Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(97,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.bd (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 97.5 | ||
Character | \(\chi\) | \(=\) | 637.97 |
Dual form | 637.2.bd.b.440.5 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.179714 | + | 0.670702i | 0.127077 | + | 0.474258i | 0.999905 | − | 0.0137696i | \(-0.00438313\pi\) |
−0.872828 | + | 0.488028i | \(0.837716\pi\) | |||||||
\(3\) | 2.71085 | + | 1.56511i | 1.56511 | + | 0.903616i | 0.996726 | + | 0.0808518i | \(0.0257641\pi\) |
0.568383 | + | 0.822764i | \(0.307569\pi\) | |||||||
\(4\) | 1.31451 | − | 0.758931i | 0.657253 | − | 0.379465i | ||||
\(5\) | −0.0263009 | − | 0.0263009i | −0.0117621 | − | 0.0117621i | 0.701201 | − | 0.712963i | \(-0.252647\pi\) |
−0.712963 | + | 0.701201i | \(0.752647\pi\) | |||||||
\(6\) | −0.562545 | + | 2.09944i | −0.229658 | + | 0.857095i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.72723 | + | 1.72723i | 0.610667 | + | 0.610667i | ||||
\(9\) | 3.39913 | + | 5.88747i | 1.13304 | + | 1.96249i | ||||
\(10\) | 0.0129135 | − | 0.0223668i | 0.00408359 | − | 0.00707299i | ||||
\(11\) | −1.09015 | + | 0.292106i | −0.328694 | + | 0.0880732i | −0.419392 | − | 0.907805i | \(-0.637757\pi\) |
0.0906984 | + | 0.995878i | \(0.471090\pi\) | |||||||
\(12\) | 4.75124 | 1.37156 | ||||||||
\(13\) | −3.58326 | − | 0.400306i | −0.993818 | − | 0.111025i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0301340 | − | 0.112462i | −0.00778057 | − | 0.0290375i | ||||
\(16\) | 0.669812 | − | 1.16015i | 0.167453 | − | 0.290037i | ||||
\(17\) | −3.20096 | − | 5.54423i | −0.776347 | − | 1.34467i | −0.934034 | − | 0.357184i | \(-0.883737\pi\) |
0.157687 | − | 0.987489i | \(-0.449596\pi\) | |||||||
\(18\) | −3.33787 | + | 3.33787i | −0.786743 | + | 0.786743i | ||||
\(19\) | −0.954087 | + | 3.56070i | −0.218883 | + | 0.816881i | 0.765881 | + | 0.642982i | \(0.222303\pi\) |
−0.984764 | + | 0.173899i | \(0.944363\pi\) | |||||||
\(20\) | −0.0545333 | − | 0.0146122i | −0.0121940 | − | 0.00326738i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.391832 | − | 0.678673i | −0.0835389 | − | 0.144694i | ||||
\(23\) | −2.41997 | − | 1.39717i | −0.504599 | − | 0.291331i | 0.226011 | − | 0.974125i | \(-0.427431\pi\) |
−0.730611 | + | 0.682794i | \(0.760765\pi\) | |||||||
\(24\) | 1.97895 | + | 7.38555i | 0.403952 | + | 1.50757i | ||||
\(25\) | − | 4.99862i | − | 0.999723i | ||||||
\(26\) | −0.375476 | − | 2.47524i | −0.0736370 | − | 0.485435i | ||||
\(27\) | 11.8894i | 2.28811i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.84998 | − | 3.20426i | 0.343532 | − | 0.595015i | −0.641554 | − | 0.767078i | \(-0.721710\pi\) |
0.985086 | + | 0.172063i | \(0.0550432\pi\) | |||||||
\(30\) | 0.0700128 | − | 0.0404219i | 0.0127825 | − | 0.00738000i | ||||
\(31\) | 1.93054 | + | 1.93054i | 0.346735 | + | 0.346735i | 0.858892 | − | 0.512157i | \(-0.171153\pi\) |
−0.512157 | + | 0.858892i | \(0.671153\pi\) | |||||||
\(32\) | 5.61737 | + | 1.50517i | 0.993019 | + | 0.266079i | ||||
\(33\) | −3.41242 | − | 0.914355i | −0.594026 | − | 0.159169i | ||||
\(34\) | 3.14327 | − | 3.14327i | 0.539066 | − | 0.539066i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.93636 | + | 5.15941i | 1.48939 | + | 0.859902i | ||||
\(37\) | 5.39204 | − | 1.44479i | 0.886445 | − | 0.237522i | 0.213259 | − | 0.976996i | \(-0.431592\pi\) |
0.673186 | + | 0.739473i | \(0.264925\pi\) | |||||||
\(38\) | −2.55963 | −0.415228 | ||||||||
\(39\) | −9.08715 | − | 6.69336i | −1.45511 | − | 1.07180i | ||||
\(40\) | − | 0.0908555i | − | 0.0143655i | ||||||
\(41\) | −0.188789 | + | 0.0505859i | −0.0294839 | + | 0.00790020i | −0.273531 | − | 0.961863i | \(-0.588192\pi\) |
0.244047 | + | 0.969763i | \(0.421525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.84817 | − | 1.06704i | 0.281843 | − | 0.162722i | −0.352414 | − | 0.935844i | \(-0.614639\pi\) |
0.634258 | + | 0.773122i | \(0.281306\pi\) | |||||||
\(44\) | −1.21133 | + | 1.21133i | −0.182614 | + | 0.182614i | ||||
\(45\) | 0.0654456 | − | 0.244246i | 0.00975605 | − | 0.0364101i | ||||
\(46\) | 0.502183 | − | 1.87417i | 0.0740429 | − | 0.276332i | ||||
\(47\) | −3.97588 | + | 3.97588i | −0.579942 | + | 0.579942i | −0.934887 | − | 0.354945i | \(-0.884500\pi\) |
0.354945 | + | 0.934887i | \(0.384500\pi\) | |||||||
\(48\) | 3.63152 | − | 2.09666i | 0.524164 | − | 0.302627i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.35258 | − | 0.898322i | 0.474127 | − | 0.127042i | ||||
\(51\) | − | 20.0394i | − | 2.80608i | ||||||
\(52\) | −5.01402 | + | 2.19324i | −0.695320 | + | 0.304148i | ||||
\(53\) | 0.591643 | 0.0812684 | 0.0406342 | − | 0.999174i | \(-0.487062\pi\) | ||||
0.0406342 | + | 0.999174i | \(0.487062\pi\) | |||||||
\(54\) | −7.97425 | + | 2.13669i | −1.08516 | + | 0.290767i | ||||
\(55\) | 0.0363547 | + | 0.0209894i | 0.00490207 | + | 0.00283021i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.15927 | + | 8.15927i | −1.08072 | + | 1.08072i | ||||
\(58\) | 2.48157 | + | 0.664935i | 0.325846 | + | 0.0873102i | ||||
\(59\) | −10.8879 | − | 2.91741i | −1.41749 | − | 0.379814i | −0.532895 | − | 0.846181i | \(-0.678896\pi\) |
−0.884591 | + | 0.466367i | \(0.845563\pi\) | |||||||
\(60\) | −0.124962 | − | 0.124962i | −0.0161325 | − | 0.0161325i | ||||
\(61\) | 1.18838 | − | 0.686113i | 0.152157 | − | 0.0878478i | −0.421989 | − | 0.906601i | \(-0.638668\pi\) |
0.574145 | + | 0.818753i | \(0.305334\pi\) | |||||||
\(62\) | −0.947871 | + | 1.64176i | −0.120380 | + | 0.208504i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.35883i | 0.169854i | ||||||||
\(65\) | 0.0837147 | + | 0.104772i | 0.0103835 | + | 0.0129953i | ||||
\(66\) | − | 2.45304i | − | 0.301948i | ||||||
\(67\) | 1.95238 | + | 7.28639i | 0.238522 | + | 0.890174i | 0.976530 | + | 0.215383i | \(0.0690999\pi\) |
−0.738008 | + | 0.674792i | \(0.764233\pi\) | |||||||
\(68\) | −8.41537 | − | 4.85861i | −1.02051 | − | 0.589194i | ||||
\(69\) | −4.37346 | − | 7.57505i | −0.526502 | − | 0.911928i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.88214 | − | 2.64791i | −1.17279 | − | 0.314249i | −0.380729 | − | 0.924686i | \(-0.624327\pi\) |
−0.792065 | + | 0.610437i | \(0.790994\pi\) | |||||||
\(72\) | −4.29793 | + | 16.0401i | −0.506516 | + | 1.89034i | ||||
\(73\) | 1.93317 | − | 1.93317i | 0.226261 | − | 0.226261i | −0.584868 | − | 0.811129i | \(-0.698854\pi\) |
0.811129 | + | 0.584868i | \(0.198854\pi\) | |||||||
\(74\) | 1.93805 | + | 3.35680i | 0.225294 | + | 0.390220i | ||||
\(75\) | 7.82338 | − | 13.5505i | 0.903366 | − | 1.56468i | ||||
\(76\) | 1.44817 | + | 5.40465i | 0.166117 | + | 0.619956i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.85616 | − | 7.29767i | 0.323397 | − | 0.826298i | ||||
\(79\) | 3.26258 | 0.367069 | 0.183535 | − | 0.983013i | \(-0.441246\pi\) | ||||
0.183535 | + | 0.983013i | \(0.441246\pi\) | |||||||
\(80\) | −0.0481297 | + | 0.0128963i | −0.00538106 | + | 0.00144185i | ||||
\(81\) | −8.41080 | + | 14.5679i | −0.934533 | + | 1.61866i | ||||
\(82\) | −0.0678562 | − | 0.117530i | −0.00749347 | − | 0.0129791i | ||||
\(83\) | −4.92754 | − | 4.92754i | −0.540868 | − | 0.540868i | 0.382915 | − | 0.923783i | \(-0.374920\pi\) |
−0.923783 | + | 0.382915i | \(0.874920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0616301 | + | 0.230007i | −0.00668472 | + | 0.0249477i | ||||
\(86\) | 1.04781 | + | 1.04781i | 0.112988 | + | 0.112988i | ||||
\(87\) | 10.0300 | − | 5.79083i | 1.07533 | − | 0.620843i | ||||
\(88\) | −2.38748 | − | 1.37841i | −0.254506 | − | 0.146939i | ||||
\(89\) | 4.36016 | + | 16.2723i | 0.462176 | + | 1.72486i | 0.666087 | + | 0.745874i | \(0.267968\pi\) |
−0.203911 | + | 0.978989i | \(0.565365\pi\) | |||||||
\(90\) | 0.175578 | 0.0185076 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.24143 | −0.442199 | ||||||||
\(93\) | 2.21189 | + | 8.25489i | 0.229363 | + | 0.855993i | ||||
\(94\) | −3.38116 | − | 1.95211i | −0.348740 | − | 0.201345i | ||||
\(95\) | 0.118743 | − | 0.0685564i | 0.0121828 | − | 0.00703374i | ||||
\(96\) | 12.8721 | + | 12.8721i | 1.31375 | + | 1.31375i | ||||
\(97\) | −0.663884 | + | 2.47765i | −0.0674072 | + | 0.251567i | −0.991405 | − | 0.130832i | \(-0.958235\pi\) |
0.923997 | + | 0.382399i | \(0.124902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.42534 | − | 5.42534i | −0.545267 | − | 0.545267i | ||||
\(100\) | −3.79360 | − | 6.57071i | −0.379360 | − | 0.657071i | ||||
\(101\) | 2.30855 | − | 3.99852i | 0.229709 | − | 0.397868i | −0.728013 | − | 0.685564i | \(-0.759556\pi\) |
0.957722 | + | 0.287696i | \(0.0928892\pi\) | |||||||
\(102\) | 13.4405 | − | 3.60137i | 1.33081 | − | 0.356588i | ||||
\(103\) | 11.7367 | 1.15645 | 0.578227 | − | 0.815876i | \(-0.303745\pi\) | ||||
0.578227 | + | 0.815876i | \(0.303745\pi\) | |||||||
\(104\) | −5.49769 | − | 6.88053i | −0.539093 | − | 0.674691i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.106327 | + | 0.396817i | 0.0103274 | + | 0.0385422i | ||||
\(107\) | −6.53667 | + | 11.3218i | −0.631923 | + | 1.09452i | 0.355235 | + | 0.934777i | \(0.384401\pi\) |
−0.987158 | + | 0.159746i | \(0.948932\pi\) | |||||||
\(108\) | 9.02322 | + | 15.6287i | 0.868260 | + | 1.50387i | ||||
\(109\) | 9.22077 | − | 9.22077i | 0.883189 | − | 0.883189i | −0.110668 | − | 0.993857i | \(-0.535299\pi\) |
0.993857 | + | 0.110668i | \(0.0352990\pi\) | |||||||
\(110\) | −0.00754419 | + | 0.0281553i | −0.000719310 | + | 0.00268450i | ||||
\(111\) | 16.8782 | + | 4.52251i | 1.60201 | + | 0.429258i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.85773 | + | 3.21769i | 0.174761 | + | 0.302694i | 0.940078 | − | 0.340958i | \(-0.110751\pi\) |
−0.765318 | + | 0.643653i | \(0.777418\pi\) | |||||||
\(114\) | −6.93878 | − | 4.00611i | −0.649876 | − | 0.375206i | ||||
