Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,3,Mod(5,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.d (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: | \(0.354224343668\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(1.58114 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.8 |
Dual form | 13.3.d.a.5.2 |
$q$-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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.581139 | + | 0.581139i | 0.290569 | + | 0.290569i | 0.837305 | − | 0.546736i | \(-0.184130\pi\) |
−0.546736 | + | 0.837305i | \(0.684130\pi\) | |||||||
\(3\) | −4.16228 | −1.38743 | −0.693713 | − | 0.720252i | \(-0.744026\pi\) | ||||
−0.693713 | + | 0.720252i | \(0.744026\pi\) | |||||||
\(4\) | − | 3.32456i | − | 0.831139i | ||||||
\(5\) | 3.58114 | + | 3.58114i | 0.716228 | + | 0.716228i | 0.967831 | − | 0.251603i | \(-0.0809577\pi\) |
−0.251603 | + | 0.967831i | \(0.580958\pi\) | |||||||
\(6\) | −2.41886 | − | 2.41886i | −0.403144 | − | 0.403144i | ||||
\(7\) | −4.58114 | + | 4.58114i | −0.654448 | + | 0.654448i | −0.954061 | − | 0.299613i | \(-0.903143\pi\) |
0.299613 | + | 0.954061i | \(0.403143\pi\) | |||||||
\(8\) | 4.25658 | − | 4.25658i | 0.532073 | − | 0.532073i | ||||
\(9\) | 8.32456 | 0.924951 | ||||||||
\(10\) | 4.16228i | 0.416228i | ||||||||
\(11\) | 5.32456 | − | 5.32456i | 0.484050 | − | 0.484050i | −0.422372 | − | 0.906423i | \(-0.638802\pi\) |
0.906423 | + | 0.422372i | \(0.138802\pi\) | |||||||
\(12\) | 13.8377i | 1.15314i | ||||||||
\(13\) | −5.90569 | − | 11.5811i | −0.454284 | − | 0.890857i | ||||
\(14\) | −5.32456 | −0.380325 | ||||||||
\(15\) | −14.9057 | − | 14.9057i | −0.993713 | − | 0.993713i | ||||
\(16\) | −8.35089 | −0.521931 | ||||||||
\(17\) | 21.9737i | 1.29257i | 0.763097 | + | 0.646284i | \(0.223678\pi\) | ||||
−0.763097 | + | 0.646284i | \(0.776322\pi\) | |||||||
\(18\) | 4.83772 | + | 4.83772i | 0.268762 | + | 0.268762i | ||||
\(19\) | 3.16228 | + | 3.16228i | 0.166436 | + | 0.166436i | 0.785411 | − | 0.618975i | \(-0.212452\pi\) |
−0.618975 | + | 0.785411i | \(0.712452\pi\) | |||||||
\(20\) | 11.9057 | − | 11.9057i | 0.595285 | − | 0.595285i | ||||
\(21\) | 19.0680 | − | 19.0680i | 0.907999 | − | 0.907999i | ||||
\(22\) | 6.18861 | 0.281301 | ||||||||
\(23\) | 8.51317i | 0.370138i | 0.982726 | + | 0.185069i | \(0.0592508\pi\) | ||||
−0.982726 | + | 0.185069i | \(0.940749\pi\) | |||||||
\(24\) | −17.7171 | + | 17.7171i | −0.738212 | + | 0.738212i | ||||
\(25\) | 0.649111i | 0.0259644i | ||||||||
\(26\) | 3.29822 | − | 10.1623i | 0.126855 | − | 0.390857i | ||||
\(27\) | 2.81139 | 0.104125 | ||||||||
\(28\) | 15.2302 | + | 15.2302i | 0.543937 | + | 0.543937i | ||||
\(29\) | −5.81139 | −0.200393 | −0.100196 | − | 0.994968i | \(-0.531947\pi\) | ||||
−0.100196 | + | 0.994968i | \(0.531947\pi\) | |||||||
\(30\) | − | 17.3246i | − | 0.577485i | ||||||
\(31\) | 0.513167 | + | 0.513167i | 0.0165538 | + | 0.0165538i | 0.715335 | − | 0.698781i | \(-0.246274\pi\) |
−0.698781 | + | 0.715335i | \(0.746274\pi\) | |||||||
\(32\) | −21.8794 | − | 21.8794i | −0.683730 | − | 0.683730i | ||||
\(33\) | −22.1623 | + | 22.1623i | −0.671584 | + | 0.671584i | ||||
\(34\) | −12.7698 | + | 12.7698i | −0.375581 | + | 0.375581i | ||||
\(35\) | −32.8114 | −0.937468 | ||||||||
\(36\) | − | 27.6754i | − | 0.768762i | ||||||
\(37\) | 24.2302 | − | 24.2302i | 0.654872 | − | 0.654872i | −0.299290 | − | 0.954162i | \(-0.596750\pi\) |
0.954162 | + | 0.299290i | \(0.0967499\pi\) | |||||||
\(38\) | 3.67544i | 0.0967222i | ||||||||
\(39\) | 24.5811 | + | 48.2039i | 0.630286 | + | 1.23600i | ||||
\(40\) | 30.4868 | 0.762171 | ||||||||
\(41\) | 4.83772 | + | 4.83772i | 0.117993 | + | 0.117993i | 0.763638 | − | 0.645645i | \(-0.223411\pi\) |
−0.645645 | + | 0.763638i | \(0.723411\pi\) | |||||||
\(42\) | 22.1623 | 0.527673 | ||||||||
\(43\) | − | 30.4868i | − | 0.708996i | −0.935057 | − | 0.354498i | \(-0.884652\pi\) | ||
0.935057 | − | 0.354498i | \(-0.115348\pi\) | |||||||
\(44\) | −17.7018 | − | 17.7018i | −0.402313 | − | 0.402313i | ||||
\(45\) | 29.8114 | + | 29.8114i | 0.662475 | + | 0.662475i | ||||
\(46\) | −4.94733 | + | 4.94733i | −0.107551 | + | 0.107551i | ||||
\(47\) | −37.3662 | + | 37.3662i | −0.795025 | + | 0.795025i | −0.982306 | − | 0.187281i | \(-0.940033\pi\) |
0.187281 | + | 0.982306i | \(0.440033\pi\) | |||||||
\(48\) | 34.7587 | 0.724140 | ||||||||
\(49\) | 7.02633i | 0.143395i | ||||||||
\(50\) | −0.377223 | + | 0.377223i | −0.00754447 | + | 0.00754447i | ||||
\(51\) | − | 91.4605i | − | 1.79334i | ||||||
\(52\) | −38.5021 | + | 19.6338i | −0.740426 | + | 0.377573i | ||||
\(53\) | −35.8114 | −0.675687 | −0.337843 | − | 0.941202i | \(-0.609697\pi\) | ||||
−0.337843 | + | 0.941202i | \(0.609697\pi\) | |||||||
\(54\) | 1.63381 | + | 1.63381i | 0.0302557 | + | 0.0302557i | ||||
\(55\) | 38.1359 | 0.693381 | ||||||||
\(56\) | 39.0000i | 0.696429i | ||||||||
\(57\) | −13.1623 | − | 13.1623i | −0.230917 | − | 0.230917i | ||||
\(58\) | −3.37722 | − | 3.37722i | −0.0582280 | − | 0.0582280i | ||||
\(59\) | 58.2719 | − | 58.2719i | 0.987659 | − | 0.987659i | −0.0122657 | − | 0.999925i | \(-0.503904\pi\) |
0.999925 | + | 0.0122657i | \(0.00390438\pi\) | |||||||
\(60\) | −49.5548 | + | 49.5548i | −0.825913 | + | 0.825913i | ||||
\(61\) | −80.3246 | −1.31680 | −0.658398 | − | 0.752670i | \(-0.728766\pi\) | ||||
−0.658398 | + | 0.752670i | \(0.728766\pi\) | |||||||
\(62\) | 0.596443i | 0.00962004i | ||||||||
\(63\) | −38.1359 | + | 38.1359i | −0.605332 | + | 0.605332i | ||||
\(64\) | 7.97367i | 0.124589i | ||||||||
\(65\) | 20.3246 | − | 62.6228i | 0.312685 | − | 0.963427i | ||||
\(66\) | −25.7587 | −0.390284 | ||||||||
\(67\) | 39.0833 | + | 39.0833i | 0.583332 | + | 0.583332i | 0.935817 | − | 0.352485i | \(-0.114663\pi\) |
−0.352485 | + | 0.935817i | \(0.614663\pi\) | |||||||
\(68\) | 73.0527 | 1.07430 | ||||||||
\(69\) | − | 35.4342i | − | 0.513539i | ||||||
\(70\) | −19.0680 | − | 19.0680i | −0.272400 | − | 0.272400i | ||||
\(71\) | 91.5548 | + | 91.5548i | 1.28950 | + | 1.28950i | 0.935088 | + | 0.354417i | \(0.115321\pi\) |
0.354417 | + | 0.935088i | \(0.384679\pi\) | |||||||
\(72\) | 35.4342 | − | 35.4342i | 0.492141 | − | 0.492141i | ||||
\(73\) | 31.6228 | − | 31.6228i | 0.433189 | − | 0.433189i | −0.456523 | − | 0.889712i | \(-0.650905\pi\) |
0.889712 | + | 0.456523i | \(0.150905\pi\) | |||||||
\(74\) | 28.1623 | 0.380571 | ||||||||
\(75\) | − | 2.70178i | − | 0.0360237i | ||||||
\(76\) | 10.5132 | − | 10.5132i | 0.138331 | − | 0.138331i | ||||
\(77\) | 48.7851i | 0.633572i | ||||||||
\(78\) | −13.7281 | + | 42.2982i | −0.176001 | + | 0.542285i | ||||
\(79\) | −18.7851 | −0.237785 | −0.118893 | − | 0.992907i | \(-0.537934\pi\) | ||||
−0.118893 | + | 0.992907i | \(0.537934\pi\) | |||||||
\(80\) | −29.9057 | − | 29.9057i | −0.373821 | − | 0.373821i | ||||
\(81\) | −86.6228 | −1.06942 | ||||||||
\(82\) | 5.62278i | 0.0685704i | ||||||||
\(83\) | −44.6228 | − | 44.6228i | −0.537624 | − | 0.537624i | 0.385207 | − | 0.922830i | \(-0.374130\pi\) |
−0.922830 | + | 0.385207i | \(0.874130\pi\) | |||||||
\(84\) | −63.3925 | − | 63.3925i | −0.754673 | − | 0.754673i | ||||
\(85\) | −78.6907 | + | 78.6907i | −0.925774 | + | 0.925774i | ||||
\(86\) | 17.7171 | − | 17.7171i | 0.206013 | − | 0.206013i | ||||
\(87\) | 24.1886 | 0.278030 | ||||||||
\(88\) | − | 45.3288i | − | 0.515100i | ||||||
\(89\) | 8.89039 | − | 8.89039i | 0.0998920 | − | 0.0998920i | −0.655395 | − | 0.755287i | \(-0.727498\pi\) |
0.755287 | + | 0.655395i | \(0.227498\pi\) | |||||||
\(90\) | 34.6491i | 0.384990i | ||||||||
\(91\) | 80.1096 | + | 26.0000i | 0.880325 | + | 0.285714i | ||||
\(92\) | 28.3025 | 0.307636 | ||||||||
\(93\) | −2.13594 | − | 2.13594i | −0.0229671 | − | 0.0229671i | ||||
\(94\) | −43.4299 | −0.462020 | ||||||||
\(95\) | 22.6491i | 0.238412i | ||||||||
\(96\) | 91.0680 | + | 91.0680i | 0.948625 | + | 0.948625i | ||||
\(97\) | −121.355 | − | 121.355i | −1.25108 | − | 1.25108i | −0.955235 | − | 0.295850i | \(-0.904397\pi\) |
−0.295850 | − | 0.955235i | \(-0.595603\pi\) | |||||||
\(98\) | −4.08328 | + | 4.08328i | −0.0416661 | + | 0.0416661i | ||||
\(99\) | 44.3246 | − | 44.3246i | 0.447723 | − | 0.447723i | ||||
\(100\) | 2.15800 | 0.0215800 | ||||||||
\(101\) | 104.921i | 1.03882i | 0.854525 | + | 0.519411i | \(0.173849\pi\) | ||||
−0.854525 | + | 0.519411i | \(0.826151\pi\) | |||||||
\(102\) | 53.1512 | − | 53.1512i | 0.521091 | − | 0.521091i | ||||
\(103\) | − | 35.4342i | − | 0.344021i | −0.985095 | − | 0.172011i | \(-0.944974\pi\) | ||
0.985095 | − | 0.172011i | \(-0.0550263\pi\) | |||||||
\(104\) | −74.4342 | − | 24.1580i | −0.715713 | − | 0.232289i | ||||
\(105\) | 136.570 | 1.30067 | ||||||||
\(106\) | −20.8114 | − | 20.8114i | −0.196334 | − | 0.196334i | ||||
\(107\) | −4.42989 | −0.0414009 | −0.0207004 | − | 0.999786i | \(-0.506590\pi\) | ||||
−0.0207004 | + | 0.999786i | \(0.506590\pi\) | |||||||
\(108\) | − | 9.34662i | − | 0.0865427i | ||||||
\(109\) | 120.774 | + | 120.774i | 1.10802 | + | 1.10802i | 0.993411 | + | 0.114608i | \(0.0365611\pi\) |
0.114608 | + | 0.993411i | \(0.463439\pi\) | |||||||
\(110\) | 22.1623 | + | 22.1623i | 0.201475 | + | 0.201475i | ||||
\(111\) | −100.853 | + | 100.853i | −0.908586 | + | 0.908586i | ||||
\(112\) | 38.2566 | − | 38.2566i | 0.341577 | − | 0.341577i | ||||
\(113\) | 68.5438 | 0.606582 | 0.303291 | − | 0.952898i | \(-0.401915\pi\) | ||||
