Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(236,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.236");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 236.2 | ||
Character | \(\chi\) | \(=\) | 315.236 |
Dual form | 315.2.be.b.311.2 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02825 | + | 1.17101i | −1.43419 | + | 0.828028i | −0.997437 | − | 0.0715553i | \(-0.977204\pi\) |
−0.436750 | + | 0.899583i | \(0.643870\pi\) | |||||||
\(3\) | 0.587320 | + | 1.62943i | 0.339089 | + | 0.940754i | ||||
\(4\) | 1.74252 | − | 3.01813i | 0.871260 | − | 1.50907i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.09931 | − | 2.61714i | −1.26529 | − | 1.06844i | ||||
\(7\) | 2.45764 | + | 0.979787i | 0.928902 | + | 0.370325i | ||||
\(8\) | 3.47799i | 1.22966i | ||||||||
\(9\) | −2.31011 | + | 1.91400i | −0.770037 | + | 0.638000i | ||||
\(10\) | −2.02825 | + | 1.17101i | −0.641388 | + | 0.370305i | ||||
\(11\) | 0.240982i | 0.0726589i | 0.999340 | + | 0.0363295i | \(0.0115666\pi\) | ||||
−0.999340 | + | 0.0363295i | \(0.988433\pi\) | |||||||
\(12\) | 5.94127 | + | 1.06671i | 1.71510 | + | 0.307933i | ||||
\(13\) | 5.02640 | − | 2.90199i | 1.39407 | − | 0.804868i | 0.400309 | − | 0.916380i | \(-0.368903\pi\) |
0.993763 | + | 0.111513i | \(0.0355696\pi\) | |||||||
\(14\) | −6.13205 | + | 0.890673i | −1.63886 | + | 0.238042i | ||||
\(15\) | 0.587320 | + | 1.62943i | 0.151645 | + | 0.420718i | ||||
\(16\) | −0.587714 | − | 1.01795i | −0.146928 | − | 0.254488i | ||||
\(17\) | 3.01284 | + | 5.21840i | 0.730722 | + | 1.26565i | 0.956575 | + | 0.291486i | \(0.0941496\pi\) |
−0.225853 | + | 0.974161i | \(0.572517\pi\) | |||||||
\(18\) | 2.44416 | − | 6.58722i | 0.576094 | − | 1.55262i | ||||
\(19\) | 0.688475 | + | 0.397491i | 0.157947 | + | 0.0911908i | 0.576890 | − | 0.816822i | \(-0.304266\pi\) |
−0.418943 | + | 0.908012i | \(0.637599\pi\) | |||||||
\(20\) | 1.74252 | − | 3.01813i | 0.389639 | − | 0.674875i | ||||
\(21\) | −0.153074 | + | 4.58002i | −0.0334034 | + | 0.999442i | ||||
\(22\) | −0.282192 | − | 0.488771i | −0.0601636 | − | 0.104206i | ||||
\(23\) | 0.396557i | 0.0826878i | 0.999145 | + | 0.0413439i | \(0.0131639\pi\) | ||||
−0.999145 | + | 0.0413439i | \(0.986836\pi\) | |||||||
\(24\) | −5.66715 | + | 2.04269i | −1.15680 | + | 0.416963i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.79651 | + | 11.7719i | −1.33291 | + | 2.30866i | ||||
\(27\) | −4.47551 | − | 2.64004i | −0.861312 | − | 0.508076i | ||||
\(28\) | 7.23962 | − | 5.71020i | 1.36816 | − | 1.07913i | ||||
\(29\) | −4.83674 | − | 2.79249i | −0.898160 | − | 0.518553i | −0.0215574 | − | 0.999768i | \(-0.506862\pi\) |
−0.876603 | + | 0.481215i | \(0.840196\pi\) | |||||||
\(30\) | −3.09931 | − | 2.61714i | −0.565854 | − | 0.477821i | ||||
\(31\) | −7.62683 | − | 4.40335i | −1.36982 | − | 0.790865i | −0.378914 | − | 0.925432i | \(-0.623702\pi\) |
−0.990905 | + | 0.134566i | \(0.957036\pi\) | |||||||
\(32\) | −3.64000 | − | 2.10155i | −0.643467 | − | 0.371506i | ||||
\(33\) | −0.392665 | + | 0.141534i | −0.0683542 | + | 0.0246379i | ||||
\(34\) | −12.2216 | − | 7.05613i | −2.09598 | − | 1.21012i | ||||
\(35\) | 2.45764 | + | 0.979787i | 0.415418 | + | 0.165614i | ||||
\(36\) | 1.75129 | + | 10.3074i | 0.291882 | + | 1.71790i | ||||
\(37\) | −5.50596 | + | 9.53660i | −0.905174 | + | 1.56781i | −0.0844904 | + | 0.996424i | \(0.526926\pi\) |
−0.820684 | + | 0.571383i | \(0.806407\pi\) | |||||||
\(38\) | −1.86186 | −0.302034 | ||||||||
\(39\) | 7.68071 | + | 6.48578i | 1.22990 | + | 1.03856i | ||||
\(40\) | 3.47799i | 0.549918i | ||||||||
\(41\) | 0.493886 | + | 0.855435i | 0.0771320 | + | 0.133596i | 0.902011 | − | 0.431712i | \(-0.142090\pi\) |
−0.824879 | + | 0.565309i | \(0.808757\pi\) | |||||||
\(42\) | −5.05277 | − | 9.46865i | −0.779659 | − | 1.46104i | ||||
\(43\) | 2.80477 | − | 4.85800i | 0.427723 | − | 0.740838i | −0.568947 | − | 0.822374i | \(-0.692649\pi\) |
0.996670 | + | 0.0815357i | \(0.0259825\pi\) | |||||||
\(44\) | 0.727317 | + | 0.419917i | 0.109647 | + | 0.0633048i | ||||
\(45\) | −2.31011 | + | 1.91400i | −0.344371 | + | 0.285322i | ||||
\(46\) | −0.464371 | − | 0.804314i | −0.0684678 | − | 0.118590i | ||||
\(47\) | 1.05437 | + | 1.82622i | 0.153796 | + | 0.266382i | 0.932620 | − | 0.360860i | \(-0.117517\pi\) |
−0.778824 | + | 0.627242i | \(0.784184\pi\) | |||||||
\(48\) | 1.31351 | − | 1.55550i | 0.189588 | − | 0.224518i | ||||
\(49\) | 5.08003 | + | 4.81594i | 0.725719 | + | 0.687991i | ||||
\(50\) | −2.02825 | + | 1.17101i | −0.286837 | + | 0.165606i | ||||
\(51\) | −6.73353 | + | 7.97410i | −0.942883 | + | 1.11660i | ||||
\(52\) | − | 20.2271i | − | 2.80500i | ||||||
\(53\) | −0.327502 | + | 0.189083i | −0.0449858 | + | 0.0259726i | −0.522324 | − | 0.852747i | \(-0.674935\pi\) |
0.477338 | + | 0.878720i | \(0.341602\pi\) | |||||||
\(54\) | 12.1689 | + | 0.113794i | 1.65598 | + | 0.0154854i | ||||
\(55\) | 0.240982i | 0.0324941i | ||||||||
\(56\) | −3.40769 | + | 8.54766i | −0.455372 | + | 1.14223i | ||||
\(57\) | −0.243330 | + | 1.35528i | −0.0322299 | + | 0.179511i | ||||
\(58\) | 13.0801 | 1.71751 | ||||||||
\(59\) | 7.36945 | − | 12.7643i | 0.959421 | − | 1.66177i | 0.235510 | − | 0.971872i | \(-0.424324\pi\) |
0.723911 | − | 0.689893i | \(-0.242343\pi\) | |||||||
\(60\) | 5.94127 | + | 1.06671i | 0.767014 | + | 0.137712i | ||||
\(61\) | −3.45074 | + | 1.99229i | −0.441822 | + | 0.255086i | −0.704370 | − | 0.709833i | \(-0.748771\pi\) |
0.262548 | + | 0.964919i | \(0.415437\pi\) | |||||||
\(62\) | 20.6254 | 2.61943 | ||||||||
\(63\) | −7.55274 | + | 2.44051i | −0.951556 | + | 0.307476i | ||||
\(64\) | 12.1946 | 1.52433 | ||||||||
\(65\) | 5.02640 | − | 2.90199i | 0.623448 | − | 0.359948i | ||||
\(66\) | 0.630683 | − | 0.746879i | 0.0776318 | − | 0.0919345i | ||||
\(67\) | −1.02677 | + | 1.77842i | −0.125440 | + | 0.217269i | −0.921905 | − | 0.387416i | \(-0.873368\pi\) |
0.796465 | + | 0.604685i | \(0.206701\pi\) | |||||||
\(68\) | 20.9998 | 2.54659 | ||||||||
\(69\) | −0.646163 | + | 0.232906i | −0.0777889 | + | 0.0280386i | ||||
\(70\) | −6.13205 | + | 0.890673i | −0.732920 | + | 0.106456i | ||||
\(71\) | − | 2.66240i | − | 0.315968i | −0.987442 | − | 0.157984i | \(-0.949500\pi\) | ||
0.987442 | − | 0.157984i | \(-0.0504995\pi\) | |||||||
\(72\) | −6.65687 | − | 8.03454i | −0.784520 | − | 0.946879i | ||||
\(73\) | −7.46653 | + | 4.31080i | −0.873891 | + | 0.504541i | −0.868639 | − | 0.495445i | \(-0.835005\pi\) |
−0.00525172 | + | 0.999986i | \(0.501672\pi\) | |||||||
\(74\) | − | 25.7901i | − | 2.99804i | ||||||
\(75\) | 0.587320 | + | 1.62943i | 0.0678179 | + | 0.188151i | ||||
\(76\) | 2.39936 | − | 1.38527i | 0.275226 | − | 0.158902i | ||||
\(77\) | −0.236111 | + | 0.592249i | −0.0269074 | + | 0.0674930i | ||||
\(78\) | −23.1733 | − | 4.16059i | −2.62386 | − | 0.471094i | ||||
\(79\) | 0.939111 | + | 1.62659i | 0.105658 | + | 0.183005i | 0.914007 | − | 0.405699i | \(-0.132972\pi\) |
−0.808349 | + | 0.588704i | \(0.799638\pi\) | |||||||
\(80\) | −0.587714 | − | 1.01795i | −0.0657084 | − | 0.113810i | ||||
\(81\) | 1.67322 | − | 8.84310i | 0.185913 | − | 0.982566i | ||||
\(82\) | −2.00344 | − | 1.15669i | −0.221243 | − | 0.127735i | ||||
\(83\) | −1.10515 | + | 1.91417i | −0.121306 | + | 0.210108i | −0.920283 | − | 0.391254i | \(-0.872042\pi\) |
0.798977 | + | 0.601362i | \(0.205375\pi\) | |||||||
\(84\) | 13.5564 | + | 8.44277i | 1.47912 | + | 0.921182i | ||||
\(85\) | 3.01284 | + | 5.21840i | 0.326789 | + | 0.566015i | ||||
\(86\) | 13.1376i | 1.41667i | ||||||||
\(87\) | 1.70947 | − | 9.52124i | 0.183274 | − | 1.02078i | ||||
\(88\) | −0.838134 | −0.0893454 | ||||||||
\(89\) | 2.86854 | − | 4.96845i | 0.304064 | − | 0.526655i | −0.672988 | − | 0.739653i | \(-0.734990\pi\) |
0.977053 | + | 0.212998i | \(0.0683229\pi\) | |||||||
\(90\) | 2.44416 | − | 6.58722i | 0.257637 | − | 0.694354i | ||||
\(91\) | 15.1964 | − | 2.20727i | 1.59302 | − | 0.231384i | ||||
\(92\) | 1.19686 | + | 0.691008i | 0.124781 | + | 0.0720426i | ||||
\(93\) | 2.69558 | − | 15.0136i | 0.279519 | − | 1.55684i | ||||
\(94\) | −4.27704 | − | 2.46935i | −0.441143 | − | 0.254694i | ||||
\(95\) | 0.688475 | + | 0.397491i | 0.0706361 | + | 0.0407818i | ||||
\(96\) | 1.28650 | − | 7.16542i | 0.131303 | − | 0.731318i | ||||
\(97\) | 13.7481 | + | 7.93745i | 1.39591 | + | 0.805926i | 0.993961 | − | 0.109738i | \(-0.0350011\pi\) |
0.401944 | + | 0.915664i | \(0.368334\pi\) | |||||||
\(98\) | −15.9431 | − | 3.81914i | −1.61049 | − | 0.385791i | ||||
\(99\) | −0.461240 | − | 0.556696i | −0.0463564 | − | 0.0559500i | ||||
\(100\) | 1.74252 | − | 3.01813i | 0.174252 | − | 0.301813i | ||||
\(101\) | 0.331838 | 0.0330191 | 0.0165096 | − | 0.999864i | \(-0.494745\pi\) | ||||
0.0165096 | + | 0.999864i | \(0.494745\pi\) | |||||||
\(102\) | 4.31952 | − | 24.0584i | 0.427696 | − | 2.38214i | ||||
\(103\) | − | 10.4715i | − | 1.03179i | −0.856652 | − | 0.515895i | \(-0.827460\pi\) | ||
0.856652 | − | 0.515895i | \(-0.172540\pi\) | |||||||
\(104\) | 10.0931 | + | 17.4818i | 0.989710 | + | 1.71423i | ||||
\(105\) | −0.153074 | + | 4.58002i | −0.0149385 | + | 0.446964i | ||||
\(106\) | 0.442836 | − | 0.767015i | 0.0430120 | − | 0.0744990i | ||||
\(107\) | −0.490862 | − | 0.283399i | −0.0474534 | − | 0.0273972i | 0.476086 | − | 0.879399i | \(-0.342055\pi\) |
−0.523539 | + | 0.852002i | \(0.675389\pi\) | |||||||
\(108\) | −15.7667 | + | 8.90736i | −1.51715 | + | 0.857111i | ||||
\(109\) | −2.43326 | − | 4.21452i | −0.233064 | − | 0.403678i | 0.725644 | − | 0.688070i | \(-0.241542\pi\) |
−0.958708 | + | 0.284392i | \(0.908208\pi\) | |||||||
\(110\) | −0.282192 | − | 0.488771i | −0.0269060 | − | 0.0466025i | ||||
\(111\) | −18.7730 | − | 3.37056i | −1.78186 | − | 0.319919i | ||||
\(112\) | −0.447017 | − | 3.07759i | −0.0422392 | − | 0.290805i | ||||
\(113\) | 13.6410 | − | 7.87562i | 1.28324 | − | 0.740876i | 0.305797 | − | 0.952097i | \(-0.401077\pi\) |
0.977438 | + | 0.211221i | \(0.0677439\pi\) | |||||||
\(114\) | −1.09351 | − | 3.03378i | −0.102417 | − | 0.284140i | ||||