\(115\) | 0.0269006 | + | 0.100395i | 0.00250850 | + | 0.00936184i | ||||
\(116\) | − | 5.61602i | − | 0.521434i | ||||||
\(117\) | −9.82319 | − | 22.4570i | −0.908154 | − | 2.07615i | ||||
\(118\) | − | 7.82685i | − | 0.720520i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.142199 | − | 0.246295i | 0.0129809 | − | 0.0224836i | ||||
\(121\) | −8.42317 | + | 4.86312i | −0.765743 | + | 0.442102i | ||||
\(122\) | 0.673747 | + | 0.673747i | 0.0609982 | + | 0.0609982i | ||||
\(123\) | −0.590952 | − | 0.158345i | −0.0532843 | − | 0.0142775i | ||||
\(124\) | 4.00285 | + | 1.07256i | 0.359466 | + | 0.0963187i | ||||
\(125\) | −0.262973 | + | 0.262973i | −0.0235210 | + | 0.0235210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.47692 | + | 1.43005i | 0.219791 | + | 0.126897i | 0.605854 | − | 0.795576i | \(-0.292832\pi\) |
−0.386062 | + | 0.922473i | \(0.626165\pi\) | |||||||
\(128\) | 10.3234 | − | 2.76614i | 0.912465 | − | 0.244494i | ||||
\(129\) | 6.68014 | 0.588154 | ||||||||
\(130\) | −0.0552258 | + | 0.0749766i | −0.00484362 | + | 0.00657588i | ||||
\(131\) | 0.138319i | 0.0120850i | 0.999982 | + | 0.00604249i | \(0.00192340\pi\) | ||||
−0.999982 | + | 0.00604249i | \(0.998077\pi\) | |||||||
\(132\) | −5.17958 | + | 1.38786i | −0.450824 | + | 0.120798i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.53613 | + | 2.61894i | −0.391862 | + | 0.226242i | ||||
\(135\) | 0.312702 | − | 0.312702i | 0.0269131 | − | 0.0269131i | ||||
\(136\) | 4.04736 | − | 15.1049i | 0.347058 | − | 1.29524i | ||||
\(137\) | −4.41512 | + | 16.4774i | −0.377209 | + | 1.40776i | 0.472882 | + | 0.881126i | \(0.343214\pi\) |
−0.850090 | + | 0.526637i | \(0.823453\pi\) | |||||||
\(138\) | 4.29463 | − | 4.29463i | 0.365583 | − | 0.365583i | ||||
\(139\) | −13.3885 | + | 7.72988i | −1.13560 | + | 0.655640i | −0.945338 | − | 0.326093i | \(-0.894268\pi\) |
−0.190264 | + | 0.981733i | \(0.560934\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.0007 | + | 4.55532i | −1.43172 | + | 0.383627i | ||||
\(142\) | − | 7.10384i | − | 0.596141i | ||||||
\(143\) | 4.02324 | − | 0.610296i | 0.336440 | − | 0.0510355i | ||||
\(144\) | 9.10712 | 0.758927 | ||||||||
\(145\) | −0.132931 | + | 0.0356188i | −0.0110393 | + | 0.00295798i | ||||
\(146\) | 1.64400 | + | 0.949165i | 0.136059 | + | 0.0785534i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.99137 | − | 5.99137i | 0.492487 | − | 0.492487i | ||||
\(149\) | 5.50075 | + | 1.47392i | 0.450639 | + | 0.120748i | 0.476998 | − | 0.878904i | \(-0.341725\pi\) |
−0.0263595 | + | 0.999653i | \(0.508391\pi\) | |||||||
\(150\) | 10.4943 | + | 2.81194i | 0.856858 | + | 0.229594i | ||||
\(151\) | −14.6357 | − | 14.6357i | −1.19103 | − | 1.19103i | −0.976778 | − | 0.214256i | \(-0.931267\pi\) |
−0.214256 | − | 0.976778i | \(-0.568733\pi\) | |||||||
\(152\) | −7.79807 | + | 4.50222i | −0.632507 | + | 0.365178i | ||||
\(153\) | 21.7610 | − | 37.6911i | 1.75927 | − | 3.04715i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.101550i | − | 0.00815668i | ||||||
\(156\) | −17.0249 | − | 1.90195i | −1.36308 | − | 0.152278i | ||||
\(157\) | − | 9.26373i | − | 0.739326i | −0.929166 | − | 0.369663i | \(-0.879473\pi\) | ||
0.929166 | − | 0.369663i | \(-0.120527\pi\) | |||||||
\(158\) | 0.586332 | + | 2.18822i | 0.0466461 | + | 0.174086i | ||||
\(159\) | 1.60385 | + | 0.925986i | 0.127194 | + | 0.0734355i | ||||
\(160\) | −0.108155 | − | 0.187329i | −0.00855037 | − | 0.0148097i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.2823 | − | 3.02308i | −0.886420 | − | 0.237516i | ||||
\(163\) | 1.06612 | − | 3.97880i | 0.0835047 | − | 0.311644i | −0.911522 | − | 0.411251i | \(-0.865092\pi\) |
0.995027 | + | 0.0996072i | \(0.0317586\pi\) | |||||||
\(164\) | −0.209773 | + | 0.209773i | −0.0163806 | + | 0.0163806i | ||||
\(165\) | 0.0657014 | + | 0.113798i | 0.00511485 | + | 0.00885918i | ||||
\(166\) | 2.41936 | − | 4.19046i | 0.187779 | − | 0.325243i | ||||
\(167\) | −4.15955 | − | 15.5237i | −0.321876 | − | 1.20126i | −0.917415 | − | 0.397931i | \(-0.869728\pi\) |
0.595540 | − | 0.803326i | \(-0.296938\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6795 | + | 2.86880i | 0.975347 | + | 0.220677i | ||||
\(170\) | −0.165342 | −0.0126811 | ||||||||
\(171\) | −24.2066 | + | 6.48614i | −1.85112 | + | 0.496007i | ||||
\(172\) | 1.61962 | − | 2.80526i | 0.123495 | − | 0.213899i | ||||
\(173\) | −10.5332 | − | 18.2440i | −0.800821 | − | 1.38706i | −0.919076 | − | 0.394080i | \(-0.871063\pi\) |
0.118255 | − | 0.992983i | \(-0.462270\pi\) | |||||||
\(174\) | 5.68646 | + | 5.68646i | 0.431090 | + | 0.431090i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.391312 | + | 1.46040i | −0.0294963 | + | 0.110082i | ||||
\(177\) | −24.9494 | − | 24.9494i | −1.87531 | − | 1.87531i | ||||
\(178\) | −10.1303 | + | 5.84874i | −0.759299 | + | 0.438381i | ||||
\(179\) | 7.89629 | + | 4.55893i | 0.590196 | + | 0.340750i | 0.765175 | − | 0.643822i | \(-0.222652\pi\) |
−0.174979 | + | 0.984572i | \(0.555986\pi\) | |||||||
\(180\) | −0.0993373 | − | 0.370732i | −0.00740417 | − | 0.0276327i | ||||
\(181\) | 15.7169 | 1.16823 | 0.584113 | − | 0.811672i | \(-0.301443\pi\) | ||||
0.584113 | + | 0.811672i | \(0.301443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.29537 | 0.317523 | ||||||||
\(184\) | −1.76661 | − | 6.59308i | −0.130236 | − | 0.486049i | ||||
\(185\) | −0.179815 | − | 0.103816i | −0.0132203 | − | 0.00763272i | ||||
\(186\) | −5.13907 | + | 2.96704i | −0.376815 | + | 0.217554i | ||||
\(187\) | 5.10904 | + | 5.10904i | 0.373610 | + | 0.373610i | ||||
\(188\) | −2.20890 | + | 8.24374i | −0.161101 | + | 0.601236i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0673208 | + | 0.0673208i | 0.00488396 | + | 0.00488396i | ||||
\(191\) | 8.65358 | + | 14.9884i | 0.626151 | + | 1.08453i | 0.988317 | + | 0.152412i | \(0.0487039\pi\) |
−0.362166 | + | 0.932114i | \(0.617963\pi\) | |||||||
\(192\) | −2.12672 | + | 3.68359i | −0.153483 | + | 0.265840i | ||||
\(193\) | 12.1595 | − | 3.25813i | 0.875260 | − | 0.234525i | 0.206899 | − | 0.978362i | \(-0.433663\pi\) |
0.668361 | + | 0.743837i | \(0.266996\pi\) | |||||||
\(194\) | −1.78107 | −0.127874 | ||||||||
\(195\) | 0.0629589 | + | 0.415042i | 0.00450858 | + | 0.0297218i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.43206 | − | 24.0048i | −0.458265 | − | 1.71027i | −0.678307 | − | 0.734778i | \(-0.737286\pi\) |
0.220042 | − | 0.975490i | \(-0.429381\pi\) | |||||||
\(198\) | 2.66378 | − | 4.61380i | 0.189306 | − | 0.327888i | ||||
\(199\) | 5.29889 | + | 9.17795i | 0.375629 | + | 0.650608i | 0.990421 | − | 0.138081i | \(-0.0440935\pi\) |
−0.614792 | + | 0.788689i | \(0.710760\pi\) | |||||||
\(200\) | 8.63375 | − | 8.63375i | 0.610499 | − | 0.610499i | ||||
\(201\) | −6.11138 | + | 22.8080i | −0.431064 | + | 1.60875i | ||||
\(202\) | 3.09670 | + | 0.829758i | 0.217883 | + | 0.0583815i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −15.2085 | − | 26.3419i | −1.06481 | − | 1.84430i | ||||
\(205\) | 0.00629579 | + | 0.00363488i | 0.000439717 | + | 0.000253871i | ||||
\(206\) | 2.10926 | + | 7.87186i | 0.146959 | + | 0.548458i | ||||
\(207\) | − | 18.9967i | − | 1.32036i | ||||||
\(208\) | −2.86453 | + | 3.88898i | −0.198619 | + | 0.269653i | ||||
\(209\) | − | 4.16041i | − | 0.287781i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3404 | + | 17.9102i | −0.711865 | + | 1.23299i | 0.252292 | + | 0.967651i | \(0.418816\pi\) |
−0.964156 | + | 0.265335i | \(0.914518\pi\) | |||||||
\(212\) | 0.777719 | − | 0.449016i | 0.0534139 | − | 0.0308386i | ||||
\(213\) | −22.6447 | − | 22.6447i | −1.55159 | − | 1.55159i | ||||
\(214\) | −8.76832 | − | 2.34946i | −0.599390 | − | 0.160606i | ||||
\(215\) | −0.0766728 | − | 0.0205444i | −0.00522904 | − | 0.00140112i | ||||
\(216\) | −20.5357 | + | 20.5357i | −1.39728 | + | 1.39728i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.84149 | + | 4.52729i | 0.531093 | + | 0.306627i | ||||
\(219\) | 8.26616 | − | 2.21491i | 0.558575 | − | 0.149670i | ||||
\(220\) | 0.0637180 | 0.00429587 | ||||||||
\(221\) | 9.25049 | + | 21.1478i | 0.622255 | + | 1.42255i | ||||
\(222\) | 12.1330i | 0.814316i | ||||||||
\(223\) | −3.17269 | + | 0.850119i | −0.212459 | + | 0.0569282i | −0.363479 | − | 0.931603i | \(-0.618411\pi\) |
0.151020 | + | 0.988531i | \(0.451744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 29.4292 | − | 16.9910i | 1.96195 | − | 1.13273i | ||||
\(226\) | −1.82425 | + | 1.82425i | −0.121347 | + | 0.121347i | ||||
\(227\) | −4.76219 | + | 17.7728i | −0.316078 | + | 1.17962i | 0.606904 | + | 0.794775i | \(0.292411\pi\) |
−0.922982 | + | 0.384844i | \(0.874255\pi\) | |||||||
\(228\) | −4.53309 | + | 16.9177i | −0.300211 | + | 1.12040i | ||||
\(229\) | 7.75613 | − | 7.75613i | 0.512540 | − | 0.512540i | −0.402764 | − | 0.915304i | \(-0.631951\pi\) |
0.915304 | + | 0.402764i | \(0.131951\pi\) | |||||||
\(230\) | −0.0625004 | + | 0.0360846i | −0.00412116 | + | 0.00237935i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.72982 | − | 2.33915i | 0.573141 | − | 0.153573i | ||||
\(233\) | 8.62527i | 0.565060i | 0.959258 | + | 0.282530i | \(0.0911737\pi\) | ||||
−0.959258 | + | 0.282530i | \(0.908826\pi\) | |||||||
\(234\) | 13.2966 | − | 10.6243i | 0.869227 | − | 0.694531i | ||||
\(235\) | 0.209139 | 0.0136427 | ||||||||
\(236\) | −16.5263 | + | 4.42822i | −1.07577 | + | 0.288253i | ||||
\(237\) | 8.84437 | + | 5.10630i | 0.574503 | + | 0.331690i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.82164 | + | 5.82164i | −0.376571 | + | 0.376571i | −0.869863 | − | 0.493293i | \(-0.835793\pi\) |
0.493293 | + | 0.869863i | \(0.335793\pi\) | |||||||
\(240\) | −0.150656 | − | 0.0403683i | −0.00972483 | − | 0.00260576i | ||||