0.303291 | + | 0.952898i | \(0.401915\pi\) | |||||||
\(114\) | − | 15.2982i | − | 0.134195i | ||||||
\(115\) | −30.4868 | + | 30.4868i | −0.265103 | + | 0.265103i | ||||
\(116\) | 19.3203i | 0.166554i | ||||||||
\(117\) | −49.1623 | − | 96.4078i | −0.420190 | − | 0.823999i | ||||
\(118\) | 67.7281 | 0.573967 | ||||||||
\(119\) | −100.664 | − | 100.664i | −0.845919 | − | 0.845919i | ||||
\(120\) | −126.895 | −1.05746 | ||||||||
\(121\) | 64.2982i | 0.531390i | ||||||||
\(122\) | −46.6797 | − | 46.6797i | −0.382621 | − | 0.382621i | ||||
\(123\) | −20.1359 | − | 20.1359i | −0.163707 | − | 0.163707i | ||||
\(124\) | 1.70605 | − | 1.70605i | 0.0137585 | − | 0.0137585i | ||||
\(125\) | 87.2039 | − | 87.2039i | 0.697631 | − | 0.697631i | ||||
\(126\) | −44.3246 | −0.351782 | ||||||||
\(127\) | − | 101.162i | − | 0.796553i | −0.917265 | − | 0.398277i | \(-0.869608\pi\) | ||
0.917265 | − | 0.398277i | \(-0.130392\pi\) | |||||||
\(128\) | −92.1512 | + | 92.1512i | −0.719932 | + | 0.719932i | ||||
\(129\) | 126.895i | 0.983680i | ||||||||
\(130\) | 48.2039 | − | 24.5811i | 0.370799 | − | 0.189086i | ||||
\(131\) | −257.732 | −1.96742 | −0.983711 | − | 0.179755i | \(-0.942469\pi\) | ||||
−0.983711 | + | 0.179755i | \(0.942469\pi\) | |||||||
\(132\) | 73.6797 | + | 73.6797i | 0.558180 | + | 0.558180i | ||||
\(133\) | −28.9737 | −0.217847 | ||||||||
\(134\) | 45.4256i | 0.338997i | ||||||||
\(135\) | 10.0680 | + | 10.0680i | 0.0745776 | + | 0.0745776i | ||||
\(136\) | 93.5327 | + | 93.5327i | 0.687741 | + | 0.687741i | ||||
\(137\) | 175.272 | − | 175.272i | 1.27936 | − | 1.27936i | 0.338329 | − | 0.941028i | \(-0.390138\pi\) |
0.941028 | − | 0.338329i | \(-0.109862\pi\) | |||||||
\(138\) | 20.5922 | − | 20.5922i | 0.149219 | − | 0.149219i | ||||
\(139\) | 135.460 | 0.974536 | 0.487268 | − | 0.873252i | \(-0.337993\pi\) | ||||
0.487268 | + | 0.873252i | \(0.337993\pi\) | |||||||
\(140\) | 109.083i | 0.779166i | ||||||||
\(141\) | 155.528 | − | 155.528i | 1.10304 | − | 1.10304i | ||||
\(142\) | 106.412i | 0.749381i | ||||||||
\(143\) | −93.1096 | − | 30.2192i | −0.651116 | − | 0.211323i | ||||
\(144\) | −69.5174 | −0.482760 | ||||||||
\(145\) | −20.8114 | − | 20.8114i | −0.143527 | − | 0.143527i | ||||
\(146\) | 36.7544 | 0.251743 | ||||||||
\(147\) | − | 29.2456i | − | 0.198949i | ||||||
\(148\) | −80.5548 | − | 80.5548i | −0.544289 | − | 0.544289i | ||||
\(149\) | 36.2192 | + | 36.2192i | 0.243082 | + | 0.243082i | 0.818124 | − | 0.575042i | \(-0.195014\pi\) |
−0.575042 | + | 0.818124i | \(0.695014\pi\) | |||||||
\(150\) | 1.57011 | − | 1.57011i | 0.0104674 | − | 0.0104674i | ||||
\(151\) | −75.1776 | + | 75.1776i | −0.497865 | + | 0.497865i | −0.910773 | − | 0.412908i | \(-0.864513\pi\) |
0.412908 | + | 0.910773i | \(0.364513\pi\) | |||||||
\(152\) | 26.9210 | 0.177112 | ||||||||
\(153\) | 182.921i | 1.19556i | ||||||||
\(154\) | −28.3509 | + | 28.3509i | −0.184097 | + | 0.184097i | ||||
\(155\) | 3.67544i | 0.0237125i | ||||||||
\(156\) | 160.257 | − | 81.7214i | 1.02729 | − | 0.523855i | ||||
\(157\) | 55.4562 | 0.353224 | 0.176612 | − | 0.984281i | \(-0.443486\pi\) | ||||
0.176612 | + | 0.984281i | \(0.443486\pi\) | |||||||
\(158\) | −10.9167 | − | 10.9167i | −0.0690932 | − | 0.0690932i | ||||
\(159\) | 149.057 | 0.937465 | ||||||||
\(160\) | − | 156.706i | − | 0.979413i | ||||||
\(161\) | −39.0000 | − | 39.0000i | −0.242236 | − | 0.242236i | ||||
\(162\) | −50.3399 | − | 50.3399i | −0.310740 | − | 0.310740i | ||||
\(163\) | −45.4605 | + | 45.4605i | −0.278899 | + | 0.278899i | −0.832669 | − | 0.553771i | \(-0.813188\pi\) |
0.553771 | + | 0.832669i | \(0.313188\pi\) | |||||||
\(164\) | 16.0833 | − | 16.0833i | 0.0980688 | − | 0.0980688i | ||||
\(165\) | −158.732 | −0.962014 | ||||||||
\(166\) | − | 51.8641i | − | 0.312434i | ||||||
\(167\) | −137.215 | + | 137.215i | −0.821646 | + | 0.821646i | −0.986344 | − | 0.164698i | \(-0.947335\pi\) |
0.164698 | + | 0.986344i | \(0.447335\pi\) | |||||||
\(168\) | − | 162.329i | − | 0.966243i | ||||||
\(169\) | −99.2456 | + | 136.789i | −0.587252 | + | 0.809404i | ||||
\(170\) | −91.4605 | −0.538003 | ||||||||
\(171\) | 26.3246 | + | 26.3246i | 0.153945 | + | 0.153945i | ||||
\(172\) | −101.355 | −0.589274 | ||||||||
\(173\) | 79.3815i | 0.458853i | 0.973326 | + | 0.229426i | \(0.0736850\pi\) | ||||
−0.973326 | + | 0.229426i | \(0.926315\pi\) | |||||||
\(174\) | 14.0569 | + | 14.0569i | 0.0807870 | + | 0.0807870i | ||||
\(175\) | −2.97367 | − | 2.97367i | −0.0169924 | − | 0.0169924i | ||||
\(176\) | −44.4648 | + | 44.4648i | −0.252641 | + | 0.252641i | ||||
\(177\) | −242.544 | + | 242.544i | −1.37030 | + | 1.37030i | ||||
\(178\) | 10.3331 | 0.0580511 | ||||||||
\(179\) | − | 318.329i | − | 1.77837i | −0.457545 | − | 0.889187i | \(-0.651271\pi\) | ||
0.457545 | − | 0.889187i | \(-0.348729\pi\) | |||||||
\(180\) | 99.1096 | − | 99.1096i | 0.550609 | − | 0.550609i | ||||
\(181\) | − | 238.144i | − | 1.31572i | −0.753142 | − | 0.657858i | \(-0.771463\pi\) | ||
0.753142 | − | 0.657858i | \(-0.228537\pi\) | |||||||
\(182\) | 31.4452 | + | 61.6644i | 0.172776 | + | 0.338815i | ||||
\(183\) | 334.333 | 1.82696 | ||||||||
\(184\) | 36.2370 | + | 36.2370i | 0.196940 | + | 0.196940i | ||||
\(185\) | 173.544 | 0.938074 | ||||||||
\(186\) | − | 2.48256i | − | 0.0133471i | ||||||
\(187\) | 117.000 | + | 117.000i | 0.625668 | + | 0.625668i | ||||
\(188\) | 124.226 | + | 124.226i | 0.660776 | + | 0.660776i | ||||
\(189\) | −12.8794 | + | 12.8794i | −0.0681448 | + | 0.0681448i | ||||
\(190\) | −13.1623 | + | 13.1623i | −0.0692751 | + | 0.0692751i | ||||
\(191\) | −3.70605 | −0.0194034 | −0.00970171 | − | 0.999953i | \(-0.503088\pi\) | ||||
−0.00970171 | + | 0.999953i | \(0.503088\pi\) | |||||||
\(192\) | − | 33.1886i | − | 0.172857i | ||||||
\(193\) | 43.1359 | − | 43.1359i | 0.223502 | − | 0.223502i | −0.586469 | − | 0.809972i | \(-0.699483\pi\) |
0.809972 | + | 0.586469i | \(0.199483\pi\) | |||||||
\(194\) | − | 141.048i | − | 0.727054i | ||||||
\(195\) | −84.5964 | + | 260.653i | −0.433828 | + | 1.33668i | ||||
\(196\) | 23.3594 | 0.119181 | ||||||||
\(197\) | 126.094 | + | 126.094i | 0.640073 | + | 0.640073i | 0.950573 | − | 0.310501i | \(-0.100497\pi\) |
−0.310501 | + | 0.950573i | \(0.600497\pi\) | |||||||
\(198\) | 51.5174 | 0.260189 | ||||||||
\(199\) | − | 152.241i | − | 0.765032i | −0.923949 | − | 0.382516i | \(-0.875058\pi\) | ||
0.923949 | − | 0.382516i | \(-0.124942\pi\) | |||||||
\(200\) | 2.76299 | + | 2.76299i | 0.0138150 | + | 0.0138150i | ||||
\(201\) | −162.675 | − | 162.675i | −0.809331 | − | 0.809331i | ||||
\(202\) | −60.9737 | + | 60.9737i | −0.301850 | + | 0.301850i | ||||
\(203\) | 26.6228 | − | 26.6228i | 0.131147 | − | 0.131147i | ||||
\(204\) | −304.065 | −1.49052 | ||||||||
\(205\) | 34.6491i | 0.169020i | ||||||||
\(206\) | 20.5922 | − | 20.5922i | 0.0999620 | − | 0.0999620i | ||||
\(207\) | 70.8683i | 0.342359i | ||||||||
\(208\) | 49.3178 | + | 96.7128i | 0.237105 | + | 0.464965i | ||||
\(209\) | 33.6754 | 0.161127 | ||||||||
\(210\) | 79.3662 | + | 79.3662i | 0.377934 | + | 0.377934i | ||||
\(211\) | −47.5744 | −0.225471 | −0.112736 | − | 0.993625i | \(-0.535961\pi\) | ||||
−0.112736 | + | 0.993625i | \(0.535961\pi\) | |||||||
\(212\) | 119.057i | 0.561589i | ||||||||
\(213\) | −381.077 | − | 381.077i | −1.78909 | − | 1.78909i | ||||
\(214\) | −2.57438 | − | 2.57438i | −0.0120298 | − | 0.0120298i | ||||
\(215\) | 109.178 | − | 109.178i | 0.507803 | − | 0.507803i | ||||
\(216\) | 11.9669 | − | 11.9669i | 0.0554024 | − | 0.0554024i | ||||
\(217\) | −4.70178 | −0.0216672 | ||||||||
\(218\) | 140.373i | 0.643913i | ||||||||
\(219\) | −131.623 | + | 131.623i | −0.601017 | + | 0.601017i | ||||
\(220\) | − | 126.785i | − | 0.576296i | ||||||
\(221\) | 254.480 | − | 129.770i | 1.15149 | − | 0.587193i | ||||
\(222\) | −117.219 | −0.528015 | ||||||||
\(223\) | −38.2260 | − | 38.2260i | −0.171417 | − | 0.171417i | 0.616185 | − | 0.787602i | \(-0.288677\pi\) |
−0.787602 | + | 0.616185i | \(0.788677\pi\) | |||||||
\(224\) | 200.465 | 0.894932 | ||||||||
\(225\) | 5.40356i | 0.0240158i | ||||||||
\(226\) | 39.8334 | + | 39.8334i | 0.176254 | + | 0.176254i | ||||
\(227\) | 44.7324 | + | 44.7324i | 0.197059 | + | 0.197059i | 0.798738 | − | 0.601679i | \(-0.205501\pi\) |
−0.601679 | + | 0.798738i | \(0.705501\pi\) | |||||||
\(228\) | −43.7587 | + | 43.7587i | −0.191924 | + | 0.191924i | ||||
\(229\) | −167.634 | + | 167.634i | −0.732025 | + | 0.732025i | −0.971021 | − | 0.238995i | \(-0.923182\pi\) |
0.238995 | + | 0.971021i | \(0.423182\pi\) | |||||||
\(230\) | −35.4342 | −0.154062 | ||||||||
\(231\) | − | 203.057i | − | 0.879034i | ||||||
\(232\) | −24.7367 | + | 24.7367i | −0.106624 | + | 0.106624i | ||||
\(233\) | 292.789i | 1.25661i | 0.777969 | + | 0.628303i | \(0.216250\pi\) | ||||
−0.777969 | + | 0.628303i | \(0.783750\pi\) | |||||||
\(234\) | 27.4562 | − | 84.5964i | 0.117334 | − | 0.361523i | ||||
\(235\) | −267.627 | −1.13884 | ||||||||
\(236\) | −193.728 | − | 193.728i | −0.820882 | − | 0.820882i | ||||
\(237\) | 78.1886 | 0.329910 | ||||||||
\(238\) | − | 117.000i | − | 0.491597i | ||||||
\(239\) | 0.0153037 | + | 0.0153037i | 6.40324e−5 | + | 6.40324e-5i | 0.707139 | − | 0.707075i | \(-0.249986\pi\) |
−0.707075 | + | 0.707139i | \(0.749986\pi\) | |||||||
\(240\) | 124.476 | + | 124.476i | 0.518649 | + | 0.518649i | ||||
