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 | 440.2 | ||
Character | \(\chi\) | \(=\) | 637.440 |
Dual form | 637.2.bd.b.97.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.360315 | + | 1.34471i | −0.254781 | + | 0.950856i | 0.713431 | + | 0.700725i | \(0.247140\pi\) |
−0.968212 | + | 0.250130i | \(0.919527\pi\) | |||||||
\(3\) | 1.25446 | − | 0.724265i | 0.724265 | − | 0.418155i | −0.0920554 | − | 0.995754i | \(-0.529344\pi\) |
0.816320 | + | 0.577599i | \(0.196010\pi\) | |||||||
\(4\) | 0.0536242 | + | 0.0309600i | 0.0268121 | + | 0.0154800i | ||||
\(5\) | −0.470766 | + | 0.470766i | −0.210533 | + | 0.210533i | −0.804494 | − | 0.593961i | \(-0.797563\pi\) |
0.593961 | + | 0.804494i | \(0.297563\pi\) | |||||||
\(6\) | 0.521927 | + | 1.94786i | 0.213076 | + | 0.795210i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.02975 | + | 2.02975i | −0.717625 | + | 0.717625i | ||||
\(9\) | −0.450880 | + | 0.780947i | −0.150293 | + | 0.260316i | ||||
\(10\) | −0.463421 | − | 0.802669i | −0.146547 | − | 0.253826i | ||||
\(11\) | 4.65687 | + | 1.24780i | 1.40410 | + | 0.376227i | 0.879815 | − | 0.475317i | \(-0.157667\pi\) |
0.524283 | + | 0.851544i | \(0.324333\pi\) | |||||||
\(12\) | 0.0896929 | 0.0258921 | ||||||||
\(13\) | 3.60544 | + | 0.0282257i | 0.999969 | + | 0.00782840i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.249600 | + | 0.931519i | −0.0644463 | + | 0.240517i | ||||
\(16\) | −1.93616 | − | 3.35353i | −0.484041 | − | 0.838383i | ||||
\(17\) | −0.233952 | + | 0.405217i | −0.0567417 | + | 0.0982794i | −0.893001 | − | 0.450055i | \(-0.851404\pi\) |
0.836259 | + | 0.548334i | \(0.184738\pi\) | |||||||
\(18\) | −0.887691 | − | 0.887691i | −0.209231 | − | 0.209231i | ||||
\(19\) | −0.873976 | − | 3.26172i | −0.200504 | − | 0.748290i | −0.990773 | − | 0.135531i | \(-0.956726\pi\) |
0.790269 | − | 0.612760i | \(-0.209941\pi\) | |||||||
\(20\) | −0.0398194 | + | 0.0106696i | −0.00890388 | + | 0.00238579i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.35587 | + | 5.81255i | −0.715475 | + | 1.23924i | ||||
\(23\) | −6.02331 | + | 3.47756i | −1.25595 | + | 0.725122i | −0.972284 | − | 0.233802i | \(-0.924883\pi\) |
−0.283663 | + | 0.958924i | \(0.591550\pi\) | |||||||
\(24\) | −1.07617 | + | 4.01633i | −0.219673 | + | 0.819829i | ||||
\(25\) | 4.55676i | 0.911352i | ||||||||
\(26\) | −1.33705 | + | 4.83811i | −0.262217 | + | 0.948832i | ||||
\(27\) | 5.65182i | 1.08769i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.01911 | − | 3.49720i | −0.374940 | − | 0.649414i | 0.615378 | − | 0.788232i | \(-0.289003\pi\) |
−0.990318 | + | 0.138817i | \(0.955670\pi\) | |||||||
\(30\) | −1.16269 | − | 0.671280i | −0.212277 | − | 0.122558i | ||||
\(31\) | 3.00205 | − | 3.00205i | 0.539184 | − | 0.539184i | −0.384105 | − | 0.923289i | \(-0.625490\pi\) |
0.923289 | + | 0.384105i | \(0.125490\pi\) | |||||||
\(32\) | −0.338214 | + | 0.0906241i | −0.0597883 | + | 0.0160202i | ||||
\(33\) | 6.74561 | − | 1.80748i | 1.17426 | − | 0.314642i | ||||
\(34\) | −0.460604 | − | 0.460604i | −0.0789929 | − | 0.0789929i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0483562 | + | 0.0279185i | −0.00805937 | + | 0.00465308i | ||||
\(37\) | 3.26109 | + | 0.873807i | 0.536120 | + | 0.143653i | 0.516713 | − | 0.856159i | \(-0.327155\pi\) |
0.0194074 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(38\) | 4.70099 | 0.762601 | ||||||||
\(39\) | 4.54334 | − | 2.57589i | 0.727516 | − | 0.412472i | ||||
\(40\) | − | 1.91108i | − | 0.302168i | ||||||
\(41\) | 3.68025 | + | 0.986119i | 0.574758 | + | 0.154006i | 0.534478 | − | 0.845182i | \(-0.320508\pi\) |
0.0402801 | + | 0.999188i | \(0.487175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.42191 | + | 1.97564i | 0.521836 | + | 0.301282i | 0.737686 | − | 0.675144i | \(-0.235919\pi\) |
−0.215849 | + | 0.976427i | \(0.569252\pi\) | |||||||
\(44\) | 0.211089 | + | 0.211089i | 0.0318228 | + | 0.0318228i | ||||
\(45\) | −0.155384 | − | 0.579902i | −0.0231633 | − | 0.0864468i | ||||
\(46\) | −2.50603 | − | 9.35265i | −0.369495 | − | 1.37897i | ||||
\(47\) | 7.06171 | + | 7.06171i | 1.03006 | + | 1.03006i | 0.999534 | + | 0.0305229i | \(0.00971724\pi\) |
0.0305229 | + | 0.999534i | \(0.490283\pi\) | |||||||
\(48\) | −4.85769 | − | 2.80459i | −0.701148 | − | 0.404808i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.12753 | − | 1.64187i | −0.866564 | − | 0.232195i | ||||
\(51\) | 0.677773i | 0.0949072i | ||||||||
\(52\) | 0.192465 | + | 0.113138i | 0.0266901 | + | 0.0156894i | ||||
\(53\) | −4.40103 | −0.604528 | −0.302264 | − | 0.953224i | \(-0.597742\pi\) | ||||
−0.302264 | + | 0.953224i | \(0.597742\pi\) | |||||||
\(54\) | −7.60007 | − | 2.03643i | −1.03424 | − | 0.277123i | ||||
\(55\) | −2.77972 | + | 1.60487i | −0.374817 | + | 0.216401i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.45872 | − | 3.45872i | −0.458119 | − | 0.458119i | ||||
\(58\) | 5.43025 | − | 1.45503i | 0.713027 | − | 0.191055i | ||||
\(59\) | −5.91907 | + | 1.58601i | −0.770598 | + | 0.206481i | −0.622635 | − | 0.782512i | \(-0.713938\pi\) |
−0.147962 | + | 0.988993i | \(0.547271\pi\) | |||||||
\(60\) | −0.0422244 | + | 0.0422244i | −0.00545114 | + | 0.00545114i | ||||
\(61\) | −4.21802 | − | 2.43528i | −0.540062 | − | 0.311805i | 0.205042 | − | 0.978753i | \(-0.434267\pi\) |
−0.745104 | + | 0.666948i | \(0.767600\pi\) | |||||||
\(62\) | 2.95521 | + | 5.11858i | 0.375312 | + | 0.650060i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.23211i | − | 1.02901i | ||||||
\(65\) | −1.71061 | + | 1.68403i | −0.212175 | + | 0.208878i | ||||
\(66\) | 9.72217i | 1.19672i | ||||||||
\(67\) | 2.42145 | − | 9.03697i | 0.295827 | − | 1.10404i | −0.644731 | − | 0.764409i | \(-0.723031\pi\) |
0.940558 | − | 0.339633i | \(-0.110303\pi\) | |||||||
\(68\) | −0.0250910 | + | 0.0144863i | −0.00304273 | + | 0.00175672i | ||||
\(69\) | −5.03735 | + | 8.72495i | −0.606426 | + | 1.05036i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.19935 | − | 0.857263i | 0.379693 | − | 0.101738i | −0.0639244 | − | 0.997955i | \(-0.520362\pi\) |
0.443617 | + | 0.896216i | \(0.353695\pi\) | |||||||
\(72\) | −0.669954 | − | 2.50030i | −0.0789548 | − | 0.294663i | ||||
\(73\) | −0.0824857 | − | 0.0824857i | −0.00965422 | − | 0.00965422i | 0.702263 | − | 0.711917i | \(-0.252173\pi\) |
−0.711917 | + | 0.702263i | \(0.752173\pi\) | |||||||
\(74\) | −2.35004 | + | 4.07039i | −0.273187 | + | 0.473173i | ||||
\(75\) | 3.30030 | + | 5.71629i | 0.381086 | + | 0.660060i | ||||
\(76\) | 0.0541165 | − | 0.201966i | 0.00620759 | − | 0.0231670i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.82680 | + | 7.03762i | 0.206844 | + | 0.796853i | ||||
\(79\) | −0.389839 | −0.0438604 | −0.0219302 | − | 0.999760i | \(-0.506981\pi\) | ||||
−0.0219302 | + | 0.999760i | \(0.506981\pi\) | |||||||
\(80\) | 2.49021 | + | 0.667250i | 0.278414 | + | 0.0746008i | ||||
\(81\) | 2.74077 | + | 4.74716i | 0.304530 | + | 0.527462i | ||||
\(82\) | −2.65209 | + | 4.59356i | −0.292875 | + | 0.507274i | ||||
\(83\) | 11.5572 | − | 11.5572i | 1.26857 | − | 1.26857i | 0.321741 | − | 0.946828i | \(-0.395732\pi\) |
0.946828 | − | 0.321741i | \(-0.104268\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0806256 | − | 0.300899i | −0.00874507 | − | 0.0326371i | ||||
\(86\) | −3.88964 | + | 3.88964i | −0.419430 | + | 0.419430i | ||||
\(87\) | −5.06581 | − | 2.92474i | −0.543111 | − | 0.313565i | ||||
\(88\) | −11.9850 | + | 6.91955i | −1.27761 | + | 0.737626i | ||||
\(89\) | 2.50295 | − | 9.34114i | 0.265312 | − | 0.990159i | −0.696747 | − | 0.717317i | \(-0.745370\pi\) |
0.962059 | − | 0.272842i | \(-0.0879636\pi\) | |||||||
\(90\) | 0.835790 | 0.0881000 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.430661 | −0.0448995 | ||||||||
\(93\) | 1.59168 | − | 5.94024i | 0.165050 | − | 0.615974i | ||||
\(94\) | −12.0404 | + | 6.95154i | −1.24187 | + | 0.716997i | ||||
\(95\) | 1.94695 | + | 1.12407i | 0.199752 | + | 0.115327i | ||||
\(96\) | −0.358641 | + | 0.358641i | −0.0366037 | + | 0.0366037i | ||||
\(97\) | −4.61378 | − | 17.2188i | −0.468458 | − | 1.74831i | −0.645163 | − | 0.764045i | \(-0.723210\pi\) |
0.176705 | − | 0.984264i | \(-0.443456\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.07416 | + | 3.07416i | −0.308964 | + | 0.308964i | ||||
\(100\) | −0.141077 | + | 0.244353i | −0.0141077 | + | 0.0244353i | ||||
\(101\) | −5.57293 | − | 9.65259i | −0.554527 | − | 0.960469i | −0.997940 | − | 0.0641517i | \(-0.979566\pi\) |
0.443413 | − | 0.896317i | \(-0.353767\pi\) | |||||||
\(102\) | −0.911410 | − | 0.244212i | −0.0902430 | − | 0.0241805i | ||||
\(103\) | −7.47232 | −0.736270 | −0.368135 | − | 0.929772i | \(-0.620003\pi\) | ||||
−0.368135 | + | 0.929772i | \(0.620003\pi\) | |||||||
\(104\) | −7.37544 | + | 7.26085i | −0.723221 | + | 0.711985i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.58576 | − | 5.91812i | 0.154022 | − | 0.574819i | ||||
\(107\) | 2.07553 | + | 3.59492i | 0.200649 | + | 0.347534i | 0.948738 | − | 0.316065i | \(-0.102362\pi\) |
−0.748089 | + | 0.663598i | \(0.769028\pi\) | |||||||
\(108\) | −0.174980 | + | 0.303074i | −0.0168375 | + | 0.0291633i | ||||
\(109\) | −4.34964 | − | 4.34964i | −0.416620 | − | 0.416620i | 0.467417 | − | 0.884037i | \(-0.345185\pi\) |
−0.884037 | + | 0.467417i | \(0.845185\pi\) | |||||||
\(110\) | −1.15652 | − | 4.31618i | −0.110270 | − | 0.411532i | ||||
\(111\) | 4.72379 | − | 1.26574i | 0.448363 | − | 0.120138i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.554932 | + | 0.961171i | −0.0522036 | + | 0.0904194i | −0.890946 | − | 0.454109i | \(-0.849958\pi\) |
0.838743 | + | 0.544528i | \(0.183291\pi\) | |||||||
\(114\) | 5.89722 | − | 3.40476i | 0.552325 | − | 0.318885i | ||||
\(115\) | 1.19845 | − | 4.47269i | 0.111756 | − | 0.417080i | ||||
