Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,4,Mod(69,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.69");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.g (of order \(5\), 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: | \(11.0333571711\) |
Analytic rank: | \(0\) |
Dimension: | \(104\) |
Relative dimension: | \(26\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 103.2 | ||
Character | \(\chi\) | \(=\) | 187.103 |
Dual form | 187.4.g.b.69.2 |
$q$-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 \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.87240 | − | 2.81346i | −1.36910 | − | 0.994709i | −0.997807 | − | 0.0661929i | \(-0.978915\pi\) |
−0.371292 | − | 0.928516i | \(-0.621085\pi\) | |||||||
\(3\) | 1.76969 | − | 5.44656i | 0.340578 | − | 1.04819i | −0.623331 | − | 0.781958i | \(-0.714221\pi\) |
0.963909 | − | 0.266232i | \(-0.0857788\pi\) | |||||||
\(4\) | 4.60776 | + | 14.1812i | 0.575970 | + | 1.77265i | ||||
\(5\) | −0.349264 | + | 0.253755i | −0.0312391 | + | 0.0226965i | −0.603295 | − | 0.797518i | \(-0.706146\pi\) |
0.572056 | + | 0.820214i | \(0.306146\pi\) | |||||||
\(6\) | −22.1766 | + | 16.1123i | −1.50893 | + | 1.09630i | ||||
\(7\) | 8.05391 | + | 24.7874i | 0.434870 | + | 1.33839i | 0.893219 | + | 0.449621i | \(0.148441\pi\) |
−0.458349 | + | 0.888772i | \(0.651559\pi\) | |||||||
\(8\) | 10.2223 | − | 31.4609i | 0.451765 | − | 1.39039i | ||||
\(9\) | −4.68969 | − | 3.40726i | −0.173692 | − | 0.126195i | ||||
\(10\) | 2.06642 | 0.0653458 | ||||||||
\(11\) | 27.0757 | − | 24.4521i | 0.742148 | − | 0.670236i | ||||
\(12\) | 85.3932 | 2.05424 | ||||||||
\(13\) | −52.1882 | − | 37.9169i | −1.11341 | − | 0.808943i | −0.130217 | − | 0.991486i | \(-0.541567\pi\) |
−0.983198 | + | 0.182543i | \(0.941567\pi\) | |||||||
\(14\) | 38.5504 | − | 118.646i | 0.735931 | − | 2.26496i | ||||
\(15\) | 0.764000 | + | 2.35135i | 0.0131509 | + | 0.0404744i | ||||
\(16\) | −31.5926 | + | 22.9533i | −0.493634 | + | 0.358646i | ||||
\(17\) | 13.7533 | − | 9.99235i | 0.196215 | − | 0.142559i | ||||
\(18\) | 8.57415 | + | 26.3885i | 0.112275 | + | 0.345546i | ||||
\(19\) | 26.9379 | − | 82.9063i | 0.325262 | − | 1.00105i | −0.646060 | − | 0.763286i | \(-0.723585\pi\) |
0.971322 | − | 0.237767i | \(-0.0764155\pi\) | |||||||
\(20\) | −5.20788 | − | 3.78375i | −0.0582259 | − | 0.0423036i | ||||
\(21\) | 149.259 | 1.55100 | ||||||||
\(22\) | −173.643 | + | 18.5119i | −1.68276 | + | 0.179398i | ||||
\(23\) | 197.571 | 1.79115 | 0.895574 | − | 0.444912i | \(-0.146765\pi\) | ||||
0.895574 | + | 0.444912i | \(0.146765\pi\) | |||||||
\(24\) | −153.263 | − | 111.352i | −1.30353 | − | 0.947071i | ||||
\(25\) | −38.5695 | + | 118.705i | −0.308556 | + | 0.949638i | ||||
\(26\) | 95.4155 | + | 293.659i | 0.719712 | + | 2.21505i | ||||
\(27\) | 98.2370 | − | 71.3734i | 0.700212 | − | 0.508734i | ||||
\(28\) | −314.405 | + | 228.429i | −2.12204 | + | 1.54175i | ||||
\(29\) | −47.6275 | − | 146.582i | −0.304972 | − | 0.938609i | −0.979687 | − | 0.200530i | \(-0.935733\pi\) |
0.674715 | − | 0.738078i | \(-0.264267\pi\) | |||||||
\(30\) | 3.65692 | − | 11.2549i | 0.0222553 | − | 0.0684949i | ||||
\(31\) | −96.2946 | − | 69.9621i | −0.557904 | − | 0.405341i | 0.272787 | − | 0.962074i | \(-0.412054\pi\) |
−0.830691 | + | 0.556734i | \(0.812054\pi\) | |||||||
\(32\) | −77.7224 | −0.429360 | ||||||||
\(33\) | −85.2641 | − | 190.742i | −0.449775 | − | 1.00618i | ||||
\(34\) | −81.3713 | −0.410443 | ||||||||
\(35\) | −9.10286 | − | 6.61361i | −0.0439618 | − | 0.0319401i | ||||
\(36\) | 26.7102 | − | 82.2054i | 0.123658 | − | 0.380581i | ||||
\(37\) | −107.745 | − | 331.604i | −0.478733 | − | 1.47339i | −0.840856 | − | 0.541259i | \(-0.817948\pi\) |
0.362122 | − | 0.932131i | \(-0.382052\pi\) | |||||||
\(38\) | −337.568 | + | 245.257i | −1.44107 | + | 1.04700i | ||||
\(39\) | −298.874 | + | 217.144i | −1.22713 | + | 0.891562i | ||||
\(40\) | 4.41309 | + | 13.5821i | 0.0174443 | + | 0.0536880i | ||||
\(41\) | −82.1323 | + | 252.777i | −0.312851 | + | 0.962858i | 0.663778 | + | 0.747929i | \(0.268952\pi\) |
−0.976630 | + | 0.214929i | \(0.931048\pi\) | |||||||
\(42\) | −577.990 | − | 419.934i | −2.12347 | − | 1.54279i | ||||
\(43\) | 295.791 | 1.04901 | 0.524507 | − | 0.851406i | \(-0.324250\pi\) | ||||
0.524507 | + | 0.851406i | \(0.324250\pi\) | |||||||
\(44\) | 471.520 | + | 271.297i | 1.61555 | + | 0.929537i | ||||
\(45\) | 2.50255 | 0.00829017 | ||||||||
\(46\) | −765.074 | − | 555.859i | −2.45226 | − | 1.78167i | ||||
\(47\) | 40.3626 | − | 124.223i | 0.125266 | − | 0.385528i | −0.868684 | − | 0.495367i | \(-0.835034\pi\) |
0.993949 | + | 0.109839i | \(0.0350335\pi\) | |||||||
\(48\) | 69.1075 | + | 212.691i | 0.207809 | + | 0.639569i | ||||
\(49\) | −272.057 | + | 197.661i | −0.793168 | + | 0.576270i | ||||
\(50\) | 483.328 | − | 351.158i | 1.36706 | − | 0.993226i | ||||
\(51\) | −30.0848 | − | 92.5914i | −0.0826022 | − | 0.254223i | ||||
\(52\) | 297.238 | − | 914.804i | 0.792682 | − | 2.43963i | ||||
\(53\) | 396.606 | + | 288.151i | 1.02789 | + | 0.746804i | 0.967885 | − | 0.251394i | \(-0.0808891\pi\) |
0.0600026 | + | 0.998198i | \(0.480889\pi\) | |||||||
\(54\) | −581.219 | −1.46470 | ||||||||
\(55\) | −3.25171 | + | 15.4108i | −0.00797202 | + | 0.0377817i | ||||
\(56\) | 862.163 | 2.05735 | ||||||||
\(57\) | −403.882 | − | 293.437i | −0.938517 | − | 0.681873i | ||||
\(58\) | −227.971 | + | 701.623i | −0.516105 | + | 1.58841i | ||||
\(59\) | −175.317 | − | 539.570i | −0.386853 | − | 1.19061i | −0.935127 | − | 0.354312i | \(-0.884715\pi\) |
0.548274 | − | 0.836299i | \(-0.315285\pi\) | |||||||
\(60\) | −29.8247 | + | 21.6689i | −0.0641726 | + | 0.0466241i | ||||
\(61\) | −174.959 | + | 127.115i | −0.367232 | + | 0.266810i | −0.756062 | − | 0.654500i | \(-0.772879\pi\) |
0.388830 | + | 0.921309i | \(0.372879\pi\) | |||||||
\(62\) | 176.055 | + | 541.842i | 0.360630 | + | 1.10990i | ||||
\(63\) | 46.6867 | − | 143.687i | 0.0933647 | − | 0.287347i | ||||
\(64\) | 553.713 | + | 402.296i | 1.08147 | + | 0.785734i | ||||
\(65\) | 27.8490 | 0.0531422 | ||||||||
\(66\) | −206.469 | + | 978.516i | −0.385069 | + | 1.82496i | ||||
\(67\) | 443.190 | 0.808124 | 0.404062 | − | 0.914732i | \(-0.367598\pi\) | ||||
0.404062 | + | 0.914732i | \(0.367598\pi\) | |||||||
\(68\) | 205.076 | + | 148.996i | 0.365722 | + | 0.265712i | ||||
\(69\) | 349.640 | − | 1076.08i | 0.610025 | − | 1.87746i | ||||
\(70\) | 16.6427 | + | 51.2211i | 0.0284170 | + | 0.0874585i | ||||
\(71\) | 659.136 | − | 478.890i | 1.10176 | − | 0.800476i | 0.120415 | − | 0.992724i | \(-0.461578\pi\) |
0.981347 | + | 0.192247i | \(0.0615776\pi\) | |||||||
\(72\) | −155.135 | + | 112.712i | −0.253928 | + | 0.184489i | ||||
\(73\) | 151.455 | + | 466.132i | 0.242829 | + | 0.747351i | 0.995986 | + | 0.0895100i | \(0.0285301\pi\) |
−0.753157 | + | 0.657841i | \(0.771470\pi\) | |||||||
\(74\) | −515.725 | + | 1587.24i | −0.810160 | + | 2.49342i | ||||
\(75\) | 578.276 | + | 420.142i | 0.890314 | + | 0.646851i | ||||
\(76\) | 1299.84 | 1.96186 | ||||||||
\(77\) | 824.170 | + | 474.201i | 1.21978 | + | 0.701821i | ||||
\(78\) | 1768.28 | 2.56691 | ||||||||
\(79\) | −910.399 | − | 661.443i | −1.29656 | − | 0.942003i | −0.296640 | − | 0.954989i | \(-0.595866\pi\) |
−0.999916 | + | 0.0129868i | \(0.995866\pi\) | |||||||
\(80\) | 5.20961 | − | 16.0335i | 0.00728065 | − | 0.0224075i | ||||
\(81\) | −263.255 | − | 810.215i | −0.361118 | − | 1.11141i | ||||
\(82\) | 1029.23 | − | 747.778i | 1.38609 | − | 1.00705i | ||||
\(83\) | 230.651 | − | 167.578i | 0.305027 | − | 0.221615i | −0.424733 | − | 0.905319i | \(-0.639632\pi\) |
0.729760 | + | 0.683704i | \(0.239632\pi\) | |||||||
\(84\) | 687.749 | + | 2116.67i | 0.893328 | + | 2.74938i | ||||
\(85\) | −2.26792 | + | 6.97993i | −0.00289400 | + | 0.00890682i | ||||
\(86\) | −1145.42 | − | 832.195i | −1.43621 | − | 1.04346i | ||||
\(87\) | −882.655 | −1.08771 | ||||||||
\(88\) | −492.511 | − | 1101.78i | −0.596612 | − | 1.33466i | ||||
\(89\) | 404.506 | 0.481770 | 0.240885 | − | 0.970554i | \(-0.422562\pi\) | ||||
0.240885 | + | 0.970554i | \(0.422562\pi\) | |||||||
\(90\) | −9.69085 | − | 7.04082i | −0.0113501 | − | 0.00824630i | ||||
\(91\) | 519.543 | − | 1598.99i | 0.598493 | − | 1.84197i | ||||
\(92\) | 910.361 | + | 2801.80i | 1.03165 | + | 3.17509i | ||||
\(93\) | −551.464 | + | 400.662i | −0.614884 | + | 0.446739i | ||||
\(94\) | −505.797 | + | 367.483i | −0.554990 | + | 0.403224i | ||||
\(95\) | 11.6295 | + | 35.7918i | 0.0125595 | + | 0.0386543i | ||||
\(96\) | −137.545 | + | 423.319i | −0.146230 | + | 0.450050i | ||||
\(97\) | −335.051 | − | 243.429i | −0.350715 | − | 0.254809i | 0.398454 | − | 0.917188i | \(-0.369547\pi\) |
−0.749169 | + | 0.662379i | \(0.769547\pi\) | |||||||
\(98\) | 1609.62 | 1.65915 | ||||||||
\(99\) | −210.291 | + | 22.4189i | −0.213486 | + | 0.0227595i | ||||
\(100\) | −1861.10 | −1.86110 | ||||||||
\(101\) | −931.989 | − | 677.129i | −0.918181 | − | 0.667098i | 0.0248892 | − | 0.999690i | \(-0.492077\pi\) |
−0.943071 | + | 0.332592i | \(0.892077\pi\) | |||||||
\(102\) | −144.002 | + | 443.193i | −0.139788 | + | 0.430222i | ||||
\(103\) | 454.837 | + | 1399.84i | 0.435111 | + | 1.33913i | 0.892973 | + | 0.450111i | \(0.148615\pi\) |
−0.457862 | + | 0.889023i | \(0.651385\pi\) | |||||||
\(104\) | −1726.38 | + | 1254.29i | −1.62775 | + | 1.18263i | ||||
\(105\) | −52.1307 | + | 37.8752i | −0.0484518 | + | 0.0352023i | ||||
\(106\) | −725.114 | − | 2231.67i | −0.664427 | − | 2.04490i | ||||
\(107\) | −425.519 | + | 1309.61i | −0.384453 | + | 1.18323i | 0.552423 | + | 0.833564i | \(0.313703\pi\) |
−0.936876 | + | 0.349661i | \(0.886297\pi\) | |||||||
\(108\) | 1464.81 | + | 1064.25i | 1.30511 | + | 0.948218i | ||||
\(109\) | 12.6352 | 0.0111030 | 0.00555152 | − | 0.999985i | \(-0.498233\pi\) | ||||
0.00555152 | + | 0.999985i | \(0.498233\pi\) | |||||||
\(110\) | 55.9497 | − | 50.5283i | 0.0484963 | − | 0.0437971i | ||||
\(111\) | −1996.78 | −1.70744 | ||||||||
