Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(26,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(50))
chi = DirichletCharacter(H, H._module([14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.g (of order \(25\), degree \(20\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(480\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{25})\) |
Twist minimal: | no (minimal twist has level 125) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{25}]$ |
Embedding invariants
Embedding label | 451.8 | ||
Character | \(\chi\) | \(=\) | 625.451 |
Dual form | 625.2.g.b.176.8 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{25}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28126 | − | 0.161861i | −0.905991 | − | 0.114453i | −0.341489 | − | 0.939886i | \(-0.610931\pi\) |
−0.564501 | + | 0.825432i | \(0.690931\pi\) | |||||||
\(3\) | −1.41863 | − | 1.71483i | −0.819048 | − | 0.990059i | −0.999978 | − | 0.00656345i | \(-0.997911\pi\) |
0.180930 | − | 0.983496i | \(-0.442089\pi\) | |||||||
\(4\) | −0.321728 | − | 0.0826056i | −0.160864 | − | 0.0413028i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.54008 | + | 2.42678i | 0.628735 | + | 0.990727i | ||||
\(7\) | −0.740638 | − | 2.27945i | −0.279935 | − | 0.861551i | −0.987871 | − | 0.155275i | \(-0.950374\pi\) |
0.707936 | − | 0.706276i | \(-0.249626\pi\) | |||||||
\(8\) | 2.80036 | + | 1.10874i | 0.990078 | + | 0.391999i | ||||
\(9\) | −0.365988 | + | 1.91858i | −0.121996 | + | 0.639526i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.57197 | + | 0.577574i | 1.37850 | + | 0.174145i | 0.779399 | − | 0.626528i | \(-0.215524\pi\) |
0.599102 | + | 0.800673i | \(0.295524\pi\) | |||||||
\(12\) | 0.314759 | + | 0.668897i | 0.0908631 | + | 0.193094i | ||||
\(13\) | 1.08143 | − | 5.66906i | 0.299935 | − | 1.57231i | −0.438969 | − | 0.898502i | \(-0.644656\pi\) |
0.738903 | − | 0.673811i | \(-0.235344\pi\) | |||||||
\(14\) | 0.579998 | + | 3.04046i | 0.155011 | + | 0.812597i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.82639 | − | 1.55382i | −0.706597 | − | 0.388455i | ||||
\(17\) | 4.20471 | − | 1.07959i | 1.01979 | − | 0.261838i | 0.298456 | − | 0.954423i | \(-0.403528\pi\) |
0.721336 | + | 0.692586i | \(0.243528\pi\) | |||||||
\(18\) | 0.779471 | − | 2.39897i | 0.183723 | − | 0.565442i | ||||
\(19\) | 3.02560 | − | 3.65732i | 0.694120 | − | 0.839048i | −0.299230 | − | 0.954181i | \(-0.596730\pi\) |
0.993350 | + | 0.115134i | \(0.0367296\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.85818 | + | 4.50378i | −0.623707 | + | 0.982804i | ||||
\(22\) | −5.76442 | − | 1.48005i | −1.22898 | − | 0.315548i | ||||
\(23\) | −0.587001 | − | 0.551231i | −0.122398 | − | 0.114940i | 0.620931 | − | 0.783865i | \(-0.286755\pi\) |
−0.743330 | + | 0.668925i | \(0.766755\pi\) | |||||||
\(24\) | −2.07138 | − | 6.37505i | −0.422819 | − | 1.30130i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.30320 | + | 7.08852i | −0.451695 | + | 1.39017i | ||||
\(27\) | −2.04161 | + | 1.12238i | −0.392908 | + | 0.216003i | ||||
\(28\) | 0.0499884 | + | 0.794543i | 0.00944693 | + | 0.150155i | ||||
\(29\) | −0.0122026 | − | 0.193954i | −0.00226596 | − | 0.0360164i | 0.996731 | − | 0.0807885i | \(-0.0257438\pi\) |
−0.998997 | + | 0.0447721i | \(0.985744\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.935449 | − | 0.240183i | 0.168012 | − | 0.0431381i | −0.163747 | − | 0.986502i | \(-0.552358\pi\) |
0.331759 | + | 0.943364i | \(0.392358\pi\) | |||||||
\(32\) | −1.50346 | − | 1.09233i | −0.265776 | − | 0.193098i | ||||
\(33\) | −5.49551 | − | 8.65953i | −0.956645 | − | 1.50743i | ||||
\(34\) | −5.56208 | + | 0.702655i | −0.953890 | + | 0.120504i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.276234 | − | 0.587027i | 0.0460390 | − | 0.0978378i | ||||
\(37\) | 7.25681 | + | 3.98946i | 1.19301 | + | 0.655864i | 0.949418 | − | 0.314014i | \(-0.101674\pi\) |
0.243593 | + | 0.969877i | \(0.421674\pi\) | |||||||
\(38\) | −4.46857 | + | 4.19627i | −0.724898 | + | 0.680725i | ||||
\(39\) | −11.2556 | + | 6.18784i | −1.80235 | + | 0.990848i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.442053 | − | 0.415115i | 0.0690370 | − | 0.0648301i | −0.649261 | − | 0.760566i | \(-0.724922\pi\) |
0.718298 | + | 0.695736i | \(0.244922\pi\) | |||||||
\(42\) | 4.39107 | − | 5.30790i | 0.677557 | − | 0.819026i | ||||
\(43\) | −9.09003 | + | 6.60429i | −1.38622 | + | 1.00715i | −0.389948 | + | 0.920837i | \(0.627507\pi\) |
−0.996268 | + | 0.0863081i | \(0.972493\pi\) | |||||||
\(44\) | −1.42322 | − | 0.563492i | −0.214558 | − | 0.0849497i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.662880 | + | 0.801285i | 0.0977364 | + | 0.118143i | ||||
\(47\) | −3.71428 | + | 1.47059i | −0.541783 | + | 0.214507i | −0.623046 | − | 0.782186i | \(-0.714105\pi\) |
0.0812622 | + | 0.996693i | \(0.474105\pi\) | |||||||
\(48\) | 1.34507 | + | 7.05108i | 0.194144 | + | 1.01774i | ||||
\(49\) | 1.01577 | − | 0.738000i | 0.145110 | − | 0.105429i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.81625 | − | 5.67884i | −1.09449 | − | 0.795196i | ||||
\(52\) | −0.816222 | + | 1.73456i | −0.113190 | + | 0.240540i | ||||
\(53\) | 4.41327 | − | 6.95421i | 0.606210 | − | 0.955234i | −0.393151 | − | 0.919474i | \(-0.628615\pi\) |
0.999360 | − | 0.0357596i | \(-0.0113851\pi\) | |||||||
\(54\) | 2.79751 | − | 1.10761i | 0.380693 | − | 0.150727i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.453266 | − | 7.20446i | 0.0605703 | − | 0.962737i | ||||
\(57\) | −10.5639 | −1.39923 | ||||||||
\(58\) | −0.0157590 | + | 0.250482i | −0.00206926 | + | 0.0328899i | ||||
\(59\) | −2.33894 | − | 4.97049i | −0.304504 | − | 0.647103i | 0.692749 | − | 0.721179i | \(-0.256399\pi\) |
−0.997253 | + | 0.0740756i | \(0.976399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.65640 | − | 8.12890i | −1.10834 | − | 1.04080i | −0.998904 | − | 0.0468051i | \(-0.985096\pi\) |
−0.109434 | − | 0.993994i | \(-0.534904\pi\) | |||||||
\(62\) | −1.23743 | + | 0.156324i | −0.157154 | + | 0.0198532i | ||||
\(63\) | 4.64437 | − | 0.586720i | 0.585135 | − | 0.0739198i | ||||
\(64\) | 6.45186 | + | 6.05870i | 0.806483 | + | 0.757338i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.63955 | + | 11.9847i | 0.694181 | + | 1.47521i | ||||
\(67\) | −0.0683896 | + | 1.08702i | −0.00835511 | + | 0.132801i | 0.991638 | + | 0.129052i | \(0.0411933\pi\) |
−0.999993 | + | 0.00374898i | \(0.998807\pi\) | |||||||
\(68\) | −1.44195 | −0.174862 | ||||||||
\(69\) | −0.112529 | + | 1.78860i | −0.0135469 | + | 0.215322i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.401350 | − | 0.158906i | 0.0476315 | − | 0.0188587i | −0.344188 | − | 0.938901i | \(-0.611846\pi\) |
0.391820 | + | 0.920042i | \(0.371846\pi\) | |||||||
\(72\) | −3.15211 | + | 4.96693i | −0.371479 | + | 0.585358i | ||||
\(73\) | −6.24516 | + | 13.2717i | −0.730941 | + | 1.55333i | 0.0987536 | + | 0.995112i | \(0.468514\pi\) |
−0.829695 | + | 0.558217i | \(0.811486\pi\) | |||||||
\(74\) | −8.65215 | − | 6.28615i | −1.00579 | − | 0.730750i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.27554 | + | 0.926731i | −0.146314 | + | 0.106303i | ||||
\(77\) | −2.06963 | − | 10.8494i | −0.235856 | − | 1.23640i | ||||
\(78\) | 15.4230 | − | 6.10641i | 1.74631 | − | 0.691414i | ||||
\(79\) | −0.594972 | − | 0.719197i | −0.0669396 | − | 0.0809160i | 0.735981 | − | 0.677003i | \(-0.236721\pi\) |
−0.802920 | + | 0.596087i | \(0.796721\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.2690 | + | 4.06580i | 1.14100 | + | 0.451756i | ||||
\(82\) | −0.633577 | + | 0.460321i | −0.0699669 | + | 0.0508339i | ||||
\(83\) | 1.16915 | − | 1.41326i | 0.128331 | − | 0.155125i | −0.702434 | − | 0.711749i | \(-0.747903\pi\) |
0.830765 | + | 0.556624i | \(0.187903\pi\) | |||||||
\(84\) | 1.29159 | − | 1.21289i | 0.140924 | − | 0.132337i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.7157 | − | 6.99052i | 1.37117 | − | 0.753807i | ||||
\(87\) | −0.315288 | + | 0.296076i | −0.0338025 | + | 0.0317426i | ||||
\(88\) | 12.1628 | + | 6.68655i | 1.29656 | + | 0.712789i | ||||
\(89\) | 1.00941 | − | 2.14511i | 0.106998 | − | 0.227381i | −0.844157 | − | 0.536096i | \(-0.819899\pi\) |
0.951155 | + | 0.308714i | \(0.0998987\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.7233 | + | 1.73365i | −1.43859 | + | 0.181736i | ||||
\(92\) | 0.143320 | + | 0.225836i | 0.0149421 | + | 0.0235450i | ||||
\(93\) | −1.73893 | − | 1.26341i | −0.180319 | − | 0.131009i | ||||
\(94\) | 4.99700 | − | 1.28301i | 0.515402 | − | 0.132333i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.259698 | + | 4.12779i | 0.0265053 | + | 0.421290i | ||||
\(97\) | −0.464575 | − | 7.38421i | −0.0471705 | − | 0.749753i | −0.948531 | − | 0.316684i | \(-0.897431\pi\) |
0.901361 | − | 0.433069i | \(-0.142569\pi\) | |||||||
\(98\) | −1.42092 | + | 0.781159i | −0.143535 | + | 0.0789090i | ||||
\(99\) | −2.78141 | + | 8.56030i | −0.279542 | + | 0.860342i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00233 | − | 9.24022i | −0.298743 | − | 0.919436i | −0.981938 | − | 0.189201i | \(-0.939410\pi\) |
0.683195 | − | 0.730236i | \(-0.260590\pi\) | |||||||
\(102\) | 9.09549 | + | 8.54124i | 0.900588 | + | 0.845708i | ||||
\(103\) | −6.59022 | − | 1.69208i | −0.649353 | − | 0.166726i | −0.0903749 | − | 0.995908i | \(-0.528807\pi\) |
−0.558978 | + | 0.829182i | \(0.688807\pi\) | |||||||
\(104\) | 9.31392 | − | 14.6764i | 0.913305 | − | 1.43914i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.78019 | + | 8.19584i | −0.658550 | + | 0.796050i | ||||
\(107\) | 3.45898 | − | 10.6456i | 0.334392 | − | 1.02915i | −0.632629 | − | 0.774455i | \(-0.718024\pi\) |
0.967021 | − | 0.254697i | \(-0.0819759\pi\) | |||||||
\(108\) | 0.749557 | − | 0.192454i | 0.0721262 | − | 0.0185189i | ||||
