ||||
−0.377358 | + | 0.926067i | \(0.623168\pi\) | |||||||
\(702\) | 0.123220 | + | 0.169597i | 0.00465062 | + | 0.00640104i | ||||
\(703\) | 2.77386 | + | 0.901281i | 0.104618 | + | 0.0339924i | ||||
\(704\) | 12.6412 | − | 38.9056i | 0.476432 | − | 1.46631i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.726319 | − | 2.23538i | −0.0273354 | − | 0.0841296i | ||||
\(707\) | 5.76830i | 0.216939i | ||||||||
\(708\) | 9.69914 | − | 3.15144i | 0.364516 | − | 0.118438i | ||||
\(709\) | −21.7026 | − | 15.7679i | −0.815059 | − | 0.592175i | 0.100234 | − | 0.994964i | \(-0.468041\pi\) |
−0.915293 | + | 0.402789i | \(0.868041\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.00872 | + | 1.45942i | −0.0753329 | + | 0.0547325i | ||||
\(712\) | 1.65365 | − | 2.27605i | 0.0619730 | − | 0.0852985i | ||||
\(713\) | 5.68735 | − | 7.82797i | 0.212993 | − | 0.293160i | ||||
\(714\) | −9.71475 | + | 7.05818i | −0.363565 | + | 0.264146i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.84560 | − | 1.34090i | −0.0689732 | − | 0.0501120i | ||||
\(717\) | −4.39086 | + | 1.42668i | −0.163980 | + | 0.0532802i | ||||
\(718\) | 38.4602i | 1.43532i | ||||||||
\(719\) | −11.9968 | − | 36.9223i | −0.447404 | − | 1.37697i | −0.879825 | − | 0.475297i | \(-0.842341\pi\) |
0.432421 | − | 0.901672i | \(-0.357659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.187174 | − | 0.576062i | 0.00697072 | − | 0.0214537i | ||||
\(722\) | 35.4736 | + | 11.5261i | 1.32019 | + | 0.428956i | ||||
\(723\) | 17.1646 | + | 23.6251i | 0.638360 | + | 0.878627i | ||||
\(724\) | 31.0954 | 1.15565 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23.5277 | 0.873196 | ||||||||
\(727\) | −17.3846 | − | 23.9278i | −0.644759 | − | 0.887434i | 0.354099 | − | 0.935208i | \(-0.384787\pi\) |
−0.998858 | + | 0.0477734i | \(0.984787\pi\) | |||||||
\(728\) | −0.0154053 | − | 0.00500548i | −0.000570958 | − | 0.000185515i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.5645 | − | 47.9025i | −0.575673 | − | 1.77174i | ||||
\(732\) | − | 14.4569i | − | 0.534341i | ||||||
\(733\) | −46.4859 | + | 15.1042i | −1.71700 | + | 0.557886i | −0.991473 | − | 0.130311i | \(-0.958402\pi\) |
−0.725524 | + | 0.688197i | \(0.758402\pi\) | |||||||
\(734\) | −27.3895 | − | 19.8997i | −1.01097 | − | 0.734510i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 59.1808 | − | 42.9974i | 2.18143 | − | 1.58490i | ||||
\(737\) | −27.7524 | + | 38.1979i | −1.02227 | + | 1.40704i | ||||
\(738\) | 8.55556 | − | 11.7757i | 0.314934 | − | 0.433470i | ||||
\(739\) | 17.6045 | − | 12.7904i | 0.647590 | − | 0.470502i | −0.214859 | − | 0.976645i | \(-0.568929\pi\) |
0.862450 | + | 0.506143i | \(0.168929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0608543 | + | 0.0442132i | 0.00223554 | + | 0.00162421i | ||||
\(742\) | −8.54351 | + | 2.77595i | −0.313642 | + | 0.101908i | ||||
\(743\) | 9.75724i | 0.357959i | 0.983853 | + | 0.178979i | \(0.0572795\pi\) | ||||
−0.983853 | + | 0.178979i | \(0.942720\pi\) | |||||||
\(744\) | −0.0504645 | − | 0.155314i | −0.00185012 | − | 0.00569408i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.6382 | − | 32.7409i | 0.389491 | − | 1.19873i | ||||
\(747\) | 4.03614 | + | 1.31142i | 0.147675 | + | 0.0479824i | ||||