\(241\) | 240.197 | − | 240.197i | 0.996669 | − | 0.996669i | −0.00332576 | − | 0.999994i | \(-0.501059\pi\) |
0.999994 | + | 0.00332576i | \(0.00105862\pi\) | |||||||
\(242\) | −37.3662 | + | 37.3662i | −0.154406 | + | 0.154406i | ||||
\(243\) | 335.246 | 1.37961 | ||||||||
\(244\) | 267.043i | 1.09444i | ||||||||
\(245\) | −25.1623 | + | 25.1623i | −0.102703 | + | 0.102703i | ||||
\(246\) | − | 23.4036i | − | 0.0951364i | ||||||
\(247\) | 17.9473 | − | 55.2982i | 0.0726613 | − | 0.223879i | ||||
\(248\) | 4.36868 | 0.0176156 | ||||||||
\(249\) | 185.732 | + | 185.732i | 0.745913 | + | 0.745913i | ||||
\(250\) | 101.355 | 0.405421 | ||||||||
\(251\) | 131.842i | 0.525267i | 0.964896 | + | 0.262633i | \(0.0845910\pi\) | ||||
−0.964896 | + | 0.262633i | \(0.915409\pi\) | |||||||
\(252\) | 126.785 | + | 126.785i | 0.503115 | + | 0.503115i | ||||
\(253\) | 45.3288 | + | 45.3288i | 0.179165 | + | 0.179165i | ||||
\(254\) | 58.7893 | − | 58.7893i | 0.231454 | − | 0.231454i | ||||
\(255\) | 327.533 | − | 327.533i | 1.28444 | − | 1.28444i | ||||
\(256\) | −75.2107 | −0.293792 | ||||||||
\(257\) | − | 156.579i | − | 0.609255i | −0.952471 | − | 0.304628i | \(-0.901468\pi\) | ||
0.952471 | − | 0.304628i | \(-0.0985320\pi\) | |||||||
\(258\) | −73.7434 | + | 73.7434i | −0.285827 | + | 0.285827i | ||||
\(259\) | 222.004i | 0.857159i | ||||||||
\(260\) | −208.193 | − | 67.5701i | −0.800742 | − | 0.259885i | ||||
\(261\) | −48.3772 | −0.185353 | ||||||||
\(262\) | −149.778 | − | 149.778i | −0.571673 | − | 0.571673i | ||||
\(263\) | −338.982 | −1.28891 | −0.644453 | − | 0.764644i | \(-0.722915\pi\) | ||||
−0.644453 | + | 0.764644i | \(0.722915\pi\) | |||||||
\(264\) | 188.671i | 0.714664i | ||||||||
\(265\) | −128.246 | − | 128.246i | −0.483945 | − | 0.483945i | ||||
\(266\) | −16.8377 | − | 16.8377i | −0.0632997 | − | 0.0632997i | ||||
\(267\) | −37.0043 | + | 37.0043i | −0.138593 | + | 0.138593i | ||||
\(268\) | 129.935 | − | 129.935i | 0.484830 | − | 0.484830i | ||||
\(269\) | −222.061 | −0.825506 | −0.412753 | − | 0.910843i | \(-0.635433\pi\) | ||||
−0.412753 | + | 0.910843i | \(0.635433\pi\) | |||||||
\(270\) | 11.7018i | 0.0433399i | ||||||||
\(271\) | 39.0722 | − | 39.0722i | 0.144178 | − | 0.144178i | −0.631333 | − | 0.775511i | \(-0.717492\pi\) |
0.775511 | + | 0.631333i | \(0.217492\pi\) | |||||||
\(272\) | − | 183.500i | − | 0.674631i | ||||||
\(273\) | −333.438 | − | 108.219i | −1.22139 | − | 0.396407i | ||||
\(274\) | 203.715 | 0.743484 | ||||||||
\(275\) | 3.45623 | + | 3.45623i | 0.0125681 | + | 0.0125681i | ||||
\(276\) | −117.803 | −0.426822 | ||||||||
\(277\) | 112.053i | 0.404522i | 0.979332 | + | 0.202261i | \(0.0648290\pi\) | ||||
−0.979332 | + | 0.202261i | \(0.935171\pi\) | |||||||
\(278\) | 78.7214 | + | 78.7214i | 0.283170 | + | 0.283170i | ||||
\(279\) | 4.27189 | + | 4.27189i | 0.0153114 | + | 0.0153114i | ||||
\(280\) | −139.664 | + | 139.664i | −0.498801 | + | 0.498801i | ||||
\(281\) | −174.846 | + | 174.846i | −0.622229 | + | 0.622229i | −0.946101 | − | 0.323872i | \(-0.895015\pi\) |
0.323872 | + | 0.946101i | \(0.395015\pi\) | |||||||
\(282\) | 180.767 | 0.641019 | ||||||||
\(283\) | 271.201i | 0.958309i | 0.877731 | + | 0.479154i | \(0.159057\pi\) | ||||
−0.877731 | + | 0.479154i | \(0.840943\pi\) | |||||||
\(284\) | 304.379 | − | 304.379i | 1.07176 | − | 1.07176i | ||||
\(285\) | − | 94.2719i | − | 0.330779i | ||||||
\(286\) | −36.5480 | − | 71.6712i | −0.127790 | − | 0.250599i | ||||
\(287\) | −44.3246 | −0.154441 | ||||||||
\(288\) | −182.136 | − | 182.136i | −0.632416 | − | 0.632416i | ||||
\(289\) | −193.842 | −0.670734 | ||||||||
\(290\) | − | 24.1886i | − | 0.0834090i | ||||||
\(291\) | 505.114 | + | 505.114i | 1.73579 | + | 1.73579i | ||||
\(292\) | −105.132 | − | 105.132i | −0.360040 | − | 0.360040i | ||||
\(293\) | −240.156 | + | 240.156i | −0.819643 | + | 0.819643i | −0.986056 | − | 0.166413i | \(-0.946782\pi\) |
0.166413 | + | 0.986056i | \(0.446782\pi\) | |||||||
\(294\) | 16.9957 | − | 16.9957i | 0.0578086 | − | 0.0578086i | ||||
\(295\) | 417.359 | 1.41478 | ||||||||
\(296\) | − | 206.276i | − | 0.696879i | ||||||
\(297\) | 14.9694 | − | 14.9694i | 0.0504020 | − | 0.0504020i | ||||
\(298\) | 42.0968i | 0.141264i | ||||||||
\(299\) | 98.5922 | − | 50.2762i | 0.329740 | − | 0.168148i | ||||
\(300\) | −8.98221 | −0.0299407 | ||||||||
\(301\) | 139.664 | + | 139.664i | 0.464001 | + | 0.464001i | ||||
\(302\) | −87.3772 | −0.289329 | ||||||||
\(303\) | − | 436.710i | − | 1.44129i | ||||||
\(304\) | −26.4078 | − | 26.4078i | −0.0868679 | − | 0.0868679i | ||||
\(305\) | −287.653 | − | 287.653i | −0.943126 | − | 0.943126i | ||||
\(306\) | −106.302 | + | 106.302i | −0.347394 | + | 0.347394i | ||||
\(307\) | 219.684 | − | 219.684i | 0.715583 | − | 0.715583i | −0.252114 | − | 0.967697i | \(-0.581126\pi\) |
0.967697 | + | 0.252114i | \(0.0811259\pi\) | |||||||
\(308\) | 162.189 | 0.526586 | ||||||||
\(309\) | 147.487i | 0.477304i | ||||||||
\(310\) | −2.13594 | + | 2.13594i | −0.00689014 | + | 0.00689014i | ||||
\(311\) | 341.684i | 1.09866i | 0.835605 | + | 0.549331i | \(0.185117\pi\) | ||||
−0.835605 | + | 0.549331i | \(0.814883\pi\) | |||||||
\(312\) | 309.816 | + | 100.552i | 0.992999 | + | 0.322283i | ||||
\(313\) | 438.517 | 1.40101 | 0.700507 | − | 0.713645i | \(-0.252957\pi\) | ||||
0.700507 | + | 0.713645i | \(0.252957\pi\) | |||||||
\(314\) | 32.2278 | + | 32.2278i | 0.102636 | + | 0.102636i | ||||
\(315\) | −273.140 | −0.867112 | ||||||||
\(316\) | 62.4520i | 0.197633i | ||||||||
\(317\) | 153.140 | + | 153.140i | 0.483092 | + | 0.483092i | 0.906118 | − | 0.423026i | \(-0.139032\pi\) |
−0.423026 | + | 0.906118i | \(0.639032\pi\) | |||||||
\(318\) | 86.6228 | + | 86.6228i | 0.272399 | + | 0.272399i | ||||
\(319\) | −30.9431 | + | 30.9431i | −0.0970002 | + | 0.0970002i | ||||
\(320\) | −28.5548 | + | 28.5548i | −0.0892338 | + | 0.0892338i | ||||
\(321\) | 18.4384 | 0.0574406 | ||||||||
\(322\) | − | 45.3288i | − | 0.140773i | ||||||
\(323\) | −69.4868 | + | 69.4868i | −0.215130 | + | 0.215130i | ||||
\(324\) | 287.982i | 0.888834i | ||||||||
\(325\) | 7.51744 | − | 3.83345i | 0.0231306 | − | 0.0117952i | ||||
\(326\) | −52.8377 | −0.162079 | ||||||||
\(327\) | −502.695 | − | 502.695i | −1.53729 | − | 1.53729i | ||||
\(328\) | 41.1843 | 0.125562 | ||||||||
\(329\) | − | 342.359i | − | 1.04061i | ||||||
\(330\) | −92.2456 | − | 92.2456i | −0.279532 | − | 0.279532i | ||||
\(331\) | −195.982 | − | 195.982i | −0.592091 | − | 0.592091i | 0.346105 | − | 0.938196i | \(-0.387504\pi\) |
−0.938196 | + | 0.346105i | \(0.887504\pi\) | |||||||
\(332\) | −148.351 | + | 148.351i | −0.446840 | + | 0.446840i | ||||
\(333\) | 201.706 | − | 201.706i | 0.605724 | − | 0.605724i | ||||
\(334\) | −159.482 | −0.477491 | ||||||||
\(335\) | 279.925i | 0.835598i | ||||||||
\(336\) | −159.235 | + | 159.235i | −0.473912 | + | 0.473912i | ||||
\(337\) | − | 7.32456i | − | 0.0217346i | −0.999941 | − | 0.0108673i | \(-0.996541\pi\) | ||
0.999941 | − | 0.0108673i | \(-0.00345923\pi\) | |||||||
\(338\) | −137.169 | + | 21.8181i | −0.405826 | + | 0.0645507i | ||||
\(339\) | −285.298 | −0.841588 | ||||||||
\(340\) | 261.612 | + | 261.612i | 0.769446 | + | 0.769446i | ||||
\(341\) | 5.46477 | 0.0160257 | ||||||||
\(342\) | 30.5964i | 0.0894633i | ||||||||
\(343\) | −256.664 | − | 256.664i | −0.748293 | − | 0.748293i | ||||
\(344\) | −129.770 | − | 129.770i | −0.377238 | − | 0.377238i | ||||
\(345\) | 126.895 | − | 126.895i | 0.367811 | − | 0.367811i | ||||
\(346\) | −46.1317 | + | 46.1317i | −0.133329 | + | 0.133329i | ||||
\(347\) | −154.759 | −0.445991 | −0.222995 | − | 0.974820i | \(-0.571583\pi\) | ||||
−0.222995 | + | 0.974820i | \(0.571583\pi\) | |||||||
\(348\) | − | 80.4164i | − | 0.231082i | ||||||
\(349\) | 220.419 | − | 220.419i | 0.631573 | − | 0.631573i | −0.316890 | − | 0.948462i | \(-0.602639\pi\) |
0.948462 | + | 0.316890i | \(0.102639\pi\) | |||||||
\(350\) | − | 3.45623i | − | 0.00987493i | ||||||
\(351\) | −16.6032 | − | 32.5591i | −0.0473026 | − | 0.0927609i | ||||
\(352\) | −232.996 | −0.661920 | ||||||||
\(353\) | 331.680 | + | 331.680i | 0.939603 | + | 0.939603i | 0.998277 | − | 0.0586746i | \(-0.0186874\pi\) |
−0.0586746 | + | 0.998277i | \(0.518687\pi\) | |||||||
\(354\) | −281.903 | −0.796337 | ||||||||
\(355\) | 655.741i | 1.84716i | ||||||||
\(356\) | −29.5566 | − | 29.5566i | −0.0830241 | − | 0.0830241i | ||||
\(357\) | 418.993 | + | 418.993i | 1.17365 | + | 1.17365i | ||||
\(358\) | 184.993 | − | 184.993i | 0.516741 | − | 0.516741i | ||||
\(359\) | 132.785 | − | 132.785i | 0.369875 | − | 0.369875i | −0.497557 | − | 0.867431i | \(-0.665769\pi\) |
0.867431 | + | 0.497557i | \(0.165769\pi\) | |||||||
\(360\) | 253.789 | 0.704970 | ||||||||
\(361\) | − | 341.000i | − | 0.944598i | ||||||
\(362\) | 138.395 | − | 138.395i | 0.382307 | − | 0.382307i | ||||
\(363\) | − | 267.627i | − | 0.737265i | ||||||
\(364\) | 86.4384 | − | 266.329i | 0.237468 | − | 0.731673i | ||||
\(365\) | 226.491 | 0.620524 | ||||||||
\(366\) | 194.294 | + | 194.294i | 0.530858 | + | 0.530858i | ||||
\(367\) | 282.416 | 0.769527 | 0.384763 | − | 0.923015i | \(-0.374283\pi\) | ||||
0.384763 | + | 0.923015i | \(0.374283\pi\) | |||||||
\(368\) | − | 71.0925i | − | 0.193186i | ||||||
\(369\) | 40.2719 | + | 40.2719i | 0.109138 | + | 0.109138i | ||||