\(115\) | 0.396557i | 0.0369791i | ||||||||
\(116\) | −16.8562 | + | 9.73195i | −1.56506 | + | 0.903589i | ||||
\(117\) | −6.05712 | + | 16.3244i | −0.559981 | + | 1.50919i | ||||
\(118\) | 34.5187i | 3.17771i | ||||||||
\(119\) | 2.29158 | + | 15.7769i | 0.210069 | + | 1.44627i | ||||
\(120\) | −5.66715 | + | 2.04269i | −0.517338 | + | 0.186472i | ||||
\(121\) | 10.9419 | 0.994721 | ||||||||
\(122\) | 4.66597 | − | 8.08170i | 0.422437 | − | 0.731683i | ||||
\(123\) | −1.10381 | + | 1.30717i | −0.0995268 | + | 0.117863i | ||||
\(124\) | −26.5798 | + | 15.3459i | −2.38694 | + | 1.37810i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 12.4610 | − | 13.7943i | 1.11011 | − | 1.22889i | ||||
\(127\) | −12.0618 | −1.07031 | −0.535154 | − | 0.844754i | \(-0.679746\pi\) | ||||
−0.535154 | + | 0.844754i | \(0.679746\pi\) | |||||||
\(128\) | −17.4537 | + | 10.0769i | −1.54270 | + | 0.890678i | ||||
\(129\) | 9.56309 | + | 1.71698i | 0.841983 | + | 0.151172i | ||||
\(130\) | −6.79651 | + | 11.7719i | −0.596094 | + | 1.03246i | ||||
\(131\) | −14.3505 | −1.25381 | −0.626905 | − | 0.779096i | \(-0.715679\pi\) | ||||
−0.626905 | + | 0.779096i | \(0.715679\pi\) | |||||||
\(132\) | −0.257058 | + | 1.43174i | −0.0223741 | + | 0.124617i | ||||
\(133\) | 1.30257 | + | 1.65145i | 0.112947 | + | 0.143199i | ||||
\(134\) | − | 4.80943i | − | 0.415472i | ||||||
\(135\) | −4.47551 | − | 2.64004i | −0.385191 | − | 0.227219i | ||||
\(136\) | −18.1495 | + | 10.4786i | −1.55631 | + | 0.898536i | ||||
\(137\) | − | 2.15340i | − | 0.183977i | −0.995760 | − | 0.0919886i | \(-0.970678\pi\) | ||
0.995760 | − | 0.0919886i | \(-0.0293223\pi\) | |||||||
\(138\) | 1.03784 | − | 1.22905i | 0.0883470 | − | 0.104624i | ||||
\(139\) | −13.8296 | + | 7.98451i | −1.17301 | + | 0.677237i | −0.954387 | − | 0.298572i | \(-0.903490\pi\) |
−0.218623 | + | 0.975810i | \(0.570156\pi\) | |||||||
\(140\) | 7.23962 | − | 5.71020i | 0.611860 | − | 0.482600i | ||||
\(141\) | −2.35646 | + | 2.79060i | −0.198449 | + | 0.235011i | ||||
\(142\) | 3.11769 | + | 5.40000i | 0.261631 | + | 0.453158i | ||||
\(143\) | 0.699329 | + | 1.21127i | 0.0584808 | + | 0.101292i | ||||
\(144\) | 3.30604 | + | 1.22669i | 0.275503 | + | 0.102224i | ||||
\(145\) | −4.83674 | − | 2.79249i | −0.401669 | − | 0.231904i | ||||
\(146\) | 10.0960 | − | 17.4867i | 0.835548 | − | 1.44721i | ||||
\(147\) | −4.86364 | + | 11.1061i | −0.401147 | + | 0.916014i | ||||
\(148\) | 19.1885 | + | 33.2354i | 1.57728 | + | 2.73194i | ||||
\(149\) | − | 1.36724i | − | 0.112009i | −0.998431 | − | 0.0560044i | \(-0.982164\pi\) | ||
0.998431 | − | 0.0560044i | \(-0.0178361\pi\) | |||||||
\(150\) | −3.09931 | − | 2.61714i | −0.253058 | − | 0.213688i | ||||
\(151\) | 4.22191 | 0.343574 | 0.171787 | − | 0.985134i | \(-0.445046\pi\) | ||||
0.171787 | + | 0.985134i | \(0.445046\pi\) | |||||||
\(152\) | −1.38247 | + | 2.39451i | −0.112133 | + | 0.194220i | ||||
\(153\) | −16.9480 | − | 6.28849i | −1.37016 | − | 0.508394i | ||||
\(154\) | −0.214637 | − | 1.47771i | −0.0172959 | − | 0.119078i | ||||
\(155\) | −7.62683 | − | 4.40335i | −0.612602 | − | 0.353686i | ||||
\(156\) | 32.9588 | − | 11.8798i | 2.63881 | − | 0.951145i | ||||
\(157\) | 2.06559 | + | 1.19257i | 0.164852 | + | 0.0951772i | 0.580156 | − | 0.814505i | \(-0.302992\pi\) |
−0.415304 | + | 0.909683i | \(0.636325\pi\) | |||||||
\(158\) | −3.80950 | − | 2.19941i | −0.303067 | − | 0.174976i | ||||
\(159\) | −0.500447 | − | 0.422590i | −0.0396880 | − | 0.0335136i | ||||
\(160\) | −3.64000 | − | 2.10155i | −0.287767 | − | 0.166142i | ||||
\(161\) | −0.388541 | + | 0.974596i | −0.0306213 | + | 0.0768089i | ||||
\(162\) | 6.96165 | + | 19.8953i | 0.546959 | + | 1.56312i | ||||
\(163\) | 8.75207 | − | 15.1590i | 0.685515 | − | 1.18735i | −0.287759 | − | 0.957703i | \(-0.592910\pi\) |
0.973275 | − | 0.229644i | \(-0.0737563\pi\) | |||||||
\(164\) | 3.44242 | 0.268808 | ||||||||
\(165\) | −0.392665 | + | 0.141534i | −0.0305689 | + | 0.0110184i | ||||
\(166\) | − | 5.17655i | − | 0.401778i | ||||||
\(167\) | −8.17532 | − | 14.1601i | −0.632625 | − | 1.09574i | −0.987013 | − | 0.160640i | \(-0.948644\pi\) |
0.354388 | − | 0.935098i | \(-0.384689\pi\) | |||||||
\(168\) | −15.9293 | − | 0.532389i | −1.22897 | − | 0.0410747i | ||||
\(169\) | 10.3431 | − | 17.9148i | 0.795624 | − | 1.37806i | ||||
\(170\) | −12.2216 | − | 7.05613i | −0.937352 | − | 0.541180i | ||||
\(171\) | −2.35125 | + | 0.399492i | −0.179805 | + | 0.0305499i | ||||
\(172\) | −9.77473 | − | 16.9303i | −0.745316 | − | 1.29093i | ||||
\(173\) | 9.25630 | + | 16.0324i | 0.703743 | + | 1.21892i | 0.967143 | + | 0.254233i | \(0.0818229\pi\) |
−0.263400 | + | 0.964687i | \(0.584844\pi\) | |||||||
\(174\) | 7.68223 | + | 21.3132i | 0.582388 | + | 1.61575i | ||||
\(175\) | 2.45764 | + | 0.979787i | 0.185780 | + | 0.0740649i | ||||
\(176\) | 0.245308 | − | 0.141629i | 0.0184908 | − | 0.0106757i | ||||
\(177\) | 25.1267 | + | 4.51132i | 1.88864 | + | 0.339092i | ||||
\(178\) | 13.4363i | 1.00709i | ||||||||
\(179\) | 16.3655 | − | 9.44863i | 1.22322 | − | 0.706224i | 0.257613 | − | 0.966248i | \(-0.417064\pi\) |
0.965602 | + | 0.260025i | \(0.0837307\pi\) | |||||||
\(180\) | 1.75129 | + | 10.3074i | 0.130534 | + | 0.768268i | ||||
\(181\) | − | 12.5008i | − | 0.929175i | −0.885527 | − | 0.464588i | \(-0.846203\pi\) | ||
0.885527 | − | 0.464588i | \(-0.153797\pi\) | |||||||
\(182\) | −28.2374 | + | 22.2720i | −2.09309 | + | 1.65091i | ||||
\(183\) | −5.27299 | − | 4.45265i | −0.389791 | − | 0.329149i | ||||
\(184\) | −1.37922 | −0.101677 | ||||||||
\(185\) | −5.50596 | + | 9.53660i | −0.404806 | + | 0.701145i | ||||
\(186\) | 12.1137 | + | 33.6078i | 0.888223 | + | 2.46424i | ||||
\(187\) | −1.25754 | + | 0.726042i | −0.0919605 | + | 0.0530934i | ||||
\(188\) | 7.34904 | 0.535984 | ||||||||
\(189\) | −8.41253 | − | 10.8733i | −0.611922 | − | 0.790918i | ||||
\(190\) | −1.86186 | −0.135074 | ||||||||
\(191\) | 7.55653 | − | 4.36277i | 0.546771 | − | 0.315679i | −0.201047 | − | 0.979582i | \(-0.564435\pi\) |
0.747819 | + | 0.663903i | \(0.231101\pi\) | |||||||
\(192\) | 7.16214 | + | 19.8703i | 0.516883 | + | 1.43402i | ||||
\(193\) | −5.69624 | + | 9.86618i | −0.410025 | + | 0.710183i | −0.994892 | − | 0.100945i | \(-0.967813\pi\) |
0.584867 | + | 0.811129i | \(0.301147\pi\) | |||||||
\(194\) | −37.1793 | −2.66932 | ||||||||
\(195\) | 7.68071 | + | 6.48578i | 0.550027 | + | 0.464457i | ||||
\(196\) | 23.3872 | − | 6.94036i | 1.67051 | − | 0.495740i | ||||
\(197\) | − | 18.6026i | − | 1.32538i | −0.748893 | − | 0.662690i | \(-0.769415\pi\) | ||
0.748893 | − | 0.662690i | \(-0.230585\pi\) | |||||||
\(198\) | 1.58740 | + | 0.589000i | 0.112812 | + | 0.0418584i | ||||
\(199\) | −19.5486 | + | 11.2864i | −1.38577 | + | 0.800072i | −0.992835 | − | 0.119496i | \(-0.961872\pi\) |
−0.392931 | + | 0.919568i | \(0.628539\pi\) | |||||||
\(200\) | 3.47799i | 0.245931i | ||||||||
\(201\) | −3.50086 | − | 0.628554i | −0.246932 | − | 0.0443348i | ||||
\(202\) | −0.673050 | + | 0.388585i | −0.0473556 | + | 0.0273408i | ||||
\(203\) | −9.15094 | − | 11.6019i | −0.642270 | − | 0.814296i | ||||
\(204\) | 12.3336 | + | 34.2177i | 0.863524 | + | 2.39572i | ||||
\(205\) | 0.493886 | + | 0.855435i | 0.0344945 | + | 0.0597462i | ||||
\(206\) | 12.2622 | + | 21.2388i | 0.854350 | + | 1.47978i | ||||
\(207\) | −0.759009 | − | 0.916090i | −0.0527548 | − | 0.0636726i | ||||
\(208\) | −5.90817 | − | 3.41108i | −0.409658 | − | 0.236516i | ||||
\(209\) | −0.0957884 | + | 0.165910i | −0.00662582 | + | 0.0114763i | ||||
\(210\) | −5.05277 | − | 9.46865i | −0.348674 | − | 0.653399i | ||||
\(211\) | −4.97834 | − | 8.62274i | −0.342723 | − | 0.593614i | 0.642214 | − | 0.766525i | \(-0.278016\pi\) |
−0.984937 | + | 0.172911i | \(0.944683\pi\) | |||||||
\(212\) | 1.31793i | 0.0905155i | ||||||||
\(213\) | 4.33820 | − | 1.56368i | 0.297249 | − | 0.107142i | ||||
\(214\) | 1.32745 | 0.0907427 | ||||||||
\(215\) | 2.80477 | − | 4.85800i | 0.191284 | − | 0.331313i | ||||
\(216\) | 9.18204 | − | 15.5658i | 0.624758 | − | 1.05912i | ||||
\(217\) | −14.4297 | − | 18.2945i | −0.979551 | − | 1.24191i | ||||
\(218\) | 9.87049 | + | 5.69873i | 0.668514 | + | 0.385967i | ||||
\(219\) | −11.4094 | − | 9.63439i | −0.770977 | − | 0.651032i | ||||
\(220\) | 0.727317 | + | 0.419917i | 0.0490357 | + | 0.0283108i | ||||
\(221\) | 30.2875 | + | 17.4865i | 2.03736 | + | 1.17627i | ||||
\(222\) | 42.0232 | − | 15.1470i | 2.82042 | − | 1.01660i | ||||
\(223\) | −2.06000 | − | 1.18934i | −0.137948 | − | 0.0796443i | 0.429438 | − | 0.903096i | \(-0.358712\pi\) |
−0.567386 | + | 0.823452i | \(0.692045\pi\) | |||||||
\(224\) | −6.88675 | − | 8.73130i | −0.460140 | − | 0.583384i | ||||
\(225\) | −2.31011 | + | 1.91400i | −0.154007 | + | 0.127600i | ||||
\(226\) | −18.4448 | + | 31.9474i | −1.22693 | + | 2.12511i | ||||
\(227\) | 6.16323 | 0.409068 | 0.204534 | − | 0.978859i | \(-0.434432\pi\) | ||||
0.204534 | + | 0.978859i | \(0.434432\pi\) | |||||||
\(228\) | 3.66641 | + | 3.09601i | 0.242814 | + | 0.205038i | ||||
\(229\) | − | 26.8755i | − | 1.77598i | −0.459862 | − | 0.887990i | \(-0.652101\pi\) | ||
0.459862 | − | 0.887990i | \(-0.347899\pi\) | |||||||
\(230\) | −0.464371 | − | 0.804314i | −0.0306197 | − | 0.0530349i | ||||
\(231\) | −1.10370 | − | 0.0368881i | −0.0726184 | − | 0.00242706i | ||||
\(232\) | 9.71226 | − | 16.8221i | 0.637641 | − | 1.10443i | ||||
\(233\) | 1.10739 | + | 0.639354i | 0.0725478 | + | 0.0418855i | 0.535835 | − | 0.844323i | \(-0.319997\pi\) |
−0.463287 | + | 0.886208i | \(0.653330\pi\) | |||||||
\(234\) | −6.83072 | − | 40.2029i | −0.446538 | − | 2.62815i | ||||
\(235\) | 1.05437 | + | 1.82622i | 0.0687795 | + | 0.119130i | ||||
\(236\) | −25.6828 | − | 44.4840i | −1.67181 | − | 2.89566i | ||||
\(237\) | −2.09886 | + | 2.48555i | −0.136336 | + | 0.161454i | ||||
\(238\) | −23.1228 | − | 29.3160i | −1.49883 | − | 1.90027i | ||||
\(239\) | −10.8351 | + | 6.25563i | −0.700862 | + | 0.404643i | −0.807668 | − | 0.589637i | \(-0.799271\pi\) |
0.106806 | + | 0.994280i | \(0.465937\pi\) | |||||||