\(109\) | 10.8208 | + | 5.94880i | 1.03645 | + | 0.569791i | 0.906709 | − | 0.421757i | \(-0.138586\pi\) |
0.129738 | + | 0.991548i | \(0.458586\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.45348 | − | 18.1038i | −0.327790 | − | 1.71834i | ||||
\(112\) | −1.44852 | + | 7.59343i | −0.136873 | + | 0.717512i | ||||
\(113\) | 6.34083 | + | 13.4749i | 0.596495 | + | 1.26762i | 0.944002 | + | 0.329939i | \(0.107028\pi\) |
−0.347507 | + | 0.937677i | \(0.612972\pi\) | |||||||
\(114\) | 13.5352 | + | 1.70989i | 1.26768 | + | 0.160146i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0120958 | + | 0.0634085i | −0.00112307 | + | 0.00588733i | ||||
\(117\) | 10.4807 | + | 4.14962i | 0.968944 | + | 0.383632i | ||||
\(118\) | 2.19227 | + | 6.74710i | 0.201814 | + | 0.621121i | ||||
\(119\) | −5.57503 | − | 8.78484i | −0.511062 | − | 0.805305i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.91492 | + | 2.54572i | 0.901356 | + | 0.231429i | ||||
\(122\) | 9.77538 | + | 11.8164i | 0.885021 | + | 1.06981i | ||||
\(123\) | −1.33896 | − | 0.169150i | −0.120730 | − | 0.0152518i | ||||
\(124\) | −0.320800 | −0.0288087 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.04563 | −0.538587 | ||||||||
\(127\) | −1.54903 | − | 0.195688i | −0.137454 | − | 0.0173645i | 0.0563052 | − | 0.998414i | \(-0.482068\pi\) |
−0.193759 | + | 0.981049i | \(0.562068\pi\) | |||||||
\(128\) | −4.91673 | − | 5.94330i | −0.434581 | − | 0.525319i | ||||
\(129\) | 24.2207 | + | 6.21881i | 2.13251 | + | 0.547536i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.25967 | − | 1.98492i | −0.110058 | − | 0.173423i | 0.784835 | − | 0.619705i | \(-0.212748\pi\) |
−0.894892 | + | 0.446282i | \(0.852748\pi\) | |||||||
\(132\) | 1.05273 | + | 3.23997i | 0.0916285 | + | 0.282003i | ||||
\(133\) | −10.5776 | − | 4.18795i | −0.917191 | − | 0.363142i | ||||
\(134\) | 0.263572 | − | 1.38169i | 0.0227691 | − | 0.119360i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.9717 | + | 1.63871i | 1.11231 | + | 0.140518i | ||||
\(137\) | 3.16951 | + | 6.73554i | 0.270789 | + | 0.575456i | 0.993255 | − | 0.115950i | \(-0.0369913\pi\) |
−0.722466 | + | 0.691407i | \(0.756991\pi\) | |||||||
\(138\) | 0.433685 | − | 2.27346i | 0.0369177 | − | 0.193530i | ||||
\(139\) | 1.36337 | + | 7.14706i | 0.115640 | + | 0.606206i | 0.992174 | + | 0.124865i | \(0.0398499\pi\) |
−0.876534 | + | 0.481340i | \(0.840150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.79101 | + | 4.28315i | 0.656122 | + | 0.360706i | ||||
\(142\) | −0.539957 | + | 0.138637i | −0.0453121 | + | 0.0116342i | ||||
\(143\) | 8.21857 | − | 25.2942i | 0.687272 | − | 2.11520i | ||||
\(144\) | 4.01555 | − | 4.85396i | 0.334629 | − | 0.404497i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.1499 | − | 15.9936i | 0.840009 | − | 1.32364i | ||||
\(147\) | −2.70655 | − | 0.694925i | −0.223233 | − | 0.0573164i | ||||
\(148\) | −2.00516 | − | 1.88297i | −0.164823 | − | 0.154780i | ||||
\(149\) | 6.51667 | + | 20.0563i | 0.533867 | + | 1.64307i | 0.746085 | + | 0.665850i | \(0.231931\pi\) |
−0.212219 | + | 0.977222i | \(0.568069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.38145 | + | 4.25168i | −0.112421 | + | 0.345997i | −0.991400 | − | 0.130863i | \(-0.958225\pi\) |
0.878979 | + | 0.476860i | \(0.158225\pi\) | |||||||
\(152\) | 12.5278 | − | 6.88722i | 1.01614 | − | 0.558627i | ||||
\(153\) | 0.532395 | + | 8.46217i | 0.0430416 | + | 0.684126i | ||||
\(154\) | 0.895646 | + | 14.2359i | 0.0721732 | + | 1.14716i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.13240 | − | 1.06102i | 0.330857 | − | 0.0849497i | ||||
\(157\) | −4.06955 | − | 2.95670i | −0.324786 | − | 0.235971i | 0.413429 | − | 0.910536i | \(-0.364331\pi\) |
−0.738215 | + | 0.674566i | \(0.764331\pi\) | |||||||
\(158\) | 0.645906 | + | 1.01778i | 0.0513855 | + | 0.0809706i | ||||
\(159\) | −18.1861 | + | 2.29744i | −1.44225 | + | 0.182199i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.821747 | + | 1.74630i | −0.0647628 | + | 0.137628i | ||||
\(162\) | −12.4993 | − | 6.87152i | −0.982034 | − | 0.539878i | ||||
\(163\) | 3.62971 | − | 3.40852i | 0.284301 | − | 0.266976i | −0.529255 | − | 0.848463i | \(-0.677529\pi\) |
0.813556 | + | 0.581486i | \(0.197529\pi\) | |||||||
\(164\) | −0.176511 | + | 0.0970380i | −0.0137832 | + | 0.00757739i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.72674 | + | 1.62152i | −0.134021 | + | 0.125854i | ||||
\(167\) | −4.88355 | + | 5.90320i | −0.377901 | + | 0.456803i | −0.924833 | − | 0.380373i | \(-0.875795\pi\) |
0.546932 | + | 0.837177i | \(0.315795\pi\) | |||||||
\(168\) | −12.9975 | + | 9.44322i | −1.00278 | + | 0.728560i | ||||
\(169\) | −18.8816 | − | 7.47577i | −1.45243 | − | 0.575059i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.90952 | + | 7.14339i | 0.451913 | + | 0.546269i | ||||
\(172\) | 3.47007 | − | 1.37390i | 0.264590 | − | 0.104759i | ||||
\(173\) | 0.250079 | + | 1.31096i | 0.0190132 | + | 0.0996704i | 0.990529 | − | 0.137305i | \(-0.0438440\pi\) |
−0.971516 | + | 0.236975i | \(0.923844\pi\) | |||||||
\(174\) | 0.451891 | − | 0.328318i | 0.0342578 | − | 0.0248897i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0247 | − | 8.73647i | −0.906397 | − | 0.658536i | ||||
\(177\) | −5.20547 | + | 11.0622i | −0.391267 | + | 0.831485i | ||||
\(178\) | −1.64053 | + | 2.58507i | −0.122963 | + | 0.193759i | ||||
\(179\) | −13.7021 | + | 5.42503i | −1.02414 | + | 0.405486i | −0.819334 | − | 0.573317i | \(-0.805656\pi\) |
−0.204806 | + | 0.978803i | \(0.565656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0768556 | + | 1.22159i | −0.00571263 | + | 0.0907997i | −0.999850 | − | 0.0173257i | \(-0.994485\pi\) |
0.994137 | + | 0.108125i | \(0.0344848\pi\) | |||||||
\(182\) | 17.8638 | 1.32415 | ||||||||
\(183\) | −1.65945 | + | 26.3762i | −0.122670 | + | 1.94979i | ||||
\(184\) | −1.03264 | − | 2.19448i | −0.0761274 | − | 0.161779i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.02354 | + | 1.90023i | 0.148373 | + | 0.139331i | ||||
\(187\) | 19.8473 | − | 2.50730i | 1.45138 | − | 0.183352i | ||||
\(188\) | 1.31647 | − | 0.166308i | 0.0960131 | − | 0.0121293i | ||||
\(189\) | 4.07051 | + | 3.82247i | 0.296086 | + | 0.278043i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.92625 | − | 6.21860i | −0.211736 | − | 0.449962i | 0.770542 | − | 0.637389i | \(-0.219985\pi\) |
−0.982279 | + | 0.187426i | \(0.939985\pi\) | |||||||
\(192\) | 1.23684 | − | 19.6590i | 0.0892610 | − | 1.41876i | ||||
\(193\) | 22.1313 | 1.59304 | 0.796522 | − | 0.604609i | \(-0.206671\pi\) | ||||
0.796522 | + | 0.604609i | \(0.206671\pi\) | |||||||
\(194\) | −0.599975 | + | 9.53632i | −0.0430757 | + | 0.684668i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.387764 | + | 0.153527i | −0.0276975 | + | 0.0109662i | ||||
\(197\) | −5.76869 | + | 9.09001i | −0.411002 | + | 0.647636i | −0.985265 | − | 0.171035i | \(-0.945289\pi\) |
0.574263 | + | 0.818671i | \(0.305289\pi\) | |||||||
\(198\) | 4.94930 | − | 10.5178i | 0.351731 | − | 0.747467i | ||||
\(199\) | −5.76789 | − | 4.19062i | −0.408875 | − | 0.297065i | 0.364271 | − | 0.931293i | \(-0.381318\pi\) |
−0.773146 | + | 0.634228i | \(0.781318\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.96108 | − | 1.42481i | 0.138324 | − | 0.100498i | ||||
\(202\) | 2.35114 | + | 12.3251i | 0.165426 | + | 0.867193i | ||||
\(203\) | −0.433072 | + | 0.171465i | −0.0303957 | + | 0.0120345i | ||||
\(204\) | 2.04560 | + | 2.47271i | 0.143221 | + | 0.173124i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.16992 | + | 3.23470i | 0.569226 | + | 0.225372i | ||||
\(207\) | 1.27241 | − | 0.924463i | 0.0884389 | − | 0.0642546i | ||||
\(208\) | −11.8652 | + | 14.3426i | −0.822706 | + | 0.994481i | ||||
\(209\) | 15.9453 | − | 14.9737i | 1.10296 | − | 1.03575i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.5752 | + | 12.9606i | −1.62298 | + | 0.892243i | −0.629662 | + | 0.776869i | \(0.716807\pi\) |
−0.993322 | + | 0.115374i | \(0.963193\pi\) | |||||||
\(212\) | −1.99433 | + | 1.87280i | −0.136971 | + | 0.128624i | ||||
\(213\) | −0.841866 | − | 0.462820i | −0.0576837 | − | 0.0317119i | ||||
\(214\) | −6.15498 | + | 13.0800i | −0.420746 | + | 0.894130i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.96168 | + | 0.879465i | −0.473682 | + | 0.0598400i | ||||
\(217\) | −1.24031 | − | 1.95442i | −0.0841980 | − | 0.132675i | ||||
\(218\) | −12.9014 | − | 9.37345i | −0.873796 | − | 0.634850i | ||||
\(219\) | 31.6183 | − | 8.11819i | 2.13656 | − | 0.548577i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.57313 | − | 25.0042i | −0.105820 | − | 1.68197i | ||||
\(222\) | 1.49452 | + | 23.7547i | 0.100306 | + | 1.59431i | ||||
\(223\) | −11.3649 | + | 6.24793i | −0.761053 | + | 0.418393i | −0.814489 | − | 0.580179i | \(-0.802983\pi\) |
0.0534360 | + | 0.998571i | \(0.482983\pi\) | |||||||
\(224\) | −1.37638 | + | 4.23607i | −0.0919635 | + | 0.283034i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.94320 | − | 18.2913i | −0.395336 | − | 1.21672i | ||||
\(227\) | 16.2278 | + | 15.2390i | 1.07708 | + | 1.01144i | 0.999896 | + | 0.0144279i | \(0.00459270\pi\) |
0.0771834 | + | 0.997017i | \(0.475407\pi\) | |||||||
\(228\) | 3.39871 | + | 0.872639i | 0.225085 | + | 0.0577920i | ||||
\(229\) | −0.467076 | + | 0.735995i | −0.0308653 | + | 0.0486359i | −0.859410 | − | 0.511287i | \(-0.829169\pi\) |
0.828545 | + | 0.559922i | \(0.189169\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.6688 | + | 18.9403i | −1.03093 | + | 1.24618i | ||||
\(232\) | 0.180874 | − | 0.556672i | 0.0118749 | − | 0.0365473i | ||||
\(233\) | 16.6353 | − | 4.27122i | 1.08981 | − | 0.279817i | 0.339305 | − | 0.940677i | \(-0.389808\pi\) |
0.750509 | + | 0.660860i | \(0.229808\pi\) | |||||||
