Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(26,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.26");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.12 | ||
Character | \(\chi\) | \(=\) | 105.26 |
Dual form | 105.4.s.a.101.12 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.43022 | + | 1.40309i | 0.859211 | + | 0.496066i | 0.863748 | − | 0.503924i | \(-0.168111\pi\) |
−0.00453667 | + | 0.999990i | \(0.501444\pi\) | |||||||
\(3\) | −2.49879 | − | 4.55588i | −0.480892 | − | 0.876780i | ||||
\(4\) | −0.0626967 | − | 0.108594i | −0.00783708 | − | 0.0135742i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0.319698 | − | 14.5778i | 0.0217527 | − | 0.991893i | ||||
\(7\) | −12.1846 | − | 13.9476i | −0.657909 | − | 0.753098i | ||||
\(8\) | − | 22.8013i | − | 1.00768i | ||||||
\(9\) | −14.5121 | + | 22.7684i | −0.537486 | + | 0.843273i | ||||
\(10\) | −12.1511 | + | 7.01543i | −0.384251 | + | 0.221847i | ||||
\(11\) | −24.0891 | + | 13.9078i | −0.660284 | + | 0.381215i | −0.792385 | − | 0.610021i | \(-0.791161\pi\) |
0.132101 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(12\) | −0.338075 | + | 0.556992i | −0.00813282 | + | 0.0133991i | ||||
\(13\) | − | 85.9357i | − | 1.83341i | −0.399568 | − | 0.916703i | \(-0.630840\pi\) | ||
0.399568 | − | 0.916703i | \(-0.369160\pi\) | |||||||
\(14\) | −10.0417 | − | 50.9917i | −0.191697 | − | 0.973436i | ||||
\(15\) | 25.9745 | + | 0.569634i | 0.447106 | + | 0.00980526i | ||||
\(16\) | 31.4906 | − | 54.5433i | 0.492040 | − | 0.852238i | ||||
\(17\) | 18.2622 | + | 31.6311i | 0.260544 | + | 0.451275i | 0.966386 | − | 0.257094i | \(-0.0827649\pi\) |
−0.705843 | + | 0.708368i | \(0.749432\pi\) | |||||||
\(18\) | −67.2136 | + | 34.9703i | −0.880133 | + | 0.457921i | ||||
\(19\) | −55.3090 | − | 31.9327i | −0.667829 | − | 0.385571i | 0.127424 | − | 0.991848i | \(-0.459329\pi\) |
−0.795254 | + | 0.606277i | \(0.792662\pi\) | |||||||
\(20\) | 0.626967 | 0.00700970 | ||||||||
\(21\) | −33.0966 | + | 90.3638i | −0.343918 | + | 0.939000i | ||||
\(22\) | −78.0556 | −0.756432 | ||||||||
\(23\) | 100.947 | + | 58.2816i | 0.915166 | + | 0.528372i | 0.882090 | − | 0.471081i | \(-0.156136\pi\) |
0.0330766 | + | 0.999453i | \(0.489469\pi\) | |||||||
\(24\) | −103.880 | + | 56.9755i | −0.883516 | + | 0.484587i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 120.575 | − | 208.843i | 0.909491 | − | 1.57528i | ||||
\(27\) | 139.993 | + | 9.22216i | 0.997837 | + | 0.0657335i | ||||
\(28\) | −0.750683 | + | 2.19764i | −0.00506663 | + | 0.0148327i | ||||
\(29\) | 80.6309i | 0.516303i | 0.966104 | + | 0.258151i | \(0.0831133\pi\) | ||||
−0.966104 | + | 0.258151i | \(0.916887\pi\) | |||||||
\(30\) | 62.3245 | + | 37.8288i | 0.379295 | + | 0.230219i | ||||
\(31\) | 268.943 | − | 155.274i | 1.55818 | − | 0.899615i | 0.560748 | − | 0.827987i | \(-0.310514\pi\) |
0.997431 | − | 0.0716286i | \(-0.0228196\pi\) | |||||||
\(32\) | −4.91394 | + | 2.83706i | −0.0271459 | + | 0.0156727i | ||||
\(33\) | 123.556 | + | 74.9942i | 0.651767 | + | 0.395601i | ||||
\(34\) | 102.494i | 0.516987i | ||||||||
\(35\) | 90.8563 | − | 17.8921i | 0.438786 | − | 0.0864092i | ||||
\(36\) | 3.38237 | + | 0.148425i | 0.0156591 | + | 0.000687154i | ||||
\(37\) | −41.0061 | + | 71.0246i | −0.182199 | + | 0.315578i | −0.942629 | − | 0.333842i | \(-0.891655\pi\) |
0.760430 | + | 0.649420i | \(0.224988\pi\) | |||||||
\(38\) | −89.6086 | − | 155.207i | −0.382538 | − | 0.662575i | ||||
\(39\) | −391.513 | + | 214.735i | −1.60749 | + | 0.881671i | ||||
\(40\) | 98.7323 | + | 57.0031i | 0.390274 | + | 0.225325i | ||||
\(41\) | −85.8751 | −0.327108 | −0.163554 | − | 0.986534i | \(-0.552296\pi\) | ||||
−0.163554 | + | 0.986534i | \(0.552296\pi\) | |||||||
\(42\) | −207.220 | + | 173.166i | −0.761304 | + | 0.636194i | ||||
\(43\) | −94.2097 | −0.334113 | −0.167056 | − | 0.985947i | \(-0.553426\pi\) | ||||
−0.167056 | + | 0.985947i | \(0.553426\pi\) | |||||||
\(44\) | 3.02061 | + | 1.74395i | 0.0103494 | + | 0.00597523i | ||||
\(45\) | −62.3096 | − | 119.760i | −0.206413 | − | 0.396729i | ||||
\(46\) | 163.548 | + | 283.274i | 0.524214 | + | 0.907966i | ||||
\(47\) | 199.272 | − | 345.149i | 0.618443 | − | 1.07117i | −0.371327 | − | 0.928502i | \(-0.621097\pi\) |
0.989770 | − | 0.142672i | \(-0.0455696\pi\) | |||||||
\(48\) | −327.181 | − | 7.17524i | −0.983844 | − | 0.0215762i | ||||
\(49\) | −46.0690 | + | 339.892i | −0.134312 | + | 0.990939i | ||||
\(50\) | − | 70.1543i | − | 0.198426i | ||||||
\(51\) | 98.4741 | − | 162.240i | 0.270375 | − | 0.445454i | ||||
\(52\) | −9.33209 | + | 5.38789i | −0.0248871 | + | 0.0143686i | ||||
\(53\) | −121.612 | + | 70.2126i | −0.315182 | + | 0.181971i | −0.649243 | − | 0.760581i | \(-0.724914\pi\) |
0.334061 | + | 0.942552i | \(0.391581\pi\) | |||||||
\(54\) | 327.273 | + | 218.834i | 0.824745 | + | 0.551472i | ||||
\(55\) | − | 139.078i | − | 0.340969i | ||||||
\(56\) | −318.022 | + | 277.825i | −0.758884 | + | 0.662963i | ||||
\(57\) | −7.27597 | + | 331.774i | −0.0169075 | + | 0.770958i | ||||
\(58\) | −113.132 | + | 195.951i | −0.256120 | + | 0.443613i | ||||
\(59\) | −443.739 | − | 768.579i | −0.979151 | − | 1.69594i | −0.665494 | − | 0.746403i | \(-0.731779\pi\) |
−0.313657 | − | 0.949536i | \(-0.601554\pi\) | |||||||
\(60\) | −1.56666 | − | 2.85639i | −0.00337091 | − | 0.00614596i | ||||
\(61\) | 98.2925 | + | 56.7492i | 0.206313 | + | 0.119115i | 0.599597 | − | 0.800302i | \(-0.295328\pi\) |
−0.393284 | + | 0.919417i | \(0.628661\pi\) | |||||||
\(62\) | 871.453 | 1.78507 | ||||||||
\(63\) | 494.388 | − | 75.0157i | 0.988683 | − | 0.150017i | ||||
\(64\) | −519.772 | −1.01518 | ||||||||
\(65\) | 372.113 | + | 214.839i | 0.710075 | + | 0.409962i | ||||
\(66\) | 195.044 | + | 355.612i | 0.363762 | + | 0.663224i | ||||
\(67\) | 130.409 | + | 225.874i | 0.237790 | + | 0.411865i | 0.960080 | − | 0.279726i | \(-0.0902436\pi\) |
−0.722290 | + | 0.691591i | \(0.756910\pi\) | |||||||
\(68\) | 2.28996 | − | 3.96633i | 0.00408380 | − | 0.00707336i | ||||
\(69\) | 13.2797 | − | 605.534i | 0.0231693 | − | 1.05649i | ||||
\(70\) | 245.905 | + | 83.9975i | 0.419875 | + | 0.143423i | ||||
\(71\) | − | 390.768i | − | 0.653178i | −0.945166 | − | 0.326589i | \(-0.894101\pi\) | ||
0.945166 | − | 0.326589i | \(-0.105899\pi\) | |||||||
\(72\) | 519.147 | + | 330.895i | 0.849752 | + | 0.541615i | ||||
\(73\) | −183.140 | + | 105.736i | −0.293629 | + | 0.169527i | −0.639577 | − | 0.768727i | \(-0.720891\pi\) |
0.345948 | + | 0.938254i | \(0.387557\pi\) | |||||||
\(74\) | −199.307 | + | 115.070i | −0.313095 | + | 0.180765i | ||||
\(75\) | −67.4029 | + | 111.049i | −0.103774 | + | 0.170971i | ||||
\(76\) | 8.00829i | 0.0120870i | ||||||||
\(77\) | 487.497 | + | 166.522i | 0.721499 | + | 0.246454i | ||||
\(78\) | −1252.75 | − | 27.4735i | −1.81854 | − | 0.0398816i | ||||
\(79\) | 529.006 | − | 916.266i | 0.753390 | − | 1.30491i | −0.192780 | − | 0.981242i | \(-0.561750\pi\) |
0.946171 | − | 0.323669i | \(-0.104916\pi\) | |||||||
\(80\) | 157.453 | + | 272.716i | 0.220047 | + | 0.381133i | ||||
\(81\) | −307.797 | − | 660.834i | −0.422218 | − | 0.906494i | ||||
\(82\) | −208.695 | − | 120.490i | −0.281055 | − | 0.162267i | ||||
\(83\) | 1000.70 | 1.32338 | 0.661691 | − | 0.749777i | \(-0.269839\pi\) | ||||
0.661691 | + | 0.749777i | \(0.269839\pi\) | |||||||
\(84\) | 11.8880 | − | 2.07142i | 0.0154415 | − | 0.00269060i | ||||
\(85\) | −182.622 | −0.233037 | ||||||||
\(86\) | −228.950 | − | 132.184i | −0.287073 | − | 0.165742i | ||||
\(87\) | 367.345 | − | 201.480i | 0.452684 | − | 0.248286i | ||||
\(88\) | 317.116 | + | 549.261i | 0.384144 | + | 0.665357i | ||||
\(89\) | −490.935 | + | 850.325i | −0.584708 | + | 1.01274i | 0.410204 | + | 0.911994i | \(0.365458\pi\) |
−0.994912 | + | 0.100750i | \(0.967876\pi\) | |||||||
\(90\) | 16.6080 | − | 378.469i | 0.0194515 | − | 0.443268i | ||||
\(91\) | −1198.59 | + | 1047.10i | −1.38073 | + | 1.20621i | ||||
\(92\) | − | 14.6162i | − | 0.0165636i | ||||||
\(93\) | −1379.44 | − | 837.274i | −1.53808 | − | 0.933562i | ||||
\(94\) | 968.549 | − | 559.192i | 1.06275 | − | 0.613577i | ||||
\(95\) | 276.545 | − | 159.663i | 0.298662 | − | 0.172433i | ||||
\(96\) | 25.2042 | + | 15.2981i | 0.0267958 | + | 0.0162641i | ||||
\(97\) | − | 1695.07i | − | 1.77431i | −0.461471 | − | 0.887155i | \(-0.652678\pi\) | ||
0.461471 | − | 0.887155i | \(-0.347322\pi\) | |||||||
\(98\) | −588.856 | + | 761.373i | −0.606974 | + | 0.784799i | ||||
\(99\) | 32.9248 | − | 750.301i | 0.0334249 | − | 0.761698i | ||||
\(100\) | −1.56742 | + | 2.71485i | −0.00156742 | + | 0.00271485i | ||||
\(101\) | −425.895 | − | 737.672i | −0.419586 | − | 0.726744i | 0.576312 | − | 0.817230i | \(-0.304491\pi\) |
−0.995898 | + | 0.0904858i | \(0.971158\pi\) | |||||||
\(102\) | 466.950 | − | 256.111i | 0.453284 | − | 0.248615i | ||||
\(103\) | 464.853 | + | 268.383i | 0.444692 | + | 0.256743i | 0.705586 | − | 0.708624i | \(-0.250684\pi\) |
−0.260894 | + | 0.965368i | \(0.584017\pi\) | |||||||
\(104\) | −1959.44 | −1.84749 | ||||||||
\(105\) | −308.545 | − | 369.222i | −0.286771 | − | 0.343166i | ||||
\(106\) | −394.058 | −0.361078 | ||||||||
\(107\) | −302.571 | − | 174.690i | −0.273371 | − | 0.157831i | 0.357048 | − | 0.934086i | \(-0.383783\pi\) |
−0.630418 | + | 0.776255i | \(0.717117\pi\) | |||||||
\(108\) | −7.77561 | − | 15.7805i | −0.00692785 | − | 0.0140600i | ||||
\(109\) | −451.455 | − | 781.943i | −0.396711 | − | 0.687124i | 0.596607 | − | 0.802534i | \(-0.296515\pi\) |
−0.993318 | + | 0.115410i | \(0.963182\pi\) | |||||||
\(110\) | 195.139 | − | 337.990i | 0.169143 | − | 0.292965i | ||||
\(111\) | 426.045 | + | 9.34339i | 0.364310 | + | 0.00798950i | ||||
\(112\) | −1144.45 | + | 225.373i | −0.965536 | + | 0.190141i | ||||
\(113\) | 593.728i | 0.494277i | 0.968980 | + | 0.247138i | \(0.0794902\pi\) | ||||
−0.968980 | + | 0.247138i | \(0.920510\pi\) | |||||||