\(112\) | −823.397 | − | 598.233i | −0.694676 | − | 0.504712i | ||||
\(113\) | 481.017 | − | 1480.42i | 0.400445 | − | 1.23244i | −0.524194 | − | 0.851599i | \(-0.675634\pi\) |
0.924639 | − | 0.380844i | \(-0.124366\pi\) | |||||||
\(114\) | 738.417 | + | 2272.61i | 0.606658 | + | 1.86710i | ||||
\(115\) | −69.0044 | + | 50.1346i | −0.0559539 | + | 0.0406529i | ||||
\(116\) | 1859.26 | − | 1350.83i | 1.48817 | − | 1.08122i | ||||
\(117\) | 115.554 | + | 355.637i | 0.0913071 | + | 0.281014i | ||||
\(118\) | −839.163 | + | 2582.68i | −0.654671 | + | 2.01487i | ||||
\(119\) | 358.452 | + | 260.431i | 0.276128 | + | 0.200619i | ||||
\(120\) | 81.7855 | 0.0622163 | ||||||||
\(121\) | 135.188 | − | 1324.12i | 0.101568 | − | 0.994829i | ||||
\(122\) | 1035.14 | 0.768175 | ||||||||
\(123\) | 1231.42 | + | 894.676i | 0.902708 | + | 0.655856i | ||||
\(124\) | 548.446 | − | 1687.94i | 0.397193 | − | 1.22243i | ||||
\(125\) | −33.3268 | − | 102.569i | −0.0238467 | − | 0.0733927i | ||||
\(126\) | −585.047 | + | 425.062i | −0.413652 | + | 0.300536i | ||||
\(127\) | −383.706 | + | 278.778i | −0.268097 | + | 0.194784i | −0.713709 | − | 0.700442i | \(-0.752986\pi\) |
0.445612 | + | 0.895226i | \(0.352986\pi\) | |||||||
\(128\) | −820.211 | − | 2524.35i | −0.566384 | − | 1.74315i | ||||
\(129\) | 523.458 | − | 1611.04i | 0.357271 | − | 1.09957i | ||||
\(130\) | −107.842 | − | 78.3521i | −0.0727570 | − | 0.0528611i | ||||
\(131\) | −123.779 | −0.0825547 | −0.0412773 | − | 0.999148i | \(-0.513143\pi\) | ||||
−0.0412773 | + | 0.999148i | \(0.513143\pi\) | |||||||
\(132\) | 2312.08 | − | 2088.04i | 1.52455 | − | 1.37683i | ||||
\(133\) | 2271.99 | 1.48125 | ||||||||
\(134\) | −1716.21 | − | 1246.90i | −1.10640 | − | 0.803848i | ||||
\(135\) | −16.1993 | + | 49.8562i | −0.0103275 | + | 0.0317848i | ||||
\(136\) | −173.779 | − | 534.836i | −0.109569 | − | 0.337219i | ||||
\(137\) | 481.472 | − | 349.810i | 0.300255 | − | 0.218148i | −0.427449 | − | 0.904040i | \(-0.640588\pi\) |
0.727704 | + | 0.685892i | \(0.240588\pi\) | |||||||
\(138\) | −4381.46 | + | 3183.32i | −2.70272 | + | 1.96364i | ||||
\(139\) | −334.487 | − | 1029.45i | −0.204107 | − | 0.628176i | −0.999749 | − | 0.0224093i | \(-0.992866\pi\) |
0.795642 | − | 0.605767i | \(-0.207134\pi\) | |||||||
\(140\) | 51.8454 | − | 159.564i | 0.0312981 | − | 0.0963257i | ||||
\(141\) | −605.160 | − | 439.674i | −0.361444 | − | 0.262605i | ||||
\(142\) | −3899.78 | −2.30466 | ||||||||
\(143\) | −2340.18 | + | 249.484i | −1.36850 | + | 0.145894i | ||||
\(144\) | 226.367 | 0.131000 | ||||||||
\(145\) | 53.8305 | + | 39.1102i | 0.0308302 | + | 0.0223995i | ||||
\(146\) | 724.949 | − | 2231.16i | 0.410939 | − | 1.26474i | ||||
\(147\) | 595.113 | + | 1831.57i | 0.333905 | + | 1.02766i | ||||
\(148\) | 4206.10 | − | 3055.91i | 2.33607 | − | 1.69726i | ||||
\(149\) | 1923.90 | − | 1397.79i | 1.05780 | − | 0.768536i | 0.0841187 | − | 0.996456i | \(-0.473193\pi\) |
0.973680 | + | 0.227920i | \(0.0731925\pi\) | |||||||
\(150\) | −1057.26 | − | 3253.91i | −0.575500 | − | 1.77121i | ||||
\(151\) | −372.785 | + | 1147.31i | −0.200906 | + | 0.618325i | 0.798951 | + | 0.601396i | \(0.205389\pi\) |
−0.999857 | + | 0.0169283i | \(0.994611\pi\) | |||||||
\(152\) | −2332.94 | − | 1694.98i | −1.24491 | − | 0.904481i | ||||
\(153\) | −98.5452 | −0.0520713 | ||||||||
\(154\) | −1857.37 | − | 4155.06i | −0.971889 | − | 2.17419i | ||||
\(155\) | 51.3854 | 0.0266282 | ||||||||
\(156\) | −4456.51 | − | 3237.85i | −2.28722 | − | 1.66176i | ||||
\(157\) | 377.465 | − | 1161.72i | 0.191879 | − | 0.590542i | −0.808120 | − | 0.589018i | \(-0.799515\pi\) |
0.999999 | − | 0.00152429i | \(-0.000485197\pi\) | |||||||
\(158\) | 1664.48 | + | 5122.74i | 0.838095 | + | 2.57939i | ||||
\(159\) | 2271.30 | − | 1650.20i | 1.13287 | − | 0.823077i | ||||
\(160\) | 27.1456 | − | 19.7224i | 0.0134128 | − | 0.00974497i | ||||
\(161\) | 1591.22 | + | 4897.27i | 0.778918 | + | 2.39726i | ||||
\(162\) | −1260.08 | + | 3878.13i | −0.611119 | + | 1.88083i | ||||
\(163\) | 594.916 | + | 432.232i | 0.285874 | + | 0.207699i | 0.721475 | − | 0.692440i | \(-0.243464\pi\) |
−0.435602 | + | 0.900140i | \(0.643464\pi\) | |||||||
\(164\) | −3963.14 | −1.88701 | ||||||||
\(165\) | 78.1814 | + | 44.9831i | 0.0368873 | + | 0.0212238i | ||||
\(166\) | −1364.64 | −0.638054 | ||||||||
\(167\) | 29.8835 | + | 21.7116i | 0.0138470 | + | 0.0100604i | 0.594687 | − | 0.803957i | \(-0.297276\pi\) |
−0.580840 | + | 0.814018i | \(0.697276\pi\) | |||||||
\(168\) | 1525.76 | − | 4695.82i | 0.700686 | − | 2.15649i | ||||
\(169\) | 607.001 | + | 1868.16i | 0.276286 | + | 0.850321i | ||||
\(170\) | 28.4200 | − | 20.6484i | 0.0128219 | − | 0.00931563i | ||||
\(171\) | −408.814 | + | 297.021i | −0.182823 | + | 0.132829i | ||||
\(172\) | 1362.93 | + | 4194.67i | 0.604201 | + | 1.85954i | ||||
\(173\) | −366.918 | + | 1129.26i | −0.161250 | + | 0.496277i | −0.998740 | − | 0.0501755i | \(-0.984022\pi\) |
0.837490 | + | 0.546452i | \(0.184022\pi\) | |||||||
\(174\) | 3417.99 | + | 2483.31i | 1.48918 | + | 1.08195i | ||||
\(175\) | −3253.02 | −1.40517 | ||||||||
\(176\) | −294.133 | + | 1393.98i | −0.125972 | + | 0.597020i | ||||
\(177\) | −3249.05 | −1.37974 | ||||||||
\(178\) | −1566.41 | − | 1138.06i | −0.659591 | − | 0.479221i | ||||
\(179\) | −695.826 | + | 2141.53i | −0.290550 | + | 0.894221i | 0.694130 | + | 0.719850i | \(0.255789\pi\) |
−0.984680 | + | 0.174371i | \(0.944211\pi\) | |||||||
\(180\) | 11.5311 | + | 35.4892i | 0.00477489 | + | 0.0146956i | ||||
\(181\) | −3505.10 | + | 2546.60i | −1.43940 | + | 1.04579i | −0.451237 | + | 0.892404i | \(0.649017\pi\) |
−0.988167 | + | 0.153384i | \(0.950983\pi\) | |||||||
\(182\) | −6510.57 | + | 4730.20i | −2.65162 | + | 1.92652i | ||||
\(183\) | 382.715 | + | 1177.88i | 0.154596 | + | 0.475798i | ||||
\(184\) | 2019.63 | − | 6215.77i | 0.809178 | − | 2.49039i | ||||
\(185\) | 121.778 | + | 88.4766i | 0.0483960 | + | 0.0351618i | ||||
\(186\) | 3262.74 | 1.28621 | ||||||||
\(187\) | 128.046 | − | 606.847i | 0.0500730 | − | 0.237310i | ||||
\(188\) | 1947.62 | 0.755558 | ||||||||
\(189\) | 2560.35 | + | 1860.20i | 0.985387 | + | 0.715926i | ||||
\(190\) | 55.6649 | − | 171.319i | 0.0212545 | − | 0.0654147i | ||||
\(191\) | 884.876 | + | 2723.37i | 0.335222 | + | 1.03171i | 0.966613 | + | 0.256242i | \(0.0824845\pi\) |
−0.631391 | + | 0.775465i | \(0.717516\pi\) | |||||||
\(192\) | 3171.03 | − | 2303.89i | 1.19192 | − | 0.865983i | ||||
\(193\) | 2857.29 | − | 2075.94i | 1.06566 | − | 0.774246i | 0.0905309 | − | 0.995894i | \(-0.471144\pi\) |
0.975127 | + | 0.221648i | \(0.0711436\pi\) | |||||||
\(194\) | 612.574 | + | 1885.31i | 0.226702 | + | 0.697718i | ||||
\(195\) | 49.2842 | − | 151.681i | 0.0180991 | − | 0.0557032i | ||||
\(196\) | −4056.64 | − | 2947.32i | −1.47837 | − | 1.07410i | ||||
\(197\) | 422.185 | 0.152688 | 0.0763438 | − | 0.997082i | \(-0.475675\pi\) | ||||
0.0763438 | + | 0.997082i | \(0.475675\pi\) | |||||||
\(198\) | 877.407 | + | 504.832i | 0.314922 | + | 0.181196i | ||||
\(199\) | −3802.36 | −1.35448 | −0.677241 | − | 0.735761i | \(-0.736825\pi\) | ||||
−0.677241 | + | 0.735761i | \(0.736825\pi\) | |||||||
\(200\) | 3340.29 | + | 2426.87i | 1.18097 | + | 0.858027i | ||||
\(201\) | 784.311 | − | 2413.86i | 0.275229 | − | 0.847068i | ||||
\(202\) | 1703.95 | + | 5244.23i | 0.593513 | + | 1.82665i | ||||
\(203\) | 3249.81 | − | 2361.12i | 1.12360 | − | 0.816346i | ||||
\(204\) | 1174.44 | − | 853.278i | 0.403074 | − | 0.292850i | ||||
\(205\) | −35.4576 | − | 109.127i | −0.0120803 | − | 0.0371794i | ||||
\(206\) | 2177.10 | − | 6700.42i | 0.736338 | − | 2.26622i | ||||
\(207\) | −926.547 | − | 673.176i | −0.311109 | − | 0.226034i | ||||
\(208\) | 2519.08 | 0.839743 | ||||||||
\(209\) | −1297.87 | − | 2903.44i | −0.429549 | − | 0.960932i | ||||
\(210\) | 308.431 | 0.101351 | ||||||||
\(211\) | 502.380 | + | 365.000i | 0.163911 | + | 0.119088i | 0.666717 | − | 0.745311i | \(-0.267699\pi\) |
−0.502806 | + | 0.864399i | \(0.667699\pi\) | |||||||
\(212\) | −2258.87 | + | 6952.09i | −0.731792 | + | 2.25223i | ||||
\(213\) | −1441.83 | − | 4437.51i | −0.463816 | − | 1.42748i | ||||
\(214\) | 5332.33 | − | 3874.16i | 1.70332 | − | 1.23753i | ||||
\(215\) | −103.309 | + | 75.0583i | −0.0327703 | + | 0.0238090i | ||||
\(216\) | −1241.27 | − | 3820.22i | −0.391007 | − | 1.20340i | ||||
\(217\) | 958.630 | − | 2950.36i | 0.299890 | − | 0.922965i | ||||
\(218\) | −48.9285 | − | 35.5486i | −0.0152012 | − | 0.0110443i | ||||
\(219\) | 2806.84 | 0.866068 | ||||||||
\(220\) | −233.528 | + | 24.8961i | −0.0715656 | + | 0.00762952i | ||||
\(221\) | −1096.64 | −0.333791 | ||||||||
\(222\) | 7732.31 | + | 5617.85i | 2.33765 | + | 1.69840i | ||||
\(223\) | −1317.64 | + | 4055.28i | −0.395676 | + | 1.21777i | 0.532757 | + | 0.846268i | \(0.321156\pi\) |
−0.928434 | + | 0.371498i | \(0.878844\pi\) | |||||||
\(224\) | −625.969 | − | 1926.54i | −0.186716 | − | 0.574652i | ||||
\(225\) | 585.337 | − | 425.272i | 0.173433 | − | 0.126007i | ||||
\(226\) | −6027.79 | + | 4379.44i | −1.77417 | + | 1.28901i | ||||
\(227\) | 763.136 | + | 2348.69i | 0.223133 | + | 0.686732i | 0.998476 | + | 0.0551914i | \(0.0175769\pi\) |
−0.775343 | + | 0.631540i | \(0.782423\pi\) | |||||||
\(228\) | 2300.31 | − | 7079.63i | 0.668166 | − | 2.05640i | ||||
\(229\) | 2742.59 | + | 1992.61i | 0.791422 | + | 0.575001i | 0.908385 | − | 0.418135i | \(-0.137316\pi\) |
−0.116963 | + | 0.993136i | \(0.537316\pi\) | |||||||
\(230\) | 408.264 | 0.117044 | ||||||||
\(231\) | 4041.29 | − | 3649.70i | 1.15107 | − | 1.03953i | ||||
\(232\) | −5098.47 | −1.44281 | ||||||||
\(233\) | 4724.12 | + | 3432.27i | 1.32827 | + | 0.965045i | 0.999789 | + | 0.0205348i | \(0.00653688\pi\) |
0.328482 | + | 0.944510i | \(0.393463\pi\) | |||||||
\(234\) | 553.102 | − | 1702.27i | 0.154519 | − | 0.475560i | ||||
\(235\) | 17.4251 | + | 53.6289i | 0.00483697 | + | 0.0148866i | ||||
\(236\) | 6843.95 | − | 4972.42i | 1.88772 | − | 1.37151i | ||||