\(234\) | −12.7569 | − | 7.01318i | −0.833947 | − | 0.458466i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.341910 | + | 1.79236i | 0.0222564 | + | 0.116672i | ||||
\(237\) | −0.389257 | + | 2.04055i | −0.0252849 | + | 0.132548i | ||||
\(238\) | 5.72116 | + | 12.1581i | 0.370848 | + | 0.788091i | ||||
\(239\) | −26.2269 | − | 3.31323i | −1.69648 | − | 0.214315i | −0.783234 | − | 0.621727i | \(-0.786431\pi\) |
−0.913244 | + | 0.407412i | \(0.866431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0299061 | + | 0.156773i | −0.00192642 | + | 0.0100987i | −0.983237 | − | 0.182330i | \(-0.941636\pi\) |
0.981311 | + | 0.192428i | \(0.0616362\pi\) | |||||||
\(242\) | −12.2916 | − | 4.86658i | −0.790132 | − | 0.312835i | ||||
\(243\) | −5.43600 | − | 16.7303i | −0.348720 | − | 1.07325i | ||||
\(244\) | 2.11351 | + | 3.33036i | 0.135304 | + | 0.213204i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.68819 | + | 0.433453i | 0.107635 | + | 0.0276359i | ||||
\(247\) | −17.4616 | − | 21.1074i | −1.11106 | − | 1.34303i | ||||
\(248\) | 2.88590 | + | 0.364574i | 0.183255 | + | 0.0231505i | ||||
\(249\) | −4.08210 | −0.258692 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.7462 | 1.49885 | 0.749423 | − | 0.662091i | \(-0.230331\pi\) | ||||
0.749423 | + | 0.662091i | \(0.230331\pi\) | |||||||
\(252\) | −1.54269 | − | 0.194887i | −0.0971802 | − | 0.0122767i | ||||
\(253\) | −2.36537 | − | 2.85925i | −0.148710 | − | 0.179759i | ||||
\(254\) | 1.95304 | + | 0.501455i | 0.122545 | + | 0.0314641i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.14722 | − | 6.53498i | −0.259201 | − | 0.408436i | ||||
\(257\) | −8.26780 | − | 25.4457i | −0.515731 | − | 1.58726i | −0.781947 | − | 0.623345i | \(-0.785773\pi\) |
0.266216 | − | 0.963913i | \(-0.414227\pi\) | |||||||
\(258\) | −30.0265 | − | 11.8883i | −1.86937 | − | 0.740135i | ||||
\(259\) | 3.71911 | − | 19.4963i | 0.231095 | − | 1.21144i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.376582 | + | 0.0475734i | 0.0233099 | + | 0.00294472i | ||||
\(262\) | 1.29269 | + | 2.74710i | 0.0798624 | + | 0.169716i | ||||
\(263\) | 4.46169 | − | 23.3890i | 0.275120 | − | 1.44223i | −0.529435 | − | 0.848350i | \(-0.677596\pi\) |
0.804555 | − | 0.593878i | \(-0.202404\pi\) | |||||||
\(264\) | −5.78822 | − | 30.3429i | −0.356241 | − | 1.86748i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.8748 | + | 7.07797i | 0.789404 | + | 0.433978i | ||||
\(267\) | −5.11049 | + | 1.31215i | −0.312757 | + | 0.0803024i | ||||
\(268\) | 0.111797 | − | 0.344075i | 0.00682908 | − | 0.0210178i | ||||
\(269\) | −1.43803 | + | 1.73828i | −0.0876782 | + | 0.105985i | −0.812528 | − | 0.582922i | \(-0.801909\pi\) |
0.724850 | + | 0.688907i | \(0.241909\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.43111 | − | 11.7096i | 0.451408 | − | 0.711305i | −0.540064 | − | 0.841624i | \(-0.681600\pi\) |
0.991472 | + | 0.130319i | \(0.0416001\pi\) | |||||||
\(272\) | −13.5616 | − | 3.48203i | −0.822294 | − | 0.211129i | ||||
\(273\) | 22.4412 | + | 21.0737i | 1.35821 | + | 1.27544i | ||||
\(274\) | −2.97075 | − | 9.14303i | −0.179470 | − | 0.552351i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.183952 | − | 0.566148i | 0.0110726 | − | 0.0340781i | ||||
\(277\) | 23.5279 | − | 12.9346i | 1.41366 | − | 0.777164i | 0.422063 | − | 0.906566i | \(-0.361306\pi\) |
0.991592 | + | 0.129403i | \(0.0413060\pi\) | |||||||
\(278\) | −0.590010 | − | 9.37795i | −0.0353865 | − | 0.562452i | ||||
\(279\) | 0.118445 | + | 1.88264i | 0.00709114 | + | 0.112710i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.9870 | + | 5.13179i | −1.19232 | + | 0.306137i | −0.792164 | − | 0.610309i | \(-0.791045\pi\) |
−0.400160 | + | 0.916445i | \(0.631045\pi\) | |||||||
\(282\) | −9.28907 | − | 6.74890i | −0.553156 | − | 0.401891i | ||||
\(283\) | 1.47686 | + | 2.32715i | 0.0877900 | + | 0.138335i | 0.885385 | − | 0.464858i | \(-0.153895\pi\) |
−0.797595 | + | 0.603193i | \(0.793895\pi\) | |||||||
\(284\) | −0.142252 | + | 0.0179706i | −0.00844111 | + | 0.00106636i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.6243 | + | 31.0782i | −0.864753 | + | 1.83769i | ||||
\(287\) | −1.27364 | − | 0.700187i | −0.0751803 | − | 0.0413307i | ||||
\(288\) | 2.64596 | − | 2.48472i | 0.155915 | − | 0.146414i | ||||
\(289\) | 1.61685 | − | 0.888870i | 0.0951087 | − | 0.0522864i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0036 | + | 11.2722i | −0.703665 | + | 0.660786i | ||||
\(292\) | 3.10556 | − | 3.75397i | 0.181739 | − | 0.219685i | ||||
\(293\) | 1.91207 | − | 1.38920i | 0.111704 | − | 0.0811581i | −0.530531 | − | 0.847666i | \(-0.678007\pi\) |
0.642235 | + | 0.766508i | \(0.278007\pi\) | |||||||
\(294\) | 3.35533 | + | 1.32847i | 0.195687 | + | 0.0774778i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.8984 | + | 19.2179i | 0.924076 | + | 1.11702i | ||||
\(297\) | −9.98244 | + | 3.95233i | −0.579240 | + | 0.229337i | ||||
\(298\) | −5.10325 | − | 26.7522i | −0.295623 | − | 1.54971i | ||||
\(299\) | −3.75976 | + | 2.73162i | −0.217432 | + | 0.157974i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.7866 | + | 15.8289i | 1.25576 | + | 0.912361i | ||||
\(302\) | 2.45819 | − | 5.22392i | 0.141453 | − | 0.300603i | ||||
\(303\) | −11.5862 | + | 18.2570i | −0.665612 | + | 1.04884i | ||||
\(304\) | −14.2343 | + | 5.63578i | −0.816396 | + | 0.323234i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.687560 | − | 10.9285i | 0.0393052 | − | 0.624738i | ||||
\(307\) | −15.4005 | −0.878950 | −0.439475 | − | 0.898255i | \(-0.644836\pi\) | ||||
−0.439475 | + | 0.898255i | \(0.644836\pi\) | |||||||
\(308\) | −0.230362 | + | 3.66150i | −0.0131261 | + | 0.208633i | ||||
\(309\) | 6.44746 | + | 13.7016i | 0.366783 | + | 0.779455i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.28486 | + | 1.20657i | 0.0728579 | + | 0.0684182i | 0.720121 | − | 0.693849i | \(-0.244086\pi\) |
−0.647263 | + | 0.762267i | \(0.724086\pi\) | |||||||
\(312\) | −38.3806 | + | 4.84860i | −2.17287 | + | 0.274498i | ||||
\(313\) | −29.5069 | + | 3.72758i | −1.66783 | + | 0.210695i | −0.901812 | − | 0.432129i | \(-0.857763\pi\) |
−0.766014 | + | 0.642824i | \(0.777763\pi\) | |||||||
\(314\) | 4.73560 | + | 4.44702i | 0.267245 | + | 0.250960i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.132009 | + | 0.280534i | 0.00742610 | + | 0.0157813i | ||||
\(317\) | −0.388273 | + | 6.17143i | −0.0218076 | + | 0.346622i | 0.971960 | + | 0.235147i | \(0.0755573\pi\) |
−0.993767 | + | 0.111474i | \(0.964443\pi\) | |||||||
\(318\) | 23.6731 | 1.32752 | ||||||||
\(319\) | 0.0562332 | − | 0.893802i | 0.00314846 | − | 0.0500433i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.1625 | + | 9.17069i | −1.29281 | + | 0.511858i | ||||
\(322\) | 1.33553 | − | 2.10446i | 0.0744264 | − | 0.117277i | ||||
\(323\) | 8.77337 | − | 18.6444i | 0.488164 | − | 1.03740i | ||||
\(324\) | −2.96798 | − | 2.15636i | −0.164888 | − | 0.119798i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.20232 | + | 3.77971i | −0.288130 | + | 0.209339i | ||||
\(327\) | −5.14958 | − | 26.9951i | −0.284773 | − | 1.49283i | ||||
\(328\) | 1.69816 | − | 0.672350i | 0.0937654 | − | 0.0371243i | ||||
\(329\) | 6.10307 | + | 7.37734i | 0.336473 | + | 0.406726i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.4519 | + | 10.8690i | 1.50889 | + | 0.597413i | 0.969598 | − | 0.244704i | \(-0.0786907\pi\) |
0.539295 | + | 0.842117i | \(0.318691\pi\) | |||||||
\(332\) | −0.492891 | + | 0.358106i | −0.0270509 | + | 0.0196536i | ||||
\(333\) | −10.3100 | + | 12.4627i | −0.564985 | + | 0.682949i | ||||
\(334\) | 7.21262 | − | 6.77310i | 0.394657 | − | 0.370608i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 15.0764 | − | 8.28832i | 0.822484 | − | 0.452165i | ||||
\(337\) | −14.6391 | + | 13.7470i | −0.797442 | + | 0.748848i | −0.971793 | − | 0.235836i | \(-0.924217\pi\) |
0.174351 | + | 0.984684i | \(0.444217\pi\) | |||||||
\(338\) | 22.9823 | + | 12.6346i | 1.25007 | + | 0.687234i | ||||
\(339\) | 14.1120 | − | 29.9895i | 0.766457 | − | 1.62880i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.41557 | − | 0.557816i | 0.239117 | − | 0.0302074i | ||||
\(342\) | −6.41542 | − | 10.1091i | −0.346906 | − | 0.546637i | ||||
\(343\) | −16.0077 | − | 11.6303i | −0.864333 | − | 0.627975i | ||||
\(344\) | −32.7778 | + | 8.41592i | −1.76726 | + | 0.453756i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.108224 | − | 1.72016i | −0.00581813 | − | 0.0924766i | ||||
\(347\) | −0.696960 | − | 11.0779i | −0.0374148 | − | 0.594690i | −0.971410 | − | 0.237406i | \(-0.923703\pi\) |
0.933996 | − | 0.357284i | \(-0.116297\pi\) | |||||||
\(348\) | 0.125895 | − | 0.0692111i | 0.00674866 | − | 0.00371010i | ||||
\(349\) | −4.53597 | + | 13.9603i | −0.242805 | + | 0.747276i | 0.753185 | + | 0.657809i | \(0.228517\pi\) |
−0.995990 | + | 0.0894676i | \(0.971483\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.15500 | + | 12.7878i | 0.221778 | + | 0.682561i | ||||
\(352\) | −6.24286 | − | 5.86244i | −0.332746 | − | 0.312469i | ||||
\(353\) | 8.24304 | + | 2.11645i | 0.438733 | + | 0.112647i | 0.461594 | − | 0.887091i | \(-0.347278\pi\) |
−0.0228614 | + | 0.999739i | \(0.507278\pi\) | |||||||
\(354\) | 8.46013 | − | 13.3310i | 0.449651 | − | 0.708536i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.501954 | + | 0.606759i | −0.0266035 | + | 0.0321581i | ||||
\(357\) | −7.15561 | + | 22.0227i | −0.378715 | + | 1.16557i | ||||
\(358\) | 18.4341 | − | 4.73306i | 0.974270 | − | 0.250150i | ||||
\(359\) | −23.5213 | − | 12.9310i | −1.24141 | − | 0.682469i | −0.280637 | − | 0.959814i | \(-0.590546\pi\) |
−0.960771 | + | 0.277345i | \(0.910546\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.661508 | − | 3.46774i | −0.0348162 | − | 0.182513i | ||||