\(114\) | −483.190 | + | 796.075i | −0.396973 | + | 0.654028i | ||||
\(115\) | −504.733 | + | 291.408i | −0.409275 | + | 0.236295i | ||||
\(116\) | 8.75602 | − | 5.05529i | 0.00700841 | − | 0.00404631i | ||||
\(117\) | 1956.62 | + | 1247.11i | 1.54606 | + | 0.985430i | ||||
\(118\) | − | 2490.42i | − | 1.94289i | ||||||
\(119\) | 218.658 | − | 640.127i | 0.168440 | − | 0.493112i | ||||
\(120\) | 12.9884 | − | 592.252i | 0.00988059 | − | 0.450541i | ||||
\(121\) | −278.644 | + | 482.626i | −0.209350 | + | 0.362604i | ||||
\(122\) | 159.248 | + | 275.826i | 0.118177 | + | 0.204689i | ||||
\(123\) | 214.584 | + | 391.237i | 0.157304 | + | 0.286802i | ||||
\(124\) | −33.7236 | − | 19.4704i | −0.0244232 | − | 0.0141007i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 1306.72 | + | 511.365i | 0.923907 | + | 0.361556i | ||||
\(127\) | 1046.00 | 0.730846 | 0.365423 | − | 0.930842i | \(-0.380924\pi\) | ||||
0.365423 | + | 0.930842i | \(0.380924\pi\) | |||||||
\(128\) | −1223.85 | − | 706.588i | −0.845107 | − | 0.487923i | ||||
\(129\) | 235.410 | + | 429.208i | 0.160672 | + | 0.292943i | ||||
\(130\) | 602.876 | + | 1044.21i | 0.406737 | + | 0.704489i | ||||
\(131\) | −825.312 | + | 1429.48i | −0.550442 | + | 0.953393i | 0.447801 | + | 0.894133i | \(0.352207\pi\) |
−0.998243 | + | 0.0592598i | \(0.981126\pi\) | |||||||
\(132\) | 0.397365 | − | 18.1193i | 0.000262017 | − | 0.0119476i | ||||
\(133\) | 228.537 | + | 1160.51i | 0.148998 | + | 0.756612i | ||||
\(134\) | 731.898i | 0.471838i | ||||||||
\(135\) | −389.915 | + | 583.131i | −0.248582 | + | 0.371762i | ||||
\(136\) | 721.229 | − | 416.402i | 0.454742 | − | 0.262545i | ||||
\(137\) | 1238.14 | − | 714.842i | 0.772129 | − | 0.445789i | −0.0615043 | − | 0.998107i | \(-0.519590\pi\) |
0.833634 | + | 0.552318i | \(0.186256\pi\) | |||||||
\(138\) | 881.889 | − | 1452.95i | 0.543996 | − | 0.896254i | ||||
\(139\) | 2068.52i | 1.26223i | 0.775691 | + | 0.631113i | \(0.217401\pi\) | ||||
−0.775691 | + | 0.631113i | \(0.782599\pi\) | |||||||
\(140\) | −7.63937 | − | 8.74466i | −0.00461174 | − | 0.00527899i | ||||
\(141\) | −2070.40 | − | 45.4049i | −1.23659 | − | 0.0271190i | ||||
\(142\) | 548.281 | − | 949.651i | 0.324019 | − | 0.561218i | ||||
\(143\) | 1195.18 | + | 2070.11i | 0.698923 | + | 1.21057i | ||||
\(144\) | 784.866 | + | 1508.53i | 0.454205 | + | 0.872990i | ||||
\(145\) | −349.142 | − | 201.577i | −0.199963 | − | 0.115449i | ||||
\(146\) | −593.426 | −0.336386 | ||||||||
\(147\) | 1663.62 | − | 639.433i | 0.933425 | − | 0.358773i | ||||
\(148\) | 10.2838 | 0.00571163 | ||||||||
\(149\) | 1879.74 | + | 1085.27i | 1.03352 | + | 0.596702i | 0.917990 | − | 0.396602i | \(-0.129811\pi\) |
0.115527 | + | 0.993304i | \(0.463144\pi\) | |||||||
\(150\) | −319.615 | + | 175.301i | −0.173976 | + | 0.0954217i | ||||
\(151\) | 124.075 | + | 214.904i | 0.0668679 | + | 0.115819i | 0.897521 | − | 0.440972i | \(-0.145366\pi\) |
−0.830653 | + | 0.556790i | \(0.812033\pi\) | |||||||
\(152\) | −728.105 | + | 1261.12i | −0.388534 | + | 0.672960i | ||||
\(153\) | −985.212 | − | 43.2332i | −0.520586 | − | 0.0228444i | ||||
\(154\) | 951.079 | + | 1088.68i | 0.497663 | + | 0.569667i | ||||
\(155\) | 1552.74i | 0.804640i | ||||||||
\(156\) | 47.8655 | + | 29.0527i | 0.0245661 | + | 0.0149108i | ||||
\(157\) | 936.894 | − | 540.916i | 0.476256 | − | 0.274967i | −0.242599 | − | 0.970127i | \(-0.578000\pi\) |
0.718855 | + | 0.695160i | \(0.244666\pi\) | |||||||
\(158\) | 2571.20 | − | 1484.48i | 1.29464 | − | 0.747463i | ||||
\(159\) | 623.763 | + | 378.603i | 0.311117 | + | 0.188837i | ||||
\(160\) | − | 28.3706i | − | 0.0140181i | ||||||
\(161\) | −417.113 | − | 2118.10i | −0.204181 | − | 1.03683i | ||||
\(162\) | 179.194 | − | 2037.84i | 0.0869063 | − | 0.988318i | ||||
\(163\) | 1562.95 | − | 2707.12i | 0.751043 | − | 1.30085i | −0.196274 | − | 0.980549i | \(-0.562884\pi\) |
0.947317 | − | 0.320296i | \(-0.103782\pi\) | |||||||
\(164\) | 5.38408 | + | 9.32550i | 0.00256357 | + | 0.00444024i | ||||
\(165\) | −633.624 | + | 347.527i | −0.298955 | + | 0.163969i | ||||
\(166\) | 2431.91 | + | 1404.06i | 1.13706 | + | 0.656485i | ||||
\(167\) | −2280.34 | −1.05664 | −0.528318 | − | 0.849047i | \(-0.677177\pi\) | ||||
−0.528318 | + | 0.849047i | \(0.677177\pi\) | |||||||
\(168\) | 2060.41 | + | 754.644i | 0.946214 | + | 0.346560i | ||||
\(169\) | −5187.95 | −2.36138 | ||||||||
\(170\) | −443.812 | − | 256.235i | −0.200228 | − | 0.115602i | ||||
\(171\) | 1529.71 | − | 795.885i | 0.684091 | − | 0.355923i | ||||
\(172\) | 5.90663 | + | 10.2306i | 0.00261847 | + | 0.00453532i | ||||
\(173\) | −1382.85 | + | 2395.16i | −0.607721 | + | 1.05260i | 0.383894 | + | 0.923377i | \(0.374583\pi\) |
−0.991615 | + | 0.129227i | \(0.958750\pi\) | |||||||
\(174\) | 1175.42 | + | 25.7776i | 0.512117 | + | 0.0112310i | ||||
\(175\) | −149.666 | + | 438.150i | −0.0646495 | + | 0.189263i | ||||
\(176\) | 1751.86i | 0.750293i | ||||||||
\(177\) | −2392.74 | + | 3942.14i | −1.01610 | + | 1.67406i | ||||
\(178\) | −2386.16 | + | 1377.65i | −1.00478 | + | 0.580108i | ||||
\(179\) | −40.5047 | + | 23.3854i | −0.0169132 | + | 0.00976485i | −0.508433 | − | 0.861102i | \(-0.669775\pi\) |
0.491520 | + | 0.870867i | \(0.336442\pi\) | |||||||
\(180\) | −9.09861 | + | 14.2750i | −0.00376761 | + | 0.00591109i | ||||
\(181\) | 2972.20i | 1.22056i | 0.792185 | + | 0.610281i | \(0.208943\pi\) | ||||
−0.792185 | + | 0.610281i | \(0.791057\pi\) | |||||||
\(182\) | −4382.01 | + | 862.940i | −1.78470 | + | 0.351458i | ||||
\(183\) | 12.9305 | − | 589.614i | 0.00522323 | − | 0.238172i | ||||
\(184\) | 1328.89 | − | 2301.71i | 0.532431 | − | 0.922197i | ||||
\(185\) | −205.030 | − | 355.123i | −0.0814818 | − | 0.141131i | ||||
\(186\) | −2177.58 | − | 3970.23i | −0.858428 | − | 1.56512i | ||||
\(187\) | −879.840 | − | 507.976i | −0.344066 | − | 0.198646i | ||||
\(188\) | −49.9748 | −0.0193872 | ||||||||
\(189\) | −1577.13 | − | 2064.93i | −0.606982 | − | 0.794715i | ||||
\(190\) | 896.086 | 0.342152 | ||||||||
\(191\) | −1299.10 | − | 750.038i | −0.492146 | − | 0.284140i | 0.233318 | − | 0.972400i | \(-0.425042\pi\) |
−0.725464 | + | 0.688260i | \(0.758375\pi\) | |||||||
\(192\) | 1298.80 | + | 2368.02i | 0.488191 | + | 0.890088i | ||||
\(193\) | 1372.79 | + | 2377.75i | 0.512000 | + | 0.886809i | 0.999903 | + | 0.0139118i | \(0.00442842\pi\) |
−0.487904 | + | 0.872898i | \(0.662238\pi\) | |||||||
\(194\) | 2378.33 | − | 4119.38i | 0.880175 | − | 1.52451i | ||||
\(195\) | 48.9519 | − | 2232.14i | 0.0179770 | − | 0.819727i | ||||
\(196\) | 39.7986 | − | 16.3073i | 0.0145038 | − | 0.00594289i | ||||
\(197\) | 965.562i | 0.349205i | 0.984639 | + | 0.174603i | \(0.0558641\pi\) | ||||
−0.984639 | + | 0.174603i | \(0.944136\pi\) | |||||||
\(198\) | 1132.75 | − | 1777.20i | 0.406571 | − | 0.637878i | ||||
\(199\) | 1443.98 | − | 833.685i | 0.514379 | − | 0.296977i | −0.220253 | − | 0.975443i | \(-0.570688\pi\) |
0.734632 | + | 0.678466i | \(0.237355\pi\) | |||||||
\(200\) | −493.662 | + | 285.016i | −0.174536 | + | 0.100768i | ||||
\(201\) | 703.193 | − | 1158.54i | 0.246763 | − | 0.406552i | ||||
\(202\) | − | 2390.27i | − | 0.832569i | ||||||
\(203\) | 1124.60 | − | 982.458i | 0.388826 | − | 0.339680i | ||||
\(204\) | −23.7923 | − | 0.521776i | −0.00816565 | − | 0.000179077i | ||||
\(205\) | 214.688 | − | 371.850i | 0.0731436 | − | 0.126688i | ||||
\(206\) | 753.129 | + | 1304.46i | 0.254723 | + | 0.441194i | ||||
\(207\) | −2791.93 | + | 1452.60i | −0.937450 | + | 0.487743i | ||||
\(208\) | −4687.22 | − | 2706.17i | −1.56250 | − | 0.902110i | ||||
\(209\) | 1776.46 | 0.587943 | ||||||||
\(210\) | −231.781 | − | 1330.21i | −0.0761640 | − | 0.437109i | ||||
\(211\) | 3997.61 | 1.30430 | 0.652148 | − | 0.758091i | \(-0.273868\pi\) | ||||
0.652148 | + | 0.758091i | \(0.273868\pi\) | |||||||
\(212\) | 15.2493 | + | 8.80420i | 0.00494022 | + | 0.00285224i | ||||
\(213\) | −1780.29 | + | 976.447i | −0.572693 | + | 0.314108i | ||||
\(214\) | −490.209 | − | 849.067i | −0.156589 | − | 0.271220i | ||||
\(215\) | 235.524 | − | 407.940i | 0.0747099 | − | 0.129401i | ||||
\(216\) | 210.277 | − | 3192.01i | 0.0662385 | − | 1.00550i | ||||
\(217\) | −5442.67 | − | 1859.14i | −1.70264 | − | 0.581596i | ||||
\(218\) | − | 2533.72i | − | 0.787180i | ||||||
\(219\) | 939.348 | + | 570.152i | 0.289841 | + | 0.175924i | ||||
\(220\) | −15.1030 | + | 8.71975i | −0.00462840 | + | 0.00267221i | ||||
\(221\) | 2718.24 | − | 1569.38i | 0.827370 | − | 0.477682i | ||||
\(222\) | 1022.27 | + | 620.485i | 0.309056 | + | 0.187587i | ||||
\(223\) | 2415.43i | 0.725332i | 0.931919 | + | 0.362666i | \(0.118133\pi\) | ||||
−0.931919 | + | 0.362666i | \(0.881867\pi\) | |||||||
\(224\) | 99.4447 | + | 33.9689i | 0.0296626 | + | 0.0101323i | ||||
\(225\) | 674.351 | + | 29.5919i | 0.199808 | + | 0.00876798i | ||||
\(226\) | −833.052 | + | 1442.89i | −0.245194 | + | 0.424688i | ||||
\(227\) | −2731.73 | − | 4731.50i | −0.798728 | − | 1.38344i | −0.920445 | − | 0.390873i | \(-0.872173\pi\) |
0.121716 | − | 0.992565i | \(-0.461160\pi\) | |||||||
\(228\) | 36.4848 | − | 20.0110i | 0.0105977 | − | 0.00581255i | ||||
\(229\) | −1834.84 | − | 1059.35i | −0.529475 | − | 0.305692i | 0.211328 | − | 0.977415i | \(-0.432221\pi\) |
−0.740803 | + | 0.671723i | \(0.765555\pi\) | |||||||
\(230\) | −1635.48 | −0.468872 | ||||||||
\(231\) | −459.498 | − | 2637.08i | −0.130878 | − | 0.751114i | ||||
\(232\) | 1838.49 | 0.520269 | ||||||||
\(233\) | 5622.64 | + | 3246.23i | 1.58091 | + | 0.912738i | 0.994727 | + | 0.102557i | \(0.0327025\pi\) |
0.586181 | + | 0.810180i | \(0.300631\pi\) | |||||||
\(234\) | 3005.20 | + | 5776.05i | 0.839556 | + | 1.61364i | ||||
\(235\) | 996.360 | + | 1725.75i | 0.276576 | + | 0.479044i | ||||
\(236\) | −55.6419 | + | 96.3747i | −0.0153474 | + | 0.0265824i | ||||
\(237\) | −5496.27 | − | 120.536i | −1.50642 | − | 0.0330365i | ||||
\(238\) | 1429.54 | − | 1248.85i | 0.389342 | − | 0.340130i | ||||