\(241\) | 6.06856 | + | 1.62607i | 0.390910 | + | 0.104744i | 0.448920 | − | 0.893572i | \(-0.351809\pi\) |
−0.0580097 | + | 0.998316i | \(0.518475\pi\) | |||||||
\(242\) | −4.77547 | − | 4.77547i | −0.306979 | − | 0.306979i | ||||
\(243\) | −14.7113 | + | 8.49355i | −0.943728 | + | 0.544861i | ||||
\(244\) | 1.04142 | − | 1.80380i | 0.0666704 | − | 0.115476i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 0.424810i | − | 0.0270849i | ||||||
\(247\) | 4.84411 | − | 12.3770i | 0.308224 | − | 0.787529i | ||||
\(248\) | 6.66896i | 0.423479i | ||||||||
\(249\) | −5.64568 | − | 21.0700i | −0.357780 | − | 1.33525i | ||||
\(250\) | −0.223637 | − | 0.129117i | −0.0141440 | − | 0.00816605i | ||||
\(251\) | 5.23454 | + | 9.06650i | 0.330402 | + | 0.572272i | 0.982591 | − | 0.185784i | \(-0.0594825\pi\) |
−0.652189 | + | 0.758056i | \(0.726149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.04627 | + | 0.816245i | 0.191517 | + | 0.0513169i | ||||
\(254\) | −0.514001 | + | 1.91828i | −0.0322513 | + | 0.120364i | ||||
\(255\) | −0.527055 | + | 0.527055i | −0.0330055 | + | 0.0330055i | ||||
\(256\) | 5.06934 | + | 8.78035i | 0.316834 | + | 0.548772i | ||||
\(257\) | 2.67510 | − | 4.63341i | 0.166868 | − | 0.289024i | −0.770449 | − | 0.637502i | \(-0.779968\pi\) |
0.937317 | + | 0.348477i | \(0.113301\pi\) | |||||||
\(258\) | 1.20052 | + | 4.48039i | 0.0747409 | + | 0.278937i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.189558 | + | 0.0741892i | 0.0117559 | + | 0.00460102i | ||||
\(261\) | 25.1533 | 1.55695 | ||||||||
\(262\) | −0.0927709 | + | 0.0248579i | −0.00573140 | + | 0.00153573i | ||||
\(263\) | −3.08129 | + | 5.33695i | −0.190000 | + | 0.329090i | −0.945250 | − | 0.326347i | \(-0.894182\pi\) |
0.755250 | + | 0.655437i | \(0.227516\pi\) | |||||||
\(264\) | −4.31473 | − | 7.47333i | −0.265553 | − | 0.459951i | ||||
\(265\) | −0.0155608 | − | 0.0155608i | −0.000955891 | − | 0.000955891i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.6482 | + | 50.9359i | −0.835259 | + | 3.11723i | ||||
\(268\) | 8.09628 | + | 8.09628i | 0.494559 | + | 0.494559i | ||||
\(269\) | 17.7974 | − | 10.2754i | 1.08513 | − | 0.626500i | 0.152854 | − | 0.988249i | \(-0.451154\pi\) |
0.932275 | + | 0.361749i | \(0.117820\pi\) | |||||||
\(270\) | 0.265927 | + | 0.153533i | 0.0161838 | + | 0.00934373i | ||||
\(271\) | −2.62991 | − | 9.81495i | −0.159756 | − | 0.596216i | −0.998651 | − | 0.0519233i | \(-0.983465\pi\) |
0.838896 | − | 0.544292i | \(-0.183202\pi\) | |||||||
\(272\) | −8.57617 | −0.520007 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.8449 | −0.715578 | ||||||||
\(275\) | 1.46012 | + | 5.44926i | 0.0880488 | + | 0.328603i | ||||
\(276\) | −11.4979 | − | 6.63830i | −0.692090 | − | 0.399579i | ||||
\(277\) | −17.6889 | + | 10.2127i | −1.06283 | + | 0.613623i | −0.926213 | − | 0.377002i | \(-0.876955\pi\) |
−0.136613 | + | 0.990624i | \(0.543622\pi\) | |||||||
\(278\) | −7.59056 | − | 7.59056i | −0.455251 | − | 0.455251i | ||||
\(279\) | −4.80383 | + | 17.9281i | −0.287598 | + | 1.07333i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0423 | − | 13.0423i | −0.778037 | − | 0.778037i | 0.201460 | − | 0.979497i | \(-0.435431\pi\) |
−0.979497 | + | 0.201460i | \(0.935431\pi\) | |||||||
\(282\) | −6.11053 | − | 10.5838i | −0.363877 | − | 0.630253i | ||||
\(283\) | −1.00784 | + | 1.74563i | −0.0599100 | + | 0.103767i | −0.894425 | − | 0.447218i | \(-0.852415\pi\) |
0.834515 | + | 0.550986i | \(0.185748\pi\) | |||||||
\(284\) | −14.9997 | + | 4.01916i | −0.890069 | + | 0.238493i | ||||
\(285\) | 0.429193 | 0.0254232 | ||||||||
\(286\) | 1.13236 | + | 2.58872i | 0.0669578 | + | 0.153074i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 10.2325 | + | 38.1883i | 0.602958 | + | 2.25027i | ||||
\(289\) | −11.9923 | + | 20.7713i | −0.705430 | + | 1.22184i | ||||
\(290\) | −0.0477792 | − | 0.0827560i | −0.00280569 | − | 0.00485960i | ||||
\(291\) | −5.67748 | + | 5.67748i | −0.332819 | + | 0.332819i | ||||
\(292\) | 1.07402 | − | 4.00831i | 0.0628525 | − | 0.234569i | ||||
\(293\) | −11.4688 | − | 3.07306i | −0.670016 | − | 0.179530i | −0.0922540 | − | 0.995736i | \(-0.529407\pi\) |
−0.577762 | + | 0.816205i | \(0.696074\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.209632 | + | 0.363093i | 0.0122052 | + | 0.0211401i | ||||
\(296\) | 11.8088 | + | 6.81779i | 0.686370 | + | 0.396276i | ||||
\(297\) | −3.47296 | − | 12.9613i | −0.201522 | − | 0.752089i | ||||
\(298\) | 3.95425i | 0.229063i | ||||||||
\(299\) | 8.11210 | + | 5.97516i | 0.469135 | + | 0.345553i | ||||
\(300\) | − | 23.7496i | − | 1.37118i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.18594 | − | 12.4464i | 0.413504 | − | 0.716211i | ||||
\(303\) | 12.5162 | − | 7.22626i | 0.719040 | − | 0.415138i | ||||
\(304\) | 3.49188 | + | 3.49188i | 0.200273 | + | 0.200273i | ||||
\(305\) | −0.0493010 | − | 0.0132102i | −0.00282297 | − | 0.000756412i | ||||
\(306\) | 29.1903 | + | 7.82151i | 1.66870 | + | 0.447126i | ||||
\(307\) | 1.46571 | − | 1.46571i | 0.0836528 | − | 0.0836528i | −0.664042 | − | 0.747695i | \(-0.731161\pi\) |
0.747695 | + | 0.664042i | \(0.231161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.8165 | + | 18.3693i | 1.80998 | + | 1.04499i | ||||
\(310\) | 0.0681097 | − | 0.0182500i | 0.00386837 | − | 0.00103653i | ||||
\(311\) | 2.74774 | 0.155810 | 0.0779051 | − | 0.996961i | \(-0.475177\pi\) | ||||
0.0779051 | + | 0.996961i | \(0.475177\pi\) | |||||||
\(312\) | −4.13462 | − | 27.2566i | −0.234077 | − | 1.54310i | ||||
\(313\) | 7.59112i | 0.429075i | 0.976716 | + | 0.214538i | \(0.0688245\pi\) | ||||
−0.976716 | + | 0.214538i | \(0.931176\pi\) | |||||||
\(314\) | 6.21321 | − | 1.66482i | 0.350632 | − | 0.0939514i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.28869 | − | 2.47607i | 0.241257 | − | 0.139290i | ||||
\(317\) | −7.05236 | + | 7.05236i | −0.396100 | + | 0.396100i | −0.876855 | − | 0.480755i | \(-0.840363\pi\) |
0.480755 | + | 0.876855i | \(0.340363\pi\) | |||||||
\(318\) | −0.332826 | + | 1.24212i | −0.0186639 | + | 0.0696548i | ||||
\(319\) | −1.08078 | + | 4.03352i | −0.0605120 | + | 0.225834i | ||||
\(320\) | 0.0357386 | − | 0.0357386i | 0.00199785 | − | 0.00199785i | ||||
\(321\) | −35.4398 | + | 20.4612i | −1.97806 | + | 1.14203i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.7953 | − | 6.10799i | 1.26837 | − | 0.339858i | ||||
\(324\) | 25.5329i | 1.41849i | ||||||||
\(325\) | −2.00098 | + | 17.9113i | −0.110994 | + | 0.993543i | ||||
\(326\) | 2.86019 | 0.158411 | ||||||||
\(327\) | 39.4276 | − | 10.5646i | 2.18035 | − | 0.584223i | ||||
\(328\) | −0.413456 | − | 0.238709i | −0.0228293 | − | 0.0131805i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.0645173 | + | 0.0645173i | −0.00355156 | + | 0.00355156i | ||||
\(331\) | 16.3370 | + | 4.37748i | 0.897962 | + | 0.240608i | 0.678141 | − | 0.734932i | \(-0.262786\pi\) |
0.219821 | + | 0.975540i | \(0.429453\pi\) | |||||||
\(332\) | −10.2169 | − | 2.73762i | −0.560728 | − | 0.150247i | ||||
\(333\) | 26.8344 | + | 26.8344i | 1.47052 | + | 1.47052i | ||||
\(334\) | 9.66423 | − | 5.57964i | 0.528803 | − | 0.305305i | ||||
\(335\) | 0.140289 | − | 0.242988i | 0.00766483 | − | 0.0132759i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.92125i | 0.431498i | 0.976449 | + | 0.215749i | \(0.0692193\pi\) | ||||
−0.976449 | + | 0.215749i | \(0.930781\pi\) | |||||||
\(338\) | 0.354576 | + | 9.01974i | 0.0192864 | + | 0.490609i | ||||
\(339\) | 11.6302i | 0.631666i | ||||||||
\(340\) | 0.0935459 | + | 0.349118i | 0.00507324 | + | 0.0189336i | ||||
\(341\) | −2.66850 | − | 1.54066i | −0.144508 | − | 0.0834315i | ||||
\(342\) | −8.70054 | − | 15.0698i | −0.470471 | − | 0.814880i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.03523 | + | 1.34919i | 0.271482 | + | 0.0727433i | ||||
\(345\) | −0.0842049 | + | 0.314257i | −0.00453344 | + | 0.0169190i | ||||
\(346\) | 10.3433 | − | 10.3433i | 0.556060 | − | 0.556060i | ||||
\(347\) | −12.1691 | − | 21.0776i | −0.653274 | − | 1.13150i | −0.982324 | − | 0.187191i | \(-0.940062\pi\) |
0.329050 | − | 0.944313i | \(-0.393272\pi\) | |||||||
\(348\) | 8.78968 | − | 15.2242i | 0.471176 | − | 0.816101i | ||||
\(349\) | 4.20514 | + | 15.6938i | 0.225096 | + | 0.840070i | 0.982366 | + | 0.186968i | \(0.0598660\pi\) |
−0.757270 | + | 0.653102i | \(0.773467\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.75940 | − | 42.6028i | 0.254038 | − | 2.27397i | ||||
\(352\) | −6.56346 | −0.349834 | ||||||||
\(353\) | 15.8182 | − | 4.23848i | 0.841919 | − | 0.225591i | 0.188012 | − | 0.982167i | \(-0.439796\pi\) |
0.653907 | + | 0.756575i | \(0.273129\pi\) | |||||||
\(354\) | 12.2499 | − | 21.2174i | 0.651074 | − | 1.12769i | ||||
\(355\) | 0.190267 | + | 0.329552i | 0.0100983 | + | 0.0174908i | ||||
\(356\) | 18.0810 | + | 18.0810i | 0.958292 | + | 0.958292i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.63861 | + | 6.11536i | −0.0866031 | + | 0.323207i | ||||
\(359\) | 4.88620 | + | 4.88620i | 0.257884 | + | 0.257884i | 0.824193 | − | 0.566309i | \(-0.191629\pi\) |
−0.566309 | + | 0.824193i | \(0.691629\pi\) | |||||||
\(360\) | 0.534909 | − | 0.308830i | 0.0281922 | − | 0.0162768i | ||||
\(361\) | 4.68617 | + | 2.70556i | 0.246640 | + | 0.142398i | ||||
\(362\) | 2.82454 | + | 10.5413i | 0.148455 | + | 0.554041i | ||||
\(363\) | −30.4452 | −1.59796 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.101688 | −0.00532262 | ||||||||
\(366\) | 0.771939 | + | 2.88091i | 0.0403499 | + | 0.150588i | ||||
\(367\) | 12.3820 | + | 7.14874i | 0.646335 | + | 0.373161i | 0.787050 | − | 0.616889i | \(-0.211607\pi\) |
−0.140716 | + | 0.990050i | \(0.544940\pi\) | |||||||
\(368\) | −3.24186 | + | 1.87169i | −0.168993 | + | 0.0975684i | ||||
\(369\) | −0.939543 | − | 0.939543i | −0.0489106 | − | 0.0489106i | ||||