\(237\) | −5213.71 | + | 3787.99i | −1.42898 | + | 1.03821i | ||||
\(238\) | −655.357 | − | 2016.98i | −0.178490 | − | 0.549334i | ||||
\(239\) | −1304.15 | + | 4013.76i | −0.352964 | + | 1.08631i | 0.604217 | + | 0.796820i | \(0.293486\pi\) |
−0.957181 | + | 0.289492i | \(0.906514\pi\) | |||||||
\(240\) | −78.1081 | − | 56.7489i | −0.0210077 | − | 0.0152630i | ||||
\(241\) | 1025.73 | 0.274162 | 0.137081 | − | 0.990560i | \(-0.456228\pi\) | ||||
0.137081 | + | 0.990560i | \(0.456228\pi\) | |||||||
\(242\) | −4248.85 | + | 4747.16i | −1.12862 | + | 1.26099i | ||||
\(243\) | −1600.21 | −0.422444 | ||||||||
\(244\) | −2608.81 | − | 1895.41i | −0.684476 | − | 0.497301i | ||||
\(245\) | 44.8621 | − | 138.071i | 0.0116985 | − | 0.0360043i | ||||
\(246\) | −2251.40 | − | 6929.08i | −0.583511 | − | 1.79586i | ||||
\(247\) | −4549.39 | + | 3305.33i | −1.17195 | + | 0.851469i | ||||
\(248\) | −3185.42 | + | 2314.34i | −0.815623 | + | 0.592585i | ||||
\(249\) | −504.540 | − | 1552.81i | −0.128409 | − | 0.395203i | ||||
\(250\) | −159.520 | + | 490.954i | −0.0403558 | + | 0.124203i | ||||
\(251\) | 265.703 | + | 193.044i | 0.0668168 | + | 0.0485452i | 0.620692 | − | 0.784054i | \(-0.286852\pi\) |
−0.553875 | + | 0.832600i | \(0.686852\pi\) | |||||||
\(252\) | 2252.78 | 0.563142 | ||||||||
\(253\) | 5349.38 | − | 4831.03i | 1.32930 | − | 1.20049i | ||||
\(254\) | 2270.19 | 0.560806 | ||||||||
\(255\) | 34.0030 | + | 24.7047i | 0.00835040 | + | 0.00606692i | ||||
\(256\) | −2233.98 | + | 6875.50i | −0.545406 | + | 1.67859i | ||||
\(257\) | −434.853 | − | 1338.34i | −0.105546 | − | 0.324838i | 0.884312 | − | 0.466896i | \(-0.154628\pi\) |
−0.989858 | + | 0.142058i | \(0.954628\pi\) | |||||||
\(258\) | −6559.64 | + | 4765.85i | −1.58289 | + | 1.15004i | ||||
\(259\) | 7351.84 | − | 5341.43i | 1.76379 | − | 1.28147i | ||||
\(260\) | 128.322 | + | 394.933i | 0.0306083 | + | 0.0942028i | ||||
\(261\) | −276.086 | + | 849.705i | −0.0654762 | + | 0.201515i | ||||
\(262\) | 479.323 | + | 348.249i | 0.113026 | + | 0.0821179i | ||||
\(263\) | 1640.74 | 0.384686 | 0.192343 | − | 0.981328i | \(-0.438391\pi\) | ||||
0.192343 | + | 0.981328i | \(0.438391\pi\) | |||||||
\(264\) | −6872.51 | + | 732.671i | −1.60217 | + | 0.170806i | ||||
\(265\) | −211.640 | −0.0490601 | ||||||||
\(266\) | −8798.04 | − | 6392.15i | −2.02798 | − | 1.47341i | ||||
\(267\) | 715.851 | − | 2203.16i | 0.164080 | − | 0.504986i | ||||
\(268\) | 2042.12 | + | 6284.99i | 0.465455 | + | 1.43252i | ||||
\(269\) | −1595.26 | + | 1159.03i | −0.361579 | + | 0.262703i | −0.753710 | − | 0.657207i | \(-0.771738\pi\) |
0.392131 | + | 0.919909i | \(0.371738\pi\) | |||||||
\(270\) | 202.999 | − | 147.487i | 0.0457559 | − | 0.0332436i | ||||
\(271\) | 783.781 | + | 2412.23i | 0.175687 | + | 0.540710i | 0.999664 | − | 0.0259132i | \(-0.00824934\pi\) |
−0.823977 | + | 0.566624i | \(0.808249\pi\) | |||||||
\(272\) | −205.144 | + | 631.368i | −0.0457304 | + | 0.140744i | ||||
\(273\) | −7789.54 | − | 5659.44i | −1.72690 | − | 1.25467i | ||||
\(274\) | −2848.63 | −0.628073 | ||||||||
\(275\) | 1858.29 | + | 4157.12i | 0.407487 | + | 0.911578i | ||||
\(276\) | 16871.2 | 3.67945 | ||||||||
\(277\) | 2834.37 | + | 2059.29i | 0.614804 | + | 0.446681i | 0.851103 | − | 0.524999i | \(-0.175934\pi\) |
−0.236299 | + | 0.971680i | \(0.575934\pi\) | |||||||
\(278\) | −1601.04 | + | 4927.49i | −0.345410 | + | 1.06306i | ||||
\(279\) | 213.213 | + | 656.201i | 0.0457516 | + | 0.140809i | ||||
\(280\) | −301.122 | + | 218.778i | −0.0642696 | + | 0.0466946i | ||||
\(281\) | −1102.89 | + | 801.294i | −0.234138 | + | 0.170111i | −0.698668 | − | 0.715446i | \(-0.746223\pi\) |
0.464530 | + | 0.885557i | \(0.346223\pi\) | |||||||
\(282\) | 1106.41 | + | 3405.19i | 0.233638 | + | 0.719064i | ||||
\(283\) | 1013.46 | − | 3119.11i | 0.212876 | − | 0.655165i | −0.786422 | − | 0.617690i | \(-0.788069\pi\) |
0.999298 | − | 0.0374749i | \(-0.0119314\pi\) | |||||||
\(284\) | 9828.40 | + | 7140.75i | 2.05355 | + | 1.49199i | ||||
\(285\) | 215.522 | 0.0447946 | ||||||||
\(286\) | 9764.02 | + | 5617.91i | 2.01874 | + | 1.16152i | ||||
\(287\) | −6927.18 | −1.42473 | ||||||||
\(288\) | 364.494 | + | 264.820i | 0.0745764 | + | 0.0541829i | ||||
\(289\) | 89.3059 | − | 274.855i | 0.0181775 | − | 0.0559445i | ||||
\(290\) | −98.4182 | − | 302.900i | −0.0199287 | − | 0.0613342i | ||||
\(291\) | −1918.79 | + | 1394.08i | −0.386534 | + | 0.280833i | ||||
\(292\) | −5912.45 | + | 4295.65i | −1.18493 | + | 0.860904i | ||||
\(293\) | −1375.80 | − | 4234.27i | −0.274318 | − | 0.844263i | −0.989399 | − | 0.145222i | \(-0.953610\pi\) |
0.715082 | − | 0.699041i | \(-0.246390\pi\) | |||||||
\(294\) | 2848.54 | − | 8766.90i | 0.565068 | − | 1.73910i | ||||
\(295\) | 198.150 | + | 143.965i | 0.0391077 | + | 0.0284134i | ||||
\(296\) | −11534.0 | −2.26486 | ||||||||
\(297\) | 914.606 | − | 4334.59i | 0.178690 | − | 0.846863i | ||||
\(298\) | −11382.7 | −2.21270 | ||||||||
\(299\) | −10310.9 | − | 7491.29i | −1.99429 | − | 1.44894i | ||||
\(300\) | −3293.57 | + | 10136.6i | −0.633849 | + | 1.95079i | ||||
\(301\) | 2382.27 | + | 7331.88i | 0.456185 | + | 1.40399i | ||||
\(302\) | 4671.49 | − | 3394.04i | 0.890113 | − | 0.646705i | ||||
\(303\) | −5337.36 | + | 3877.82i | −1.01196 | + | 0.735230i | ||||
\(304\) | 1051.94 | + | 3237.54i | 0.198463 | + | 0.610808i | ||||
\(305\) | 28.8507 | − | 88.7932i | 0.00541634 | − | 0.0166698i | ||||
\(306\) | 381.606 | + | 277.253i | 0.0712908 | + | 0.0517958i | ||||
\(307\) | −4356.29 | −0.809858 | −0.404929 | − | 0.914348i | \(-0.632704\pi\) | ||||
−0.404929 | + | 0.914348i | \(0.632704\pi\) | |||||||
\(308\) | −2927.18 | + | 13872.7i | −0.541530 | + | 2.56647i | ||||
\(309\) | 8429.25 | 1.55186 | ||||||||
\(310\) | −198.985 | − | 144.571i | −0.0364567 | − | 0.0264873i | ||||
\(311\) | 1258.21 | − | 3872.39i | 0.229411 | − | 0.706054i | −0.768403 | − | 0.639966i | \(-0.778948\pi\) |
0.997814 | − | 0.0660878i | \(-0.0210517\pi\) | |||||||
\(312\) | 3776.39 | + | 11622.5i | 0.685244 | + | 2.10896i | ||||
\(313\) | −8790.20 | + | 6386.46i | −1.58739 | + | 1.15330i | −0.679831 | + | 0.733368i | \(0.737947\pi\) |
−0.907554 | + | 0.419935i | \(0.862053\pi\) | |||||||
\(314\) | −4730.14 | + | 3436.65i | −0.850118 | + | 0.617647i | ||||
\(315\) | 20.1553 | + | 62.0316i | 0.00360515 | + | 0.0110955i | ||||
\(316\) | 5185.18 | − | 15958.4i | 0.923067 | − | 2.84091i | ||||
\(317\) | 1506.24 | + | 1094.35i | 0.266874 | + | 0.193896i | 0.713172 | − | 0.700989i | \(-0.247258\pi\) |
−0.446298 | + | 0.894884i | \(0.647258\pi\) | |||||||
\(318\) | −13438.2 | −2.36973 | ||||||||
\(319\) | −4873.80 | − | 2804.23i | −0.855424 | − | 0.492184i | ||||
\(320\) | −295.476 | −0.0516176 | ||||||||
\(321\) | 6379.84 | + | 4635.23i | 1.10931 | + | 0.805960i | ||||
\(322\) | 7616.45 | − | 23441.0i | 1.31816 | − | 4.05689i | ||||
\(323\) | −457.944 | − | 1409.41i | −0.0788876 | − | 0.242791i | ||||
\(324\) | 10276.8 | − | 7466.55i | 1.76214 | − | 1.28027i | ||||
\(325\) | 6513.79 | − | 4732.55i | 1.11175 | − | 0.807737i | ||||
\(326\) | −1087.68 | − | 3347.55i | −0.184789 | − | 0.568722i | ||||
\(327\) | 22.3604 | − | 68.8182i | 0.00378145 | − | 0.0116381i | ||||
\(328\) | 7113.02 | + | 5167.92i | 1.19741 | + | 0.869971i | ||||
\(329\) | 3404.25 | 0.570463 | ||||||||
\(330\) | −176.191 | − | 394.153i | −0.0293909 | − | 0.0657497i | ||||
\(331\) | 841.650 | 0.139762 | 0.0698811 | − | 0.997555i | \(-0.477738\pi\) | ||||
0.0698811 | + | 0.997555i | \(0.477738\pi\) | |||||||
\(332\) | 3439.24 | + | 2498.75i | 0.568533 | + | 0.413063i | ||||
\(333\) | −624.572 | + | 1922.24i | −0.102782 | + | 0.316330i | ||||
\(334\) | −54.6359 | − | 168.152i | −0.00895072 | − | 0.0275475i | ||||
\(335\) | −154.790 | + | 112.462i | −0.0252451 | + | 0.0183416i | ||||
\(336\) | −4715.47 | + | 3425.99i | −0.765625 | + | 0.556259i | ||||
\(337\) | 2138.41 | + | 6581.35i | 0.345657 | + | 1.06382i | 0.961231 | + | 0.275745i | \(0.0889245\pi\) |
−0.615573 | + | 0.788080i | \(0.711076\pi\) | |||||||
\(338\) | 2905.44 | − | 8942.02i | 0.467559 | − | 1.43900i | ||||
\(339\) | −7211.93 | − | 5239.77i | −1.15545 | − | 0.839485i | ||||
\(340\) | −109.434 | −0.0174556 | ||||||||
\(341\) | −4317.97 | + | 460.333i | −0.685721 | + | 0.0731039i | ||||
\(342\) | 2418.75 | 0.382429 | ||||||||
\(343\) | 141.684 | + | 102.940i | 0.0223039 | + | 0.0162047i | ||||
\(344\) | 3023.65 | − | 9305.84i | 0.473908 | − | 1.45854i | ||||
\(345\) | 150.944 | + | 464.559i | 0.0235553 | + | 0.0724957i | ||||
\(346\) | 4597.97 | − | 3340.62i | 0.714418 | − | 0.519055i | ||||
\(347\) | 3219.73 | − | 2339.27i | 0.498109 | − | 0.361898i | −0.310185 | − | 0.950676i | \(-0.600391\pi\) |
0.808294 | + | 0.588779i | \(0.200391\pi\) | |||||||
\(348\) | −4067.06 | − | 12517.1i | −0.626487 | − | 1.92813i | ||||
\(349\) | −3359.54 | + | 10339.6i | −0.515278 | + | 1.58586i | 0.267498 | + | 0.963558i | \(0.413803\pi\) |
−0.782776 | + | 0.622304i | \(0.786197\pi\) | |||||||
\(350\) | 12597.0 | + | 9152.24i | 1.92382 | + | 1.39774i | ||||
\(351\) | −7833.07 | −1.19116 | ||||||||
\(352\) | −2104.39 | + | 1900.48i | −0.318649 | + | 0.287772i | ||||
\(353\) | 10094.0 | 1.52196 | 0.760980 | − | 0.648775i | \(-0.224718\pi\) | ||||
0.760980 | + | 0.648775i | \(0.224718\pi\) | |||||||
\(354\) | 12581.6 | + | 9141.09i | 1.88900 | + | 1.37244i | ||||
\(355\) | −108.691 | + | 334.518i | −0.0162500 | + | 0.0500123i | ||||
\(356\) | 1863.87 | + | 5736.39i | 0.277485 | + | 0.854011i | ||||
\(357\) | 2052.80 | − | 1491.45i | 0.304330 | − | 0.221108i | ||||
\(358\) | 8719.63 | − | 6335.18i | 1.28728 | − | 0.935265i | ||||
\(359\) | −3271.78 | − | 10069.5i | −0.480998 | − | 1.48036i | −0.837695 | − | 0.546138i | \(-0.816097\pi\) |
0.356698 | − | 0.934220i | \(-0.383903\pi\) | |||||||
\(360\) | 25.5817 | − | 78.7324i | 0.00374521 | − | 0.0115266i | ||||
\(361\) | −598.760 | − | 435.024i | −0.0872955 | − | 0.0634239i | ||||
\(362\) | 20737.9 | 3.01094 | ||||||||
\(363\) | −6972.63 | − | 3079.59i | −1.00818 | − | 0.445279i | ||||