\(748\) | −33.9024 | − | 46.6626i | −1.23959 | − | 1.70615i | ||||
\(749\) | −1.41267 | −0.0516178 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6413 | −0.643741 | −0.321871 | − | 0.946784i | \(-0.604312\pi\) | ||||
−0.321871 | + | 0.946784i | \(0.604312\pi\) | |||||||
\(752\) | −18.5160 | − | 25.4851i | −0.675209 | − | 0.929346i | ||||
\(753\) | 0.370593 | + | 0.120413i | 0.0135052 | + | 0.00438809i | ||||
\(754\) | 0.258375 | − | 0.795196i | 0.00940945 | − | 0.0289593i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.653574 | − | 2.01149i | −0.0237702 | − | 0.0731573i | ||||
\(757\) | − | 44.2551i | − | 1.60848i | −0.594305 | − | 0.804240i | \(-0.702573\pi\) | ||
0.594305 | − | 0.804240i | \(-0.297427\pi\) | |||||||
\(758\) | −3.19904 | + | 1.03943i | −0.116194 | + | 0.0377538i | ||||
\(759\) | 34.9308 | + | 25.3787i | 1.26791 | + | 0.921190i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.2600 | + | 23.4382i | −1.16942 | + | 0.849636i | −0.990940 | − | 0.134307i | \(-0.957119\pi\) |
−0.178483 | + | 0.983943i | \(0.557119\pi\) | |||||||
\(762\) | −8.65248 | + | 11.9091i | −0.313446 | + | 0.431422i | ||||
\(763\) | 5.30412 | − | 7.30049i | 0.192022 | − | 0.264295i | ||||
\(764\) | −21.3960 | + | 15.5451i | −0.774082 | + | 0.562403i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.98747 | + | 3.62361i | 0.180205 | + | 0.130926i | ||||
\(767\) | −0.485169 | + | 0.157641i | −0.0175184 | + | 0.00569208i | ||||
\(768\) | 14.7185i | 0.531108i | ||||||||
\(769\) | −10.8980 | − | 33.5407i | −0.392993 | − | 1.20951i | −0.930514 | − | 0.366257i | \(-0.880639\pi\) |
0.537521 | − | 0.843250i | \(-0.319361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.48241 | + | 7.64007i | −0.0894018 | + | 0.275150i | ||||
\(772\) | −8.65479 | − | 2.81211i | −0.311493 | − | 0.101210i | ||||
\(773\) | −13.6611 | − | 18.8029i | −0.491357 | − | 0.676295i | 0.489281 | − | 0.872126i | \(-0.337259\pi\) |
−0.980638 | + | 0.195832i | \(0.937259\pi\) | |||||||
\(774\) | 17.4186 | 0.626100 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.02562 | −0.0368176 | ||||||||
\(777\) | 2.41121 | + | 3.31874i | 0.0865015 | + | 0.119059i | ||||
\(778\) | 54.2850 | + | 17.6383i | 1.94621 | + | 0.632362i | ||||
\(779\) | 1.61393 | − | 4.96717i | 0.0578250 | − | 0.177967i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8649 | − | 48.8272i | −0.567691 | − | 1.74717i | ||||
\(782\) | − | 106.914i | − | 3.82324i | ||||||
\(783\) | 3.79326 | − | 1.23251i | 0.135560 | − | 0.0440462i | ||||
\(784\) | 18.5338 | + | 13.4656i | 0.661922 | + | 0.480914i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.6043 | − | 11.3372i | 0.556588 | − | 0.404385i | ||||
\(787\) | 4.01513 | − | 5.52636i | 0.143124 | − | 0.196993i | −0.731437 | − | 0.681909i | \(-0.761150\pi\) |
0.874561 | + | 0.484916i | \(0.161150\pi\) | |||||||
\(788\) | −3.93089 | + | 5.41040i | −0.140032 | + | 0.192738i | ||||
\(789\) | 19.5888 | − | 14.2321i | 0.697381 | − | 0.506677i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.43235 | − | 3.94683i | −0.193152 | − | 0.140333i | ||||
\(792\) | 0.693058 | − | 0.225188i | 0.0246267 | − | 0.00800172i | ||||
\(793\) | 0.723159i | 0.0256801i | ||||||||