\(116\) | − | 0.250046i | − | 0.0232162i | ||||||
\(117\) | −1.64766 | + | 2.80293i | −0.152327 | + | 0.259131i | ||||
\(118\) | − | 8.53092i | − | 0.785335i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.38413 | − | 2.39738i | −0.126353 | − | 0.218849i | ||||
\(121\) | 10.6031 | + | 6.12170i | 0.963918 | + | 0.556519i | ||||
\(122\) | 4.79456 | − | 4.79456i | 0.434079 | − | 0.434079i | ||||
\(123\) | 5.33095 | − | 1.42842i | 0.480675 | − | 0.128797i | ||||
\(124\) | 0.253926 | − | 0.0680392i | 0.0228032 | − | 0.00611010i | ||||
\(125\) | −4.49900 | − | 4.49900i | −0.402403 | − | 0.402403i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.2552 | − | 9.96228i | 1.53115 | − | 0.884009i | 0.531840 | − | 0.846845i | \(-0.321501\pi\) |
0.999309 | − | 0.0371647i | \(-0.0118326\pi\) | |||||||
\(128\) | 10.3934 | + | 2.78490i | 0.918655 | + | 0.246153i | ||||
\(129\) | 5.72355 | 0.503931 | ||||||||
\(130\) | −1.64818 | − | 2.90706i | −0.144555 | − | 0.254966i | ||||
\(131\) | − | 7.63701i | − | 0.667249i | −0.942706 | − | 0.333625i | \(-0.891728\pi\) | ||
0.942706 | − | 0.333625i | \(-0.108272\pi\) | |||||||
\(132\) | 0.417688 | + | 0.111919i | 0.0363550 | + | 0.00974131i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.2797 | + | 6.51231i | 0.974414 | + | 0.562578i | ||||
\(135\) | −2.66068 | − | 2.66068i | −0.228995 | − | 0.228995i | ||||
\(136\) | −0.347625 | − | 1.29735i | −0.0298086 | − | 0.111247i | ||||
\(137\) | 3.40822 | + | 12.7196i | 0.291184 | + | 1.08671i | 0.944201 | + | 0.329369i | \(0.106836\pi\) |
−0.653018 | + | 0.757343i | \(0.726497\pi\) | |||||||
\(138\) | −9.91752 | − | 9.91752i | −0.844236 | − | 0.844236i | ||||
\(139\) | −14.9082 | − | 8.60724i | −1.26449 | − | 0.730056i | −0.290554 | − | 0.956859i | \(-0.593839\pi\) |
−0.973941 | + | 0.226802i | \(0.927173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.9732 | + | 3.74411i | 1.17676 | + | 0.315311i | ||||
\(142\) | 4.61109i | 0.386954i | ||||||||
\(143\) | 16.7548 | + | 4.63032i | 1.40111 | + | 0.387207i | ||||
\(144\) | 3.49191 | 0.290992 | ||||||||
\(145\) | 2.59689 | + | 0.695836i | 0.215660 | + | 0.0577860i | ||||
\(146\) | 0.140640 | − | 0.0811987i | 0.0116395 | − | 0.00672006i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.147821 | + | 0.147821i | 0.0121508 | + | 0.0121508i | ||||
\(149\) | −3.63443 | + | 0.973843i | −0.297744 | + | 0.0797804i | −0.404599 | − | 0.914494i | \(-0.632589\pi\) |
0.106854 | + | 0.994275i | \(0.465922\pi\) | |||||||
\(150\) | −8.87592 | + | 2.37829i | −0.724716 | + | 0.194187i | ||||
\(151\) | −5.34620 | + | 5.34620i | −0.435067 | + | 0.435067i | −0.890348 | − | 0.455281i | \(-0.849539\pi\) |
0.455281 | + | 0.890348i | \(0.349539\pi\) | |||||||
\(152\) | 8.39443 | + | 4.84653i | 0.680879 | + | 0.393105i | ||||
\(153\) | −0.210968 | − | 0.365408i | −0.0170558 | − | 0.0295415i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.82653i | 0.227032i | ||||||||
\(156\) | 0.323382 | + | 0.00253164i | 0.0258913 | + | 0.000202694i | ||||
\(157\) | − | 24.6389i | − | 1.96640i | −0.182537 | − | 0.983199i | \(-0.558431\pi\) | ||
0.182537 | − | 0.983199i | \(-0.441569\pi\) | |||||||
\(158\) | 0.140465 | − | 0.524222i | 0.0111748 | − | 0.0417049i | ||||
\(159\) | −5.52093 | + | 3.18751i | −0.437838 | + | 0.252786i | ||||
\(160\) | 0.116557 | − | 0.201882i | 0.00921463 | − | 0.0159602i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.37111 | + | 1.97508i | −0.579129 | + | 0.155177i | ||||
\(163\) | −5.37364 | − | 20.0547i | −0.420896 | − | 1.57081i | −0.772724 | − | 0.634742i | \(-0.781107\pi\) |
0.351828 | − | 0.936065i | \(-0.385560\pi\) | |||||||
\(164\) | 0.166820 | + | 0.166820i | 0.0130265 | + | 0.0130265i | ||||
\(165\) | −2.32470 | + | 4.02651i | −0.180978 | + | 0.313463i | ||||
\(166\) | 11.3769 | + | 19.7054i | 0.883018 | + | 1.52943i | ||||
\(167\) | −4.53457 | + | 16.9233i | −0.350896 | + | 1.30956i | 0.534676 | + | 0.845057i | \(0.320434\pi\) |
−0.885571 | + | 0.464503i | \(0.846233\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9984 | + | 0.203532i | 0.999877 | + | 0.0156563i | ||||
\(170\) | 0.433673 | 0.0332612 | ||||||||
\(171\) | 2.94129 | + | 0.788117i | 0.224926 | + | 0.0602688i | ||||
\(172\) | 0.122332 | + | 0.211884i | 0.00932769 | + | 0.0161560i | ||||
\(173\) | 2.96030 | − | 5.12740i | 0.225068 | − | 0.389829i | −0.731272 | − | 0.682086i | \(-0.761073\pi\) |
0.956340 | + | 0.292257i | \(0.0944063\pi\) | |||||||
\(174\) | 5.75823 | − | 5.75823i | 0.436530 | − | 0.436530i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.83190 | − | 18.0329i | −0.364218 | − | 1.35928i | ||||
\(177\) | −6.27657 | + | 6.27657i | −0.471776 | + | 0.471776i | ||||
\(178\) | 11.6593 | + | 6.73150i | 0.873902 | + | 0.504548i | ||||
\(179\) | −3.26505 | + | 1.88508i | −0.244041 | + | 0.140897i | −0.617033 | − | 0.786938i | \(-0.711665\pi\) |
0.372992 | + | 0.927835i | \(0.378332\pi\) | |||||||
\(180\) | 0.00962139 | − | 0.0359075i | 0.000717136 | − | 0.00267639i | ||||
\(181\) | 5.68899 | 0.422859 | 0.211430 | − | 0.977393i | \(-0.432188\pi\) | ||||
0.211430 | + | 0.977393i | \(0.432188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.05514 | −0.521531 | ||||||||
\(184\) | 5.16724 | − | 19.2844i | 0.380934 | − | 1.42167i | ||||
\(185\) | −1.94657 | + | 1.12385i | −0.143115 | + | 0.0826273i | ||||
\(186\) | 7.41441 | + | 4.28071i | 0.543651 | + | 0.313877i | ||||
\(187\) | −1.59511 | + | 1.59511i | −0.116646 | + | 0.116646i | ||||
\(188\) | 0.160049 | + | 0.597309i | 0.0116727 | + | 0.0435633i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.21307 | + | 2.21307i | −0.160553 | + | 0.160553i | ||||
\(191\) | 4.58382 | − | 7.93941i | 0.331674 | − | 0.574476i | −0.651167 | − | 0.758935i | \(-0.725720\pi\) |
0.982840 | + | 0.184459i | \(0.0590534\pi\) | |||||||
\(192\) | −5.96223 | − | 10.3269i | −0.430287 | − | 0.745278i | ||||
\(193\) | 24.5455 | + | 6.57695i | 1.76682 | + | 0.473419i | 0.988082 | − | 0.153926i | \(-0.0491917\pi\) |
0.778742 | + | 0.627345i | \(0.215858\pi\) | |||||||
\(194\) | 24.8168 | 1.78174 | ||||||||
\(195\) | −0.926209 | + | 3.35149i | −0.0663272 | + | 0.240005i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.371638 | + | 1.38697i | −0.0264781 | + | 0.0988175i | −0.977900 | − | 0.209071i | \(-0.932956\pi\) |
0.951422 | + | 0.307889i | \(0.0996225\pi\) | |||||||
\(198\) | −3.02619 | − | 5.24152i | −0.215062 | − | 0.372499i | ||||
\(199\) | −5.50792 | + | 9.53999i | −0.390446 | + | 0.676272i | −0.992508 | − | 0.122177i | \(-0.961012\pi\) |
0.602062 | + | 0.798449i | \(0.294346\pi\) | |||||||
\(200\) | −9.24908 | − | 9.24908i | −0.654009 | − | 0.654009i | ||||
\(201\) | −3.50754 | − | 13.0903i | −0.247403 | − | 0.923321i | ||||
\(202\) | 14.9880 | − | 4.01602i | 1.05455 | − | 0.282566i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0209838 | + | 0.0363450i | −0.00146916 | + | 0.00254466i | ||||
\(205\) | −2.19677 | + | 1.26830i | −0.153429 | + | 0.0885822i | ||||
\(206\) | 2.69239 | − | 10.0481i | 0.187588 | − | 0.700086i | ||||
\(207\) | − | 6.27185i | − | 0.435924i | ||||||
\(208\) | −6.88607 | − | 12.1456i | −0.477463 | − | 0.842147i | ||||
\(209\) | − | 16.2800i | − | 1.12611i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5485 | + | 20.0025i | 0.795029 | + | 1.37703i | 0.922821 | + | 0.385229i | \(0.125878\pi\) |
−0.127792 | + | 0.991801i | \(0.540789\pi\) | |||||||
\(212\) | −0.236002 | − | 0.136256i | −0.0162087 | − | 0.00935808i | ||||
\(213\) | 3.39258 | − | 3.39258i | 0.232456 | − | 0.232456i | ||||
\(214\) | −5.58197 | + | 1.49569i | −0.381576 | + | 0.102243i | ||||
\(215\) | −2.54098 | + | 0.680855i | −0.173294 | + | 0.0464339i | ||||
\(216\) | −11.4718 | − | 11.4718i | −0.780556 | − | 0.780556i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.41625 | − | 4.28178i | 0.502292 | − | 0.289998i | ||||
\(219\) | −0.163217 | − | 0.0437338i | −0.0110292 | − | 0.00295526i | ||||
\(220\) | −0.198747 | −0.0133995 | ||||||||
\(221\) | −0.854937 | + | 1.45438i | −0.0575093 | + | 0.0978322i | ||||
\(222\) | 6.80821i | 0.456937i | ||||||||
\(223\) | −3.57776 | − | 0.958657i | −0.239584 | − | 0.0641964i | 0.137029 | − | 0.990567i | \(-0.456245\pi\) |
−0.376613 | + | 0.926371i | \(0.622911\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.55859 | − | 2.05455i | −0.237239 | − | 0.136970i | ||||
\(226\) | −1.09255 | − | 1.09255i | −0.0726753 | − | 0.0726753i | ||||
\(227\) | 6.23954 | + | 23.2863i | 0.414133 | + | 1.54556i | 0.786566 | + | 0.617506i | \(0.211857\pi\) |
−0.372433 | + | 0.928059i | \(0.621476\pi\) | |||||||
\(228\) | −0.0783894 | − | 0.292553i | −0.00519147 | − | 0.0193748i | ||||
\(229\) | −13.1839 | − | 13.1839i | −0.871216 | − | 0.871216i | 0.121389 | − | 0.992605i | \(-0.461265\pi\) |
−0.992605 | + | 0.121389i | \(0.961265\pi\) | |||||||
\(230\) | 5.58266 | + | 3.22315i | 0.368110 | + | 0.212528i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.1967 | + | 3.00016i | 0.735102 | + | 0.196970i | ||||
\(233\) | 4.52263i | 0.296288i | 0.988966 | + | 0.148144i | \(0.0473299\pi\) | ||||
−0.988966 | + | 0.148144i | \(0.952670\pi\) | |||||||
\(234\) | −3.17546 | − | 3.22557i | −0.207586 | − | 0.210862i | ||||
\(235\) | −6.64883 | −0.433722 | ||||||||
\(236\) | −0.366509 | − | 0.0982057i | −0.0238577 | − | 0.00639264i | ||||
\(237\) | −0.489040 | + | 0.282347i | −0.0317665 | + | 0.0183404i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1608 | − | 11.1608i | −0.721931 | − | 0.721931i | 0.247067 | − | 0.968998i | \(-0.420533\pi\) |
−0.968998 | + | 0.247067i | \(0.920533\pi\) | |||||||
\(240\) | 3.60714 | − | 0.966531i | 0.232840 | − | 0.0623893i | ||||
\(241\) | 7.31049 | − | 1.95884i | 0.470910 | − | 0.126180i | −0.0155569 | − | 0.999879i | \(-0.504952\pi\) |