\(370\) | 0.0373145 | − | 0.139260i | 0.00193989 | − | 0.00723976i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.17244 | + | 9.17244i | 0.475569 | + | 0.475569i | ||||
\(373\) | −11.3326 | − | 19.6286i | −0.586780 | − | 1.01633i | −0.994651 | − | 0.103293i | \(-0.967062\pi\) |
0.407871 | − | 0.913039i | \(-0.366271\pi\) | |||||||
\(374\) | −2.50848 | + | 4.34481i | −0.129710 | + | 0.224665i | ||||
\(375\) | −1.12446 | + | 0.301298i | −0.0580669 | + | 0.0155590i | ||||
\(376\) | −13.7345 | −0.708303 | ||||||||
\(377\) | −7.91164 | + | 10.7411i | −0.407470 | + | 0.553196i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.37163 | − | 12.5831i | −0.173189 | − | 0.646349i | −0.996853 | − | 0.0792716i | \(-0.974741\pi\) |
0.823664 | − | 0.567078i | \(-0.191926\pi\) | |||||||
\(380\) | 0.104059 | − | 0.180236i | 0.00533812 | − | 0.00924589i | ||||
\(381\) | 4.47638 | + | 7.75331i | 0.229332 | + | 0.397214i | ||||
\(382\) | −8.49761 | + | 8.49761i | −0.434776 | + | 0.434776i | ||||
\(383\) | −0.594401 | + | 2.21834i | −0.0303725 | + | 0.113352i | −0.979448 | − | 0.201697i | \(-0.935354\pi\) |
0.949075 | + | 0.315049i | \(0.102021\pi\) | |||||||
\(384\) | 32.3144 | + | 8.65861i | 1.64904 | + | 0.441858i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.37047 | + | 7.56988i | 0.222451 | + | 0.385297i | ||||
\(387\) | 12.5643 | + | 7.25403i | 0.638681 | + | 0.368743i | ||||
\(388\) | 1.00768 | + | 3.76072i | 0.0511574 | + | 0.190922i | ||||
\(389\) | 12.6070i | 0.639198i | 0.947553 | + | 0.319599i | \(0.103548\pi\) | ||||
−0.947553 | + | 0.319599i | \(0.896452\pi\) | |||||||
\(390\) | −0.267055 | + | 0.116816i | −0.0135229 | + | 0.00591519i | ||||
\(391\) | 17.8892i | 0.904695i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.216484 | + | 0.374962i | −0.0109202 | + | 0.0189143i | ||||
\(394\) | 14.9441 | − | 8.62799i | 0.752874 | − | 0.434672i | ||||
\(395\) | −0.0858090 | − | 0.0858090i | −0.00431752 | − | 0.00431752i | ||||
\(396\) | −11.2491 | − | 3.01419i | −0.565289 | − | 0.151469i | ||||
\(397\) | 2.16498 | + | 0.580104i | 0.108657 | + | 0.0291146i | 0.312738 | − | 0.949839i | \(-0.398754\pi\) |
−0.204081 | + | 0.978954i | \(0.565421\pi\) | |||||||
\(398\) | −5.20339 | + | 5.20339i | −0.260822 | + | 0.260822i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.79914 | − | 3.34813i | −0.289957 | − | 0.167407i | ||||
\(401\) | −34.8284 | + | 9.33225i | −1.73925 | + | 0.466030i | −0.982280 | − | 0.187421i | \(-0.939987\pi\) |
−0.756969 | + | 0.653451i | \(0.773320\pi\) | |||||||
\(402\) | −16.3957 | −0.817742 | ||||||||
\(403\) | −6.14481 | − | 7.69042i | −0.306095 | − | 0.383087i | ||||
\(404\) | − | 7.00811i | − | 0.348666i | ||||||
\(405\) | 0.604362 | − | 0.161938i | 0.0300310 | − | 0.00804678i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.45612 | + | 3.15009i | −0.270450 | + | 0.156144i | ||||
\(408\) | 34.6126 | − | 34.6126i | 1.71358 | − | 1.71358i | ||||
\(409\) | −2.38876 | + | 8.91498i | −0.118117 | + | 0.440817i | −0.999501 | − | 0.0315823i | \(-0.989945\pi\) |
0.881385 | + | 0.472400i | \(0.156612\pi\) | |||||||
\(410\) | −0.00130648 | + | 0.00487584i | −6.45224e−5 | + | 0.000240801i | ||||
\(411\) | −37.7577 | + | 37.7577i | −1.86245 | + | 1.86245i | ||||
\(412\) | 15.4280 | − | 8.90737i | 0.760084 | − | 0.438834i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.7411 | − | 3.41398i | 0.626192 | − | 0.167788i | ||||
\(415\) | 0.259198i | 0.0127235i | ||||||||
\(416\) | −19.5260 | − | 7.64208i | −0.957339 | − | 0.374684i | ||||
\(417\) | −48.3924 | −2.36979 | ||||||||
\(418\) | 2.79040 | − | 0.747684i | 0.136483 | − | 0.0365704i | ||||
\(419\) | 15.4156 | + | 8.90022i | 0.753103 | + | 0.434804i | 0.826814 | − | 0.562475i | \(-0.190151\pi\) |
−0.0737108 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.59661 | + | 5.59661i | −0.272762 | + | 0.272762i | −0.830211 | − | 0.557449i | \(-0.811780\pi\) |
0.557449 | + | 0.830211i | \(0.311780\pi\) | |||||||
\(422\) | −13.8707 | − | 3.71664i | −0.675215 | − | 0.180923i | ||||
\(423\) | −36.9224 | − | 9.89333i | −1.79523 | − | 0.481030i | ||||
\(424\) | 1.02190 | + | 1.02190i | 0.0496280 | + | 0.0496280i | ||||
\(425\) | −27.7135 | + | 16.0004i | −1.34430 | + | 0.776132i | ||||
\(426\) | 11.1183 | − | 19.2574i | 0.538683 | − | 0.933026i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19.8435i | 0.959172i | ||||||||
\(429\) | 11.8616 | + | 4.64238i | 0.572682 | + | 0.224136i | ||||
\(430\) | − | 0.0551167i | − | 0.00265796i | ||||||
\(431\) | 3.00628 | + | 11.2196i | 0.144807 | + | 0.540428i | 0.999764 | + | 0.0217286i | \(0.00691696\pi\) |
−0.854957 | + | 0.518699i | \(0.826416\pi\) | |||||||
\(432\) | 13.7935 | + | 7.96366i | 0.663638 | + | 0.383152i | ||||
\(433\) | −14.5052 | − | 25.1237i | −0.697073 | − | 1.20737i | −0.969477 | − | 0.245183i | \(-0.921152\pi\) |
0.272403 | − | 0.962183i | \(-0.412181\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.416103 | − | 0.111495i | −0.0199506 | − | 0.00534575i | ||||
\(436\) | 5.12283 | − | 19.1187i | 0.245339 | − | 0.915619i | ||||
\(437\) | 7.28378 | − | 7.28378i | 0.348431 | − | 0.348431i | ||||
\(438\) | 2.97109 | + | 5.14608i | 0.141964 | + | 0.245889i | ||||
\(439\) | −8.42786 | + | 14.5975i | −0.402240 | + | 0.696700i | −0.993996 | − | 0.109417i | \(-0.965102\pi\) |
0.591756 | + | 0.806117i | \(0.298435\pi\) | |||||||
\(440\) | 0.0265394 | + | 0.0990464i | 0.00126522 | + | 0.00472185i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.5214 | + | 10.0049i | −0.595583 | + | 0.475884i | ||||
\(443\) | −32.2737 | −1.53337 | −0.766685 | − | 0.642023i | \(-0.778095\pi\) | ||||
−0.766685 | + | 0.642023i | \(0.778095\pi\) | |||||||
\(444\) | 25.6188 | − | 6.86455i | 1.21582 | − | 0.325777i | ||||
\(445\) | 0.313301 | − | 0.542654i | 0.0148519 | − | 0.0257243i | ||||
\(446\) | −1.14035 | − | 1.97515i | −0.0539973 | − | 0.0935261i | ||||
\(447\) | 12.6048 | + | 12.6048i | 0.596189 | + | 0.596189i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.40700 | − | 16.4471i | 0.207979 | − | 0.776188i | −0.780542 | − | 0.625103i | \(-0.785057\pi\) |
0.988521 | − | 0.151085i | \(-0.0482766\pi\) | |||||||
\(450\) | 16.6847 | + | 16.6847i | 0.786525 | + | 0.786525i | ||||
\(451\) | 0.191033 | − | 0.110293i | 0.00899539 | − | 0.00519349i | ||||
\(452\) | 4.88400 | + | 2.81978i | 0.229724 | + | 0.132631i | ||||
\(453\) | −16.7687 | − | 62.5815i | −0.787860 | − | 2.94033i | ||||
\(454\) | −12.7761 | −0.599610 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −28.1859 | −1.31992 | ||||||||
\(457\) | −1.47846 | − | 5.51768i | −0.0691593 | − | 0.258106i | 0.922686 | − | 0.385552i | \(-0.125989\pi\) |
−0.991846 | + | 0.127446i | \(0.959322\pi\) | |||||||
\(458\) | 6.59594 | + | 3.80817i | 0.308208 | + | 0.177944i | ||||
\(459\) | 65.9175 | − | 38.0575i | 3.07677 | − | 1.77637i | ||||
\(460\) | 0.111554 | + | 0.111554i | 0.00520121 | + | 0.00520121i | ||||
\(461\) | −7.08521 | + | 26.4424i | −0.329991 | + | 1.23154i | 0.579207 | + | 0.815180i | \(0.303362\pi\) |
−0.909198 | + | 0.416363i | \(0.863305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.6953 | − | 13.6953i | −0.636477 | − | 0.636477i | 0.313208 | − | 0.949685i | \(-0.398596\pi\) |
−0.949685 | + | 0.313208i | \(0.898596\pi\) | |||||||
\(464\) | −2.47828 | − | 4.29250i | −0.115051 | − | 0.199274i | ||||
\(465\) | 0.158937 | − | 0.275286i | 0.00737051 | − | 0.0127661i | ||||
\(466\) | −5.78499 | + | 1.55008i | −0.267984 | + | 0.0718062i | ||||
\(467\) | −16.7364 | −0.774470 | −0.387235 | − | 0.921981i | \(-0.626570\pi\) | ||||
−0.387235 | + | 0.921981i | \(0.626570\pi\) | |||||||
\(468\) | −29.9560 | − | 22.0648i | −1.38471 | − | 1.01995i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.0375852 | + | 0.140270i | 0.00173368 | + | 0.00647017i | ||||
\(471\) | 14.4987 | − | 25.1126i | 0.668067 | − | 1.15713i | ||||
\(472\) | −13.7669 | − | 23.8450i | −0.633672 | − | 1.09755i | ||||
\(473\) | −1.70310 | + | 1.70310i | −0.0783086 | + | 0.0783086i | ||||
\(474\) | −1.83535 | + | 6.84961i | −0.0843003 | + | 0.314613i | ||||
\(475\) | 17.7986 | + | 4.76912i | 0.816655 | + | 0.218822i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.01107 | + | 3.48328i | 0.0920807 | + | 0.159488i | ||||
\(478\) | −4.95082 | − | 2.85836i | −0.226445 | − | 0.130738i | ||||
\(479\) | 5.83074 | + | 21.7606i | 0.266413 | + | 0.994267i | 0.961380 | + | 0.275225i | \(0.0887525\pi\) |
−0.694967 | + | 0.719042i | \(0.744581\pi\) | |||||||
\(480\) | − | 0.677095i | − | 0.0309050i | ||||||
\(481\) | −19.8994 | + | 3.01860i | −0.907336 | + | 0.137636i | ||||
\(482\) | 4.36243i | 0.198703i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.38154 | + | 12.7852i | −0.335525 | + | 0.581146i | ||||
\(485\) | 0.0826252 | − | 0.0477037i | 0.00375182 | − | 0.00216611i | ||||
\(486\) | −8.34047 | − | 8.34047i | −0.378331 | − | 0.378331i | ||||
\(487\) | 6.74263 | + | 1.80668i | 0.305538 | + | 0.0818685i | 0.408330 | − | 0.912834i | \(-0.366111\pi\) |
−0.102793 | + | 0.994703i | \(0.532778\pi\) | |||||||
\(488\) | 3.23768 | + | 0.867535i | 0.146563 | + | 0.0392714i | ||||
\(489\) | 9.11734 | − | 9.11734i | 0.412300 | − | 0.412300i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.12954 | − | 1.22949i | −0.0961048 | − | 0.0554861i | 0.451177 | − | 0.892434i | \(-0.351004\pi\) |
−0.547282 | + | 0.836948i | \(0.684338\pi\) | |||||||
\(492\) | −0.896982 | + | 0.240346i | −0.0404391 | + | 0.0108356i | ||||
\(493\) | −23.6868 | −1.06680 | ||||||||
\(494\) | 9.17184 | + | 1.02464i | 0.412660 | + | 0.0461006i | ||||
\(495\) | 0.285383i | 0.0128270i | ||||||||
\(496\) | 3.53281 | − | 0.946613i | 0.158628 | − | 0.0425042i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.1171 | − | 7.57314i | 0.587790 | − | 0.339360i | ||||