\(362\) | 0.296200 | − | 1.55273i | 0.0155679 | − | 0.0816099i | ||||
\(363\) | −9.70015 | − | 20.6139i | −0.509126 | − | 1.08195i | ||||
\(364\) | 4.55837 | + | 0.575856i | 0.238924 | + | 0.0301831i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.39548 | − | 33.5263i | 0.334297 | − | 1.75245i | ||||
\(367\) | −13.9716 | − | 5.53176i | −0.729313 | − | 0.288755i | −0.0260258 | − | 0.999661i | \(-0.508285\pi\) |
−0.703287 | + | 0.710906i | \(0.748285\pi\) | |||||||
\(368\) | 0.802579 | + | 2.47008i | 0.0418373 | + | 0.128762i | ||||
\(369\) | 0.634644 | + | 1.00004i | 0.0330383 | + | 0.0520600i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.1204 | − | 4.90929i | −0.992682 | − | 0.254877i | ||||
\(372\) | 0.455098 | + | 0.550119i | 0.0235957 | + | 0.0285224i | ||||
\(373\) | 4.34579 | + | 0.549001i | 0.225017 | + | 0.0284262i | 0.237033 | − | 0.971502i | \(-0.423825\pi\) |
−0.0120164 | + | 0.999928i | \(0.503825\pi\) | |||||||
\(374\) | −25.8355 | −1.33592 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.0318 | −0.620494 | ||||||||
\(377\) | −1.11273 | − | 0.140571i | −0.0573088 | − | 0.00723978i | ||||
\(378\) | −4.59669 | − | 5.55645i | −0.236428 | − | 0.285793i | ||||
\(379\) | 4.75810 | + | 1.22167i | 0.244407 | + | 0.0627531i | 0.368906 | − | 0.929467i | \(-0.379732\pi\) |
−0.124499 | + | 0.992220i | \(0.539732\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.86193 | + | 2.93393i | 0.0953896 | + | 0.150310i | ||||
\(382\) | 2.74275 | + | 8.44132i | 0.140331 | + | 0.431896i | ||||
\(383\) | 25.0307 | + | 9.91036i | 1.27901 | + | 0.506396i | 0.906725 | − | 0.421723i | \(-0.138574\pi\) |
0.372285 | + | 0.928119i | \(0.378574\pi\) | |||||||
\(384\) | −3.21674 | + | 16.8627i | −0.164154 | + | 0.860523i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.3560 | − | 3.58220i | −1.44328 | − | 0.182329i | ||||
\(387\) | −9.34400 | − | 19.8570i | −0.474982 | − | 1.00939i | ||||
\(388\) | −0.460511 | + | 2.41408i | −0.0233789 | + | 0.122557i | ||||
\(389\) | −2.32366 | − | 12.1810i | −0.117814 | − | 0.617603i | −0.991393 | − | 0.130920i | \(-0.958207\pi\) |
0.873579 | − | 0.486683i | \(-0.161793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.06327 | − | 1.68405i | −0.154916 | − | 0.0851658i | ||||
\(392\) | 3.66278 | − | 0.940441i | 0.184998 | − | 0.0474995i | ||||
\(393\) | −1.61680 | + | 4.97599i | −0.0815567 | + | 0.251006i | ||||
\(394\) | 8.86254 | − | 10.7130i | 0.446488 | − | 0.539712i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.60199 | − | 2.52432i | 0.0805028 | − | 0.126852i | ||||
\(397\) | 31.9058 | + | 8.19202i | 1.60131 | + | 0.411146i | 0.940605 | − | 0.339503i | \(-0.110259\pi\) |
0.660701 | + | 0.750649i | \(0.270259\pi\) | |||||||
\(398\) | 6.71189 | + | 6.30288i | 0.336437 | + | 0.315935i | ||||
\(399\) | 7.82404 | + | 24.0799i | 0.391692 | + | 1.20550i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.45252 | − | 7.54808i | 0.122473 | − | 0.376933i | −0.870959 | − | 0.491355i | \(-0.836502\pi\) |
0.993432 | + | 0.114422i | \(0.0365016\pi\) | |||||||
\(402\) | −2.74328 | + | 1.50813i | −0.136822 | + | 0.0752188i | ||||
\(403\) | −0.349985 | − | 5.56286i | −0.0174340 | − | 0.277106i | ||||
\(404\) | 0.202638 | + | 3.22084i | 0.0100816 | + | 0.160243i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.582633 | − | 0.149595i | 0.0289156 | − | 0.00742426i | ||||
\(407\) | 30.8737 | + | 22.4311i | 1.53035 | + | 1.11187i | ||||
\(408\) | −15.5920 | − | 24.5690i | −0.771917 | − | 1.21635i | ||||
\(409\) | 3.01037 | − | 0.380298i | 0.148853 | − | 0.0188045i | −0.0505535 | − | 0.998721i | \(-0.516099\pi\) |
0.199407 | + | 0.979917i | \(0.436099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.05397 | − | 14.9904i | 0.347946 | − | 0.739424i | ||||
\(412\) | 1.98048 | + | 1.08878i | 0.0975712 | + | 0.0536402i | ||||
\(413\) | −9.59769 | + | 9.01283i | −0.472271 | + | 0.443492i | ||||
\(414\) | −1.77993 | + | 0.978526i | −0.0874789 | + | 0.0480920i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.81834 | + | 7.34191i | −0.383326 | + | 0.359967i | ||||
\(417\) | 10.3219 | − | 12.4770i | 0.505465 | − | 0.611002i | ||||
\(418\) | −22.8538 | + | 16.6043i | −1.11782 | + | 0.812142i | ||||
\(419\) | 7.19409 | + | 2.84834i | 0.351454 | + | 0.139151i | 0.537217 | − | 0.843444i | \(-0.319476\pi\) |
−0.185763 | + | 0.982595i | \(0.559476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1357 | + | 19.5047i | 0.786405 | + | 0.950600i | 0.999651 | − | 0.0263985i | \(-0.00840387\pi\) |
−0.213247 | + | 0.976998i | \(0.568404\pi\) | |||||||
\(422\) | 32.3039 | − | 12.7900i | 1.57253 | − | 0.622608i | ||||
\(423\) | −1.46205 | − | 7.66435i | −0.0710875 | − | 0.372654i | ||||
\(424\) | 20.0692 | − | 14.5811i | 0.974646 | − | 0.708122i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.00374 | + | 0.729260i | 0.0486314 | + | 0.0353328i | ||||
\(427\) | −12.1182 | + | 25.7524i | −0.586439 | + | 1.24625i | ||||
\(428\) | −1.99224 | + | 3.13927i | −0.0962985 | + | 0.151742i | ||||
\(429\) | −55.0344 | + | 21.7897i | −2.65709 | + | 1.05201i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.77100 | + | 28.1492i | −0.0853061 | + | 1.35590i | 0.689768 | + | 0.724031i | \(0.257713\pi\) |
−0.775074 | + | 0.631871i | \(0.782287\pi\) | |||||||
\(432\) | 7.51436 | 0.361535 | ||||||||
\(433\) | 0.599701 | − | 9.53198i | 0.0288198 | − | 0.458078i | −0.956980 | − | 0.290153i | \(-0.906294\pi\) |
0.985800 | − | 0.167924i | \(-0.0537063\pi\) | |||||||
\(434\) | 1.27282 | + | 2.70489i | 0.0610975 | + | 0.129839i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.98995 | − | 2.80775i | −0.143193 | − | 0.134467i | ||||
\(437\) | −3.79206 | + | 0.479048i | −0.181399 | + | 0.0229160i | ||||
\(438\) | −41.8254 | + | 5.28377i | −1.99849 | + | 0.252468i | ||||
\(439\) | 22.0611 | + | 20.7167i | 1.05292 | + | 0.988756i | 0.999952 | − | 0.00984037i | \(-0.00313234\pi\) |
0.0529665 | + | 0.998596i | \(0.483132\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.04415 | + | 2.21893i | 0.0497215 | + | 0.105663i | ||||
\(442\) | −2.03162 | + | 32.2916i | −0.0966342 | + | 1.53596i | ||||
\(443\) | 19.6665 | 0.934382 | 0.467191 | − | 0.884156i | \(-0.345266\pi\) | ||||
0.467191 | + | 0.884156i | \(0.345266\pi\) | |||||||
\(444\) | −0.384394 | + | 6.10977i | −0.0182425 | + | 0.289957i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.5728 | − | 6.16571i | 0.737393 | − | 0.291955i | ||||
\(447\) | 25.1484 | − | 39.6275i | 1.18948 | − | 1.87432i | ||||
\(448\) | 9.03202 | − | 19.1940i | 0.426723 | − | 0.906832i | ||||
\(449\) | 10.1828 | + | 7.39826i | 0.480558 | + | 0.349146i | 0.801542 | − | 0.597939i | \(-0.204014\pi\) |
−0.320984 | + | 0.947085i | \(0.604014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.26081 | − | 1.64258i | 0.106457 | − | 0.0773459i | ||||
\(452\) | −0.926914 | − | 4.85905i | −0.0435984 | − | 0.228551i | ||||
\(453\) | 9.25070 | − | 3.66261i | 0.434636 | − | 0.172084i | ||||
\(454\) | −18.3255 | − | 22.1518i | −0.860061 | − | 1.03963i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −29.5828 | − | 11.7127i | −1.38534 | − | 0.548496i | ||||
\(457\) | −13.6982 | + | 9.95236i | −0.640777 | + | 0.465552i | −0.860117 | − | 0.510097i | \(-0.829610\pi\) |
0.219340 | + | 0.975648i | \(0.429610\pi\) | |||||||
\(458\) | 0.717577 | − | 0.867402i | 0.0335302 | − | 0.0405310i | ||||
\(459\) | −7.37266 | + | 6.92339i | −0.344126 | + | 0.323156i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.03750 | − | 3.86890i | 0.327769 | − | 0.180193i | −0.309369 | − | 0.950942i | \(-0.600118\pi\) |
0.637138 | + | 0.770749i | \(0.280118\pi\) | |||||||
\(462\) | 23.1416 | − | 21.7314i | 1.07664 | − | 1.01104i | ||||
\(463\) | 1.19737 | + | 0.658259i | 0.0556464 | + | 0.0305919i | 0.509334 | − | 0.860569i | \(-0.329892\pi\) |
−0.453688 | + | 0.891161i | \(0.649892\pi\) | |||||||
\(464\) | −0.266881 | + | 0.567151i | −0.0123896 | + | 0.0263293i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.0055 | + | 2.77995i | −1.01939 | + | 0.128779i | ||||
\(467\) | 15.1304 | + | 23.8417i | 0.700152 | + | 1.10326i | 0.989288 | + | 0.145975i | \(0.0466319\pi\) |
−0.289136 | + | 0.957288i | \(0.593368\pi\) | |||||||
\(468\) | −3.02916 | − | 2.20082i | −0.140023 | − | 0.101733i | ||||
\(469\) | 2.52846 | − | 0.649199i | 0.116754 | − | 0.0299772i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.702951 | + | 11.1731i | 0.0323903 | + | 0.514829i | ||||
\(472\) | −1.03888 | − | 16.5125i | −0.0478181 | − | 0.760048i | ||||
\(473\) | −45.3738 | + | 24.9445i | −2.08629 | + | 1.14695i | ||||
\(474\) | 0.829027 | − | 2.55148i | 0.0380785 | − | 0.117194i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.06796 | + | 3.28686i | 0.0489501 | + | 0.150653i | ||||
\(477\) | 11.7270 | + | 11.0124i | 0.536941 | + | 0.504222i | ||||
\(478\) | 33.0673 | + | 8.49025i | 1.51246 | + | 0.388335i | ||||
\(479\) | 21.3622 | − | 33.6614i | 0.976062 | − | 1.53803i | 0.139452 | − | 0.990229i | \(-0.455466\pi\) |
0.836610 | − | 0.547799i | \(-0.184534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.4642 | − | 36.8249i | 1.38905 | − | 1.67907i | ||||
\(482\) | 0.0636932 | − | 0.196027i | 0.00290115 | − | 0.00892881i | ||||
\(483\) | 4.16037 | − | 1.06820i | 0.189304 | − | 0.0486049i | ||||
\(484\) | −2.97961 | − | 1.63806i | −0.135437 | − | 0.0744571i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.25697 | + | 22.3158i | 0.193100 | + | 1.01227i | ||||
\(487\) | 1.91076 | − | 10.0166i | 0.0865848 | − | 0.453893i | −0.912419 | − | 0.409258i | \(-0.865788\pi\) |
0.999003 | − | 0.0446350i | \(-0.0142125\pi\) | |||||||
\(488\) | −15.2282 | − | 32.3616i | −0.689349 | − | 1.46494i | ||||