\(239\) | 5184.62i | 1.40320i | 0.712571 | + | 0.701600i | \(0.247531\pi\) | ||||
−0.712571 | + | 0.701600i | \(0.752469\pi\) | |||||||
\(240\) | 849.022 | − | 1398.80i | 0.228351 | − | 0.376216i | ||||
\(241\) | 2579.58 | − | 1489.32i | 0.689483 | − | 0.398073i | −0.113936 | − | 0.993488i | \(-0.536346\pi\) |
0.803418 | + | 0.595415i | \(0.203012\pi\) | |||||||
\(242\) | −1354.33 | + | 781.925i | −0.359751 | + | 0.207703i | ||||
\(243\) | −2241.56 | + | 3053.57i | −0.591755 | + | 0.806118i | ||||
\(244\) | − | 14.2320i | − | 0.00373405i | ||||||
\(245\) | −1356.60 | − | 1049.22i | −0.353756 | − | 0.273600i | ||||
\(246\) | −27.4541 | + | 1251.87i | −0.00711549 | + | 0.324456i | ||||
\(247\) | −2744.16 | + | 4753.02i | −0.706909 | + | 1.22440i | ||||
\(248\) | −3540.45 | − | 6132.24i | −0.906527 | − | 1.57015i | ||||
\(249\) | −2500.53 | − | 4559.05i | −0.636404 | − | 1.16031i | ||||
\(250\) | 303.777 | + | 175.386i | 0.0768502 | + | 0.0443695i | ||||
\(251\) | 3306.05 | 0.831377 | 0.415689 | − | 0.909507i | \(-0.363541\pi\) | ||||
0.415689 | + | 0.909507i | \(0.363541\pi\) | |||||||
\(252\) | −39.1427 | − | 48.9843i | −0.00978477 | − | 0.0122449i | ||||
\(253\) | −3242.28 | −0.805693 | ||||||||
\(254\) | 2542.00 | + | 1467.63i | 0.627951 | + | 0.362548i | ||||
\(255\) | 456.334 | + | 832.006i | 0.112066 | + | 0.204322i | ||||
\(256\) | 96.2783 | + | 166.759i | 0.0235054 | + | 0.0407126i | ||||
\(257\) | 1647.41 | − | 2853.40i | 0.399855 | − | 0.692569i | −0.593853 | − | 0.804574i | \(-0.702394\pi\) |
0.993708 | + | 0.112005i | \(0.0357273\pi\) | |||||||
\(258\) | −30.1187 | + | 1373.37i | −0.00726786 | + | 0.331404i | ||||
\(259\) | 1490.27 | − | 293.475i | 0.357531 | − | 0.0704078i | ||||
\(260\) | − | 53.8789i | − | 0.0128516i | ||||||
\(261\) | −1835.83 | − | 1170.12i | −0.435384 | − | 0.277505i | ||||
\(262\) | −4011.38 | + | 2315.97i | −0.945892 | + | 0.546111i | ||||
\(263\) | 541.149 | − | 312.433i | 0.126877 | − | 0.0732526i | −0.435218 | − | 0.900325i | \(-0.643329\pi\) |
0.562095 | + | 0.827072i | \(0.309995\pi\) | |||||||
\(264\) | 1709.96 | − | 2817.23i | 0.398640 | − | 0.656775i | ||||
\(265\) | − | 702.126i | − | 0.162760i | ||||||
\(266\) | −1072.91 | + | 3140.96i | −0.247309 | + | 0.724002i | ||||
\(267\) | 5100.72 | + | 111.861i | 1.16914 | + | 0.0256397i | ||||
\(268\) | 16.3524 | − | 28.3231i | 0.00372716 | − | 0.00645564i | ||||
\(269\) | −462.054 | − | 800.301i | −0.104728 | − | 0.181395i | 0.808899 | − | 0.587948i | \(-0.200064\pi\) |
−0.913627 | + | 0.406553i | \(0.866731\pi\) | |||||||
\(270\) | −1765.76 | + | 870.050i | −0.398003 | + | 0.196109i | ||||
\(271\) | 1455.03 | + | 840.059i | 0.326149 | + | 0.188302i | 0.654130 | − | 0.756382i | \(-0.273035\pi\) |
−0.327981 | + | 0.944684i | \(0.606368\pi\) | |||||||
\(272\) | 2300.35 | 0.512792 | ||||||||
\(273\) | 7765.48 | + | 2844.18i | 1.72157 | + | 0.630541i | ||||
\(274\) | 4011.94 | 0.884563 | ||||||||
\(275\) | 602.227 | + | 347.696i | 0.132057 | + | 0.0762431i | ||||
\(276\) | −66.5899 | + | 36.5229i | −0.0145226 | + | 0.00796529i | ||||
\(277\) | −2112.42 | − | 3658.82i | −0.458206 | − | 0.793635i | 0.540661 | − | 0.841241i | \(-0.318174\pi\) |
−0.998866 | + | 0.0476055i | \(0.984841\pi\) | |||||||
\(278\) | −2902.31 | + | 5026.95i | −0.626147 | + | 1.08452i | ||||
\(279\) | −367.589 | + | 8376.75i | −0.0788781 | + | 1.79750i | ||||
\(280\) | −407.963 | − | 2071.64i | −0.0870731 | − | 0.442157i | ||||
\(281\) | − | 3709.92i | − | 0.787598i | −0.919197 | − | 0.393799i | \(-0.871161\pi\) | ||
0.919197 | − | 0.393799i | \(-0.128839\pi\) | |||||||
\(282\) | −4967.81 | − | 3015.29i | −1.04904 | − | 0.636731i | ||||
\(283\) | 2822.28 | − | 1629.44i | 0.592817 | − | 0.342263i | −0.173394 | − | 0.984853i | \(-0.555473\pi\) |
0.766210 | + | 0.642590i | \(0.222140\pi\) | |||||||
\(284\) | −42.4350 | + | 24.4999i | −0.00886639 | + | 0.00511901i | ||||
\(285\) | −1418.43 | − | 860.942i | −0.294810 | − | 0.178940i | ||||
\(286\) | 6707.76i | 1.38685i | ||||||||
\(287\) | 1046.36 | + | 1197.75i | 0.215207 | + | 0.246344i | ||||
\(288\) | 6.71634 | − | 153.054i | 0.00137418 | − | 0.0313153i | ||||
\(289\) | 1789.48 | − | 3099.47i | 0.364234 | − | 0.630872i | ||||
\(290\) | −565.661 | − | 979.753i | −0.114540 | − | 0.198390i | ||||
\(291\) | −7722.53 | + | 4235.62i | −1.55568 | + | 0.853252i | ||||
\(292\) | 22.9645 | + | 13.2586i | 0.00460239 | + | 0.00265719i | ||||
\(293\) | 3214.82 | 0.640995 | 0.320498 | − | 0.947249i | \(-0.396150\pi\) | ||||
0.320498 | + | 0.947249i | \(0.396150\pi\) | |||||||
\(294\) | 4940.15 | + | 780.248i | 0.979984 | + | 0.154779i | ||||
\(295\) | 4437.39 | 0.875779 | ||||||||
\(296\) | 1619.45 | + | 934.991i | 0.318002 | + | 0.183599i | ||||
\(297\) | −3500.55 | + | 1724.84i | −0.683915 | + | 0.336988i | ||||
\(298\) | 3045.45 | + | 5274.87i | 0.592007 | + | 1.02539i | ||||
\(299\) | 5008.47 | − | 8674.92i | 0.968720 | − | 1.67787i | ||||
\(300\) | 16.2852 | + | 0.357142i | 0.00313408 | + | 6.87319e-5i | ||||
\(301\) | 1147.91 | + | 1314.00i | 0.219816 | + | 0.251619i | ||||
\(302\) | 696.350i | 0.132684i | ||||||||
\(303\) | −2296.53 | + | 3783.62i | −0.435419 | + | 0.717370i | ||||
\(304\) | −3483.42 | + | 2011.16i | −0.657198 | + | 0.379433i | ||||
\(305\) | −491.463 | + | 283.746i | −0.0922658 | + | 0.0532697i | ||||
\(306\) | −2333.62 | − | 1487.40i | −0.435961 | − | 0.277873i | ||||
\(307\) | − | 2608.00i | − | 0.484841i | −0.970171 | − | 0.242421i | \(-0.922059\pi\) | ||
0.970171 | − | 0.242421i | \(-0.0779414\pi\) | |||||||
\(308\) | −12.4812 | − | 63.3795i | −0.00230903 | − | 0.0117253i | ||||
\(309\) | 61.1520 | − | 2788.45i | 0.0112583 | − | 0.513363i | ||||
\(310\) | −2178.63 | + | 3773.50i | −0.399155 | + | 0.691356i | ||||
\(311\) | −1745.39 | − | 3023.10i | −0.318237 | − | 0.551203i | 0.661883 | − | 0.749607i | \(-0.269757\pi\) |
−0.980120 | + | 0.198404i | \(0.936424\pi\) | |||||||
\(312\) | 4896.23 | + | 8926.99i | 0.888444 | + | 1.61984i | ||||
\(313\) | 106.942 | + | 61.7431i | 0.0193122 | + | 0.0111499i | 0.509625 | − | 0.860397i | \(-0.329784\pi\) |
−0.490313 | + | 0.871547i | \(0.663117\pi\) | |||||||
\(314\) | 3035.81 | 0.545607 | ||||||||
\(315\) | −911.143 | + | 2328.30i | −0.162975 | + | 0.416460i | ||||
\(316\) | −132.668 | −0.0236175 | ||||||||
\(317\) | −1236.29 | − | 713.773i | −0.219044 | − | 0.126465i | 0.386463 | − | 0.922305i | \(-0.373697\pi\) |
−0.605508 | + | 0.795840i | \(0.707030\pi\) | |||||||
\(318\) | 984.666 | + | 1795.28i | 0.173639 | + | 0.316586i | ||||
\(319\) | −1121.40 | − | 1942.32i | −0.196823 | − | 0.340907i | ||||
\(320\) | 1299.43 | − | 2250.68i | 0.227001 | − | 0.393177i | ||||
\(321\) | −39.8037 | + | 1814.99i | −0.00692094 | + | 0.315585i | ||||
\(322\) | 1958.20 | − | 5732.69i | 0.338902 | − | 0.992143i | ||||
\(323\) | − | 2332.65i | − | 0.401833i | ||||||
\(324\) | −52.4647 | + | 74.8570i | −0.00899600 | + | 0.0128356i | ||||
\(325\) | −1860.56 | + | 1074.20i | −0.317555 | + | 0.183341i | ||||
\(326\) | 7596.64 | − | 4385.92i | 1.29061 | − | 0.745134i | ||||
\(327\) | −2434.35 | + | 4010.68i | −0.411681 | + | 0.678261i | ||||
\(328\) | 1958.06i | 0.329621i | ||||||||
\(329\) | −7242.05 | + | 1426.16i | −1.21358 | + | 0.238987i | ||||
\(330\) | −2027.46 | − | 44.4631i | −0.338205 | − | 0.00741701i | ||||
\(331\) | 628.044 | − | 1087.80i | 0.104291 | − | 0.180638i | −0.809157 | − | 0.587592i | \(-0.800076\pi\) |
0.913448 | + | 0.406954i | \(0.133409\pi\) | |||||||
\(332\) | −62.7403 | − | 108.669i | −0.0103715 | − | 0.0179639i | ||||
\(333\) | −1022.03 | − | 1964.36i | −0.168189 | − | 0.323262i | ||||
\(334\) | −5541.73 | − | 3199.52i | −0.907874 | − | 0.524161i | ||||
\(335\) | −1304.09 | −0.212686 | ||||||||
\(336\) | 3886.50 | + | 4650.80i | 0.631030 | + | 0.755125i | ||||
\(337\) | 9967.19 | 1.61112 | 0.805560 | − | 0.592514i | \(-0.201865\pi\) | ||||
0.805560 | + | 0.592514i | \(0.201865\pi\) | |||||||
\(338\) | −12607.9 | − | 7279.15i | −2.02893 | − | 1.17140i | ||||
\(339\) | 2704.96 | − | 1483.60i | 0.433372 | − | 0.237694i | ||||
\(340\) | 11.4498 | + | 19.8317i | 0.00182633 | + | 0.00316330i | ||||
\(341\) | −4319.06 | + | 7480.82i | −0.685894 | + | 1.18800i | ||||
\(342\) | 4834.21 | + | 212.135i | 0.764340 | + | 0.0335408i | ||||
\(343\) | 5302.00 | − | 3498.91i | 0.834639 | − | 0.550797i | ||||
\(344\) | 2148.10i | 0.336680i | ||||||||
\(345\) | 2588.84 | + | 1571.34i | 0.403996 | + | 0.245212i | ||||
\(346\) | −6721.23 | + | 3880.50i | −1.04432 | + | 0.602940i | ||||
\(347\) | −1070.64 | + | 618.133i | −0.165634 | + | 0.0956286i | −0.580525 | − | 0.814242i | \(-0.697153\pi\) |
0.414892 | + | 0.909871i | \(0.363819\pi\) | |||||||
\(348\) | −44.9107 | − | 27.2593i | −0.00691801 | − | 0.00419900i | ||||
\(349\) | 5146.90i | 0.789419i | 0.918806 | + | 0.394709i | \(0.129155\pi\) | ||||
−0.918806 | + | 0.394709i | \(0.870845\pi\) | |||||||
\(350\) | −978.482 | + | 854.805i | −0.149434 | + | 0.130546i | ||||
\(351\) | 792.513 | − | 12030.4i | 0.120516 | − | 1.82944i | ||||
\(352\) | 78.9148 | − | 136.685i | 0.0119494 | − | 0.0206969i | ||||
\(353\) | −2739.65 | − | 4745.21i | −0.413078 | − | 0.715473i | 0.582146 | − | 0.813084i | \(-0.302213\pi\) |
−0.995225 | + | 0.0976115i | \(0.968880\pi\) | |||||||
\(354\) | −11346.0 | + | 6223.03i | −1.70349 | + | 0.934322i | ||||
\(355\) | 1692.08 | + | 976.920i | 0.252975 | + | 0.146055i | ||||
\(356\) | 123.120 | 0.0183296 | ||||||||
\(357\) | −3462.72 | + | 603.362i | −0.513352 | + | 0.0894490i | ||||
\(358\) | −131.247 | −0.0193760 | ||||||||
\(359\) | 6276.82 | + | 3623.92i | 0.922779 | + | 0.532767i | 0.884521 | − | 0.466501i | \(-0.154486\pi\) |
0.0382584 | + | 0.999268i | \(0.487819\pi\) | |||||||
\(360\) | −2730.68 | + | 1420.74i | −0.399777 | + | 0.207999i | ||||
\(361\) | −1390.11 | − | 2407.74i | −0.202669 | − | 0.351034i | ||||
\(362\) | −4170.25 | + | 7223.08i | −0.605479 | + | 1.04872i | ||||