\(499\) | −13.1882 | + | 13.1882i | −0.590385 | + | 0.590385i | −0.937735 | − | 0.347350i | \(-0.887082\pi\) |
0.347350 | + | 0.937735i | \(0.387082\pi\) | |||||||
\(500\) | −0.146101 | + | 0.545258i | −0.00653385 | + | 0.0243847i | ||||
\(501\) | 13.0203 | − | 48.5924i | 0.581704 | − | 2.17095i | ||||
\(502\) | −5.14020 | + | 5.14020i | −0.229418 | + | 0.229418i | ||||
\(503\) | 29.6335 | − | 17.1089i | 1.32129 | − | 0.762849i | 0.337359 | − | 0.941376i | \(-0.390467\pi\) |
0.983935 | + | 0.178527i | \(0.0571332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.165882 | + | 0.0444479i | −0.00738165 | + | 0.00197791i | ||||
\(506\) | 2.18983i | 0.0973498i | ||||||||
\(507\) | 29.8822 | + | 27.6217i | 1.32712 | + | 1.22672i | ||||
\(508\) | 4.34124 | 0.192611 | ||||||||
\(509\) | −8.28991 | + | 2.22128i | −0.367444 | + | 0.0984563i | −0.437816 | − | 0.899065i | \(-0.644248\pi\) |
0.0703723 | + | 0.997521i | \(0.477581\pi\) | |||||||
\(510\) | −0.448217 | − | 0.258778i | −0.0198474 | − | 0.0114589i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10.1365 | − | 10.1365i | 0.447973 | − | 0.447973i | ||||
\(513\) | −42.3346 | − | 11.3435i | −1.86912 | − | 0.500829i | ||||
\(514\) | 3.58839 | + | 0.961507i | 0.158277 | + | 0.0424103i | ||||
\(515\) | −0.308687 | − | 0.308687i | −0.0136024 | − | 0.0136024i | ||||
\(516\) | 8.78109 | − | 5.06976i | 0.386566 | − | 0.223184i | ||||
\(517\) | 3.17294 | − | 5.49570i | 0.139546 | − | 0.241701i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 65.9422i | − | 2.89454i | ||||||
\(520\) | −0.0363700 | + | 0.325559i | −0.00159493 | + | 0.0142767i | ||||
\(521\) | 22.9781i | 1.00669i | 0.864086 | + | 0.503344i | \(0.167897\pi\) | ||||
−0.864086 | + | 0.503344i | \(0.832103\pi\) | |||||||
\(522\) | 4.52040 | + | 16.8704i | 0.197853 | + | 0.738396i | ||||
\(523\) | 25.8931 | + | 14.9494i | 1.13222 | + | 0.653690i | 0.944493 | − | 0.328530i | \(-0.106553\pi\) |
0.187731 | + | 0.982220i | \(0.439887\pi\) | |||||||
\(524\) | 0.104975 | + | 0.181821i | 0.00458583 | + | 0.00794289i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.13326 | − | 1.10750i | −0.180218 | − | 0.0482894i | ||||
\(527\) | 4.52376 | − | 16.8829i | 0.197058 | − | 0.735431i | ||||
\(528\) | −3.34647 | + | 3.34647i | −0.145636 | + | 0.145636i | ||||
\(529\) | −7.59582 | − | 13.1563i | −0.330253 | − | 0.572015i | ||||
\(530\) | 0.00764016 | − | 0.0132331i | 0.000331867 | − | 0.000574811i | ||||
\(531\) | −19.8333 | − | 74.0189i | −0.860692 | − | 3.21215i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.696731 | − | 0.105689i | 0.0301788 | − | 0.00457790i | ||||
\(534\) | −36.6156 | −1.58451 | ||||||||
\(535\) | 0.469695 | − | 0.125854i | 0.0203067 | − | 0.00544116i | ||||
\(536\) | −9.21305 | + | 15.9575i | −0.397943 | + | 0.689258i | ||||
\(537\) | 14.2704 | + | 24.7171i | 0.615814 | + | 1.06662i | ||||
\(538\) | 10.0902 | + | 10.0902i | 0.435018 | + | 0.435018i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.173730 | − | 0.648368i | 0.00747614 | − | 0.0279013i | ||||
\(541\) | 9.06984 | + | 9.06984i | 0.389943 | + | 0.389943i | 0.874667 | − | 0.484724i | \(-0.161080\pi\) |
−0.484724 | + | 0.874667i | \(0.661080\pi\) | |||||||
\(542\) | 6.11028 | − | 3.52777i | 0.262459 | − | 0.151531i | ||||
\(543\) | 42.6060 | + | 24.5986i | 1.82840 | + | 1.05563i | ||||
\(544\) | −9.63597 | − | 35.9619i | −0.413139 | − | 1.54186i | ||||
\(545\) | −0.485030 | −0.0207764 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.5639 | 1.43509 | 0.717543 | − | 0.696514i | \(-0.245267\pi\) | ||||
0.717543 | + | 0.696514i | \(0.245267\pi\) | |||||||
\(548\) | 6.70153 | + | 25.0105i | 0.286275 | + | 1.06839i | ||||
\(549\) | 8.07894 | + | 4.66438i | 0.344801 | + | 0.199071i | ||||
\(550\) | −3.39243 | + | 1.95862i | −0.144654 | + | 0.0835158i | ||||
\(551\) | 9.64436 | + | 9.64436i | 0.410864 | + | 0.410864i | ||||
\(552\) | 5.52988 | − | 20.6378i | 0.235367 | − | 0.878403i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.0286 | − | 10.0286i | −0.426076 | − | 0.426076i | ||||
\(555\) | −0.324967 | − | 0.562860i | −0.0137941 | − | 0.0238921i | ||||
\(556\) | −11.7329 | + | 20.3219i | −0.497585 | + | 0.861842i | ||||
\(557\) | −22.9234 | + | 6.14230i | −0.971294 | + | 0.260257i | −0.709374 | − | 0.704832i | \(-0.751022\pi\) |
−0.261920 | + | 0.965090i | \(0.584356\pi\) | |||||||
\(558\) | −12.8878 | −0.545582 | ||||||||
\(559\) | −7.04961 | + | 3.08365i | −0.298167 | + | 0.130425i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.85363 | + | 21.8460i | 0.247140 | + | 0.922340i | ||||
\(562\) | 6.40360 | − | 11.0914i | 0.270120 | − | 0.467861i | ||||
\(563\) | −12.3766 | − | 21.4369i | −0.521611 | − | 0.903457i | −0.999684 | − | 0.0251369i | \(-0.991998\pi\) |
0.478073 | − | 0.878320i | \(-0.341336\pi\) | |||||||
\(564\) | −18.8904 | + | 18.8904i | −0.795427 | + | 0.795427i | ||||
\(565\) | 0.0357681 | − | 0.133488i | 0.00150477 | − | 0.00561589i | ||||
\(566\) | −1.35193 | − | 0.362247i | −0.0568257 | − | 0.0152264i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.4952 | − | 21.6423i | −0.524285 | − | 0.908089i | ||||
\(569\) | 33.4106 | + | 19.2896i | 1.40064 | + | 0.808663i | 0.994459 | − | 0.105128i | \(-0.0335252\pi\) |
0.406186 | + | 0.913790i | \(0.366859\pi\) | |||||||
\(570\) | 0.0771321 | + | 0.287861i | 0.00323071 | + | 0.0120572i | ||||
\(571\) | 29.3080i | 1.22650i | 0.789888 | + | 0.613252i | \(0.210139\pi\) | ||||
−0.789888 | + | 0.613252i | \(0.789861\pi\) | |||||||
\(572\) | 4.82540 | − | 3.85559i | 0.201760 | − | 0.161211i | ||||
\(573\) | 54.1752i | 2.26320i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.98393 | + | 12.0965i | −0.291250 | + | 0.504460i | ||||
\(576\) | −8.00008 | + | 4.61885i | −0.333337 | + | 0.192452i | ||||
\(577\) | 28.2123 | + | 28.2123i | 1.17449 | + | 1.17449i | 0.981127 | + | 0.193367i | \(0.0619408\pi\) |
0.193367 | + | 0.981127i | \(0.438059\pi\) | |||||||
\(578\) | −16.0865 | − | 4.31037i | −0.669112 | − | 0.179288i | ||||
\(579\) | 38.0619 | + | 10.1987i | 1.58180 | + | 0.423842i | ||||
\(580\) | −0.147707 | + | 0.147707i | −0.00613318 | + | 0.00613318i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.82822 | − | 2.78757i | −0.200136 | − | 0.115549i | ||||
\(583\) | −0.644982 | + | 0.172822i | −0.0267124 | + | 0.00715757i | ||||
\(584\) | 6.67806 | 0.276340 | ||||||||
\(585\) | −0.332282 | + | 0.849000i | −0.0137382 | + | 0.0351018i | ||||
\(586\) | − | 8.24444i | − | 0.340575i | ||||||
\(587\) | 31.6109 | − | 8.47012i | 1.30472 | − | 0.349599i | 0.461489 | − | 0.887146i | \(-0.347316\pi\) |
0.843234 | + | 0.537547i | \(0.180649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.71597 | + | 5.03217i | −0.359135 | + | 0.207347i | ||||
\(590\) | −0.205854 | + | 0.205854i | −0.00847486 | + | 0.00847486i | ||||
\(591\) | 20.1337 | − | 75.1401i | 0.828191 | − | 3.09085i | ||||
\(592\) | 1.93548 | − | 7.22330i | 0.0795477 | − | 0.296876i | ||||
\(593\) | 15.3805 | − | 15.3805i | 0.631601 | − | 0.631601i | −0.316868 | − | 0.948470i | \(-0.602631\pi\) |
0.948470 | + | 0.316868i | \(0.102631\pi\) | |||||||
\(594\) | 8.06901 | − | 4.65865i | 0.331076 | − | 0.191147i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.34937 | − | 2.23721i | 0.342003 | − | 0.0916396i | ||||
\(597\) | 33.1734i | 1.35770i | ||||||||
\(598\) | −2.54970 | + | 6.51463i | −0.104265 | + | 0.266403i | ||||
\(599\) | 30.1072 | 1.23015 | 0.615073 | − | 0.788470i | \(-0.289126\pi\) | ||||
0.615073 | + | 0.788470i | \(0.289126\pi\) | |||||||
\(600\) | 36.9176 | − | 9.89203i | 1.50715 | − | 0.403840i | ||||
\(601\) | −16.4105 | − | 9.47460i | −0.669398 | − | 0.386477i | 0.126450 | − | 0.991973i | \(-0.459642\pi\) |
−0.795849 | + | 0.605496i | \(0.792975\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.2620 | + | 36.2620i | −1.47670 | + | 1.47670i | ||||
\(604\) | −30.3461 | − | 8.13122i | −1.23477 | − | 0.330855i | ||||
\(605\) | 0.349442 | + | 0.0936327i | 0.0142068 | + | 0.00380671i | ||||
\(606\) | 7.09602 | + | 7.09602i | 0.288256 | + | 0.288256i | ||||
\(607\) | 18.4475 | − | 10.6507i | 0.748763 | − | 0.432298i | −0.0764838 | − | 0.997071i | \(-0.524369\pi\) |
0.825247 | + | 0.564772i | \(0.191036\pi\) | |||||||
\(608\) | −10.7189 | + | 18.5657i | −0.434709 | + | 0.752939i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 0.0354404i | − | 0.00143494i | ||||||
\(611\) | 15.8382 | − | 12.6550i | 0.640745 | − | 0.511968i | ||||
\(612\) | − | 66.0603i | − | 2.67033i | ||||||
\(613\) | −6.47832 | − | 24.1774i | −0.261657 | − | 0.976518i | −0.964265 | − | 0.264940i | \(-0.914648\pi\) |
0.702608 | − | 0.711577i | \(-0.252019\pi\) | |||||||
\(614\) | 1.24647 | + | 0.719649i | 0.0503034 | + | 0.0290427i | ||||
\(615\) | 0.0113780 | + | 0.0197072i | 0.000458804 | + | 0.000794671i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.1852 | − | 7.82015i | −1.17495 | − | 0.314827i | −0.382029 | − | 0.924150i | \(-0.624775\pi\) |
−0.792922 | + | 0.609323i | \(0.791441\pi\) | |||||||
\(618\) | −6.60244 | + | 24.6406i | −0.265589 | + | 0.991191i | ||||
\(619\) | 30.0154 | − | 30.0154i | 1.20642 | − | 1.20642i | 0.234240 | − | 0.972179i | \(-0.424740\pi\) |
0.972179 | − | 0.234240i | \(-0.0752601\pi\) | |||||||
\(620\) | −0.0770693 | − | 0.133488i | −0.00309518 | − | 0.00536100i | ||||
\(621\) | 16.6115 | − | 28.7720i | 0.666598 | − | 1.15458i | ||||
\(622\) | 0.493808 | + | 1.84292i | 0.0197999 | + | 0.0738942i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −13.8520 | + | 6.05915i | −0.554523 | + | 0.242560i | ||||
\(625\) | −24.9792 | −0.999170 | ||||||||
\(626\) | −5.09138 | + | 1.36423i | −0.203493 | + | 0.0545257i | ||||
\(627\) | 6.51149 | − | 11.2782i | 0.260044 | − | 0.450409i | ||||