0.486467 | + | 0.873699i | \(0.338285\pi\) | |||||||
\(242\) | −12.0524 | + | 12.0524i | −0.774757 | + | 0.774757i | ||||
\(243\) | −7.80745 | − | 4.50763i | −0.500848 | − | 0.289165i | ||||
\(244\) | −0.150792 | − | 0.261180i | −0.00965348 | − | 0.0167203i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.68328i | 0.489868i | ||||||||
\(247\) | −3.05900 | − | 11.7846i | −0.194640 | − | 0.749837i | ||||
\(248\) | 12.1868i | 0.773864i | ||||||||
\(249\) | 6.12762 | − | 22.8686i | 0.388322 | − | 1.44924i | ||||
\(250\) | 7.67092 | − | 4.42881i | 0.485151 | − | 0.280102i | ||||
\(251\) | −10.6165 | + | 18.3883i | −0.670106 | + | 1.16066i | 0.307767 | + | 0.951462i | \(0.400418\pi\) |
−0.977874 | + | 0.209197i | \(0.932915\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.3891 | + | 8.67863i | −2.03628 | + | 0.545621i | ||||
\(254\) | 7.17911 | + | 26.7928i | 0.450458 | + | 1.68113i | ||||
\(255\) | −0.319072 | − | 0.319072i | −0.0199811 | − | 0.0199811i | ||||
\(256\) | 0.742320 | − | 1.28574i | 0.0463950 | − | 0.0803584i | ||||
\(257\) | 12.6205 | + | 21.8594i | 0.787245 | + | 1.36355i | 0.927648 | + | 0.373455i | \(0.121827\pi\) |
−0.140403 | + | 0.990094i | \(0.544840\pi\) | |||||||
\(258\) | −2.06228 | + | 7.69653i | −0.128392 | + | 0.479165i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.143868 | + | 0.0373446i | −0.00892229 | + | 0.00231601i | ||||
\(261\) | 3.64151 | 0.225404 | ||||||||
\(262\) | 10.2696 | + | 2.75173i | 0.634458 | + | 0.170002i | ||||
\(263\) | −0.152018 | − | 0.263302i | −0.00937381 | − | 0.0162359i | 0.861300 | − | 0.508096i | \(-0.169650\pi\) |
−0.870674 | + | 0.491860i | \(0.836317\pi\) | |||||||
\(264\) | −10.0232 | + | 17.3606i | −0.616884 | + | 1.06847i | ||||
\(265\) | 2.07186 | − | 2.07186i | 0.127273 | − | 0.127273i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.62560 | − | 13.5309i | −0.221883 | − | 0.828079i | ||||
\(268\) | 0.409633 | − | 0.409633i | 0.0250223 | − | 0.0250223i | ||||
\(269\) | −15.5352 | − | 8.96926i | −0.947199 | − | 0.546865i | −0.0549891 | − | 0.998487i | \(-0.517512\pi\) |
−0.892210 | + | 0.451622i | \(0.850846\pi\) | |||||||
\(270\) | 4.53654 | − | 2.61917i | 0.276085 | − | 0.159398i | ||||
\(271\) | −3.36065 | + | 12.5421i | −0.204145 | + | 0.761879i | 0.785563 | + | 0.618781i | \(0.212373\pi\) |
−0.989708 | + | 0.143098i | \(0.954293\pi\) | |||||||
\(272\) | 1.81188 | 0.109861 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.3323 | −1.10749 | ||||||||
\(275\) | −5.68594 | + | 21.2202i | −0.342875 | + | 1.27963i | ||||
\(276\) | −0.540248 | + | 0.311913i | −0.0325191 | + | 0.0187749i | ||||
\(277\) | 5.38051 | + | 3.10644i | 0.323283 | + | 0.186648i | 0.652855 | − | 0.757483i | \(-0.273571\pi\) |
−0.329572 | + | 0.944130i | \(0.606904\pi\) | |||||||
\(278\) | 16.9459 | − | 16.9459i | 1.01635 | − | 1.01635i | ||||
\(279\) | 0.990877 | + | 3.69801i | 0.0593223 | + | 0.221394i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.72841 | − | 1.72841i | 0.103108 | − | 0.103108i | −0.653671 | − | 0.756779i | \(-0.726772\pi\) |
0.756779 | + | 0.653671i | \(0.226772\pi\) | |||||||
\(282\) | −10.0695 | + | 17.4409i | −0.599631 | + | 1.03859i | ||||
\(283\) | −9.00809 | − | 15.6025i | −0.535475 | − | 0.927471i | −0.999140 | − | 0.0414599i | \(-0.986799\pi\) |
0.463665 | − | 0.886011i | \(-0.346534\pi\) | |||||||
\(284\) | 0.198103 | + | 0.0530817i | 0.0117553 | + | 0.00314982i | ||||
\(285\) | 3.25650 | 0.192898 | ||||||||
\(286\) | −12.2635 | + | 20.8621i | −0.725154 | + | 1.23360i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.0817212 | − | 0.304988i | 0.00481547 | − | 0.0179716i | ||||
\(289\) | 8.39053 | + | 14.5328i | 0.493561 | + | 0.854872i | ||||
\(290\) | −1.87140 | + | 3.24136i | −0.109892 | + | 0.190339i | ||||
\(291\) | −18.2588 | − | 18.2588i | −1.07035 | − | 1.07035i | ||||
\(292\) | −0.00186948 | − | 0.00697698i | −0.000109403 | − | 0.000408297i | ||||
\(293\) | 4.38187 | − | 1.17412i | 0.255992 | − | 0.0685927i | −0.128541 | − | 0.991704i | \(-0.541029\pi\) |
0.384532 | + | 0.923111i | \(0.374363\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.03986 | − | 3.53314i | 0.118765 | − | 0.205707i | ||||
\(296\) | −8.39282 | + | 4.84559i | −0.487823 | + | 0.281644i | ||||
\(297\) | −7.05236 | + | 26.3198i | −0.409219 | + | 1.52723i | ||||
\(298\) | − | 5.23816i | − | 0.303438i | ||||||
\(299\) | −21.8149 | + | 12.3681i | −1.26159 | + | 0.715267i | ||||
\(300\) | 0.408709i | 0.0235968i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.26279 | − | 9.11542i | −0.302839 | − | 0.524533i | ||||
\(303\) | −13.9821 | − | 8.07256i | −0.803249 | − | 0.463756i | ||||
\(304\) | −9.24613 | + | 9.24613i | −0.530302 | + | 0.530302i | ||||
\(305\) | 3.13215 | − | 0.839256i | 0.179346 | − | 0.0480557i | ||||
\(306\) | 0.567384 | − | 0.152030i | 0.0324352 | − | 0.00869098i | ||||
\(307\) | 11.5340 | + | 11.5340i | 0.658282 | + | 0.658282i | 0.954973 | − | 0.296691i | \(-0.0958832\pi\) |
−0.296691 | + | 0.954973i | \(0.595883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.37376 | + | 5.41194i | −0.533254 | + | 0.307875i | ||||
\(310\) | −3.80087 | − | 1.01844i | −0.215875 | − | 0.0578434i | ||||
\(311\) | −10.8487 | −0.615173 | −0.307587 | − | 0.951520i | \(-0.599521\pi\) | ||||
−0.307587 | + | 0.951520i | \(0.599521\pi\) | |||||||
\(312\) | −3.99344 | + | 14.4503i | −0.226084 | + | 0.818084i | ||||
\(313\) | 7.18694i | 0.406230i | 0.979155 | + | 0.203115i | \(0.0651065\pi\) | ||||
−0.979155 | + | 0.203115i | \(0.934893\pi\) | |||||||
\(314\) | 33.1322 | + | 8.87776i | 1.86976 | + | 0.501001i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0209048 | − | 0.0120694i | −0.00117599 | − | 0.000678958i | ||||
\(317\) | −6.69590 | − | 6.69590i | −0.376079 | − | 0.376079i | 0.493606 | − | 0.869685i | \(-0.335678\pi\) |
−0.869685 | + | 0.493606i | \(0.835678\pi\) | |||||||
\(318\) | −2.29702 | − | 8.57258i | −0.128810 | − | 0.480726i | ||||
\(319\) | −5.03891 | − | 18.8055i | −0.282125 | − | 1.05290i | ||||
\(320\) | 3.87540 | + | 3.87540i | 0.216641 | + | 0.216641i | ||||
\(321\) | 5.20734 | + | 3.00646i | 0.290646 | + | 0.167804i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.52617 | + | 0.408937i | 0.0849185 | + | 0.0227538i | ||||
\(324\) | 0.339417i | 0.0188565i | ||||||||
\(325\) | −0.128618 | + | 16.4291i | −0.00713442 | + | 0.911324i | ||||
\(326\) | 28.9040 | 1.60085 | ||||||||
\(327\) | −8.60675 | − | 2.30617i | −0.475955 | − | 0.127532i | ||||
\(328\) | −9.47156 | + | 5.46841i | −0.522979 | + | 0.301942i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.57687 | − | 4.57687i | −0.251948 | − | 0.251948i | ||||
\(331\) | −5.73166 | + | 1.53579i | −0.315040 | + | 0.0844148i | −0.412875 | − | 0.910788i | \(-0.635475\pi\) |
0.0978341 | + | 0.995203i | \(0.468809\pi\) | |||||||
\(332\) | 0.977557 | − | 0.261936i | 0.0536504 | − | 0.0143756i | ||||
\(333\) | −2.15276 | + | 2.15276i | −0.117970 | + | 0.117970i | ||||
\(334\) | −21.1230 | − | 12.1954i | −1.15580 | − | 0.667302i | ||||
\(335\) | 3.11436 | + | 5.39424i | 0.170156 | + | 0.294719i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0448i | 0.874014i | 0.899458 | + | 0.437007i | \(0.143961\pi\) | ||||
−0.899458 | + | 0.437007i | \(0.856039\pi\) | |||||||
\(338\) | −4.95721 | + | 17.4058i | −0.269637 | + | 0.946750i | ||||
\(339\) | 1.60767i | 0.0873168i | ||||||||
\(340\) | 0.00499233 | − | 0.0186316i | 0.000270747 | − | 0.00101044i | ||||
\(341\) | 17.7261 | − | 10.2342i | 0.959922 | − | 0.554211i | ||||
\(342\) | −2.11958 | + | 3.67122i | −0.114614 | + | 0.198517i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.9557 | + | 2.93557i | −0.590691 | + | 0.158275i | ||||
\(345\) | −1.73600 | − | 6.47883i | −0.0934629 | − | 0.348808i | ||||
\(346\) | 5.82823 | + | 5.82823i | 0.313328 | + | 0.313328i | ||||
\(347\) | −11.4687 | + | 19.8644i | −0.615673 | + | 1.06638i | 0.374593 | + | 0.927189i | \(0.377782\pi\) |
−0.990266 | + | 0.139187i | \(0.955551\pi\) | |||||||
\(348\) | −0.181100 | − | 0.313674i | −0.00970798 | − | 0.0168147i | ||||
\(349\) | −3.69715 | + | 13.7979i | −0.197904 | + | 0.738587i | 0.793592 | + | 0.608450i | \(0.208208\pi\) |
−0.991496 | + | 0.130137i | \(0.958458\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.159526 | + | 20.3773i | −0.00851489 | + | 1.08766i | ||||
\(352\) | −1.68810 | −0.0899759 | ||||||||
\(353\) | −4.49235 | − | 1.20372i | −0.239104 | − | 0.0640677i | 0.137277 | − | 0.990533i | \(-0.456165\pi\) |
−0.376381 | + | 0.926465i | \(0.622832\pi\) | |||||||
\(354\) | −6.17865 | − | 10.7017i | −0.328391 | − | 0.568790i | ||||
\(355\) | −1.10257 | + | 1.90972i | −0.0585186 | + | 0.101357i | ||||
\(356\) | 0.423420 | − | 0.423420i | 0.0224412 | − | 0.0224412i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.35844 | − | 5.06977i | −0.0717959 | − | 0.267946i | ||||
\(359\) | 12.8517 | − | 12.8517i | 0.678287 | − | 0.678287i | −0.281326 | − | 0.959612i | \(-0.590774\pi\) |
0.959612 | + | 0.281326i | \(0.0907741\pi\) | |||||||
\(360\) | 1.49245 | + | 0.861666i | 0.0786590 | + | 0.0454138i | ||||
\(361\) | 6.57949 | − | 3.79867i | 0.346289 | − | 0.199930i | ||||
\(362\) | −2.04983 | + | 7.65006i | −0.107736 | + | 0.402078i | ||||
\(363\) | 17.7349 | 0.930843 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0776629 | 0.00406506 | ||||||||
\(366\) | 2.54207 | − | 9.48714i | 0.132876 | − | 0.495901i | ||||
\(367\) | −12.6911 | + | 7.32723i | −0.662472 | + | 0.382478i | −0.793218 | − | 0.608937i | \(-0.791596\pi\) |
0.130746 | + | 0.991416i | \(0.458263\pi\) | |||||||
\(368\) | 23.3242 | + | 13.4663i | 1.21586 | + | 0.701977i | ||||
\(369\) | −2.42946 | + | 2.42946i | −0.126472 | + | 0.126472i | ||||