\(240\) | 1.31351 | − | 1.55550i | 0.0847865 | − | 0.100407i | ||||
\(241\) | − | 11.4155i | − | 0.735335i | −0.929957 | − | 0.367667i | \(-0.880156\pi\) | ||
0.929957 | − | 0.367667i | \(-0.119844\pi\) | |||||||
\(242\) | −22.1929 | + | 12.8131i | −1.42661 | + | 0.823656i | ||||
\(243\) | 15.3920 | − | 2.46734i | 0.987394 | − | 0.158280i | ||||
\(244\) | 13.8864i | 0.888986i | ||||||||
\(245\) | 5.08003 | + | 4.81594i | 0.324552 | + | 0.307679i | ||||
\(246\) | 0.708084 | − | 3.94382i | 0.0451458 | − | 0.251449i | ||||
\(247\) | 4.61407 | 0.293586 | ||||||||
\(248\) | 15.3148 | − | 26.5260i | 0.972492 | − | 1.68440i | ||||
\(249\) | −3.76810 | − | 0.676534i | −0.238793 | − | 0.0428736i | ||||
\(250\) | −2.02825 | + | 1.17101i | −0.128278 | + | 0.0740611i | ||||
\(251\) | 3.48345 | 0.219873 | 0.109937 | − | 0.993939i | \(-0.464935\pi\) | ||||
0.109937 | + | 0.993939i | \(0.464935\pi\) | |||||||
\(252\) | −5.79501 | + | 27.0478i | −0.365051 | + | 1.70385i | ||||
\(253\) | −0.0955632 | −0.00600800 | ||||||||
\(254\) | 24.4642 | − | 14.1244i | 1.53502 | − | 0.886245i | ||||
\(255\) | −6.73353 | + | 7.97410i | −0.421670 | + | 0.499357i | ||||
\(256\) | 11.4056 | − | 19.7551i | 0.712850 | − | 1.23469i | ||||
\(257\) | −25.6042 | −1.59715 | −0.798574 | − | 0.601897i | \(-0.794412\pi\) | ||||
−0.798574 | + | 0.601897i | \(0.794412\pi\) | |||||||
\(258\) | −21.4069 | + | 7.71600i | −1.33274 | + | 0.480377i | ||||
\(259\) | −22.8755 | + | 18.0429i | −1.42142 | + | 1.12113i | ||||
\(260\) | − | 20.2271i | − | 1.25443i | ||||||
\(261\) | 16.5182 | − | 2.80655i | 1.02245 | − | 0.173721i | ||||
\(262\) | 29.1064 | − | 16.8046i | 1.79820 | − | 1.03819i | ||||
\(263\) | − | 1.93451i | − | 0.119287i | −0.998220 | − | 0.0596434i | \(-0.981004\pi\) | ||
0.998220 | − | 0.0596434i | \(-0.0189964\pi\) | |||||||
\(264\) | −0.492253 | − | 1.36568i | −0.0302961 | − | 0.0840521i | ||||
\(265\) | −0.327502 | + | 0.189083i | −0.0201183 | + | 0.0116153i | ||||
\(266\) | −4.57580 | − | 1.82423i | −0.280560 | − | 0.111851i | ||||
\(267\) | 9.78051 | + | 1.75602i | 0.598557 | + | 0.107467i | ||||
\(268\) | 3.57834 | + | 6.19787i | 0.218582 | + | 0.378595i | ||||
\(269\) | 5.96644 | + | 10.3342i | 0.363780 | + | 0.630086i | 0.988580 | − | 0.150700i | \(-0.0481526\pi\) |
−0.624799 | + | 0.780785i | \(0.714819\pi\) | |||||||
\(270\) | 12.1689 | + | 0.113794i | 0.740578 | + | 0.00692527i | ||||
\(271\) | −15.6502 | − | 9.03565i | −0.950682 | − | 0.548877i | −0.0573895 | − | 0.998352i | \(-0.518278\pi\) |
−0.893293 | + | 0.449475i | \(0.851611\pi\) | |||||||
\(272\) | 3.54138 | − | 6.13385i | 0.214728 | − | 0.371919i | ||||
\(273\) | 12.5218 | + | 23.4652i | 0.757852 | + | 1.42018i | ||||
\(274\) | 2.52165 | + | 4.36762i | 0.152338 | + | 0.263858i | ||||
\(275\) | 0.240982i | 0.0145318i | ||||||||
\(276\) | −0.423011 | + | 2.35605i | −0.0254623 | + | 0.141818i | ||||
\(277\) | 18.3023 | 1.09968 | 0.549838 | − | 0.835271i | \(-0.314689\pi\) | ||||
0.549838 | + | 0.835271i | \(0.314689\pi\) | |||||||
\(278\) | 18.6999 | − | 32.3891i | 1.12154 | − | 1.94257i | ||||
\(279\) | 26.0468 | − | 4.42552i | 1.55938 | − | 0.264949i | ||||
\(280\) | −3.40769 | + | 8.54766i | −0.203648 | + | 0.510821i | ||||
\(281\) | 18.3680 | + | 10.6048i | 1.09575 | + | 0.632629i | 0.935100 | − | 0.354384i | \(-0.115309\pi\) |
0.160645 | + | 0.987012i | \(0.448643\pi\) | |||||||
\(282\) | 1.51165 | − | 8.41946i | 0.0900175 | − | 0.501371i | ||||
\(283\) | 1.43261 | + | 0.827120i | 0.0851601 | + | 0.0491672i | 0.541975 | − | 0.840394i | \(-0.317677\pi\) |
−0.456815 | + | 0.889562i | \(0.651010\pi\) | |||||||
\(284\) | −8.03547 | − | 4.63928i | −0.476817 | − | 0.275291i | ||||
\(285\) | −0.243330 | + | 1.35528i | −0.0144137 | + | 0.0802798i | ||||
\(286\) | −2.83682 | − | 1.63784i | −0.167745 | − | 0.0968475i | ||||
\(287\) | 0.375651 | + | 2.58626i | 0.0221740 | + | 0.152662i | ||||
\(288\) | 12.4312 | − | 2.11213i | 0.732514 | − | 0.124459i | ||||
\(289\) | −9.65444 | + | 16.7220i | −0.567908 | + | 0.983646i | ||||
\(290\) | 13.0801 | 0.768092 | ||||||||
\(291\) | −4.85903 | + | 27.0634i | −0.284842 | + | 1.58648i | ||||
\(292\) | 30.0466i | 1.75835i | ||||||||
\(293\) | −11.7536 | − | 20.3579i | −0.686655 | − | 1.18932i | −0.972914 | − | 0.231169i | \(-0.925745\pi\) |
0.286259 | − | 0.958152i | \(-0.407588\pi\) | |||||||
\(294\) | −3.14065 | − | 28.2212i | −0.183166 | − | 1.64590i | ||||
\(295\) | 7.36945 | − | 12.7643i | 0.429066 | − | 0.743164i | ||||
\(296\) | −33.1682 | − | 19.1497i | −1.92786 | − | 1.11305i | ||||
\(297\) | 0.636203 | − | 1.07852i | 0.0369163 | − | 0.0625820i | ||||
\(298\) | 1.60105 | + | 2.77310i | 0.0927464 | + | 0.160641i | ||||
\(299\) | 1.15080 | + | 1.99325i | 0.0665527 | + | 0.115273i | ||||
\(300\) | 5.94127 | + | 1.06671i | 0.343019 | + | 0.0615866i | ||||
\(301\) | 11.6529 | − | 9.19117i | 0.671664 | − | 0.529770i | ||||
\(302\) | −8.56307 | + | 4.94389i | −0.492749 | + | 0.284489i | ||||
\(303\) | 0.194895 | + | 0.540709i | 0.0111964 | + | 0.0310629i | ||||
\(304\) | − | 0.934445i | − | 0.0535941i | ||||||
\(305\) | −3.45074 | + | 1.99229i | −0.197589 | + | 0.114078i | ||||
\(306\) | 41.7386 | − | 7.09165i | 2.38604 | − | 0.405402i | ||||
\(307\) | 15.5809i | 0.889246i | 0.895718 | + | 0.444623i | \(0.146662\pi\) | ||||
−0.895718 | + | 0.444623i | \(0.853338\pi\) | |||||||
\(308\) | 1.37606 | + | 1.74462i | 0.0784082 | + | 0.0994090i | ||||
\(309\) | 17.0626 | − | 6.15014i | 0.970660 | − | 0.349869i | ||||
\(310\) | 20.6254 | 1.17145 | ||||||||
\(311\) | −9.23270 | + | 15.9915i | −0.523539 | + | 0.906796i | 0.476086 | + | 0.879399i | \(0.342055\pi\) |
−0.999625 | + | 0.0273968i | \(0.991278\pi\) | |||||||
\(312\) | −22.5575 | + | 26.7134i | −1.27707 | + | 1.51235i | ||||
\(313\) | −14.3818 | + | 8.30334i | −0.812908 | + | 0.469333i | −0.847965 | − | 0.530053i | \(-0.822172\pi\) |
0.0350566 | + | 0.999385i | \(0.488839\pi\) | |||||||
\(314\) | −5.58602 | −0.315237 | ||||||||
\(315\) | −7.55274 | + | 2.44051i | −0.425549 | + | 0.137507i | ||||
\(316\) | 6.54568 | 0.368223 | ||||||||
\(317\) | −11.7602 | + | 6.78974i | −0.660517 | + | 0.381350i | −0.792474 | − | 0.609906i | \(-0.791207\pi\) |
0.131957 | + | 0.991255i | \(0.457874\pi\) | |||||||
\(318\) | 1.50989 | + | 0.271089i | 0.0846702 | + | 0.0152019i | ||||
\(319\) | 0.672942 | − | 1.16557i | 0.0376775 | − | 0.0652593i | ||||
\(320\) | 12.1946 | 0.681699 | ||||||||
\(321\) | 0.173487 | − | 0.966273i | 0.00968311 | − | 0.0539321i | ||||
\(322\) | −0.353203 | − | 2.43170i | −0.0196832 | − | 0.135514i | ||||
\(323\) | 4.79032i | 0.266540i | ||||||||
\(324\) | −23.7740 | − | 20.4593i | −1.32078 | − | 1.13663i | ||||
\(325\) | 5.02640 | − | 2.90199i | 0.278814 | − | 0.160974i | ||||
\(326\) | 40.9950i | 2.27050i | ||||||||
\(327\) | 5.43819 | − | 6.44011i | 0.300732 | − | 0.356139i | ||||
\(328\) | −2.97519 | + | 1.71773i | −0.164278 | + | 0.0948457i | ||||
\(329\) | 0.801958 | + | 5.52126i | 0.0442134 | + | 0.304397i | ||||
\(330\) | 0.630683 | − | 0.746879i | 0.0347180 | − | 0.0411143i | ||||
\(331\) | −14.8106 | − | 25.6528i | −0.814066 | − | 1.41000i | −0.909997 | − | 0.414616i | \(-0.863916\pi\) |
0.0959307 | − | 0.995388i | \(-0.469417\pi\) | |||||||
\(332\) | 3.85149 | + | 6.67097i | 0.211378 | + | 0.366117i | ||||
\(333\) | −5.53367 | − | 32.5690i | −0.303243 | − | 1.78477i | ||||
\(334\) | 33.1631 | + | 19.1467i | 1.81460 | + | 1.04766i | ||||
\(335\) | −1.02677 | + | 1.77842i | −0.0560986 | + | 0.0971655i | ||||
\(336\) | 4.75219 | − | 2.53592i | 0.259253 | − | 0.138346i | ||||
\(337\) | 5.12883 | + | 8.88339i | 0.279385 | + | 0.483909i | 0.971232 | − | 0.238135i | \(-0.0765361\pi\) |
−0.691847 | + | 0.722044i | \(0.743203\pi\) | |||||||
\(338\) | 48.4475i | 2.63520i | ||||||||
\(339\) | 20.8444 | + | 17.6016i | 1.13211 | + | 0.955985i | ||||
\(340\) | 20.9998 | 1.13887 | ||||||||
\(341\) | 1.06113 | − | 1.83793i | 0.0574634 | − | 0.0995295i | ||||
\(342\) | 4.30111 | − | 3.56360i | 0.232577 | − | 0.192698i | ||||
\(343\) | 7.76633 | + | 16.8132i | 0.419342 | + | 0.907828i | ||||
\(344\) | 16.8961 | + | 9.75496i | 0.910976 | + | 0.525952i | ||||
\(345\) | −0.646163 | + | 0.232906i | −0.0347882 | + | 0.0125392i | ||||
\(346\) | −37.5481 | − | 21.6784i | −2.01860 | − | 1.16544i | ||||
\(347\) | 24.6586 | + | 14.2367i | 1.32374 | + | 0.764264i | 0.984324 | − | 0.176371i | \(-0.0564360\pi\) |
0.339420 | + | 0.940635i | \(0.389769\pi\) | |||||||
\(348\) | −25.7576 | − | 21.7504i | −1.38075 | − | 1.16594i | ||||
\(349\) | 1.01722 | + | 0.587291i | 0.0544504 | + | 0.0314370i | 0.526978 | − | 0.849879i | \(-0.323325\pi\) |
−0.472528 | + | 0.881316i | \(0.656658\pi\) | |||||||
\(350\) | −6.13205 | + | 0.890673i | −0.327772 | + | 0.0476085i | ||||
\(351\) | −30.1571 | − | 0.282004i | −1.60966 | − | 0.0150523i | ||||
\(352\) | 0.506437 | − | 0.877175i | 0.0269932 | − | 0.0467536i | ||||
\(353\) | −31.6082 | −1.68234 | −0.841168 | − | 0.540773i | \(-0.818132\pi\) | ||||
−0.841168 | + | 0.540773i | \(0.818132\pi\) | |||||||
\(354\) | −56.2460 | + | 20.2736i | −2.98944 | + | 1.07753i | ||||
\(355\) | − | 2.66240i | − | 0.141305i | ||||||
\(356\) | −9.99696 | − | 17.3153i | −0.529838 | − | 0.917706i | ||||
\(357\) | −24.3615 | + | 13.0001i | −1.28935 | + | 0.688037i | ||||
\(358\) | −22.1288 | + | 38.3283i | −1.16955 | + | 2.02571i | ||||
\(359\) | −19.5928 | − | 11.3119i | −1.03407 | − | 0.597019i | −0.115920 | − | 0.993259i | \(-0.536982\pi\) |
−0.918147 | + | 0.396240i | \(0.870315\pi\) | |||||||
\(360\) | −6.65687 | − | 8.03454i | −0.350848 | − | 0.423457i | ||||
\(361\) | −9.18400 | − | 15.9072i | −0.483368 | − | 0.837219i | ||||
\(362\) | 14.6385 | + | 25.3546i | 0.769383 | + | 1.33261i | ||||
\(363\) | 6.42642 | + | 17.8291i | 0.337299 | + | 0.935788i | ||||
\(364\) | 19.8183 | − | 49.7111i | 1.03876 | − | 2.60557i | ||||
\(365\) | −7.46653 | + | 4.31080i | −0.390816 | + | 0.225638i | ||||
\(366\) | 15.9090 | + | 2.85635i | 0.831577 | + | 0.149304i | ||||
\(367\) | − | 9.82818i | − | 0.513027i | −0.966541 | − | 0.256514i | \(-0.917426\pi\) | ||