\(364\) | 25069.5 | 3.60989 | ||||||||
\(365\) | −171.181 | − | 124.370i | −0.0245480 | − | 0.0178352i | ||||
\(366\) | 1831.88 | − | 5637.96i | 0.261623 | − | 0.805193i | ||||
\(367\) | 4026.77 | + | 12393.1i | 0.572740 | + | 1.76271i | 0.643749 | + | 0.765237i | \(0.277378\pi\) |
−0.0710086 | + | 0.997476i | \(0.522622\pi\) | |||||||
\(368\) | −6241.78 | + | 4534.92i | −0.884172 | + | 0.642388i | ||||
\(369\) | 1246.45 | − | 905.601i | 0.175848 | − | 0.127761i | ||||
\(370\) | −222.646 | − | 685.233i | −0.0312832 | − | 0.0962799i | ||||
\(371\) | −3948.29 | + | 12151.6i | −0.552520 | + | 1.70048i | ||||
\(372\) | −8222.90 | − | 5974.29i | −1.14607 | − | 0.832668i | ||||
\(373\) | −5132.56 | −0.712477 | −0.356239 | − | 0.934395i | \(-0.615941\pi\) | ||||
−0.356239 | + | 0.934395i | \(0.615941\pi\) | |||||||
\(374\) | −2203.19 | + | 1989.70i | −0.304610 | + | 0.275094i | ||||
\(375\) | −617.629 | −0.0850512 | ||||||||
\(376\) | −3495.58 | − | 2539.69i | −0.479444 | − | 0.348336i | ||||
\(377\) | −3072.36 | + | 9455.75i | −0.419720 | + | 1.29177i | ||||
\(378\) | −4681.09 | − | 14406.9i | −0.636955 | − | 1.96035i | ||||
\(379\) | 9824.60 | − | 7137.99i | 1.33155 | − | 0.967425i | 0.331836 | − | 0.943337i | \(-0.392332\pi\) |
0.999710 | − | 0.0240878i | \(-0.00766814\pi\) | |||||||
\(380\) | −453.986 | + | 329.840i | −0.0612868 | + | 0.0445275i | ||||
\(381\) | 839.341 | + | 2583.23i | 0.112863 | + | 0.347356i | ||||
\(382\) | 4235.50 | − | 13035.5i | 0.567296 | − | 1.74596i | ||||
\(383\) | −6941.82 | − | 5043.53i | −0.926137 | − | 0.672878i | 0.0189068 | − | 0.999821i | \(-0.493981\pi\) |
−0.945044 | + | 0.326943i | \(0.893981\pi\) | |||||||
\(384\) | −15200.5 | −2.02005 | ||||||||
\(385\) | −408.183 | + | 43.5159i | −0.0540336 | + | 0.00576046i | ||||
\(386\) | −16905.1 | −2.22914 | ||||||||
\(387\) | −1387.17 | − | 1007.83i | −0.182206 | − | 0.132380i | ||||
\(388\) | 1908.29 | − | 5873.10i | 0.249687 | − | 0.768458i | ||||
\(389\) | −1432.56 | − | 4408.97i | −0.186719 | − | 0.574663i | 0.813255 | − | 0.581908i | \(-0.197694\pi\) |
−0.999974 | + | 0.00724551i | \(0.997694\pi\) | |||||||
\(390\) | −617.597 | + | 448.711i | −0.0801878 | + | 0.0582599i | ||||
\(391\) | 2717.25 | − | 1974.20i | 0.351451 | − | 0.255344i | ||||
\(392\) | 3437.55 | + | 10579.7i | 0.442915 | + | 1.36315i | ||||
\(393\) | −219.052 | + | 674.172i | −0.0281163 | + | 0.0865330i | ||||
\(394\) | −1634.87 | − | 1187.80i | −0.209045 | − | 0.151880i | ||||
\(395\) | 485.814 | 0.0618834 | ||||||||
\(396\) | −1286.90 | − | 2878.89i | −0.163306 | − | 0.365327i | ||||
\(397\) | −13641.4 | −1.72454 | −0.862272 | − | 0.506446i | \(-0.830959\pi\) | ||||
−0.862272 | + | 0.506446i | \(0.830959\pi\) | |||||||
\(398\) | 14724.2 | + | 10697.8i | 1.85442 | + | 1.34732i | ||||
\(399\) | 4020.72 | − | 12374.5i | 0.504481 | − | 1.55263i | ||||
\(400\) | −1506.16 | − | 4635.49i | −0.188270 | − | 0.579436i | ||||
\(401\) | 6565.13 | − | 4769.85i | 0.817574 | − | 0.594002i | −0.0984425 | − | 0.995143i | \(-0.531386\pi\) |
0.916017 | + | 0.401140i | \(0.131386\pi\) | |||||||
\(402\) | −9828.47 | + | 7140.80i | −1.21940 | + | 0.885947i | ||||
\(403\) | 2372.69 | + | 7302.39i | 0.293281 | + | 0.902625i | ||||
\(404\) | 5308.15 | − | 16336.8i | 0.653689 | − | 2.01185i | ||||
\(405\) | 297.541 | + | 216.176i | 0.0365060 | + | 0.0265232i | ||||
\(406\) | −19227.5 | −2.35035 | ||||||||
\(407\) | −11025.7 | − | 6343.83i | −1.34281 | − | 0.772610i | ||||
\(408\) | −3220.55 | −0.390786 | ||||||||
\(409\) | 3904.47 | + | 2836.76i | 0.472038 | + | 0.342956i | 0.798235 | − | 0.602346i | \(-0.205767\pi\) |
−0.326197 | + | 0.945302i | \(0.605767\pi\) | |||||||
\(410\) | −169.720 | + | 522.343i | −0.0204435 | + | 0.0629188i | ||||
\(411\) | −1053.20 | − | 3241.42i | −0.126400 | − | 0.389021i | ||||
\(412\) | −17755.7 | + | 12900.3i | −2.12321 | + | 1.54260i | ||||
\(413\) | 11962.5 | − | 8691.30i | 1.42527 | − | 1.03552i | ||||
\(414\) | 1694.00 | + | 5213.61i | 0.201101 | + | 0.618925i | ||||
\(415\) | −38.0343 | + | 117.058i | −0.00449887 | + | 0.0138461i | ||||
\(416\) | 4056.19 | + | 2946.99i | 0.478055 | + | 0.347327i | ||||
\(417\) | −6198.88 | −0.727962 | ||||||||
\(418\) | −3142.83 | + | 14894.8i | −0.367753 | + | 1.74289i | ||||
\(419\) | 5981.25 | 0.697382 | 0.348691 | − | 0.937238i | \(-0.386626\pi\) | ||||
0.348691 | + | 0.937238i | \(0.386626\pi\) | |||||||
\(420\) | −777.322 | − | 564.758i | −0.0903082 | − | 0.0656127i | ||||
\(421\) | −3048.64 | + | 9382.76i | −0.352926 | + | 1.08619i | 0.604276 | + | 0.796775i | \(0.293462\pi\) |
−0.957202 | + | 0.289420i | \(0.906538\pi\) | |||||||
\(422\) | −918.500 | − | 2826.85i | −0.105952 | − | 0.326088i | ||||
\(423\) | −612.549 | + | 445.043i | −0.0704093 | + | 0.0511554i | ||||
\(424\) | 13119.7 | − | 9532.03i | 1.50271 | − | 1.09178i | ||||
\(425\) | 655.682 | + | 2017.98i | 0.0748359 | + | 0.230321i | ||||
\(426\) | −6901.41 | + | 21240.3i | −0.784916 | + | 2.41572i | ||||
\(427\) | −4559.95 | − | 3313.00i | −0.516795 | − | 0.375473i | ||||
\(428\) | −20532.6 | −2.31888 | ||||||||
\(429\) | −2782.57 | + | 13187.4i | −0.313156 | + | 1.48414i | ||||
\(430\) | 611.227 | 0.0685487 | ||||||||
\(431\) | −10550.9 | − | 7665.69i | −1.17916 | − | 0.856713i | −0.187087 | − | 0.982343i | \(-0.559905\pi\) |
−0.992077 | + | 0.125630i | \(0.959905\pi\) | |||||||
\(432\) | −1465.30 | + | 4509.74i | −0.163193 | + | 0.502256i | ||||
\(433\) | 1319.20 | + | 4060.09i | 0.146413 | + | 0.450613i | 0.997190 | − | 0.0749141i | \(-0.0238682\pi\) |
−0.850777 | + | 0.525527i | \(0.823868\pi\) | |||||||
\(434\) | −12012.9 | + | 8727.90i | −1.32866 | + | 0.965328i | ||||
\(435\) | 308.279 | − | 223.978i | 0.0339790 | − | 0.0246872i | ||||
\(436\) | 58.2199 | + | 179.183i | 0.00639502 | + | 0.0196818i | ||||
\(437\) | 5322.15 | − | 16379.9i | 0.582593 | − | 1.79304i | ||||
\(438\) | −10869.2 | − | 7896.94i | −1.18573 | − | 0.861485i | ||||
\(439\) | −326.848 | −0.0355344 | −0.0177672 | − | 0.999842i | \(-0.505656\pi\) | ||||
−0.0177672 | + | 0.999842i | \(0.505656\pi\) | |||||||
\(440\) | 451.599 | + | 259.836i | 0.0489298 | + | 0.0281527i | ||||
\(441\) | 1949.34 | 0.210489 | ||||||||
\(442\) | 4246.62 | + | 3085.35i | 0.456993 | + | 0.332025i | ||||
\(443\) | −1679.40 | + | 5168.67i | −0.180115 | + | 0.554336i | −0.999830 | − | 0.0184353i | \(-0.994132\pi\) |
0.819715 | + | 0.572771i | \(0.194132\pi\) | |||||||
\(444\) | −9200.67 | − | 28316.8i | −0.983433 | − | 3.02670i | ||||
\(445\) | −141.279 | + | 102.645i | −0.0150500 | + | 0.0109345i | ||||
\(446\) | 16511.8 | − | 11996.5i | 1.75304 | − | 1.27366i | ||||
\(447\) | −4208.45 | − | 12952.3i | −0.445309 | − | 1.37052i | ||||
\(448\) | −5512.31 | + | 16965.1i | −0.581322 | + | 1.78912i | ||||
\(449\) | −4194.35 | − | 3047.37i | −0.440854 | − | 0.320299i | 0.345120 | − | 0.938559i | \(-0.387838\pi\) |
−0.785974 | + | 0.618259i | \(0.787838\pi\) | |||||||
\(450\) | −3463.15 | −0.362787 | ||||||||
\(451\) | 3957.15 | + | 8852.43i | 0.413159 | + | 0.924268i | ||||
\(452\) | 23210.6 | 2.41534 | ||||||||
\(453\) | 5589.19 | + | 4060.78i | 0.579698 | + | 0.421175i | ||||
\(454\) | 3652.79 | − | 11242.1i | 0.377607 | − | 1.16216i | ||||
\(455\) | 224.294 | + | 690.305i | 0.0231100 | + | 0.0711252i | ||||
\(456\) | −13360.4 | + | 9706.90i | −1.37206 | + | 0.996858i | ||||
\(457\) | −10824.6 | + | 7864.54i | −1.10799 | + | 0.805005i | −0.982347 | − | 0.187070i | \(-0.940101\pi\) |
−0.125648 | + | 0.992075i | \(0.540101\pi\) | |||||||
\(458\) | −5014.27 | − | 15432.3i | −0.511576 | − | 1.57447i | ||||
\(459\) | 637.894 | − | 1963.24i | 0.0648679 | − | 0.199643i | ||||
\(460\) | −1028.93 | − | 747.559i | −0.104291 | − | 0.0757720i | ||||
\(461\) | 415.191 | 0.0419466 | 0.0209733 | − | 0.999780i | \(-0.493324\pi\) | ||||
0.0209733 | + | 0.999780i | \(0.493324\pi\) | |||||||
\(462\) | −25917.8 | + | 2763.06i | −2.60996 | + | 0.278245i | ||||
\(463\) | −1874.52 | −0.188156 | −0.0940781 | − | 0.995565i | \(-0.529990\pi\) | ||||
−0.0940781 | + | 0.995565i | \(0.529990\pi\) | |||||||
\(464\) | 4869.23 | + | 3537.70i | 0.487173 | + | 0.353952i | ||||
\(465\) | 90.9364 | − | 279.873i | 0.00906898 | − | 0.0279114i | ||||
\(466\) | −8637.09 | − | 26582.2i | −0.858596 | − | 2.64249i | ||||
\(467\) | −10500.8 | + | 7629.26i | −1.04051 | + | 0.755974i | −0.970385 | − | 0.241564i | \(-0.922340\pi\) |
−0.0701244 | + | 0.997538i | \(0.522340\pi\) | |||||||
\(468\) | −4510.93 | + | 3277.38i | −0.445551 | + | 0.323712i | ||||
\(469\) | 3569.42 | + | 10985.5i | 0.351429 | + | 1.08159i | ||||
\(470\) | 83.4060 | − | 256.697i | 0.00818560 | − | 0.0251927i | ||||
\(471\) | −5659.36 | − | 4111.76i | −0.553651 | − | 0.402251i | ||||
\(472\) | −18767.5 | −1.83018 | ||||||||
\(473\) | 8008.74 | − | 7232.70i | 0.778525 | − | 0.703087i | ||||
\(474\) | 30846.9 | 2.98913 | ||||||||
\(475\) | 8802.40 | + | 6395.32i | 0.850277 | + | 0.617763i | ||||
\(476\) | −2041.57 | + | 6283.29i | −0.196586 | + | 0.605030i | ||||
\(477\) | −878.154 | − | 2702.68i | −0.0842933 | − | 0.259428i | ||||
\(478\) | 16342.7 | − | 11873.7i | 1.56381 | − | 1.13617i | ||||
\(479\) | 8272.09 | − | 6010.02i | 0.789063 | − | 0.573288i | −0.118622 | − | 0.992939i | \(-0.537848\pi\) |
0.907685 | + | 0.419651i | \(0.137848\pi\) | |||||||
\(480\) | −59.3799 | − | 182.753i | −0.00564648 | − | 0.0173781i | ||||
\(481\) | −6950.41 | + | 21391.2i | −0.658860 | + | 2.02776i | ||||
\(482\) | −3972.04 | − | 2885.85i | −0.375355 | − | 0.272712i | ||||
\(483\) | 29489.2 | 2.77807 | ||||||||
\(484\) | 19400.5 | − | 4184.09i | 1.82199 | − | 0.392946i | ||||
\(485\) | 178.793 | 0.0167393 | ||||||||
\(486\) | 6196.67 | + | 4502.14i | 0.578367 | + | 0.420208i | ||||
\(487\) | −1109.31 | + | 3414.10i | −0.103219 | + | 0.317674i | −0.989308 | − | 0.145840i | \(-0.953412\pi\) |
0.886090 | + | 0.463514i | \(0.153412\pi\) | |||||||
\(488\) | 2210.68 | + | 6803.76i | 0.205067 | + | 0.631131i | ||||