\(370\) | −0.809882 | − | 3.02252i | −0.0421038 | − | 0.157133i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.269262 | − | 0.269262i | 0.0139606 | − | 0.0139606i | ||||
\(373\) | 2.86259 | − | 4.95816i | 0.148220 | − | 0.256724i | −0.782350 | − | 0.622839i | \(-0.785979\pi\) |
0.930569 | + | 0.366115i | \(0.119312\pi\) | |||||||
\(374\) | −1.57023 | − | 2.71971i | −0.0811945 | − | 0.140633i | ||||
\(375\) | −8.90230 | − | 2.38536i | −0.459713 | − | 0.123180i | ||||
\(376\) | −28.6670 | −1.47839 | ||||||||
\(377\) | −7.18108 | − | 12.6660i | −0.369844 | − | 0.652330i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.283332 | + | 1.05741i | −0.0145538 | + | 0.0543156i | −0.972821 | − | 0.231559i | \(-0.925617\pi\) |
0.958267 | + | 0.285875i | \(0.0922840\pi\) | |||||||
\(380\) | 0.0696023 | + | 0.120555i | 0.00357052 | + | 0.00618433i | ||||
\(381\) | 14.4307 | − | 24.9946i | 0.739305 | − | 1.28051i | ||||
\(382\) | 9.02461 | + | 9.02461i | 0.461739 | + | 0.461739i | ||||
\(383\) | 0.131981 | + | 0.492561i | 0.00674393 | + | 0.0251687i | 0.969216 | − | 0.246213i | \(-0.0791862\pi\) |
−0.962472 | + | 0.271381i | \(0.912520\pi\) | |||||||
\(384\) | 15.0551 | − | 4.03401i | 0.768280 | − | 0.205860i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.6882 | + | 30.6369i | −0.900306 | + | 1.55938i | ||||
\(387\) | −3.08574 | + | 1.78155i | −0.156857 | + | 0.0905615i | ||||
\(388\) | 0.285685 | − | 1.06619i | 0.0145034 | − | 0.0541276i | ||||
\(389\) | − | 20.5695i | − | 1.04291i | −0.853277 | − | 0.521457i | \(-0.825389\pi\) | ||
0.853277 | − | 0.521457i | \(-0.174611\pi\) | |||||||
\(390\) | −4.17307 | − | 2.45308i | −0.211311 | − | 0.124216i | ||||
\(391\) | − | 3.25433i | − | 0.164578i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.53122 | − | 9.58036i | −0.279013 | − | 0.483265i | ||||
\(394\) | −1.73117 | − | 0.999492i | −0.0872151 | − | 0.0503537i | ||||
\(395\) | 0.183523 | − | 0.183523i | 0.00923405 | − | 0.00923405i | ||||
\(396\) | −0.260025 | + | 0.0696735i | −0.0130667 | + | 0.00350122i | ||||
\(397\) | 28.5505 | − | 7.65009i | 1.43291 | − | 0.383947i | 0.542864 | − | 0.839820i | \(-0.317340\pi\) |
0.890045 | + | 0.455874i | \(0.150673\pi\) | |||||||
\(398\) | −10.8440 | − | 10.8440i | −0.543559 | − | 0.543559i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.2812 | − | 8.82263i | 0.764062 | − | 0.441131i | ||||
\(401\) | 6.38727 | + | 1.71146i | 0.318965 | + | 0.0854664i | 0.414749 | − | 0.909936i | \(-0.363869\pi\) |
−0.0957844 | + | 0.995402i | \(0.530536\pi\) | |||||||
\(402\) | 18.8666 | 0.940978 | ||||||||
\(403\) | 10.9084 | − | 10.7390i | 0.543388 | − | 0.534946i | ||||
\(404\) | − | 0.690151i | − | 0.0343363i | ||||||
\(405\) | −3.52507 | − | 0.944538i | −0.175162 | − | 0.0469345i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.0961 | + | 8.13841i | 0.698719 | + | 0.403406i | ||||
\(408\) | −1.37571 | − | 1.37571i | −0.0681078 | − | 0.0681078i | ||||
\(409\) | 0.618563 | + | 2.30851i | 0.0305860 | + | 0.114148i | 0.979531 | − | 0.201293i | \(-0.0645142\pi\) |
−0.948945 | + | 0.315441i | \(0.897848\pi\) | |||||||
\(410\) | −0.913977 | − | 3.41101i | −0.0451381 | − | 0.168458i | ||||
\(411\) | 13.4879 | + | 13.4879i | 0.665308 | + | 0.665308i | ||||
\(412\) | −0.400697 | − | 0.231343i | −0.0197409 | − | 0.0113974i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.43384 | + | 2.25984i | 0.414501 | + | 0.111065i | ||||
\(415\) | 10.8815i | 0.534151i | ||||||||
\(416\) | −1.22197 | + | 0.317194i | −0.0599119 | + | 0.0155517i | ||||
\(417\) | −24.9357 | −1.22111 | ||||||||
\(418\) | 21.8919 | + | 5.86591i | 1.07077 | + | 0.286911i | ||||
\(419\) | 13.1791 | − | 7.60897i | 0.643842 | − | 0.371722i | −0.142251 | − | 0.989831i | \(-0.545434\pi\) |
0.786093 | + | 0.618108i | \(0.212101\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.0076 | − | 15.0076i | −0.731425 | − | 0.731425i | 0.239477 | − | 0.970902i | \(-0.423024\pi\) |
−0.970902 | + | 0.239477i | \(0.923024\pi\) | |||||||
\(422\) | −31.0587 | + | 8.32216i | −1.51192 | + | 0.405116i | ||||
\(423\) | −8.69881 | + | 2.33084i | −0.422951 | + | 0.113329i | ||||
\(424\) | 8.93299 | − | 8.93299i | 0.433824 | − | 0.433824i | ||||
\(425\) | −1.84647 | − | 1.06606i | −0.0895671 | − | 0.0517116i | ||||
\(426\) | 3.33965 | + | 5.78445i | 0.161807 | + | 0.280257i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.257033i | 0.0124241i | ||||||||
\(429\) | 24.3719 | − | 6.32637i | 1.17669 | − | 0.305440i | ||||
\(430\) | − | 3.66222i | − | 0.176608i | ||||||
\(431\) | −7.77536 | + | 29.0180i | −0.374526 | + | 1.39775i | 0.479511 | + | 0.877536i | \(0.340814\pi\) |
−0.854037 | + | 0.520213i | \(0.825853\pi\) | |||||||
\(432\) | 18.9536 | − | 10.9428i | 0.911903 | − | 0.526488i | ||||
\(433\) | −7.75396 | + | 13.4302i | −0.372631 | + | 0.645417i | −0.989969 | − | 0.141281i | \(-0.954878\pi\) |
0.617338 | + | 0.786698i | \(0.288211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.76168 | − | 1.00794i | 0.180359 | − | 0.0483270i | ||||
\(436\) | −0.0985813 | − | 0.367911i | −0.00472119 | − | 0.0176197i | ||||
\(437\) | 16.6071 | + | 16.6071i | 0.794424 | + | 0.794424i | ||||
\(438\) | 0.117619 | − | 0.203722i | 0.00562005 | − | 0.00973420i | ||||
\(439\) | −7.21696 | − | 12.5001i | −0.344447 | − | 0.596599i | 0.640806 | − | 0.767703i | \(-0.278600\pi\) |
−0.985253 | + | 0.171103i | \(0.945267\pi\) | |||||||
\(440\) | 2.38465 | − | 8.89962i | 0.113684 | − | 0.424273i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.64768 | − | 1.67368i | −0.0783721 | − | 0.0796088i | ||||
\(443\) | −12.4771 | −0.592805 | −0.296403 | − | 0.955063i | \(-0.595787\pi\) | ||||
−0.296403 | + | 0.955063i | \(0.595787\pi\) | |||||||
\(444\) | 0.292497 | + | 0.0783743i | 0.0138813 | + | 0.00371948i | ||||
\(445\) | 3.21919 | + | 5.57580i | 0.152604 | + | 0.264318i | ||||
\(446\) | 2.57824 | − | 4.46564i | 0.122083 | − | 0.211454i | ||||
\(447\) | −3.85394 | + | 3.85394i | −0.182285 | + | 0.182285i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.24956 | − | 27.0557i | −0.342128 | − | 1.27684i | −0.895932 | − | 0.444191i | \(-0.853491\pi\) |
0.553804 | − | 0.832647i | \(-0.313176\pi\) | |||||||
\(450\) | 4.04499 | − | 4.04499i | 0.190683 | − | 0.190683i | ||||
\(451\) | 15.9079 | + | 9.18445i | 0.749075 | + | 0.432479i | ||||
\(452\) | −0.0595156 | + | 0.0343614i | −0.00279938 | + | 0.00161622i | ||||
\(453\) | −2.83455 | + | 10.5787i | −0.133179 | + | 0.497030i | ||||
\(454\) | −33.5616 | −1.57512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.0407 | 0.657515 | ||||||||
\(457\) | −4.55910 | + | 17.0148i | −0.213266 | + | 0.795919i | 0.773504 | + | 0.633791i | \(0.218502\pi\) |
−0.986770 | + | 0.162128i | \(0.948164\pi\) | |||||||
\(458\) | 22.4789 | − | 12.9782i | 1.05037 | − | 0.606431i | ||||
\(459\) | −2.29021 | − | 1.32225i | −0.106898 | − | 0.0617175i | ||||
\(460\) | 0.202740 | − | 0.202740i | 0.00945282 | − | 0.00945282i | ||||
\(461\) | 1.39627 | + | 5.21097i | 0.0650310 | + | 0.242699i | 0.990788 | − | 0.135419i | \(-0.0432381\pi\) |
−0.925757 | + | 0.378118i | \(0.876571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.4789 | + | 19.4789i | −0.905259 | + | 0.905259i | −0.995885 | − | 0.0906259i | \(-0.971113\pi\) |
0.0906259 | + | 0.995885i | \(0.471113\pi\) | |||||||
\(464\) | −7.81866 | + | 13.5423i | −0.362972 | + | 0.628686i | ||||
\(465\) | 2.04715 | + | 3.54577i | 0.0949345 | + | 0.164431i | ||||
\(466\) | −6.08165 | − | 1.62957i | −0.281727 | − | 0.0754885i | ||||
\(467\) | −9.59610 | −0.444055 | −0.222027 | − | 0.975040i | \(-0.571267\pi\) | ||||
−0.222027 | + | 0.975040i | \(0.571267\pi\) | |||||||
\(468\) | −0.175133 | + | 0.0992935i | −0.00809554 | + | 0.00458984i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.39567 | − | 8.94077i | 0.110504 | − | 0.412407i | ||||
\(471\) | −17.8451 | − | 30.9086i | −0.822259 | − | 1.42419i | ||||
\(472\) | 8.79503 | − | 15.2334i | 0.404824 | − | 0.701176i | ||||
\(473\) | 13.4702 | + | 13.4702i | 0.619359 | + | 0.619359i | ||||
\(474\) | −0.203468 | − | 0.759352i | −0.00934558 | − | 0.0348782i | ||||
\(475\) | 14.8629 | − | 3.98250i | 0.681956 | − | 0.182729i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.98434 | − | 3.43697i | 0.0908565 | − | 0.157368i | ||||
\(478\) | 19.0295 | − | 10.9867i | 0.870387 | − | 0.502518i | ||||
\(479\) | 8.01018 | − | 29.8944i | 0.365994 | − | 1.36591i | −0.500073 | − | 0.865983i | \(-0.666694\pi\) |
0.866068 | − | 0.499927i | \(-0.166640\pi\) | |||||||
\(480\) | − | 0.337672i | − | 0.0154126i | ||||||
\(481\) | 11.7330 | + | 3.24251i | 0.534979 | + | 0.147846i | ||||
\(482\) | 10.5363i | 0.479916i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.379055 | + | 0.656543i | 0.0172298 | + | 0.0298429i | ||||
\(485\) | 10.2781 | + | 5.93404i | 0.466703 | + | 0.269451i | ||||
\(486\) | 8.87461 | − | 8.87461i | 0.402561 | − | 0.402561i | ||||
\(487\) | −5.40538 | + | 1.44837i | −0.244941 | + | 0.0656318i | −0.379201 | − | 0.925314i | \(-0.623801\pi\) |
0.134260 | + | 0.990946i | \(0.457134\pi\) | |||||||
\(488\) | 13.5045 | − | 3.61853i | 0.611322 | − | 0.163803i | ||||
\(489\) | −21.2660 | − | 21.2660i | −0.961680 | − | 0.961680i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0113 | − | 6.93474i | 0.542063 | − | 0.312960i | −0.203851 | − | 0.979002i | \(-0.565346\pi\) |
0.745915 | + | 0.666041i | \(0.232013\pi\) | |||||||
\(492\) | 0.330092 | + | 0.0884479i | 0.0148817 | + | 0.00398754i | ||||
\(493\) | 1.88950 | 0.0850988 | ||||||||
\(494\) | 16.9491 | + | 0.132689i | 0.762577 | + | 0.00596994i | ||||
\(495\) | − | 2.89442i | − | 0.130094i | ||||||
\(496\) | −15.8799 | − | 4.25501i | −0.713030 | − | 0.191056i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 28.5438 | + | 16.4798i | 1.27908 | + | 0.738477i | ||||