\(628\) | −7.03053 | − | 12.1772i | −0.280549 | − | 0.485924i | ||||
\(629\) | −25.2700 | − | 25.2700i | −1.00758 | − | 1.00758i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.55956 | + | 35.6768i | −0.380560 | + | 1.42027i | 0.464488 | + | 0.885579i | \(0.346238\pi\) |
−0.845048 | + | 0.534690i | \(0.820428\pi\) | |||||||
\(632\) | 5.63523 | + | 5.63523i | 0.224157 | + | 0.224157i | ||||
\(633\) | −56.0627 | + | 32.3678i | −2.22829 | + | 1.28650i | ||||
\(634\) | −5.99744 | − | 3.46263i | −0.238189 | − | 0.137518i | ||||
\(635\) | −0.0275337 | − | 0.102757i | −0.00109264 | − | 0.00407779i | ||||
\(636\) | 2.81104 | 0.111465 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.89952 | −0.114793 | ||||||||
\(639\) | −18.0012 | − | 67.1814i | −0.712116 | − | 2.65765i | ||||
\(640\) | −0.344266 | − | 0.198762i | −0.0136083 | − | 0.00785676i | ||||
\(641\) | −7.17353 | + | 4.14164i | −0.283338 | + | 0.163585i | −0.634933 | − | 0.772567i | \(-0.718972\pi\) |
0.351596 | + | 0.936152i | \(0.385639\pi\) | |||||||
\(642\) | −20.0924 | − | 20.0924i | −0.792984 | − | 0.792984i | ||||
\(643\) | 8.56893 | − | 31.9797i | 0.337926 | − | 1.26116i | −0.562737 | − | 0.826636i | \(-0.690252\pi\) |
0.900663 | − | 0.434519i | \(-0.143082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.175694 | − | 0.175694i | −0.00691794 | − | 0.00691794i | ||||
\(646\) | 8.19329 | + | 14.1912i | 0.322361 | + | 0.558345i | ||||
\(647\) | −6.58281 | + | 11.4018i | −0.258797 | + | 0.448250i | −0.965920 | − | 0.258841i | \(-0.916659\pi\) |
0.707123 | + | 0.707091i | \(0.249993\pi\) | |||||||
\(648\) | −39.6895 | + | 10.6348i | −1.55915 | + | 0.417773i | ||||
\(649\) | 12.7217 | 0.499370 | ||||||||
\(650\) | −12.3728 | + | 1.87686i | −0.485301 | + | 0.0736166i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.61822 | − | 6.03927i | −0.0633743 | − | 0.236516i | ||||
\(653\) | 23.6676 | − | 40.9935i | 0.926184 | − | 1.60420i | 0.136539 | − | 0.990635i | \(-0.456402\pi\) |
0.789645 | − | 0.613564i | \(-0.210265\pi\) | |||||||
\(654\) | 14.1714 | + | 24.5456i | 0.554146 | + | 0.959808i | ||||
\(655\) | 0.00363792 | − | 0.00363792i | 0.000142145 | − | 0.000142145i | ||||
\(656\) | −0.0677662 | + | 0.252907i | −0.00264582 | + | 0.00987435i | ||||
\(657\) | 17.9526 | + | 4.81038i | 0.700397 | + | 0.187671i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.76562 | − | 4.79019i | −0.107733 | − | 0.186599i | 0.807118 | − | 0.590390i | \(-0.201026\pi\) |
−0.914852 | + | 0.403790i | \(0.867693\pi\) | |||||||
\(660\) | 0.172730 | + | 0.0997256i | 0.00672350 | + | 0.00388181i | ||||
\(661\) | −4.70431 | − | 17.5567i | −0.182976 | − | 0.682877i | −0.995055 | − | 0.0993289i | \(-0.968330\pi\) |
0.812078 | − | 0.583549i | \(-0.198336\pi\) | |||||||
\(662\) | 11.7440i | 0.456442i | ||||||||
\(663\) | −8.02190 | + | 71.8064i | −0.311545 | + | 2.78873i | ||||
\(664\) | − | 17.0220i | − | 0.660581i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.1754 | + | 22.8204i | −0.510536 | + | 0.884274i | ||||
\(667\) | −8.95380 | + | 5.16948i | −0.346692 | + | 0.200163i | ||||
\(668\) | −17.2491 | − | 17.2491i | −0.667389 | − | 0.667389i | ||||
\(669\) | −9.93120 | − | 2.66106i | −0.383962 | − | 0.102882i | ||||
\(670\) | 0.188185 | + | 0.0504240i | 0.00727022 | + | 0.00194805i | ||||
\(671\) | −1.09510 | + | 1.09510i | −0.0422760 | + | 0.0422760i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.86827 | − | 2.23334i | −0.149111 | − | 0.0860891i | 0.423588 | − | 0.905855i | \(-0.360770\pi\) |
−0.572699 | + | 0.819766i | \(0.694104\pi\) | |||||||
\(674\) | −5.31280 | + | 1.42356i | −0.204641 | + | 0.0548335i | ||||
\(675\) | 59.4305 | 2.28748 | ||||||||
\(676\) | 18.8445 | − | 5.85181i | 0.724789 | − | 0.225070i | ||||
\(677\) | − | 23.2495i | − | 0.893549i | −0.894647 | − | 0.446775i | \(-0.852573\pi\) | ||
0.894647 | − | 0.446775i | \(-0.147427\pi\) | |||||||
\(678\) | −7.80041 | + | 2.09011i | −0.299573 | + | 0.0802703i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.503723 | + | 0.290825i | −0.0193169 | + | 0.0111526i | ||||
\(681\) | −40.7259 | + | 40.7259i | −1.56062 | + | 1.56062i | ||||
\(682\) | 0.553757 | − | 2.06665i | 0.0212045 | − | 0.0791361i | ||||
\(683\) | 2.05374 | − | 7.66466i | 0.0785842 | − | 0.293280i | −0.915438 | − | 0.402459i | \(-0.868156\pi\) |
0.994022 | + | 0.109179i | \(0.0348222\pi\) | |||||||
\(684\) | −26.8972 | + | 26.8972i | −1.02844 | + | 1.02844i | ||||
\(685\) | 0.549494 | − | 0.317250i | 0.0209951 | − | 0.0121215i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.1649 | − | 8.88651i | 1.26532 | − | 0.339041i | ||||
\(688\) | − | 2.85887i | − | 0.108993i | ||||||
\(689\) | −2.12001 | − | 0.236838i | −0.0807660 | − | 0.00902282i | ||||
\(690\) | −0.225906 | −0.00860008 | ||||||||
\(691\) | 11.1445 | − | 2.98617i | 0.423958 | − | 0.113599i | −0.0405305 | − | 0.999178i | \(-0.512905\pi\) |
0.464489 | + | 0.885579i | \(0.346238\pi\) | |||||||
\(692\) | −27.6918 | − | 15.9879i | −1.05268 | − | 0.607768i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.9498 | − | 11.9498i | 0.453609 | − | 0.453609i | ||||
\(695\) | 0.555434 | + | 0.148828i | 0.0210688 | + | 0.00564537i | ||||
\(696\) | 27.3262 | + | 7.32204i | 1.03580 | + | 0.277541i | ||||
\(697\) | 0.884767 | + | 0.884767i | 0.0335129 | + | 0.0335129i | ||||
\(698\) | −9.77014 | + | 5.64079i | −0.369805 | + | 0.213507i | ||||
\(699\) | −13.4995 | + | 23.3818i | −0.510597 | + | 0.884380i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.0088i | 0.415797i | 0.978150 | + | 0.207898i | \(0.0666624\pi\) | ||||
−0.978150 | + | 0.207898i | \(0.933338\pi\) | |||||||
\(702\) | 29.4291 | − | 4.46419i | 1.11073 | − | 0.168490i | ||||
\(703\) | 20.5779i | 0.776110i | ||||||||
\(704\) | −0.396923 | − | 1.48134i | −0.0149596 | − | 0.0558299i | ||||
\(705\) | 0.566944 | + | 0.327325i | 0.0213523 | + | 0.0123278i | ||||
\(706\) | 5.68552 | + | 9.84760i | 0.213977 | + | 0.370619i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −51.7311 | − | 13.8613i | −1.94417 | − | 0.520939i | ||||
\(709\) | −7.69277 | + | 28.7098i | −0.288908 | + | 1.07822i | 0.657028 | + | 0.753866i | \(0.271813\pi\) |
−0.945936 | + | 0.324353i | \(0.894853\pi\) | |||||||
\(710\) | −0.186838 | + | 0.186838i | −0.00701189 | + | 0.00701189i | ||||
\(711\) | 11.0900 | + | 19.2084i | 0.415906 | + | 0.720370i | ||||
\(712\) | −20.5750 | + | 35.6370i | −0.771082 | + | 1.33555i | ||||
\(713\) | −1.97456 | − | 7.36914i | −0.0739477 | − | 0.275977i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.121866 | − | 0.0897635i | −0.00455754 | − | 0.00335697i | ||||
\(716\) | 13.8396 | 0.517211 | ||||||||
\(717\) | −24.8931 | + | 6.67008i | −0.929649 | + | 0.249099i | ||||
\(718\) | −2.39907 | + | 4.15530i | −0.0895323 | + | 0.155075i | ||||
\(719\) | −12.1922 | − | 21.1175i | −0.454693 | − | 0.787552i | 0.543977 | − | 0.839100i | \(-0.316918\pi\) |
−0.998671 | + | 0.0515483i | \(0.983584\pi\) | |||||||
\(720\) | −0.239526 | − | 0.239526i | −0.00892660 | − | 0.00892660i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.972454 | + | 3.62925i | −0.0361910 | + | 0.135067i | ||||
\(723\) | 13.9060 | + | 13.9060i | 0.517169 | + | 0.517169i | ||||
\(724\) | 20.6599 | − | 11.9280i | 0.767820 | − | 0.443301i | ||||
\(725\) | −16.0168 | − | 9.24733i | −0.594851 | − | 0.343437i | ||||
\(726\) | −5.47144 | − | 20.4197i | −0.203064 | − | 0.757846i | ||||
\(727\) | 20.3008 | 0.752915 | 0.376458 | − | 0.926434i | \(-0.377142\pi\) | ||||
0.376458 | + | 0.926434i | \(0.377142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.70851 | −0.100315 | ||||||||
\(730\) | −0.0182749 | − | 0.0682027i | −0.000676383 | − | 0.00252429i | ||||
\(731\) | −11.8318 | − | 6.83111i | −0.437616 | − | 0.252658i | ||||
\(732\) | 5.64629 | − | 3.25989i | 0.208693 | − | 0.120489i | ||||
\(733\) | −11.6143 | − | 11.6143i | −0.428983 | − | 0.428983i | 0.459299 | − | 0.888282i | \(-0.348101\pi\) |
−0.888282 | + | 0.459299i | \(0.848101\pi\) | |||||||
\(734\) | −2.56946 | + | 9.58936i | −0.0948406 | + | 0.353950i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.4909 | − | 11.4909i | −0.423560 | − | 0.423560i | ||||
\(737\) | −4.25679 | − | 7.37298i | −0.156801 | − | 0.271587i | ||||
\(738\) | 0.461305 | − | 0.799003i | 0.0169809 | − | 0.0294117i | ||||
\(739\) | 41.3778 | − | 11.0872i | 1.52211 | − | 0.407847i | 0.601672 | − | 0.798743i | \(-0.294501\pi\) |
0.920435 | + | 0.390896i | \(0.127835\pi\) | |||||||
\(740\) | −0.315157 | −0.0115854 | ||||||||
\(741\) | 32.5030 | − | 25.9706i | 1.19403 | − | 0.954054i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.7481 | + | 47.5766i | 0.467683 | + | 1.74542i | 0.647838 | + | 0.761778i | \(0.275673\pi\) |
−0.180155 | + | 0.983638i | \(0.557660\pi\) | |||||||
\(744\) | −10.4376 | + | 18.0785i | −0.382663 | + | 0.662791i | ||||
\(745\) | −0.105909 | − | 0.183440i | −0.00388022 | − | 0.00672073i | ||||
\(746\) | 11.1283 | − | 11.1283i | 0.407438 | − | 0.407438i | ||||
\(747\) | 12.2614 | − | 45.7601i | 0.448621 | − | 1.67427i | ||||
\(748\) | 10.5933 | + | 2.83846i | 0.387328 | + | 0.103784i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.404163 | − | 0.700031i | −0.0147580 | − | 0.0255615i | ||||
\(751\) | −19.9626 | − | 11.5254i | −0.728444 | − | 0.420567i | 0.0894086 | − | 0.995995i | \(-0.471502\pi\) |
−0.817853 | + | 0.575428i | \(0.804836\pi\) | |||||||
\(752\) | 1.94952 | + | 7.27571i | 0.0710917 | + | 0.265318i | ||||
\(753\) | 32.7705i | 1.19422i | ||||||||
\(754\) | −8.62593 | − | 3.37602i | −0.314138 | − | 0.122947i | ||||
\(755\) | 0.769863i | 0.0280182i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.1858 | − | 41.8911i | 0.879049 | − | 1.52256i | 0.0266620 | − | 0.999645i | \(-0.491512\pi\) |
0.852387 | − | 0.522912i | \(-0.175154\pi\) | |||||||