0.966541 | − | 0.256514i | \(-0.0825738\pi\) | |||||||
\(368\) | 0.403675 | − | 0.233062i | 0.0210430 | − | 0.0121492i | ||||
\(369\) | −2.77823 | − | 1.03085i | −0.144629 | − | 0.0536640i | ||||
\(370\) | − | 25.7901i | − | 1.34076i | ||||||
\(371\) | −0.990144 | + | 0.143817i | −0.0514057 | + | 0.00746663i | ||||
\(372\) | −40.6159 | − | 34.2971i | −2.10584 | − | 1.77822i | ||||
\(373\) | 14.4369 | 0.747517 | 0.373758 | − | 0.927526i | \(-0.378069\pi\) | ||||
0.373758 | + | 0.927526i | \(0.378069\pi\) | |||||||
\(374\) | 1.70040 | − | 2.94518i | 0.0879257 | − | 0.152292i | ||||
\(375\) | 0.587320 | + | 1.62943i | 0.0303291 | + | 0.0841436i | ||||
\(376\) | −6.35158 | + | 3.66709i | −0.327558 | + | 0.189116i | ||||
\(377\) | −32.4152 | −1.66947 | ||||||||
\(378\) | 29.7954 | + | 12.2026i | 1.53251 | + | 0.627636i | ||||
\(379\) | 26.1822 | 1.34489 | 0.672444 | − | 0.740148i | \(-0.265244\pi\) | ||||
0.672444 | + | 0.740148i | \(0.265244\pi\) | |||||||
\(380\) | 2.39936 | − | 1.38527i | 0.123085 | − | 0.0710630i | ||||
\(381\) | −7.08412 | − | 19.6538i | −0.362930 | − | 1.00690i | ||||
\(382\) | −10.2177 | + | 17.6975i | −0.522781 | + | 0.905484i | ||||
\(383\) | 2.10791 | 0.107709 | 0.0538545 | − | 0.998549i | \(-0.482849\pi\) | ||||
0.0538545 | + | 0.998549i | \(0.482849\pi\) | |||||||
\(384\) | −26.6705 | − | 22.5212i | −1.36102 | − | 1.14928i | ||||
\(385\) | −0.236111 | + | 0.592249i | −0.0120333 | + | 0.0301838i | ||||
\(386\) | − | 26.6814i | − | 1.35805i | ||||||
\(387\) | 2.81889 | + | 16.5908i | 0.143292 | + | 0.843360i | ||||
\(388\) | 47.9126 | − | 27.6623i | 2.43239 | − | 1.40434i | ||||
\(389\) | 28.3647i | 1.43815i | 0.694933 | + | 0.719075i | \(0.255434\pi\) | ||||
−0.694933 | + | 0.719075i | \(0.744566\pi\) | |||||||
\(390\) | −23.1733 | − | 4.16059i | −1.17342 | − | 0.210680i | ||||
\(391\) | −2.06939 | + | 1.19476i | −0.104654 | + | 0.0604218i | ||||
\(392\) | −16.7498 | + | 17.6683i | −0.845992 | + | 0.892384i | ||||
\(393\) | −8.42835 | − | 23.3832i | −0.425154 | − | 1.17953i | ||||
\(394\) | 21.7838 | + | 37.7307i | 1.09745 | + | 1.90084i | ||||
\(395\) | 0.939111 | + | 1.62659i | 0.0472518 | + | 0.0818425i | ||||
\(396\) | −2.48390 | + | 0.422030i | −0.124821 | + | 0.0212078i | ||||
\(397\) | 12.0308 | + | 6.94599i | 0.603809 | + | 0.348609i | 0.770538 | − | 0.637394i | \(-0.219987\pi\) |
−0.166730 | + | 0.986003i | \(0.553321\pi\) | |||||||
\(398\) | 26.4330 | − | 45.7832i | 1.32496 | − | 2.29491i | ||||
\(399\) | −1.92591 | + | 3.09238i | −0.0964159 | + | 0.154813i | ||||
\(400\) | −0.587714 | − | 1.01795i | −0.0293857 | − | 0.0508975i | ||||
\(401\) | − | 21.0354i | − | 1.05046i | −0.850961 | − | 0.525229i | \(-0.823980\pi\) | ||
0.850961 | − | 0.525229i | \(-0.176020\pi\) | |||||||
\(402\) | 7.83666 | − | 2.82468i | 0.390857 | − | 0.140882i | ||||
\(403\) | −51.1140 | −2.54617 | ||||||||
\(404\) | 0.578235 | − | 1.00153i | 0.0287683 | − | 0.0498281i | ||||
\(405\) | 1.67322 | − | 8.84310i | 0.0831427 | − | 0.439417i | ||||
\(406\) | 32.1463 | + | 12.8157i | 1.59539 | + | 0.636035i | ||||
\(407\) | −2.29815 | − | 1.32684i | −0.113915 | − | 0.0657690i | ||||
\(408\) | −27.7338 | − | 23.4191i | −1.37303 | − | 1.15942i | ||||
\(409\) | 13.7622 | + | 7.94558i | 0.680495 | + | 0.392884i | 0.800041 | − | 0.599945i | \(-0.204811\pi\) |
−0.119547 | + | 0.992829i | \(0.538144\pi\) | |||||||
\(410\) | −2.00344 | − | 1.15669i | −0.0989430 | − | 0.0571248i | ||||
\(411\) | 3.50882 | − | 1.26473i | 0.173077 | − | 0.0623847i | ||||
\(412\) | −31.6044 | − | 18.2468i | −1.55704 | − | 0.898957i | ||||
\(413\) | 30.6177 | − | 24.1495i | 1.50660 | − | 1.18832i | ||||
\(414\) | 2.61221 | + | 0.969249i | 0.128383 | + | 0.0476360i | ||||
\(415\) | −1.10515 | + | 1.91417i | −0.0542496 | + | 0.0939631i | ||||
\(416\) | −24.3948 | −1.19605 | ||||||||
\(417\) | −21.1326 | − | 17.8449i | −1.03487 | − | 0.873870i | ||||
\(418\) | − | 0.448676i | − | 0.0219455i | ||||||
\(419\) | 17.4324 | + | 30.1939i | 0.851631 | + | 1.47507i | 0.879736 | + | 0.475463i | \(0.157719\pi\) |
−0.0281052 | + | 0.999605i | \(0.508947\pi\) | |||||||
\(420\) | 13.5564 | + | 8.44277i | 0.661483 | + | 0.411965i | ||||
\(421\) | 3.61723 | − | 6.26523i | 0.176293 | − | 0.305349i | −0.764315 | − | 0.644843i | \(-0.776923\pi\) |
0.940608 | + | 0.339495i | \(0.110256\pi\) | |||||||
\(422\) | 20.1946 | + | 11.6594i | 0.983058 | + | 0.567569i | ||||
\(423\) | −5.93110 | − | 2.20071i | −0.288380 | − | 0.107002i | ||||
\(424\) | −0.657630 | − | 1.13905i | −0.0319373 | − | 0.0553171i | ||||
\(425\) | 3.01284 | + | 5.21840i | 0.146144 | + | 0.253129i | ||||
\(426\) | −6.96785 | + | 8.25159i | −0.337594 | + | 0.399791i | ||||
\(427\) | −10.4327 | + | 1.51534i | −0.504875 | + | 0.0733325i | ||||
\(428\) | −1.71067 | + | 0.987658i | −0.0826885 | + | 0.0477402i | ||||
\(429\) | −1.56296 | + | 1.85092i | −0.0754604 | + | 0.0893630i | ||||
\(430\) | 13.1376i | 0.633553i | ||||||||
\(431\) | 23.1880 | − | 13.3876i | 1.11693 | − | 0.644859i | 0.176314 | − | 0.984334i | \(-0.443583\pi\) |
0.940615 | + | 0.339475i | \(0.110249\pi\) | |||||||
\(432\) | −0.0571117 | + | 6.10743i | −0.00274779 | + | 0.293844i | ||||
\(433\) | 11.2142i | 0.538921i | 0.963011 | + | 0.269460i | \(0.0868453\pi\) | ||||
−0.963011 | + | 0.269460i | \(0.913155\pi\) | |||||||
\(434\) | 50.6900 | + | 20.2085i | 2.43320 | + | 0.970041i | ||||
\(435\) | 1.70947 | − | 9.52124i | 0.0819627 | − | 0.456508i | ||||
\(436\) | −16.9600 | −0.812237 | ||||||||
\(437\) | −0.157628 | + | 0.273019i | −0.00754036 | + | 0.0130603i | ||||
\(438\) | 34.4230 | + | 6.18040i | 1.64480 | + | 0.295311i | ||||
\(439\) | −14.6450 | + | 8.45528i | −0.698967 | + | 0.403548i | −0.806962 | − | 0.590603i | \(-0.798890\pi\) |
0.107996 | + | 0.994151i | \(0.465557\pi\) | |||||||
\(440\) | −0.838134 | −0.0399565 | ||||||||
\(441\) | −20.9531 | − | 1.40216i | −0.997768 | − | 0.0667695i | ||||
\(442\) | −81.9073 | −3.89593 | ||||||||
\(443\) | −11.8410 | + | 6.83642i | −0.562584 | + | 0.324808i | −0.754182 | − | 0.656665i | \(-0.771966\pi\) |
0.191598 | + | 0.981474i | \(0.438633\pi\) | |||||||
\(444\) | −42.8852 | + | 50.7862i | −2.03524 | + | 2.41021i | ||||
\(445\) | 2.86854 | − | 4.96845i | 0.135982 | − | 0.235527i | ||||
\(446\) | 5.57092 | 0.263791 | ||||||||
\(447\) | 2.22783 | − | 0.803009i | 0.105373 | − | 0.0379810i | ||||
\(448\) | 29.9700 | + | 11.9481i | 1.41595 | + | 0.564495i | ||||
\(449\) | 10.8478i | 0.511940i | 0.966685 | + | 0.255970i | \(0.0823948\pi\) | ||||
−0.966685 | + | 0.255970i | \(0.917605\pi\) | |||||||
\(450\) | 2.44416 | − | 6.58722i | 0.115219 | − | 0.310524i | ||||
\(451\) | −0.206145 | + | 0.119018i | −0.00970697 | + | 0.00560432i | ||||
\(452\) | − | 54.8937i | − | 2.58198i | ||||||
\(453\) | 2.47961 | + | 6.87932i | 0.116502 | + | 0.323219i | ||||
\(454\) | −12.5005 | + | 7.21719i | −0.586679 | + | 0.338719i | ||||
\(455\) | 15.1964 | − | 2.20727i | 0.712420 | − | 0.103478i | ||||
\(456\) | −4.71365 | − | 0.846301i | −0.220737 | − | 0.0396317i | ||||
\(457\) | 4.15591 | + | 7.19824i | 0.194405 | + | 0.336719i | 0.946705 | − | 0.322101i | \(-0.104389\pi\) |
−0.752300 | + | 0.658820i | \(0.771056\pi\) | |||||||
\(458\) | 31.4714 | + | 54.5100i | 1.47056 | + | 2.54709i | ||||
\(459\) | 0.292776 | − | 31.3090i | 0.0136656 | − | 1.46138i | ||||
\(460\) | 1.19686 | + | 0.691008i | 0.0558039 | + | 0.0322184i | ||||
\(461\) | 0.892772 | − | 1.54633i | 0.0415805 | − | 0.0720196i | −0.844486 | − | 0.535577i | \(-0.820094\pi\) |
0.886067 | + | 0.463558i | \(0.153427\pi\) | |||||||
\(462\) | 2.28178 | − | 1.21763i | 0.106158 | − | 0.0566492i | ||||
\(463\) | −2.30815 | − | 3.99784i | −0.107269 | − | 0.185795i | 0.807394 | − | 0.590013i | \(-0.200877\pi\) |
−0.914663 | + | 0.404217i | \(0.867544\pi\) | |||||||
\(464\) | 6.56475i | 0.304761i | ||||||||
\(465\) | 2.69558 | − | 15.0136i | 0.125005 | − | 0.696239i | ||||
\(466\) | −2.99476 | −0.138729 | ||||||||
\(467\) | 7.71918 | − | 13.3700i | 0.357201 | − | 0.618690i | −0.630291 | − | 0.776359i | \(-0.717065\pi\) |
0.987492 | + | 0.157669i | \(0.0503978\pi\) | |||||||
\(468\) | 38.7147 | + | 46.7269i | 1.78959 | + | 2.15995i | ||||
\(469\) | −4.26592 | + | 3.36471i | −0.196982 | + | 0.155368i | ||||
\(470\) | −4.27704 | − | 2.46935i | −0.197285 | − | 0.113903i | ||||
\(471\) | −0.730048 | + | 4.06616i | −0.0336388 | + | 0.187359i | ||||
\(472\) | 44.3940 | + | 25.6309i | 2.04340 | + | 1.17976i | ||||
\(473\) | 1.17069 | + | 0.675900i | 0.0538285 | + | 0.0310779i | ||||
\(474\) | 1.34640 | − | 7.49908i | 0.0618424 | − | 0.344444i | ||||
\(475\) | 0.688475 | + | 0.397491i | 0.0315894 | + | 0.0182382i | ||||
\(476\) | 51.6099 | + | 20.5753i | 2.36554 | + | 0.943067i | ||||
\(477\) | 0.394660 | − | 1.06364i | 0.0180702 | − | 0.0487008i | ||||
\(478\) | 14.6508 | − | 25.3759i | 0.670111 | − | 1.16067i | ||||
\(479\) | −8.52828 | −0.389667 | −0.194834 | − | 0.980836i | \(-0.562417\pi\) | ||||
−0.194834 | + | 0.980836i | \(0.562417\pi\) | |||||||
\(480\) | 1.28650 | − | 7.16542i | 0.0587204 | − | 0.327055i | ||||
\(481\) | 63.9130i | 2.91418i | ||||||||
\(482\) | 13.3676 | + | 23.1534i | 0.608878 | + | 1.05461i | ||||
\(483\) | −1.81624 | − | 0.0607024i | −0.0826417 | − | 0.00276205i | ||||
\(484\) | 19.0665 | − | 33.0242i | 0.866661 | − | 1.50110i | ||||
\(485\) | 13.7481 | + | 7.93745i | 0.624268 | + | 0.360421i | ||||
\(486\) | −28.3294 | + | 23.0285i | −1.28505 | + | 1.04459i | ||||
\(487\) | 1.42319 | + | 2.46503i | 0.0644907 | + | 0.111701i | 0.896468 | − | 0.443109i | \(-0.146124\pi\) |
−0.831977 | + | 0.554810i | \(0.812791\pi\) | |||||||
\(488\) | −6.92916 | − | 12.0017i | −0.313668 | − | 0.543289i | ||||
\(489\) | 29.8409 | + | 5.35772i | 1.34945 | + | 0.242284i | ||||
\(490\) | −15.9431 | − | 3.81914i | −0.720234 | − | 0.172531i | ||||
\(491\) | −30.4913 | + | 17.6042i | −1.37605 | + | 0.794465i | −0.991682 | − | 0.128713i | \(-0.958915\pi\) |
−0.384372 | + | 0.923178i | \(0.625582\pi\) | |||||||
\(492\) | 2.02180 | + | 5.60920i | 0.0911500 | + | 0.252882i | ||||