\(489\) | 3406.99 | − | 2475.33i | 0.315071 | − | 0.228912i | ||||
\(490\) | −562.182 | + | 408.449i | −0.0518302 | + | 0.0376569i | ||||
\(491\) | −1934.03 | − | 5952.33i | −0.177763 | − | 0.547097i | 0.821986 | − | 0.569508i | \(-0.192866\pi\) |
−0.999749 | + | 0.0224101i | \(0.992866\pi\) | |||||||
\(492\) | −7013.54 | + | 21585.5i | −0.642672 | + | 1.97794i | ||||
\(493\) | −2119.74 | − | 1540.08i | −0.193647 | − | 0.140693i | ||||
\(494\) | 26916.5 | 2.45147 | ||||||||
\(495\) | 67.7582 | − | 61.1926i | 0.00615254 | − | 0.00555637i | ||||
\(496\) | 4648.06 | 0.420774 | ||||||||
\(497\) | 17179.1 | + | 12481.3i | 1.55048 | + | 1.12649i | ||||
\(498\) | −2415.00 | + | 7432.61i | −0.217307 | + | 0.668802i | ||||
\(499\) | −4254.92 | − | 13095.3i | −0.381716 | − | 1.17480i | −0.938835 | − | 0.344368i | \(-0.888093\pi\) |
0.557119 | − | 0.830433i | \(-0.311907\pi\) | |||||||
\(500\) | 1301.00 | − | 945.231i | 0.116365 | − | 0.0845441i | ||||
\(501\) | 171.138 | − | 124.339i | 0.0152612 | − | 0.0110879i | ||||
\(502\) | −485.784 | − | 1495.09i | −0.0431904 | − | 0.132927i | ||||
\(503\) | −2155.55 | + | 6634.11i | −0.191076 | + | 0.588073i | 0.808924 | + | 0.587914i | \(0.200051\pi\) |
−1.00000 | 0.000158814i | \(0.999949\pi\) | ||||||||
\(504\) | −4043.28 | − | 2937.61i | −0.357345 | − | 0.259626i | ||||
\(505\) | 497.334 | 0.0438239 | ||||||||
\(506\) | −34306.8 | + | 3657.41i | −3.01408 | + | 0.321328i | ||||
\(507\) | 11249.2 | 0.985395 | ||||||||
\(508\) | −5721.45 | − | 4156.87i | −0.499701 | − | 0.363054i | ||||
\(509\) | −333.121 | + | 1025.24i | −0.0290085 | + | 0.0892791i | −0.964513 | − | 0.264037i | \(-0.914946\pi\) |
0.935504 | + | 0.353316i | \(0.114946\pi\) | |||||||
\(510\) | −62.1677 | − | 191.333i | −0.00539771 | − | 0.0166124i | ||||
\(511\) | −10334.4 | + | 7508.37i | −0.894650 | + | 0.650002i | ||||
\(512\) | 10816.1 | − | 7858.35i | 0.933610 | − | 0.678308i | ||||
\(513\) | −3271.00 | − | 10067.1i | −0.281517 | − | 0.866421i | ||||
\(514\) | −2081.44 | + | 6406.03i | −0.178616 | + | 0.549723i | ||||
\(515\) | −514.075 | − | 373.498i | −0.0439862 | − | 0.0319578i | ||||
\(516\) | 25258.5 | 2.15493 | ||||||||
\(517\) | −1944.68 | − | 4350.38i | −0.165429 | − | 0.370077i | ||||
\(518\) | −43497.1 | −3.68949 | ||||||||
\(519\) | 5501.23 | + | 3996.88i | 0.465274 | + | 0.338041i | ||||
\(520\) | 284.680 | − | 876.156i | 0.0240078 | − | 0.0738884i | ||||
\(521\) | 4915.82 | + | 15129.3i | 0.413370 | + | 1.27222i | 0.913701 | + | 0.406388i | \(0.133212\pi\) |
−0.500330 | + | 0.865835i | \(0.666788\pi\) | |||||||
\(522\) | 3459.73 | − | 2513.64i | 0.290092 | − | 0.210764i | ||||
\(523\) | −909.256 | + | 660.613i | −0.0760210 | + | 0.0552325i | −0.625147 | − | 0.780507i | \(-0.714961\pi\) |
0.549126 | + | 0.835740i | \(0.314961\pi\) | |||||||
\(524\) | −570.346 | − | 1755.35i | −0.0475490 | − | 0.146341i | ||||
\(525\) | −5756.84 | + | 17717.7i | −0.478570 | + | 1.47289i | ||||
\(526\) | −6353.61 | − | 4616.17i | −0.526674 | − | 0.382651i | ||||
\(527\) | −2023.45 | −0.167254 | ||||||||
\(528\) | 7071.88 | + | 4068.93i | 0.582887 | + | 0.335374i | ||||
\(529\) | 26867.3 | 2.20821 | ||||||||
\(530\) | 819.553 | + | 595.440i | 0.0671682 | + | 0.0488005i | ||||
\(531\) | −1016.27 | + | 3127.77i | −0.0830555 | + | 0.255619i | ||||
\(532\) | 10468.8 | + | 32219.6i | 0.853156 | + | 2.62574i | ||||
\(533\) | 13870.9 | − | 10077.8i | 1.12723 | − | 0.818981i | ||||
\(534\) | −8970.57 | + | 6517.50i | −0.726956 | + | 0.528165i | ||||
\(535\) | −183.702 | − | 565.378i | −0.0148451 | − | 0.0456886i | ||||
\(536\) | 4530.41 | − | 13943.2i | 0.365082 | − | 1.12361i | ||||
\(537\) | 10432.6 | + | 7579.71i | 0.838359 | + | 0.609103i | ||||
\(538\) | 9438.36 | 0.756351 | ||||||||
\(539\) | −2532.90 | + | 12004.2i | −0.202411 | + | 0.959287i | ||||
\(540\) | −781.665 | −0.0622917 | ||||||||
\(541\) | −7080.84 | − | 5144.53i | −0.562715 | − | 0.408837i | 0.269736 | − | 0.962934i | \(-0.413063\pi\) |
−0.832452 | + | 0.554098i | \(0.813063\pi\) | |||||||
\(542\) | 3751.60 | − | 11546.3i | 0.297316 | − | 0.915044i | ||||
\(543\) | 7667.27 | + | 23597.4i | 0.605956 | + | 1.86494i | ||||
\(544\) | −1068.94 | + | 776.629i | −0.0842470 | + | 0.0612090i | ||||
\(545\) | −4.41301 | + | 3.20624i | −0.000346849 | + | 0.000252000i | ||||
\(546\) | 14241.6 | + | 43831.2i | 1.11627 | + | 3.43553i | ||||
\(547\) | 2883.77 | − | 8875.34i | 0.225413 | − | 0.693751i | −0.772836 | − | 0.634606i | \(-0.781162\pi\) |
0.998249 | − | 0.0591454i | \(-0.0188376\pi\) | |||||||
\(548\) | 7179.24 | + | 5216.03i | 0.559639 | + | 0.406602i | ||||
\(549\) | 1253.61 | 0.0974553 | ||||||||
\(550\) | 4499.88 | − | 21326.3i | 0.348865 | − | 1.65337i | ||||
\(551\) | −13435.6 | −1.03879 | ||||||||
\(552\) | −30280.4 | − | 22000.0i | −2.33482 | − | 1.69634i | ||||
\(553\) | 9063.19 | − | 27893.6i | 0.696937 | − | 2.14495i | ||||
\(554\) | −5182.07 | − | 15948.8i | −0.397410 | − | 1.22310i | ||||
\(555\) | 697.401 | − | 506.692i | 0.0533388 | − | 0.0387529i | ||||
\(556\) | 13057.6 | − | 9486.89i | 0.995980 | − | 0.723622i | ||||
\(557\) | −3387.01 | − | 10424.1i | −0.257652 | − | 0.792971i | −0.993296 | − | 0.115602i | \(-0.963120\pi\) |
0.735644 | − | 0.677369i | \(-0.236880\pi\) | |||||||
\(558\) | 1020.55 | − | 3140.94i | 0.0774255 | − | 0.238291i | ||||
\(559\) | −15436.8 | − | 11215.5i | −1.16799 | − | 0.848593i | ||||
\(560\) | 439.387 | 0.0331563 | ||||||||
\(561\) | −3078.62 | − | 1771.34i | −0.231693 | − | 0.133309i | ||||
\(562\) | 6525.23 | 0.489769 | ||||||||
\(563\) | −7784.82 | − | 5656.00i | −0.582755 | − | 0.423396i | 0.256961 | − | 0.966422i | \(-0.417279\pi\) |
−0.839716 | + | 0.543026i | \(0.817279\pi\) | |||||||
\(564\) | 3446.69 | − | 10607.8i | 0.257326 | − | 0.791968i | ||||
\(565\) | 207.662 | + | 639.116i | 0.0154626 | + | 0.0475891i | ||||
\(566\) | −12700.0 | + | 9227.10i | −0.943147 | + | 0.685236i | ||||
\(567\) | 17962.9 | − | 13050.8i | 1.33046 | − | 0.966635i | ||||
\(568\) | −8328.46 | − | 25632.4i | −0.615237 | − | 1.89350i | ||||
\(569\) | −4395.77 | + | 13528.8i | −0.323867 | + | 0.996761i | 0.648082 | + | 0.761570i | \(0.275571\pi\) |
−0.971949 | + | 0.235190i | \(0.924429\pi\) | |||||||
\(570\) | −834.589 | − | 606.364i | −0.0613282 | − | 0.0445575i | ||||
\(571\) | 6056.91 | 0.443912 | 0.221956 | − | 0.975057i | \(-0.428756\pi\) | ||||
0.221956 | + | 0.975057i | \(0.428756\pi\) | |||||||
\(572\) | −14321.0 | − | 32037.1i | −1.04684 | − | 2.34185i | ||||
\(573\) | 16398.9 | 1.19559 | ||||||||
\(574\) | 26824.8 | + | 19489.3i | 1.95060 | + | 1.41719i | ||||
\(575\) | −7620.23 | + | 23452.6i | −0.552670 | + | 1.70094i | ||||
\(576\) | −1226.01 | − | 3773.28i | −0.0886874 | − | 0.272952i | ||||
\(577\) | 322.897 | − | 234.598i | 0.0232970 | − | 0.0169263i | −0.576076 | − | 0.817396i | \(-0.695417\pi\) |
0.599373 | + | 0.800470i | \(0.295417\pi\) | |||||||
\(578\) | −1119.12 | + | 813.090i | −0.0805353 | + | 0.0585123i | ||||
\(579\) | −6250.20 | − | 19236.1i | −0.448617 | − | 1.38070i | ||||
\(580\) | −306.592 | + | 943.593i | −0.0219492 | + | 0.0675527i | ||||
\(581\) | 6011.45 | + | 4367.58i | 0.429255 | + | 0.311872i | ||||
\(582\) | 11352.5 | 0.808550 | ||||||||
\(583\) | 17784.3 | − | 1895.96i | 1.26338 | − | 0.134687i | ||||
\(584\) | 16213.2 | 1.14881 | ||||||||
\(585\) | −130.603 | − | 94.8888i | −0.00923039 | − | 0.00670627i | ||||
\(586\) | −6585.33 | + | 20267.6i | −0.464228 | + | 1.42875i | ||||
\(587\) | 713.376 | + | 2195.55i | 0.0501605 | + | 0.154378i | 0.972999 | − | 0.230809i | \(-0.0741371\pi\) |
−0.922839 | + | 0.385187i | \(0.874137\pi\) | |||||||
\(588\) | −23231.8 | + | 16878.9i | −1.62936 | + | 1.18380i | ||||
\(589\) | −8394.27 | + | 6098.80i | −0.587233 | + | 0.426649i | ||||
\(590\) | −362.278 | − | 1114.98i | −0.0252792 | − | 0.0778015i | ||||
\(591\) | 747.139 | − | 2299.46i | 0.0520020 | − | 0.160046i | ||||
\(592\) | 11015.4 | + | 8003.13i | 0.764744 | + | 0.555619i | ||||
\(593\) | 12753.2 | 0.883154 | 0.441577 | − | 0.897223i | \(-0.354419\pi\) | ||||
0.441577 | + | 0.897223i | \(0.354419\pi\) | |||||||
\(594\) | −15736.9 | + | 14212.0i | −1.08703 | + | 0.981695i | ||||
\(595\) | −191.280 | −0.0131793 | ||||||||
\(596\) | 28687.3 | + | 20842.6i | 1.97161 | + | 1.43246i | ||||
\(597\) | −6729.01 | + | 20709.8i | −0.461306 | + | 1.41976i | ||||
\(598\) | 18851.3 | + | 58018.5i | 1.28911 | + | 3.96748i | ||||
\(599\) | −13453.1 | + | 9774.27i | −0.917663 | + | 0.666721i | −0.942941 | − | 0.332959i | \(-0.891953\pi\) |
0.0252783 | + | 0.999680i | \(0.491953\pi\) | |||||||
\(600\) | 19129.4 | − | 13898.3i | 1.30159 | − | 0.945659i | ||||
\(601\) | 3444.43 | + | 10600.9i | 0.233779 | + | 0.719498i | 0.997281 | + | 0.0736925i | \(0.0234783\pi\) |
−0.763502 | + | 0.645806i | \(0.776522\pi\) | |||||||
\(602\) | 11402.9 | − | 35094.4i | 0.772003 | − | 2.37598i | ||||
\(603\) | −2078.43 | − | 1510.06i | −0.140365 | − | 0.101981i | ||||
\(604\) | −17988.0 | −1.21179 | ||||||||
\(605\) | 288.785 | + | 496.770i | 0.0194062 | + | 0.0333828i | ||||
\(606\) | 31578.4 | 2.11681 | ||||||||
\(607\) | 14975.2 | + | 10880.1i | 1.00136 | + | 0.727529i | 0.962379 | − | 0.271711i | \(-0.0875895\pi\) |
0.0389789 | + | 0.999240i | \(0.487589\pi\) | |||||||
\(608\) | −2093.68 | + | 6443.68i | −0.139654 | + | 0.429812i | ||||
\(609\) | −7108.82 | − | 21878.7i | −0.473012 | − | 1.45578i | ||||
\(610\) | −361.537 | + | 262.672i | −0.0239971 | + | 0.0174349i | ||||
\(611\) | −6816.61 | + | 4952.56i | −0.451343 | + | 0.327920i | ||||
\(612\) | −454.073 | − | 1397.49i | −0.0299915 | − | 0.0923044i | ||||
\(613\) | 5179.84 | − | 15941.9i | 0.341291 | − | 1.05039i | −0.622248 | − | 0.782820i | \(-0.713780\pi\) |
0.963539 | − | 0.267567i | \(-0.0862196\pi\) | |||||||
\(614\) | 16869.3 | + | 12256.2i | 1.10878 | + | 0.805573i | ||||
\(615\) | −657.117 | −0.0430854 | ||||||||
\(616\) | 23343.7 | − | 21081.7i | 1.52686 | − | 1.37891i | ||||
\(617\) | −19193.4 | −1.25235 | −0.626173 | − | 0.779684i | \(-0.715380\pi\) | ||||