\(794\) | −12.7757 | − | 39.3195i | −0.453392 | − | 1.39540i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.73529 | + | 5.34067i | −0.0615056 | + | 0.189295i | ||||
\(797\) | 51.2892 | + | 16.6649i | 1.81676 | + | 0.590301i | 0.999910 | + | 0.0134488i | \(0.00428103\pi\) |
0.816849 | + | 0.576852i | \(0.195719\pi\) | |||||||
\(798\) | −0.875844 | − | 1.20550i | −0.0310046 | − | 0.0426741i | ||||
\(799\) | −47.8578 | −1.69309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.3752 | −0.649256 | ||||||||
\(802\) | 30.3728 | + | 41.8046i | 1.07250 | + | 1.47617i | ||||
\(803\) | −39.0703 | − | 12.6947i | −1.37876 | − | 0.447987i | ||||
\(804\) | −6.36336 | + | 19.5844i | −0.224418 | + | 0.690689i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.0690964 | + | 0.212657i | 0.00243382 | + | 0.00749052i | ||||
\(807\) | − | 26.4063i | − | 0.929544i | ||||||
\(808\) | −0.824380 | + | 0.267857i | −0.0290016 | + | 0.00942318i | ||||
\(809\) | −14.8943 | − | 10.8214i | −0.523656 | − | 0.380459i | 0.294323 | − | 0.955706i | \(-0.404906\pi\) |
−0.817980 | + | 0.575247i | \(0.804906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.53916 | − | 6.93060i | 0.334965 | − | 0.243366i | −0.407569 | − | 0.913174i | \(-0.633624\pi\) |
0.742534 | + | 0.669808i | \(0.233624\pi\) | |||||||
\(812\) | −4.95835 | + | 6.82459i | −0.174004 | + | 0.239496i | ||||
\(813\) | −6.11811 | + | 8.42086i | −0.214572 | + | 0.295333i | ||||
\(814\) | −31.2993 | + | 22.7403i | −1.09704 | + | 0.797046i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 18.1479 | + | 13.1852i | 0.635304 | + | 0.461575i | ||||
\(817\) | 5.94419 | − | 1.93139i | 0.207961 | − | 0.0675706i | ||||
\(818\) | − | 24.3076i | − | 0.849895i | ||||||
\(819\) | 0.0326929 | + | 0.100619i | 0.00114238 | + | 0.00351590i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.80899 | + | 11.7229i | −0.132935 | + | 0.409130i | −0.995263 | − | 0.0972189i | \(-0.969005\pi\) |
0.862329 | + | 0.506349i | \(0.169005\pi\) | |||||||
\(822\) | −11.9041 | − | 3.86787i | −0.415202 | − | 0.134907i | ||||
\(823\) | 1.65668 | + | 2.28023i | 0.0577484 | + | 0.0794839i | 0.836914 | − | 0.547334i | \(-0.184357\pi\) |
−0.779166 | + | 0.626818i | \(0.784357\pi\) | |||||||
\(824\) | 0.0910197 | 0.00317082 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.1056 | 0.351618 | ||||||||
\(827\) | 21.9979 | + | 30.2776i | 0.764943 | + | 1.05285i | 0.996787 | + | 0.0801008i | \(0.0255242\pi\) |
−0.231844 | + | 0.972753i | \(0.574476\pi\) | |||||||
\(828\) | 17.9093 | + | 5.81910i | 0.622393 | + | 0.202228i | ||||
\(829\) | −9.56205 | + | 29.4289i | −0.332104 | + | 1.02211i | 0.636028 | + | 0.771666i | \(0.280576\pi\) |
−0.968131 | + | 0.250443i | \(0.919424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.57731 | + | 23.3206i | 0.262854 | + | 0.808981i | ||||
\(832\) | 0.892455i | 0.0309403i | ||||||||
\(833\) | 33.1008 | − | 10.7551i | 1.14687 | − | 0.372642i | ||||
\(834\) | −1.48064 | − | 1.07575i | −0.0512703 | − | 0.0372501i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.79033 | − | 4.20692i | 0.200263 | − | 0.145499i | ||||
\(837\) | −0.626946 | + | 0.862918i | −0.0216704 | + | 0.0298268i | ||||
\(838\) | −41.0638 | + | 56.5195i | −1.41853 | + | 1.95243i | ||||