\(499\) | −6.46517 | − | 6.46517i | −0.289421 | − | 0.289421i | 0.547430 | − | 0.836851i | \(-0.315606\pi\) |
−0.836851 | + | 0.547430i | \(0.815606\pi\) | |||||||
\(500\) | −0.101966 | − | 0.380544i | −0.00456008 | − | 0.0170184i | ||||
\(501\) | 6.56846 | + | 24.5138i | 0.293457 | + | 1.09520i | ||||
\(502\) | −20.9017 | − | 20.9017i | −0.932888 | − | 0.932888i | ||||
\(503\) | −27.9587 | − | 16.1420i | −1.24662 | − | 0.719736i | −0.276185 | − | 0.961104i | \(-0.589070\pi\) |
−0.970434 | + | 0.241369i | \(0.922404\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.16766 | + | 1.92057i | 0.318957 | + | 0.0854642i | ||||
\(506\) | − | 46.6810i | − | 2.07523i | ||||||
\(507\) | 16.4534 | − | 9.15897i | 0.730723 | − | 0.406764i | ||||
\(508\) | 1.23373 | 0.0547378 | ||||||||
\(509\) | 11.6648 | + | 3.12559i | 0.517035 | + | 0.138539i | 0.507895 | − | 0.861419i | \(-0.330424\pi\) |
0.00914032 | + | 0.999958i | \(0.497091\pi\) | |||||||
\(510\) | 0.544027 | − | 0.314094i | 0.0240899 | − | 0.0139083i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.6785 | + | 16.6785i | 0.737091 | + | 0.737091i | ||||
\(513\) | 18.4347 | − | 4.93955i | 0.813910 | − | 0.218087i | ||||
\(514\) | −33.9419 | + | 9.09471i | −1.49711 | + | 0.401150i | ||||
\(515\) | 3.51771 | − | 3.51771i | 0.155009 | − | 0.155009i | ||||
\(516\) | 0.306921 | + | 0.177201i | 0.0135114 | + | 0.00780084i | ||||
\(517\) | 24.0738 | + | 41.6971i | 1.05877 | + | 1.83384i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.57618i | − | 0.376452i | ||||||
\(520\) | 0.0539414 | − | 6.89027i | 0.00236549 | − | 0.302158i | ||||
\(521\) | 11.7697i | 0.515641i | 0.966193 | + | 0.257821i | \(0.0830043\pi\) | ||||
−0.966193 | + | 0.257821i | \(0.916996\pi\) | |||||||
\(522\) | −1.31209 | + | 4.89678i | −0.0574286 | + | 0.214326i | ||||
\(523\) | −13.2762 | + | 7.66503i | −0.580529 | + | 0.335168i | −0.761344 | − | 0.648349i | \(-0.775460\pi\) |
0.180815 | + | 0.983517i | \(0.442127\pi\) | |||||||
\(524\) | 0.236442 | − | 0.409529i | 0.0103290 | − | 0.0178904i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.408840 | − | 0.109548i | 0.0178263 | − | 0.00477654i | ||||
\(527\) | 0.514145 | + | 1.91881i | 0.0223965 | + | 0.0835849i | ||||
\(528\) | −19.1220 | − | 19.1220i | −0.832180 | − | 0.832180i | ||||
\(529\) | 12.6869 | − | 21.9743i | 0.551603 | − | 0.955404i | ||||
\(530\) | 2.03953 | + | 3.53257i | 0.0885916 | + | 0.153445i | ||||
\(531\) | 1.43020 | − | 5.33758i | 0.0620654 | − | 0.231631i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.2411 | + | 3.65927i | 0.573535 | + | 0.158501i | ||||
\(534\) | 19.5016 | 0.843916 | ||||||||
\(535\) | −2.66945 | − | 0.715277i | −0.115410 | − | 0.0309241i | ||||
\(536\) | 13.4279 | + | 23.2577i | 0.579995 | + | 1.00458i | ||||
\(537\) | −2.73059 | + | 4.72952i | −0.117834 | + | 0.204094i | ||||
\(538\) | 17.6586 | − | 17.6586i | 0.761318 | − | 0.761318i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.0603024 | − | 0.225052i | −0.00259500 | − | 0.00968469i | ||||
\(541\) | −10.6257 | + | 10.6257i | −0.456836 | + | 0.456836i | −0.897616 | − | 0.440779i | \(-0.854702\pi\) |
0.440779 | + | 0.897616i | \(0.354702\pi\) | |||||||
\(542\) | −15.6547 | − | 9.03822i | −0.672425 | − | 0.388225i | ||||
\(543\) | 7.13663 | − | 4.12034i | 0.306262 | − | 0.176821i | ||||
\(544\) | 0.0424034 | − | 0.158252i | 0.00181803 | − | 0.00678498i | ||||
\(545\) | 4.09532 | 0.175424 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0277 | 0.856322 | 0.428161 | − | 0.903702i | \(-0.359162\pi\) | ||||
0.428161 | + | 0.903702i | \(0.359162\pi\) | |||||||
\(548\) | −0.211036 | + | 0.787599i | −0.00901503 | + | 0.0336446i | ||||
\(549\) | 3.80364 | − | 2.19603i | 0.162336 | − | 0.0937245i | ||||
\(550\) | −26.4864 | − | 15.2919i | −1.12938 | − | 0.652049i | ||||
\(551\) | −9.64225 | + | 9.64225i | −0.410774 | + | 0.410774i | ||||
\(552\) | −7.48490 | − | 27.9340i | −0.318579 | − | 1.18895i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.11594 | + | 6.11594i | −0.259841 | + | 0.259841i | ||||
\(555\) | −1.62794 | + | 2.81967i | −0.0691020 | + | 0.119688i | ||||
\(556\) | −0.532959 | − | 0.923113i | −0.0226025 | − | 0.0391487i | ||||
\(557\) | −2.40703 | − | 0.644961i | −0.101989 | − | 0.0273279i | 0.207464 | − | 0.978243i | \(-0.433479\pi\) |
−0.309453 | + | 0.950915i | \(0.600146\pi\) | |||||||
\(558\) | −5.32978 | −0.225628 | ||||||||
\(559\) | 12.2817 | + | 7.21964i | 0.519462 | + | 0.305358i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.845727 | + | 3.15630i | −0.0357066 | + | 0.133259i | ||||
\(562\) | 1.70144 | + | 2.94698i | 0.0717710 | + | 0.124311i | ||||
\(563\) | −9.85804 | + | 17.0746i | −0.415467 | + | 0.719609i | −0.995477 | − | 0.0949995i | \(-0.969715\pi\) |
0.580011 | + | 0.814609i | \(0.303048\pi\) | |||||||
\(564\) | 0.633386 | + | 0.633386i | 0.0266703 | + | 0.0266703i | ||||
\(565\) | −0.191243 | − | 0.713730i | −0.00804567 | − | 0.0300268i | ||||
\(566\) | 24.2266 | − | 6.49150i | 1.01832 | − | 0.272858i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.75385 | + | 8.23391i | −0.199467 | + | 0.345487i | ||||
\(569\) | 38.6991 | − | 22.3429i | 1.62235 | − | 0.936664i | 0.636059 | − | 0.771640i | \(-0.280563\pi\) |
0.986290 | − | 0.165023i | \(-0.0527700\pi\) | |||||||
\(570\) | −1.17336 | + | 4.37906i | −0.0491468 | + | 0.183418i | ||||
\(571\) | 27.5399i | 1.15251i | 0.817270 | + | 0.576255i | \(0.195486\pi\) | ||||
−0.817270 | + | 0.576255i | \(0.804514\pi\) | |||||||
\(572\) | 0.755110 | + | 0.767027i | 0.0315727 | + | 0.0320710i | ||||
\(573\) | − | 13.2796i | − | 0.554763i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.8464 | − | 27.4468i | −0.660841 | − | 1.14461i | ||||
\(576\) | 6.42884 | + | 3.71169i | 0.267868 | + | 0.154654i | ||||
\(577\) | −13.0084 | + | 13.0084i | −0.541546 | + | 0.541546i | −0.923982 | − | 0.382436i | \(-0.875085\pi\) |
0.382436 | + | 0.923982i | \(0.375085\pi\) | |||||||
\(578\) | −22.5657 | + | 6.04647i | −0.938610 | + | 0.251500i | ||||
\(579\) | 35.5549 | − | 9.52691i | 1.47761 | − | 0.395925i | ||||
\(580\) | 0.117713 | + | 0.117713i | 0.00488778 | + | 0.00488778i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 31.1318 | − | 17.9740i | 1.29046 | − | 0.745045i | ||||
\(583\) | −20.4950 | − | 5.49162i | −0.848816 | − | 0.227440i | ||||
\(584\) | 0.334851 | 0.0138562 | ||||||||
\(585\) | −0.543861 | − | 2.09519i | −0.0224859 | − | 0.0866254i | ||||
\(586\) | 6.31541i | 0.260887i | ||||||||
\(587\) | −20.1767 | − | 5.40633i | −0.832781 | − | 0.223143i | −0.182855 | − | 0.983140i | \(-0.558534\pi\) |
−0.649927 | + | 0.759997i | \(0.725200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4156 | − | 7.16813i | −0.511574 | − | 0.295358i | ||||
\(590\) | 4.01607 | + | 4.01607i | 0.165339 | + | 0.165339i | ||||
\(591\) | 0.538328 | + | 2.00907i | 0.0221439 | + | 0.0826420i | ||||
\(592\) | −3.38367 | − | 12.6280i | −0.139068 | − | 0.519008i | ||||
\(593\) | −6.26353 | − | 6.26353i | −0.257212 | − | 0.257212i | 0.566707 | − | 0.823919i | \(-0.308217\pi\) |
−0.823919 | + | 0.566707i | \(0.808217\pi\) | |||||||
\(594\) | −32.8514 | − | 18.9668i | −1.34791 | − | 0.778217i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.225044 | − | 0.0603003i | −0.00921815 | − | 0.00247000i | ||||
\(597\) | 15.9568i | 0.653067i | ||||||||
\(598\) | −8.77137 | − | 33.7911i | −0.358688 | − | 1.38182i | ||||
\(599\) | −36.2754 | −1.48217 | −0.741087 | − | 0.671409i | \(-0.765689\pi\) | ||||
−0.741087 | + | 0.671409i | \(0.765689\pi\) | |||||||
\(600\) | −18.3014 | − | 4.90385i | −0.747153 | − | 0.200199i | ||||
\(601\) | 30.7163 | − | 17.7340i | 1.25294 | − | 0.723387i | 0.281250 | − | 0.959635i | \(-0.409251\pi\) |
0.971693 | + | 0.236248i | \(0.0759177\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.96562 | + | 5.96562i | 0.242939 | + | 0.242939i | ||||
\(604\) | −0.452204 | + | 0.121168i | −0.0183999 | + | 0.00493024i | ||||
\(605\) | −7.87347 | + | 2.10969i | −0.320102 | + | 0.0857711i | ||||
\(606\) | 15.8932 | − | 15.8932i | 0.645618 | − | 0.645618i | ||||
\(607\) | 22.2647 | + | 12.8545i | 0.903697 | + | 0.521749i | 0.878398 | − | 0.477930i | \(-0.158613\pi\) |
0.0252989 | + | 0.999680i | \(0.491946\pi\) | |||||||
\(608\) | 0.591182 | + | 1.02396i | 0.0239756 | + | 0.0415269i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.51424i | 0.182776i | ||||||||
\(611\) | 25.2613 | + | 25.6599i | 1.02196 | + | 1.03809i | ||||
\(612\) | − | 0.0261263i | − | 0.00105609i | ||||||
\(613\) | −11.8082 | + | 44.0688i | −0.476928 | + | 1.77992i | 0.137013 | + | 0.990569i | \(0.456250\pi\) |
−0.613941 | + | 0.789352i | \(0.710417\pi\) | |||||||
\(614\) | −19.6659 | + | 11.3541i | −0.793649 | + | 0.458214i | ||||
\(615\) | −1.83718 | + | 3.18208i | −0.0740821 | + | 0.128314i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.5733 | − | 9.53183i | 1.43213 | − | 0.383737i | 0.542357 | − | 0.840148i | \(-0.317532\pi\) |
0.889769 | + | 0.456411i | \(0.150865\pi\) | |||||||
\(618\) | −3.90000 | − | 14.5550i | −0.156881 | − | 0.585489i | ||||
\(619\) | −3.75724 | − | 3.75724i | −0.151016 | − | 0.151016i | 0.627556 | − | 0.778572i | \(-0.284056\pi\) |
−0.778572 | + | 0.627556i | \(0.784056\pi\) | |||||||
\(620\) | −0.0875091 | + | 0.151570i | −0.00351445 | + | 0.00608721i | ||||
\(621\) | −19.6545 | − | 34.0427i | −0.788710 | − | 1.36609i | ||||
\(622\) | 3.90895 | − | 14.5884i | 0.156734 | − | 0.584941i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −17.4350 | − | 10.2489i | −0.697957 | − | 0.410284i | ||||
\(625\) | −18.5478 | −0.741914 | ||||||||
\(626\) | −9.66437 | − | 2.58956i | −0.386266 | − | 0.103500i | ||||
\(627\) | −11.7910 | − | 20.4226i | −0.470887 | − | 0.815601i | ||||