\(758\) | 7.83357 | − | 4.52272i | 0.284528 | − | 0.164272i | ||||
\(759\) | 6.98045 | + | 6.98045i | 0.253374 | + | 0.253374i | ||||
\(760\) | 0.323509 | + | 0.0866840i | 0.0117349 | + | 0.00314436i | ||||
\(761\) | 28.2385 | + | 7.56647i | 1.02364 | + | 0.274284i | 0.731320 | − | 0.682035i | \(-0.238905\pi\) |
0.292324 | + | 0.956319i | \(0.405571\pi\) | |||||||
\(762\) | −4.39570 | + | 4.39570i | −0.159239 | + | 0.159239i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 22.7504 | + | 13.1349i | 0.823079 | + | 0.475205i | ||||
\(765\) | −1.56365 | + | 0.418978i | −0.0565337 | + | 0.0151482i | ||||
\(766\) | −1.59467 | −0.0576176 | ||||||||
\(767\) | 37.8464 | + | 14.8123i | 1.36655 | + | 0.534842i | ||||
\(768\) | 31.7363i | 1.14518i | ||||||||
\(769\) | 1.87337 | − | 0.501968i | 0.0675554 | − | 0.0181014i | −0.224883 | − | 0.974386i | \(-0.572200\pi\) |
0.292438 | + | 0.956284i | \(0.405533\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.5036 | − | 8.37365i | 0.522334 | − | 0.301570i | ||||
\(772\) | 13.5111 | − | 13.5111i | 0.486273 | − | 0.486273i | ||||
\(773\) | −1.31839 | + | 4.92031i | −0.0474193 | + | 0.176971i | −0.985574 | − | 0.169245i | \(-0.945867\pi\) |
0.938155 | + | 0.346216i | \(0.112534\pi\) | |||||||
\(774\) | −2.60730 | + | 9.73059i | −0.0937176 | + | 0.349759i | ||||
\(775\) | 9.65001 | − | 9.65001i | 0.346639 | − | 0.346639i | ||||
\(776\) | −5.42614 | + | 3.13278i | −0.194787 | + | 0.112460i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.45552 | + | 2.26565i | −0.303145 | + | 0.0812275i | ||||
\(779\) | − | 0.720486i | − | 0.0258141i | ||||||
\(780\) | 0.397748 | + | 0.497794i | 0.0142417 | + | 0.0178239i | ||||
\(781\) | 11.5465 | 0.413167 | ||||||||
\(782\) | −11.9983 | + | 3.21494i | −0.429059 | + | 0.114966i | ||||
\(783\) | 38.0967 | + | 21.9951i | 1.36146 | + | 0.786041i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.243645 | + | 0.243645i | −0.00869606 | + | 0.00869606i | ||||
\(786\) | −0.290393 | − | 0.0778106i | −0.0103580 | − | 0.00277541i | ||||
\(787\) | −29.6181 | − | 7.93615i | −1.05577 | − | 0.282893i | −0.311137 | − | 0.950365i | \(-0.600710\pi\) |
−0.744635 | + | 0.667472i | \(0.767376\pi\) | |||||||
\(788\) | −26.6729 | − | 26.6729i | −0.950184 | − | 0.950184i | ||||
\(789\) | −16.7058 | + | 9.64510i | −0.594743 | + | 0.343375i | ||||
\(790\) | 0.0421312 | − | 0.0729734i | 0.00149896 | − | 0.00259628i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 18.7416i | − | 0.665954i | ||||||
\(793\) | −4.53294 | + | 1.98281i | −0.160969 | + | 0.0704115i | ||||
\(794\) | 1.55631i | 0.0552313i | ||||||||
\(795\) | −0.0178286 | − | 0.0665372i | −0.000632315 | − | 0.00235983i | ||||
\(796\) | 13.9309 | + | 8.04298i | 0.493766 | + | 0.285076i | ||||
\(797\) | −15.8566 | − | 27.4644i | −0.561669 | − | 0.972839i | −0.997351 | − | 0.0727386i | \(-0.976826\pi\) |
0.435682 | − | 0.900101i | \(-0.356507\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.7698 | + | 9.31655i | 1.23007 | + | 0.329596i | ||||
\(800\) | 7.52376 | − | 28.0791i | 0.266005 | − | 0.992745i | ||||
\(801\) | −80.9821 | + | 80.9821i | −2.86136 | + | 2.86136i | ||||
\(802\) | −12.5183 | − | 21.6824i | −0.442037 | − | 0.765631i | ||||
\(803\) | −1.54276 | + | 2.67214i | −0.0544429 | + | 0.0942979i | ||||
\(804\) | 9.27623 | + | 34.6194i | 0.327147 | + | 1.22093i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.05368 | − | 5.50342i | 0.142785 | − | 0.193850i | ||||
\(807\) | 64.3282 | 2.26446 | ||||||||
\(808\) | 10.8938 | − | 2.91897i | 0.383241 | − | 0.102689i | ||||
\(809\) | −4.55711 | + | 7.89315i | −0.160219 | + | 0.277508i | −0.934947 | − | 0.354787i | \(-0.884554\pi\) |
0.774728 | + | 0.632295i | \(0.217887\pi\) | |||||||
\(810\) | 0.217225 | + | 0.376245i | 0.00763251 | + | 0.0132199i | ||||
\(811\) | −21.0935 | − | 21.0935i | −0.740695 | − | 0.740695i | 0.232017 | − | 0.972712i | \(-0.425467\pi\) |
−0.972712 | + | 0.232017i | \(0.925467\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.23219 | − | 30.7229i | 0.288715 | − | 1.07750i | ||||
\(814\) | −3.09331 | − | 3.09331i | −0.108421 | − | 0.108421i | ||||
\(815\) | −0.132686 | + | 0.0766063i | −0.00464779 | + | 0.00268340i | ||||
\(816\) | −23.2487 | − | 13.4226i | −0.813867 | − | 0.469886i | ||||
\(817\) | 2.03610 | + | 7.59883i | 0.0712341 | + | 0.265849i | ||||
\(818\) | −6.40859 | −0.224071 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0110345 | 0.000385341 | ||||||||
\(821\) | −10.1294 | − | 37.8035i | −0.353519 | − | 1.31935i | −0.882338 | − | 0.470615i | \(-0.844032\pi\) |
0.528820 | − | 0.848734i | \(-0.322635\pi\) | |||||||
\(822\) | −32.1098 | − | 18.5386i | −1.11996 | − | 0.646607i | ||||
\(823\) | −31.6926 | + | 18.2977i | −1.10473 | + | 0.637819i | −0.937460 | − | 0.348092i | \(-0.886830\pi\) |
−0.167274 | + | 0.985910i | \(0.553496\pi\) | |||||||
\(824\) | 20.2720 | + | 20.2720i | 0.706209 | + | 0.706209i | ||||
\(825\) | −4.57051 | + | 17.0574i | −0.159125 | + | 0.593861i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.61851 | − | 4.61851i | −0.160601 | − | 0.160601i | 0.622232 | − | 0.782833i | \(-0.286226\pi\) |
−0.782833 | + | 0.622232i | \(0.786226\pi\) | |||||||
\(828\) | −14.4172 | − | 24.9713i | −0.501031 | − | 0.867812i | ||||
\(829\) | 5.83825 | − | 10.1121i | 0.202771 | − | 0.351209i | −0.746649 | − | 0.665218i | \(-0.768339\pi\) |
0.949420 | + | 0.314009i | \(0.101672\pi\) | |||||||
\(830\) | −0.173845 | + | 0.0465815i | −0.00603424 | + | 0.00161687i | ||||
\(831\) | −63.9361 | −2.21792 | ||||||||
\(832\) | 0.543949 | − | 4.86905i | 0.0188580 | − | 0.168804i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.69680 | − | 32.4569i | −0.301146 | − | 1.12389i | ||||
\(835\) | −0.298887 | + | 0.517687i | −0.0103434 | + | 0.0179153i | ||||
\(836\) | −3.15746 | − | 5.46888i | −0.109203 | − | 0.189145i | ||||
\(837\) | −22.9529 | + | 22.9529i | −0.793369 | + | 0.793369i | ||||
\(838\) | −3.19899 | + | 11.9388i | −0.110507 | + | 0.412419i | ||||
\(839\) | 22.6006 | + | 6.05583i | 0.780261 | + | 0.209070i | 0.626900 | − | 0.779100i | \(-0.284324\pi\) |
0.153361 | + | 0.988170i | \(0.450990\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.65516 | + | 13.2591i | 0.263971 | + | 0.457211i | ||||
\(842\) | −4.75945 | − | 2.74787i | −0.164021 | − | 0.0946978i | ||||
\(843\) | −14.9430 | − | 55.7682i | −0.514666 | − | 1.92076i | ||||
\(844\) | 31.3907i | 1.08051i | ||||||||
\(845\) | −0.258031 | − | 0.408935i | −0.00887653 | − | 0.0140678i | ||||
\(846\) | − | 26.5419i | − | 0.912530i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.396290 | − | 0.686394i | 0.0136086 | − | 0.0235709i | ||||
\(849\) | −5.46422 | + | 3.15477i | −0.187531 | + | 0.108271i | ||||
\(850\) | −15.7120 | − | 15.7120i | −0.538917 | − | 0.538917i | ||||
\(851\) | −15.0672 | − | 4.03725i | −0.516497 | − | 0.138395i | ||||
\(852\) | −46.9524 | − | 12.5808i | −1.60856 | − | 0.431013i | ||||
\(853\) | −34.6514 | + | 34.6514i | −1.18644 | + | 1.18644i | −0.208398 | + | 0.978044i | \(0.566825\pi\) |
−0.978044 | + | 0.208398i | \(0.933175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.807248 | + | 0.466065i | 0.0276073 | + | 0.0159391i | ||||
\(856\) | −30.8457 | + | 8.26508i | −1.05428 | + | 0.282495i | ||||
\(857\) | 2.39334 | 0.0817550 | 0.0408775 | − | 0.999164i | \(-0.486985\pi\) | ||||
0.0408775 | + | 0.999164i | \(0.486985\pi\) | |||||||
\(858\) | −0.981967 | + | 8.78988i | −0.0335238 | + | 0.300082i | ||||
\(859\) | 1.98266i | 0.0676476i | 0.999428 | + | 0.0338238i | \(0.0107685\pi\) | ||||
−0.999428 | + | 0.0338238i | \(0.989231\pi\) | |||||||
\(860\) | −0.116379 | + | 0.0311836i | −0.00396848 | + | 0.00106335i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.98473 | + | 4.03263i | −0.237901 | + | 0.137352i | ||||
\(863\) | 10.0713 | − | 10.0713i | 0.342832 | − | 0.342832i | −0.514599 | − | 0.857431i | \(-0.672059\pi\) |
0.857431 | + | 0.514599i | \(0.172059\pi\) | |||||||
\(864\) | −17.8955 | + | 66.7871i | −0.608819 | + | 2.27214i | ||||
\(865\) | −0.202802 | + | 0.756866i | −0.00689546 | + | 0.0257342i | ||||
\(866\) | 14.2437 | − | 14.2437i | 0.484021 | − | 0.484021i | ||||
\(867\) | −65.0186 | + | 37.5385i | −2.20815 | + | 1.27488i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.55672 | + | 0.953020i | −0.120653 | + | 0.0323290i | ||||
\(870\) | − | 0.299119i | − | 0.0101411i | ||||||
\(871\) | −4.07911 | − | 26.8906i | −0.138215 | − | 0.911153i | ||||
\(872\) | 31.8527 | 1.07867 | ||||||||
\(873\) | −16.8437 | + | 4.51326i | −0.570073 | + | 0.152751i | ||||
\(874\) | 6.19425 | + | 3.57625i | 0.209524 | + | 0.120969i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.18495 | − | 9.18495i | 0.310331 | − | 0.310331i | ||||
\(877\) | 47.4938 | + | 12.7259i | 1.60375 | + | 0.429724i | 0.946173 | − | 0.323660i | \(-0.104914\pi\) |
0.657580 | + | 0.753385i | \(0.271580\pi\) | |||||||
\(878\) | −11.3052 | − | 3.02921i | −0.381531 | − | 0.102231i | ||||
\(879\) | −26.2806 | − | 26.2806i | −0.886422 | − | 0.886422i | ||||
\(880\) | 0.0487017 | − | 0.0281179i | 0.00164173 | − | 0.000947855i | ||||
\(881\) | 13.0843 | − | 22.6627i | 0.440821 | − | 0.763525i | −0.556930 | − | 0.830560i | \(-0.688021\pi\) |
0.997751 | + | 0.0670352i | \(0.0213540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.56808i | 0.153728i | 0.997042 | + | 0.0768640i | \(0.0244907\pi\) | ||||
−0.997042 | + | 0.0768640i | \(0.975509\pi\) | |||||||
\(884\) | 28.2095 | + | 20.7784i | 0.948789 | + | 0.698853i | ||||
\(885\) | 1.31239i | 0.0441154i | ||||||||
\(886\) | −5.80004 | − | 21.6461i | −0.194856 | − | 0.727214i | ||||
\(887\) | −1.04425 | − | 0.602895i | −0.0350623 | − | 0.0202432i | 0.482366 | − | 0.875970i | \(-0.339777\pi\) |
−0.517429 | + | 0.855726i | \(0.673111\pi\) | |||||||