\(839\) | −21.5988 | + | 15.6924i | −0.745672 | + | 0.541762i | −0.894482 | − | 0.447103i | \(-0.852456\pi\) |
0.148810 | + | 0.988866i | \(0.452456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5917 | + | 7.69534i | 0.365232 | + | 0.265356i | ||||
\(842\) | −28.7096 | + | 9.32832i | −0.989399 | + | 0.321475i | ||||
\(843\) | − | 14.4228i | − | 0.496748i | ||||||
\(844\) | −16.9627 | − | 52.2057i | −0.583879 | − | 1.79699i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.11443 | − | 15.7406i | 0.175838 | − | 0.541173i | ||||
\(847\) | 11.2927 | + | 3.66921i | 0.388021 | + | 0.126076i | ||||
\(848\) | 9.86378 | + | 13.5763i | 0.338724 | + | 0.466213i | ||||
\(849\) | 2.14925 | 0.0737620 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.5239 | −1.25202 | ||||||||
\(852\) | −13.1612 | − | 18.1148i | −0.450895 | − | 0.620604i | ||||
\(853\) | −27.8279 | − | 9.04183i | −0.952808 | − | 0.309586i | −0.208952 | − | 0.977926i | \(-0.567005\pi\) |
−0.743856 | + | 0.668340i | \(0.767005\pi\) | |||||||
\(854\) | 4.42681 | − | 13.6243i | 0.151482 | − | 0.466214i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.0655988 | − | 0.201892i | −0.00224212 | − | 0.00690054i | ||||
\(857\) | − | 33.5284i | − | 1.14531i | −0.819797 | − | 0.572654i | \(-0.805914\pi\) | ||
0.819797 | − | 0.572654i | \(-0.194086\pi\) | |||||||
\(858\) | −0.948941 | + | 0.308329i | −0.0323963 | + | 0.0105262i | ||||
\(859\) | −20.8923 | − | 15.1792i | −0.712837 | − | 0.517906i | 0.171251 | − | 0.985227i | \(-0.445219\pi\) |
−0.884088 | + | 0.467321i | \(0.845219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.94289 | − | 4.31776i | 0.202533 | − | 0.147149i | ||||
\(862\) | −5.70911 | + | 7.85792i | −0.194453 | + | 0.267642i | ||||
\(863\) | 16.9803 | − | 23.3713i | 0.578015 | − | 0.795569i | −0.415461 | − | 0.909611i | \(-0.636380\pi\) |
0.993476 | + | 0.114042i | \(0.0363797\pi\) | |||||||
\(864\) | −6.52381 | + | 4.73982i | −0.221944 | + | 0.161252i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.8940 | + | 12.2742i | 0.574083 | + | 0.417096i | ||||
\(867\) | 16.2436 | − | 5.27785i | 0.551660 | − | 0.179245i | ||||
\(868\) | − | 2.25592i | − | 0.0765710i | ||||||
\(869\) | −3.65187 | − | 11.2393i | −0.123881 | − | 0.381267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.318307 | − | 0.979647i | 0.0107854 | − | 0.0331941i | ||||
\(872\) | 1.28965 | + | 0.419034i | 0.0436732 | + | 0.0141903i | ||||
\(873\) | 3.93743 | + | 5.41941i | 0.133262 | + | 0.183419i | ||||
\(874\) | 13.2669 | 0.448759 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.9169 | −0.605355 | ||||||||
\(877\) | 8.87581 | + | 12.2165i | 0.299715 | + | 0.412522i | 0.932139 | − | 0.362100i | \(-0.117940\pi\) |
−0.632425 | + | 0.774622i | \(0.717940\pi\) | |||||||
\(878\) | 59.0688 | + | 19.1926i | 1.99347 | + | 0.647719i | ||||
\(879\) | −2.79033 | + | 8.58775i | −0.0941155 | + | 0.289658i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.3167 | + | 34.8292i | 0.381269 | + | 1.17342i | 0.939151 | + | 0.343505i | \(0.111614\pi\) |
−0.557882 | + | 0.829920i | \(0.688386\pi\) | |||||||
\(882\) | 12.0363i | 0.405284i | ||||||||
\(883\) | −32.8551 | + | 10.6753i | −1.10566 | + | 0.359251i | −0.804279 | − | 0.594252i | \(-0.797448\pi\) |