\(628\) | 0.762819 | − | 1.32124i | 0.0304398 | − | 0.0527233i | ||||
\(629\) | −1.11702 | + | 1.11702i | −0.0445385 | + | 0.0445385i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.50380 | − | 13.0763i | −0.139484 | − | 0.520561i | −0.999939 | − | 0.0110350i | \(-0.996487\pi\) |
0.860455 | − | 0.509526i | \(-0.170179\pi\) | |||||||
\(632\) | 0.791277 | − | 0.791277i | 0.0314753 | − | 0.0314753i | ||||
\(633\) | 28.9743 | + | 16.7283i | 1.15162 | + | 0.664890i | ||||
\(634\) | 11.4167 | − | 6.59143i | 0.453415 | − | 0.261779i | ||||
\(635\) | −3.43325 | + | 12.8131i | −0.136244 | + | 0.508471i | ||||
\(636\) | −0.394741 | −0.0156525 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 27.1035 | 1.07304 | ||||||||
\(639\) | −0.773046 | + | 2.88505i | −0.0305812 | + | 0.114131i | ||||
\(640\) | −6.20389 | + | 3.58182i | −0.245230 | + | 0.141584i | ||||
\(641\) | −18.5489 | − | 10.7092i | −0.732638 | − | 0.422989i | 0.0867484 | − | 0.996230i | \(-0.472352\pi\) |
−0.819386 | + | 0.573241i | \(0.805686\pi\) | |||||||
\(642\) | −5.91911 | + | 5.91911i | −0.233609 | + | 0.233609i | ||||
\(643\) | −3.68080 | − | 13.7369i | −0.145157 | − | 0.541732i | −0.999748 | − | 0.0224315i | \(-0.992859\pi\) |
0.854592 | − | 0.519300i | \(-0.173807\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.69445 | + | 2.69445i | −0.106094 | + | 0.106094i | ||||
\(646\) | −1.09980 | + | 1.90492i | −0.0432712 | + | 0.0749480i | ||||
\(647\) | 10.2738 | + | 17.7948i | 0.403906 | + | 0.699585i | 0.994193 | − | 0.107608i | \(-0.0343191\pi\) |
−0.590288 | + | 0.807193i | \(0.700986\pi\) | |||||||
\(648\) | −15.1986 | − | 4.07246i | −0.597059 | − | 0.159981i | ||||
\(649\) | −29.5434 | −1.15968 | ||||||||
\(650\) | −22.0461 | − | 6.09261i | −0.864720 | − | 0.238972i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.332736 | − | 1.24179i | 0.0130309 | − | 0.0486321i | ||||
\(653\) | 21.8478 | + | 37.8415i | 0.854972 | + | 1.48085i | 0.876671 | + | 0.481090i | \(0.159759\pi\) |
−0.0216997 | + | 0.999765i | \(0.506908\pi\) | |||||||
\(654\) | 6.20228 | − | 10.7427i | 0.242528 | − | 0.420072i | ||||
\(655\) | 3.59525 | + | 3.59525i | 0.140478 | + | 0.140478i | ||||
\(656\) | −3.81857 | − | 14.2511i | −0.149090 | − | 0.556413i | ||||
\(657\) | 0.101608 | − | 0.0272258i | 0.00396411 | − | 0.00106218i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.26381 | + | 10.8492i | −0.244003 | + | 0.422626i | −0.961851 | − | 0.273574i | \(-0.911794\pi\) |
0.717848 | + | 0.696200i | \(0.245127\pi\) | |||||||
\(660\) | −0.249321 | + | 0.143945i | −0.00970480 | + | 0.00560307i | ||||
\(661\) | −5.95454 | + | 22.2227i | −0.231605 | + | 0.864361i | 0.748045 | + | 0.663648i | \(0.230993\pi\) |
−0.979650 | + | 0.200713i | \(0.935674\pi\) | |||||||
\(662\) | − | 8.26081i | − | 0.321065i | ||||||
\(663\) | −0.0191306 | + | 2.44367i | −0.000742971 | + | 0.0949043i | ||||
\(664\) | 46.9165i | 1.82071i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.11917 | − | 3.67051i | −0.0821163 | − | 0.142230i | ||||
\(667\) | 24.3235 | + | 14.0432i | 0.941809 | + | 0.543754i | ||||
\(668\) | −0.767106 | + | 0.767106i | −0.0296802 | + | 0.0296802i | ||||
\(669\) | −5.18249 | + | 1.38864i | −0.200367 | + | 0.0536881i | ||||
\(670\) | −8.37585 | + | 2.24430i | −0.323587 | + | 0.0867050i | ||||
\(671\) | −16.6040 | − | 16.6040i | −0.640991 | − | 0.640991i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0684 | + | 6.96769i | −0.465202 | + | 0.268585i | −0.714229 | − | 0.699912i | \(-0.753223\pi\) |
0.249027 | + | 0.968497i | \(0.419889\pi\) | |||||||
\(674\) | −21.5756 | − | 5.78116i | −0.831061 | − | 0.222682i | ||||
\(675\) | −25.7540 | −0.991271 | ||||||||
\(676\) | 0.690728 | + | 0.413344i | 0.0265665 | + | 0.0158979i | ||||
\(677\) | − | 51.7651i | − | 1.98949i | −0.102360 | − | 0.994747i | \(-0.532639\pi\) | ||
0.102360 | − | 0.994747i | \(-0.467361\pi\) | |||||||
\(678\) | −2.16186 | − | 0.579268i | −0.0830257 | − | 0.0222467i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.774399 | + | 0.447100i | 0.0296969 | + | 0.0171455i | ||||
\(681\) | 24.6927 | + | 24.6927i | 0.946227 | + | 0.946227i | ||||
\(682\) | 7.37505 | + | 27.5240i | 0.282405 | + | 1.05395i | ||||
\(683\) | −7.38605 | − | 27.5651i | −0.282620 | − | 1.05475i | −0.950561 | − | 0.310537i | \(-0.899491\pi\) |
0.667942 | − | 0.744213i | \(-0.267175\pi\) | |||||||
\(684\) | 0.133324 | + | 0.133324i | 0.00509779 | + | 0.00509779i | ||||
\(685\) | −7.59245 | − | 4.38350i | −0.290092 | − | 0.167485i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.0873 | − | 6.99008i | −0.995294 | − | 0.266688i | ||||
\(688\) | − | 15.3007i | − | 0.583332i | ||||||
\(689\) | −15.8677 | − | 0.124222i | −0.604509 | − | 0.00473248i | ||||
\(690\) | 9.33767 | 0.355479 | ||||||||
\(691\) | 18.0966 | + | 4.84897i | 0.688427 | + | 0.184463i | 0.586041 | − | 0.810281i | \(-0.300686\pi\) |
0.102386 | + | 0.994745i | \(0.467352\pi\) | |||||||
\(692\) | 0.317488 | − | 0.183302i | 0.0120691 | − | 0.00696809i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.5796 | − | 22.5796i | −0.857108 | − | 0.857108i | ||||
\(695\) | 11.0703 | − | 2.96627i | 0.419919 | − | 0.112517i | ||||
\(696\) | 16.2188 | − | 4.34582i | 0.614773 | − | 0.164728i | ||||
\(697\) | −1.26059 | + | 1.26059i | −0.0477483 | + | 0.0477483i | ||||
\(698\) | −17.2221 | − | 9.94320i | −0.651867 | − | 0.376356i | ||||
\(699\) | 3.27559 | + | 5.67348i | 0.123894 | + | 0.214591i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20.1282i | − | 0.760231i | −0.924939 | − | 0.380115i | \(-0.875884\pi\) | ||
0.924939 | − | 0.380115i | \(-0.124116\pi\) | |||||||
\(702\) | −27.3441 | − | 7.55676i | −1.03204 | − | 0.285211i | ||||
\(703\) | − | 11.4005i | − | 0.429977i | ||||||
\(704\) | 10.2720 | − | 38.3358i | 0.387142 | − | 1.44484i | ||||
\(705\) | −8.34072 | + | 4.81552i | −0.314130 | + | 0.181363i | ||||
\(706\) | 3.23732 | − | 5.60721i | 0.121838 | − | 0.211030i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.530899 | + | 0.142254i | −0.0199524 | + | 0.00534623i | ||||
\(709\) | −1.11532 | − | 4.16243i | −0.0418867 | − | 0.156323i | 0.941815 | − | 0.336132i | \(-0.109119\pi\) |
−0.983702 | + | 0.179809i | \(0.942452\pi\) | |||||||
\(710\) | −2.17075 | − | 2.17075i | −0.0814666 | − | 0.0814666i | ||||
\(711\) | 0.175771 | − | 0.304444i | 0.00659192 | − | 0.0114175i | ||||
\(712\) | 13.8798 | + | 24.0406i | 0.520168 | + | 0.900958i | ||||
\(713\) | −7.64247 | + | 28.5221i | −0.286213 | + | 1.06816i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0674 | + | 5.70781i | −0.376500 | + | 0.213460i | ||||
\(716\) | −0.233448 | −0.00872435 | ||||||||
\(717\) | −22.0842 | − | 5.91744i | −0.824749 | − | 0.220991i | ||||
\(718\) | 12.6512 | + | 21.9125i | 0.472138 | + | 0.817767i | ||||
\(719\) | −15.9230 | + | 27.5794i | −0.593827 | + | 1.02854i | 0.399884 | + | 0.916566i | \(0.369050\pi\) |
−0.993711 | + | 0.111973i | \(0.964283\pi\) | |||||||
\(720\) | −1.64387 | + | 1.64387i | −0.0612635 | + | 0.0612635i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.73743 | + | 10.2162i | 0.101877 | + | 0.380209i | ||||
\(723\) | 7.75203 | − | 7.75203i | 0.288301 | − | 0.288301i | ||||
\(724\) | 0.305068 | + | 0.176131i | 0.0113377 | + | 0.00654585i | ||||
\(725\) | 15.9359 | − | 9.20060i | 0.591845 | − | 0.341702i | ||||
\(726\) | −6.39016 | + | 23.8484i | −0.237161 | + | 0.885098i | ||||
\(727\) | −49.3169 | −1.82906 | −0.914531 | − | 0.404516i | \(-0.867440\pi\) | ||||
−0.914531 | + | 0.404516i | \(0.867440\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.5035 | −1.09272 | ||||||||
\(730\) | −0.0279831 | + | 0.104434i | −0.00103570 | + | 0.00386529i | ||||
\(731\) | −1.60112 | + | 0.924410i | −0.0592197 | + | 0.0341905i | ||||
\(732\) | −0.378327 | − | 0.218427i | −0.0139834 | − | 0.00807329i | ||||
\(733\) | 11.5196 | − | 11.5196i | 0.425487 | − | 0.425487i | −0.461601 | − | 0.887088i | \(-0.652725\pi\) |
0.887088 | + | 0.461601i | \(0.152725\pi\) | |||||||
\(734\) | −5.28022 | − | 19.7061i | −0.194896 | − | 0.727364i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.72202 | − | 1.72202i | 0.0634744 | − | 0.0634744i | ||||
\(737\) | 22.5527 | − | 39.0625i | 0.830741 | − | 1.43888i | ||||
\(738\) | −2.39155 | − | 4.14229i | −0.0880343 | − | 0.152480i | ||||
\(739\) | −24.3845 | − | 6.53382i | −0.897000 | − | 0.240350i | −0.219273 | − | 0.975664i | \(-0.570368\pi\) |
−0.677727 | + | 0.735313i | \(0.737035\pi\) | |||||||
\(740\) | −0.139178 | −0.00511628 | ||||||||
\(741\) | −12.3726 | − | 12.5678i | −0.454519 | − | 0.461691i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.17652 | − | 8.12290i | 0.0798489 | − | 0.298000i | −0.914440 | − | 0.404721i | \(-0.867369\pi\) |
0.994289 | + | 0.106721i | \(0.0340352\pi\) | |||||||
\(744\) | 8.82649 | + | 15.2879i | 0.323595 | + | 0.560483i | ||||
\(745\) | 1.25252 | − | 2.16942i | 0.0458886 | − | 0.0794814i | ||||
\(746\) | 5.63587 | + | 5.63587i | 0.206344 | + | 0.206344i | ||||
\(747\) | 3.81465 | + | 14.2365i | 0.139571 | + | 0.520886i | ||||
\(748\) | −0.134921 | + | 0.0361521i | −0.00493321 | + | 0.00132185i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.41526 | − | 11.1116i | 0.234252 | − | 0.405737i | ||||
\(751\) | −29.6007 | + | 17.0900i | −1.08015 | + | 0.623623i | −0.930936 | − | 0.365183i | \(-0.881007\pi\) |
−0.149211 | + | 0.988805i | \(0.547673\pi\) | |||||||
\(752\) | 10.0091 | − | 37.3543i | 0.364993 | − | 1.36217i | ||||
\(753\) | 30.7566i | 1.12083i | ||||||||
\(754\) | 19.6195 | − | 5.09276i | 0.714501 | − | 0.185467i | ||||
\(755\) | − | 5.03362i | − | 0.183192i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.77459 | − | 11.7339i | −0.246227 | − | 0.426477i | 0.716249 | − | 0.697845i | \(-0.245857\pi\) |
−0.962476 | + | 0.271368i | \(0.912524\pi\) | |||||||