\(363\) | 2895.06 | + | 63.4901i | 0.418599 | + | 0.00918008i | ||||
\(364\) | 188.856 | + | 64.5105i | 0.0271944 | + | 0.00928920i | ||||
\(365\) | − | 1057.36i | − | 0.151629i | ||||||
\(366\) | 858.703 | − | 1414.75i | 0.122637 | − | 0.202049i | ||||
\(367\) | 6955.56 | − | 4015.79i | 0.989311 | − | 0.571179i | 0.0842427 | − | 0.996445i | \(-0.473153\pi\) |
0.905068 | + | 0.425266i | \(0.139820\pi\) | |||||||
\(368\) | 6357.73 | − | 3670.64i | 0.900597 | − | 0.519960i | ||||
\(369\) | 1246.23 | − | 1955.24i | 0.175816 | − | 0.275841i | ||||
\(370\) | − | 1150.70i | − | 0.161681i | ||||||
\(371\) | 2461.09 | + | 840.673i | 0.344403 | + | 0.117643i | ||||
\(372\) | −4.43639 | + | 202.293i | −0.000618323 | + | 0.0281947i | ||||
\(373\) | 2282.32 | − | 3953.10i | 0.316821 | − | 0.548750i | −0.663002 | − | 0.748618i | \(-0.730718\pi\) |
0.979823 | + | 0.199868i | \(0.0640512\pi\) | |||||||
\(374\) | −1425.47 | − | 2468.98i | −0.197083 | − | 0.341359i | ||||
\(375\) | −312.349 | − | 569.485i | −0.0430123 | − | 0.0784216i | ||||
\(376\) | −7869.84 | − | 4543.65i | −1.07940 | − | 0.623194i | ||||
\(377\) | 6929.08 | 0.946593 | ||||||||
\(378\) | −935.509 | − | 7231.07i | −0.127295 | − | 0.983932i | ||||
\(379\) | −1417.61 | −0.192131 | −0.0960654 | − | 0.995375i | \(-0.530626\pi\) | ||||
−0.0960654 | + | 0.995375i | \(0.530626\pi\) | |||||||
\(380\) | −34.6769 | − | 20.0207i | −0.00468128 | − | 0.00270274i | ||||
\(381\) | −2613.73 | − | 4765.45i | −0.351458 | − | 0.640791i | ||||
\(382\) | −2104.74 | − | 3645.51i | −0.281905 | − | 0.488273i | ||||
\(383\) | −3347.60 | + | 5798.21i | −0.446617 | + | 0.773563i | −0.998163 | − | 0.0605810i | \(-0.980705\pi\) |
0.551546 | + | 0.834144i | \(0.314038\pi\) | |||||||
\(384\) | −160.999 | + | 7341.31i | −0.0213956 | + | 0.975611i | ||||
\(385\) | −1939.80 | + | 1694.62i | −0.256783 | + | 0.224327i | ||||
\(386\) | 7704.60i | 1.01594i | ||||||||
\(387\) | 1367.18 | − | 2145.00i | 0.179581 | − | 0.281748i | ||||
\(388\) | −184.074 | + | 106.275i | −0.0240849 | + | 0.0139054i | ||||
\(389\) | −4110.14 | + | 2372.99i | −0.535714 | + | 0.309294i | −0.743340 | − | 0.668914i | \(-0.766760\pi\) |
0.207626 | + | 0.978208i | \(0.433426\pi\) | |||||||
\(390\) | 3250.85 | − | 5355.90i | 0.422085 | − | 0.695401i | ||||
\(391\) | 4257.41i | 0.550655i | ||||||||
\(392\) | 7749.97 | + | 1050.43i | 0.998552 | + | 0.135344i | ||||
\(393\) | 8574.84 | + | 188.050i | 1.10062 | + | 0.0241371i | ||||
\(394\) | −1354.77 | + | 2346.53i | −0.173229 | + | 0.300041i | ||||
\(395\) | 2645.03 | + | 4581.33i | 0.336926 | + | 0.583574i | ||||
\(396\) | −83.5423 | + | 43.4659i | −0.0106014 | + | 0.00551577i | ||||
\(397\) | −6938.85 | − | 4006.14i | −0.877206 | − | 0.506455i | −0.00746972 | − | 0.999972i | \(-0.502378\pi\) |
−0.869736 | + | 0.493517i | \(0.835711\pi\) | |||||||
\(398\) | 4678.93 | 0.589280 | ||||||||
\(399\) | 4716.10 | − | 3941.07i | 0.591730 | − | 0.494487i | ||||
\(400\) | −1574.53 | −0.196816 | ||||||||
\(401\) | 2244.94 | + | 1296.12i | 0.279569 | + | 0.161409i | 0.633228 | − | 0.773965i | \(-0.281729\pi\) |
−0.353659 | + | 0.935374i | \(0.615063\pi\) | |||||||
\(402\) | 3334.44 | − | 1828.86i | 0.413698 | − | 0.226903i | ||||
\(403\) | −13343.6 | − | 23111.8i | −1.64936 | − | 2.85678i | ||||
\(404\) | −53.4045 | + | 92.4992i | −0.00657666 | + | 0.0113911i | ||||
\(405\) | 3630.99 | + | 319.286i | 0.445495 | + | 0.0391739i | ||||
\(406\) | 4111.51 | − | 809.670i | 0.502588 | − | 0.0989735i | ||||
\(407\) | − | 2281.22i | − | 0.277828i | ||||||
\(408\) | −3699.28 | − | 2245.33i | −0.448876 | − | 0.272452i | ||||
\(409\) | −261.391 | + | 150.914i | −0.0316014 | + | 0.0182451i | −0.515717 | − | 0.856759i | \(-0.672475\pi\) |
0.484116 | + | 0.875004i | \(0.339141\pi\) | |||||||
\(410\) | 1043.48 | − | 602.451i | 0.125692 | − | 0.0725681i | ||||
\(411\) | −6350.60 | − | 3854.60i | −0.762170 | − | 0.462611i | ||||
\(412\) | − | 67.3069i | − | 0.00804848i | ||||||
\(413\) | −5313.00 | + | 15553.9i | −0.633016 | + | 1.85317i | ||||
\(414\) | −8823.11 | − | 387.176i | −1.04742 | − | 0.0459630i | ||||
\(415\) | −2501.74 | + | 4333.14i | −0.295917 | + | 0.512543i | ||||
\(416\) | 243.805 | + | 422.283i | 0.0287345 | + | 0.0497696i | ||||
\(417\) | 9423.92 | − | 5168.79i | 1.10669 | − | 0.606994i | ||||
\(418\) | 4317.18 | + | 2492.52i | 0.505167 | + | 0.291659i | ||||
\(419\) | −10783.5 | −1.25730 | −0.628649 | − | 0.777689i | \(-0.716392\pi\) | ||||
−0.628649 | + | 0.777689i | \(0.716392\pi\) | |||||||
\(420\) | −20.7505 | + | 56.6551i | −0.00241076 | + | 0.00658211i | ||||
\(421\) | −5534.80 | −0.640735 | −0.320368 | − | 0.947293i | \(-0.603806\pi\) | ||||
−0.320368 | + | 0.947293i | \(0.603806\pi\) | |||||||
\(422\) | 9715.05 | + | 5608.99i | 1.12067 | + | 0.647017i | ||||
\(423\) | 4966.63 | + | 9545.95i | 0.570888 | + | 1.09726i | ||||
\(424\) | 1600.94 | + | 2772.90i | 0.183369 | + | 0.317604i | ||||
\(425\) | 456.556 | − | 790.778i | 0.0521087 | − | 0.0902549i | ||||
\(426\) | −5696.54 | − | 124.928i | −0.647883 | − | 0.0142084i | ||||
\(427\) | −406.146 | − | 2062.41i | −0.0460299 | − | 0.233740i | ||||
\(428\) | 43.8098i | 0.00494773i | ||||||||
\(429\) | 6444.69 | − | 10617.9i | 0.725297 | − | 1.19495i | ||||
\(430\) | 1144.75 | − | 660.922i | 0.128383 | − | 0.0741220i | ||||
\(431\) | 6212.61 | − | 3586.85i | 0.694318 | − | 0.400865i | −0.110910 | − | 0.993830i | \(-0.535376\pi\) |
0.805228 | + | 0.592966i | \(0.202043\pi\) | |||||||
\(432\) | 4911.46 | − | 7345.25i | 0.546997 | − | 0.818052i | ||||
\(433\) | 10709.7i | 1.18862i | 0.804235 | + | 0.594312i | \(0.202575\pi\) | ||||
−0.804235 | + | 0.594312i | \(0.797425\pi\) | |||||||
\(434\) | −10618.3 | − | 12154.6i | −1.17442 | − | 1.34434i | ||||
\(435\) | −45.9301 | + | 2094.35i | −0.00506248 | + | 0.230842i | ||||
\(436\) | −56.6094 | + | 98.0504i | −0.00621812 | + | 0.0107701i | ||||
\(437\) | −3722.17 | − | 6446.99i | −0.407450 | − | 0.705724i | ||||
\(438\) | 1482.85 | + | 2703.58i | 0.161765 | + | 0.294936i | ||||
\(439\) | 10964.7 | + | 6330.49i | 1.19207 | + | 0.688241i | 0.958775 | − | 0.284166i | \(-0.0917166\pi\) |
0.233293 | + | 0.972407i | \(0.425050\pi\) | |||||||
\(440\) | −3171.16 | −0.343589 | ||||||||
\(441\) | −7070.23 | − | 5981.47i | −0.763441 | − | 0.645877i | ||||
\(442\) | 8807.89 | 0.947848 | ||||||||
\(443\) | −11816.8 | − | 6822.43i | −1.26734 | − | 0.731701i | −0.292859 | − | 0.956156i | \(-0.594607\pi\) |
−0.974485 | + | 0.224454i | \(0.927940\pi\) | |||||||
\(444\) | −25.6970 | − | 46.8517i | −0.00274668 | − | 0.00500785i | ||||
\(445\) | −2454.68 | − | 4251.62i | −0.261489 | − | 0.452913i | ||||
\(446\) | −3389.05 | + | 5870.01i | −0.359812 | + | 0.623213i | ||||
\(447\) | 247.282 | − | 11275.7i | 0.0261656 | − | 1.19312i | ||||
\(448\) | 6333.23 | + | 7249.55i | 0.667895 | + | 0.764529i | ||||
\(449\) | 14986.9i | 1.57523i | 0.616170 | + | 0.787613i | \(0.288683\pi\) | ||||
−0.616170 | + | 0.787613i | \(0.711317\pi\) | |||||||
\(450\) | 1597.30 | + | 1018.09i | 0.167328 | + | 0.106651i | ||||
\(451\) | 2068.65 | − | 1194.34i | 0.215984 | − | 0.124699i | ||||
\(452\) | 64.4752 | − | 37.2248i | 0.00670943 | − | 0.00387369i | ||||
\(453\) | 669.039 | − | 1102.27i | 0.0693912 | − | 0.114325i | ||||
\(454\) | − | 15331.4i | − | 1.58489i | ||||||
\(455\) | −1537.57 | − | 7807.81i | −0.158423 | − | 0.804474i | ||||
\(456\) | 7564.87 | + | 165.901i | 0.776881 | + | 0.0170374i | ||||
\(457\) | −3558.68 | + | 6163.82i | −0.364263 | + | 0.630922i | −0.988658 | − | 0.150187i | \(-0.952012\pi\) |
0.624395 | + | 0.781109i | \(0.285346\pi\) | |||||||
\(458\) | −2972.71 | − | 5148.88i | −0.303287 | − | 0.525309i | ||||
\(459\) | 2264.87 | + | 4596.54i | 0.230316 | + | 0.467425i | ||||
\(460\) | 63.2902 | + | 36.5406i | 0.00641504 | + | 0.00370373i | ||||
\(461\) | −13314.0 | −1.34511 | −0.672554 | − | 0.740048i | \(-0.734803\pi\) | ||||
−0.672554 | + | 0.740048i | \(0.734803\pi\) | |||||||
\(462\) | 2583.37 | − | 7053.40i | 0.260150 | − | 0.710289i | ||||
\(463\) | −4293.87 | −0.431000 | −0.215500 | − | 0.976504i | \(-0.569138\pi\) | ||||
−0.215500 | + | 0.976504i | \(0.569138\pi\) | |||||||
\(464\) | 4397.87 | + | 2539.11i | 0.440013 | + | 0.254042i | ||||
\(465\) | 7074.11 | − | 3879.97i | 0.705492 | − | 0.386945i | ||||
\(466\) | 9109.49 | + | 15778.1i | 0.905556 | + | 1.56847i | ||||
\(467\) | 2815.93 | − | 4877.34i | 0.279027 | − | 0.483290i | −0.692116 | − | 0.721786i | \(-0.743321\pi\) |
0.971143 | + | 0.238497i | \(0.0766546\pi\) | |||||||
\(468\) | 12.7550 | − | 290.666i | 0.00125983 | − | 0.0287095i | ||||
\(469\) | 1561.41 | − | 4571.08i | 0.153730 | − | 0.450049i | ||||
\(470\) | 5591.92i | 0.548800i | ||||||||
\(471\) | −4805.45 | − | 2916.74i | −0.470113 | − | 0.285343i | ||||
\(472\) | −17524.6 | + | 10117.8i | −1.70897 | + | 0.986674i | ||||
\(473\) | 2269.42 | − | 1310.25i | 0.220609 | − | 0.127369i | ||||
\(474\) | −13188.0 | − | 8004.67i | −1.27794 | − | 0.775668i | ||||
\(475\) | 1596.63i | 0.154229i | ||||||||
\(476\) | −83.2230 | + | 16.3889i | −0.00801370 | + | 0.00157812i | ||||
\(477\) | 166.218 | − | 3787.84i | 0.0159552 | − | 0.363591i | ||||
\(478\) | −7274.47 | + | 12599.7i | −0.696080 | + | 1.20565i | ||||
\(479\) | −1528.74 | − | 2647.85i | −0.145824 | − | 0.252575i | 0.783856 | − | 0.620943i | \(-0.213250\pi\) |
−0.929680 | + | 0.368368i | \(0.879917\pi\) | |||||||
\(480\) | −129.253 | + | 70.8922i | −0.0122908 | + | 0.00674119i | ||||
\(481\) | 6103.56 | + | 3523.89i | 0.578582 | + | 0.334045i | ||||
\(482\) | 8358.58 | 0.789882 | ||||||||
\(483\) | −8607.53 | + | 7193.00i | −0.810883 | + | 0.677625i | ||||
\(484\) | 69.8803 | 0.00656277 | ||||||||
\(485\) | 7339.86 | + | 4237.67i | 0.687187 | + | 0.396748i | ||||
\(486\) | −9731.91 | + | 4275.73i | −0.908330 | + | 0.399077i | ||||
\(487\) | 6763.76 | + | 11715.2i | 0.629354 | + | 1.09007i | 0.987682 | + | 0.156477i | \(0.0500137\pi\) |