\(493\) | − | 33.6534i | − | 1.51567i | ||||||
\(494\) | −9.35846 | + | 5.40311i | −0.421057 | + | 0.243097i | ||||
\(495\) | −0.461240 | − | 0.556696i | −0.0207312 | − | 0.0250216i | ||||
\(496\) | 10.3516i | 0.464802i | ||||||||
\(497\) | 2.60858 | − | 6.54323i | 0.117011 | − | 0.293504i | ||||
\(498\) | 8.43485 | − | 3.04029i | 0.377975 | − | 0.136239i | ||||
\(499\) | −14.4168 | −0.645385 | −0.322692 | − | 0.946504i | \(-0.604588\pi\) | ||||
−0.322692 | + | 0.946504i | \(0.604588\pi\) | |||||||
\(500\) | 1.74252 | − | 3.01813i | 0.0779279 | − | 0.134975i | ||||
\(501\) | 18.2714 | − | 21.6376i | 0.816304 | − | 0.966698i | ||||
\(502\) | −7.06529 | + | 4.07915i | −0.315339 | + | 0.182061i | ||||
\(503\) | −3.65662 | −0.163041 | −0.0815204 | − | 0.996672i | \(-0.525978\pi\) | ||||
−0.0815204 | + | 0.996672i | \(0.525978\pi\) | |||||||
\(504\) | −8.48808 | − | 26.2684i | −0.378089 | − | 1.17009i | ||||
\(505\) | 0.331838 | 0.0147666 | ||||||||
\(506\) | 0.193826 | − | 0.111905i | 0.00861660 | − | 0.00497480i | ||||
\(507\) | 35.2657 | + | 6.33170i | 1.56620 | + | 0.281200i | ||||
\(508\) | −21.0179 | + | 36.4040i | −0.932517 | + | 1.61517i | ||||
\(509\) | 20.6591 | 0.915697 | 0.457849 | − | 0.889030i | \(-0.348620\pi\) | ||||
0.457849 | + | 0.889030i | \(0.348620\pi\) | |||||||
\(510\) | 4.31952 | − | 24.0584i | 0.191271 | − | 1.06533i | ||||
\(511\) | −22.5737 | + | 3.27881i | −0.998604 | + | 0.145046i | ||||
\(512\) | 13.1167i | 0.579682i | ||||||||
\(513\) | −2.03188 | − | 3.59658i | −0.0897099 | − | 0.158793i | ||||
\(514\) | 51.9317 | − | 29.9828i | 2.29061 | − | 1.32248i | ||||
\(515\) | − | 10.4715i | − | 0.461430i | ||||||
\(516\) | 21.8460 | − | 25.8708i | 0.961715 | − | 1.13890i | ||||
\(517\) | −0.440087 | + | 0.254084i | −0.0193550 | + | 0.0111746i | ||||
\(518\) | 25.2688 | − | 63.3829i | 1.11025 | − | 2.78488i | ||||
\(519\) | −20.6873 | + | 24.4987i | −0.908071 | + | 1.07537i | ||||
\(520\) | 10.0931 | + | 17.4818i | 0.442612 | + | 0.766626i | ||||
\(521\) | 15.7853 | + | 27.3410i | 0.691567 | + | 1.19783i | 0.971324 | + | 0.237758i | \(0.0764127\pi\) |
−0.279757 | + | 0.960071i | \(0.590254\pi\) | |||||||
\(522\) | −30.2165 | + | 25.0354i | −1.32254 | + | 1.09577i | ||||
\(523\) | −31.3429 | − | 18.0958i | −1.37053 | − | 0.791274i | −0.379533 | − | 0.925178i | \(-0.623915\pi\) |
−0.990994 | + | 0.133904i | \(0.957249\pi\) | |||||||
\(524\) | −25.0061 | + | 43.3118i | −1.09239 | + | 1.89208i | ||||
\(525\) | −0.153074 | + | 4.58002i | −0.00668068 | + | 0.199888i | ||||
\(526\) | 2.26532 | + | 3.92366i | 0.0987728 | + | 0.171080i | ||||
\(527\) | − | 53.0664i | − | 2.31161i | ||||||
\(528\) | 0.374849 | + | 0.316532i | 0.0163132 | + | 0.0137753i | ||||
\(529\) | 22.8427 | 0.993163 | ||||||||
\(530\) | 0.442836 | − | 0.767015i | 0.0192356 | − | 0.0333170i | ||||
\(531\) | 7.40655 | + | 43.5920i | 0.321417 | + | 1.89173i | ||||
\(532\) | 7.25406 | − | 1.05364i | 0.314503 | − | 0.0456813i | ||||
\(533\) | 4.96493 | + | 2.86650i | 0.215055 | + | 0.124162i | ||||
\(534\) | −21.8936 | + | 7.89142i | −0.947428 | + | 0.341495i | ||||
\(535\) | −0.490862 | − | 0.283399i | −0.0212218 | − | 0.0122524i | ||||
\(536\) | −6.18533 | − | 3.57110i | −0.267166 | − | 0.154248i | ||||
\(537\) | 25.0077 | + | 21.1171i | 1.07916 | + | 0.911272i | ||||
\(538\) | −24.2028 | − | 13.9735i | −1.04346 | − | 0.602440i | ||||
\(539\) | −1.16056 | + | 1.22420i | −0.0499887 | + | 0.0527300i | ||||
\(540\) | −15.7667 | + | 8.90736i | −0.678489 | + | 0.383312i | ||||
\(541\) | 20.8272 | − | 36.0737i | 0.895429 | − | 1.55093i | 0.0621567 | − | 0.998066i | \(-0.480202\pi\) |
0.833273 | − | 0.552862i | \(-0.186465\pi\) | |||||||
\(542\) | 42.3233 | 1.81794 | ||||||||
\(543\) | 20.3692 | − | 7.34196i | 0.874126 | − | 0.315074i | ||||
\(544\) | − | 25.3266i | − | 1.08587i | ||||||
\(545\) | −2.43326 | − | 4.21452i | −0.104229 | − | 0.180530i | ||||
\(546\) | −52.8752 | − | 32.9301i | −2.26285 | − | 1.40928i | ||||
\(547\) | 12.2984 | − | 21.3015i | 0.525843 | − | 0.910787i | −0.473704 | − | 0.880684i | \(-0.657083\pi\) |
0.999547 | − | 0.0301027i | \(-0.00958343\pi\) | |||||||
\(548\) | −6.49924 | − | 3.75234i | −0.277634 | − | 0.160292i | ||||
\(549\) | 4.15836 | − | 11.2071i | 0.177474 | − | 0.478308i | ||||
\(550\) | −0.282192 | − | 0.488771i | −0.0120327 | − | 0.0208413i | ||||
\(551\) | −2.21998 | − | 3.84513i | −0.0945745 | − | 0.163808i | ||||
\(552\) | −0.810044 | − | 2.24735i | −0.0344778 | − | 0.0956535i | ||||
\(553\) | 0.714291 | + | 4.91770i | 0.0303748 | + | 0.209122i | ||||
\(554\) | −37.1215 | + | 21.4321i | −1.57714 | + | 0.910563i | ||||
\(555\) | −18.7730 | − | 3.37056i | −0.796870 | − | 0.143072i | ||||
\(556\) | 55.6527i | 2.36020i | ||||||||
\(557\) | −1.86698 | + | 1.07790i | −0.0791065 | + | 0.0456722i | −0.539032 | − | 0.842286i | \(-0.681210\pi\) |
0.459925 | + | 0.887958i | \(0.347876\pi\) | |||||||
\(558\) | −47.6470 | + | 39.4771i | −2.01706 | + | 1.67120i | ||||
\(559\) | − | 32.5577i | − | 1.37704i | ||||||
\(560\) | −0.447017 | − | 3.07759i | −0.0188899 | − | 0.130052i | ||||
\(561\) | −1.92162 | − | 1.62266i | −0.0811307 | − | 0.0685088i | ||||
\(562\) | −49.6732 | −2.09534 | ||||||||
\(563\) | 0.453715 | − | 0.785857i | 0.0191218 | − | 0.0331199i | −0.856306 | − | 0.516469i | \(-0.827246\pi\) |
0.875428 | + | 0.483349i | \(0.160580\pi\) | |||||||
\(564\) | 4.31624 | + | 11.9748i | 0.181747 | + | 0.504229i | ||||
\(565\) | 13.6410 | − | 7.87562i | 0.573880 | − | 0.331330i | ||||
\(566\) | −3.87426 | −0.162847 | ||||||||
\(567\) | 12.7765 | − | 20.0938i | 0.536563 | − | 0.843860i | ||||
\(568\) | 9.25979 | 0.388532 | ||||||||
\(569\) | −33.2443 | + | 19.1936i | −1.39367 | + | 0.804638i | −0.993720 | − | 0.111897i | \(-0.964307\pi\) |
−0.399954 | + | 0.916535i | \(0.630974\pi\) | |||||||
\(570\) | −1.09351 | − | 3.03378i | −0.0458021 | − | 0.127071i | ||||
\(571\) | −6.24499 | + | 10.8166i | −0.261345 | + | 0.452663i | −0.966600 | − | 0.256291i | \(-0.917499\pi\) |
0.705255 | + | 0.708954i | \(0.250833\pi\) | |||||||
\(572\) | 4.87438 | 0.203808 | ||||||||
\(573\) | 11.5469 | + | 9.75053i | 0.482380 | + | 0.407334i | ||||
\(574\) | −3.79044 | − | 4.80568i | −0.158210 | − | 0.200585i | ||||
\(575\) | 0.396557i | 0.0165376i | ||||||||
\(576\) | −28.1709 | + | 23.3405i | −1.17379 | + | 0.972519i | ||||
\(577\) | −18.9922 | + | 10.9652i | −0.790656 | + | 0.456485i | −0.840193 | − | 0.542287i | \(-0.817559\pi\) |
0.0495375 | + | 0.998772i | \(0.484225\pi\) | |||||||
\(578\) | − | 45.2217i | − | 1.88098i | ||||||
\(579\) | −19.4218 | − | 3.48704i | −0.807143 | − | 0.144917i | ||||
\(580\) | −16.8562 | + | 9.73195i | −0.699917 | + | 0.404097i | ||||
\(581\) | −4.59154 | + | 3.62155i | −0.190489 | + | 0.150247i | ||||
\(582\) | −21.8361 | − | 60.5812i | −0.905137 | − | 2.51117i | ||||
\(583\) | −0.0455657 | − | 0.0789222i | −0.00188714 | − | 0.00326862i | ||||
\(584\) | −14.9929 | − | 25.9685i | −0.620412 | − | 1.07458i | ||||
\(585\) | −6.05712 | + | 16.3244i | −0.250431 | + | 0.674932i | ||||
\(586\) | 47.6785 | + | 27.5272i | 1.96958 | + | 1.13714i | ||||
\(587\) | 2.41365 | − | 4.18057i | 0.0996221 | − | 0.172550i | −0.811906 | − | 0.583788i | \(-0.801570\pi\) |
0.911528 | + | 0.411237i | \(0.134903\pi\) | |||||||
\(588\) | 25.0446 | + | 34.0317i | 1.03282 | + | 1.40344i | ||||
\(589\) | −3.50059 | − | 6.06320i | −0.144239 | − | 0.249830i | ||||
\(590\) | 34.5187i | 1.42111i | ||||||||
\(591\) | 30.3117 | − | 10.9257i | 1.24686 | − | 0.449423i | ||||
\(592\) | 12.9437 | 0.531983 | ||||||||
\(593\) | −10.9883 | + | 19.0323i | −0.451236 | + | 0.781563i | −0.998463 | − | 0.0554206i | \(-0.982350\pi\) |
0.547227 | + | 0.836984i | \(0.315683\pi\) | |||||||
\(594\) | −0.0274223 | + | 2.93250i | −0.00112515 | + | 0.120322i | ||||
\(595\) | 2.29158 | + | 15.7769i | 0.0939456 | + | 0.646790i | ||||
\(596\) | −4.12652 | − | 2.38245i | −0.169029 | − | 0.0975888i | ||||
\(597\) | −29.8718 | − | 25.2245i | −1.22257 | − | 1.03237i | ||||
\(598\) | −4.66823 | − | 2.69520i | −0.190898 | − | 0.110215i | ||||
\(599\) | 0.394818 | + | 0.227948i | 0.0161318 | + | 0.00931371i | 0.508044 | − | 0.861331i | \(-0.330369\pi\) |
−0.491912 | + | 0.870645i | \(0.663702\pi\) | |||||||
\(600\) | −5.66715 | + | 2.04269i | −0.231361 | + | 0.0833926i | ||||
\(601\) | 17.3200 | + | 9.99972i | 0.706498 | + | 0.407897i | 0.809763 | − | 0.586757i | \(-0.199596\pi\) |
−0.103265 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(602\) | −12.8721 | + | 32.2876i | −0.524627 | + | 1.31595i | ||||
\(603\) | −1.03194 | − | 6.07359i | −0.0420239 | − | 0.247336i | ||||
\(604\) | 7.35676 | − | 12.7423i | 0.299342 | − | 0.518476i | ||||
\(605\) | 10.9419 | 0.444853 | ||||||||
\(606\) | −1.02847 | − | 0.868466i | −0.0417787 | − | 0.0352790i | ||||
\(607\) | 20.2057i | 0.820122i | 0.912058 | + | 0.410061i | \(0.134493\pi\) | ||||
−0.912058 | + | 0.410061i | \(0.865507\pi\) | |||||||
\(608\) | −1.67070 | − | 2.89374i | −0.0677558 | − | 0.117357i | ||||
\(609\) | 13.5301 | − | 21.7249i | 0.548265 | − | 0.880338i | ||||
\(610\) | 4.66597 | − | 8.08170i | 0.188920 | − | 0.327218i | ||||
\(611\) | 10.5994 | + | 6.11954i | 0.428804 | + | 0.247570i | ||||
\(612\) | −48.5118 | + | 40.1935i | −1.96097 | + | 1.62473i | ||||
\(613\) | 7.62154 | + | 13.2009i | 0.307831 | + | 0.533179i | 0.977888 | − | 0.209131i | \(-0.0670635\pi\) |
−0.670057 | + | 0.742310i | \(0.733730\pi\) | |||||||
\(614\) | −18.2453 | − | 31.6018i | −0.736321 | − | 1.27534i | ||||
\(615\) | −1.10381 | + | 1.30717i | −0.0445097 | + | 0.0527101i | ||||
\(616\) | −2.05984 | − | 0.821193i | −0.0829932 | − | 0.0330868i | ||||
\(617\) | −6.80537 | + | 3.92908i | −0.273974 | + | 0.158179i | −0.630692 | − | 0.776033i | \(-0.717229\pi\) |
0.356718 | + | 0.934212i | \(0.383896\pi\) | |||||||
\(618\) | −27.4054 | + | 32.4545i | −1.10241 | + | 1.30551i | ||||
\(619\) | − | 4.71850i | − | 0.189653i | −0.995494 | − | 0.0948263i | \(-0.969770\pi\) | ||
0.995494 | − | 0.0948263i | \(-0.0302296\pi\) | |||||||