\(758\) | −1.31983 | − | 0.762002i | −0.0479382 | − | 0.0276771i | ||||
\(759\) | −34.3453 | + | 34.3453i | −1.24666 | + | 1.24666i | ||||
\(760\) | −6.23340 | + | 1.67023i | −0.226109 | + | 0.0605857i | ||||
\(761\) | 19.3069 | − | 5.17326i | 0.699873 | − | 0.187531i | 0.108700 | − | 0.994075i | \(-0.465331\pi\) |
0.591174 | + | 0.806544i | \(0.298665\pi\) | |||||||
\(762\) | 28.4110 | + | 28.4110i | 1.02922 | + | 1.02922i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.491608 | − | 0.283830i | 0.0177857 | − | 0.0102686i | ||||
\(765\) | 0.271339 | + | 0.0727049i | 0.00981027 | + | 0.00262865i | ||||
\(766\) | −0.709908 | −0.0256500 | ||||||||
\(767\) | −21.3856 | + | 5.55120i | −0.772190 | + | 0.200442i | ||||
\(768\) | − | 2.15054i | − | 0.0776011i | ||||||
\(769\) | 30.3963 | + | 8.14467i | 1.09612 | + | 0.293704i | 0.761184 | − | 0.648536i | \(-0.224619\pi\) |
0.334936 | + | 0.942241i | \(0.391285\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.6639 | + | 18.2812i | 1.14035 | + | 0.658381i | ||||
\(772\) | 1.11261 | + | 1.11261i | 0.0400438 | + | 0.0400438i | ||||
\(773\) | −9.91105 | − | 36.9885i | −0.356476 | − | 1.33039i | −0.878617 | − | 0.477527i | \(-0.841533\pi\) |
0.522142 | − | 0.852859i | \(-0.325133\pi\) | |||||||
\(774\) | −1.28384 | − | 4.79136i | −0.0461467 | − | 0.172222i | ||||
\(775\) | 13.6796 | + | 13.6796i | 0.491386 | + | 0.491386i | ||||
\(776\) | 44.3148 | + | 25.5852i | 1.59081 | + | 0.918453i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.6601 | + | 7.41149i | 0.991661 | + | 0.265715i | ||||
\(779\) | − | 12.8658i | − | 0.460965i | ||||||
\(780\) | −0.153429 | + | 0.151046i | −0.00549365 | + | 0.00540830i | ||||
\(781\) | 15.9686 | 0.571403 | ||||||||
\(782\) | 4.37614 | + | 1.17258i | 0.156490 | + | 0.0419315i | ||||
\(783\) | 19.7656 | − | 11.4116i | 0.706363 | − | 0.407819i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.5992 | + | 11.5992i | 0.413992 | + | 0.413992i | ||||
\(786\) | 14.8758 | − | 3.98596i | 0.530603 | − | 0.142175i | ||||
\(787\) | 21.4436 | − | 5.74579i | 0.764381 | − | 0.204815i | 0.144494 | − | 0.989506i | \(-0.453845\pi\) |
0.619888 | + | 0.784690i | \(0.287178\pi\) | |||||||
\(788\) | −0.0628693 | + | 0.0628693i | −0.00223963 | + | 0.00223963i | ||||
\(789\) | −0.381401 | − | 0.220202i | −0.0135782 | − | 0.00783940i | ||||
\(790\) | 0.180660 | + | 0.312912i | 0.00642759 | + | 0.0111329i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 12.4795i | − | 0.443441i | ||||||
\(793\) | −15.1391 | − | 8.89930i | −0.537605 | − | 0.316023i | ||||
\(794\) | 41.1487i | 1.46031i | ||||||||
\(795\) | 1.09850 | − | 4.09964i | 0.0389596 | − | 0.145399i | ||||
\(796\) | −0.590716 | + | 0.341050i | −0.0209374 | + | 0.0120882i | ||||
\(797\) | 15.2784 | − | 26.4630i | 0.541189 | − | 0.937367i | −0.457647 | − | 0.889134i | \(-0.651308\pi\) |
0.998836 | − | 0.0482334i | \(-0.0153591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.51362 | + | 1.20942i | −0.159681 | + | 0.0427863i | ||||
\(800\) | −0.412952 | − | 1.54116i | −0.0146001 | − | 0.0544882i | ||||
\(801\) | 6.16641 | + | 6.16641i | 0.217879 | + | 0.217879i | ||||
\(802\) | −4.60285 | + | 7.97238i | −0.162532 | + | 0.281514i | ||||
\(803\) | −0.281199 | − | 0.487050i | −0.00992329 | − | 0.0171876i | ||||
\(804\) | 0.217187 | − | 0.810552i | 0.00765959 | − | 0.0285860i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.5104 | + | 18.5381i | 0.370212 | + | 0.652978i | ||||
\(807\) | −25.9845 | −0.914697 | ||||||||
\(808\) | 30.9040 | + | 8.28071i | 1.08720 | + | 0.291314i | ||||
\(809\) | −13.3877 | − | 23.1882i | −0.470688 | − | 0.815255i | 0.528750 | − | 0.848778i | \(-0.322661\pi\) |
−0.999438 | + | 0.0335223i | \(0.989328\pi\) | |||||||
\(810\) | 2.54027 | − | 4.39987i | 0.0892559 | − | 0.154596i | ||||
\(811\) | −7.94016 | + | 7.94016i | −0.278817 | + | 0.278817i | −0.832637 | − | 0.553820i | \(-0.813170\pi\) |
0.553820 | + | 0.832637i | \(0.313170\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.86800 | + | 18.1676i | 0.170728 | + | 0.637167i | ||||
\(814\) | −16.0229 | + | 16.0229i | −0.561601 | + | 0.561601i | ||||
\(815\) | 11.9708 | + | 6.91135i | 0.419319 | + | 0.242094i | ||||
\(816\) | 2.27293 | − | 1.31228i | 0.0795686 | − | 0.0459389i | ||||
\(817\) | 3.45332 | − | 12.8880i | 0.120817 | − | 0.450893i | ||||
\(818\) | −3.32716 | −0.116331 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.157067 | −0.00548500 | ||||||||
\(821\) | 2.37896 | − | 8.87838i | 0.0830261 | − | 0.309858i | −0.911907 | − | 0.410397i | \(-0.865390\pi\) |
0.994933 | + | 0.100539i | \(0.0320568\pi\) | |||||||
\(822\) | −22.9972 | + | 13.2774i | −0.802119 | + | 0.463104i | ||||
\(823\) | 29.9975 | + | 17.3191i | 1.04565 | + | 0.603705i | 0.921428 | − | 0.388550i | \(-0.127024\pi\) |
0.124220 | + | 0.992255i | \(0.460357\pi\) | |||||||
\(824\) | 15.1669 | − | 15.1669i | 0.528366 | − | 0.528366i | ||||
\(825\) | 8.23625 | + | 30.7381i | 0.286750 | + | 1.07016i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.6739 | + | 18.6739i | −0.649355 | + | 0.649355i | −0.952837 | − | 0.303482i | \(-0.901851\pi\) |
0.303482 | + | 0.952837i | \(0.401851\pi\) | |||||||
\(828\) | 0.194176 | − | 0.336323i | 0.00674809 | − | 0.0116880i | ||||
\(829\) | 16.3278 | + | 28.2806i | 0.567089 | + | 0.982228i | 0.996852 | + | 0.0792856i | \(0.0252639\pi\) |
−0.429763 | + | 0.902942i | \(0.641403\pi\) | |||||||
\(830\) | −14.6325 | − | 3.92076i | −0.507901 | − | 0.136092i | ||||
\(831\) | 8.99953 | 0.312190 | ||||||||
\(832\) | 0.232357 | − | 29.6804i | 0.00805552 | − | 1.02898i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.98470 | − | 33.5313i | 0.311115 | − | 1.16110i | ||||
\(835\) | −5.83217 | − | 10.1016i | −0.201831 | − | 0.349581i | ||||
\(836\) | 0.504027 | − | 0.873000i | 0.0174321 | − | 0.0301933i | ||||
\(837\) | 16.9670 | + | 16.9670i | 0.586466 | + | 0.586466i | ||||
\(838\) | 5.48325 | + | 20.4638i | 0.189416 | + | 0.706909i | ||||
\(839\) | −38.6060 | + | 10.3444i | −1.33283 | + | 0.357130i | −0.853768 | − | 0.520654i | \(-0.825688\pi\) |
−0.479058 | + | 0.877783i | \(0.659022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.34638 | − | 10.9922i | 0.218841 | − | 0.379043i | ||||
\(842\) | 25.5883 | − | 14.7734i | 0.881833 | − | 0.509126i | ||||
\(843\) | 0.916400 | − | 3.42005i | 0.0315625 | − | 0.117793i | ||||
\(844\) | 1.43016i | 0.0492281i | ||||||||
\(845\) | −6.21502 | + | 6.02339i | −0.213803 | + | 0.207211i | ||||
\(846\) | − | 12.5372i | − | 0.431039i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.52111 | + | 14.7590i | 0.292616 | + | 0.506826i | ||||
\(849\) | −22.6007 | − | 13.0485i | −0.775652 | − | 0.447823i | ||||
\(850\) | 2.09886 | − | 2.09886i | 0.0719903 | − | 0.0719903i | ||||
\(851\) | −22.6813 | + | 6.07744i | −0.777505 | + | 0.208332i | ||||
\(852\) | 0.286959 | − | 0.0768904i | 0.00983105 | − | 0.00263422i | ||||
\(853\) | 20.1071 | + | 20.1071i | 0.688454 | + | 0.688454i | 0.961890 | − | 0.273436i | \(-0.0881603\pi\) |
−0.273436 | + | 0.961890i | \(0.588160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.75568 | + | 1.01364i | −0.0600429 | + | 0.0346658i | ||||
\(856\) | −11.5096 | − | 3.08398i | −0.393389 | − | 0.105408i | ||||
\(857\) | −13.3280 | −0.455276 | −0.227638 | − | 0.973746i | \(-0.573100\pi\) | ||||
−0.227638 | + | 0.973746i | \(0.573100\pi\) | |||||||
\(858\) | −0.274415 | + | 35.0527i | −0.00936837 | + | 1.19668i | ||||
\(859\) | 12.8706i | 0.439141i | 0.975597 | + | 0.219570i | \(0.0704656\pi\) | ||||
−0.975597 | + | 0.219570i | \(0.929534\pi\) | |||||||
\(860\) | −0.157338 | − | 0.0421585i | −0.00536517 | − | 0.00143759i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.2193 | − | 20.9112i | −1.23364 | − | 0.712240i | ||||
\(863\) | −10.5940 | − | 10.5940i | −0.360623 | − | 0.360623i | 0.503419 | − | 0.864042i | \(-0.332075\pi\) |
−0.864042 | + | 0.503419i | \(0.832075\pi\) | |||||||
\(864\) | −0.512191 | − | 1.91152i | −0.0174251 | − | 0.0650313i | ||||
\(865\) | 1.02019 | + | 3.80741i | 0.0346876 | + | 0.129456i | ||||
\(866\) | −15.2660 | − | 15.2660i | −0.518759 | − | 0.518759i | ||||
\(867\) | 21.0512 | + | 12.1539i | 0.714938 | + | 0.412769i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.81543 | − | 0.486443i | −0.0615842 | − | 0.0165014i | ||||
\(870\) | 5.42155i | 0.183808i | ||||||||
\(871\) | 8.98547 | − | 32.5139i | 0.304461 | − | 1.10169i | ||||
\(872\) | 17.6574 | 0.597954 | ||||||||
\(873\) | 15.5273 | + | 4.16052i | 0.525518 | + | 0.140812i | ||||
\(874\) | −28.3155 | + | 16.3480i | −0.957787 | + | 0.552978i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.00739838 | − | 0.00739838i | −0.000249968 | − | 0.000249968i | ||||
\(877\) | −17.9811 | + | 4.81802i | −0.607178 | + | 0.162693i | −0.549292 | − | 0.835630i | \(-0.685103\pi\) |
−0.0578858 | + | 0.998323i | \(0.518436\pi\) | |||||||
\(878\) | 19.4095 | − | 5.20076i | 0.655038 | − | 0.175517i | ||||
\(879\) | 4.64652 | − | 4.64652i | 0.156723 | − | 0.156723i | ||||
\(880\) | 10.7640 | + | 6.21458i | 0.362853 | + | 0.209494i | ||||
\(881\) | −4.17631 | − | 7.23358i | −0.140703 | − | 0.243705i | 0.787058 | − | 0.616879i | \(-0.211603\pi\) |
−0.927762 | + | 0.373173i | \(0.878270\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.6713i | 1.50331i | 0.659557 | + | 0.751655i | \(0.270744\pi\) | ||||
−0.659557 | + | 0.751655i | \(0.729256\pi\) | |||||||
\(884\) | −0.0908729 | + | 0.0515212i | −0.00305639 | + | 0.00173285i | ||||
\(885\) | − | 5.90959i | − | 0.198649i | ||||||
\(886\) | 4.49569 | − | 16.7781i | 0.151036 | − | 0.563672i | ||||
\(887\) | 1.68229 | − | 0.971270i | 0.0564858 | − | 0.0326121i | −0.471491 | − | 0.881871i | \(-0.656284\pi\) |
0.527977 | + | 0.849259i | \(0.322951\pi\) | |||||||