\(489\) | −10.9943 | − | 1.38890i | −0.497178 | − | 0.0628082i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.157079 | − | 0.823439i | 0.00708889 | − | 0.0371613i | −0.978567 | − | 0.205928i | \(-0.933979\pi\) |
0.985656 | + | 0.168767i | \(0.0539786\pi\) | |||||||
\(492\) | 0.416809 | + | 0.165026i | 0.0187912 | + | 0.00743996i | ||||
\(493\) | −0.260699 | − | 0.802348i | −0.0117413 | − | 0.0361359i | ||||
\(494\) | 18.9564 | + | 29.8706i | 0.852891 | + | 1.34394i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.01714 | − | 0.774671i | −0.135474 | − | 0.0347837i | ||||
\(497\) | −0.659473 | − | 0.797166i | −0.0295814 | − | 0.0357578i | ||||
\(498\) | 5.23024 | + | 0.660733i | 0.234373 | + | 0.0296082i | ||||
\(499\) | 21.9417 | 0.982246 | 0.491123 | − | 0.871090i | \(-0.336586\pi\) | ||||
0.491123 | + | 0.871090i | \(0.336586\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.0510 | 0.761781 | ||||||||
\(502\) | −30.4252 | − | 3.84359i | −1.35794 | − | 0.171548i | ||||
\(503\) | −8.87103 | − | 10.7232i | −0.395540 | − | 0.478125i | 0.534719 | − | 0.845030i | \(-0.320417\pi\) |
−0.930259 | + | 0.366905i | \(0.880417\pi\) | |||||||
\(504\) | 13.6564 | + | 3.50638i | 0.608306 | + | 0.156186i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.56787 | + | 4.04631i | 0.114156 | + | 0.179881i | ||||
\(507\) | 13.9664 | + | 42.9842i | 0.620270 | + | 1.90900i | ||||
\(508\) | 0.482200 | + | 0.190917i | 0.0213942 | + | 0.00847055i | ||||
\(509\) | 1.37195 | − | 7.19204i | 0.0608108 | − | 0.318782i | −0.938864 | − | 0.344289i | \(-0.888120\pi\) |
0.999675 | + | 0.0255072i | \(0.00812008\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.8775 | + | 4.40605i | 1.54289 | + | 0.194912i | ||||
\(512\) | 10.8244 | + | 23.0030i | 0.478374 | + | 1.01660i | ||||
\(513\) | −2.07217 | + | 10.8627i | −0.0914887 | + | 0.479600i | ||||
\(514\) | 6.47457 | + | 33.9409i | 0.285581 | + | 1.49707i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.27875 | − | 4.00153i | −0.320429 | − | 0.176158i | ||||
\(517\) | −17.8310 | + | 4.57821i | −0.784204 | + | 0.201349i | ||||
\(518\) | −7.92086 | + | 24.3779i | −0.348023 | + | 1.07110i | ||||
\(519\) | 1.89331 | − | 2.28862i | 0.0831070 | − | 0.100459i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.92542 | − | 4.60972i | 0.128165 | − | 0.201956i | −0.774185 | − | 0.632959i | \(-0.781840\pi\) |
0.902350 | + | 0.431003i | \(0.141840\pi\) | |||||||
\(522\) | −0.474801 | − | 0.121908i | −0.0207815 | − | 0.00533578i | ||||
\(523\) | 15.0102 | + | 14.0955i | 0.656349 | + | 0.616353i | 0.939429 | − | 0.342743i | \(-0.111356\pi\) |
−0.283080 | + | 0.959096i | \(0.591356\pi\) | |||||||
\(524\) | 0.241305 | + | 0.742659i | 0.0105414 | + | 0.0324432i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.50238 | + | 29.2453i | −0.414324 | + | 1.27516i | ||||
\(527\) | 3.67399 | − | 2.01979i | 0.160042 | − | 0.0879836i | ||||
\(528\) | 2.07708 | + | 33.0142i | 0.0903933 | + | 1.43676i | ||||
\(529\) | −1.40347 | − | 22.3075i | −0.0610203 | − | 0.969890i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3923 | − | 2.66829i | 0.450987 | − | 0.115794i | ||||
\(532\) | 3.05715 | + | 2.22115i | 0.132544 | + | 0.0962990i | ||||
\(533\) | −1.87526 | − | 2.95494i | −0.0812266 | − | 0.127993i | ||||
\(534\) | 6.76028 | − | 0.854022i | 0.292546 | − | 0.0369571i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.39674 | + | 2.96823i | −0.0603300 | + | 0.128208i | ||||
\(537\) | 28.7412 | + | 15.8006i | 1.24027 | + | 0.681847i | ||||
\(538\) | 2.12386 | − | 1.99443i | 0.0915659 | − | 0.0859861i | ||||
\(539\) | 5.07032 | − | 2.78743i | 0.218394 | − | 0.120063i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.5737 | − | 16.5028i | 0.755553 | − | 0.709511i | −0.207675 | − | 0.978198i | \(-0.566590\pi\) |
0.963228 | + | 0.268687i | \(0.0865896\pi\) | |||||||
\(542\) | −11.4165 | + | 13.8002i | −0.490382 | + | 0.592770i | ||||
\(543\) | 2.20385 | − | 1.60119i | 0.0945761 | − | 0.0687135i | ||||
\(544\) | −7.50085 | − | 2.96980i | −0.321596 | − | 0.127329i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −25.3421 | − | 30.6334i | −1.08454 | − | 1.31099i | ||||
\(547\) | −38.2616 | + | 15.1488i | −1.63595 | + | 0.647717i | −0.992991 | − | 0.118186i | \(-0.962292\pi\) |
−0.642955 | + | 0.765904i | \(0.722292\pi\) | |||||||
\(548\) | −0.463324 | − | 2.42883i | −0.0197922 | − | 0.103754i | ||||
\(549\) | 18.7641 | − | 13.6329i | 0.800831 | − | 0.581838i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.746274 | − | 0.542200i | −0.0317923 | − | 0.0230985i | ||||
\(552\) | −2.29822 | + | 4.88397i | −0.0978188 | + | 0.207876i | ||||
\(553\) | −1.19872 | + | 1.88887i | −0.0509746 | + | 0.0803231i | ||||
\(554\) | −32.2391 | + | 12.7644i | −1.36971 | + | 0.542306i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.151752 | − | 2.41203i | 0.00643572 | − | 0.102293i | ||||
\(557\) | 11.6966 | 0.495599 | 0.247799 | − | 0.968811i | \(-0.420293\pi\) | ||||
0.247799 | + | 0.968811i | \(0.420293\pi\) | |||||||
\(558\) | 0.152966 | − | 2.43133i | 0.00647557 | − | 0.102926i | ||||
\(559\) | 27.6099 | + | 58.6740i | 1.16777 | + | 2.48164i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.4557 | − | 30.4779i | −1.37028 | − | 1.28678i | ||||
\(562\) | 26.4392 | − | 3.34005i | 1.11527 | − | 0.140892i | ||||
\(563\) | 25.6113 | − | 3.23546i | 1.07939 | − | 0.136359i | 0.434528 | − | 0.900658i | \(-0.356915\pi\) |
0.644861 | + | 0.764300i | \(0.276915\pi\) | |||||||
\(564\) | −2.15277 | − | 2.02159i | −0.0906481 | − | 0.0851242i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.51557 | − | 3.22074i | −0.0637040 | − | 0.135378i | ||||
\(567\) | 1.66215 | − | 26.4191i | 0.0698036 | − | 1.10950i | ||||
\(568\) | 1.30011 | 0.0545515 | ||||||||
\(569\) | −1.08886 | + | 17.3070i | −0.0456476 | + | 0.725548i | 0.906936 | + | 0.421269i | \(0.138415\pi\) |
−0.952583 | + | 0.304278i | \(0.901585\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.6876 | + | 14.5256i | −1.53533 | + | 0.607879i | −0.975357 | − | 0.220634i | \(-0.929188\pi\) |
−0.559970 | + | 0.828513i | \(0.689188\pi\) | |||||||
\(572\) | −4.73358 | + | 7.45893i | −0.197921 | + | 0.311874i | ||||
\(573\) | −6.51259 | + | 13.8400i | −0.272067 | + | 0.578172i | ||||
\(574\) | 1.51853 | + | 1.10328i | 0.0633822 | + | 0.0460499i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.9854 | + | 10.1610i | −0.582725 | + | 0.423375i | ||||
\(577\) | 0.727434 | + | 3.81334i | 0.0302835 | + | 0.158751i | 0.994217 | − | 0.107393i | \(-0.0342502\pi\) |
−0.963933 | + | 0.266144i | \(0.914250\pi\) | |||||||
\(578\) | −2.21548 | + | 0.877172i | −0.0921519 | + | 0.0364855i | ||||
\(579\) | −31.3962 | − | 37.9515i | −1.30478 | − | 1.57721i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.08737 | − | 1.61830i | −0.169573 | − | 0.0671385i | ||||
\(582\) | 17.2044 | − | 12.4997i | 0.713143 | − | 0.518129i | ||||
\(583\) | 24.1939 | − | 29.2454i | 1.00201 | − | 1.21122i | ||||
\(584\) | −32.2036 | + | 30.2412i | −1.33259 | + | 1.25139i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.67473 | + | 1.47044i | −0.110492 | + | 0.0607435i | ||||
\(587\) | 9.27951 | − | 8.71404i | 0.383006 | − | 0.359667i | −0.469000 | − | 0.883198i | \(-0.655386\pi\) |
0.852007 | + | 0.523531i | \(0.175386\pi\) | |||||||
\(588\) | 0.813368 | + | 0.447153i | 0.0335427 | + | 0.0184403i | ||||
\(589\) | 1.95187 | − | 4.14794i | 0.0804254 | − | 0.170913i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.7715 | − | 3.00304i | 0.977829 | − | 0.123529i | ||||
\(592\) | −14.3116 | − | 22.5515i | −0.588205 | − | 0.926863i | ||||
\(593\) | 24.0634 | + | 17.4831i | 0.988166 | + | 0.717945i | 0.959519 | − | 0.281645i | \(-0.0908800\pi\) |
0.0286475 | + | 0.999590i | \(0.490880\pi\) | |||||||
\(594\) | 13.4299 | − | 3.44820i | 0.551034 | − | 0.141482i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.439834 | − | 6.99097i | −0.0180163 | − | 0.286361i | ||||
\(597\) | 0.996311 | + | 15.8359i | 0.0407763 | + | 0.648121i | ||||
\(598\) | 5.25939 | − | 2.89137i | 0.215072 | − | 0.118237i | ||||
\(599\) | 12.5249 | − | 38.5477i | 0.511754 | − | 1.57502i | −0.277358 | − | 0.960767i | \(-0.589459\pi\) |
0.789112 | − | 0.614250i | \(-0.210541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.17440 | − | 12.8475i | −0.170277 | − | 0.524059i | 0.829109 | − | 0.559087i | \(-0.188848\pi\) |
−0.999386 | + | 0.0350274i | \(0.988848\pi\) | |||||||
\(602\) | −25.3523 | − | 23.8074i | −1.03328 | − | 0.970316i | ||||
\(603\) | −2.06050 | − | 0.529048i | −0.0839102 | − | 0.0215445i | ||||
\(604\) | 0.795665 | − | 1.25377i | 0.0323751 | − | 0.0510151i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 17.8001 | − | 21.5166i | 0.723080 | − | 0.874054i | ||||
\(607\) | −2.54307 | + | 7.82677i | −0.103220 | + | 0.317679i | −0.989309 | − | 0.145837i | \(-0.953412\pi\) |
0.886089 | + | 0.463516i | \(0.153412\pi\) | |||||||
\(608\) | −8.54385 | + | 2.19369i | −0.346499 | + | 0.0889657i | ||||
\(609\) | 0.908404 | + | 0.499399i | 0.0368104 | + | 0.0202367i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.32011 | + | 22.6468i | 0.174773 | + | 0.916192i | ||||
\(612\) | 0.527737 | − | 2.76649i | 0.0213325 | − | 0.111829i | ||||
\(613\) | −5.52546 | − | 11.7422i | −0.223171 | − | 0.474263i | 0.761616 | − | 0.648029i | \(-0.224406\pi\) |
−0.984787 | + | 0.173766i | \(0.944406\pi\) | |||||||
\(614\) | 19.7320 | + | 2.49274i | 0.796320 | + | 0.100599i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.23343 | − | 32.6768i | 0.251152 | − | 1.31659i | ||||
\(617\) | 12.4029 | + | 4.91066i | 0.499322 | + | 0.197696i | 0.604266 | − | 0.796782i | \(-0.293466\pi\) |
−0.104944 | + | 0.994478i | \(0.533466\pi\) | |||||||
\(618\) | −6.04315 | − | 18.5989i | −0.243091 | − | 0.748158i | ||||