\(620\) | −26.5798 | + | 15.3459i | −1.06747 | + | 0.616305i | ||||
\(621\) | 1.04693 | − | 1.77479i | 0.0420117 | − | 0.0712200i | ||||
\(622\) | − | 43.2463i | − | 1.73402i | ||||||
\(623\) | 11.9179 | − | 9.40013i | 0.477479 | − | 0.376608i | ||||
\(624\) | 2.08815 | − | 11.6304i | 0.0835927 | − | 0.465587i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.4466 | − | 33.6824i | 0.777241 | − | 1.34622i | ||||
\(627\) | −0.326598 | − | 0.0586384i | −0.0130431 | − | 0.00234179i | ||||
\(628\) | 7.19865 | − | 4.15614i | 0.287258 | − | 0.165848i | ||||
\(629\) | −66.3543 | −2.64572 | ||||||||
\(630\) | 12.4610 | − | 13.7943i | 0.496456 | − | 0.549577i | ||||
\(631\) | −24.0883 | −0.958938 | −0.479469 | − | 0.877559i | \(-0.659171\pi\) | ||||
−0.479469 | + | 0.877559i | \(0.659171\pi\) | |||||||
\(632\) | −5.65726 | + | 3.26622i | −0.225034 | + | 0.129923i | ||||
\(633\) | 11.1263 | − | 13.1762i | 0.442231 | − | 0.523707i | ||||
\(634\) | 15.9017 | − | 27.5425i | 0.631537 | − | 1.09385i | ||||
\(635\) | −12.0618 | −0.478656 | ||||||||
\(636\) | −2.14747 | + | 0.774045i | −0.0851528 | + | 0.0306929i | ||||
\(637\) | 39.5101 | + | 9.46459i | 1.56545 | + | 0.375001i | ||||
\(638\) | 3.15208i | 0.124792i | ||||||||
\(639\) | 5.09583 | + | 6.15043i | 0.201588 | + | 0.243307i | ||||
\(640\) | −17.4537 | + | 10.0769i | −0.689916 | + | 0.398323i | ||||
\(641\) | 3.97240i | 0.156901i | 0.996918 | + | 0.0784503i | \(0.0249972\pi\) | ||||
−0.996918 | + | 0.0784503i | \(0.975003\pi\) | |||||||
\(642\) | 0.779639 | + | 2.16299i | 0.0307699 | + | 0.0853666i | ||||
\(643\) | 13.2235 | − | 7.63462i | 0.521486 | − | 0.301080i | −0.216057 | − | 0.976381i | \(-0.569320\pi\) |
0.737542 | + | 0.675301i | \(0.235986\pi\) | |||||||
\(644\) | 2.26442 | + | 2.87092i | 0.0892306 | + | 0.113130i | ||||
\(645\) | 9.56309 | + | 1.71698i | 0.376546 | + | 0.0676061i | ||||
\(646\) | −5.60950 | − | 9.71594i | −0.220703 | − | 0.382268i | ||||
\(647\) | −12.1791 | − | 21.0948i | −0.478809 | − | 0.829322i | 0.520895 | − | 0.853621i | \(-0.325598\pi\) |
−0.999705 | + | 0.0242984i | \(0.992265\pi\) | |||||||
\(648\) | 30.7562 | + | 5.81943i | 1.20822 | + | 0.228609i | ||||
\(649\) | 3.07596 | + | 1.77591i | 0.120742 | + | 0.0697105i | ||||
\(650\) | −6.79651 | + | 11.7719i | −0.266581 | + | 0.461732i | ||||
\(651\) | 21.3349 | − | 34.2570i | 0.836181 | − | 1.34264i | ||||
\(652\) | −30.5013 | − | 52.8299i | −1.19452 | − | 2.06898i | ||||
\(653\) | 34.0255i | 1.33152i | 0.746166 | + | 0.665760i | \(0.231893\pi\) | ||||
−0.746166 | + | 0.665760i | \(0.768107\pi\) | |||||||
\(654\) | −3.48856 | + | 19.4303i | −0.136414 | + | 0.759784i | ||||
\(655\) | −14.3505 | −0.560721 | ||||||||
\(656\) | 0.580527 | − | 1.00550i | 0.0226658 | − | 0.0392583i | ||||
\(657\) | 8.99763 | − | 24.2494i | 0.351031 | − | 0.946057i | ||||
\(658\) | −8.09201 | − | 10.2594i | −0.315459 | − | 0.399952i | ||||
\(659\) | 41.1434 | + | 23.7542i | 1.60272 | + | 0.925331i | 0.990940 | + | 0.134302i | \(0.0428792\pi\) |
0.611779 | + | 0.791029i | \(0.290454\pi\) | |||||||
\(660\) | −0.257058 | + | 1.43174i | −0.0100060 | + | 0.0557304i | ||||
\(661\) | −5.66794 | − | 3.27239i | −0.220457 | − | 0.127281i | 0.385705 | − | 0.922622i | \(-0.373958\pi\) |
−0.606162 | + | 0.795341i | \(0.707292\pi\) | |||||||
\(662\) | 60.0792 | + | 34.6867i | 2.33504 | + | 1.34814i | ||||
\(663\) | −10.7046 | + | 59.6216i | −0.415733 | + | 2.31551i | ||||
\(664\) | −6.65748 | − | 3.84370i | −0.258360 | − | 0.149164i | ||||
\(665\) | 1.30257 | + | 1.65145i | 0.0505115 | + | 0.0640405i | ||||
\(666\) | 49.3622 | + | 59.5779i | 1.91275 | + | 2.30860i | ||||
\(667\) | 1.10738 | − | 1.91804i | 0.0428780 | − | 0.0742669i | ||||
\(668\) | −56.9826 | −2.20472 | ||||||||
\(669\) | 0.728075 | − | 4.05516i | 0.0281490 | − | 0.156782i | ||||
\(670\) | − | 4.80943i | − | 0.185805i | ||||||
\(671\) | −0.480106 | − | 0.831568i | −0.0185343 | − | 0.0321023i | ||||
\(672\) | 10.1823 | − | 16.3496i | 0.392793 | − | 0.630698i | ||||
\(673\) | −5.47917 | + | 9.49020i | −0.211207 | + | 0.365820i | −0.952092 | − | 0.305810i | \(-0.901073\pi\) |
0.740886 | + | 0.671631i | \(0.234406\pi\) | |||||||
\(674\) | −20.8050 | − | 12.0118i | −0.801381 | − | 0.462677i | ||||
\(675\) | −4.47551 | − | 2.64004i | −0.172262 | − | 0.101615i | ||||
\(676\) | −36.0462 | − | 62.4338i | −1.38639 | − | 2.40130i | ||||
\(677\) | −9.78771 | − | 16.9528i | −0.376172 | − | 0.651549i | 0.614330 | − | 0.789050i | \(-0.289427\pi\) |
−0.990502 | + | 0.137500i | \(0.956093\pi\) | |||||||
\(678\) | −62.8892 | − | 11.2913i | −2.41524 | − | 0.433639i | ||||
\(679\) | 26.0109 | + | 32.9776i | 0.998205 | + | 1.26556i | ||||
\(680\) | −18.1495 | + | 10.4786i | −0.696003 | + | 0.401837i | ||||
\(681\) | 3.61979 | + | 10.0426i | 0.138711 | + | 0.384832i | ||||
\(682\) | 4.97037i | 0.190325i | ||||||||
\(683\) | −26.1931 | + | 15.1226i | −1.00225 | + | 0.578649i | −0.908913 | − | 0.416986i | \(-0.863087\pi\) |
−0.0933363 | + | 0.995635i | \(0.529753\pi\) | |||||||
\(684\) | −2.89138 | + | 7.79252i | −0.110555 | + | 0.297954i | ||||
\(685\) | − | 2.15340i | − | 0.0822771i | ||||||
\(686\) | −35.4404 | − | 25.0069i | −1.35312 | − | 0.954768i | ||||
\(687\) | 43.7918 | − | 15.7845i | 1.67076 | − | 0.602216i | ||||
\(688\) | −6.59361 | −0.251379 | ||||||||
\(689\) | −1.09744 | + | 1.90082i | −0.0418090 | + | 0.0724153i | ||||
\(690\) | 1.03784 | − | 1.22905i | 0.0395100 | − | 0.0467892i | ||||
\(691\) | 37.6554 | − | 21.7404i | 1.43248 | − | 0.827043i | 0.435170 | − | 0.900348i | \(-0.356688\pi\) |
0.997310 | + | 0.0733056i | \(0.0233549\pi\) | |||||||
\(692\) | 64.5172 | 2.45257 | ||||||||
\(693\) | −0.588121 | − | 1.82008i | −0.0223409 | − | 0.0691390i | ||||
\(694\) | −66.6850 | −2.53133 | ||||||||
\(695\) | −13.8296 | + | 7.98451i | −0.524586 | + | 0.302870i | ||||
\(696\) | 33.1148 | + | 5.94551i | 1.25521 | + | 0.225364i | ||||
\(697\) | −2.97600 | + | 5.15458i | −0.112724 | + | 0.195244i | ||||
\(698\) | −2.75089 | −0.104123 | ||||||||
\(699\) | −0.391391 | + | 2.17993i | −0.0148038 | + | 0.0824526i | ||||
\(700\) | 7.23962 | − | 5.71020i | 0.273632 | − | 0.215825i | ||||
\(701\) | 10.1452i | 0.383179i | 0.981475 | + | 0.191589i | \(0.0613642\pi\) | ||||
−0.981475 | + | 0.191589i | \(0.938636\pi\) | |||||||
\(702\) | 61.4962 | − | 34.7422i | 2.32102 | − | 1.31126i | ||||
\(703\) | −7.58143 | + | 4.37714i | −0.285939 | + | 0.165087i | ||||
\(704\) | 2.93868i | 0.110756i | ||||||||
\(705\) | −2.35646 | + | 2.79060i | −0.0887492 | + | 0.105100i | ||||
\(706\) | 64.1093 | − | 37.0135i | 2.41278 | − | 1.39302i | ||||
\(707\) | 0.815541 | + | 0.325131i | 0.0306716 | + | 0.0122278i | ||||
\(708\) | 57.3996 | − | 67.9748i | 2.15721 | − | 2.55465i | ||||
\(709\) | 16.5445 | + | 28.6560i | 0.621343 | + | 1.07620i | 0.989236 | + | 0.146329i | \(0.0467459\pi\) |
−0.367893 | + | 0.929868i | \(0.619921\pi\) | |||||||
\(710\) | 3.11769 | + | 5.40000i | 0.117005 | + | 0.202658i | ||||
\(711\) | −5.28274 | − | 1.96014i | −0.198118 | − | 0.0735110i | ||||
\(712\) | 17.2802 | + | 9.97674i | 0.647604 | + | 0.373894i | ||||
\(713\) | 1.74618 | − | 3.02447i | 0.0653949 | − | 0.113267i | ||||
\(714\) | 34.1880 | − | 54.8949i | 1.27945 | − | 2.05439i | ||||
\(715\) | 0.699329 | + | 1.21127i | 0.0261534 | + | 0.0452990i | ||||
\(716\) | − | 65.8577i | − | 2.46122i | ||||||
\(717\) | −16.5568 | − | 13.9810i | −0.618324 | − | 0.522129i | ||||
\(718\) | 52.9853 | 1.97739 | ||||||||
\(719\) | 6.27591 | − | 10.8702i | 0.234052 | − | 0.405390i | −0.724945 | − | 0.688807i | \(-0.758135\pi\) |
0.958997 | + | 0.283417i | \(0.0914681\pi\) | |||||||
\(720\) | 3.30604 | + | 1.22669i | 0.123209 | + | 0.0457162i | ||||
\(721\) | 10.2599 | − | 25.7353i | 0.382097 | − | 0.958432i | ||||
\(722\) | 37.2548 | + | 21.5091i | 1.38648 | + | 0.800485i | ||||
\(723\) | 18.6008 | − | 6.70454i | 0.691769 | − | 0.249344i | ||||
\(724\) | −37.7290 | − | 21.7829i | −1.40219 | − | 0.809554i | ||||
\(725\) | −4.83674 | − | 2.79249i | −0.179632 | − | 0.103711i | ||||
\(726\) | −33.9124 | − | 28.6365i | −1.25861 | − | 1.06280i | ||||
\(727\) | 24.1312 | + | 13.9322i | 0.894978 | + | 0.516716i | 0.875567 | − | 0.483096i | \(-0.160488\pi\) |
0.0194103 | + | 0.999812i | \(0.493821\pi\) | |||||||
\(728\) | 7.67685 | + | 52.8530i | 0.284523 | + | 1.95886i | ||||
\(729\) | 13.0604 | + | 23.6311i | 0.483717 | + | 0.875224i | ||||
\(730\) | 10.0960 | − | 17.4867i | 0.373669 | − | 0.647213i | ||||
\(731\) | 33.8013 | 1.25019 | ||||||||
\(732\) | −22.6270 | + | 8.15577i | −0.836317 | + | 0.301446i | ||||
\(733\) | − | 17.7064i | − | 0.654000i | −0.945024 | − | 0.327000i | \(-0.893962\pi\) | ||
0.945024 | − | 0.327000i | \(-0.106038\pi\) | |||||||
\(734\) | 11.5089 | + | 19.9340i | 0.424801 | + | 0.735776i | ||||
\(735\) | −4.86364 | + | 11.1061i | −0.179398 | + | 0.409654i | ||||
\(736\) | 0.833386 | − | 1.44347i | 0.0307190 | − | 0.0532069i | ||||
\(737\) | −0.428568 | − | 0.247434i | −0.0157865 | − | 0.00911435i | ||||
\(738\) | 6.84207 | − | 1.16251i | 0.251860 | − | 0.0427926i | ||||
\(739\) | 7.88534 | + | 13.6578i | 0.290067 | + | 0.502411i | 0.973825 | − | 0.227298i | \(-0.0729891\pi\) |
−0.683758 | + | 0.729709i | \(0.739656\pi\) | |||||||
\(740\) | 19.1885 | + | 33.2354i | 0.705383 | + | 1.22176i | ||||
\(741\) | 2.70993 | + | 7.51832i | 0.0995519 | + | 0.276192i | ||||
\(742\) | 1.83984 | − | 1.45116i | 0.0675428 | − | 0.0532739i | ||||
\(743\) | 11.7646 | − | 6.79232i | 0.431603 | − | 0.249186i | −0.268426 | − | 0.963300i | \(-0.586504\pi\) |
0.700029 | + | 0.714114i | \(0.253170\pi\) | |||||||
\(744\) | 52.2171 | + | 9.37520i | 1.91437 | + | 0.343711i | ||||
\(745\) | − | 1.36724i | − | 0.0500918i | ||||||
\(746\) | −29.2817 | + | 16.9058i | −1.07208 | + | 0.618965i | ||||
\(747\) | −1.11071 | − | 6.53720i | −0.0406388 | − | 0.239184i | ||||
\(748\) | 5.06057i | 0.185033i | ||||||||
\(749\) | −0.928693 | − | 1.17743i | −0.0339337 | − | 0.0430225i | ||||
\(750\) | −3.09931 | − | 2.61714i | −0.113171 | − | 0.0955643i | ||||