\(370\) | 100.853 | + | 100.853i | 0.272576 | + | 0.272576i | ||||
\(371\) | 164.057 | − | 164.057i | 0.442202 | − | 0.442202i | ||||
\(372\) | −7.10106 | + | 7.10106i | −0.0190889 | + | 0.0190889i | ||||
\(373\) | −648.877 | −1.73962 | −0.869808 | − | 0.493390i | \(-0.835758\pi\) | ||||
−0.869808 | + | 0.493390i | \(0.835758\pi\) | |||||||
\(374\) | 135.986i | 0.363600i | ||||||||
\(375\) | −362.967 | + | 362.967i | −0.967912 | + | 0.967912i | ||||
\(376\) | 318.105i | 0.846023i | ||||||||
\(377\) | 34.3203 | + | 67.3025i | 0.0910352 | + | 0.178521i | ||||
\(378\) | −14.9694 | −0.0396016 | ||||||||
\(379\) | −429.302 | − | 429.302i | −1.13272 | − | 1.13272i | −0.989722 | − | 0.143002i | \(-0.954325\pi\) |
−0.143002 | − | 0.989722i | \(-0.545675\pi\) | |||||||
\(380\) | 75.2982 | 0.198153 | ||||||||
\(381\) | 421.065i | 1.10516i | ||||||||
\(382\) | −2.15373 | − | 2.15373i | −0.00563804 | − | 0.00563804i | ||||
\(383\) | 132.739 | + | 132.739i | 0.346577 | + | 0.346577i | 0.858833 | − | 0.512256i | \(-0.171190\pi\) |
−0.512256 | + | 0.858833i | \(0.671190\pi\) | |||||||
\(384\) | 383.559 | − | 383.559i | 0.998852 | − | 0.998852i | ||||
\(385\) | −174.706 | + | 174.706i | −0.453782 | + | 0.453782i | ||||
\(386\) | 50.1359 | 0.129886 | ||||||||
\(387\) | − | 253.789i | − | 0.655786i | ||||||
\(388\) | −403.452 | + | 403.452i | −1.03982 | + | 1.03982i | ||||
\(389\) | − | 510.342i | − | 1.31193i | −0.754790 | − | 0.655966i | \(-0.772261\pi\) | ||
0.754790 | − | 0.655966i | \(-0.227739\pi\) | |||||||
\(390\) | −200.638 | + | 102.314i | −0.514457 | + | 0.262342i | ||||
\(391\) | −187.065 | −0.478428 | ||||||||
\(392\) | 29.9082 | + | 29.9082i | 0.0762964 | + | 0.0762964i | ||||
\(393\) | 1072.75 | 2.72965 | ||||||||
\(394\) | 146.557i | 0.371971i | ||||||||
\(395\) | −67.2719 | − | 67.2719i | −0.170309 | − | 0.170309i | ||||
\(396\) | −147.359 | − | 147.359i | −0.372120 | − | 0.372120i | ||||
\(397\) | −142.061 | + | 142.061i | −0.357837 | + | 0.357837i | −0.863015 | − | 0.505178i | \(-0.831427\pi\) |
0.505178 | + | 0.863015i | \(0.331427\pi\) | |||||||
\(398\) | 88.4733 | − | 88.4733i | 0.222295 | − | 0.222295i | ||||
\(399\) | 120.596 | 0.302247 | ||||||||
\(400\) | − | 5.42065i | − | 0.0135516i | ||||||
\(401\) | 144.298 | − | 144.298i | 0.359846 | − | 0.359846i | −0.503910 | − | 0.863756i | \(-0.668106\pi\) |
0.863756 | + | 0.503910i | \(0.168106\pi\) | |||||||
\(402\) | − | 189.074i | − | 0.470333i | ||||||
\(403\) | 2.91245 | − | 8.97367i | 0.00722693 | − | 0.0222672i | ||||
\(404\) | 348.816 | 0.863405 | ||||||||
\(405\) | −310.208 | − | 310.208i | −0.765946 | − | 0.765946i | ||||
\(406\) | 30.9431 | 0.0762144 | ||||||||
\(407\) | − | 258.031i | − | 0.633982i | ||||||
\(408\) | −389.309 | − | 389.309i | −0.954189 | − | 0.954189i | ||||
\(409\) | 91.8598 | + | 91.8598i | 0.224596 | + | 0.224596i | 0.810431 | − | 0.585835i | \(-0.199233\pi\) |
−0.585835 | + | 0.810431i | \(0.699233\pi\) | |||||||
\(410\) | −20.1359 | + | 20.1359i | −0.0491121 | + | 0.0491121i | ||||
\(411\) | −729.530 | + | 729.530i | −1.77501 | + | 1.77501i | ||||
\(412\) | −117.803 | −0.285929 | ||||||||
\(413\) | 533.903i | 1.29274i | ||||||||
\(414\) | −41.1843 | + | 41.1843i | −0.0994791 | + | 0.0994791i | ||||
\(415\) | − | 319.601i | − | 0.770122i | ||||||
\(416\) | −124.175 | + | 382.601i | −0.298498 | + | 0.919713i | ||||
\(417\) | −563.824 | −1.35210 | ||||||||
\(418\) | 19.5701 | + | 19.5701i | 0.0468184 | + | 0.0468184i | ||||
\(419\) | −83.2327 | −0.198646 | −0.0993231 | − | 0.995055i | \(-0.531668\pi\) | ||||
−0.0993231 | + | 0.995055i | \(0.531668\pi\) | |||||||
\(420\) | − | 454.035i | − | 1.08104i | ||||||
\(421\) | 68.3135 | + | 68.3135i | 0.162265 | + | 0.162265i | 0.783569 | − | 0.621304i | \(-0.213397\pi\) |
−0.621304 | + | 0.783569i | \(0.713397\pi\) | |||||||
\(422\) | −27.6473 | − | 27.6473i | −0.0655150 | − | 0.0655150i | ||||
\(423\) | −311.057 | + | 311.057i | −0.735359 | + | 0.735359i | ||||
\(424\) | −152.434 | + | 152.434i | −0.359515 | + | 0.359515i | ||||
\(425\) | −14.2633 | −0.0335608 | ||||||||
\(426\) | − | 442.917i | − | 1.03971i | ||||||
\(427\) | 367.978 | − | 367.978i | 0.861775 | − | 0.861775i | ||||
\(428\) | 14.7274i | 0.0344099i | ||||||||
\(429\) | 387.548 | + | 125.781i | 0.903375 | + | 0.293195i | ||||
\(430\) | 126.895 | 0.295104 | ||||||||
\(431\) | 469.963 | + | 469.963i | 1.09040 | + | 1.09040i | 0.995485 | + | 0.0949152i | \(0.0302580\pi\) |
0.0949152 | + | 0.995485i | \(0.469742\pi\) | |||||||
\(432\) | −23.4776 | −0.0543463 | ||||||||
\(433\) | − | 122.140i | − | 0.282079i | −0.990004 | − | 0.141040i | \(-0.954956\pi\) | ||
0.990004 | − | 0.141040i | \(-0.0450445\pi\) | |||||||
\(434\) | −2.73239 | − | 2.73239i | −0.00629582 | − | 0.00629582i | ||||
\(435\) | 86.6228 | + | 86.6228i | 0.199133 | + | 0.199133i | ||||
\(436\) | 401.520 | − | 401.520i | 0.920917 | − | 0.920917i | ||||
\(437\) | −26.9210 | + | 26.9210i | −0.0616041 | + | 0.0616041i | ||||
\(438\) | −152.982 | −0.349274 | ||||||||
\(439\) | 31.2897i | 0.0712749i | 0.999365 | + | 0.0356374i | \(0.0113462\pi\) | ||||
−0.999365 | + | 0.0356374i | \(0.988654\pi\) | |||||||
\(440\) | 162.329 | − | 162.329i | 0.368929 | − | 0.368929i | ||||
\(441\) | 58.4911i | 0.132633i | ||||||||
\(442\) | 223.302 | + | 72.4740i | 0.505209 | + | 0.163968i | ||||
\(443\) | 567.372 | 1.28075 | 0.640375 | − | 0.768062i | \(-0.278779\pi\) | ||||
0.640375 | + | 0.768062i | \(0.278779\pi\) | |||||||
\(444\) | 335.291 | + | 335.291i | 0.755161 | + | 0.755161i | ||||
\(445\) | 63.6754 | 0.143091 | ||||||||
\(446\) | − | 44.4292i | − | 0.0996170i | ||||||
\(447\) | −150.754 | − | 150.754i | −0.337258 | − | 0.337258i | ||||
\(448\) | −36.5285 | − | 36.5285i | −0.0815368 | − | 0.0815368i | ||||
\(449\) | −530.873 | + | 530.873i | −1.18234 | + | 1.18234i | −0.203209 | + | 0.979135i | \(0.565137\pi\) |
−0.979135 | + | 0.203209i | \(0.934863\pi\) | |||||||
\(450\) | −3.14022 | + | 3.14022i | −0.00697826 | + | 0.00697826i | ||||
\(451\) | 51.5174 | 0.114229 | ||||||||
\(452\) | − | 227.878i | − | 0.504154i | ||||||
\(453\) | 312.910 | − | 312.910i | 0.690750 | − | 0.690750i | ||||
\(454\) | 51.9915i | 0.114519i | ||||||||
\(455\) | 193.774 | + | 379.993i | 0.425877 | + | 0.835150i | ||||
\(456\) | −112.053 | −0.245730 | ||||||||
\(457\) | 232.092 | + | 232.092i | 0.507860 | + | 0.507860i | 0.913869 | − | 0.406009i | \(-0.133080\pi\) |
−0.406009 | + | 0.913869i | \(0.633080\pi\) | |||||||
\(458\) | −194.837 | −0.425408 | ||||||||
\(459\) | 61.7765i | 0.134589i | ||||||||
\(460\) | 101.355 | + | 101.355i | 0.220337 | + | 0.220337i | ||||
\(461\) | −209.748 | − | 209.748i | −0.454984 | − | 0.454984i | 0.442021 | − | 0.897005i | \(-0.354262\pi\) |
−0.897005 | + | 0.442021i | \(0.854262\pi\) | |||||||
\(462\) | 118.004 | − | 118.004i | 0.255421 | − | 0.255421i | ||||
\(463\) | 127.645 | − | 127.645i | 0.275691 | − | 0.275691i | −0.555695 | − | 0.831386i | \(-0.687548\pi\) |
0.831386 | + | 0.555695i | \(0.187548\pi\) | |||||||
\(464\) | 48.5303 | 0.104591 | ||||||||
\(465\) | − | 15.2982i | − | 0.0328994i | ||||||
\(466\) | −170.151 | + | 170.151i | −0.365131 | + | 0.365131i | ||||
\(467\) | − | 687.737i | − | 1.47267i | −0.676617 | − | 0.736335i | \(-0.736555\pi\) | ||
0.676617 | − | 0.736335i | \(-0.263445\pi\) | |||||||
\(468\) | −320.513 | + | 163.443i | −0.684857 | + | 0.349237i | ||||
\(469\) | −358.092 | −0.763522 | ||||||||
\(470\) | −155.528 | − | 155.528i | −0.330912 | − | 0.330912i | ||||
\(471\) | −230.824 | −0.490073 | ||||||||
\(472\) | − | 496.078i | − | 1.05101i | ||||||
\(473\) | −162.329 | − | 162.329i | −0.343190 | − | 0.343190i | ||||
\(474\) | 45.4384 | + | 45.4384i | 0.0958617 | + | 0.0958617i | ||||
\(475\) | −2.05267 | + | 2.05267i | −0.00432141 | + | 0.00432141i | ||||
\(476\) | −334.664 | + | 334.664i | −0.703077 | + | 0.703077i | ||||
\(477\) | −298.114 | −0.624977 | ||||||||
\(478\) | 0.0177872i | 3.72117e-5i | ||||||||
\(479\) | −318.642 | + | 318.642i | −0.665224 | + | 0.665224i | −0.956607 | − | 0.291383i | \(-0.905885\pi\) |
0.291383 | + | 0.956607i | \(0.405885\pi\) | |||||||
\(480\) | 652.254i | 1.35886i | ||||||||
\(481\) | −423.710 | − | 137.517i | −0.880895 | − | 0.285899i | ||||
\(482\) | 279.176 | 0.579203 | ||||||||
\(483\) | 162.329 | + | 162.329i | 0.336085 | + | 0.336085i | ||||
\(484\) | 213.763 | 0.441659 | ||||||||
\(485\) | − | 869.179i | − | 1.79212i | ||||||
\(486\) | 194.824 | + | 194.824i | 0.400873 | + | 0.400873i | ||||
\(487\) | 557.065 | + | 557.065i | 1.14387 | + | 1.14387i | 0.987736 | + | 0.156136i | \(0.0499038\pi\) |
0.156136 | + | 0.987736i | \(0.450096\pi\) | |||||||
\(488\) | −341.908 | + | 341.908i | −0.700632 | + | 0.700632i | ||||
\(489\) | 189.219 | − | 189.219i | 0.386951 | − | 0.386951i | ||||
\(490\) | −29.2456 | −0.0596848 | ||||||||
\(491\) | − | 400.698i | − | 0.816085i | −0.912963 | − | 0.408042i | \(-0.866212\pi\) | ||
0.912963 | − | 0.408042i | \(-0.133788\pi\) | |||||||
\(492\) | −66.9431 | + | 66.9431i | −0.136063 | + | 0.136063i | ||||
\(493\) | − | 127.698i | − | 0.259021i | ||||||
\(494\) | 42.5658 | − | 21.7061i | 0.0861657 | − | 0.0439394i | ||||
\(495\) | 317.465 | 0.641343 | ||||||||
\(496\) | −4.28540 | − | 4.28540i | −0.00863992 | − | 0.00863992i | ||||
\(497\) | −838.851 | −1.68783 | ||||||||
\(498\) | 215.873i | 0.433479i | ||||||||