\(888\) | −7.01899 | + | 12.1572i | −0.235542 | + | 0.407971i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.65777 | + | 2.31984i | −0.290209 | + | 0.0777613i | ||||
\(891\) | 6.83989 | + | 25.5268i | 0.229145 | + | 0.855181i | ||||
\(892\) | −0.162175 | − | 0.162175i | −0.00543000 | − | 0.00543000i | ||||
\(893\) | 16.8616 | − | 29.2051i | 0.564251 | − | 0.977312i | ||||
\(894\) | −3.79382 | − | 6.57108i | −0.126884 | − | 0.219770i | ||||
\(895\) | 0.649644 | − | 2.42450i | 0.0217152 | − | 0.0810422i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.4081 | + | 31.3151i | −0.614630 | + | 1.04558i | ||||
\(898\) | 38.9943 | 1.30126 | ||||||||
\(899\) | −16.5602 | − | 4.43730i | −0.552315 | − | 0.147992i | ||||
\(900\) | −0.127218 | − | 0.220347i | −0.00424059 | − | 0.00734492i | ||||
\(901\) | 1.02963 | − | 1.78337i | 0.0343019 | − | 0.0594127i | ||||
\(902\) | −18.0823 | + | 18.0823i | −0.602075 | + | 0.602075i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.824563 | − | 3.07731i | −0.0274246 | − | 0.102350i | ||||
\(905\) | −2.67818 | + | 2.67818i | −0.0890258 | + | 0.0890258i | ||||
\(906\) | −13.2040 | − | 7.62331i | −0.438672 | − | 0.253267i | ||||
\(907\) | 45.1033 | − | 26.0404i | 1.49763 | − | 0.864656i | 0.497633 | − | 0.867388i | \(-0.334203\pi\) |
0.999996 | + | 0.00273135i | \(0.000869417\pi\) | |||||||
\(908\) | −0.386352 | + | 1.44188i | −0.0128215 | + | 0.0478506i | ||||
\(909\) | 10.0509 | 0.333367 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.8065 | −1.61703 | −0.808516 | − | 0.588474i | \(-0.799729\pi\) | ||||
−0.808516 | + | 0.588474i | \(0.799729\pi\) | |||||||
\(912\) | −4.90229 | + | 18.2956i | −0.162331 | + | 0.605828i | ||||
\(913\) | 68.2415 | − | 39.3992i | 2.25846 | − | 1.30392i | ||||
\(914\) | −21.2373 | − | 12.2614i | −0.702468 | − | 0.405570i | ||||
\(915\) | 3.32132 | − | 3.32132i | 0.109800 | − | 0.109800i | ||||
\(916\) | −0.298803 | − | 1.11515i | −0.00987273 | − | 0.0368455i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.60325 | − | 2.60325i | 0.0859200 | − | 0.0859200i | ||||
\(919\) | −3.72510 | + | 6.45206i | −0.122880 | + | 0.212834i | −0.920902 | − | 0.389794i | \(-0.872546\pi\) |
0.798022 | + | 0.602628i | \(0.205880\pi\) | |||||||
\(920\) | 6.64588 | + | 11.5110i | 0.219108 | + | 0.379507i | ||||
\(921\) | 22.8227 | + | 6.11533i | 0.752035 | + | 0.201507i | ||||
\(922\) | −7.51035 | −0.247340 | ||||||||
\(923\) | 11.5593 | − | 3.00051i | 0.380478 | − | 0.0987629i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.98173 | + | 14.8600i | −0.130918 | + | 0.488594i | ||||
\(926\) | −19.1750 | − | 33.2120i | −0.630128 | − | 1.09141i | ||||
\(927\) | 3.36912 | − | 5.83549i | 0.110656 | − | 0.191663i | ||||
\(928\) | 0.999823 | + | 0.999823i | 0.0328208 | + | 0.0328208i | ||||
\(929\) | −3.87096 | − | 14.4466i | −0.127002 | − | 0.473978i | 0.872901 | − | 0.487897i | \(-0.162236\pi\) |
−0.999903 | + | 0.0139191i | \(0.995569\pi\) | |||||||
\(930\) | −5.50567 | + | 1.47524i | −0.180538 | + | 0.0483750i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.140021 | + | 0.242523i | −0.00458653 | + | 0.00794410i | ||||
\(933\) | −13.6093 | + | 7.85733i | −0.445548 | + | 0.257238i | ||||
\(934\) | 3.45762 | − | 12.9040i | 0.113137 | − | 0.422232i | ||||
\(935\) | − | 1.50185i | − | 0.0491157i | ||||||
\(936\) | −2.34491 | − | 9.03360i | −0.0766457 | − | 0.295272i | ||||
\(937\) | − | 0.823290i | − | 0.0268957i | −0.999910 | − | 0.0134479i | \(-0.995719\pi\) | ||
0.999910 | − | 0.0134479i | \(-0.00428071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.20525 | + | 9.01576i | 0.169867 | + | 0.294218i | ||||
\(940\) | −0.356538 | − | 0.205848i | −0.0116290 | − | 0.00671401i | ||||
\(941\) | 17.6405 | − | 17.6405i | 0.575064 | − | 0.575064i | −0.358475 | − | 0.933539i | \(-0.616703\pi\) |
0.933539 | + | 0.358475i | \(0.116703\pi\) | |||||||
\(942\) | 47.9931 | − | 12.8597i | 1.56370 | − | 0.418992i | ||||
\(943\) | −25.5966 | + | 6.85858i | −0.833539 | + | 0.223346i | ||||
\(944\) | 16.7790 | + | 16.7790i | 0.546111 | + | 0.546111i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.9670 | + | 13.2600i | −0.746722 | + | 0.431120i | ||||
\(947\) | −11.9157 | − | 3.19280i | −0.387207 | − | 0.103752i | 0.0599632 | − | 0.998201i | \(-0.480902\pi\) |
−0.447171 | + | 0.894449i | \(0.647568\pi\) | |||||||
\(948\) | −0.0349658 | −0.00113564 | ||||||||
\(949\) | −0.295069 | − | 0.299725i | −0.00957834 | − | 0.00972950i | ||||
\(950\) | 21.4213i | 0.694998i | ||||||||
\(951\) | −13.2494 | − | 3.55016i | −0.429640 | − | 0.115122i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.9140 | − | 10.3426i | −0.580291 | − | 0.335031i | 0.180958 | − | 0.983491i | \(-0.442080\pi\) |
−0.761249 | + | 0.648460i | \(0.775414\pi\) | |||||||
\(954\) | 3.90676 | + | 3.90676i | 0.126486 | + | 0.126486i | ||||
\(955\) | 1.57970 | + | 5.89551i | 0.0511178 | + | 0.190774i | ||||
\(956\) | −0.252951 | − | 0.944026i | −0.00818102 | − | 0.0305320i | ||||
\(957\) | −19.9413 | − | 19.9413i | −0.644610 | − | 0.644610i | ||||
\(958\) | 37.3132 | + | 21.5428i | 1.20553 | + | 0.696016i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7.66836 | + | 2.05473i | 0.247495 | + | 0.0663161i | ||||
\(961\) | 12.9754i | 0.418562i | ||||||||
\(962\) | −8.58782 | + | 14.6092i | −0.276882 | + | 0.471020i | ||||
\(963\) | −3.74325 | −0.120625 | ||||||||
\(964\) | 0.452665 | + | 0.121291i | 0.0145794 | + | 0.00390653i | ||||
\(965\) | −14.6514 | + | 8.45899i | −0.471645 | + | 0.272304i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.39351 | + | 6.39351i | 0.205601 | + | 0.205601i | 0.802395 | − | 0.596793i | \(-0.203559\pi\) |
−0.596793 | + | 0.802395i | \(0.703559\pi\) | |||||||
\(968\) | −33.9472 | + | 9.09612i | −1.09110 | + | 0.292360i | ||||
\(969\) | 2.21071 | − | 0.592357i | 0.0710181 | − | 0.0190292i | ||||
\(970\) | −11.6829 | + | 11.6829i | −0.375116 | + | 0.375116i | ||||
\(971\) | −14.9575 | − | 8.63569i | −0.480008 | − | 0.277133i | 0.240412 | − | 0.970671i | \(-0.422717\pi\) |
−0.720420 | + | 0.693538i | \(0.756051\pi\) | |||||||
\(972\) | −0.279112 | − | 0.483437i | −0.00895253 | − | 0.0155062i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 7.79056i | − | 0.249626i | ||||||
\(975\) | 11.7377 | + | 20.7029i | 0.375907 | + | 0.663023i | ||||
\(976\) | 18.8604i | 0.603706i | ||||||||
\(977\) | −14.0046 | + | 52.2660i | −0.448048 | + | 1.67214i | 0.259714 | + | 0.965686i | \(0.416372\pi\) |
−0.707761 | + | 0.706452i | \(0.750295\pi\) | |||||||
\(978\) | 36.2591 | − | 20.9342i | 1.15944 | − | 0.669401i | ||||
\(979\) | 23.3118 | − | 40.3773i | 0.745049 | − | 1.29046i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.35800 | − | 1.43567i | 0.171068 | − | 0.0458375i | ||||
\(982\) | 4.99738 | + | 18.6505i | 0.159473 | + | 0.595161i | ||||
\(983\) | 26.5265 | + | 26.5265i | 0.846065 | + | 0.846065i | 0.989640 | − | 0.143574i | \(-0.0458596\pi\) |
−0.143574 | + | 0.989640i | \(0.545860\pi\) | |||||||
\(984\) | −7.92115 | + | 13.7198i | −0.252517 | + | 0.437372i | ||||
\(985\) | −0.477984 | − | 0.827893i | −0.0152298 | − | 0.0263789i | ||||
\(986\) | −0.680815 | + | 2.54083i | −0.0216816 | + | 0.0809167i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.200815 | − | 0.726648i | 0.00638876 | − | 0.0231177i | ||||
\(989\) | −27.4817 | −0.873866 | ||||||||
\(990\) | 3.89216 | + | 1.04290i | 0.123701 | + | 0.0331456i | ||||
\(991\) | −17.4270 | − | 30.1845i | −0.553587 | − | 0.958841i | −0.998012 | − | 0.0630250i | \(-0.979925\pi\) |
0.444425 | − | 0.895816i | \(-0.353408\pi\) | |||||||
\(992\) | −0.743276 | + | 1.28739i | −0.0235990 | + | 0.0408748i | ||||
\(993\) | −6.07784 | + | 6.07784i | −0.192874 | + | 0.192874i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.89816 | − | 7.08404i | −0.0601758 | − | 0.224579i | ||||
\(996\) | 1.03660 | − | 1.03660i | 0.0328459 | − | 0.0328459i | ||||
\(997\) | 13.1836 | + | 7.61153i | 0.417528 | + | 0.241060i | 0.694019 | − | 0.719957i | \(-0.255838\pi\) |
−0.276491 | + | 0.961016i | \(0.589172\pi\) | |||||||
\(998\) | 11.0233 | − | 6.36431i | 0.348936 | − | 0.201459i | ||||
\(999\) | −4.93860 | + | 18.4311i | −0.156250 | + | 0.583134i |
(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.440.2 | 28 | ||
7.2 | even | 3 | 637.2.x.a.570.6 | 28 | |||
7.3 | odd | 6 | 637.2.bb.a.362.2 | 28 | |||
7.4 | even | 3 | 91.2.ba.a.89.2 | yes | 28 | ||
7.5 | odd | 6 | 91.2.w.a.24.6 | yes | 28 | ||
7.6 | odd | 2 | 637.2.bd.a.440.2 | 28 | |||
13.6 | odd | 12 | 637.2.bd.a.97.2 | 28 | |||
21.5 | even | 6 | 819.2.gh.b.388.2 | 28 | |||
21.11 | odd | 6 | 819.2.et.b.271.6 | 28 | |||
91.6 | even | 12 | inner | 637.2.bd.b.97.2 | 28 | ||
91.19 | even | 12 | 91.2.ba.a.45.2 | yes | 28 | ||
91.32 | odd | 12 | 91.2.w.a.19.6 | ✓ | 28 | ||
91.45 | even | 12 | 637.2.x.a.19.6 | 28 | |||
91.58 | odd | 12 | 637.2.bb.a.227.2 | 28 | |||
273.32 | even | 12 | 819.2.gh.b.19.2 | 28 | |||
273.110 | odd | 12 | 819.2.et.b.136.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.19.6 | ✓ | 28 | 91.32 | odd | 12 | ||
91.2.w.a.24.6 | yes | 28 | 7.5 | odd | 6 | ||
91.2.ba.a.45.2 | yes | 28 | 91.19 | even | 12 | ||
91.2.ba.a.89.2 | yes | 28 | 7.4 | even | 3 | ||
637.2.x.a.19.6 | 28 | 91.45 | even | 12 | |||
637.2.x.a.570.6 | 28 | 7.2 | even | 3 | |||
637.2.bb.a.227.2 | 28 | 91.58 | odd | 12 | |||
637.2.bb.a.362.2 | 28 | 7.3 | odd | 6 | |||
637.2.bd.a.97.2 | 28 | 13.6 | odd | 12 | |||
637.2.bd.a.440.2 | 28 | 7.6 | odd | 2 | |||
637.2.bd.b.97.2 | 28 | 91.6 | even | 12 | inner | ||
637.2.bd.b.440.2 | 28 | 1.1 | even | 1 | trivial | ||
819.2.et.b.136.6 | 28 | 273.110 | odd | 12 | |||
819.2.et.b.271.6 | 28 | 21.11 | odd | 6 | |||
819.2.gh.b.19.2 | 28 | 273.32 | even | 12 | |||
819.2.gh.b.388.2 | 28 | 21.5 | even | 6 |