\(751\) | −36.8812 | −1.34582 | −0.672908 | − | 0.739726i | \(-0.734955\pi\) | ||||
−0.672908 | + | 0.739726i | \(0.734955\pi\) | |||||||
\(752\) | 1.23934 | − | 2.14659i | 0.0451939 | − | 0.0782781i | ||||
\(753\) | 2.04590 | + | 5.67605i | 0.0745567 | + | 0.206847i | ||||
\(754\) | 65.7459 | − | 37.9584i | 2.39433 | − | 1.38236i | ||||
\(755\) | 4.22191 | 0.153651 | ||||||||
\(756\) | −47.4762 | + | 6.44316i | −1.72669 | + | 0.234335i | ||||
\(757\) | 12.8740 | 0.467914 | 0.233957 | − | 0.972247i | \(-0.424833\pi\) | ||||
0.233957 | + | 0.972247i | \(0.424833\pi\) | |||||||
\(758\) | −53.1039 | + | 30.6596i | −1.92882 | + | 1.11361i | ||||
\(759\) | −0.0561262 | − | 0.155714i | −0.00203725 | − | 0.00565206i | ||||
\(760\) | −1.38247 | + | 2.39451i | −0.0501475 | + | 0.0868580i | ||||
\(761\) | −34.7474 | −1.25959 | −0.629795 | − | 0.776761i | \(-0.716861\pi\) | ||||
−0.629795 | + | 0.776761i | \(0.716861\pi\) | |||||||
\(762\) | 37.3831 | + | 31.5673i | 1.35425 | + | 1.14356i | ||||
\(763\) | −1.85074 | − | 12.7419i | −0.0670014 | − | 0.461287i | ||||
\(764\) | − | 30.4088i | − | 1.10015i | ||||||
\(765\) | −16.9480 | − | 6.28849i | −0.612756 | − | 0.227361i | ||||
\(766\) | −4.27535 | + | 2.46837i | −0.154475 | + | 0.0891860i | ||||
\(767\) | − | 85.5443i | − | 3.08883i | ||||||
\(768\) | 38.8883 | + | 6.98211i | 1.40326 | + | 0.251945i | ||||
\(769\) | 26.0271 | − | 15.0267i | 0.938560 | − | 0.541878i | 0.0490513 | − | 0.998796i | \(-0.484380\pi\) |
0.889509 | + | 0.456918i | \(0.151047\pi\) | |||||||
\(770\) | −0.214637 | − | 1.47771i | −0.00773496 | − | 0.0532531i | ||||
\(771\) | −15.0379 | − | 41.7204i | −0.541576 | − | 1.50252i | ||||
\(772\) | 19.8516 | + | 34.3841i | 0.714476 | + | 1.23751i | ||||
\(773\) | −16.9927 | − | 29.4323i | −0.611186 | − | 1.05861i | −0.991041 | − | 0.133559i | \(-0.957359\pi\) |
0.379855 | − | 0.925046i | \(-0.375974\pi\) | |||||||
\(774\) | −25.1454 | − | 30.3494i | −0.903833 | − | 1.09089i | ||||
\(775\) | −7.62683 | − | 4.40335i | −0.273964 | − | 0.158173i | ||||
\(776\) | −27.6064 | + | 47.8156i | −0.991011 | + | 1.71648i | ||||
\(777\) | −42.8350 | − | 26.6772i | −1.53670 | − | 0.957039i | ||||
\(778\) | −33.2153 | − | 57.5307i | −1.19083 | − | 2.06257i | ||||
\(779\) | 0.785261i | 0.0281349i | ||||||||
\(780\) | 32.9588 | − | 11.8798i | 1.18011 | − | 0.425365i | ||||
\(781\) | 0.641591 | 0.0229579 | ||||||||
\(782\) | 2.79815 | − | 4.84655i | 0.100062 | − | 0.173312i | ||||
\(783\) | 14.2746 | + | 25.2670i | 0.510132 | + | 0.902970i | ||||
\(784\) | 1.91678 | − | 8.00162i | 0.0684563 | − | 0.285772i | ||||
\(785\) | 2.06559 | + | 1.19257i | 0.0737239 | + | 0.0425645i | ||||
\(786\) | 44.4767 | + | 37.5572i | 1.58643 | + | 1.33962i | ||||
\(787\) | −18.2990 | − | 10.5650i | −0.652290 | − | 0.376600i | 0.137043 | − | 0.990565i | \(-0.456240\pi\) |
−0.789333 | + | 0.613965i | \(0.789574\pi\) | |||||||
\(788\) | −56.1452 | − | 32.4154i | −2.00009 | − | 1.15475i | ||||
\(789\) | 3.15215 | − | 1.13618i | 0.112220 | − | 0.0404489i | ||||
\(790\) | −3.80950 | − | 2.19941i | −0.135536 | − | 0.0782516i | ||||
\(791\) | 41.2411 | − | 5.99023i | 1.46636 | − | 0.212988i | ||||
\(792\) | 1.93618 | − | 1.60419i | 0.0687992 | − | 0.0570023i | ||||
\(793\) | −11.5632 | + | 20.0281i | −0.410621 | + | 0.711217i | ||||
\(794\) | −32.5352 | −1.15463 | ||||||||
\(795\) | −0.500447 | − | 0.422590i | −0.0177490 | − | 0.0149877i | ||||
\(796\) | 78.6672i | 2.78828i | ||||||||
\(797\) | −6.65988 | − | 11.5352i | −0.235905 | − | 0.408599i | 0.723630 | − | 0.690188i | \(-0.242472\pi\) |
−0.959535 | + | 0.281588i | \(0.909139\pi\) | |||||||
\(798\) | 0.285002 | − | 8.52737i | 0.0100890 | − | 0.301865i | ||||
\(799\) | −6.35330 | + | 11.0042i | −0.224764 | + | 0.389302i | ||||
\(800\) | −3.64000 | − | 2.10155i | −0.128693 | − | 0.0743012i | ||||
\(801\) | 2.88298 | + | 16.9680i | 0.101865 | + | 0.599536i | ||||
\(802\) | 24.6326 | + | 42.6650i | 0.869808 | + | 1.50655i | ||||
\(803\) | −1.03883 | − | 1.79930i | −0.0366594 | − | 0.0634960i | ||||
\(804\) | −7.99739 | + | 9.47081i | −0.282046 | + | 0.334010i | ||||
\(805\) | −0.388541 | + | 0.974596i | −0.0136943 | + | 0.0343500i | ||||
\(806\) | 103.672 | − | 59.8549i | 3.65168 | − | 2.10830i | ||||
\(807\) | −13.3346 | + | 15.7914i | −0.469402 | + | 0.555883i | ||||
\(808\) | 1.15413i | 0.0406022i | ||||||||
\(809\) | −2.78023 | + | 1.60517i | −0.0977477 | + | 0.0564347i | −0.548077 | − | 0.836428i | \(-0.684640\pi\) |
0.450329 | + | 0.892863i | \(0.351307\pi\) | |||||||
\(810\) | 6.96165 | + | 19.8953i | 0.244607 | + | 0.699050i | ||||
\(811\) | 26.0147i | 0.913501i | 0.889595 | + | 0.456750i | \(0.150987\pi\) | ||||
−0.889595 | + | 0.456750i | \(0.849013\pi\) | |||||||
\(812\) | −50.9619 | + | 7.40216i | −1.78841 | + | 0.259765i | ||||
\(813\) | 5.53131 | − | 30.8078i | 0.193992 | − | 1.08048i | ||||
\(814\) | 6.21496 | 0.217834 | ||||||||
\(815\) | 8.75207 | − | 15.1590i | 0.306572 | − | 0.530998i | ||||
\(816\) | 12.0746 | + | 2.16791i | 0.422696 | + | 0.0758920i | ||||
\(817\) | 3.86203 | − | 2.22974i | 0.135115 | − | 0.0780088i | ||||
\(818\) | −37.2174 | −1.30127 | ||||||||
\(819\) | −30.8807 | + | 34.1850i | −1.07906 | + | 1.19452i | ||||
\(820\) | 3.44242 | 0.120215 | ||||||||
\(821\) | −29.6423 | + | 17.1140i | −1.03452 | + | 0.597283i | −0.918277 | − | 0.395937i | \(-0.870420\pi\) |
−0.116247 | + | 0.993220i | \(0.537086\pi\) | |||||||
\(822\) | −5.63573 | + | 6.67405i | −0.196569 | + | 0.232784i | ||||
\(823\) | −25.6594 | + | 44.4433i | −0.894429 | + | 1.54920i | −0.0599200 | + | 0.998203i | \(0.519085\pi\) |
−0.834509 | + | 0.550994i | \(0.814249\pi\) | |||||||
\(824\) | 36.4198 | 1.26875 | ||||||||
\(825\) | −0.392665 | + | 0.141534i | −0.0136708 | + | 0.00492757i | ||||
\(826\) | −33.8210 | + | 84.8348i | −1.17678 | + | 2.95178i | ||||
\(827\) | 46.4687i | 1.61587i | 0.589269 | + | 0.807937i | \(0.299416\pi\) | ||||
−0.589269 | + | 0.807937i | \(0.700584\pi\) | |||||||
\(828\) | −4.08747 | + | 0.694487i | −0.142049 | + | 0.0241351i | ||||
\(829\) | 6.01685 | − | 3.47383i | 0.208974 | − | 0.120651i | −0.391861 | − | 0.920025i | \(-0.628168\pi\) |
0.600834 | + | 0.799374i | \(0.294835\pi\) | |||||||
\(830\) | − | 5.17655i | − | 0.179681i | ||||||
\(831\) | 10.7493 | + | 29.8223i | 0.372889 | + | 1.03453i | ||||
\(832\) | 61.2949 | − | 35.3886i | 2.12502 | − | 1.22688i | ||||
\(833\) | −9.82612 | + | 41.0193i | −0.340455 | + | 1.42123i | ||||
\(834\) | 63.7587 | + | 11.4474i | 2.20778 | + | 0.396391i | ||||
\(835\) | −8.17532 | − | 14.1601i | −0.282918 | − | 0.490029i | ||||
\(836\) | 0.333826 | + | 0.578204i | 0.0115456 | + | 0.0199976i | ||||
\(837\) | 22.5089 | + | 39.8424i | 0.778022 | + | 1.37715i | ||||
\(838\) | −70.7146 | − | 40.8271i | −2.44279 | − | 1.41035i | ||||
\(839\) | 19.3614 | − | 33.5349i | 0.668429 | − | 1.15775i | −0.309914 | − | 0.950765i | \(-0.600300\pi\) |
0.978343 | − | 0.206989i | \(-0.0663665\pi\) | |||||||
\(840\) | −15.9293 | − | 0.532389i | −0.549612 | − | 0.0183692i | ||||
\(841\) | 1.09604 | + | 1.89840i | 0.0377946 | + | 0.0654621i | ||||
\(842\) | 16.9432i | 0.583902i | ||||||||
\(843\) | −6.49189 | + | 36.1579i | −0.223592 | + | 1.24534i | ||||
\(844\) | −34.6995 | −1.19440 | ||||||||
\(845\) | 10.3431 | − | 17.9148i | 0.355814 | − | 0.616288i | ||||
\(846\) | 14.6068 | − | 2.48178i | 0.502191 | − | 0.0853254i | ||||
\(847\) | 26.8914 | + | 10.7208i | 0.923998 | + | 0.368370i | ||||
\(848\) | 0.384955 | + | 0.222254i | 0.0132194 | + | 0.00763222i | ||||
\(849\) | −0.506334 | + | 2.82013i | −0.0173774 | + | 0.0967868i | ||||
\(850\) | −12.2216 | − | 7.05613i | −0.419196 | − | 0.242023i | ||||
\(851\) | −3.78180 | − | 2.18342i | −0.129639 | − | 0.0748468i | ||||
\(852\) | 2.84001 | − | 15.8180i | 0.0972971 | − | 0.541916i | ||||
\(853\) | 1.59392 | + | 0.920253i | 0.0545749 | + | 0.0315089i | 0.527039 | − | 0.849841i | \(-0.323302\pi\) |
−0.472464 | + | 0.881350i | \(0.656635\pi\) | |||||||
\(854\) | 19.3856 | − | 15.2903i | 0.663363 | − | 0.523223i | ||||
\(855\) | −2.35125 | + | 0.399492i | −0.0804111 | + | 0.0136623i | ||||
\(856\) | 0.985660 | − | 1.70721i | 0.0336891 | − | 0.0583513i | ||||
\(857\) | −34.0224 | −1.16218 | −0.581092 | − | 0.813838i | \(-0.697374\pi\) | ||||
−0.581092 | + | 0.813838i | \(0.697374\pi\) | |||||||
\(858\) | 1.00263 | − | 5.58435i | 0.0342292 | − | 0.190647i | ||||
\(859\) | 6.75581i | 0.230505i | 0.993336 | + | 0.115253i | \(0.0367677\pi\) | ||||
−0.993336 | + | 0.115253i | \(0.963232\pi\) | |||||||
\(860\) | −9.77473 | − | 16.9303i | −0.333316 | − | 0.577320i | ||||
\(861\) | −3.99351 | + | 2.13106i | −0.136098 | + | 0.0726263i | ||||
\(862\) | −31.3540 | + | 54.3068i | −1.06792 | + | 1.84970i | ||||
\(863\) | 9.99636 | + | 5.77140i | 0.340280 | + | 0.196461i | 0.660396 | − | 0.750918i | \(-0.270388\pi\) |
−0.320116 | + | 0.947378i | \(0.603722\pi\) | |||||||
\(864\) | 10.7427 | + | 19.0153i | 0.365473 | + | 0.646913i | ||||
\(865\) | 9.25630 | + | 16.0324i | 0.314724 | + | 0.545117i | ||||
\(866\) | −13.1319 | − | 22.7452i | −0.446241 | − | 0.772913i | ||||
\(867\) | −32.9176 | − | 5.91012i | −1.11794 | − | 0.200718i | ||||
\(868\) | −80.3594 | + | 11.6721i | −2.72758 | + | 0.396178i | ||||
\(869\) | −0.391979 | + | 0.226309i | −0.0132970 | + | 0.00767701i | ||||
\(870\) | 7.68223 | + | 21.3132i | 0.260452 | + | 0.722586i | ||||
\(871\) | 11.9187i | 0.403851i | ||||||||
\(872\) | 14.6581 | − | 8.46284i | 0.496385 | − | 0.286588i | ||||
\(873\) | −46.9518 | + | 7.97741i | −1.58908 | + | 0.269994i | ||||
\(874\) | − | 0.738334i | − | 0.0249745i | ||||||
\(875\) | 2.45764 | + | 0.979787i | 0.0830836 | + | 0.0331228i | ||||
\(876\) | −48.9590 | + | 17.6470i | −1.65417 | + | 0.596237i | ||||
\(877\) | −48.2495 | −1.62927 | −0.814636 | − | 0.579973i | \(-0.803063\pi\) | ||||
−0.814636 | + | 0.579973i | \(0.803063\pi\) | |||||||
\(878\) | 19.8024 | − | 34.2988i | 0.668299 | − | 1.15753i | ||||
\(879\) | 26.2687 | − | 31.1084i | 0.886021 | − | 1.04926i | ||||
\(880\) | 0.245308 | − | 0.141629i | 0.00826933 | − | 0.00477430i | ||||