−0.301383 | + | 0.953503i | \(0.597448\pi\) | |||||||
\(884\) | 1.01801 | + | 0.739625i | 0.0342392 | + | 0.0248763i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.9985 | + | 21.0686i | −0.974223 | + | 0.707814i | ||||
\(887\) | 19.4181 | − | 26.7267i | 0.651995 | − | 0.897394i | −0.347189 | − | 0.937795i | \(-0.612864\pi\) |
0.999184 | + | 0.0404016i | \(0.0128637\pi\) | |||||||
\(888\) | −0.362332 | + | 0.498708i | −0.0121591 | + | 0.0167355i | ||||
\(889\) | −6.01021 | + | 4.36668i | −0.201576 | + | 0.146454i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.85061 | − | 2.79763i | −0.129000 | − | 0.0937241i | ||||
\(892\) | 15.8580 | − | 5.15257i | 0.530964 | − | 0.172521i | ||||
\(893\) | − | 5.93864i | − | 0.198729i | ||||||
\(894\) | 3.05574 | + | 9.40461i | 0.102199 | + | 0.314537i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.385364 | − | 1.18603i | 0.0128741 | − | 0.0396224i | ||||
\(897\) | −0.895858 | − | 0.291082i | −0.0299118 | − | 0.00971894i | ||||
\(898\) | 44.1657 | + | 60.7889i | 1.47383 | + | 2.02855i | ||||
\(899\) | 4.25420 | 0.141886 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.4947 | 0.849350 | ||||||||
\(902\) | 40.7211 | + | 56.0478i | 1.35587 | + | 1.86619i | ||||
\(903\) | 8.36047 | + | 2.71648i | 0.278219 | + | 0.0903989i | ||||
\(904\) | 0.311806 | − | 0.959641i | 0.0103705 | − | 0.0319172i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.40250 | − | 19.7049i | −0.212709 | − | 0.654650i | ||||
\(907\) | − | 44.2708i | − | 1.46999i | −0.678074 | − | 0.734994i | \(-0.737185\pi\) | ||
0.678074 | − | 0.734994i | \(-0.262815\pi\) | |||||||
\(908\) | 32.4913 | − | 10.5571i | 1.07826 | − | 0.350348i | ||||
\(909\) | 4.58022 | + | 3.32773i | 0.151916 | + | 0.110374i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.4581 | − | 22.8556i | 1.04225 | − | 0.757241i | 0.0715293 | − | 0.997439i | \(-0.477212\pi\) |
0.970724 | + | 0.240197i | \(0.0772121\pi\) | |||||||
\(912\) | −1.63615 | + | 2.25196i | −0.0541782 | + | 0.0745699i | ||||
\(913\) | −11.8727 | + | 16.3414i | −0.392930 | + | 0.540821i | ||||
\(914\) | 45.2403 | − | 32.8690i | 1.49642 | − | 1.08721i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.687348 | − | 0.499387i | −0.0227106 | − | 0.0165002i | ||||
\(917\) | 9.25772 | − | 3.00802i | 0.305717 | − | 0.0993334i | ||||
\(918\) | 11.7857i | 0.388986i | ||||||||
\(919\) | 8.81634 | + | 27.1339i | 0.290824 | + | 0.895065i | 0.984592 | + | 0.174866i | \(0.0559493\pi\) |
−0.693768 | + | 0.720198i | \(0.744051\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.55576 | + | 4.78813i | −0.0512640 | + | 0.157774i | ||||
\(922\) | −18.8500 | − | 6.12474i | −0.620793 | − | 0.201708i | ||||
\(923\) | 0.658347 | + | 0.906137i | 0.0216698 | + | 0.0298259i | ||||
\(924\) | 10.0666 | 0.331168 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.52497 | 0.247286 | ||||||||
\(927\) | −0.349432 | − | 0.480952i | −0.0114768 | − | 0.0157965i | ||||
\(928\) | 30.5884 | + | 9.93877i | 1.00411 | + | 0.326256i | ||||
\(929\) | −11.2447 | + | 34.6076i | −0.368926 | + | 1.13544i | 0.578559 | + | 0.815640i | \(0.303615\pi\) |
−0.947486 | + | 0.319798i | \(0.896385\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.33459 | + | 4.10745i | 0.0437395 | + | 0.134616i | ||||