\(499\) | 102.671 | + | 102.671i | 0.205754 | + | 0.205754i | 0.802460 | − | 0.596706i | \(-0.203524\pi\) |
−0.596706 | + | 0.802460i | \(0.703524\pi\) | |||||||
\(500\) | −289.914 | − | 289.914i | −0.579828 | − | 0.579828i | ||||
\(501\) | 571.127 | − | 571.127i | 1.13997 | − | 1.13997i | ||||
\(502\) | −76.6185 | + | 76.6185i | −0.152627 | + | 0.152627i | ||||
\(503\) | −46.2719 | −0.0919918 | −0.0459959 | − | 0.998942i | \(-0.514646\pi\) | ||||
−0.0459959 | + | 0.998942i | \(0.514646\pi\) | |||||||
\(504\) | 324.658i | 0.644162i | ||||||||
\(505\) | −375.737 | + | 375.737i | −0.744033 | + | 0.744033i | ||||
\(506\) | 52.6847i | 0.104120i | ||||||||
\(507\) | 413.088 | − | 569.355i | 0.814768 | − | 1.12299i | ||||
\(508\) | −336.320 | −0.662046 | ||||||||
\(509\) | −372.280 | − | 372.280i | −0.731396 | − | 0.731396i | 0.239500 | − | 0.970896i | \(-0.423016\pi\) |
−0.970896 | + | 0.239500i | \(0.923016\pi\) | |||||||
\(510\) | 380.684 | 0.746439 | ||||||||
\(511\) | 289.737i | 0.566999i | ||||||||
\(512\) | 324.897 | + | 324.897i | 0.634565 | + | 0.634565i | ||||
\(513\) | 8.89039 | + | 8.89039i | 0.0173302 | + | 0.0173302i | ||||
\(514\) | 90.9939 | − | 90.9939i | 0.177031 | − | 0.177031i | ||||
\(515\) | 126.895 | − | 126.895i | 0.246397 | − | 0.246397i | ||||
\(516\) | 421.868 | 0.817574 | ||||||||
\(517\) | 397.917i | 0.769665i | ||||||||
\(518\) | −129.015 | + | 129.015i | −0.249064 | + | 0.249064i | ||||
\(519\) | − | 330.408i | − | 0.636624i | ||||||
\(520\) | −180.046 | − | 353.072i | −0.346242 | − | 0.678985i | ||||
\(521\) | 27.1224 | 0.0520584 | 0.0260292 | − | 0.999661i | \(-0.491714\pi\) | ||||
0.0260292 | + | 0.999661i | \(0.491714\pi\) | |||||||
\(522\) | −28.1139 | − | 28.1139i | −0.0538580 | − | 0.0538580i | ||||
\(523\) | 473.851 | 0.906024 | 0.453012 | − | 0.891504i | \(-0.350349\pi\) | ||||
0.453012 | + | 0.891504i | \(0.350349\pi\) | |||||||
\(524\) | 856.846i | 1.63520i | ||||||||
\(525\) | 12.3772 | + | 12.3772i | 0.0235757 | + | 0.0235757i | ||||
\(526\) | −196.996 | − | 196.996i | −0.374517 | − | 0.374517i | ||||
\(527\) | −11.2762 | + | 11.2762i | −0.0213969 | + | 0.0213969i | ||||
\(528\) | 185.075 | − | 185.075i | 0.350520 | − | 0.350520i | ||||
\(529\) | 456.526 | 0.862998 | ||||||||
\(530\) | − | 149.057i | − | 0.281240i | ||||||
\(531\) | 485.088 | − | 485.088i | 0.913536 | − | 0.913536i | ||||
\(532\) | 96.3246i | 0.181061i | ||||||||
\(533\) | 27.4562 | − | 84.5964i | 0.0515126 | − | 0.158718i | ||||
\(534\) | −43.0092 | −0.0805416 | ||||||||
\(535\) | −15.8641 | − | 15.8641i | −0.0296524 | − | 0.0296524i | ||||
\(536\) | 332.722 | 0.620751 | ||||||||
\(537\) | 1324.97i | 2.46736i | ||||||||
\(538\) | −129.048 | − | 129.048i | −0.239867 | − | 0.239867i | ||||
\(539\) | 37.4121 | + | 37.4121i | 0.0694102 | + | 0.0694102i | ||||
\(540\) | 33.4715 | − | 33.4715i | 0.0619843 | − | 0.0619843i | ||||
\(541\) | 531.379 | − | 531.379i | 0.982216 | − | 0.982216i | −0.0176283 | − | 0.999845i | \(-0.505612\pi\) |
0.999845 | + | 0.0176283i | \(0.00561156\pi\) | |||||||
\(542\) | 45.4128 | 0.0837874 | ||||||||
\(543\) | 991.223i | 1.82546i | ||||||||
\(544\) | 480.770 | − | 480.770i | 0.883768 | − | 0.883768i | ||||
\(545\) | 865.017i | 1.58719i | ||||||||
\(546\) | −130.884 | − | 256.664i | −0.239714 | − | 0.470081i | ||||
\(547\) | −716.223 | −1.30937 | −0.654683 | − | 0.755903i | \(-0.727198\pi\) | ||||
−0.654683 | + | 0.755903i | \(0.727198\pi\) | |||||||
\(548\) | −582.701 | − | 582.701i | −1.06332 | − | 1.06332i | ||||
\(549\) | −668.666 | −1.21797 | ||||||||
\(550\) | 4.01709i | 0.00730381i | ||||||||
\(551\) | −18.3772 | − | 18.3772i | −0.0333525 | − | 0.0333525i | ||||
\(552\) | −150.828 | − | 150.828i | −0.273240 | − | 0.273240i | ||||
\(553\) | 86.0569 | − | 86.0569i | 0.155618 | − | 0.155618i | ||||
\(554\) | −65.1182 | + | 65.1182i | −0.117542 | + | 0.117542i | ||||
\(555\) | −722.337 | −1.30151 | ||||||||
\(556\) | − | 450.346i | − | 0.809975i | ||||||
\(557\) | −248.577 | + | 248.577i | −0.446278 | + | 0.446278i | −0.894115 | − | 0.447837i | \(-0.852194\pi\) |
0.447837 | + | 0.894115i | \(0.352194\pi\) | |||||||
\(558\) | 4.96512i | 0.00889806i | ||||||||
\(559\) | −353.072 | + | 180.046i | −0.631614 | + | 0.322086i | ||||
\(560\) | 274.004 | 0.489293 | ||||||||
\(561\) | −486.986 | − | 486.986i | −0.868069 | − | 0.868069i | ||||
\(562\) | −203.220 | −0.361601 | ||||||||
\(563\) | − | 708.329i | − | 1.25813i | −0.777352 | − | 0.629066i | \(-0.783437\pi\) | ||
0.777352 | − | 0.629066i | \(-0.216563\pi\) | |||||||
\(564\) | −517.063 | − | 517.063i | −0.916778 | − | 0.916778i | ||||
\(565\) | 245.465 | + | 245.465i | 0.434451 | + | 0.434451i | ||||
\(566\) | −157.606 | + | 157.606i | −0.278455 | + | 0.278455i | ||||
\(567\) | 396.831 | − | 396.831i | 0.699878 | − | 0.699878i | ||||
\(568\) | 779.421 | 1.37222 | ||||||||
\(569\) | − | 349.394i | − | 0.614050i | −0.951701 | − | 0.307025i | \(-0.900667\pi\) | ||
0.951701 | − | 0.307025i | \(-0.0993335\pi\) | |||||||
\(570\) | 54.7851 | − | 54.7851i | 0.0961141 | − | 0.0961141i | ||||
\(571\) | 906.285i | 1.58719i | 0.608447 | + | 0.793594i | \(0.291793\pi\) | ||||
−0.608447 | + | 0.793594i | \(0.708207\pi\) | |||||||
\(572\) | −100.465 | + | 309.548i | −0.175639 | + | 0.541168i | ||||
\(573\) | 15.4256 | 0.0269208 | ||||||||
\(574\) | −25.7587 | − | 25.7587i | −0.0448758 | − | 0.0448758i | ||||
\(575\) | −5.52599 | −0.00961041 | ||||||||
\(576\) | 66.3772i | 0.115238i | ||||||||
\(577\) | 357.842 | + | 357.842i | 0.620177 | + | 0.620177i | 0.945577 | − | 0.325400i | \(-0.105499\pi\) |
−0.325400 | + | 0.945577i | \(0.605499\pi\) | |||||||
\(578\) | −112.649 | − | 112.649i | −0.194895 | − | 0.194895i | ||||
\(579\) | −179.544 | + | 179.544i | −0.310093 | + | 0.310093i | ||||
\(580\) | −69.1886 | + | 69.1886i | −0.119291 | + | 0.119291i | ||||
\(581\) | 408.846 | 0.703694 | ||||||||
\(582\) | 587.083i | 1.00873i | ||||||||
\(583\) | −190.680 | + | 190.680i | −0.327066 | + | 0.327066i | ||||
\(584\) | − | 269.210i | − | 0.460976i | ||||||
\(585\) | 169.193 | − | 521.307i | 0.289219 | − | 0.891123i | ||||
\(586\) | −279.127 | −0.476327 | ||||||||
\(587\) | 405.311 | + | 405.311i | 0.690479 | + | 0.690479i | 0.962337 | − | 0.271858i | \(-0.0876383\pi\) |
−0.271858 | + | 0.962337i | \(0.587638\pi\) | |||||||
\(588\) | −97.2285 | −0.165355 | ||||||||
\(589\) | 3.24555i | 0.00551028i | ||||||||
\(590\) | 242.544 | + | 242.544i | 0.411091 | + | 0.411091i | ||||
\(591\) | −524.840 | − | 524.840i | −0.888053 | − | 0.888053i | ||||
\(592\) | −202.344 | + | 202.344i | −0.341798 | + | 0.341798i | ||||
\(593\) | 550.285 | − | 550.285i | 0.927967 | − | 0.927967i | −0.0696070 | − | 0.997574i | \(-0.522175\pi\) |
0.997574 | + | 0.0696070i | \(0.0221745\pi\) | |||||||
\(594\) | 17.3986 | 0.0292906 | ||||||||
\(595\) | − | 720.986i | − | 1.21174i | ||||||
\(596\) | 120.413 | − | 120.413i | 0.202035 | − | 0.202035i | ||||
\(597\) | 633.670i | 1.06142i | ||||||||
\(598\) | 86.5132 | + | 28.0783i | 0.144671 | + | 0.0469537i | ||||
\(599\) | 235.228 | 0.392702 | 0.196351 | − | 0.980534i | \(-0.437091\pi\) | ||||
0.196351 | + | 0.980534i | \(0.437091\pi\) | |||||||
\(600\) | −11.5003 | − | 11.5003i | −0.0191672 | − | 0.0191672i | ||||
\(601\) | −559.298 | −0.930612 | −0.465306 | − | 0.885150i | \(-0.654056\pi\) | ||||
−0.465306 | + | 0.885150i | \(0.654056\pi\) | |||||||
\(602\) | 162.329i | 0.269649i | ||||||||
\(603\) | 325.351 | + | 325.351i | 0.539554 | + | 0.539554i | ||||
\(604\) | 249.932 | + | 249.932i | 0.413795 | + | 0.413795i | ||||
\(605\) | −230.261 | + | 230.261i | −0.380596 | + | 0.380596i | ||||
\(606\) | 253.789 | − | 253.789i | 0.418794 | − | 0.418794i | ||||
\(607\) | −507.912 | −0.836757 | −0.418379 | − | 0.908273i | \(-0.637402\pi\) | ||||
−0.418379 | + | 0.908273i | \(0.637402\pi\) | |||||||
\(608\) | − | 138.377i | − | 0.227594i | ||||||
\(609\) | −110.811 | + | 110.811i | −0.181956 | + | 0.181956i | ||||
\(610\) | − | 334.333i | − | 0.548087i | ||||||
\(611\) | 653.416 | + | 212.070i | 1.06942 | + | 0.347086i | ||||
\(612\) | 608.131 | 0.993678 | ||||||||
\(613\) | −231.540 | − | 231.540i | −0.377715 | − | 0.377715i | 0.492562 | − | 0.870277i | \(-0.336060\pi\) |
−0.870277 | + | 0.492562i | \(0.836060\pi\) | |||||||
\(614\) | 255.334 | 0.415853 | ||||||||
\(615\) | − | 144.219i | − | 0.234503i | ||||||
\(616\) | 207.658 | + | 207.658i | 0.337107 | + | 0.337107i | ||||
\(617\) | −271.412 | − | 271.412i | −0.439890 | − | 0.439890i | 0.452085 | − | 0.891975i | \(-0.350680\pi\) |
−0.891975 | + | 0.452085i | \(0.850680\pi\) | |||||||
\(618\) | −85.7103 | + | 85.7103i | −0.138690 | + | 0.138690i | ||||
\(619\) | −235.048 | + | 235.048i | −0.379723 | + | 0.379723i | −0.871002 | − | 0.491279i | \(-0.836529\pi\) |
0.491279 | + | 0.871002i | \(0.336529\pi\) | |||||||
\(620\) | 12.2192 | 0.0197084 | ||||||||
\(621\) | 23.9338i | 0.0385408i | ||||||||
\(622\) | −198.566 | + | 198.566i | −0.319238 | + | 0.319238i | ||||
\(623\) | 81.4562i | 0.130748i | ||||||||
\(624\) | −205.274 | − | 402.546i | −0.328965 | − | 0.645105i | ||||
\(625\) | 640.806 | 1.02529 | ||||||||
\(626\) | 254.840 | + | 254.840i | 0.407092 | + | 0.407092i | ||||
\(627\) | −140.167 | −0.223551 | ||||||||
\(628\) | − | 184.367i | − | 0.293578i | ||||||
\(629\) | 532.427 | + | 532.427i | 0.846466 | + | 0.846466i | ||||
\(630\) | −158.732 | − | 158.732i | −0.251956 | − | 0.251956i | ||||