−0.358328 | + | 0.933596i | \(0.616653\pi\) | |||||||
\(488\) | 1293.95 | − | 2241.19i | 0.120030 | − | 0.207898i | ||||
\(489\) | −16238.8 | − | 356.125i | −1.50173 | − | 0.0329336i | ||||
\(490\) | −1824.70 | − | 4453.25i | −0.168228 | − | 0.410566i | ||||
\(491\) | − | 1703.15i | − | 0.156542i | −0.996932 | − | 0.0782709i | \(-0.975060\pi\) | ||
0.996932 | − | 0.0782709i | \(-0.0249399\pi\) | |||||||
\(492\) | 29.0322 | − | 47.8317i | 0.00266031 | − | 0.00438297i | ||||
\(493\) | −2550.44 | + | 1472.50i | −0.232994 | + | 0.134519i | ||||
\(494\) | −13337.8 | + | 7700.58i | −1.21477 | + | 0.701347i | ||||
\(495\) | 3166.59 | + | 2018.32i | 0.287530 | + | 0.183266i | ||||
\(496\) | − | 19558.7i | − | 1.77059i | ||||||
\(497\) | −5450.26 | + | 4761.37i | −0.491907 | + | 0.429732i | ||||
\(498\) | 319.921 | − | 14587.9i | 0.0287871 | − | 1.31265i | ||||
\(499\) | −5574.26 | + | 9654.90i | −0.500077 | + | 0.866158i | 0.499923 | + | 0.866070i | \(0.333361\pi\) |
−1.00000 | 8.83931e-5i | \(0.999972\pi\) | ||||||||
\(500\) | −7.83708 | − | 13.5742i | −0.000700970 | − | 0.00121412i | ||||
\(501\) | 5698.09 | + | 10389.0i | 0.508128 | + | 0.926437i | ||||
\(502\) | 8034.41 | + | 4638.67i | 0.714329 | + | 0.412418i | ||||
\(503\) | −10859.4 | −0.962616 | −0.481308 | − | 0.876551i | \(-0.659838\pi\) | ||||
−0.481308 | + | 0.876551i | \(0.659838\pi\) | |||||||
\(504\) | −1710.45 | − | 11272.7i | −0.151170 | − | 0.996279i | ||||
\(505\) | 4258.95 | 0.375289 | ||||||||
\(506\) | −7879.45 | − | 4549.20i | −0.692261 | − | 0.399677i | ||||
\(507\) | 12963.6 | + | 23635.7i | 1.13557 | + | 2.07041i | ||||
\(508\) | −65.5807 | − | 113.589i | −0.00572770 | − | 0.00992067i | ||||
\(509\) | 2304.73 | − | 3991.90i | 0.200698 | − | 0.347619i | −0.748056 | − | 0.663636i | \(-0.769012\pi\) |
0.948753 | + | 0.316017i | \(0.102346\pi\) | |||||||
\(510\) | −58.3840 | + | 2662.23i | −0.00506919 | + | 0.231148i | ||||
\(511\) | 3706.25 | + | 1266.00i | 0.320851 | + | 0.109598i | ||||
\(512\) | 11845.8i | 1.02249i | ||||||||
\(513\) | −7448.37 | − | 4980.41i | −0.641040 | − | 0.428636i | ||||
\(514\) | 8007.13 | − | 4622.92i | 0.687119 | − | 0.396709i | ||||
\(515\) | −2324.26 | + | 1341.91i | −0.198872 | + | 0.114819i | ||||
\(516\) | 31.8499 | − | 52.4740i | 0.00271728 | − | 0.00447682i | ||||
\(517\) | 11085.8i | 0.943040i | ||||||||
\(518\) | 4033.44 | + | 1377.76i | 0.342122 | + | 0.116864i | ||||
\(519\) | 14367.5 | + | 315.086i | 1.21515 | + | 0.0266488i | ||||
\(520\) | 4898.61 | − | 8484.64i | 0.413112 | − | 0.715531i | ||||
\(521\) | 8384.02 | + | 14521.5i | 0.705011 | + | 1.22111i | 0.966688 | + | 0.255959i | \(0.0823911\pi\) |
−0.261677 | + | 0.965155i | \(0.584276\pi\) | |||||||
\(522\) | −2819.69 | − | 5419.49i | −0.236426 | − | 0.454415i | ||||
\(523\) | 12237.3 | + | 7065.19i | 1.02313 | + | 0.590706i | 0.915010 | − | 0.403432i | \(-0.132183\pi\) |
0.108123 | + | 0.994138i | \(0.465516\pi\) | |||||||
\(524\) | 206.977 | 0.0172554 | ||||||||
\(525\) | 2370.14 | − | 412.985i | 0.197031 | − | 0.0343317i | ||||
\(526\) | 1753.48 | 0.145352 | ||||||||
\(527\) | 9822.99 | + | 5671.31i | 0.811947 | + | 0.468778i | ||||
\(528\) | 7981.28 | − | 4377.53i | 0.657842 | − | 0.360810i | ||||
\(529\) | 709.982 | + | 1229.72i | 0.0583531 | + | 0.101070i | ||||
\(530\) | 985.144 | − | 1706.32i | 0.0807395 | − | 0.139845i | ||||
\(531\) | 23938.9 | + | 1050.49i | 1.95642 | + | 0.0858518i | ||||
\(532\) | 111.696 | − | 97.5781i | 0.00910271 | − | 0.00795216i | ||||
\(533\) | 7379.74i | 0.599722i | ||||||||
\(534\) | 12238.9 | + | 7428.60i | 0.991815 | + | 0.601998i | ||||
\(535\) | 1512.86 | − | 873.448i | 0.122255 | − | 0.0705840i | ||||
\(536\) | 5150.22 | − | 2973.48i | 0.415029 | − | 0.239617i | ||||
\(537\) | 207.754 | + | 126.100i | 0.0166951 | + | 0.0101333i | ||||
\(538\) | − | 2593.21i | − | 0.207809i | ||||||
\(539\) | −3617.40 | − | 8828.41i | −0.289077 | − | 0.705503i | ||||
\(540\) | 87.7708 | + | 5.78198i | 0.00699454 | + | 0.000460772i | ||||
\(541\) | 1131.29 | − | 1959.45i | 0.0899038 | − | 0.155718i | −0.817567 | − | 0.575834i | \(-0.804677\pi\) |
0.907470 | + | 0.420116i | \(0.138011\pi\) | |||||||
\(542\) | 2357.35 | + | 4083.05i | 0.186821 | + | 0.323583i | ||||
\(543\) | 13541.0 | − | 7426.89i | 1.07016 | − | 0.586958i | ||||
\(544\) | −179.479 | − | 103.622i | −0.0141454 | − | 0.00816685i | ||||
\(545\) | 4514.55 | 0.354829 | ||||||||
\(546\) | 14881.2 | + | 17807.6i | 1.16640 | + | 1.39578i | ||||
\(547\) | −19607.6 | −1.53265 | −0.766325 | − | 0.642453i | \(-0.777917\pi\) | ||||
−0.766325 | + | 0.642453i | \(0.777917\pi\) | |||||||
\(548\) | −155.255 | − | 89.6365i | −0.0121025 | − | 0.00698737i | ||||
\(549\) | −2718.52 | + | 1414.41i | −0.211336 | + | 0.109955i | ||||
\(550\) | 975.694 | + | 1689.95i | 0.0756432 | + | 0.131018i | ||||
\(551\) | 2574.76 | − | 4459.61i | 0.199072 | − | 0.344802i | ||||
\(552\) | −13806.9 | − | 302.793i | −1.06461 | − | 0.0233473i | ||||
\(553\) | −19225.4 | + | 3786.02i | −1.47839 | + | 0.291136i | ||||
\(554\) | − | 11855.6i | − | 0.909201i | ||||||
\(555\) | −1105.57 | + | 1821.47i | −0.0845566 | + | 0.139310i | ||||
\(556\) | 224.628 | − | 129.689i | 0.0171337 | − | 0.00989217i | ||||
\(557\) | 11749.7 | − | 6783.69i | 0.893807 | − | 0.516040i | 0.0186213 | − | 0.999827i | \(-0.494072\pi\) |
0.875186 | + | 0.483787i | \(0.160739\pi\) | |||||||
\(558\) | −12646.6 | + | 19841.6i | −0.959452 | + | 1.50530i | ||||
\(559\) | 8095.98i | 0.612564i | ||||||||
\(560\) | 1885.22 | − | 5519.03i | 0.142259 | − | 0.416467i | ||||
\(561\) | −115.744 | + | 5277.77i | −0.00871073 | + | 0.397197i | ||||
\(562\) | 5205.33 | − | 9015.90i | 0.390701 | − | 0.676713i | ||||
\(563\) | 5510.60 | + | 9544.64i | 0.412512 | + | 0.714491i | 0.995164 | − | 0.0982305i | \(-0.0313182\pi\) |
−0.582652 | + | 0.812722i | \(0.697985\pi\) | |||||||
\(564\) | 124.876 | + | 227.679i | 0.00932313 | + | 0.0169983i | ||||
\(565\) | −2570.92 | − | 1484.32i | −0.191433 | − | 0.110524i | ||||
\(566\) | 9145.00 | 0.679140 | ||||||||
\(567\) | −5466.63 | + | 12345.0i | −0.404898 | + | 0.914362i | ||||
\(568\) | −8910.01 | −0.658196 | ||||||||
\(569\) | 13470.2 | + | 7777.05i | 0.992447 | + | 0.572989i | 0.906005 | − | 0.423268i | \(-0.139117\pi\) |
0.0864419 | + | 0.996257i | \(0.472450\pi\) | |||||||
\(570\) | −2239.13 | − | 4082.46i | −0.164538 | − | 0.299992i | ||||
\(571\) | −10646.0 | − | 18439.3i | −0.780244 | − | 1.35142i | −0.931799 | − | 0.362974i | \(-0.881762\pi\) |
0.151555 | − | 0.988449i | \(-0.451572\pi\) | |||||||
\(572\) | 149.868 | − | 259.578i | 0.0109550 | − | 0.0189747i | ||||
\(573\) | −170.899 | + | 7792.75i | −0.0124597 | + | 0.568144i | ||||
\(574\) | 862.331 | + | 4378.92i | 0.0627055 | + | 0.318419i | ||||
\(575\) | − | 2914.08i | − | 0.211349i | ||||||
\(576\) | 7542.99 | − | 11834.4i | 0.545644 | − | 0.856073i | ||||
\(577\) | 9634.85 | − | 5562.68i | 0.695154 | − | 0.401348i | −0.110386 | − | 0.993889i | \(-0.535209\pi\) |
0.805540 | + | 0.592541i | \(0.201875\pi\) | |||||||
\(578\) | 8697.66 | − | 5021.60i | 0.625908 | − | 0.361368i | ||||
\(579\) | 7402.43 | − | 12195.8i | 0.531320 | − | 0.875370i | ||||
\(580\) | 50.5529i | 0.00361913i | ||||||||
\(581\) | −12193.1 | − | 13957.3i | −0.870664 | − | 0.996635i | ||||
\(582\) | −24710.4 | − | 541.910i | −1.75993 | − | 0.0385961i | ||||
\(583\) | 1953.01 | − | 3382.71i | 0.138740 | − | 0.240305i | ||||
\(584\) | 2410.91 | + | 4175.82i | 0.170829 | + | 0.295885i | ||||
\(585\) | −10291.7 | + | 5354.62i | −0.727365 | + | 0.378438i | ||||
\(586\) | 7812.71 | + | 4510.67i | 0.550751 | + | 0.317976i | ||||
\(587\) | −8446.93 | −0.593939 | −0.296969 | − | 0.954887i | \(-0.595976\pi\) | ||||
−0.296969 | + | 0.954887i | \(0.595976\pi\) | |||||||
\(588\) | −173.742 | − | 140.569i | −0.0121854 | − | 0.00985879i | ||||
\(589\) | −19833.3 | −1.38746 | ||||||||
\(590\) | 10783.8 | + | 6226.04i | 0.752480 | + | 0.434444i | ||||
\(591\) | 4398.99 | − | 2412.74i | 0.306176 | − | 0.167930i | ||||
\(592\) | 2582.61 | + | 4473.21i | 0.179298 | + | 0.310554i | ||||
\(593\) | −4553.02 | + | 7886.07i | −0.315296 | + | 0.546108i | −0.979500 | − | 0.201443i | \(-0.935437\pi\) |
0.664205 | + | 0.747551i | \(0.268770\pi\) | |||||||
\(594\) | −10927.2 | − | 719.840i | −0.754796 | − | 0.0497229i | ||||
\(595\) | 2225.19 | + | 2547.14i | 0.153317 | + | 0.175500i | ||||
\(596\) | − | 272.171i | − | 0.0187056i | ||||||
\(597\) | −7406.38 | − | 4495.42i | −0.507744 | − | 0.308183i | ||||
\(598\) | 24343.3 | − | 14054.6i | 1.66467 | − | 0.961098i | ||||
\(599\) | −19603.3 | + | 11318.0i | −1.33718 | + | 0.772020i | −0.986388 | − | 0.164434i | \(-0.947420\pi\) |
−0.350790 | + | 0.936454i | \(0.614087\pi\) | |||||||
\(600\) | 2532.05 | + | 1536.87i | 0.172284 | + | 0.104571i | ||||
\(601\) | − | 17057.3i | − | 1.15770i | −0.815433 | − | 0.578852i | \(-0.803501\pi\) | ||
0.815433 | − | 0.578852i | \(-0.196499\pi\) | |||||||
\(602\) | 946.024 | + | 4803.91i | 0.0640483 | + | 0.325237i | ||||
\(603\) | −7035.29 | − | 308.723i | −0.475123 | − | 0.0208494i | ||||
\(604\) | 15.5581 | − | 26.9475i | 0.00104810 | − | 0.00181536i | ||||
\(605\) | −1393.22 | − | 2413.13i | −0.0936240 | − | 0.162162i | ||||
\(606\) | −10889.8 | + | 5972.78i | −0.729980 | + | 0.400376i | ||||
\(607\) | −9937.67 | − | 5737.52i | −0.664510 | − | 0.383655i | 0.129483 | − | 0.991582i | \(-0.458668\pi\) |
−0.793993 | + | 0.607927i | \(0.792001\pi\) | |||||||
\(608\) | 362.380 | 0.0241718 | ||||||||
\(609\) | −7286.11 | − | 2668.61i | −0.484808 | − | 0.177566i | ||||
\(610\) | −1592.48 | −0.105701 | ||||||||
\(611\) | −29660.7 | − | 17124.6i | −1.96390 | − | 1.13386i | ||||
\(612\) | 57.0747 | + | 109.699i | 0.00376978 | + | 0.00724559i | ||||
\(613\) | 445.189 | + | 771.089i | 0.0293328 | + | 0.0508059i | 0.880319 | − | 0.474382i | \(-0.157328\pi\) |
−0.850986 | + | 0.525188i | \(0.823995\pi\) | |||||||