\(619\) | −12.2030 | − | 19.2288i | −0.490480 | − | 0.772872i | 0.505464 | − | 0.862847i | \(-0.331321\pi\) |
−0.995944 | + | 0.0899752i | \(0.971321\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.81712 | + | 0.466557i | 0.0729185 | + | 0.0187223i | ||||
\(622\) | −1.45095 | − | 1.75390i | −0.0581779 | − | 0.0703250i | ||||
\(623\) | −5.63728 | − | 0.712155i | −0.225853 | − | 0.0285319i | ||||
\(624\) | 41.4276 | 1.65843 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 38.4094 | 1.53515 | ||||||||
\(627\) | −48.2979 | − | 6.10145i | −1.92883 | − | 0.243668i | ||||
\(628\) | 1.06505 | + | 1.28742i | 0.0425000 | + | 0.0513737i | ||||
\(629\) | 34.8197 | + | 8.94018i | 1.38835 | + | 0.356468i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.01367 | + | 4.74878i | 0.119972 | + | 0.189046i | 0.899006 | − | 0.437936i | \(-0.144290\pi\) |
−0.779034 | + | 0.626981i | \(0.784290\pi\) | |||||||
\(632\) | −0.868732 | − | 2.67368i | −0.0345563 | − | 0.106353i | ||||
\(633\) | 55.6698 | + | 22.0412i | 2.21268 | + | 0.876060i | ||||
\(634\) | 1.49640 | − | 7.84438i | 0.0594295 | − | 0.311540i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.04076 | + | 0.763126i | 0.239532 | + | 0.0302599i | ||||
\(637\) | −3.08528 | − | 6.55656i | −0.122243 | − | 0.259780i | ||||
\(638\) | −0.216722 | + | 1.13609i | −0.00858009 | + | 0.0449784i | ||||
\(639\) | 0.157984 | + | 0.828180i | 0.00624974 | + | 0.0327623i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.06472 | + | 3.88386i | 0.279040 | + | 0.153403i | 0.615128 | − | 0.788427i | \(-0.289104\pi\) |
−0.336089 | + | 0.941830i | \(0.609104\pi\) | |||||||
\(642\) | 31.1617 | − | 8.00096i | 1.22985 | − | 0.315773i | ||||
\(643\) | −10.1454 | + | 31.2243i | −0.400095 | + | 1.23137i | 0.524827 | + | 0.851209i | \(0.324130\pi\) |
−0.924922 | + | 0.380157i | \(0.875870\pi\) | |||||||
\(644\) | 0.408633 | − | 0.493953i | 0.0161024 | − | 0.0194645i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.2588 | + | 22.4683i | −0.561005 | + | 0.884003i | ||||
\(647\) | 26.8836 | + | 6.90254i | 1.05690 | + | 0.271367i | 0.736866 | − | 0.676038i | \(-0.236305\pi\) |
0.320037 | + | 0.947405i | \(0.396305\pi\) | |||||||
\(648\) | 24.2491 | + | 22.7714i | 0.952595 | + | 0.894546i | ||||
\(649\) | −7.82272 | − | 24.0759i | −0.307069 | − | 0.945060i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.59196 | + | 4.89954i | −0.0623937 | + | 0.192028i | ||||
\(652\) | −1.44934 | + | 0.796782i | −0.0567606 | + | 0.0312044i | ||||
\(653\) | 1.02010 | + | 16.2141i | 0.0399198 | + | 0.634507i | 0.966220 | + | 0.257720i | \(0.0829712\pi\) |
−0.926300 | + | 0.376787i | \(0.877029\pi\) | |||||||
\(654\) | 2.22852 | + | 35.4213i | 0.0871421 | + | 1.38508i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.89443 | + | 0.486406i | −0.0739649 | + | 0.0189910i | ||||
\(657\) | −23.1770 | − | 16.8391i | −0.904222 | − | 0.656956i | ||||
\(658\) | −6.62554 | − | 10.4402i | −0.258290 | − | 0.407000i | ||||
\(659\) | 15.2615 | − | 1.92797i | 0.594503 | − | 0.0751032i | 0.177676 | − | 0.984089i | \(-0.443142\pi\) |
0.416827 | + | 0.908986i | \(0.363142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.75412 | − | 18.6034i | 0.340496 | − | 0.723590i | −0.659099 | − | 0.752056i | \(-0.729062\pi\) |
0.999595 | + | 0.0284660i | \(0.00906223\pi\) | |||||||
\(662\) | −33.4139 | − | 18.3694i | −1.29867 | − | 0.713948i | ||||
\(663\) | −40.6464 | + | 38.1695i | −1.57857 | + | 1.48238i | ||||
\(664\) | 4.84098 | − | 2.66135i | 0.187866 | − | 0.103280i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.2271 | − | 14.2992i | 0.590036 | − | 0.554081i | ||||
\(667\) | −0.0997506 | + | 0.120578i | −0.00386236 | + | 0.00466879i | ||||
\(668\) | 2.05881 | − | 1.49581i | 0.0796578 | − | 0.0578748i | ||||
\(669\) | 26.8369 | + | 10.6255i | 1.03757 | + | 0.410804i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.8818 | − | 42.1648i | −1.34660 | − | 1.62775i | ||||
\(672\) | 9.21674 | − | 3.64917i | 0.355543 | − | 0.140770i | ||||
\(673\) | −4.07318 | − | 21.3524i | −0.157010 | − | 0.823073i | −0.970427 | − | 0.241393i | \(-0.922396\pi\) |
0.813418 | − | 0.581680i | \(-0.197604\pi\) | |||||||
\(674\) | 20.9816 | − | 15.2441i | 0.808183 | − | 0.587179i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.45720 | + | 3.96489i | 0.209892 | + | 0.152496i | ||||
\(677\) | 3.07517 | − | 6.53506i | 0.118188 | − | 0.251163i | −0.836976 | − | 0.547240i | \(-0.815679\pi\) |
0.955164 | + | 0.296077i | \(0.0956785\pi\) | |||||||
\(678\) | −22.9353 | + | 36.1403i | −0.880825 | + | 1.38796i | ||||
\(679\) | −16.4879 | + | 6.52801i | −0.632746 | + | 0.250522i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.11091 | − | 49.4465i | 0.119210 | − | 1.89479i | ||||
\(682\) | −5.74780 | −0.220095 | ||||||||
\(683\) | −1.63344 | + | 25.9627i | −0.0625017 | + | 0.993436i | 0.834387 | + | 0.551179i | \(0.185822\pi\) |
−0.896888 | + | 0.442257i | \(0.854178\pi\) | |||||||
\(684\) | −1.31117 | − | 2.78639i | −0.0501340 | − | 0.106540i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.6276 | + | 17.4924i | 0.711204 | + | 0.667865i | ||||
\(687\) | 1.92472 | − | 0.243148i | 0.0734326 | − | 0.00927669i | ||||
\(688\) | 35.9538 | − | 4.54202i | 1.37073 | − | 0.173163i | ||||
\(689\) | −34.6511 | − | 32.5396i | −1.32010 | − | 1.23966i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.4999 | − | 26.5637i | −0.475520 | − | 1.01053i | −0.988372 | − | 0.152054i | \(-0.951411\pi\) |
0.512853 | − | 0.858477i | \(-0.328589\pi\) | |||||||
\(692\) | 0.0278353 | − | 0.442430i | 0.00105814 | − | 0.0168187i | ||||
\(693\) | 21.5728 | 0.819482 | ||||||||
\(694\) | −0.900087 | + | 14.3065i | −0.0341668 | + | 0.543066i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.21119 | + | 0.479545i | −0.0459102 | + | 0.0181771i | ||||
\(697\) | 1.41055 | − | 2.22267i | 0.0534284 | − | 0.0841897i | ||||
\(698\) | 8.07140 | − | 17.1526i | 0.305507 | − | 0.649236i | ||||
\(699\) | −30.9238 | − | 22.4675i | −1.16965 | − | 0.849797i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.21119 | − | 5.96578i | 0.310132 | − | 0.225324i | −0.421821 | − | 0.906679i | \(-0.638609\pi\) |
0.731953 | + | 0.681355i | \(0.238609\pi\) | |||||||
\(702\) | −3.25381 | − | 17.0571i | −0.122807 | − | 0.643777i | ||||
\(703\) | 36.5470 | − | 14.4700i | 1.37839 | − | 0.545745i | ||||
\(704\) | 25.9984 | + | 31.4267i | 0.979851 | + | 1.18444i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.2189 | − | 4.04596i | −0.384595 | − | 0.152272i | ||||
\(707\) | −18.8390 | + | 13.6873i | −0.708513 | + | 0.514765i | ||||
\(708\) | 2.58855 | − | 3.12901i | 0.0972835 | − | 0.117596i | ||||
\(709\) | 34.1604 | − | 32.0788i | 1.28292 | − | 1.20474i | 0.316264 | − | 0.948671i | \(-0.397571\pi\) |
0.966658 | − | 0.256072i | \(-0.0824286\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.59759 | − | 0.878282i | 0.0599142 | − | 0.0329381i | ||||
\(712\) | 5.20510 | − | 4.88791i | 0.195069 | − | 0.183182i | ||||
\(713\) | −0.681506 | − | 0.374661i | −0.0255226 | − | 0.0140312i | ||||
\(714\) | 12.7329 | − | 27.0587i | 0.476515 | − | 1.01265i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.85647 | − | 0.613515i | 0.181495 | − | 0.0229281i | ||||
\(717\) | 31.5247 | + | 49.6751i | 1.17731 | + | 1.85515i | ||||
\(718\) | 28.0440 | + | 20.3752i | 1.04659 | + | 0.760394i | ||||
\(719\) | −22.1441 | + | 5.68564i | −0.825835 | + | 0.212038i | −0.637877 | − | 0.770138i | \(-0.720187\pi\) |
−0.187959 | + | 0.982177i | \(0.560187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.02395 | + | 16.2753i | 0.0381341 | + | 0.606123i | ||||
\(722\) | 0.286272 | + | 4.55017i | 0.0106540 | + | 0.169340i | ||||
\(723\) | 0.311266 | − | 0.171120i | 0.0115761 | − | 0.00636402i | ||||
\(724\) | 0.125636 | − | 0.386669i | 0.00466924 | − | 0.0143704i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.09187 | + | 27.9819i | 0.337431 | + | 1.03851i | ||||
\(727\) | 8.51386 | + | 7.99505i | 0.315762 | + | 0.296520i | 0.826180 | − | 0.563406i | \(-0.190509\pi\) |
−0.510418 | + | 0.859926i | \(0.670509\pi\) | |||||||
\(728\) | −40.3524 | − | 10.3607i | −1.49556 | − | 0.383994i | ||||
\(729\) | −3.22394 | + | 5.08011i | −0.119405 | + | 0.188152i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.0910 | + | 37.5826i | −1.14994 | + | 1.39004i | ||||
\(732\) | 2.71272 | − | 8.34888i | 0.100265 | − | 0.308583i | ||||
\(733\) | −16.9311 | + | 4.34718i | −0.625366 | + | 0.160567i | −0.548058 | − | 0.836441i | \(-0.684633\pi\) |
−0.0773083 | + | 0.997007i | \(0.524633\pi\) | |||||||
\(734\) | 17.0060 | + | 9.34911i | 0.627702 | + | 0.345082i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.280407 | + | 1.46995i | 0.0103360 | + | 0.0541830i | ||||
\(737\) | −0.940510 | + | 4.93033i | −0.0346441 | + | 0.181611i | ||||
\(738\) | −0.651279 | − | 1.38404i | −0.0239739 | − | 0.0509472i | ||||
\(739\) | −11.5925 | − | 1.46448i | −0.426439 | − | 0.0538717i | −0.0908148 | − | 0.995868i | \(-0.528947\pi\) |
−0.335624 | + | 0.941996i | \(0.608947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.4241 | + | 59.8875i | −0.419676 | + | 2.20002i | ||||
\(742\) | 23.7037 | + | 9.38495i | 0.870189 | + | 0.344532i | ||||
\(743\) | −6.81750 | − | 20.9821i | −0.250110 | − | 0.769759i | −0.994754 | − | 0.102297i | \(-0.967381\pi\) |
0.744644 | − | 0.667462i | \(-0.232619\pi\) | |||||||
\(744\) | −3.46885 | − | 5.46603i | −0.127174 | − | 0.200394i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.47925 | − | 1.40683i | −0.200609 | − | 0.0515078i | ||||
\(747\) | 2.28355 | + | 2.76034i | 0.0835508 | + | 0.100996i | ||||
\(748\) | −6.59256 | − | 0.832834i | −0.241048 | − | 0.0304514i | ||||