\(631\) | −95.4630 | + | 95.4630i | −0.151288 | + | 0.151288i | −0.778693 | − | 0.627405i | \(-0.784117\pi\) |
0.627405 | + | 0.778693i | \(0.284117\pi\) | |||||||
\(632\) | −79.9602 | + | 79.9602i | −0.126519 | + | 0.126519i | ||||
\(633\) | 198.018 | 0.312824 | ||||||||
\(634\) | 177.991i | 0.280744i | ||||||||
\(635\) | 362.276 | − | 362.276i | 0.570514 | − | 0.570514i | ||||
\(636\) | − | 495.548i | − | 0.779164i | ||||||
\(637\) | 81.3729 | − | 41.4954i | 0.127744 | − | 0.0651419i | ||||
\(638\) | −35.9644 | −0.0563706 | ||||||||
\(639\) | 762.153 | + | 762.153i | 1.19273 | + | 1.19273i | ||||
\(640\) | −660.013 | −1.03127 | ||||||||
\(641\) | − | 904.710i | − | 1.41140i | −0.708508 | − | 0.705702i | \(-0.750632\pi\) | ||
0.708508 | − | 0.705702i | \(-0.249368\pi\) | |||||||
\(642\) | 10.7153 | + | 10.7153i | 0.0166905 | + | 0.0166905i | ||||
\(643\) | −108.312 | − | 108.312i | −0.168447 | − | 0.168447i | 0.617849 | − | 0.786297i | \(-0.288004\pi\) |
−0.786297 | + | 0.617849i | \(0.788004\pi\) | |||||||
\(644\) | −129.658 | + | 129.658i | −0.201332 | + | 0.201332i | ||||
\(645\) | −454.427 | + | 454.427i | −0.704539 | + | 0.704539i | ||||
\(646\) | −80.7630 | −0.125020 | ||||||||
\(647\) | 306.474i | 0.473685i | 0.971548 | + | 0.236842i | \(0.0761125\pi\) | ||||
−0.971548 | + | 0.236842i | \(0.923888\pi\) | |||||||
\(648\) | −368.717 | + | 368.717i | −0.569008 | + | 0.569008i | ||||
\(649\) | − | 620.544i | − | 0.956154i | ||||||
\(650\) | 6.59644 | + | 2.14091i | 0.0101484 | + | 0.00329371i | ||||
\(651\) | 19.5701 | 0.0300616 | ||||||||
\(652\) | 151.136 | + | 151.136i | 0.231804 | + | 0.231804i | ||||
\(653\) | −1009.69 | −1.54624 | −0.773118 | − | 0.634262i | \(-0.781304\pi\) | ||||
−0.773118 | + | 0.634262i | \(0.781304\pi\) | |||||||
\(654\) | − | 584.271i | − | 0.893381i | ||||||
\(655\) | −922.975 | − | 922.975i | −1.40912 | − | 1.40912i | ||||
\(656\) | −40.3993 | − | 40.3993i | −0.0615843 | − | 0.0615843i | ||||
\(657\) | 263.246 | − | 263.246i | 0.400678 | − | 0.400678i | ||||
\(658\) | 198.958 | − | 198.958i | 0.302368 | − | 0.302368i | ||||
\(659\) | −211.009 | −0.320196 | −0.160098 | − | 0.987101i | \(-0.551181\pi\) | ||||
−0.160098 | + | 0.987101i | \(0.551181\pi\) | |||||||
\(660\) | 527.715i | 0.799568i | ||||||||
\(661\) | −61.5922 | + | 61.5922i | −0.0931803 | + | 0.0931803i | −0.752160 | − | 0.658980i | \(-0.770988\pi\) |
0.658980 | + | 0.752160i | \(0.270988\pi\) | |||||||
\(662\) | − | 227.786i | − | 0.344087i | ||||||
\(663\) | −1059.22 | + | 540.138i | −1.59761 | + | 0.814687i | ||||
\(664\) | −379.881 | −0.572110 | ||||||||
\(665\) | −103.759 | − | 103.759i | −0.156028 | − | 0.156028i | ||||
\(666\) | 234.438 | 0.352010 | ||||||||
\(667\) | − | 49.4733i | − | 0.0741729i | ||||||
\(668\) | 456.179 | + | 456.179i | 0.682902 | + | 0.682902i | ||||
\(669\) | 159.107 | + | 159.107i | 0.237828 | + | 0.237828i | ||||
\(670\) | −162.675 | + | 162.675i | −0.242799 | + | 0.242799i | ||||
\(671\) | −427.693 | + | 427.693i | −0.637396 | + | 0.637396i | ||||
\(672\) | −834.390 | −1.24165 | ||||||||
\(673\) | 105.500i | 0.156760i | 0.996924 | + | 0.0783801i | \(0.0249748\pi\) | ||||
−0.996924 | + | 0.0783801i | \(0.975025\pi\) | |||||||
\(674\) | 4.25658 | − | 4.25658i | 0.00631541 | − | 0.00631541i | ||||
\(675\) | 1.82490i | 0.00270356i | ||||||||
\(676\) | 454.764 | + | 329.947i | 0.672727 | + | 0.488088i | ||||
\(677\) | −215.969 | −0.319009 | −0.159505 | − | 0.987197i | \(-0.550990\pi\) | ||||
−0.159505 | + | 0.987197i | \(0.550990\pi\) | |||||||
\(678\) | −165.798 | − | 165.798i | −0.244540 | − | 0.244540i | ||||
\(679\) | 1111.89 | 1.63754 | ||||||||
\(680\) | 669.907i | 0.985158i | ||||||||
\(681\) | −186.189 | − | 186.189i | −0.273405 | − | 0.273405i | ||||
\(682\) | 3.17579 | + | 3.17579i | 0.00465659 | + | 0.00465659i | ||||
\(683\) | 672.956 | − | 672.956i | 0.985294 | − | 0.985294i | −0.0145993 | − | 0.999893i | \(-0.504647\pi\) |
0.999893 | + | 0.0145993i | \(0.00464727\pi\) | |||||||
\(684\) | 87.5174 | − | 87.5174i | 0.127949 | − | 0.127949i | ||||
\(685\) | 1255.35 | 1.83262 | ||||||||
\(686\) | − | 298.315i | − | 0.434862i | ||||||
\(687\) | 697.738 | − | 697.738i | 1.01563 | − | 1.01563i | ||||
\(688\) | 254.592i | 0.370047i | ||||||||
\(689\) | 211.491 | + | 414.737i | 0.306954 | + | 0.601940i | ||||
\(690\) | 147.487 | 0.213749 | ||||||||
\(691\) | −563.105 | − | 563.105i | −0.814913 | − | 0.814913i | 0.170453 | − | 0.985366i | \(-0.445477\pi\) |
−0.985366 | + | 0.170453i | \(0.945477\pi\) | |||||||
\(692\) | 263.908 | 0.381370 | ||||||||
\(693\) | 406.114i | 0.586023i | ||||||||
\(694\) | −89.9363 | − | 89.9363i | −0.129591 | − | 0.129591i | ||||
\(695\) | 485.103 | + | 485.103i | 0.697990 | + | 0.697990i | ||||
\(696\) | 102.961 | − | 102.961i | 0.147932 | − | 0.147932i | ||||
\(697\) | −106.302 | + | 106.302i | −0.152514 | + | 0.152514i | ||||
\(698\) | 256.188 | 0.367031 | ||||||||
\(699\) | − | 1218.67i | − | 1.74345i | ||||||
\(700\) | −9.88612 | + | 9.88612i | −0.0141230 | + | 0.0141230i | ||||
\(701\) | − | 179.934i | − | 0.256682i | −0.991730 | − | 0.128341i | \(-0.959035\pi\) | ||
0.991730 | − | 0.128341i | \(-0.0409651\pi\) | |||||||
\(702\) | 9.27258 | − | 28.5701i | 0.0132088 | − | 0.0406982i | ||||
\(703\) | 153.246 | 0.217988 | ||||||||
\(704\) | 42.4562 | + | 42.4562i | 0.0603071 | + | 0.0603071i | ||||
\(705\) | 1113.94 | 1.58005 | ||||||||
\(706\) | 385.504i | 0.546040i | ||||||||
\(707\) | −480.658 | − | 480.658i | −0.679855 | − | 0.679855i | ||||
\(708\) | 806.350 | + | 806.350i | 1.13891 | + | 1.13891i | ||||
\(709\) | −291.315 | + | 291.315i | −0.410882 | + | 0.410882i | −0.882046 | − | 0.471164i | \(-0.843834\pi\) |
0.471164 | + | 0.882046i | \(0.343834\pi\) | |||||||
\(710\) | −381.077 | + | 381.077i | −0.536727 | + | 0.536727i | ||||
\(711\) | −156.377 | −0.219940 | ||||||||
\(712\) | − | 75.6854i | − | 0.106300i | ||||||
\(713\) | −4.36868 | + | 4.36868i | −0.00612718 | + | 0.00612718i | ||||
\(714\) | 486.986i | 0.682054i | ||||||||
\(715\) | −225.219 | − | 441.658i | −0.314992 | − | 0.617703i | ||||
\(716\) | −1058.30 | −1.47808 | ||||||||
\(717\) | −0.0636984 | − | 0.0636984i | −8.88401e−5 | − | 8.88401e-5i | ||||
\(718\) | 154.333 | 0.214949 | ||||||||
\(719\) | 487.565i | 0.678116i | 0.940766 | + | 0.339058i | \(0.110108\pi\) | ||||
−0.940766 | + | 0.339058i | \(0.889892\pi\) | |||||||
\(720\) | −248.952 | − | 248.952i | −0.345766 | − | 0.345766i | ||||
\(721\) | 162.329 | + | 162.329i | 0.225144 | + | 0.225144i | ||||
\(722\) | 198.168 | − | 198.168i | 0.274471 | − | 0.274471i | ||||
\(723\) | −999.767 | + | 999.767i | −1.38280 | + | 1.38280i | ||||
\(724\) | −791.725 | −1.09354 | ||||||||
\(725\) | − | 3.77223i | − | 0.00520308i | ||||||
\(726\) | 155.528 | − | 155.528i | 0.214227 | − | 0.214227i | ||||
\(727\) | − | 277.337i | − | 0.381482i | −0.981640 | − | 0.190741i | \(-0.938911\pi\) | ||
0.981640 | − | 0.190741i | \(-0.0610891\pi\) | |||||||
\(728\) | 451.664 | − | 230.322i | 0.620418 | − | 0.316376i | ||||
\(729\) | −615.780 | −0.844691 | ||||||||
\(730\) | 131.623 | + | 131.623i | 0.180305 | + | 0.180305i | ||||
\(731\) | 669.907 | 0.916426 | ||||||||
\(732\) | − | 1111.51i | − | 1.51845i | ||||||
\(733\) | −235.559 | − | 235.559i | −0.321363 | − | 0.321363i | 0.527927 | − | 0.849290i | \(-0.322970\pi\) |
−0.849290 | + | 0.527927i | \(0.822970\pi\) | |||||||
\(734\) | 164.123 | + | 164.123i | 0.223601 | + | 0.223601i | ||||
\(735\) | 104.732 | − | 104.732i | 0.142493 | − | 0.142493i | ||||
\(736\) | 186.263 | − | 186.263i | 0.253074 | − | 0.253074i | ||||
\(737\) | 416.202 | 0.564725 | ||||||||
\(738\) | 46.8071i | 0.0634243i | ||||||||
\(739\) | −667.732 | + | 667.732i | −0.903561 | + | 0.903561i | −0.995742 | − | 0.0921811i | \(-0.970616\pi\) |
0.0921811 | + | 0.995742i | \(0.470616\pi\) | |||||||
\(740\) | − | 576.956i | − | 0.779670i | ||||||
\(741\) | −74.7018 | + | 230.167i | −0.100812 | + | 0.310616i | ||||
\(742\) | 190.680 | 0.256981 | ||||||||
\(743\) | 335.358 | + | 335.358i | 0.451356 | + | 0.451356i | 0.895804 | − | 0.444448i | \(-0.146600\pi\) |
−0.444448 | + | 0.895804i | \(0.646600\pi\) | |||||||
\(744\) | −18.1836 | −0.0244404 | ||||||||
\(745\) | 259.412i | 0.348204i | ||||||||
\(746\) | −377.088 | − | 377.088i | −0.505479 | − | 0.505479i | ||||
\(747\) | −371.465 | − | 371.465i | −0.497275 | − | 0.497275i | ||||
\(748\) | 388.973 | − | 388.973i | 0.520017 | − | 0.520017i | ||||
\(749\) | 20.2939 | − | 20.2939i | 0.0270947 | − | 0.0270947i | ||||
\(750\) | −421.868 | −0.562491 | ||||||||
\(751\) | 1300.24i | 1.73134i | 0.500615 | + | 0.865670i | \(0.333107\pi\) | ||||
−0.500615 | + | 0.865670i | \(0.666893\pi\) | |||||||
\(752\) | 312.041 | − | 312.041i | 0.414948 | − | 0.414948i | ||||
\(753\) | − | 548.763i | − | 0.728769i | ||||||
\(754\) | −19.1672 | + | 59.0569i | −0.0254207 | + | 0.0783249i | ||||
\(755\) | −538.443 | −0.713169 | ||||||||
\(756\) | 42.8181 | + | 42.8181i | 0.0566378 | + | 0.0566378i | ||||
\(757\) | 1155.45 | 1.52636 | 0.763178 | − | 0.646188i | \(-0.223638\pi\) | ||||
0.763178 | + | 0.646188i | \(0.223638\pi\) | |||||||
\(758\) | − | 498.969i | − | 0.658270i | ||||||
\(759\) | −188.671 | − | 188.671i | −0.248579 | − | 0.248579i | ||||
\(760\) | 96.4078 | + | 96.4078i | 0.126852 | + | 0.126852i | ||||
\(761\) | −205.412 | + | 205.412i | −0.269924 | + | 0.269924i | −0.829069 | − | 0.559146i | \(-0.811129\pi\) |