−0.626173 | + | 0.779684i | \(0.715380\pi\) | |||||||
\(618\) | −32641.4 | − | 23715.4i | −2.12465 | − | 1.54365i | ||||
\(619\) | −9443.67 | + | 29064.6i | −0.613204 | + | 1.88725i | −0.187932 | + | 0.982182i | \(0.560179\pi\) |
−0.425272 | + | 0.905066i | \(0.639821\pi\) | |||||||
\(620\) | 236.772 | + | 728.708i | 0.0153371 | + | 0.0472026i | ||||
\(621\) | 19408.8 | − | 14101.3i | 1.25418 | − | 0.911218i | ||||
\(622\) | −15767.1 | + | 11455.5i | −1.01640 | + | 0.738461i | ||||
\(623\) | 3257.85 | + | 10026.6i | 0.209507 | + | 0.644798i | ||||
\(624\) | 4457.99 | − | 13720.3i | 0.285998 | − | 0.880210i | ||||
\(625\) | −12584.4 | − | 9143.08i | −0.805400 | − | 0.585157i | ||||
\(626\) | 52007.2 | 3.32049 | ||||||||
\(627\) | −18110.6 | + | 1930.75i | −1.15353 | + | 0.122977i | ||||
\(628\) | 18213.8 | 1.15734 | ||||||||
\(629\) | −4795.35 | − | 3484.03i | −0.303980 | − | 0.220854i | ||||
\(630\) | 96.4742 | − | 296.917i | 0.00610099 | − | 0.0187769i | ||||
\(631\) | −1685.84 | − | 5188.47i | −0.106358 | − | 0.327337i | 0.883689 | − | 0.468075i | \(-0.155052\pi\) |
−0.990047 | + | 0.140738i | \(0.955052\pi\) | |||||||
\(632\) | −30116.0 | + | 21880.5i | −1.89549 | + | 1.37715i | ||||
\(633\) | 2877.05 | − | 2090.30i | 0.180652 | − | 0.131251i | ||||
\(634\) | −2753.86 | − | 8475.52i | −0.172508 | − | 0.530924i | ||||
\(635\) | 63.2730 | − | 194.734i | 0.00395419 | − | 0.0121698i | ||||
\(636\) | 33867.5 | + | 24606.1i | 2.11153 | + | 1.53411i | ||||
\(637\) | 21692.8 | 1.34929 | ||||||||
\(638\) | 10983.7 | + | 24571.3i | 0.681581 | + | 1.52475i | ||||
\(639\) | −4722.85 | −0.292383 | ||||||||
\(640\) | 927.036 | + | 673.531i | 0.0572568 | + | 0.0415995i | ||||
\(641\) | 9085.86 | − | 27963.4i | 0.559859 | − | 1.72307i | −0.122893 | − | 0.992420i | \(-0.539217\pi\) |
0.682752 | − | 0.730650i | \(-0.260783\pi\) | |||||||
\(642\) | −11664.3 | − | 35898.9i | −0.717058 | − | 2.20688i | ||||
\(643\) | −3926.41 | + | 2852.70i | −0.240812 | + | 0.174960i | −0.701645 | − | 0.712527i | \(-0.747551\pi\) |
0.460833 | + | 0.887487i | \(0.347551\pi\) | |||||||
\(644\) | −62117.4 | + | 45130.9i | −3.80088 | + | 2.76150i | ||||
\(645\) | 225.984 | + | 695.507i | 0.0137955 | + | 0.0424583i | ||||
\(646\) | −2191.97 | + | 6746.19i | −0.133501 | + | 0.410875i | ||||
\(647\) | −12301.3 | − | 8937.42i | −0.747472 | − | 0.543070i | 0.147571 | − | 0.989052i | \(-0.452855\pi\) |
−0.895042 | + | 0.445982i | \(0.852855\pi\) | |||||||
\(648\) | −28181.2 | −1.70843 | ||||||||
\(649\) | −17940.5 | − | 10322.4i | −1.08509 | − | 0.624327i | ||||
\(650\) | −38538.8 | −2.32557 | ||||||||
\(651\) | −14372.8 | − | 10442.5i | −0.865307 | − | 0.628683i | ||||
\(652\) | −3388.35 | + | 10428.3i | −0.203525 | + | 0.626384i | ||||
\(653\) | −1064.91 | − | 3277.46i | −0.0638180 | − | 0.196412i | 0.914064 | − | 0.405571i | \(-0.132927\pi\) |
−0.977882 | + | 0.209159i | \(0.932927\pi\) | |||||||
\(654\) | −280.206 | + | 203.581i | −0.0167537 | + | 0.0121723i | ||||
\(655\) | 43.2317 | − | 31.4096i | 0.00257893 | − | 0.00187370i | ||||
\(656\) | −3207.31 | − | 9871.09i | −0.190891 | − | 0.587502i | ||||
\(657\) | 877.953 | − | 2702.06i | 0.0521343 | − | 0.160453i | ||||
\(658\) | −13182.6 | − | 9577.72i | −0.781020 | − | 0.567445i | ||||
\(659\) | −25007.3 | −1.47822 | −0.739108 | − | 0.673587i | \(-0.764753\pi\) | ||||
−0.739108 | + | 0.673587i | \(0.764753\pi\) | |||||||
\(660\) | −277.674 | + | 1315.98i | −0.0163764 | + | 0.0776128i | ||||
\(661\) | −1273.77 | −0.0749531 | −0.0374765 | − | 0.999298i | \(-0.511932\pi\) | ||||
−0.0374765 | + | 0.999298i | \(0.511932\pi\) | |||||||
\(662\) | −3259.20 | − | 2367.95i | −0.191348 | − | 0.139023i | ||||
\(663\) | −1940.71 | + | 5972.90i | −0.113682 | + | 0.349877i | ||||
\(664\) | −2914.37 | − | 8969.51i | −0.170331 | − | 0.524224i | ||||
\(665\) | −793.522 | + | 576.528i | −0.0462729 | + | 0.0336192i | ||||
\(666\) | 7826.73 | − | 5686.45i | 0.455375 | − | 0.330849i | ||||
\(667\) | −9409.81 | − | 28960.4i | −0.546251 | − | 1.68119i | ||||
\(668\) | −170.201 | + | 523.826i | −0.00985822 | + | 0.0303405i | ||||
\(669\) | 19755.5 | + | 14353.2i | 1.14169 | + | 0.829488i | ||||
\(670\) | 915.816 | 0.0528076 | ||||||||
\(671\) | −1628.90 | + | 7719.83i | −0.0937153 | + | 0.444144i | ||||
\(672\) | −11600.8 | −0.665936 | ||||||||
\(673\) | −9564.75 | − | 6949.20i | −0.547836 | − | 0.398026i | 0.279151 | − | 0.960247i | \(-0.409947\pi\) |
−0.826987 | + | 0.562221i | \(0.809947\pi\) | |||||||
\(674\) | 10235.6 | − | 31501.9i | 0.584956 | − | 1.80031i | ||||
\(675\) | 4683.41 | + | 14414.0i | 0.267058 | + | 0.821921i | ||||
\(676\) | −23695.8 | + | 17216.0i | −1.34819 | + | 0.979519i | ||||
\(677\) | −423.204 | + | 307.476i | −0.0240252 | + | 0.0174553i | −0.599733 | − | 0.800200i | \(-0.704727\pi\) |
0.575708 | + | 0.817655i | \(0.304727\pi\) | |||||||
\(678\) | 13185.6 | + | 40581.0i | 0.746885 | + | 2.29868i | ||||
\(679\) | 3335.50 | − | 10265.6i | 0.188519 | − | 0.580203i | ||||
\(680\) | 196.412 | + | 142.701i | 0.0110765 | + | 0.00804757i | ||||
\(681\) | 14142.8 | 0.795819 | ||||||||
\(682\) | 18016.0 | + | 10365.8i | 1.01154 | + | 0.582006i | ||||
\(683\) | −215.567 | −0.0120768 | −0.00603838 | − | 0.999982i | \(-0.501922\pi\) | ||||
−0.00603838 | + | 0.999982i | \(0.501922\pi\) | |||||||
\(684\) | −6095.83 | − | 4428.88i | −0.340760 | − | 0.247577i | ||||
\(685\) | −79.3947 | + | 244.352i | −0.00442849 | + | 0.0136295i | ||||
\(686\) | −259.041 | − | 797.248i | −0.0144173 | − | 0.0443718i | ||||
\(687\) | 15706.4 | − | 11411.4i | 0.872251 | − | 0.633728i | ||||
\(688\) | −9344.78 | + | 6789.38i | −0.517829 | + | 0.376225i | ||||
\(689\) | −9772.33 | − | 30076.2i | −0.540343 | − | 1.66300i | ||||
\(690\) | 722.502 | − | 2223.63i | 0.0398626 | − | 0.122684i | ||||
\(691\) | 1892.88 | + | 1375.26i | 0.104209 | + | 0.0757125i | 0.638670 | − | 0.769481i | \(-0.279485\pi\) |
−0.534460 | + | 0.845194i | \(0.679485\pi\) | |||||||
\(692\) | −17704.9 | −0.972602 | ||||||||
\(693\) | −2249.37 | − | 5032.02i | −0.123300 | − | 0.275830i | ||||
\(694\) | −19049.5 | −1.04194 | ||||||||
\(695\) | 378.051 | + | 274.670i | 0.0206335 | + | 0.0149911i | ||||
\(696\) | −9022.74 | + | 27769.1i | −0.491388 | + | 1.51234i | ||||
\(697\) | 1396.25 | + | 4297.21i | 0.0758776 | + | 0.233527i | ||||
\(698\) | 42099.5 | − | 30587.1i | 2.28294 | − | 1.65865i | ||||
\(699\) | 27054.3 | − | 19656.1i | 1.46393 | − | 1.06361i | ||||
\(700\) | −14989.1 | − | 46131.8i | −0.809337 | − | 2.49088i | ||||
\(701\) | 16.1379 | − | 49.6672i | 0.000869499 | − | 0.00267604i | −0.950621 | − | 0.310355i | \(-0.899552\pi\) |
0.951490 | + | 0.307679i | \(0.0995522\pi\) | |||||||
\(702\) | 30332.7 | + | 22038.0i | 1.63082 | + | 1.18486i | ||||
\(703\) | −30394.5 | −1.63066 | ||||||||
\(704\) | 24829.1 | − | 2647.01i | 1.32924 | − | 0.141708i | ||||
\(705\) | 322.930 | 0.0172514 | ||||||||
\(706\) | −39088.2 | − | 28399.2i | −2.08371 | − | 1.51391i | ||||
\(707\) | 9278.12 | − | 28555.1i | 0.493550 | − | 1.51899i | ||||
\(708\) | −14970.9 | − | 46075.6i | −0.794689 | − | 2.44580i | ||||
\(709\) | −7731.67 | + | 5617.39i | −0.409547 | + | 0.297553i | −0.773418 | − | 0.633896i | \(-0.781455\pi\) |
0.363871 | + | 0.931449i | \(0.381455\pi\) | |||||||
\(710\) | 1362.05 | − | 989.587i | 0.0719955 | − | 0.0523078i | ||||
\(711\) | 2015.78 | + | 6203.93i | 0.106326 | + | 0.327237i | ||||
\(712\) | 4134.97 | − | 12726.1i | 0.217647 | − | 0.669848i | ||||
\(713\) | −19025.0 | − | 13822.5i | −0.999289 | − | 0.726026i | ||||
\(714\) | −12145.4 | −0.636596 | ||||||||
\(715\) | 754.032 | − | 680.968i | 0.0394394 | − | 0.0356178i | ||||
\(716\) | −33575.8 | −1.75249 | ||||||||
\(717\) | 19553.2 | + | 14206.2i | 1.01845 | + | 0.739947i | ||||
\(718\) | −15660.5 | + | 48198.2i | −0.813992 | + | 2.50521i | ||||
\(719\) | 7175.04 | + | 22082.5i | 0.372161 | + | 1.14539i | 0.945374 | + | 0.325988i | \(0.105697\pi\) |
−0.573213 | + | 0.819406i | \(0.694303\pi\) | |||||||
\(720\) | −79.0619 | + | 57.4418i | −0.00409231 | + | 0.00297324i | ||||
\(721\) | −31035.3 | + | 22548.5i | −1.60307 | + | 1.16470i | ||||
\(722\) | 1094.71 | + | 3369.17i | 0.0564279 | + | 0.173667i | ||||
\(723\) | 1815.23 | − | 5586.70i | 0.0933735 | − | 0.287374i | ||||
\(724\) | −52264.7 | − | 37972.5i | −2.68287 | − | 1.94922i | ||||
\(725\) | 19237.0 | 0.985440 | ||||||||
\(726\) | 18336.5 | + | 31542.6i | 0.937372 | + | 1.61247i | ||||
\(727\) | −18386.3 | −0.937978 | −0.468989 | − | 0.883204i | \(-0.655382\pi\) | ||||
−0.468989 | + | 0.883204i | \(0.655382\pi\) | |||||||
\(728\) | −44994.7 | − | 32690.6i | −2.29068 | − | 1.66428i | ||||
\(729\) | 4275.99 | − | 13160.1i | 0.217243 | − | 0.668605i | ||||
\(730\) | 312.970 | + | 963.223i | 0.0158679 | + | 0.0488363i | ||||
\(731\) | 4068.09 | − | 2955.64i | 0.205833 | − | 0.149546i | ||||
\(732\) | −14940.3 | + | 10854.7i | −0.754383 | + | 0.548091i | ||||
\(733\) | 3234.57 | + | 9954.99i | 0.162990 | + | 0.501632i | 0.998883 | − | 0.0472615i | \(-0.0150494\pi\) |
−0.835893 | + | 0.548893i | \(0.815049\pi\) | |||||||
\(734\) | 19274.3 | − | 59320.2i | 0.969248 | − | 2.98304i | ||||
\(735\) | −672.621 | − | 488.688i | −0.0337551 | − | 0.0245245i | ||||
\(736\) | −15355.7 | −0.769047 | ||||||||
\(737\) | 11999.7 | − | 10836.9i | 0.599748 | − | 0.541634i | ||||
\(738\) | −7374.63 | −0.367837 | ||||||||
\(739\) | 3769.73 | + | 2738.87i | 0.187648 | + | 0.136334i | 0.677643 | − | 0.735391i | \(-0.263002\pi\) |
−0.489995 | + | 0.871725i | \(0.663002\pi\) | |||||||
\(740\) | −693.585 | + | 2134.63i | −0.0344550 | + | 0.106042i | ||||
\(741\) | 9951.61 | + | 30627.9i | 0.493363 | + | 1.51841i | ||||
\(742\) | 49477.3 | − | 35947.4i | 2.44794 | − | 1.77853i | ||||
\(743\) | 19783.4 | − | 14373.5i | 0.976828 | − | 0.709707i | 0.0198303 | − | 0.999803i | \(-0.493687\pi\) |
0.956997 | + | 0.290096i | \(0.0936874\pi\) | |||||||
\(744\) | 6967.98 | + | 21445.2i | 0.343358 | + | 1.05675i | ||||
\(745\) | −317.251 | + | 976.398i | −0.0156016 | + | 0.0480167i | ||||