\(932\) | − | 38.3284i | − | 1.25549i | ||||||
\(933\) | 4.65217 | − | 1.51158i | 0.152305 | − | 0.0494870i | ||||
\(934\) | 11.5952 | + | 8.42441i | 0.379407 | + | 0.275655i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.0128618 | + | 0.00934465i | −0.000420402 | + | 0.000305440i | ||||
\(937\) | −27.8230 | + | 38.2951i | −0.908939 | + | 1.25105i | 0.0585890 | + | 0.998282i | \(0.481340\pi\) |
−0.967528 | + | 0.252765i | \(0.918660\pi\) | |||||||
\(938\) | −11.9938 | + | 16.5080i | −0.391611 | + | 0.539007i | ||||
\(939\) | 2.56686 | − | 1.86494i | 0.0837664 | − | 0.0608599i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.8175 | − | 31.1087i | −1.39581 | − | 1.01412i | −0.995199 | − | 0.0978679i | \(-0.968798\pi\) |
−0.400611 | − | 0.916248i | \(-0.631202\pi\) | |||||||
\(942\) | 17.0796 | − | 5.54951i | 0.556485 | − | 0.180813i | ||||
\(943\) | 65.4035i | 2.12983i | ||||||||
\(944\) | −5.83362 | − | 17.9540i | −0.189868 | − | 0.584354i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.6193 | + | 78.8482i | −0.832957 | + | 2.56358i | ||||
\(947\) | 18.0063 | + | 5.85061i | 0.585127 | + | 0.190119i | 0.586596 | − | 0.809880i | \(-0.300468\pi\) |
−0.00146915 | + | 0.999999i | \(0.500468\pi\) | |||||||
\(948\) | −3.02952 | − | 4.16978i | −0.0983942 | − | 0.135428i | ||||
\(949\) | 0.896234 | 0.0290930 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9953 | 0.648392 | ||||||||
\(952\) | −0.535274 | − | 0.736741i | −0.0173483 | − | 0.0238779i | ||||
\(953\) | 10.8895 | + | 3.53822i | 0.352746 | + | 0.114614i | 0.480030 | − | 0.877252i | \(-0.340626\pi\) |
−0.127284 | + | 0.991866i | \(0.540626\pi\) | |||||||
\(954\) | −2.72454 | + | 8.38527i | −0.0882103 | + | 0.271483i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.96155 | − | 9.11471i | −0.0957833 | − | 0.294791i | ||||
\(957\) | 18.9836i | 0.613652i | ||||||||
\(958\) | 54.6163 | − | 17.7459i | 1.76457 | − | 0.573345i | ||||
\(959\) | −5.11043 | − | 3.71294i | −0.165024 | − | 0.119897i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.1591 | − | 17.5526i | 0.779326 | − | 0.566214i | ||||
\(962\) | 0.496108 | − | 0.682835i | 0.0159952 | − | 0.0220155i | ||||
\(963\) | −0.814968 | + | 1.12171i | −0.0262620 | + | 0.0361465i | ||||
\(964\) | −49.0419 | + | 35.6310i | −1.57953 | + | 1.14760i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.0961 | + | 10.9680i | 0.485709 | + | 0.352888i | ||||
\(967\) | 35.1821 | − | 11.4313i | 1.13138 | − | 0.367607i | 0.317279 | − | 0.948332i | \(-0.397231\pi\) |
0.814100 | + | 0.580725i | \(0.197231\pi\) | |||||||
\(968\) | 1.78428i | 0.0573490i | ||||||||
\(969\) | 1.30680 | + | 4.02192i | 0.0419805 | + | 0.129203i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.36004 | + | 28.8072i | −0.300378 | + | 0.924468i | 0.680984 | + | 0.732298i | \(0.261552\pi\) |
−0.981362 | + | 0.192170i | \(0.938448\pi\) | |||||||
\(972\) | −1.97424 | − | 0.641469i | −0.0633237 | − | 0.0205751i | ||||
\(973\) | −0.542901 | − | 0.747239i | −0.0174046 | − | 0.0239554i | ||||
\(974\) | −29.7549 | −0.953408 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.7610 | −0.856600 | ||||||||