0.559146 | + | 0.829069i | \(0.311129\pi\) | |||||||
\(762\) | −244.698 | + | 244.698i | −0.321125 | + | 0.321125i | ||||
\(763\) | −1106.57 | −1.45028 | ||||||||
\(764\) | 12.3210i | 0.0161269i | ||||||||
\(765\) | −655.065 | + | 655.065i | −0.856295 | + | 0.856295i | ||||
\(766\) | 154.280i | 0.201410i | ||||||||
\(767\) | −1018.99 | − | 330.719i | −1.32854 | − | 0.431185i | ||||
\(768\) | 313.048 | 0.407614 | ||||||||
\(769\) | 62.0527 | + | 62.0527i | 0.0806927 | + | 0.0806927i | 0.746301 | − | 0.665608i | \(-0.231828\pi\) |
−0.665608 | + | 0.746301i | \(0.731828\pi\) | |||||||
\(770\) | −203.057 | −0.263710 | ||||||||
\(771\) | 651.724i | 0.845297i | ||||||||
\(772\) | −143.408 | − | 143.408i | −0.185761 | − | 0.185761i | ||||
\(773\) | −318.813 | − | 318.813i | −0.412436 | − | 0.412436i | 0.470150 | − | 0.882586i | \(-0.344200\pi\) |
−0.882586 | + | 0.470150i | \(0.844200\pi\) | |||||||
\(774\) | 147.487 | − | 147.487i | 0.190551 | − | 0.190551i | ||||
\(775\) | −0.333102 | + | 0.333102i | −0.000429809 | + | 0.000429809i | ||||
\(776\) | −1033.12 | −1.33134 | ||||||||
\(777\) | − | 924.043i | − | 1.18925i | ||||||
\(778\) | 296.579 | − | 296.579i | 0.381207 | − | 0.381207i | ||||
\(779\) | 30.5964i | 0.0392766i | ||||||||
\(780\) | 866.557 | + | 281.246i | 1.11097 | + | 0.360571i | ||||
\(781\) | 974.977 | 1.24837 | ||||||||
\(782\) | −108.711 | − | 108.711i | −0.139017 | − | 0.139017i | ||||
\(783\) | −16.3381 | −0.0208660 | ||||||||
\(784\) | − | 58.6761i | − | 0.0748420i | ||||||
\(785\) | 198.596 | + | 198.596i | 0.252989 | + | 0.252989i | ||||
\(786\) | 623.419 | + | 623.419i | 0.793154 | + | 0.793154i | ||||
\(787\) | 634.566 | − | 634.566i | 0.806310 | − | 0.806310i | −0.177763 | − | 0.984073i | \(-0.556886\pi\) |
0.984073 | + | 0.177763i | \(0.0568862\pi\) | |||||||
\(788\) | 419.207 | − | 419.207i | 0.531989 | − | 0.531989i | ||||
\(789\) | 1410.94 | 1.78826 | ||||||||
\(790\) | − | 78.1886i | − | 0.0989729i | ||||||
\(791\) | −314.009 | + | 314.009i | −0.396977 | + | 0.396977i | ||||
\(792\) | − | 377.342i | − | 0.476442i | ||||||
\(793\) | 474.372 | + | 930.250i | 0.598200 | + | 1.17308i | ||||
\(794\) | −165.115 | −0.207953 | ||||||||
\(795\) | 533.794 | + | 533.794i | 0.671438 | + | 0.671438i | ||||
\(796\) | −506.135 | −0.635847 | ||||||||
\(797\) | 407.026i | 0.510698i | 0.966849 | + | 0.255349i | \(0.0821904\pi\) | ||||
−0.966849 | + | 0.255349i | \(0.917810\pi\) | |||||||
\(798\) | 70.0833 | + | 70.0833i | 0.0878237 | + | 0.0878237i | ||||
\(799\) | −821.072 | − | 821.072i | −1.02762 | − | 1.02762i | ||||
\(800\) | 14.2021 | − | 14.2021i | 0.0177527 | − | 0.0177527i | ||||
\(801\) | 74.0085 | − | 74.0085i | 0.0923952 | − | 0.0923952i | ||||
\(802\) | 167.715 | 0.209120 | ||||||||
\(803\) | − | 336.754i | − | 0.419370i | ||||||
\(804\) | −540.824 | + | 540.824i | −0.672666 | + | 0.672666i | ||||
\(805\) | − | 279.329i | − | 0.346992i | ||||||
\(806\) | 6.90748 | − | 3.52241i | 0.00857008 | − | 0.00437023i | ||||
\(807\) | 924.280 | 1.14533 | ||||||||
\(808\) | 446.605 | + | 446.605i | 0.552729 | + | 0.552729i | ||||
\(809\) | −647.641 | −0.800545 | −0.400272 | − | 0.916396i | \(-0.631084\pi\) | ||||
−0.400272 | + | 0.916396i | \(0.631084\pi\) | |||||||
\(810\) | − | 360.548i | − | 0.445121i | ||||||
\(811\) | 850.386 | + | 850.386i | 1.04856 | + | 1.04856i | 0.998759 | + | 0.0498055i | \(0.0158601\pi\) |
0.0498055 | + | 0.998759i | \(0.484140\pi\) | |||||||
\(812\) | −88.5089 | − | 88.5089i | −0.109001 | − | 0.109001i | ||||
\(813\) | −162.630 | + | 162.630i | −0.200036 | + | 0.200036i | ||||
\(814\) | 149.952 | − | 149.952i | 0.184216 | − | 0.184216i | ||||
\(815\) | −325.601 | −0.399510 | ||||||||
\(816\) | 763.777i | 0.936001i | ||||||||
\(817\) | 96.4078 | − | 96.4078i | 0.118002 | − | 0.118002i | ||||
\(818\) | 106.767i | 0.130521i | ||||||||
\(819\) | 666.877 | + | 216.438i | 0.814257 | + | 0.264272i | ||||
\(820\) | 115.193 | 0.140479 | ||||||||
\(821\) | 330.186 | + | 330.186i | 0.402176 | + | 0.402176i | 0.878999 | − | 0.476824i | \(-0.158212\pi\) |
−0.476824 | + | 0.878999i | \(0.658212\pi\) | |||||||
\(822\) | −847.917 | −1.03153 | ||||||||
\(823\) | − | 507.579i | − | 0.616742i | −0.951266 | − | 0.308371i | \(-0.900216\pi\) | ||
0.951266 | − | 0.308371i | \(-0.0997838\pi\) | |||||||
\(824\) | −150.828 | − | 150.828i | −0.183044 | − | 0.183044i | ||||
\(825\) | −14.3858 | − | 14.3858i | −0.0174373 | − | 0.0174373i | ||||
\(826\) | −310.272 | + | 310.272i | −0.375632 | + | 0.375632i | ||||
\(827\) | −488.452 | + | 488.452i | −0.590631 | + | 0.590631i | −0.937802 | − | 0.347171i | \(-0.887142\pi\) |
0.347171 | + | 0.937802i | \(0.387142\pi\) | |||||||
\(828\) | 235.606 | 0.284548 | ||||||||
\(829\) | − | 1391.89i | − | 1.67900i | −0.543361 | − | 0.839499i | \(-0.682848\pi\) | ||
0.543361 | − | 0.839499i | \(-0.317152\pi\) | |||||||
\(830\) | 185.732 | − | 185.732i | 0.223774 | − | 0.223774i | ||||
\(831\) | − | 466.394i | − | 0.561245i | ||||||
\(832\) | 92.3441 | − | 47.0900i | 0.110991 | − | 0.0565986i | ||||
\(833\) | −154.394 | −0.185347 | ||||||||
\(834\) | −327.660 | − | 327.660i | −0.392878 | − | 0.392878i | ||||
\(835\) | −982.772 | −1.17697 | ||||||||
\(836\) | − | 111.956i | − | 0.133919i | ||||||
\(837\) | 1.44271 | + | 1.44271i | 0.00172367 | + | 0.00172367i | ||||
\(838\) | −48.3698 | − | 48.3698i | −0.0577205 | − | 0.0577205i | ||||
\(839\) | −128.794 | + | 128.794i | −0.153508 | + | 0.153508i | −0.779683 | − | 0.626174i | \(-0.784620\pi\) |
0.626174 | + | 0.779683i | \(0.284620\pi\) | |||||||
\(840\) | 581.322 | − | 581.322i | 0.692050 | − | 0.692050i | ||||
\(841\) | −807.228 | −0.959843 | ||||||||
\(842\) | 79.3993i | 0.0942984i | ||||||||
\(843\) | 727.759 | − | 727.759i | 0.863296 | − | 0.863296i | ||||
\(844\) | 158.164i | 0.187398i | ||||||||
\(845\) | −845.274 | + | 134.449i | −1.00032 | + | 0.159112i | ||||
\(846\) | −361.535 | −0.427346 | ||||||||
\(847\) | −294.559 | − | 294.559i | −0.347768 | − | 0.347768i | ||||
\(848\) | 299.057 | 0.352661 | ||||||||
\(849\) | − | 1128.82i | − | 1.32958i | ||||||
\(850\) | −8.28898 | − | 8.28898i | −0.00975174 | − | 0.00975174i | ||||
\(851\) | 206.276 | + | 206.276i | 0.242393 | + | 0.242393i | ||||
\(852\) | −1266.91 | + | 1266.91i | −1.48698 | + | 1.48698i | ||||
\(853\) | −485.546 | + | 485.546i | −0.569221 | + | 0.569221i | −0.931910 | − | 0.362689i | \(-0.881859\pi\) |
0.362689 | + | 0.931910i | \(0.381859\pi\) | |||||||
\(854\) | 427.693 | 0.500811 | ||||||||
\(855\) | 188.544i | 0.220519i | ||||||||
\(856\) | −18.8562 | + | 18.8562i | −0.0220283 | + | 0.0220283i | ||||
\(857\) | 1245.24i | 1.45302i | 0.687157 | + | 0.726509i | \(0.258859\pi\) | ||||
−0.687157 | + | 0.726509i | \(0.741141\pi\) | |||||||
\(858\) | 152.123 | + | 298.315i | 0.177300 | + | 0.347687i | ||||
\(859\) | 1194.94 | 1.39108 | 0.695540 | − | 0.718487i | \(-0.255165\pi\) | ||||
0.695540 | + | 0.718487i | \(0.255165\pi\) | |||||||
\(860\) | −362.967 | − | 362.967i | −0.422055 | − | 0.422055i | ||||
\(861\) | 184.491 | 0.214275 | ||||||||
\(862\) | 546.227i | 0.633674i | ||||||||
\(863\) | −604.195 | − | 604.195i | −0.700111 | − | 0.700111i | 0.264324 | − | 0.964434i | \(-0.414851\pi\) |
−0.964434 | + | 0.264324i | \(0.914851\pi\) | |||||||
\(864\) | −61.5114 | − | 61.5114i | −0.0711937 | − | 0.0711937i | ||||
\(865\) | −284.276 | + | 284.276i | −0.328643 | + | 0.328643i | ||||
\(866\) | 70.9804 | − | 70.9804i | 0.0819635 | − | 0.0819635i | ||||
\(867\) | 806.824 | 0.930593 | ||||||||
\(868\) | 15.6313i | 0.0180084i | ||||||||
\(869\) | −100.022 | + | 100.022i | −0.115100 | + | 0.115100i | ||||
\(870\) | 100.680i | 0.115724i | ||||||||
\(871\) | 221.815 | − | 683.443i | 0.254667 | − | 0.784664i | ||||
\(872\) | 1028.17 | 1.17909 | ||||||||
\(873\) | −1010.23 | − | 1010.23i | −1.15719 | − | 1.15719i | ||||
\(874\) | −31.2897 | −0.0358005 | ||||||||
\(875\) | 798.986i | 0.913127i | ||||||||
\(876\) | 437.587 | + | 437.587i | 0.499529 | + | 0.499529i | ||||
\(877\) | −1065.53 | − | 1065.53i | −1.21497 | − | 1.21497i | −0.969370 | − | 0.245603i | \(-0.921014\pi\) |
−0.245603 | − | 0.969370i | \(-0.578986\pi\) | |||||||
\(878\) | −18.1836 | + | 18.1836i | −0.0207103 | + | 0.0207103i | ||||
\(879\) | 999.594 | − | 999.594i | 1.13719 | − | 1.13719i | ||||
\(880\) | −318.469 | −0.361897 | ||||||||
\(881\) | 821.315i | 0.932253i | 0.884718 | + | 0.466126i | \(0.154351\pi\) | ||||
−0.884718 | + | 0.466126i | \(0.845649\pi\) | |||||||
\(882\) | −33.9915 | + | 33.9915i | −0.0385391 | + | 0.0385391i | ||||
\(883\) | 1091.97i | 1.23666i | 0.785920 | + | 0.618329i | \(0.212190\pi\) | ||||
−0.785920 | + | 0.618329i | \(0.787810\pi\) | |||||||
\(884\) | −431.427 | − | 846.033i | −0.488039 | − | 0.957051i | ||||
\(885\) | −1737.17 | −1.96290 | ||||||||
\(886\) | 329.722 | + | 329.722i | 0.372147 | + | 0.372147i | ||||
\(887\) | 1478.73 | 1.66711 | 0.833555 | − | 0.552436i | \(-0.186302\pi\) | ||||
0.833555 | + | 0.552436i | \(0.186302\pi\) | |||||||
\(888\) | 858.579i | 0.966868i | ||||||||
\(889\) | 463.438 | + | 463.438i | 0.521303 | + | 0.521303i | ||||
\(890\) | 37.0043 | + | 37.0043i | 0.0415778 | + | 0.0415778i | ||||
\(891\) | −461.228 | + | 461.228i | −0.517652 | + | 0.517652i | ||||
\(892\) | −127.084 | + | 127.084i | −0.142471 | + | 0.142471i | ||||
\(893\) | −236.325 | −0.264641 | ||||||||