\(749\) | −26.8281 | −0.980276 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.3393 | −0.778684 | −0.389342 | − | 0.921093i | \(-0.627298\pi\) | ||||
−0.389342 | + | 0.921093i | \(0.627298\pi\) | |||||||
\(752\) | 12.7830 | + | 1.61487i | 0.466149 | + | 0.0588883i | ||||
\(753\) | −33.6872 | − | 40.7208i | −1.22763 | − | 1.48395i | ||||
\(754\) | 1.40295 | + | 0.360217i | 0.0510926 | + | 0.0131183i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.993840 | − | 1.56604i | −0.0361456 | − | 0.0569563i | ||||
\(757\) | 0.725104 | + | 2.23164i | 0.0263544 | + | 0.0811104i | 0.963369 | − | 0.268181i | \(-0.0864224\pi\) |
−0.937014 | + | 0.349291i | \(0.886422\pi\) | |||||||
\(758\) | −5.89864 | − | 2.33544i | −0.214248 | − | 0.0848269i | ||||
\(759\) | −1.54753 | + | 8.11245i | −0.0561718 | + | 0.294463i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.4792 | − | 4.73473i | −1.35862 | − | 0.171634i | −0.587966 | − | 0.808886i | \(-0.700071\pi\) |
−0.770656 | + | 0.637252i | \(0.780071\pi\) | |||||||
\(762\) | −1.91073 | − | 4.06052i | −0.0692186 | − | 0.147097i | ||||
\(763\) | 5.54567 | − | 29.0714i | 0.200767 | − | 1.05246i | ||||
\(764\) | 0.427765 | + | 2.24242i | 0.0154760 | + | 0.0811280i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.4668 | − | 16.7493i | −1.10081 | − | 0.605176i | ||||
\(767\) | −30.7074 | + | 7.88432i | −1.10878 | + | 0.284686i | ||||
\(768\) | −5.32301 | + | 16.3825i | −0.192077 | + | 0.591154i | ||||
\(769\) | −14.5843 | + | 17.6294i | −0.525924 | + | 0.635732i | −0.964853 | − | 0.262789i | \(-0.915358\pi\) |
0.438930 | + | 0.898521i | \(0.355358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.9061 | + | 50.2760i | −1.14907 | + | 1.81065i | ||||
\(772\) | −7.12025 | − | 1.82817i | −0.256263 | − | 0.0657972i | ||||
\(773\) | −17.2344 | − | 16.1842i | −0.619880 | − | 0.582106i | 0.309651 | − | 0.950850i | \(-0.399788\pi\) |
−0.929531 | + | 0.368744i | \(0.879788\pi\) | |||||||
\(774\) | 8.75805 | + | 26.9545i | 0.314802 | + | 0.968860i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.88621 | − | 21.1936i | 0.247200 | − | 0.760805i | ||||
\(777\) | −38.7089 | + | 21.2804i | −1.38868 | + | 0.763431i | ||||
\(778\) | 1.00558 | + | 15.9832i | 0.0360518 | + | 0.573027i | ||||
\(779\) | −0.180735 | − | 2.87270i | −0.00647551 | − | 0.102925i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.92674 | − | 0.494703i | 0.0689443 | − | 0.0177019i | ||||
\(782\) | 3.65227 | + | 2.65353i | 0.130605 | + | 0.0948901i | ||||
\(783\) | 0.242604 | + | 0.382283i | 0.00866996 | + | 0.0136617i | ||||
\(784\) | −4.01768 | + | 0.507551i | −0.143489 | + | 0.0181268i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.87697 | − | 6.11387i | 0.102618 | − | 0.218074i | ||||
\(787\) | −7.27172 | − | 3.99766i | −0.259209 | − | 0.142501i | 0.346851 | − | 0.937920i | \(-0.387251\pi\) |
−0.606060 | + | 0.795419i | \(0.707251\pi\) | |||||||
\(788\) | 2.60683 | − | 2.44798i | 0.0928646 | − | 0.0872057i | ||||
\(789\) | −46.4378 | + | 25.5294i | −1.65323 | + | 0.908870i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.0192 | − | 24.4337i | 0.925137 | − | 0.868761i | ||||
\(792\) | −17.2801 | + | 20.8881i | −0.614022 | + | 0.742225i | ||||
\(793\) | −55.4445 | + | 40.2828i | −1.96889 | + | 1.43048i | ||||
\(794\) | −39.5538 | − | 15.6604i | −1.40371 | − | 0.555769i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.50952 | + | 1.82470i | 0.0535036 | + | 0.0646747i | ||||
\(797\) | 12.2094 | − | 4.83404i | 0.432479 | − | 0.171231i | −0.141791 | − | 0.989897i | \(-0.545286\pi\) |
0.574270 | + | 0.818666i | \(0.305286\pi\) | |||||||
\(798\) | −6.12706 | − | 32.1192i | −0.216895 | − | 1.13701i | ||||
\(799\) | −14.0298 | + | 10.1933i | −0.496340 | + | 0.360612i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.74613 | + | 2.72172i | 0.132363 | + | 0.0961673i | ||||
\(802\) | −4.36407 | + | 9.27412i | −0.154101 | + | 0.327481i | ||||
\(803\) | −36.2181 | + | 57.0706i | −1.27811 | + | 2.01398i | ||||
\(804\) | −0.748631 | + | 0.296404i | −0.0264022 | + | 0.0104534i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.451988 | + | 7.18414i | −0.0159206 | + | 0.253050i | ||||
\(807\) | 5.02090 | 0.176744 | ||||||||
\(808\) | 1.83741 | − | 29.2048i | 0.0646398 | − | 1.02742i | ||||
\(809\) | 12.0325 | + | 25.5705i | 0.423042 | + | 0.899009i | 0.996796 | + | 0.0799821i | \(0.0254863\pi\) |
−0.573755 | + | 0.819027i | \(0.694514\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.0019 | + | 37.5643i | 1.40466 | + | 1.31906i | 0.885700 | + | 0.464259i | \(0.153679\pi\) |
0.518956 | + | 0.854801i | \(0.326321\pi\) | |||||||
\(812\) | 0.153495 | − | 0.0193909i | 0.00538662 | − | 0.000680489i | ||||
\(813\) | −30.6220 | + | 3.86845i | −1.07396 | + | 0.135673i | ||||
\(814\) | −35.9266 | − | 33.7374i | −1.25923 | − | 1.18249i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.2679 | + | 28.1956i | 0.464468 | + | 0.987045i | ||||
\(817\) | −3.34877 | + | 53.2271i | −0.117159 | + | 1.86218i | ||||
\(818\) | −3.91863 | −0.137012 | ||||||||
\(819\) | 1.69641 | − | 26.9637i | 0.0592774 | − | 0.942187i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.58760 | − | 3.40007i | 0.299709 | − | 0.118663i | −0.213457 | − | 0.976952i | \(-0.568472\pi\) |
0.513166 | + | 0.858289i | \(0.328472\pi\) | |||||||
\(822\) | −11.4644 | + | 18.0649i | −0.399866 | + | 0.630087i | ||||
\(823\) | 14.6404 | − | 31.1123i | 0.510331 | − | 1.08451i | −0.469178 | − | 0.883104i | \(-0.655450\pi\) |
0.979508 | − | 0.201404i | \(-0.0645504\pi\) | |||||||
\(824\) | −16.5789 | − | 12.0453i | −0.577554 | − | 0.419617i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.7560 | − | 9.99432i | 0.478632 | − | 0.347747i | ||||
\(827\) | −1.22971 | − | 6.44636i | −0.0427612 | − | 0.224162i | 0.954491 | − | 0.298238i | \(-0.0963991\pi\) |
−0.997253 | + | 0.0740766i | \(0.976399\pi\) | |||||||
\(828\) | −0.485737 | + | 0.192317i | −0.0168805 | + | 0.00668347i | ||||
\(829\) | −28.4362 | − | 34.3734i | −0.987629 | − | 1.19384i | −0.981029 | − | 0.193860i | \(-0.937899\pi\) |
−0.00659956 | − | 0.999978i | \(-0.502101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −55.5581 | − | 21.9970i | −1.92729 | − | 0.763068i | ||||
\(832\) | 41.3244 | − | 30.0239i | 1.43267 | − | 1.04089i | ||||
\(833\) | 3.47428 | − | 4.19969i | 0.120377 | − | 0.145510i | ||||
\(834\) | −15.2446 | + | 14.3156i | −0.527877 | + | 0.495710i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.36697 | + | 3.50027i | −0.220206 | + | 0.121059i | ||||
\(837\) | −1.64024 | + | 1.54029i | −0.0566951 | + | 0.0532403i | ||||
\(838\) | −8.75649 | − | 4.81392i | −0.302488 | − | 0.166294i | ||||
\(839\) | −6.30331 | + | 13.3952i | −0.217615 | + | 0.462454i | −0.983591 | − | 0.180415i | \(-0.942256\pi\) |
0.765976 | + | 0.642869i | \(0.222256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7339 | − | 3.62993i | 0.990823 | − | 0.125170i | ||||
\(842\) | −17.5170 | − | 27.6024i | −0.603676 | − | 0.951241i | ||||
\(843\) | 37.1544 | + | 26.9942i | 1.27966 | + | 0.929731i | ||||
\(844\) | 8.65541 | − | 2.22233i | 0.297932 | − | 0.0764958i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.632714 | + | 10.0567i | 0.0217532 | + | 0.345757i | ||||
\(847\) | −1.54053 | − | 24.4860i | −0.0529332 | − | 0.841349i | ||||
\(848\) | −23.2792 | + | 12.7979i | −0.799411 | + | 0.439480i | ||||
\(849\) | 1.89556 | − | 5.83394i | 0.0650555 | − | 0.200220i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.06064 | − | 6.34199i | −0.0706378 | − | 0.217401i | ||||
\(852\) | 0.232620 | + | 0.218445i | 0.00796944 | + | 0.00748380i | ||||
\(853\) | 4.73615 | + | 1.21604i | 0.162163 | + | 0.0416363i | 0.328898 | − | 0.944365i | \(-0.393323\pi\) |
−0.166736 | + | 0.986002i | \(0.553323\pi\) | |||||||
\(854\) | 19.6949 | − | 31.0342i | 0.673945 | − | 1.06197i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.4897 | − | 25.9765i | 0.734501 | − | 0.887860i | ||||
\(857\) | 7.31615 | − | 22.5168i | 0.249915 | − | 0.769159i | −0.744874 | − | 0.667205i | \(-0.767490\pi\) |
0.994789 | − | 0.101954i | \(-0.0325096\pi\) | |||||||
\(858\) | 74.0405 | − | 19.0104i | 2.52770 | − | 0.649003i | ||||
\(859\) | 12.2950 | + | 6.75925i | 0.419501 | + | 0.230623i | 0.677500 | − | 0.735522i | \(-0.263063\pi\) |
−0.257999 | + | 0.966145i | \(0.583063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.606118 | + | 3.17738i | 0.0206564 | + | 0.108285i | ||||
\(862\) | 6.82539 | − | 35.7800i | 0.232474 | − | 1.21867i | ||||
\(863\) | 10.4325 | + | 22.1702i | 0.355127 | + | 0.754683i | 0.999953 | − | 0.00964574i | \(-0.00307038\pi\) |
−0.644827 | + | 0.764329i | \(0.723070\pi\) | |||||||
\(864\) | 4.29548 | + | 0.542645i | 0.146135 | + | 0.0184612i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.31123 | + | 12.1159i | −0.0785389 | + | 0.411715i | ||||
\(867\) | −3.81798 | − | 1.51164i | −0.129665 | − | 0.0513381i | ||||
\(868\) | 0.237597 | + | 0.731249i | 0.00806457 | + | 0.0248202i | ||||
\(869\) | −2.30480 | − | 3.63179i | −0.0781851 | − | 0.123200i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.08843 | + | 1.56324i | 0.206298 | + | 0.0529684i | ||||
\(872\) | 23.7065 | + | 28.6563i | 0.802805 | + | 0.970424i | ||||
\(873\) | 14.3372 | + | 1.81121i | 0.485241 | + | 0.0613002i | ||||
\(874\) | 4.93617 | 0.166968 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.8431 | −0.366354 | ||||||||
\(877\) | 54.9784 | + | 6.94538i | 1.85649 | + | 0.234529i | 0.972487 | − | 0.232956i | \(-0.0748399\pi\) |
0.884001 | + | 0.467485i | \(0.154840\pi\) | |||||||
\(878\) | −24.9128 | − | 30.1144i | −0.840768 | − | 1.01631i | ||||
\(879\) | −5.09478 | − | 1.30812i | −0.171843 | − | 0.0441217i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.0306 | − | 45.7449i | −0.978065 | − | 1.54118i | −0.834109 | − | 0.551600i | \(-0.814018\pi\) |