\(746\) | 19875.3 | + | 14440.3i | 0.975452 | + | 0.708708i | ||||
\(747\) | −1652.66 | −0.0809474 | ||||||||
\(748\) | 9195.84 | − | 980.358i | 0.449510 | − | 0.0479217i | ||||
\(749\) | −35889.0 | −1.75081 | ||||||||
\(750\) | 2391.70 | + | 1737.67i | 0.116444 | + | 0.0846012i | ||||
\(751\) | −9698.79 | + | 29849.8i | −0.471257 | + | 1.45038i | 0.379683 | + | 0.925116i | \(0.376033\pi\) |
−0.850940 | + | 0.525263i | \(0.823967\pi\) | |||||||
\(752\) | 1576.18 | + | 4850.99i | 0.0764328 | + | 0.235236i | ||||
\(753\) | 1521.64 | − | 1105.54i | 0.0736409 | − | 0.0535033i | ||||
\(754\) | 38500.8 | − | 27972.4i | 1.85957 | − | 1.35106i | ||||
\(755\) | −160.936 | − | 495.311i | −0.00775770 | − | 0.0238758i | ||||
\(756\) | −14582.5 | + | 44880.3i | −0.701535 | + | 2.15910i | ||||
\(757\) | −18417.1 | − | 13380.8i | −0.884255 | − | 0.642449i | 0.0501189 | − | 0.998743i | \(-0.484040\pi\) |
−0.934374 | + | 0.356295i | \(0.884040\pi\) | |||||||
\(758\) | −58127.2 | −2.78532 | ||||||||
\(759\) | −16845.7 | − | 37685.1i | −0.805614 | − | 1.80222i | ||||
\(760\) | 1244.92 | 0.0594185 | ||||||||
\(761\) | −11761.9 | − | 8545.53i | −0.560275 | − | 0.407063i | 0.271285 | − | 0.962499i | \(-0.412551\pi\) |
−0.831559 | + | 0.555436i | \(0.812551\pi\) | |||||||
\(762\) | 4017.55 | − | 12364.7i | 0.190998 | − | 0.587831i | ||||
\(763\) | 101.763 | + | 313.193i | 0.00482838 | + | 0.0148602i | ||||
\(764\) | −34543.4 | + | 25097.3i | −1.63578 | + | 1.18847i | ||||
\(765\) | 34.4182 | − | 25.0063i | 0.00162666 | − | 0.00118184i | ||||
\(766\) | 12691.7 | + | 39061.1i | 0.598656 | + | 1.84247i | ||||
\(767\) | −11309.4 | + | 34806.6i | −0.532409 | + | 1.63859i | ||||
\(768\) | 33494.3 | + | 24335.0i | 1.57373 | + | 1.14338i | ||||
\(769\) | 31854.1 | 1.49374 | 0.746870 | − | 0.664970i | \(-0.231555\pi\) | ||||
0.746870 | + | 0.664970i | \(0.231555\pi\) | |||||||
\(770\) | 1703.08 | + | 979.897i | 0.0797074 | + | 0.0458611i | ||||
\(771\) | −8058.90 | −0.376439 | ||||||||
\(772\) | 42605.1 | + | 30954.4i | 1.98626 | + | 1.44310i | ||||
\(773\) | −4288.98 | + | 13200.1i | −0.199565 | + | 0.614198i | 0.800328 | + | 0.599563i | \(0.204659\pi\) |
−0.999893 | + | 0.0146355i | \(0.995341\pi\) | |||||||
\(774\) | 2536.15 | + | 7805.48i | 0.117778 | + | 0.362483i | ||||
\(775\) | 12018.9 | − | 8732.22i | 0.557072 | − | 0.404736i | ||||
\(776\) | −11083.5 | + | 8052.62i | −0.512724 | + | 0.372516i | ||||
\(777\) | −16081.9 | − | 49494.9i | −0.742514 | − | 2.28522i | ||||
\(778\) | −6857.02 | + | 21103.7i | −0.315985 | + | 0.972501i | ||||
\(779\) | 18744.4 | + | 13618.6i | 0.862113 | + | 0.626362i | ||||
\(780\) | 2378.12 | 0.109167 | ||||||||
\(781\) | 6136.69 | − | 29083.6i | 0.281163 | − | 1.33251i | ||||
\(782\) | −16076.6 | −0.735165 | ||||||||
\(783\) | −15140.9 | − | 11000.5i | −0.691047 | − | 0.502075i | ||||
\(784\) | 4057.99 | − | 12489.2i | 0.184858 | − | 0.568933i | ||||
\(785\) | 162.957 | + | 501.529i | 0.00740913 | + | 0.0228030i | ||||
\(786\) | 2745.01 | − | 1994.37i | 0.124569 | − | 0.0905047i | ||||
\(787\) | 13398.5 | − | 9734.57i | 0.606867 | − | 0.440915i | −0.241443 | − | 0.970415i | \(-0.577621\pi\) |
0.848310 | + | 0.529500i | \(0.177621\pi\) | |||||||
\(788\) | 1945.33 | + | 5987.11i | 0.0879435 | + | 0.270662i | ||||
\(789\) | 2903.61 | − | 8936.40i | 0.131016 | − | 0.403225i | ||||
\(790\) | −1881.26 | − | 1366.82i | −0.0847245 | − | 0.0615560i | ||||
\(791\) | 40569.8 | 1.82363 | ||||||||
\(792\) | −1444.34 | + | 6845.13i | −0.0648008 | + | 0.307110i | ||||
\(793\) | 13950.6 | 0.624715 | ||||||||
\(794\) | 52825.0 | + | 38379.6i | 2.36107 | + | 1.71542i | ||||
\(795\) | −374.537 | + | 1152.71i | −0.0167088 | + | 0.0514243i | ||||
\(796\) | −17520.4 | − | 53922.1i | −0.780142 | − | 2.40103i | ||||
\(797\) | −21212.5 | + | 15411.8i | −0.942766 | + | 0.684960i | −0.949085 | − | 0.315020i | \(-0.897989\pi\) |
0.00631891 | + | 0.999980i | \(0.497989\pi\) | |||||||
\(798\) | −50385.0 | + | 36606.9i | −2.23510 | + | 1.62390i | ||||
\(799\) | −686.164 | − | 2111.80i | −0.0303814 | − | 0.0935043i | ||||
\(800\) | 2997.72 | − | 9226.02i | 0.132482 | − | 0.407736i | ||||
\(801\) | −1897.01 | − | 1378.26i | −0.0836797 | − | 0.0607968i | ||||
\(802\) | −38842.6 | −1.71020 | ||||||||
\(803\) | 15498.7 | + | 8917.44i | 0.681116 | + | 0.391893i | ||||
\(804\) | 37845.4 | 1.66008 | ||||||||
\(805\) | −1798.46 | − | 1306.66i | −0.0787422 | − | 0.0572096i | ||||
\(806\) | 11357.0 | − | 34953.2i | 0.496319 | − | 1.52751i | ||||
\(807\) | 3489.57 | + | 10739.8i | 0.152217 | + | 0.468474i | ||||
\(808\) | −30830.1 | + | 22399.4i | −1.34233 | + | 0.975258i | ||||
\(809\) | 18070.1 | − | 13128.7i | 0.785304 | − | 0.570557i | −0.121262 | − | 0.992621i | \(-0.538694\pi\) |
0.906566 | + | 0.422064i | \(0.138694\pi\) | |||||||
\(810\) | −543.994 | − | 1674.24i | −0.0235975 | − | 0.0726258i | ||||
\(811\) | 12408.0 | − | 38187.7i | 0.537241 | − | 1.65346i | −0.201517 | − | 0.979485i | \(-0.564587\pi\) |
0.738757 | − | 0.673971i | \(-0.235413\pi\) | |||||||
\(812\) | 48458.0 | + | 35206.8i | 2.09426 | + | 1.52157i | ||||
\(813\) | 14525.4 | 0.626603 | ||||||||
\(814\) | 24847.7 | + | 55586.2i | 1.06992 | + | 2.39348i | ||||
\(815\) | −317.464 | −0.0136445 | ||||||||
\(816\) | 3075.74 | + | 2234.65i | 0.131951 | + | 0.0958683i | ||||
\(817\) | 7967.97 | − | 24522.9i | 0.341205 | − | 1.05012i | ||||
\(818\) | −7138.54 | − | 21970.2i | −0.305126 | − | 0.939081i | ||||
\(819\) | −7884.66 | + | 5728.54i | −0.336401 | + | 0.244410i | ||||
\(820\) | 1384.18 | − | 1005.67i | 0.0589484 | − | 0.0428285i | ||||
\(821\) | 4272.21 | + | 13148.5i | 0.181609 | + | 0.558936i | 0.999873 | − | 0.0159066i | \(-0.00506343\pi\) |
−0.818264 | + | 0.574842i | \(0.805063\pi\) | |||||||
\(822\) | −5041.20 | + | 15515.2i | −0.213908 | + | 0.658340i | ||||
\(823\) | −11522.4 | − | 8371.55i | −0.488028 | − | 0.354573i | 0.316397 | − | 0.948627i | \(-0.397527\pi\) |
−0.804425 | + | 0.594054i | \(0.797527\pi\) | |||||||
\(824\) | 48689.9 | 2.05849 | ||||||||
\(825\) | 25930.6 | − | 2764.43i | 1.09429 | − | 0.116661i | ||||
\(826\) | −70776.4 | −2.98139 | ||||||||
\(827\) | 19798.3 | + | 14384.3i | 0.832471 | + | 0.604825i | 0.920257 | − | 0.391314i | \(-0.127979\pi\) |
−0.0877864 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(828\) | 5277.16 | − | 16241.4i | 0.221490 | − | 0.681677i | ||||
\(829\) | 8923.11 | + | 27462.5i | 0.373839 | + | 1.15056i | 0.944259 | + | 0.329204i | \(0.106780\pi\) |
−0.570420 | + | 0.821353i | \(0.693220\pi\) | |||||||
\(830\) | 476.621 | − | 346.285i | 0.0199322 | − | 0.0144816i | ||||
\(831\) | 16232.0 | − | 11793.2i | 0.677595 | − | 0.492302i | ||||
\(832\) | −13643.4 | − | 41990.1i | −0.568510 | − | 1.74969i | ||||
\(833\) | −1766.58 | + | 5436.97i | −0.0734794 | + | 0.226146i | ||||
\(834\) | 24004.5 | + | 17440.3i | 0.996653 | + | 0.724111i | ||||
\(835\) | −15.9466 | −0.000660905 | ||||||||
\(836\) | 35194.0 | − | 31783.8i | 1.45599 | − | 1.31491i | ||||
\(837\) | −14453.1 | −0.596861 | ||||||||
\(838\) | −23161.8 | − | 16828.0i | −0.954785 | − | 0.693692i | ||||
\(839\) | −1789.17 | + | 5506.51i | −0.0736223 | + | 0.226586i | −0.981096 | − | 0.193523i | \(-0.938008\pi\) |
0.907473 | + | 0.420110i | \(0.138008\pi\) | |||||||
\(840\) | 658.693 | + | 2027.25i | 0.0270560 | + | 0.0832699i | ||||
\(841\) | 513.117 | − | 372.802i | 0.0210389 | − | 0.0152856i | ||||
\(842\) | 38203.6 | − | 27756.5i | 1.56364 | − | 1.13605i | ||||
\(843\) | 2412.52 | + | 7424.98i | 0.0985666 | + | 0.303357i | ||||
\(844\) | −2861.31 | + | 8806.20i | −0.116695 | + | 0.359149i | ||||
\(845\) | −686.057 | − | 498.449i | −0.0279303 | − | 0.0202925i | ||||
\(846\) | 3624.14 | 0.147282 | ||||||||
\(847\) | 33910.2 | − | 7313.37i | 1.37564 | − | 0.296683i | ||||
\(848\) | −19143.8 | −0.775238 | ||||||||
\(849\) | −15194.9 | − | 11039.7i | −0.614237 | − | 0.446269i | ||||
\(850\) | 3138.45 | − | 9659.16i | 0.126645 | − | 0.389772i | ||||
\(851\) | −21287.3 | − | 65515.4i | −0.857483 | − | 2.63906i | ||||
\(852\) | 56285.7 | − | 40894.0i | 2.26328 | − | 1.64437i | ||||
\(853\) | 12035.9 | − | 8744.57i | 0.483119 | − | 0.351006i | −0.319413 | − | 0.947616i | \(-0.603486\pi\) |
0.802532 | + | 0.596609i | \(0.203486\pi\) | |||||||
\(854\) | 8336.94 | + | 25658.5i | 0.334057 | + | 1.02812i | ||||
\(855\) | 67.4133 | − | 207.477i | 0.00269648 | − | 0.00829890i | ||||
\(856\) | 36851.9 | + | 26774.4i | 1.47146 | + | 1.06908i | ||||
\(857\) | 32618.4 | 1.30014 | 0.650072 | − | 0.759872i | \(-0.274739\pi\) | ||||
0.650072 | + | 0.759872i | \(0.274739\pi\) | |||||||
\(858\) | 47877.6 | − | 43238.3i | 1.90503 | − | 1.72043i | ||||
\(859\) | −13553.7 | −0.538354 | −0.269177 | − | 0.963091i | \(-0.586752\pi\) | ||||
−0.269177 | + | 0.963091i | \(0.586752\pi\) | |||||||
\(860\) | −1540.44 | − | 1119.20i | −0.0610798 | − | 0.0443771i | ||||
\(861\) | −12259.0 | + | 37729.2i | −0.485232 | + | 1.49339i | ||||
\(862\) | 19290.2 | + | 59369.2i | 0.762213 | + | 2.34585i | ||||
\(863\) | 4663.10 | − | 3387.94i | 0.183932 | − | 0.133635i | −0.492009 | − | 0.870590i | \(-0.663737\pi\) |
0.675941 | + | 0.736955i | \(0.263737\pi\) | |||||||
\(864\) | −7635.22 | + | 5547.31i | −0.300643 | + | 0.218430i | ||||
\(865\) | −158.403 | − | 487.516i | −0.00622645 | − | 0.0191630i | ||||
\(866\) | 6314.42 | − | 19433.8i | 0.247775 | − | 0.762572i | ||||
\(867\) | −1338.97 | − | 972.819i | −0.0524496 | − | 0.0381069i | ||||
\(868\) | 46256.9 | 1.80883 | ||||||||
\(869\) | −40823.4 | + | 4352.13i | −1.59360 | + | 0.169892i | ||||
\(870\) | −1823.93 | −0.0710771 | ||||||||
\(871\) | −23129.3 | − | 16804.4i | −0.899777 | − | 0.653726i | ||||
\(872\) | 129.160 | − | 397.515i | 0.00501596 | − | 0.0154375i | ||||
\(873\) | 741.861 | + | 2283.21i | 0.0287608 | + | 0.0885167i | ||||
\(874\) | −66693.7 | + | 48455.8i | −2.58118 | + | 1.87533i | ||||
\(875\) | 2274.02 | − | 1652.17i | 0.0878581 | − | 0.0638327i | ||||
\(876\) | 12933.3 | + | 39804.5i | 0.498829 | + | 1.53524i | ||||