\(888\) | 21.3412 | + | 36.9640i | 0.716163 | + | 1.24043i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.420264 | + | 0.112609i | 0.0140873 | + | 0.00377467i | ||||
\(891\) | 4.91369 | − | 18.3381i | 0.164615 | − | 0.614351i | ||||
\(892\) | −3.52534 | + | 3.52534i | −0.118037 | + | 0.118037i | ||||
\(893\) | −10.3636 | − | 17.9503i | −0.346804 | − | 0.600683i | ||||
\(894\) | −6.18883 | + | 10.7194i | −0.206985 | + | 0.358509i | ||||
\(895\) | −0.0877758 | − | 0.327584i | −0.00293402 | − | 0.0109499i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.6389 | + | 28.8941i | 0.422000 | + | 0.964745i | ||||
\(898\) | 11.8231 | 0.394543 | ||||||||
\(899\) | 9.75739 | − | 2.61448i | 0.325427 | − | 0.0871979i | ||||
\(900\) | 25.7899 | − | 44.6694i | 0.859664 | − | 1.48898i | ||||
\(901\) | −1.89383 | − | 3.28020i | −0.0630925 | − | 0.109279i | ||||
\(902\) | 0.108305 | + | 0.108305i | 0.00360616 | + | 0.00360616i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.34895 | + | 8.76641i | −0.0781250 | + | 0.291566i | ||||
\(905\) | −0.413368 | − | 0.413368i | −0.0137408 | − | 0.0137408i | ||||
\(906\) | 38.9600 | − | 22.4936i | 1.29436 | − | 0.747298i | ||||
\(907\) | 30.1251 | + | 17.3927i | 1.00029 | + | 0.577515i | 0.908333 | − | 0.418248i | \(-0.137356\pi\) |
0.0919531 | + | 0.995763i | \(0.470689\pi\) | |||||||
\(908\) | 7.22835 | + | 26.9766i | 0.239881 | + | 0.895249i | ||||
\(909\) | 31.3882 | 1.04108 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.2796 | 0.340579 | 0.170290 | − | 0.985394i | \(-0.445530\pi\) | ||||
0.170290 | + | 0.985394i | \(0.445530\pi\) | |||||||
\(912\) | 4.00079 | + | 14.9311i | 0.132479 | + | 0.494420i | ||||
\(913\) | 6.81114 | + | 3.93241i | 0.225416 | + | 0.130144i | ||||
\(914\) | 3.43502 | − | 1.98321i | 0.113620 | − | 0.0655987i | ||||
\(915\) | −0.112972 | − | 0.112972i | −0.00373475 | − | 0.00373475i | ||||
\(916\) | 4.30912 | − | 16.0818i | 0.142377 | − | 0.531359i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 37.3716 | + | 37.3716i | 1.23345 | + | 1.23345i | ||||
\(919\) | 10.5049 | + | 18.1950i | 0.346525 | + | 0.600198i | 0.985630 | − | 0.168921i | \(-0.0540284\pi\) |
−0.639105 | + | 0.769120i | \(0.720695\pi\) | |||||||
\(920\) | −0.126941 | + | 0.219868i | −0.00418511 | + | 0.00724883i | ||||
\(921\) | 6.26733 | − | 1.67933i | 0.206516 | − | 0.0553357i | ||||
\(922\) | −19.0083 | −0.626004 | ||||||||
\(923\) | 34.3503 | + | 13.4440i | 1.13065 | + | 0.442516i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.22196 | − | 26.9527i | −0.237457 | − | 0.886200i | ||||
\(926\) | 6.72425 | − | 11.6467i | 0.220973 | − | 0.382736i | ||||
\(927\) | 39.8947 | + | 69.0997i | 1.31031 | + | 2.26953i | ||||
\(928\) | 15.2149 | − | 15.2149i | 0.499455 | − | 0.499455i | ||||
\(929\) | 0.310383 | − | 1.15836i | 0.0101833 | − | 0.0380047i | −0.960647 | − | 0.277771i | \(-0.910404\pi\) |
0.970831 | + | 0.239767i | \(0.0770709\pi\) | |||||||
\(930\) | 0.213198 | + | 0.0571263i | 0.00699105 | + | 0.00187325i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.54598 | + | 11.3380i | 0.214421 | + | 0.371387i | ||||
\(933\) | 7.44871 | + | 4.30052i | 0.243860 | + | 0.140793i | ||||
\(934\) | −3.00778 | − | 11.2252i | −0.0984174 | − | 0.367299i | ||||
\(935\) | − | 0.268745i | − | 0.00878890i | ||||||
\(936\) | 21.8215 | − | 55.7553i | 0.713259 | − | 1.82242i | ||||
\(937\) | 21.5733i | 0.704768i | 0.935855 | + | 0.352384i | \(0.114629\pi\) | ||||
−0.935855 | + | 0.352384i | \(0.885371\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.8809 | + | 20.5784i | −0.387720 | + | 0.671550i | ||||
\(940\) | 0.274914 | − | 0.158722i | 0.00896672 | − | 0.00517694i | ||||
\(941\) | 26.1939 | + | 26.1939i | 0.853896 | + | 0.853896i | 0.990610 | − | 0.136715i | \(-0.0436543\pi\) |
−0.136715 | + | 0.990610i | \(0.543654\pi\) | |||||||
\(942\) | 19.4487 | + | 5.21126i | 0.633673 | + | 0.169792i | ||||
\(943\) | 0.527543 | + | 0.141355i | 0.0171791 | + | 0.00460314i | ||||
\(944\) | −10.6775 | + | 10.6775i | −0.347523 | + | 0.347523i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.44834 | − | 0.836202i | −0.0470897 | − | 0.0271873i | ||||
\(947\) | −35.9653 | + | 9.63686i | −1.16871 | + | 0.313156i | −0.790441 | − | 0.612538i | \(-0.790149\pi\) |
−0.378273 | + | 0.925694i | \(0.623482\pi\) | |||||||
\(948\) | 15.5013 | 0.503459 | ||||||||
\(949\) | −7.70092 | + | 6.15320i | −0.249982 | + | 0.199741i | ||||
\(950\) | 12.7946i | 0.415113i | ||||||||
\(951\) | −30.1556 | + | 8.08016i | −0.977862 | + | 0.262017i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.3599 | + | 21.5697i | −1.21020 | + | 0.698712i | −0.962804 | − | 0.270201i | \(-0.912910\pi\) |
−0.247401 | + | 0.968913i | \(0.579576\pi\) | |||||||
\(954\) | −1.97483 | + | 1.97483i | −0.0639374 | + | 0.0639374i | ||||
\(955\) | 0.166613 | − | 0.621807i | 0.00539146 | − | 0.0201212i | ||||
\(956\) | −3.23436 | + | 12.0708i | −0.104607 | + | 0.390398i | ||||
\(957\) | −9.24273 | + | 9.24273i | −0.298775 | + | 0.298775i | ||||
\(958\) | −13.5470 | + | 7.82138i | −0.437684 | + | 0.252697i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.152817 | − | 0.0409471i | 0.00493213 | − | 0.00132156i | ||||
\(961\) | − | 23.5461i | − | 0.759550i | ||||||
\(962\) | −5.60079 | − | 12.8041i | −0.180577 | − | 0.412821i | ||||
\(963\) | −88.8760 | −2.86399 | ||||||||
\(964\) | 9.21123 | − | 2.46814i | 0.296674 | − | 0.0794935i | ||||
\(965\) | −0.405498 | − | 0.234115i | −0.0130535 | − | 0.00753641i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.54638 | + | 6.54638i | −0.210517 | + | 0.210517i | −0.804487 | − | 0.593970i | \(-0.797560\pi\) |
0.593970 | + | 0.804487i | \(0.297560\pi\) | |||||||
\(968\) | −22.9485 | − | 6.14902i | −0.737591 | − | 0.197637i | ||||
\(969\) | 71.3544 | + | 19.1193i | 2.29223 | + | 0.614202i | ||||
\(970\) | 0.0468439 | + | 0.0468439i | 0.00150407 | + | 0.00150407i | ||||
\(971\) | 32.3192 | − | 18.6595i | 1.03717 | − | 0.598812i | 0.118142 | − | 0.992997i | \(-0.462306\pi\) |
0.919031 | + | 0.394184i | \(0.128973\pi\) | |||||||
\(972\) | −12.8920 | + | 22.3296i | −0.413512 | + | 0.716224i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.84698i | 0.155307i | ||||||||
\(975\) | −33.4575 | + | 45.4232i | −1.07150 | + | 1.45471i | ||||
\(976\) | − | 1.83827i | − | 0.0588415i | ||||||
\(977\) | −9.72109 | − | 36.2796i | −0.311005 | − | 1.16069i | −0.927651 | − | 0.373447i | \(-0.878176\pi\) |
0.616646 | − | 0.787240i | \(-0.288491\pi\) | |||||||
\(978\) | 7.75354 | + | 4.47651i | 0.247931 | + | 0.143143i | ||||
\(979\) | −9.50648 | − | 16.4657i | −0.303829 | − | 0.526246i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 85.6296 | + | 22.9444i | 2.73394 | + | 0.732558i | ||||
\(982\) | 0.441914 | − | 1.64925i | 0.0141020 | − | 0.0526295i | ||||
\(983\) | 24.6592 | − | 24.6592i | 0.786506 | − | 0.786506i | −0.194413 | − | 0.980920i | \(-0.562280\pi\) |
0.980920 | + | 0.194413i | \(0.0622803\pi\) | |||||||
\(984\) | −0.747210 | − | 1.29421i | −0.0238202 | − | 0.0412578i | ||||
\(985\) | −0.462179 | + | 0.800517i | −0.0147262 | + | 0.0255066i | ||||
\(986\) | −4.25686 | − | 15.8868i | −0.135566 | − | 0.505939i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.02566 | − | 19.9460i | −0.0962591 | − | 0.634566i | ||||
\(989\) | −5.96336 | −0.189624 | ||||||||
\(990\) | −0.191407 | + | 0.0512874i | −0.00608332 | + | 0.00163002i | ||||
\(991\) | 19.0679 | − | 33.0266i | 0.605712 | − | 1.04912i | −0.386227 | − | 0.922404i | \(-0.626222\pi\) |
0.991939 | − | 0.126720i | \(-0.0404450\pi\) | |||||||
\(992\) | 7.93875 | + | 13.7503i | 0.252055 | + | 0.436573i | ||||
\(993\) | 37.4359 | + | 37.4359i | 1.18799 | + | 1.18799i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.102023 | − | 0.380755i | 0.00323434 | − | 0.0120707i | ||||
\(996\) | −23.4119 | − | 23.4119i | −0.741835 | − | 0.741835i | ||||
\(997\) | −16.1229 | + | 9.30855i | −0.510617 | + | 0.294805i | −0.733087 | − | 0.680135i | \(-0.761921\pi\) |
0.222470 | + | 0.974939i | \(0.428588\pi\) | |||||||
\(998\) | −11.2155 | − | 6.47526i | −0.355020 | − | 0.204971i | ||||
\(999\) | 17.1777 | + | 64.1080i | 0.543478 | + | 2.02829i |
(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 | 637.2.bd.b.97.5 | 28 | ||
7.2 | even | 3 | 91.2.ba.a.45.5 | yes | 28 | ||
7.3 | odd | 6 | 91.2.w.a.19.3 | ✓ | 28 | ||
7.4 | even | 3 | 637.2.x.a.19.3 | 28 | |||
7.5 | odd | 6 | 637.2.bb.a.227.5 | 28 | |||
7.6 | odd | 2 | 637.2.bd.a.97.5 | 28 | |||
13.11 | odd | 12 | 637.2.bd.a.440.5 | 28 | |||
21.2 | odd | 6 | 819.2.et.b.136.3 | 28 | |||
21.17 | even | 6 | 819.2.gh.b.19.5 | 28 | |||
91.11 | odd | 12 | 637.2.bb.a.362.5 | 28 | |||
91.24 | even | 12 | 91.2.ba.a.89.5 | yes | 28 | ||
91.37 | odd | 12 | 91.2.w.a.24.3 | yes | 28 | ||
91.76 | even | 12 | inner | 637.2.bd.b.440.5 | 28 | ||
91.89 | even | 12 | 637.2.x.a.570.3 | 28 | |||
273.128 | even | 12 | 819.2.gh.b.388.5 | 28 | |||
273.206 | odd | 12 | 819.2.et.b.271.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.19.3 | ✓ | 28 | 7.3 | odd | 6 | ||
91.2.w.a.24.3 | yes | 28 | 91.37 | odd | 12 | ||
91.2.ba.a.45.5 | yes | 28 | 7.2 | even | 3 | ||
91.2.ba.a.89.5 | yes | 28 | 91.24 | even | 12 | ||
637.2.x.a.19.3 | 28 | 7.4 | even | 3 | |||
637.2.x.a.570.3 | 28 | 91.89 | even | 12 | |||
637.2.bb.a.227.5 | 28 | 7.5 | odd | 6 | |||
637.2.bb.a.362.5 | 28 | 91.11 | odd | 12 | |||
637.2.bd.a.97.5 | 28 | 7.6 | odd | 2 | |||
637.2.bd.a.440.5 | 28 | 13.11 | odd | 12 | |||
637.2.bd.b.97.5 | 28 | 1.1 | even | 1 | trivial | ||
637.2.bd.b.440.5 | 28 | 91.76 | even | 12 | inner | ||
819.2.et.b.136.3 | 28 | 21.2 | odd | 6 | |||
819.2.et.b.271.3 | 28 | 273.206 | odd | 12 | |||
819.2.gh.b.19.5 | 28 | 21.17 | even | 6 | |||
819.2.gh.b.388.5 | 28 | 273.128 | even | 12 |