\(881\) | −7.88554 | −0.265671 | −0.132835 | − | 0.991138i | \(-0.542408\pi\) | ||||
−0.132835 | + | 0.991138i | \(0.542408\pi\) | |||||||
\(882\) | 44.1401 | − | 21.6924i | 1.48627 | − | 0.730420i | ||||
\(883\) | 38.7887 | 1.30535 | 0.652673 | − | 0.757640i | \(-0.273648\pi\) | ||||
0.652673 | + | 0.757640i | \(0.273648\pi\) | |||||||
\(884\) | 105.553 | − | 60.9411i | 3.55014 | − | 2.04967i | ||||
\(885\) | 25.1267 | + | 4.51132i | 0.844626 | + | 0.151646i | ||||
\(886\) | 16.0110 | − | 27.7319i | 0.537901 | − | 0.931671i | ||||
\(887\) | 0.410828 | 0.0137943 | 0.00689714 | − | 0.999976i | \(-0.497805\pi\) | ||||
0.00689714 | + | 0.999976i | \(0.497805\pi\) | |||||||
\(888\) | 11.7228 | − | 65.2924i | 0.393390 | − | 2.19107i | ||||
\(889\) | −29.6435 | − | 11.8180i | −0.994212 | − | 0.396362i | ||||
\(890\) | 13.4363i | 0.450386i | ||||||||
\(891\) | 2.13103 | + | 0.403215i | 0.0713922 | + | 0.0135082i | ||||
\(892\) | −7.17919 | + | 4.14491i | −0.240377 | + | 0.138782i | ||||
\(893\) | 1.67641i | 0.0560990i | ||||||||
\(894\) | −3.57826 | + | 4.23751i | −0.119675 | + | 0.141723i | ||||
\(895\) | 16.3655 | − | 9.44863i | 0.547038 | − | 0.315833i | ||||
\(896\) | −52.7681 | + | 7.66451i | −1.76286 | + | 0.256053i | ||||
\(897\) | −2.57198 | + | 3.04584i | −0.0858759 | + | 0.101698i | ||||
\(898\) | −12.7029 | − | 22.0020i | −0.423900 | − | 0.734217i | ||||
\(899\) | 24.5927 | + | 42.5957i | 0.820211 | + | 1.42065i | ||||
\(900\) | 1.75129 | + | 10.3074i | 0.0583764 | + | 0.343580i | ||||
\(901\) | −1.97342 | − | 1.13936i | −0.0657443 | − | 0.0379575i | ||||
\(902\) | 0.278741 | − | 0.482794i | 0.00928107 | − | 0.0160753i | ||||
\(903\) | 21.8204 | + | 13.5895i | 0.726138 | + | 0.452231i | ||||
\(904\) | 27.3913 | + | 47.4432i | 0.911022 | + | 1.57794i | ||||
\(905\) | − | 12.5008i | − | 0.415540i | ||||||
\(906\) | −13.0850 | − | 11.0493i | −0.434720 | − | 0.367089i | ||||
\(907\) | 4.11936 | 0.136781 | 0.0683906 | − | 0.997659i | \(-0.478214\pi\) | ||||
0.0683906 | + | 0.997659i | \(0.478214\pi\) | |||||||
\(908\) | 10.7395 | − | 18.6014i | 0.356404 | − | 0.617310i | ||||
\(909\) | −0.766583 | + | 0.635138i | −0.0254259 | + | 0.0210662i | ||||
\(910\) | −28.2374 | + | 22.2720i | −0.936060 | + | 0.738310i | ||||
\(911\) | −1.93982 | − | 1.11995i | −0.0642690 | − | 0.0371057i | 0.467521 | − | 0.883982i | \(-0.345147\pi\) |
−0.531790 | + | 0.846876i | \(0.678481\pi\) | |||||||
\(912\) | 1.52262 | − | 0.548818i | 0.0504189 | − | 0.0181732i | ||||
\(913\) | −0.461282 | − | 0.266321i | −0.0152662 | − | 0.00881395i | ||||
\(914\) | −16.8584 | − | 9.73320i | −0.557626 | − | 0.321946i | ||||
\(915\) | −5.27299 | − | 4.45265i | −0.174320 | − | 0.147200i | ||||
\(916\) | −81.1137 | − | 46.8310i | −2.68007 | − | 1.54734i | ||||
\(917\) | −35.2685 | − | 14.0604i | −1.16467 | − | 0.464317i | ||||
\(918\) | 36.0693 | + | 63.8452i | 1.19046 | + | 2.10721i | ||||
\(919\) | 4.42519 | − | 7.66466i | 0.145974 | − | 0.252834i | −0.783762 | − | 0.621061i | \(-0.786702\pi\) |
0.929736 | + | 0.368227i | \(0.120035\pi\) | |||||||
\(920\) | −1.37922 | −0.0454715 | ||||||||
\(921\) | −25.3880 | + | 9.15095i | −0.836562 | + | 0.301534i | ||||
\(922\) | 4.18177i | 0.137719i | ||||||||
\(923\) | −7.72625 | − | 13.3823i | −0.254313 | − | 0.440483i | ||||
\(924\) | −2.03456 | + | 3.26685i | −0.0669321 | + | 0.107471i | ||||
\(925\) | −5.50596 | + | 9.53660i | −0.181035 | + | 0.313561i | ||||
\(926\) | 9.36300 | + | 5.40573i | 0.307687 | + | 0.177643i | ||||
\(927\) | 20.0425 | + | 24.1904i | 0.658281 | + | 0.794516i | ||||
\(928\) | 11.7372 | + | 20.3293i | 0.385291 | + | 0.667344i | ||||
\(929\) | −22.1259 | − | 38.3232i | −0.725927 | − | 1.25734i | −0.958591 | − | 0.284785i | \(-0.908078\pi\) |
0.232665 | − | 0.972557i | \(-0.425256\pi\) | |||||||
\(930\) | 12.1137 | + | 33.6078i | 0.397225 | + | 1.10204i | ||||
\(931\) | 1.58319 | + | 5.33492i | 0.0518868 | + | 0.174845i | ||||
\(932\) | 3.85931 | − | 2.22818i | 0.126416 | − | 0.0729863i | ||||
\(933\) | −31.4797 | − | 5.65194i | −1.03060 | − | 0.185036i | ||||
\(934\) | 36.1569i | 1.18309i | ||||||||
\(935\) | −1.25754 | + | 0.726042i | −0.0411260 | + | 0.0237441i | ||||
\(936\) | −56.7762 | − | 21.0666i | −1.85579 | − | 0.688583i | ||||
\(937\) | 2.82353i | 0.0922407i | 0.998936 | + | 0.0461203i | \(0.0146858\pi\) | ||||
−0.998936 | + | 0.0461203i | \(0.985314\pi\) | |||||||
\(938\) | 4.71222 | − | 11.8199i | 0.153859 | − | 0.385933i | ||||
\(939\) | −21.9765 | − | 18.5575i | −0.717175 | − | 0.605601i | ||||
\(940\) | 7.34904 | 0.239699 | ||||||||
\(941\) | 10.6229 | − | 18.3995i | 0.346298 | − | 0.599805i | −0.639291 | − | 0.768965i | \(-0.720772\pi\) |
0.985589 | + | 0.169160i | \(0.0541054\pi\) | |||||||
\(942\) | −3.28078 | − | 9.10205i | −0.106894 | − | 0.296561i | ||||
\(943\) | −0.339228 | + | 0.195854i | −0.0110468 | + | 0.00637787i | ||||
\(944\) | −17.3245 | −0.563865 | ||||||||
\(945\) | −8.41253 | − | 10.8733i | −0.273660 | − | 0.353709i | ||||
\(946\) | −3.16594 | −0.102933 | ||||||||
\(947\) | 31.5469 | − | 18.2136i | 1.02514 | − | 0.591862i | 0.109548 | − | 0.993982i | \(-0.465060\pi\) |
0.915587 | + | 0.402119i | \(0.131726\pi\) | |||||||
\(948\) | 3.84441 | + | 10.6658i | 0.124861 | + | 0.346408i | ||||
\(949\) | −25.0198 | + | 43.3356i | −0.812178 | + | 1.40673i | ||||
\(950\) | −1.86186 | −0.0604068 | ||||||||
\(951\) | −17.9704 | − | 15.1747i | −0.582731 | − | 0.492073i | ||||
\(952\) | −54.8719 | + | 7.97009i | −1.77841 | + | 0.258312i | ||||
\(953\) | 58.8278i | 1.90562i | 0.303569 | + | 0.952809i | \(0.401822\pi\) | ||||
−0.303569 | + | 0.952809i | \(0.598178\pi\) | |||||||
\(954\) | 0.445065 | + | 2.61948i | 0.0144095 | + | 0.0848087i | ||||
\(955\) | 7.55653 | − | 4.36277i | 0.244524 | − | 0.141176i | ||||
\(956\) | 43.6022i | 1.41020i | ||||||||
\(957\) | 2.29445 | + | 0.411952i | 0.0741690 | + | 0.0133165i | ||||
\(958\) | 17.2974 | − | 9.98668i | 0.558855 | − | 0.322655i | ||||
\(959\) | 2.10987 | − | 5.29229i | 0.0681313 | − | 0.170897i | ||||
\(960\) | 7.16214 | + | 19.8703i | 0.231157 | + | 0.641311i | ||||
\(961\) | 23.2790 | + | 40.3204i | 0.750936 | + | 1.30066i | ||||
\(962\) | −74.8426 | − | 129.631i | −2.41302 | − | 4.17948i | ||||
\(963\) | 1.67637 | − | 0.284826i | 0.0540203 | − | 0.00917838i | ||||
\(964\) | −34.4534 | − | 19.8917i | −1.10967 | − | 0.640668i | ||||
\(965\) | −5.69624 | + | 9.86618i | −0.183369 | + | 0.317604i | ||||
\(966\) | 3.75486 | − | 2.00371i | 0.120811 | − | 0.0644683i | ||||
\(967\) | 13.3155 | + | 23.0631i | 0.428196 | + | 0.741658i | 0.996713 | − | 0.0810139i | \(-0.0258158\pi\) |
−0.568517 | + | 0.822672i | \(0.692482\pi\) | |||||||
\(968\) | 38.0559i | 1.22316i | ||||||||
\(969\) | −7.80550 | + | 2.81345i | −0.250749 | + | 0.0903810i | ||||
\(970\) | −37.1793 | −1.19375 | ||||||||
\(971\) | 2.63348 | − | 4.56132i | 0.0845124 | − | 0.146380i | −0.820671 | − | 0.571401i | \(-0.806400\pi\) |
0.905183 | + | 0.425021i | \(0.139733\pi\) | |||||||
\(972\) | 19.3740 | − | 50.7544i | 0.621423 | − | 1.62795i | ||||
\(973\) | −41.8113 | + | 6.07305i | −1.34041 | + | 0.194693i | ||||
\(974\) | −5.77314 | − | 3.33312i | −0.184983 | − | 0.106800i | ||||
\(975\) | 7.68071 | + | 6.48578i | 0.245980 | + | 0.207711i | ||||
\(976\) | 4.05610 | + | 2.34179i | 0.129833 | + | 0.0749589i | ||||
\(977\) | 41.0964 | + | 23.7270i | 1.31479 | + | 0.759095i | 0.982885 | − | 0.184218i | \(-0.0589751\pi\) |
0.331906 | + | 0.943313i | \(0.392308\pi\) | |||||||
\(978\) | −66.7986 | + | 24.0772i | −2.13598 | + | 0.769904i | ||||
\(979\) | 1.19731 | + | 0.691266i | 0.0382662 | + | 0.0220930i | ||||
\(980\) | 23.3872 | − | 6.94036i | 0.747077 | − | 0.221702i | ||||
\(981\) | 13.6877 | + | 5.07876i | 0.437014 | + | 0.162152i | ||||
\(982\) | 41.2293 | − | 71.4112i | 1.31568 | − | 2.27882i | ||||
\(983\) | −6.74330 | −0.215078 | −0.107539 | − | 0.994201i | \(-0.534297\pi\) | ||||
−0.107539 | + | 0.994201i | \(0.534297\pi\) | |||||||
\(984\) | −4.54632 | − | 3.83902i | −0.144931 | − | 0.122384i | ||||
\(985\) | − | 18.6026i | − | 0.592728i | ||||||
\(986\) | 39.4084 | + | 68.2573i | 1.25502 | + | 2.17376i | ||||
\(987\) | −8.52553 | + | 4.54949i | −0.271370 | + | 0.144812i | ||||
\(988\) | 8.04011 | − | 13.9259i | 0.255790 | − | 0.443041i | ||||
\(989\) | 1.92647 | + | 1.11225i | 0.0612583 | + | 0.0353675i | ||||
\(990\) | 1.58740 | + | 0.589000i | 0.0504510 | + | 0.0187196i | ||||
\(991\) | −1.97688 | − | 3.42405i | −0.0627976 | − | 0.108769i | 0.832917 | − | 0.553397i | \(-0.186669\pi\) |
−0.895715 | + | 0.444629i | \(0.853336\pi\) | |||||||
\(992\) | 18.5078 | + | 32.0564i | 0.587622 | + | 1.01779i | ||||
\(993\) | 33.1009 | − | 39.1993i | 1.05043 | − | 1.24395i | ||||
\(994\) | 2.37133 | + | 16.3259i | 0.0752139 | + | 0.517827i | ||||
\(995\) | −19.5486 | + | 11.2864i | −0.619733 | + | 0.357803i | ||||
\(996\) | −8.60785 | + | 10.1937i | −0.272750 | + | 0.323001i | ||||
\(997\) | 18.5781i | 0.588374i | 0.955748 | + | 0.294187i | \(0.0950488\pi\) | ||||
−0.955748 | + | 0.294187i | \(0.904951\pi\) | |||||||
\(998\) | 29.2408 | − | 16.8822i | 0.925602 | − | 0.534396i | ||||
\(999\) | 49.8190 | − | 28.1452i | 1.57620 | − | 0.890474i |
(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 | 315.2.be.b.236.2 | yes | 30 | |
3.2 | odd | 2 | 945.2.be.b.656.14 | 30 | |||
7.3 | odd | 6 | 315.2.t.b.101.2 | ✓ | 30 | ||
9.4 | even | 3 | 945.2.t.b.341.2 | 30 | |||
9.5 | odd | 6 | 315.2.t.b.131.14 | yes | 30 | ||
21.17 | even | 6 | 945.2.t.b.521.14 | 30 | |||
63.31 | odd | 6 | 945.2.be.b.206.14 | 30 | |||
63.59 | even | 6 | inner | 315.2.be.b.311.2 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.t.b.101.2 | ✓ | 30 | 7.3 | odd | 6 | ||
315.2.t.b.131.14 | yes | 30 | 9.5 | odd | 6 | ||
315.2.be.b.236.2 | yes | 30 | 1.1 | even | 1 | trivial | |
315.2.be.b.311.2 | yes | 30 | 63.59 | even | 6 | inner | |
945.2.t.b.341.2 | 30 | 9.4 | even | 3 | |||
945.2.t.b.521.14 | 30 | 21.17 | even | 6 | |||
945.2.be.b.206.14 | 30 | 63.31 | odd | 6 | |||
945.2.be.b.656.14 | 30 | 3.2 | odd | 2 |