\(877\) | −3918.44 | + | 12059.7i | −0.150874 | + | 0.464342i | −0.997719 | − | 0.0674968i | \(-0.978499\pi\) |
0.846846 | + | 0.531839i | \(0.178499\pi\) | |||||||
\(878\) | 1265.68 | + | 919.573i | 0.0486501 | + | 0.0353463i | ||||
\(879\) | −25497.0 | −0.978374 | ||||||||
\(880\) | −251.000 | − | 561.505i | −0.00961501 | − | 0.0215095i | ||||
\(881\) | −17080.9 | −0.653200 | −0.326600 | − | 0.945163i | \(-0.605903\pi\) | ||||
−0.326600 | + | 0.945163i | \(0.605903\pi\) | |||||||
\(882\) | −7548.63 | − | 5484.40i | −0.288181 | − | 0.209376i | ||||
\(883\) | 10648.8 | − | 32773.7i | 0.405845 | − | 1.24906i | −0.514343 | − | 0.857585i | \(-0.671964\pi\) |
0.920188 | − | 0.391477i | \(-0.128036\pi\) | |||||||
\(884\) | −5053.05 | − | 15551.7i | −0.192254 | − | 0.591696i | ||||
\(885\) | 1134.78 | − | 824.463i | 0.0431018 | − | 0.0313153i | ||||
\(886\) | 21045.1 | − | 15290.2i | 0.797997 | − | 0.579779i | ||||
\(887\) | 9846.35 | + | 30303.9i | 0.372726 | + | 1.14713i | 0.945000 | + | 0.327070i | \(0.106061\pi\) |
−0.572274 | + | 0.820063i | \(0.693939\pi\) | |||||||
\(888\) | −20411.6 | + | 62820.4i | −0.771361 | + | 2.37400i | ||||
\(889\) | −10000.5 | − | 7265.81i | −0.377285 | − | 0.274114i | ||||
\(890\) | 835.877 | 0.0314817 | ||||||||
\(891\) | −26939.3 | − | 15500.0i | −1.01291 | − | 0.582794i | ||||
\(892\) | −63580.3 | −2.38658 | ||||||||
\(893\) | −9211.61 | − | 6692.63i | −0.345190 | − | 0.250795i | ||||
\(894\) | −20144.0 | + | 61996.7i | −0.753596 | + | 2.31933i | ||||
\(895\) | −300.397 | − | 924.528i | −0.0112192 | − | 0.0345291i | ||||
\(896\) | 55966.2 | − | 40661.8i | 2.08672 | − | 1.51609i | ||||
\(897\) | −59048.8 | + | 42901.5i | −2.19797 | + | 1.59692i | ||||
\(898\) | 7668.52 | + | 23601.3i | 0.284969 | + | 0.877043i | ||||
\(899\) | −5668.94 | + | 17447.2i | −0.210311 | + | 0.647271i | ||||
\(900\) | 8727.98 | + | 6341.25i | 0.323259 | + | 0.234861i | ||||
\(901\) | 8333.94 | 0.308151 | ||||||||
\(902\) | 9582.32 | − | 45413.4i | 0.353721 | − | 1.67639i | ||||
\(903\) | 44149.4 | 1.62702 | ||||||||
\(904\) | −41658.2 | − | 30266.5i | −1.53267 | − | 1.11355i | ||||
\(905\) | 577.991 | − | 1778.87i | 0.0212299 | − | 0.0653389i | ||||
\(906\) | −10218.7 | − | 31449.9i | −0.374717 | − | 1.15326i | ||||
\(907\) | −30348.0 | + | 22049.1i | −1.11101 | + | 0.807199i | −0.982823 | − | 0.184550i | \(-0.940917\pi\) |
−0.128191 | + | 0.991749i | \(0.540917\pi\) | |||||||
\(908\) | −29791.0 | + | 21644.4i | −1.08882 | + | 0.791074i | ||||
\(909\) | 2063.58 | + | 6351.05i | 0.0752967 | + | 0.231739i | ||||
\(910\) | 1073.59 | − | 3304.18i | 0.0391090 | − | 0.120365i | ||||
\(911\) | 40575.6 | + | 29479.9i | 1.47566 | + | 1.07213i | 0.978922 | + | 0.204234i | \(0.0654704\pi\) |
0.496742 | + | 0.867898i | \(0.334530\pi\) | |||||||
\(912\) | 19495.0 | 0.707835 | ||||||||
\(913\) | 2147.41 | − | 10177.2i | 0.0778409 | − | 0.368911i | ||||
\(914\) | 64043.7 | 2.31770 | ||||||||
\(915\) | −432.560 | − | 314.273i | −0.0156284 | − | 0.0113547i | ||||
\(916\) | −15620.4 | + | 48074.8i | −0.563443 | + | 1.73410i | ||||
\(917\) | −996.909 | − | 3068.17i | −0.0359006 | − | 0.110491i | ||||
\(918\) | −7993.67 | + | 5807.74i | −0.287397 | + | 0.208806i | ||||
\(919\) | −30774.6 | + | 22359.1i | −1.10464 | + | 0.802565i | −0.981811 | − | 0.189863i | \(-0.939196\pi\) |
−0.122826 | + | 0.992428i | \(0.539196\pi\) | |||||||
\(920\) | 871.900 | + | 2683.43i | 0.0312453 | + | 0.0961632i | ||||
\(921\) | −7709.29 | + | 23726.8i | −0.275820 | + | 0.848885i | ||||
\(922\) | −1607.78 | − | 1168.12i | −0.0574290 | − | 0.0417246i | ||||
\(923\) | −52557.1 | −1.87426 | ||||||||
\(924\) | 70378.5 | + | 40493.5i | 2.50572 | + | 1.44171i | ||||
\(925\) | 43518.7 | 1.54690 | ||||||||
\(926\) | 7258.88 | + | 5273.89i | 0.257604 | + | 0.187161i | ||||
\(927\) | 2636.59 | − | 8114.59i | 0.0934163 | − | 0.287506i | ||||
\(928\) | 3701.72 | + | 11392.7i | 0.130943 | + | 0.403001i | ||||
\(929\) | −7475.55 | + | 5431.30i | −0.264010 | + | 0.191814i | −0.711913 | − | 0.702268i | \(-0.752171\pi\) |
0.447903 | + | 0.894082i | \(0.352171\pi\) | |||||||
\(930\) | −1139.56 | + | 827.935i | −0.0401801 | + | 0.0291925i | ||||
\(931\) | 9058.69 | + | 27879.8i | 0.318890 | + | 0.981442i | ||||
\(932\) | −26906.2 | + | 82808.9i | −0.945647 | + | 2.91040i | ||||
\(933\) | −18864.5 | − | 13705.9i | −0.661947 | − | 0.480932i | ||||
\(934\) | 62127.8 | 2.17653 | ||||||||
\(935\) | 109.269 | + | 244.442i | 0.00382189 | + | 0.00854984i | ||||
\(936\) | 12369.9 | 0.431968 | ||||||||
\(937\) | 2909.29 | + | 2113.73i | 0.101433 | + | 0.0736952i | 0.637346 | − | 0.770578i | \(-0.280032\pi\) |
−0.535913 | + | 0.844273i | \(0.680032\pi\) | |||||||
\(938\) | 17085.2 | − | 52582.8i | 0.594724 | − | 1.83037i | ||||
\(939\) | 19228.2 | + | 59178.4i | 0.668253 | + | 2.05667i | ||||
\(940\) | −680.233 | + | 494.218i | −0.0236029 | + | 0.0171485i | ||||
\(941\) | −13188.5 | + | 9582.00i | −0.456889 | + | 0.331949i | −0.792310 | − | 0.610119i | \(-0.791122\pi\) |
0.335421 | + | 0.942068i | \(0.391122\pi\) | |||||||
\(942\) | 10347.0 | + | 31844.8i | 0.357880 | + | 1.10144i | ||||
\(943\) | −16227.0 | + | 49941.5i | −0.560364 | + | 1.72462i | ||||
\(944\) | 17923.6 | + | 13022.3i | 0.617971 | + | 0.448982i | ||||
\(945\) | −1366.27 | −0.0470316 | ||||||||
\(946\) | −51361.9 | + | 5475.64i | −1.76524 | + | 0.188191i | ||||
\(947\) | −30934.1 | −1.06148 | −0.530741 | − | 0.847534i | \(-0.678086\pi\) | ||||
−0.530741 | + | 0.847534i | \(0.678086\pi\) | |||||||
\(948\) | −77741.9 | − | 56482.8i | −2.66344 | − | 1.93510i | ||||
\(949\) | 9770.10 | − | 30069.3i | 0.334195 | − | 1.02855i | ||||
\(950\) | −16093.4 | − | 49530.4i | −0.549620 | − | 1.69156i | ||||
\(951\) | 8626.03 | − | 6267.18i | 0.294131 | − | 0.213698i | ||||
\(952\) | 11857.6 | − | 8615.04i | 0.403683 | − | 0.293293i | ||||
\(953\) | 14744.6 | + | 45379.2i | 0.501180 | + | 1.54247i | 0.807099 | + | 0.590416i | \(0.201036\pi\) |
−0.305919 | + | 0.952057i | \(0.598964\pi\) | |||||||
\(954\) | −4203.32 | + | 12936.5i | −0.142650 | + | 0.439030i | ||||
\(955\) | −1000.12 | − | 726.632i | −0.0338882 | − | 0.0246212i | ||||
\(956\) | −62929.3 | −2.12895 | ||||||||
\(957\) | −23898.5 | + | 21582.8i | −0.807240 | + | 0.729020i | ||||
\(958\) | −48941.8 | −1.65056 | ||||||||
\(959\) | 12548.6 | + | 9117.10i | 0.422540 | + | 0.306993i | ||||
\(960\) | −522.902 | + | 1609.33i | −0.0175798 | + | 0.0541050i | ||||
\(961\) | −4827.98 | − | 14859.0i | −0.162062 | − | 0.498774i | ||||
\(962\) | 87098.0 | − | 63280.4i | 2.91908 | − | 2.12083i | ||||
\(963\) | 6457.75 | − | 4691.83i | 0.216093 | − | 0.157001i | ||||
\(964\) | 4726.32 | + | 14546.1i | 0.157909 | + | 0.485995i | ||||
\(965\) | −471.166 | + | 1450.10i | −0.0157175 | + | 0.0483734i | ||||
\(966\) | −114194. | − | 82966.8i | −3.80345 | − | 2.76337i | ||||
\(967\) | −16213.5 | −0.539184 | −0.269592 | − | 0.962975i | \(-0.586889\pi\) | ||||
−0.269592 | + | 0.962975i | \(0.586889\pi\) | |||||||
\(968\) | −40276.0 | − | 17788.6i | −1.33731 | − | 0.590648i | ||||
\(969\) | −8486.84 | −0.281359 | ||||||||
\(970\) | −692.356 | − | 503.026i | −0.0229177 | − | 0.0166507i | ||||
\(971\) | 7055.10 | − | 21713.4i | 0.233171 | − | 0.717626i | −0.764188 | − | 0.644994i | \(-0.776860\pi\) |
0.997359 | − | 0.0726325i | \(-0.0231400\pi\) | |||||||
\(972\) | −7373.41 | − | 22693.0i | −0.243315 | − | 0.748846i | ||||
\(973\) | 22823.4 | − | 16582.1i | 0.751987 | − | 0.546351i | ||||
\(974\) | 13901.1 | − | 10099.7i | 0.457310 | − | 0.332255i | ||||
\(975\) | −14248.7 | − | 43852.9i | −0.468023 | − | 1.44043i | ||||
\(976\) | 2609.68 | − | 8031.77i | 0.0855879 | − | 0.263413i | ||||
\(977\) | −21038.0 | − | 15285.0i | −0.688909 | − | 0.500522i | 0.187392 | − | 0.982285i | \(-0.439997\pi\) |
−0.876301 | + | 0.481763i | \(0.839997\pi\) | |||||||
\(978\) | −20157.5 | −0.659064 | ||||||||
\(979\) | 10952.3 | − | 9891.02i | 0.357545 | − | 0.322899i | ||||
\(980\) | 2164.74 | 0.0705612 | ||||||||
\(981\) | −59.2551 | − | 43.0514i | −0.00192851 | − | 0.00140115i | ||||
\(982\) | −9257.32 | + | 28491.1i | −0.300828 | + | 0.925853i | ||||
\(983\) | 6600.42 | + | 20314.0i | 0.214162 | + | 0.659122i | 0.999212 | + | 0.0396898i | \(0.0126370\pi\) |
−0.785050 | + | 0.619432i | \(0.787363\pi\) | |||||||
\(984\) | 40735.2 | − | 29595.9i | 1.31971 | − | 0.958823i | ||||
\(985\) | −147.454 | + | 107.132i | −0.00476982 | + | 0.00346548i | ||||
\(986\) | 3875.51 | + | 11927.6i | 0.125174 | + | 0.385245i | ||||
\(987\) | 6024.48 | − | 18541.4i | 0.194287 | − | 0.597954i | ||||
\(988\) | −67836.1 | − | 49285.8i | −2.18437 | − | 1.58703i | ||||
\(989\) | 58439.7 | 1.87894 | ||||||||
\(990\) | −434.550 | + | 46.3268i | −0.0139504 | + | 0.00148724i | ||||
\(991\) | 40254.5 | 1.29034 | 0.645169 | − | 0.764040i | \(-0.276787\pi\) | ||||
0.645169 | + | 0.764040i | \(0.276787\pi\) | |||||||
\(992\) | 7484.24 | + | 5437.62i | 0.239541 | + | 0.174037i | ||||
\(993\) | 1489.46 | − | 4584.09i | 0.0475998 | − | 0.146497i | ||||
\(994\) | −31408.5 | − | 96665.3i | −1.00223 | − | 3.08454i | ||||
\(995\) | 1328.03 | − | 964.867i | 0.0423128 | − | 0.0307420i | ||||
\(996\) | 19696.0 | − | 14310.0i | 0.626598 | − | 0.455250i | ||||
\(997\) | 7519.17 | + | 23141.6i | 0.238851 | + | 0.735108i | 0.996587 | + | 0.0825470i | \(0.0263055\pi\) |
−0.757736 | + | 0.652561i | \(0.773695\pi\) | |||||||
\(998\) | −20366.4 | + | 62681.2i | −0.645978 | + | 1.98812i | ||||
\(999\) | −34252.2 | − | 24885.7i | −1.08478 | − | 0.788137i |
(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 | 187.4.g.b.103.2 | yes | 104 | |
11.3 | even | 5 | inner | 187.4.g.b.69.2 | ✓ | 104 | |
11.5 | even | 5 | 2057.4.a.v.1.48 | 52 | |||
11.6 | odd | 10 | 2057.4.a.u.1.5 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.4.g.b.69.2 | ✓ | 104 | 11.3 | even | 5 | inner | |
187.4.g.b.103.2 | yes | 104 | 1.1 | even | 1 | trivial | |
2057.4.a.u.1.5 | 52 | 11.6 | odd | 10 | |||
2057.4.a.v.1.48 | 52 | 11.5 | even | 5 |