\(894\) | − | 175.219i | − | 0.195994i | ||||||
\(895\) | 1139.98 | − | 1139.98i | 1.27372 | − | 1.27372i | ||||
\(896\) | − | 844.315i | − | 0.942316i | ||||||
\(897\) | −410.368 | + | 209.263i | −0.457489 | + | 0.233292i | ||||
\(898\) | −617.021 | −0.687106 | ||||||||
\(899\) | −2.98221 | − | 2.98221i | −0.00331726 | − | 0.00331726i | ||||
\(900\) | 17.9644 | 0.0199605 | ||||||||
\(901\) | − | 786.907i | − | 0.873371i | ||||||
\(902\) | 29.9388 | + | 29.9388i | 0.0331916 | + | 0.0331916i | ||||
\(903\) | −581.322 | − | 581.322i | −0.643768 | − | 0.643768i | ||||
\(904\) | 291.762 | − | 291.762i | 0.322746 | − | 0.322746i | ||||
\(905\) | 852.828 | − | 852.828i | 0.942352 | − | 0.942352i | ||||
\(906\) | 363.688 | 0.401422 | ||||||||
\(907\) | 1460.57i | 1.61033i | 0.593048 | + | 0.805167i | \(0.297925\pi\) | ||||
−0.593048 | + | 0.805167i | \(0.702075\pi\) | |||||||
\(908\) | 148.715 | − | 148.715i | 0.163783 | − | 0.163783i | ||||
\(909\) | 873.421i | 0.960859i | ||||||||
\(910\) | −108.219 | + | 333.438i | −0.118922 | + | 0.366416i | ||||
\(911\) | 287.689 | 0.315795 | 0.157897 | − | 0.987456i | \(-0.449528\pi\) | ||||
0.157897 | + | 0.987456i | \(0.449528\pi\) | |||||||
\(912\) | 109.917 | + | 109.917i | 0.120523 | + | 0.120523i | ||||
\(913\) | −475.193 | −0.520474 | ||||||||
\(914\) | 269.755i | 0.295137i | ||||||||
\(915\) | 1197.29 | + | 1197.29i | 1.30852 | + | 1.30852i | ||||
\(916\) | 557.308 | + | 557.308i | 0.608415 | + | 0.608415i | ||||
\(917\) | 1180.71 | − | 1180.71i | 1.28758 | − | 1.28758i | ||||
\(918\) | −35.9007 | + | 35.9007i | −0.0391075 | + | 0.0391075i | ||||
\(919\) | 1696.20 | 1.84570 | 0.922851 | − | 0.385156i | \(-0.125852\pi\) | ||||
0.922851 | + | 0.385156i | \(0.125852\pi\) | |||||||
\(920\) | 259.540i | 0.282108i | ||||||||
\(921\) | −914.386 | + | 914.386i | −0.992818 | + | 0.992818i | ||||
\(922\) | − | 243.785i | − | 0.264409i | ||||||
\(923\) | 519.614 | − | 1601.00i | 0.562962 | − | 1.73457i | ||||
\(924\) | −675.074 | −0.730600 | ||||||||
\(925\) | 15.7281 | + | 15.7281i | 0.0170034 | + | 0.0170034i | ||||
\(926\) | 148.359 | 0.160215 | ||||||||
\(927\) | − | 294.974i | − | 0.318202i | ||||||
\(928\) | 127.149 | + | 127.149i | 0.137015 | + | 0.137015i | ||||
\(929\) | 912.403 | + | 912.403i | 0.982134 | + | 0.982134i | 0.999843 | − | 0.0177088i | \(-0.00563717\pi\) |
−0.0177088 | + | 0.999843i | \(0.505637\pi\) | |||||||
\(930\) | 8.89039 | − | 8.89039i | 0.00955956 | − | 0.00955956i | ||||
\(931\) | −22.2192 | + | 22.2192i | −0.0238660 | + | 0.0238660i | ||||
\(932\) | 973.394 | 1.04441 | ||||||||
\(933\) | − | 1422.18i | − | 1.52431i | ||||||
\(934\) | 399.670 | − | 399.670i | 0.427913 | − | 0.427913i | ||||
\(935\) | 837.986i | 0.896242i | ||||||||
\(936\) | −619.631 | − | 201.105i | −0.661999 | − | 0.214855i | ||||
\(937\) | −1041.30 | −1.11131 | −0.555655 | − | 0.831413i | \(-0.687533\pi\) | ||||
−0.555655 | + | 0.831413i | \(0.687533\pi\) | |||||||
\(938\) | −208.101 | − | 208.101i | −0.221856 | − | 0.221856i | ||||
\(939\) | −1825.23 | −1.94380 | ||||||||
\(940\) | 889.741i | 0.946533i | ||||||||
\(941\) | −502.392 | − | 502.392i | −0.533891 | − | 0.533891i | 0.387837 | − | 0.921728i | \(-0.373222\pi\) |
−0.921728 | + | 0.387837i | \(0.873222\pi\) | |||||||
\(942\) | −134.141 | − | 134.141i | −0.142400 | − | 0.142400i | ||||
\(943\) | −41.1843 | + | 41.1843i | −0.0436737 | + | 0.0436737i | ||||
\(944\) | −486.622 | + | 486.622i | −0.515489 | + | 0.515489i | ||||
\(945\) | −92.2456 | −0.0976143 | ||||||||
\(946\) | − | 188.671i | − | 0.199441i | ||||||
\(947\) | −683.569 | + | 683.569i | −0.721826 | + | 0.721826i | −0.968977 | − | 0.247151i | \(-0.920506\pi\) |
0.247151 | + | 0.968977i | \(0.420506\pi\) | |||||||
\(948\) | − | 259.942i | − | 0.274201i | ||||||
\(949\) | −552.982 | − | 179.473i | −0.582700 | − | 0.189118i | ||||
\(950\) | −2.38577 | −0.00251134 | ||||||||
\(951\) | −637.412 | − | 637.412i | −0.670255 | − | 0.670255i | ||||
\(952\) | −856.973 | −0.900182 | ||||||||
\(953\) | 694.290i | 0.728531i | 0.931295 | + | 0.364265i | \(0.118680\pi\) | ||||
−0.931295 | + | 0.364265i | \(0.881320\pi\) | |||||||
\(954\) | −173.246 | − | 173.246i | −0.181599 | − | 0.181599i | ||||
\(955\) | −13.2719 | − | 13.2719i | −0.0138973 | − | 0.0138973i | ||||
\(956\) | 0.0508781 | − | 0.0508781i | 5.32198e−5 | − | 5.32198e-5i | ||||
\(957\) | 128.794 | − | 128.794i | 0.134581 | − | 0.134581i | ||||
\(958\) | −370.351 | −0.386588 | ||||||||
\(959\) | 1605.89i | 1.67455i | ||||||||
\(960\) | 118.853 | − | 118.853i | 0.123805 | − | 0.123805i | ||||
\(961\) | − | 960.473i | − | 0.999452i | ||||||
\(962\) | −166.318 | − | 326.151i | −0.172888 | − | 0.339035i | ||||
\(963\) | −36.8769 | −0.0382937 | ||||||||
\(964\) | −798.549 | − | 798.549i | −0.828370 | − | 0.828370i | ||||
\(965\) | 308.952 | 0.320157 | ||||||||
\(966\) | 188.671i | 0.195312i | ||||||||
\(967\) | −616.081 | − | 616.081i | −0.637106 | − | 0.637106i | 0.312735 | − | 0.949841i | \(-0.398755\pi\) |
−0.949841 | + | 0.312735i | \(0.898755\pi\) | |||||||
\(968\) | 273.691 | + | 273.691i | 0.282738 | + | 0.282738i | ||||
\(969\) | 289.223 | − | 289.223i | 0.298476 | − | 0.298476i | ||||
\(970\) | 505.114 | − | 505.114i | 0.520736 | − | 0.520736i | ||||
\(971\) | −473.890 | −0.488044 | −0.244022 | − | 0.969770i | \(-0.578467\pi\) | ||||
−0.244022 | + | 0.969770i | \(0.578467\pi\) | |||||||
\(972\) | − | 1114.54i | − | 1.14665i | ||||||
\(973\) | −620.563 | + | 620.563i | −0.637784 | + | 0.637784i | ||||
\(974\) | 647.465i | 0.664748i | ||||||||
\(975\) | −31.2897 | + | 15.9559i | −0.0320920 | + | 0.0163650i | ||||
\(976\) | 670.781 | 0.687276 | ||||||||
\(977\) | 9.56087 | + | 9.56087i | 0.00978594 | + | 0.00978594i | 0.711983 | − | 0.702197i | \(-0.247797\pi\) |
−0.702197 | + | 0.711983i | \(0.747797\pi\) | |||||||
\(978\) | 219.925 | 0.224872 | ||||||||
\(979\) | − | 94.6748i | − | 0.0967056i | ||||||
\(980\) | 83.6534 | + | 83.6534i | 0.0853606 | + | 0.0853606i | ||||
\(981\) | 1005.39 | + | 1005.39i | 1.02486 | + | 1.02486i | ||||
\(982\) | 232.861 | − | 232.861i | 0.237129 | − | 0.237129i | ||||
\(983\) | 695.475 | − | 695.475i | 0.707503 | − | 0.707503i | −0.258507 | − | 0.966009i | \(-0.583230\pi\) |
0.966009 | + | 0.258507i | \(0.0832304\pi\) | |||||||
\(984\) | −171.421 | −0.174208 | ||||||||
\(985\) | 903.122i | 0.916876i | ||||||||
\(986\) | 74.2100 | − | 74.2100i | 0.0752637 | − | 0.0752637i | ||||
\(987\) | 1425.00i | 1.44376i | ||||||||
\(988\) | −183.842 | − | 59.6669i | −0.186075 | − | 0.0603916i | ||||
\(989\) | 259.540 | 0.262426 | ||||||||
\(990\) | 184.491 | + | 184.491i | 0.186355 | + | 0.186355i | ||||
\(991\) | −1625.34 | −1.64010 | −0.820051 | − | 0.572291i | \(-0.806055\pi\) | ||||
−0.820051 | + | 0.572291i | \(0.806055\pi\) | |||||||
\(992\) | − | 22.4555i | − | 0.0226366i | ||||||
\(993\) | 815.732 | + | 815.732i | 0.821483 | + | 0.821483i | ||||
\(994\) | −487.489 | − | 487.489i | −0.490431 | − | 0.490431i | ||||
\(995\) | 545.197 | − | 545.197i | 0.547937 | − | 0.547937i | ||||
\(996\) | 617.478 | − | 617.478i | 0.619957 | − | 0.619957i | ||||
\(997\) | −31.3986 | −0.0314931 | −0.0157465 | − | 0.999876i | \(-0.505012\pi\) | ||||
−0.0157465 | + | 0.999876i | \(0.505012\pi\) | |||||||
\(998\) | 119.332i | 0.119572i | ||||||||
\(999\) | 68.1206 | − | 68.1206i | 0.0681888 | − | 0.0681888i |
(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 | 13.3.d.a.8.2 | yes | 4 | |
3.2 | odd | 2 | 117.3.j.a.73.1 | 4 | |||
4.3 | odd | 2 | 208.3.t.c.177.2 | 4 | |||
5.2 | odd | 4 | 325.3.g.b.99.1 | 4 | |||
5.3 | odd | 4 | 325.3.g.a.99.2 | 4 | |||
5.4 | even | 2 | 325.3.j.a.151.1 | 4 | |||
13.2 | odd | 12 | 169.3.f.f.19.2 | 8 | |||
13.3 | even | 3 | 169.3.f.f.150.1 | 8 | |||
13.4 | even | 6 | 169.3.f.d.89.1 | 8 | |||
13.5 | odd | 4 | inner | 13.3.d.a.5.2 | ✓ | 4 | |
13.6 | odd | 12 | 169.3.f.f.80.1 | 8 | |||
13.7 | odd | 12 | 169.3.f.d.80.2 | 8 | |||
13.8 | odd | 4 | 169.3.d.d.70.1 | 4 | |||
13.9 | even | 3 | 169.3.f.f.89.2 | 8 | |||
13.10 | even | 6 | 169.3.f.d.150.2 | 8 | |||
13.11 | odd | 12 | 169.3.f.d.19.1 | 8 | |||
13.12 | even | 2 | 169.3.d.d.99.1 | 4 | |||
39.5 | even | 4 | 117.3.j.a.109.1 | 4 | |||
52.31 | even | 4 | 208.3.t.c.161.2 | 4 | |||
65.18 | even | 4 | 325.3.g.b.174.1 | 4 | |||
65.44 | odd | 4 | 325.3.j.a.226.1 | 4 | |||
65.57 | even | 4 | 325.3.g.a.174.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.3.d.a.5.2 | ✓ | 4 | 13.5 | odd | 4 | inner | |
13.3.d.a.8.2 | yes | 4 | 1.1 | even | 1 | trivial | |
117.3.j.a.73.1 | 4 | 3.2 | odd | 2 | |||
117.3.j.a.109.1 | 4 | 39.5 | even | 4 | |||
169.3.d.d.70.1 | 4 | 13.8 | odd | 4 | |||
169.3.d.d.99.1 | 4 | 13.12 | even | 2 | |||
169.3.f.d.19.1 | 8 | 13.11 | odd | 12 | |||
169.3.f.d.80.2 | 8 | 13.7 | odd | 12 | |||
169.3.f.d.89.1 | 8 | 13.4 | even | 6 | |||
169.3.f.d.150.2 | 8 | 13.10 | even | 6 | |||
169.3.f.f.19.2 | 8 | 13.2 | odd | 12 | |||
169.3.f.f.80.1 | 8 | 13.6 | odd | 12 | |||
169.3.f.f.89.2 | 8 | 13.9 | even | 3 | |||
169.3.f.f.150.1 | 8 | 13.3 | even | 3 | |||
208.3.t.c.161.2 | 4 | 52.31 | even | 4 | |||
208.3.t.c.177.2 | 4 | 4.3 | odd | 2 | |||
325.3.g.a.99.2 | 4 | 5.3 | odd | 4 | |||
325.3.g.a.174.2 | 4 | 65.57 | even | 4 | |||
325.3.g.b.99.1 | 4 | 5.2 | odd | 4 | |||
325.3.g.b.174.1 | 4 | 65.18 | even | 4 | |||
325.3.j.a.151.1 | 4 | 5.4 | even | 2 | |||
325.3.j.a.226.1 | 4 | 65.44 | odd | 4 |