\(614\) | 3659.24 | − | 6338.00i | 0.240513 | − | 0.416581i | ||||
\(615\) | −2230.56 | − | 48.9174i | −0.146252 | − | 0.00320738i | ||||
\(616\) | 3796.91 | − | 11115.5i | 0.248347 | − | 0.727042i | ||||
\(617\) | − | 19376.2i | − | 1.26427i | −0.774858 | − | 0.632135i | \(-0.782179\pi\) | ||
0.774858 | − | 0.632135i | \(-0.217821\pi\) | |||||||
\(618\) | 4061.04 | − | 6690.73i | 0.264335 | − | 0.435503i | ||||
\(619\) | −3199.16 | + | 1847.04i | −0.207731 | + | 0.119933i | −0.600256 | − | 0.799808i | \(-0.704935\pi\) |
0.392526 | + | 0.919741i | \(0.371601\pi\) | |||||||
\(620\) | 168.618 | − | 97.3518i | 0.0109224 | − | 0.00630603i | ||||
\(621\) | 13594.3 | + | 9089.94i | 0.878455 | + | 0.587386i | ||||
\(622\) | − | 9795.71i | − | 0.631466i | ||||||
\(623\) | 17841.8 | − | 3513.55i | 1.14738 | − | 0.225951i | ||||
\(624\) | −616.609 | + | 28116.5i | −0.0395579 | + | 1.80379i | ||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 173.262 | + | 300.098i | 0.0110622 | + | 0.0191603i | ||||
\(627\) | −4438.99 | − | 8093.33i | −0.282737 | − | 0.515497i | ||||
\(628\) | −117.480 | − | 67.8273i | −0.00746492 | − | 0.00430988i | ||||
\(629\) | −2995.45 | −0.189883 | ||||||||
\(630\) | −5481.08 | + | 4379.87i | −0.346622 | + | 0.276981i | ||||
\(631\) | −23709.8 | −1.49584 | −0.747919 | − | 0.663790i | \(-0.768947\pi\) | ||||
−0.747919 | + | 0.663790i | \(0.768947\pi\) | |||||||
\(632\) | −20892.0 | − | 12062.0i | −1.31494 | − | 0.759179i | ||||
\(633\) | −9989.17 | − | 18212.6i | −0.627226 | − | 1.14358i | ||||
\(634\) | −2002.97 | − | 3469.25i | −0.125470 | − | 0.217321i | ||||
\(635\) | −2615.00 | + | 4529.31i | −0.163422 | + | 0.283055i | ||||
\(636\) | 2.00607 | − | 91.4739i | 0.000125072 | − | 0.00570311i | ||||
\(637\) | 29208.9 | + | 3958.98i | 1.81679 | + | 0.246249i | ||||
\(638\) | − | 6293.69i | − | 0.390548i | ||||||
\(639\) | 8897.15 | + | 5670.87i | 0.550807 | + | 0.351074i | ||||
\(640\) | 6119.23 | − | 3532.94i | 0.377944 | − | 0.218206i | ||||
\(641\) | 13606.1 | − | 7855.47i | 0.838389 | − | 0.484044i | −0.0183271 | − | 0.999832i | \(-0.505834\pi\) |
0.856716 | + | 0.515788i | \(0.172501\pi\) | |||||||
\(642\) | −2643.32 | + | 4354.97i | −0.162498 | + | 0.267721i | ||||
\(643\) | − | 18532.3i | − | 1.13661i | −0.822817 | − | 0.568306i | \(-0.807599\pi\) | ||
0.822817 | − | 0.568306i | \(-0.192401\pi\) | |||||||
\(644\) | −203.861 | + | 178.094i | −0.0124740 | + | 0.0108973i | ||||
\(645\) | −2447.05 | − | 53.6650i | −0.149384 | − | 0.00327606i | ||||
\(646\) | 3272.91 | − | 5668.84i | 0.199336 | − | 0.345259i | ||||
\(647\) | −9934.33 | − | 17206.8i | −0.603646 | − | 1.04555i | −0.992264 | − | 0.124146i | \(-0.960381\pi\) |
0.388618 | − | 0.921399i | \(-0.372953\pi\) | |||||||
\(648\) | −15067.9 | + | 7018.16i | −0.913459 | + | 0.425462i | ||||
\(649\) | 21378.5 | + | 12342.9i | 1.29304 | + | 0.746535i | ||||
\(650\) | −6028.76 | −0.363796 | ||||||||
\(651\) | 5130.07 | + | 29441.7i | 0.308853 | + | 1.77252i | ||||
\(652\) | −391.968 | −0.0235440 | ||||||||
\(653\) | −6427.24 | − | 3710.77i | −0.385172 | − | 0.222379i | 0.294894 | − | 0.955530i | \(-0.404716\pi\) |
−0.680066 | + | 0.733151i | \(0.738049\pi\) | |||||||
\(654\) | −11543.3 | + | 6331.23i | −0.690183 | + | 0.378549i | ||||
\(655\) | −4126.56 | − | 7147.41i | −0.246165 | − | 0.426370i | ||||
\(656\) | −2704.25 | + | 4683.91i | −0.160950 | + | 0.278774i | ||||
\(657\) | 250.314 | − | 5704.25i | 0.0148641 | − | 0.338727i | ||||
\(658\) | −19600.8 | − | 6695.34i | −1.16127 | − | 0.396674i | ||||
\(659\) | − | 17588.3i | − | 1.03967i | −0.854267 | − | 0.519835i | \(-0.825993\pi\) | ||
0.854267 | − | 0.519835i | \(-0.174007\pi\) | |||||||
\(660\) | 77.4655 | + | 47.0189i | 0.00456869 | + | 0.00277304i | ||||
\(661\) | −4632.70 | + | 2674.69i | −0.272604 | + | 0.157388i | −0.630070 | − | 0.776538i | \(-0.716974\pi\) |
0.357467 | + | 0.933926i | \(0.383641\pi\) | |||||||
\(662\) | 3052.57 | − | 1762.40i | 0.179217 | − | 0.103471i | ||||
\(663\) | −13942.2 | − | 8462.45i | −0.816698 | − | 0.495708i | ||||
\(664\) | − | 22817.1i | − | 1.33355i | ||||||
\(665\) | −5596.52 | − | 1911.69i | −0.326351 | − | 0.111477i | ||||
\(666\) | 272.412 | − | 6207.82i | 0.0158495 | − | 0.361183i | ||||
\(667\) | −4699.29 | + | 8139.42i | −0.272800 | + | 0.472503i | ||||
\(668\) | 142.970 | + | 247.631i | 0.00828095 | + | 0.0143430i | ||||
\(669\) | 11004.4 | − | 6035.64i | 0.635956 | − | 0.348806i | ||||
\(670\) | −3169.21 | − | 1829.74i | −0.182742 | − | 0.105506i | ||||
\(671\) | −3157.03 | −0.181633 | ||||||||
\(672\) | −93.7332 | − | 537.940i | −0.00538071 | − | 0.0308802i | ||||
\(673\) | 27375.7 | 1.56798 | 0.783992 | − | 0.620770i | \(-0.213180\pi\) | ||||
0.783992 | + | 0.620770i | \(0.213180\pi\) | |||||||
\(674\) | 24222.4 | + | 13984.8i | 1.38429 | + | 0.799222i | ||||
\(675\) | −1550.24 | − | 3146.21i | −0.0883983 | − | 0.179404i | ||||
\(676\) | 325.267 | + | 563.380i | 0.0185063 | + | 0.0320539i | ||||
\(677\) | 971.809 | − | 1683.22i | 0.0551693 | − | 0.0955561i | −0.837122 | − | 0.547017i | \(-0.815763\pi\) |
0.892291 | + | 0.451460i | \(0.149097\pi\) | |||||||
\(678\) | 8655.25 | + | 189.814i | 0.490270 | + | 0.0107519i | ||||
\(679\) | −23642.1 | + | 20653.8i | −1.33623 | + | 1.16733i | ||||
\(680\) | 4164.02i | 0.234828i | ||||||||
\(681\) | −14730.1 | + | 24268.4i | −0.828869 | + | 1.36559i | ||||
\(682\) | −20992.5 | + | 12120.0i | −1.17866 | + | 0.680498i | ||||
\(683\) | 19324.1 | − | 11156.8i | 1.08260 | − | 0.625039i | 0.151003 | − | 0.988533i | \(-0.451750\pi\) |
0.931597 | + | 0.363494i | \(0.118416\pi\) | |||||||
\(684\) | −182.336 | − | 116.217i | −0.0101927 | − | 0.00649660i | ||||
\(685\) | 7148.42i | 0.398726i | ||||||||
\(686\) | 17794.3 | − | 1063.95i | 0.990363 | − | 0.0592155i | ||||
\(687\) | −241.376 | + | 11006.4i | −0.0134047 | + | 0.611238i | ||||
\(688\) | −2966.72 | + | 5138.50i | −0.164397 | + | 0.284744i | ||||
\(689\) | 6033.77 | + | 10450.8i | 0.333626 | + | 0.577858i | ||||
\(690\) | 4086.72 | + | 7451.06i | 0.225477 | + | 0.411097i | ||||
\(691\) | −16757.3 | − | 9674.84i | −0.922545 | − | 0.532631i | −0.0380987 | − | 0.999274i | \(-0.512130\pi\) |
−0.884446 | + | 0.466643i | \(0.845463\pi\) | |||||||
\(692\) | 346.799 | 0.0190510 | ||||||||
\(693\) | −10866.0 | + | 8682.93i | −0.595623 | + | 0.475955i | ||||
\(694\) | −3469.18 | −0.189752 | ||||||||
\(695\) | −8956.94 | − | 5171.29i | −0.488858 | − | 0.282242i | ||||
\(696\) | −4593.99 | − | 8375.92i | −0.250193 | − | 0.456162i | ||||
\(697\) | −1568.27 | − | 2716.32i | −0.0852259 | − | 0.147616i | ||||
\(698\) | −7221.54 | + | 12508.1i | −0.391604 | + | 0.678278i | ||||
\(699\) | 739.666 | − | 33727.7i | 0.0400239 | − | 1.82504i | ||||
\(700\) | 56.9639 | − | 11.2178i | 0.00307576 | − | 0.000605703i | ||||
\(701\) | 28722.6i | 1.54756i | 0.633457 | + | 0.773778i | \(0.281635\pi\) | ||||
−0.633457 | + | 0.773778i | \(0.718365\pi\) | |||||||
\(702\) | 18805.6 | − | 28124.5i | 1.01107 | − | 1.51209i | ||||
\(703\) | 4536.01 | − | 2618.87i | 0.243356 | − | 0.140501i | ||||
\(704\) | 12520.8 | − | 7228.90i | 0.670307 | − | 0.387002i | ||||
\(705\) | 5372.60 | − | 8851.58i | 0.287013 | − | 0.472865i | ||||
\(706\) | − | 15375.8i | − | 0.819656i | ||||||
\(707\) | −5099.35 | + | 14928.5i | −0.271260 | + | 0.794120i | ||||
\(708\) | 578.109 | + | 12.6782i | 0.0306874 | + | 0.000672989i | ||||
\(709\) | 6371.21 | − | 11035.3i | 0.337483 | − | 0.584538i | −0.646475 | − | 0.762935i | \(-0.723758\pi\) |
0.983959 | + | 0.178397i | \(0.0570910\pi\) | |||||||
\(710\) | 2741.41 | + | 4748.26i | 0.144906 | + | 0.250984i | ||||
\(711\) | 13184.9 | + | 25341.6i | 0.695459 | + | 1.33668i | ||||
\(712\) | 19388.5 | + | 11193.9i | 1.02052 | + | 0.589200i | ||||
\(713\) | 36198.5 | 1.90132 | ||||||||
\(714\) | −9261.74 | − | 3392.20i | −0.485451 | − | 0.177801i | ||||
\(715\) | −11951.8 | −0.625136 | ||||||||
\(716\) | 5.07902 | + | 2.93238i | 0.000265101 | + | 0.000153056i | ||||
\(717\) | 23620.5 | − | 12955.3i | 1.23030 | − | 0.674788i | ||||
\(718\) | 10169.3 | + | 17613.8i | 0.528575 | + | 0.915518i | ||||
\(719\) | 14977.1 | − | 25941.1i | 0.776844 | − | 1.34553i | −0.156908 | − | 0.987613i | \(-0.550153\pi\) |
0.933752 | − | 0.357920i | \(-0.116514\pi\) | |||||||
\(720\) | −8494.28 | − | 372.747i | −0.439671 | − | 0.0192937i | ||||
\(721\) | −1920.78 | − | 9753.72i | −0.0992143 | − | 0.503810i | ||||
\(722\) | − | 7801.77i | − | 0.402149i | ||||||
\(723\) | −13231.0 | − | 8030.76i | −0.680589 | − | 0.413094i | ||||
\(724\) | 322.762 | − | 186.347i | 0.0165682 | − | 0.00956564i | ||||
\(725\) | 1745.71 | − | 1007.89i | 0.0894263 | − | 0.0516303i | ||||
\(726\) | 6946.55 | + | 4216.32i | 0.355111 | + | 0.215540i | ||||
\(727\) | 22314.5i | 1.13837i | 0.822208 | + | 0.569187i | \(0.192742\pi\) | ||||
−0.822208 | + | 0.569187i | \(0.807258\pi\) | |||||||
\(728\) | 23875.1 | + | 27329.5i | 1.21548 | + | 1.39134i | ||||
\(729\) | 19512.9 | + | 2582.07i | 0.991358 | + | 0.131183i | ||||
\(730\) | 1483.57 | − | 2569.61i | 0.0752181 | − | 0.130282i | ||||
\(731\) | −1720.48 | − | 2979.96i | −0.0870509 | − | 0.150777i | ||||
\(732\) | −64.8391 | + | 35.5626i | −0.00327394 | + | 0.00179567i | ||||
\(733\) | 20477.0 | + | 11822.4i | 1.03183 | + | 0.595729i | 0.917509 | − | 0.397714i | \(-0.130196\pi\) |
0.114324 | + | 0.993443i | \(0.463530\pi\) | |||||||
\(734\) | 22538.0 | 1.13337 | ||||||||
\(735\) | −1390.24 | + | 8802.29i | −0.0697682 | + | 0.441738i | ||||
\(736\) | −661.394 | −0.0331241 | ||||||||
\(737\) | −6282.84 | − | 3627.40i | −0.314018 | − | 0.181299i | ||||
\(738\) | 5771.97 | − | 3003.08i | 0.287899 | − | 0.149790i | ||||
\(739\) | 11238.4 | + | 19465.6i | 0.559422 | + | 0.968947i | 0.997545 | + | 0.0700321i | \(0.0223102\pi\) |
−0.438123 | + | 0.898915i | \(0.644356\pi\) | |||||||
\(740\) | −25.7095 | + | 44.5301i | −0.00127716 | + | 0.00221211i | ||||
\(741\) | 28511.3 | + | 625.266i | 1.41348 | + | 0.0309983i | ||||