\(977\) | −9.78136 | − | 13.4629i | −0.312934 | − | 0.430716i | 0.623360 | − | 0.781935i | \(-0.285767\pi\) |
−0.936293 | + | 0.351219i | \(0.885767\pi\) | |||||||
\(978\) | −22.6165 | − | 7.34855i | −0.723196 | − | 0.234981i | ||||
\(979\) | 27.0263 | − | 83.1783i | 0.863763 | − | 2.65839i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.73689 | − | 8.42329i | −0.0873822 | − | 0.268935i | ||||
\(982\) | 57.3388i | 1.82975i | ||||||||
\(983\) | 24.9078 | − | 8.09305i | 0.794437 | − | 0.258128i | 0.116445 | − | 0.993197i | \(-0.462850\pi\) |
0.677992 | + | 0.735069i | \(0.262850\pi\) | |||||||
\(984\) | 0.893040 | + | 0.648831i | 0.0284691 | + | 0.0206840i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 38.0294 | − | 27.6300i | 1.21110 | − | 0.879917i | ||||
\(987\) | 4.90958 | − | 6.75745i | 0.156274 | − | 0.215092i | ||||
\(988\) | −0.0917795 | + | 0.126324i | −0.00291990 | + | 0.00401889i | ||||
\(989\) | −63.3203 | + | 46.0049i | −2.01347 | + | 1.46287i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0938 | + | 14.5990i | 0.638300 | + | 0.463752i | 0.859266 | − | 0.511530i | \(-0.170921\pi\) |
−0.220966 | + | 0.975282i | \(0.570921\pi\) | |||||||
\(992\) | −8.18016 | + | 2.65789i | −0.259720 | + | 0.0843882i | ||||
\(993\) | 6.01724i | 0.190951i | ||||||||
\(994\) | −6.85635 | − | 21.1017i | −0.217470 | − | 0.669305i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.72230 | + | 8.37837i | −0.0862593 | + | 0.265479i | ||||
\(997\) | 23.8585 | + | 7.75208i | 0.755605 | + | 0.245511i | 0.661391 | − | 0.750041i | \(-0.269966\pi\) |
0.0942136 | + | 0.995552i | \(0.469966\pi\) | |||||||
\(998\) | −31.3091 | − | 43.0933i | −0.991072 | − | 1.36409i | ||||
\(999\) | 4.02621 | 0.127384 |
(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 | 375.2.i.d.199.5 | 24 | ||
5.2 | odd | 4 | 375.2.g.c.301.1 | 12 | |||
5.3 | odd | 4 | 75.2.g.c.61.3 | yes | 12 | ||
5.4 | even | 2 | inner | 375.2.i.d.199.2 | 24 | ||
15.8 | even | 4 | 225.2.h.d.136.1 | 12 | |||
25.3 | odd | 20 | 1875.2.a.j.1.2 | 6 | |||
25.4 | even | 10 | 1875.2.b.f.1249.9 | 12 | |||
25.9 | even | 10 | inner | 375.2.i.d.49.5 | 24 | ||
25.12 | odd | 20 | 375.2.g.c.76.1 | 12 | |||
25.13 | odd | 20 | 75.2.g.c.16.3 | ✓ | 12 | ||
25.16 | even | 5 | inner | 375.2.i.d.49.2 | 24 | ||
25.21 | even | 5 | 1875.2.b.f.1249.4 | 12 | |||
25.22 | odd | 20 | 1875.2.a.k.1.5 | 6 | |||
75.38 | even | 20 | 225.2.h.d.91.1 | 12 | |||
75.47 | even | 20 | 5625.2.a.q.1.2 | 6 | |||
75.53 | even | 20 | 5625.2.a.p.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.3 | ✓ | 12 | 25.13 | odd | 20 | ||
75.2.g.c.61.3 | yes | 12 | 5.3 | odd | 4 | ||
225.2.h.d.91.1 | 12 | 75.38 | even | 20 | |||
225.2.h.d.136.1 | 12 | 15.8 | even | 4 | |||
375.2.g.c.76.1 | 12 | 25.12 | odd | 20 | |||
375.2.g.c.301.1 | 12 | 5.2 | odd | 4 | |||
375.2.i.d.49.2 | 24 | 25.16 | even | 5 | inner | ||
375.2.i.d.49.5 | 24 | 25.9 | even | 10 | inner | ||
375.2.i.d.199.2 | 24 | 5.4 | even | 2 | inner | ||
375.2.i.d.199.5 | 24 | 1.1 | even | 1 | trivial | ||
1875.2.a.j.1.2 | 6 | 25.3 | odd | 20 | |||
1875.2.a.k.1.5 | 6 | 25.22 | odd | 20 | |||
1875.2.b.f.1249.4 | 12 | 25.21 | even | 5 | |||
1875.2.b.f.1249.9 | 12 | 25.4 | even | 10 | |||
5625.2.a.p.1.5 | 6 | 75.53 | even | 20 | |||
5625.2.a.q.1.2 | 6 | 75.47 | even | 20 |