−0.143956 | − | 0.989584i | \(-0.545982\pi\) | |||||||
\(882\) | −0.978673 | − | 3.01205i | −0.0329536 | − | 0.101421i | ||||
\(883\) | −9.86984 | − | 3.90775i | −0.332147 | − | 0.131506i | 0.196131 | − | 0.980578i | \(-0.437162\pi\) |
−0.528278 | + | 0.849071i | \(0.677162\pi\) | |||||||
\(884\) | −1.55937 | + | 8.17450i | −0.0524473 | + | 0.274938i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.1979 | − | 3.18324i | −0.846542 | − | 0.106943i | ||||
\(887\) | −20.1688 | − | 42.8609i | −0.677202 | − | 1.43913i | −0.887181 | − | 0.461422i | \(-0.847339\pi\) |
0.209978 | − | 0.977706i | \(-0.432661\pi\) | |||||||
\(888\) | 10.4014 | − | 54.5262i | 0.349049 | − | 1.82978i | ||||
\(889\) | 0.701209 | + | 3.67587i | 0.0235178 | + | 0.123285i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.6015 | + | 24.5199i | 1.49421 | + | 0.821446i | ||||
\(892\) | 4.17253 | − | 1.07132i | 0.139707 | − | 0.0358706i | ||||
\(893\) | −5.85951 | + | 18.0337i | −0.196081 | + | 0.603476i | ||||
\(894\) | −38.6358 | + | 46.7027i | −1.29218 | + | 1.56197i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.90595 | + | 15.6093i | −0.330934 | + | 0.521469i | ||||
\(897\) | 10.0180 | + | 2.57218i | 0.334491 | + | 0.0858828i | ||||
\(898\) | −11.8494 | − | 11.1273i | −0.395420 | − | 0.371324i | ||||
\(899\) | −0.0579993 | − | 0.178504i | −0.00193439 | − | 0.00595343i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0489 | − | 34.0049i | 0.368091 | − | 1.13287i | ||||
\(902\) | −3.16257 | + | 1.73864i | −0.105302 | + | 0.0578902i | ||||
\(903\) | −3.76329 | − | 59.8157i | −0.125234 | − | 1.99054i | ||||
\(904\) | 2.81638 | + | 44.7651i | 0.0936714 | + | 1.48886i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12.4454 | + | 3.19544i | −0.413471 | + | 0.106161i | ||||
\(907\) | −24.0545 | − | 17.4766i | −0.798715 | − | 0.580300i | 0.111822 | − | 0.993728i | \(-0.464331\pi\) |
−0.910537 | + | 0.413428i | \(0.864331\pi\) | |||||||
\(908\) | −3.96212 | − | 6.24330i | −0.131488 | − | 0.207191i | ||||
\(909\) | 18.8269 | − | 2.37839i | 0.624449 | − | 0.0788862i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.0778 | + | 23.5416i | −0.367025 | + | 0.779968i | 0.632958 | + | 0.774186i | \(0.281841\pi\) |
−0.999983 | + | 0.00578219i | \(0.998159\pi\) | |||||||
\(912\) | 29.8577 | + | 16.4144i | 0.988688 | + | 0.543536i | ||||
\(913\) | 6.16158 | − | 5.78611i | 0.203918 | − | 0.191492i | ||||
\(914\) | 19.1620 | − | 10.5344i | 0.633822 | − | 0.348446i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.211069 | − | 0.198207i | 0.00697391 | − | 0.00654893i | ||||
\(917\) | −3.59157 | + | 4.34146i | −0.118604 | + | 0.143368i | ||||
\(918\) | 10.5670 | − | 7.67734i | 0.348761 | − | 0.253390i | ||||
\(919\) | −25.5410 | − | 10.1124i | −0.842521 | − | 0.333577i | −0.0930878 | − | 0.995658i | \(-0.529674\pi\) |
−0.749433 | + | 0.662080i | \(0.769674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.8476 | + | 26.4092i | 0.719903 | + | 0.870213i | ||||
\(922\) | −9.64312 | + | 3.81798i | −0.317579 | + | 0.125739i | ||||
\(923\) | −0.466814 | − | 2.44712i | −0.0153654 | − | 0.0805481i | ||||
\(924\) | 6.60566 | − | 4.79930i | 0.217310 | − | 0.157885i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.42760 | − | 1.03721i | −0.0469138 | − | 0.0340849i | ||||
\(927\) | 5.65833 | − | 12.0246i | 0.185844 | − | 0.394938i | ||||
\(928\) | −0.193515 | + | 0.304931i | −0.00635245 | + | 0.0100099i | ||||
\(929\) | 39.3131 | − | 15.5652i | 1.28982 | − | 0.510677i | 0.379735 | − | 0.925095i | \(-0.376015\pi\) |
0.910086 | + | 0.414419i | \(0.136015\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.374210 | − | 5.94789i | 0.0122642 | − | 0.194934i | ||||
\(932\) | −5.70486 | −0.186869 | ||||||||
\(933\) | 0.246311 | − | 3.91500i | 0.00806386 | − | 0.128171i | ||||
\(934\) | −15.5270 | − | 32.9966i | −0.508059 | − | 1.07968i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 24.7490 | + | 23.2409i | 0.808947 | + | 0.759651i | ||||
\(937\) | 24.5658 | − | 3.10338i | 0.802528 | − | 0.101383i | 0.286640 | − | 0.958038i | \(-0.407462\pi\) |
0.515889 | + | 0.856656i | \(0.327462\pi\) | |||||||
\(938\) | −3.34471 | + | 0.422535i | −0.109209 | + | 0.0137963i | ||||
\(939\) | 48.2516 | + | 45.3113i | 1.57463 | + | 1.47868i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.92949 | + | 16.8510i | 0.258494 | + | 0.549328i | 0.991379 | − | 0.131025i | \(-0.0418267\pi\) |
−0.732885 | + | 0.680353i | \(0.761827\pi\) | |||||||
\(942\) | 0.907824 | − | 14.4295i | 0.0295785 | − | 0.470137i | ||||
\(943\) | −0.488309 | −0.0159015 | ||||||||
\(944\) | −1.11251 | + | 17.6828i | −0.0362091 | + | 0.575527i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62.1734 | − | 24.6162i | 2.02143 | − | 0.800341i | ||||
\(947\) | −8.54599 | + | 13.4663i | −0.277707 | + | 0.437597i | −0.954339 | − | 0.298725i | \(-0.903439\pi\) |
0.676632 | + | 0.736321i | \(0.263439\pi\) | |||||||
\(948\) | 0.293796 | − | 0.624348i | 0.00954205 | − | 0.0202779i | ||||
\(949\) | 68.4840 | + | 49.7566i | 2.22309 | + | 1.61517i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.1338 | − | 8.08917i | 0.361038 | − | 0.262309i | ||||
\(952\) | −5.87198 | − | 30.7820i | −0.190312 | − | 0.997651i | ||||
\(953\) | 8.10213 | − | 3.20786i | 0.262454 | − | 0.103913i | −0.233213 | − | 0.972426i | \(-0.574924\pi\) |
0.495667 | + | 0.868513i | \(0.334924\pi\) | |||||||
\(954\) | −13.2429 | − | 16.0079i | −0.428754 | − | 0.518275i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.16424 | + | 3.23245i | 0.264050 | + | 0.104545i | ||||
\(957\) | −1.61250 | + | 1.17155i | −0.0521246 | + | 0.0378707i | ||||
\(958\) | −32.8191 | + | 39.6714i | −1.06034 | + | 1.28173i | ||||
\(959\) | 13.0059 | − | 12.2133i | 0.419982 | − | 0.394389i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3481 | + | 14.4850i | −0.849940 | + | 0.467258i | ||||
\(962\) | −44.9933 | + | 42.2515i | −1.45064 | + | 1.36224i | ||||
\(963\) | 19.1585 | + | 10.5325i | 0.617375 | + | 0.339405i | ||||
\(964\) | 0.0225720 | − | 0.0479679i | 0.000726995 | − | 0.00154494i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.50344 | + | 0.695246i | −0.177070 | + | 0.0223692i | ||||
\(967\) | −15.5325 | − | 24.4753i | −0.499491 | − | 0.787072i | 0.497261 | − | 0.867601i | \(-0.334339\pi\) |
−0.996752 | + | 0.0805287i | \(0.974339\pi\) | |||||||
\(968\) | 24.9428 | + | 18.1220i | 0.801692 | + | 0.582464i | ||||
\(969\) | −44.4182 | + | 11.4047i | −1.42692 | + | 0.366370i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.08524 | + | 33.1440i | 0.0669187 | + | 1.06364i | 0.877985 | + | 0.478688i | \(0.158887\pi\) |
−0.811067 | + | 0.584954i | \(0.801113\pi\) | |||||||
\(972\) | 0.366896 | + | 5.83164i | 0.0117682 | + | 0.187050i | ||||
\(973\) | 15.2816 | − | 8.40113i | 0.489905 | − | 0.269328i | ||||
\(974\) | −4.06948 | + | 12.5246i | −0.130395 | + | 0.401313i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.8355 | + | 36.4259i | 0.378845 | + | 1.16597i | ||||
\(977\) | −11.1057 | − | 10.4289i | −0.355303 | − | 0.333651i | 0.486257 | − | 0.873816i | \(-0.338362\pi\) |
−0.841559 | + | 0.540165i | \(0.818362\pi\) | |||||||
\(978\) | 13.8618 | + | 3.55909i | 0.443250 | + | 0.113807i | ||||
\(979\) | 5.85397 | − | 9.22437i | 0.187094 | − | 0.294812i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.3735 | + | 18.5834i | −0.490839 | + | 0.593322i | ||||
\(982\) | −0.334543 | + | 1.02962i | −0.0106757 | + | 0.0328564i | ||||
\(983\) | 45.9413 | − | 11.7957i | 1.46530 | − | 0.376225i | 0.569984 | − | 0.821656i | \(-0.306950\pi\) |
0.895316 | + | 0.445431i | \(0.146950\pi\) | |||||||
\(984\) | −3.56204 | − | 1.95825i | −0.113554 | − | 0.0624267i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.204155 | + | 1.07022i | 0.00650161 | + | 0.0340826i | ||||
\(987\) | 3.99290 | − | 20.9315i | 0.127095 | − | 0.666257i | ||||
\(988\) | 3.87429 | + | 8.23328i | 0.123257 | + | 0.261936i | ||||
\(989\) | 8.97634 | + | 1.13398i | 0.285431 | + | 0.0360583i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.14836 | + | 21.7465i | −0.131777 | + | 0.690800i | 0.853670 | + | 0.520815i | \(0.174372\pi\) |
−0.985447 | + | 0.169985i | \(0.945628\pi\) | |||||||
\(992\) | −1.66876 | − | 0.660711i | −0.0529833 | − | 0.0209776i | ||||
\(993\) | −20.3057 | − | 62.4945i | −0.644382 | − | 1.98320i | ||||
\(994\) | 0.715929 | + | 1.12812i | 0.0227079 | + | 0.0357819i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.31332 | + | 0.337204i | 0.0416142 | + | 0.0106847i | ||||
\(997\) | −21.1642 | − | 25.5832i | −0.670278 | − | 0.810227i | 0.320279 | − | 0.947323i | \(-0.396223\pi\) |
−0.990558 | + | 0.137096i | \(0.956223\pi\) | |||||||
\(998\) | −28.1131 | − | 3.55152i | −0.889906 | − | 0.112421i | ||||
\(999\) | −19.2933 | −0.610412 |
(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 | 625.2.g.b.451.8 | 480 | ||
5.2 | odd | 4 | 125.2.h.a.109.8 | yes | 240 | ||
5.3 | odd | 4 | 625.2.h.a.174.5 | 240 | |||
5.4 | even | 2 | inner | 625.2.g.b.451.17 | 480 | ||
125.27 | odd | 100 | 625.2.h.a.449.5 | 240 | |||
125.39 | even | 50 | inner | 625.2.g.b.176.17 | 480 | ||
125.86 | even | 25 | inner | 625.2.g.b.176.8 | 480 | ||
125.98 | odd | 100 | 125.2.h.a.39.8 | ✓ | 240 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
125.2.h.a.39.8 | ✓ | 240 | 125.98 | odd | 100 | ||
125.2.h.a.109.8 | yes | 240 | 5.2 | odd | 4 | ||
625.2.g.b.176.8 | 480 | 125.86 | even | 25 | inner | ||
625.2.g.b.176.17 | 480 | 125.39 | even | 50 | inner | ||
625.2.g.b.451.8 | 480 | 1.1 | even | 1 | trivial | ||
625.2.g.b.451.17 | 480 | 5.4 | even | 2 | inner | ||
625.2.h.a.174.5 | 240 | 5.3 | odd | 4 | |||
625.2.h.a.449.5 | 240 | 125.27 | odd | 100 |