\(742\) | 4801.45 | + | 5496.14i | 0.237556 | + | 0.271927i | ||||
\(743\) | − | 9463.03i | − | 0.467247i | −0.972327 | − | 0.233624i | \(-0.924942\pi\) | ||
0.972327 | − | 0.233624i | \(-0.0750584\pi\) | |||||||
\(744\) | −19090.9 | + | 31453.0i | −0.940735 | + | 1.54990i | ||||
\(745\) | −9398.69 | + | 5426.34i | −0.462203 | + | 0.266853i | ||||
\(746\) | 11093.1 | − | 6404.59i | 0.544433 | − | 0.314328i | ||||
\(747\) | −14522.2 | + | 22784.2i | −0.711299 | + | 1.11597i | ||||
\(748\) | 127.394i | 0.00622724i | ||||||||
\(749\) | 1250.23 | + | 6348.66i | 0.0609911 | + | 0.309713i | ||||
\(750\) | 39.9623 | − | 1822.22i | 0.00194562 | − | 0.0887176i | ||||
\(751\) | −5562.36 | + | 9634.29i | −0.270271 | + | 0.468123i | −0.968931 | − | 0.247331i | \(-0.920447\pi\) |
0.698660 | + | 0.715454i | \(0.253780\pi\) | |||||||
\(752\) | −12550.4 | − | 21737.9i | −0.608597 | − | 1.05412i | ||||
\(753\) | −8261.11 | − | 15062.0i | −0.399803 | − | 0.728935i | ||||
\(754\) | 16839.2 | + | 9722.09i | 0.813324 | + | 0.469573i | ||||
\(755\) | −1240.75 | −0.0598085 | ||||||||
\(756\) | −125.357 | + | 300.731i | −0.00603068 | + | 0.0144676i | ||||
\(757\) | −8997.42 | −0.431990 | −0.215995 | − | 0.976394i | \(-0.569300\pi\) | ||||
−0.215995 | + | 0.976394i | \(0.569300\pi\) | |||||||
\(758\) | −3445.09 | − | 1989.02i | −0.165081 | − | 0.0953095i | ||||
\(759\) | 8101.77 | + | 14771.4i | 0.387452 | + | 0.706416i | ||||
\(760\) | −3640.53 | − | 6305.58i | −0.173758 | − | 0.300957i | ||||
\(761\) | −3552.99 | + | 6153.96i | −0.169245 | + | 0.293142i | −0.938155 | − | 0.346216i | \(-0.887466\pi\) |
0.768909 | + | 0.639358i | \(0.220800\pi\) | |||||||
\(762\) | 334.404 | − | 15248.4i | 0.0158979 | − | 0.724921i | ||||
\(763\) | −5405.38 | + | 15824.4i | −0.256472 | + | 0.750827i | ||||
\(764\) | 188.099i | 0.00890733i | ||||||||
\(765\) | 2650.24 | − | 4158.01i | 0.125254 | − | 0.196514i | ||||
\(766\) | −16270.8 | + | 9393.94i | −0.767477 | + | 0.443103i | ||||
\(767\) | −66048.4 | + | 38133.1i | −3.10935 | + | 1.79518i | ||||
\(768\) | 519.155 | − | 855.328i | 0.0243924 | − | 0.0401875i | ||||
\(769\) | 6684.54i | 0.313460i | 0.987641 | + | 0.156730i | \(0.0500953\pi\) | ||||
−0.987641 | + | 0.156730i | \(0.949905\pi\) | |||||||
\(770\) | −7091.84 | + | 1396.58i | −0.331912 | + | 0.0653627i | ||||
\(771\) | −17116.3 | − | 375.368i | −0.799517 | − | 0.0175338i | ||||
\(772\) | 172.139 | − | 298.154i | 0.00802517 | − | 0.0139000i | ||||
\(773\) | −6796.83 | − | 11772.5i | −0.316255 | − | 0.547770i | 0.663449 | − | 0.748222i | \(-0.269092\pi\) |
−0.979703 | + | 0.200452i | \(0.935759\pi\) | |||||||
\(774\) | 6332.17 | − | 3294.54i | 0.294064 | − | 0.152997i | ||||
\(775\) | −6723.57 | − | 3881.86i | −0.311636 | − | 0.179923i | ||||
\(776\) | −38649.7 | −1.78794 | ||||||||
\(777\) | −5060.89 | − | 6056.14i | −0.233666 | − | 0.279618i | ||||
\(778\) | −13318.1 | −0.613722 | ||||||||
\(779\) | 4749.67 | + | 2742.22i | 0.218452 | + | 0.126124i | ||||
\(780\) | −245.466 | + | 134.632i | −0.0112681 | + | 0.00618025i | ||||
\(781\) | 5434.74 | + | 9413.24i | 0.249002 | + | 0.431283i | ||||
\(782\) | −5973.51 | + | 10346.4i | −0.273161 | + | 0.473129i | ||||
\(783\) | −743.591 | + | 11287.7i | −0.0339384 | + | 0.515186i | ||||
\(784\) | 17088.1 | + | 13216.2i | 0.778429 | + | 0.602048i | ||||
\(785\) | 5409.16i | 0.245938i | ||||||||
\(786\) | 20574.9 | + | 12488.2i | 0.933691 | + | 0.566719i | ||||
\(787\) | 29235.8 | − | 16879.3i | 1.32420 | − | 0.764525i | 0.339802 | − | 0.940497i | \(-0.389640\pi\) |
0.984395 | + | 0.175972i | \(0.0563067\pi\) | |||||||
\(788\) | 104.854 | − | 60.5375i | 0.00474019 | − | 0.00273675i | ||||
\(789\) | −2775.62 | − | 1684.71i | −0.125241 | − | 0.0760168i | ||||
\(790\) | 14844.8i | 0.668551i | ||||||||
\(791\) | 8281.06 | − | 7234.37i | 0.372239 | − | 0.325189i | ||||
\(792\) | −17107.8 | − | 750.726i | −0.767550 | − | 0.0336817i | ||||
\(793\) | 4876.79 | − | 8446.84i | 0.218386 | − | 0.378255i | ||||
\(794\) | −11241.9 | − | 19471.6i | −0.502470 | − | 0.870304i | ||||
\(795\) | −3198.80 | + | 1754.46i | −0.142704 | + | 0.0782697i | ||||
\(796\) | −181.066 | − | 104.539i | −0.00806246 | − | 0.00465486i | ||||
\(797\) | 6735.51 | 0.299353 | 0.149676 | − | 0.988735i | \(-0.452177\pi\) | ||||
0.149676 | + | 0.988735i | \(0.452177\pi\) | |||||||
\(798\) | 16990.8 | − | 2960.56i | 0.753719 | − | 0.131332i | ||||
\(799\) | 14556.6 | 0.644525 | ||||||||
\(800\) | 122.849 | + | 70.9266i | 0.00542919 | + | 0.00313454i | ||||
\(801\) | −12236.0 | − | 23517.8i | −0.539747 | − | 1.03740i | ||||
\(802\) | 3637.13 | + | 6299.69i | 0.160139 | + | 0.277369i | ||||
\(803\) | 2941.11 | − | 5094.16i | 0.129252 | − | 0.223872i | ||||
\(804\) | −169.898 | − | 3.72595i | −0.00745253 | − | 0.000163438i | ||||
\(805\) | 10214.4 | + | 3489.10i | 0.447219 | + | 0.152763i | ||||
\(806\) | − | 74888.9i | − | 3.27277i | ||||||
\(807\) | −2491.50 | + | 4104.85i | −0.108680 | + | 0.179055i | ||||
\(808\) | −16819.9 | + | 9710.95i | −0.732328 | + | 0.422809i | ||||
\(809\) | −34977.4 | + | 20194.2i | −1.52007 | + | 0.877615i | −0.520353 | + | 0.853951i | \(0.674200\pi\) |
−0.999720 | + | 0.0236636i | \(0.992467\pi\) | |||||||
\(810\) | 8376.11 | + | 5870.53i | 0.363341 | + | 0.254653i | ||||
\(811\) | − | 684.087i | − | 0.0296197i | −0.999890 | − | 0.0148098i | \(-0.995286\pi\) | ||
0.999890 | − | 0.0148098i | \(-0.00471429\pi\) | |||||||
\(812\) | −177.198 | − | 60.5282i | −0.00765816 | − | 0.00261592i | ||||
\(813\) | 191.410 | − | 8728.05i | 0.00825714 | − | 0.376514i | ||||
\(814\) | 3200.75 | − | 5543.87i | 0.137821 | − | 0.238713i | ||||
\(815\) | 7814.77 | + | 13535.6i | 0.335877 | + | 0.581756i | ||||
\(816\) | −5748.09 | − | 10480.1i | −0.246597 | − | 0.449605i | ||||
\(817\) | 5210.64 | + | 3008.37i | 0.223130 | + | 0.128824i | ||||
\(818\) | −846.983 | −0.0362030 | ||||||||
\(819\) | −6446.53 | − | 42485.6i | −0.275043 | − | 1.81266i | ||||
\(820\) | −53.8408 | −0.00229293 | ||||||||
\(821\) | 22370.6 | + | 12915.7i | 0.950963 | + | 0.549039i | 0.893380 | − | 0.449302i | \(-0.148327\pi\) |
0.0575828 | + | 0.998341i | \(0.481661\pi\) | |||||||
\(822\) | −10025.0 | − | 18277.9i | −0.425379 | − | 0.775567i | ||||
\(823\) | 7811.01 | + | 13529.1i | 0.330832 | + | 0.573017i | 0.982675 | − | 0.185336i | \(-0.0593374\pi\) |
−0.651843 | + | 0.758354i | \(0.726004\pi\) | |||||||
\(824\) | 6119.47 | − | 10599.2i | 0.258716 | − | 0.448109i | ||||
\(825\) | 79.2237 | − | 3612.49i | 0.00334329 | − | 0.152449i | ||||
\(826\) | −34735.3 | + | 30344.8i | −1.46319 | + | 1.27825i | ||||
\(827\) | 9428.48i | 0.396445i | 0.980157 | + | 0.198223i | \(0.0635169\pi\) | ||||
−0.980157 | + | 0.198223i | \(0.936483\pi\) | |||||||
\(828\) | 332.788 | + | 212.113i | 0.0139676 | + | 0.00890268i | ||||
\(829\) | 7480.78 | − | 4319.03i | 0.313411 | − | 0.180948i | −0.335041 | − | 0.942204i | \(-0.608750\pi\) |
0.648452 | + | 0.761255i | \(0.275417\pi\) | |||||||
\(830\) | −12159.5 | + | 7020.32i | −0.508511 | + | 0.293589i | ||||
\(831\) | −11390.6 | + | 18766.5i | −0.475496 | + | 0.783398i | ||||
\(832\) | 44667.0i | 1.86124i | ||||||||
\(833\) | −11592.5 | + | 4749.97i | −0.482180 | + | 0.197571i | ||||
\(834\) | 30154.4 | + | 661.301i | 1.25199 | + | 0.0274568i | ||||
\(835\) | 5700.86 | − | 9874.17i | 0.236271 | − | 0.409233i | ||||
\(836\) | −111.378 | − | 192.912i | −0.00460776 | − | 0.00798087i | ||||
\(837\) | 39082.0 | − | 19257.0i | 1.61394 | − | 0.795245i | ||||
\(838\) | −26206.2 | − | 15130.2i | −1.08029 | − | 0.623703i | ||||
\(839\) | 46267.6 | 1.90386 | 0.951928 | − | 0.306323i | \(-0.0990988\pi\) | ||||
0.951928 | + | 0.306323i | \(0.0990988\pi\) | |||||||
\(840\) | −8418.73 | + | 7035.22i | −0.345802 | + | 0.288974i | ||||
\(841\) | 17887.7 | 0.733431 | ||||||||
\(842\) | −13450.8 | − | 7765.80i | −0.550527 | − | 0.317847i | ||||
\(843\) | −16901.9 | + | 9270.29i | −0.690550 | + | 0.378750i | ||||
\(844\) | −250.637 | − | 434.116i | −0.0102219 | − | 0.0177048i | ||||
\(845\) | 12969.9 | − | 22464.5i | 0.528021 | − | 0.914559i | ||||
\(846\) | −1323.81 | + | 30167.3i | −0.0537983 | + | 1.22597i | ||||
\(847\) | 10126.6 | − | 1994.22i | 0.410809 | − | 0.0808998i | ||||
\(848\) | 8844.14i | 0.358147i | ||||||||
\(849\) | −14475.8 | − | 8786.34i | −0.585170 | − | 0.355178i | ||||
\(850\) | 2219.06 | − | 1281.17i | 0.0895448 | − | 0.0516987i | ||||
\(851\) | −8278.85 | + | 4779.80i | −0.333485 | + | 0.192537i | ||||
\(852\) | 217.655 | + | 132.109i | 0.00875202 | + | 0.00531218i | ||||
\(853\) | − | 31971.2i | − | 1.28332i | −0.766989 | − | 0.641660i | \(-0.778246\pi\) | ||
0.766989 | − | 0.641660i | \(-0.221754\pi\) | |||||||
\(854\) | 1906.72 | − | 5581.96i | 0.0764011 | − | 0.223666i | ||||
\(855\) | −377.980 | + | 8613.53i | −0.0151189 | + | 0.344534i | ||||
\(856\) | −3983.14 | + | 6899.01i | −0.159043 | + | 0.275471i | ||||
\(857\) | 5393.33 | + | 9341.53i | 0.214974 | + | 0.372346i | 0.953265 | − | 0.302137i | \(-0.0977000\pi\) |
−0.738291 | + | 0.674483i | \(0.764367\pi\) | |||||||
\(858\) | 30559.8 | − | 16761.3i | 1.21596 | − | 0.666924i | ||||
\(859\) | −34980.3 | − | 20195.9i | −1.38942 | − | 0.802183i | −0.396171 | − | 0.918177i | \(-0.629661\pi\) |
−0.993250 | + | 0.115994i | \(0.962995\pi\) | |||||||
\(860\) | −59.0663 | −0.00234203 | ||||||||
\(861\) | 2842.17 | − | 7760.00i | 0.112498 | − | 0.307154i | ||||
\(862\) | 20130.7 | 0.795421 | ||||||||
\(863\) | 5078.88 | + | 2932.30i | 0.200333 | + | 0.115662i | 0.596811 | − | 0.802382i | \(-0.296434\pi\) |
−0.396478 | + | 0.918044i | \(0.629768\pi\) | |||||||
\(864\) | −714.080 | + | 351.851i | −0.0281175 | + | 0.0138544i | ||||
\(865\) | −6914.23 | − | 11975.8i | −0.271781 | − | 0.470739i | ||||
\(866\) | −15026.6 | + | 26026.8i | −0.589635 | + | 1.02128i | ||||
\(867\) | −18592.4 | − | 407.740i | −0.728293 | − | 0.0159718i | ||||
\(868\) | 139.346 | + | 707.602i | 0.00544900 | + | 0.0276700i | ||||
\(869\) | 29429.3i | 1.14882i | ||||||||
\(870\) | −3050.17 | + | 5025.28i | −0.118863 | + | 0.195831i | ||||
\(871\) | 19410.7 | − | 11206.8i | 0.755115 | − | 0.435966i | ||||
\(872\) | −17829.3 | + | 10293.7i | −0.692403 | + | 0.399759i | ||||
\(873\) | 38593.9 | + | 24599.0i | 1.49623 | + | 0.953667i | ||||
\(874\) | − | 20890.1i | − | 0.808488i | ||||||
\(875\) | −1523.08 | − | 1743.45i | −0.0588452 | − | 0.0673591i | ||||
\(876\) | 3.02101 | − | 137.754i | 0.000116519 | − | 0.00531310i | ||||
\(877\) | 18366.7 | − | 31812.0i | 0.707182 | − | 1.22487i | −0.258717 | − | 0.965953i | \(-0.583300\pi\) |
0.965898 | − | 0.258921i | \(-0.0833671\pi\) | |||||||
\(878\) | 17764.4 | + | 30768.9i | 0.682826 | + | 1.18269i | ||||
\(879\) | −8033.15 | − | 14646.3i | −0.308250 | − | 0.562012i | ||||
\(880\) | −7585.78 | − | 4379.65i | −0.290587 | − | 0.167771i | ||||
\(881\) | −10406.1 | −0.397944 | −0.198972 | − | 0.980005i | \(-0.563760\pi\) | ||||
−0.198972 | + | 0.980005i | \(0.563760\pi\) | |||||||
\(882\) | −8789.67 | − | 24456.4i | −0.335560 | − | 0.933662i | ||||
\(883\) | 2473.58 | 0.0942723 | 0.0471362 | − | 0.998888i | \(-0.484991\pi\) | ||||
0.0471362 | + | 0.998888i | \(0.484991\pi\) | |||||||
\(884\) | −340.850 | − | 196.790i | −0.0129683 | − | 0.00748727i | ||||
\(885\) | −11088.1 | − | 20216.2i | −0.421155 | − | 0.767866i | ||||
\(886\) | −19144.9 | − | 33160.0i | −0.725944 | − | 1.25737i | ||||
\(887\) | 18708.6 | − | 32404.2i | 0.708199 | − | 1.22664i | −0.257326 | − | 0.966325i | \(-0.582841\pi\) |
0.965525 | − | 0.260311i | \(-0.0838252\pi\) | |||||||
\(888\) | 213.041 | − | 9714.37i | 0.00805089 | − | 0.367109i | ||||
\(889\) | −12745.1 | − | 14589.1i | −0.480830 | − | 0.550398i | ||||
\(890\) | − | 13776.5i | − | 0.518864i | ||||||
\(891\) | 16605.3 | + | 11638.1i | 0.624354 | + | 0.437588i | ||||
\(892\) | 262.300 | − | 151.439i | 0.00984582 | − | 0.00568449i | ||||
\(893\) | −22043.1 | + | 12726.6i | −0.826029 | + | 0.476908i | ||||
\(894\) | 16421.8 | − | 27055.5i | 0.614346 | − | 1.01216i | ||||
\(895\) | − | 233.854i | − | 0.00873395i | ||||||
\(896\) | 5056.95 | + | 25679.2i | 0.188550 | + | 0.957457i | ||||
\(897\) | −52037.0 | − | 1141.20i | −1.93697 | − | 0.0424788i | ||||
\(898\) | −21028.0 | + | 36421.5i | −0.781416 | + | 1.35345i | ||||
\(899\) | 12519.9 | + | 21685.1i | 0.464474 | + | 0.804492i | ||||
\(900\) | −39.0661 | − | 75.0857i | −0.00144689 | − | 0.00278095i | ||||
\(901\) | −4441.81 | − | 2564.48i | −0.164238 | − | 0.0948226i | ||||
\(902\) | 6703.03 | 0.247435 | ||||||||
\(903\) | 3118.02 | − | 8513.14i | 0.114907 | − | 0.313732i | ||||
\(904\) | 13537.8 | 0.498074 | ||||||||
\(905\) | −12870.0 | − | 7430.49i | −0.472721 | − | 0.272926i | ||||
\(906\) | 3172.49 | − | 1740.03i | 0.116334 | − | 0.0638065i | ||||
\(907\) | −22097.6 | − | 38274.2i | −0.808975 | − | 1.40119i | −0.913575 | − | 0.406671i | \(-0.866689\pi\) |
0.104600 | − | 0.994514i | \(-0.466644\pi\) | |||||||
\(908\) | −342.541 | + | 593.298i | −0.0125194 | + | 0.0216842i | ||||
\(909\) | 22976.2 | + | 1008.25i | 0.838365 | + | 0.0367892i | ||||
\(910\) | 7218.39 | − | 21132.0i | 0.262953 | − | 0.769802i | ||||
\(911\) | 32577.6i | 1.18479i | 0.805647 | + | 0.592396i | \(0.201818\pi\) | ||||
−0.805647 | + | 0.592396i | \(0.798182\pi\) | |||||||
\(912\) | 17866.9 | + | 10844.6i | 0.648720 | + | 0.393751i | ||||
\(913\) | −24105.8 | + | 13917.5i | −0.873808 | + | 0.504493i | ||||
\(914\) | −17296.7 | + | 9986.27i | −0.625957 | + | 0.361397i | ||||
\(915\) | 2520.78 | + | 1530.02i | 0.0910757 | + | 0.0552798i | ||||
\(916\) | 265.670i | 0.00958295i | ||||||||
\(917\) | 29993.9 | − | 5906.64i | 1.08014 | − | 0.212709i | ||||
\(918\) | −945.215 | + | 14348.4i | −0.0339834 | + | 0.515869i | ||||
\(919\) | −5380.69 | + | 9319.64i | −0.193137 | + | 0.334523i | −0.946288 | − | 0.323325i | \(-0.895199\pi\) |
0.753151 | + | 0.657847i | \(0.228533\pi\) | |||||||
\(920\) | 6644.47 | + | 11508.6i | 0.238110 | + | 0.412419i | ||||
\(921\) | −11881.7 | + | 6516.83i | −0.425099 | + | 0.233156i | ||||
\(922\) | −32355.9 | − | 18680.7i | −1.15573 | − | 0.667263i | ||||
\(923\) | −33581.0 | −1.19754 | ||||||||
\(924\) | −257.562 | + | 215.235i | −0.00917009 | + | 0.00766310i | ||||
\(925\) | 2050.30 | 0.0728796 | ||||||||
\(926\) | −10435.0 | − | 6024.67i | −0.370320 | − | 0.213804i | ||||
\(927\) | −12856.6 | + | 6689.14i | −0.455520 | + | 0.237001i | ||||
\(928\) | −228.755 | − | 396.215i | −0.00809187 | − | 0.0140155i | ||||
\(929\) | 7101.10 | − | 12299.5i | 0.250785 | − | 0.434373i | −0.712957 | − | 0.701208i | \(-0.752645\pi\) |
0.963742 | + | 0.266835i | \(0.0859779\pi\) | |||||||
\(930\) | 22635.6 | + | 496.409i | 0.798117 | + | 0.0175031i | ||||
\(931\) | 13401.7 | − | 17328.0i | 0.471775 | − | 0.609991i | ||||
\(932\) | − | 814.112i | − | 0.0286128i | ||||||
\(933\) | −9411.52 | + | 15505.9i | −0.330246 | + | 0.544093i | ||||
\(934\) | 13686.7 | − | 7901.99i | 0.479487 | − | 0.276832i | ||||
\(935\) | 4399.20 | − | 2539.88i | 0.153871 | − | 0.0888374i | ||||
\(936\) | 28435.7 | − | 44613.3i | 0.993001 | − | 1.55794i | ||||
\(937\) | 50384.1i | 1.75665i | 0.478069 | + | 0.878323i | \(0.341337\pi\) | ||||
−0.478069 | + | 0.878323i | \(0.658663\pi\) | |||||||
\(938\) | 10208.2 | − | 8917.91i | 0.355340 | − | 0.310427i | ||||
\(939\) | 14.0684 | − | 641.499i | 0.000488929 | − | 0.0222945i | ||||
\(940\) | 124.937 | − | 216.397i | 0.00433510 | − | 0.00750861i | ||||
\(941\) | 20595.8 | + | 35673.0i | 0.713501 | + | 1.23582i | 0.963535 | + | 0.267583i | \(0.0862248\pi\) |
−0.250034 | + | 0.968237i | \(0.580442\pi\) | |||||||
\(942\) | −7585.84 | − | 13830.8i | −0.262378 | − | 0.478377i | ||||
\(943\) | −8668.80 | − | 5004.93i | −0.299358 | − | 0.172835i | ||||
\(944\) | −55894.4 | −1.92713 | ||||||||
\(945\) | 12884.2 | − | 1666.88i | 0.443517 | − | 0.0573794i | ||||
\(946\) | 7353.59 | 0.252733 | ||||||||
\(947\) | 10607.9 | + | 6124.48i | 0.364003 | + | 0.210157i | 0.670835 | − | 0.741606i | \(-0.265936\pi\) |
−0.306832 | + | 0.951764i | \(0.599269\pi\) | |||||||
\(948\) | 331.509 | + | 604.418i | 0.0113575 | + | 0.0207074i | ||||
\(949\) | 9086.49 | + | 15738.3i | 0.310811 | + | 0.538341i | ||||
\(950\) | −2240.22 | + | 3880.17i | −0.0765076 | + | 0.132515i | ||||
\(951\) | −162.636 | + | 7415.96i | −0.00554555 | + | 0.252870i | ||||
\(952\) | −14595.7 | − | 4985.68i | −0.496901 | − | 0.169734i | ||||
\(953\) | − | 28622.1i | − | 0.972885i | −0.873713 | − | 0.486443i | \(-0.838294\pi\) | ||
0.873713 | − | 0.486443i | \(-0.161706\pi\) | |||||||
\(954\) | 5718.61 | − | 8972.05i | 0.194074 | − | 0.304487i | ||||
\(955\) | 6495.52 | − | 3750.19i | 0.220094 | − | 0.127071i | ||||
\(956\) | 563.017 | − | 325.058i | 0.0190474 | − | 0.0109970i | ||||
\(957\) | −6046.85 | + | 9962.42i | −0.204250 | + | 0.336509i | ||||
\(958\) | − | 8579.80i | − | 0.289354i | ||||||
\(959\) | −25056.6 | − | 8558.99i | −0.843713 | − | 0.288200i | ||||
\(960\) | −13500.8 | − | 296.080i | −0.453893 | − | 0.00995409i | ||||
\(961\) | 33324.7 | − | 57720.0i | 1.11862 | − | 1.93750i | ||||
\(962\) | 9888.64 | + | 17127.6i | 0.331416 | + | 0.574030i | ||||
\(963\) | 8368.35 | − | 4353.94i | 0.280027 | − | 0.145694i | ||||
\(964\) | −323.462 | − | 186.751i | −0.0108071 | − | 0.00623946i | ||||
\(965\) | −13727.9 | −0.457946 | ||||||||
\(966\) | −31010.6 | + | 5403.43i | −1.03287 | + | 0.179972i | ||||
\(967\) | 31204.2 | 1.03770 | 0.518852 | − | 0.854864i | \(-0.326360\pi\) | ||||
0.518852 | + | 0.854864i | \(0.326360\pi\) | |||||||
\(968\) | 11004.5 | + | 6353.44i | 0.365390 | + | 0.210958i | ||||
\(969\) | −10627.3 | + | 5828.79i | −0.352319 | + | 0.193238i | ||||
\(970\) | 11891.6 | + | 20596.9i | 0.393626 | + | 0.681781i | ||||
\(971\) | 2791.00 | − | 4834.16i | 0.0922425 | − | 0.159769i | −0.816212 | − | 0.577753i | \(-0.803930\pi\) |
0.908454 | + | 0.417984i | \(0.137263\pi\) | |||||||
\(972\) | 472.138 | + | 51.9712i | 0.0155801 | + | 0.00171500i | ||||
\(973\) | 28850.8 | − | 25204.1i | 0.950579 | − | 0.830429i | ||||
\(974\) | 37960.6i | 1.24880i | ||||||||
\(975\) | 9543.07 | + | 5792.32i | 0.313459 | + | 0.190259i | ||||
\(976\) | 6190.58 | − | 3574.13i | 0.203028 | − | 0.117218i | ||||
\(977\) | 23500.1 | − | 13567.8i | 0.769533 | − | 0.444290i | −0.0631748 | − | 0.998002i | \(-0.520123\pi\) |
0.832708 | + | 0.553712i | \(0.186789\pi\) | |||||||
\(978\) | −38964.1 | − | 23649.9i | −1.27396 | − | 0.773252i | ||||
\(979\) | − | 27311.4i | − | 0.891599i | ||||||
\(980\) | −28.8838 | + | 213.101i | −0.000941488 | + | 0.00694619i | ||||
\(981\) | 24355.1 | + | 1068.75i | 0.792660 | + | 0.0347836i | ||||
\(982\) | 2389.66 | − | 4139.02i | 0.0776550 | − | 0.134502i | ||||
\(983\) | −17755.0 | − | 30752.6i | −0.576091 | − | 0.997819i | −0.995922 | − | 0.0902170i | \(-0.971244\pi\) |
0.419831 | − | 0.907602i | \(-0.362089\pi\) | |||||||
\(984\) | 8920.69 | − | 4892.78i | 0.289005 | − | 0.158512i | ||||
\(985\) | −4181.01 | − | 2413.91i | −0.135247 | − | 0.0780847i | ||||
\(986\) | −8264.18 | −0.266922 | ||||||||
\(987\) | 24593.8 | + | 29430.3i | 0.793139 | + | 0.949114i | ||||
\(988\) | 688.198 | 0.0221604 | ||||||||
\(989\) | −9510.15 | − | 5490.69i | −0.305769 | − | 0.176536i | ||||
\(990\) | 4863.61 | + | 9347.95i | 0.156137 | + | 0.300098i | ||||
\(991\) | 13584.1 | + | 23528.4i | 0.435432 | + | 0.754191i | 0.997331 | − | 0.0730155i | \(-0.0232623\pi\) |
−0.561899 | + | 0.827206i | \(0.689929\pi\) | |||||||
\(992\) | −881.046 | + | 1526.02i | −0.0281988 | + | 0.0488418i | ||||
\(993\) | −6525.26 | − | 143.102i | −0.208532 | − | 0.00457322i | ||||
\(994\) | −19925.9 | + | 3923.97i | −0.635827 | + | 0.125212i | ||||
\(995\) | 8336.85i | 0.265624i | ||||||||
\(996\) | −338.310 | + | 557.379i | −0.0107628 | + | 0.0177322i | ||||
\(997\) | −24712.5 | + | 14267.8i | −0.785008 | + | 0.453225i | −0.838202 | − | 0.545359i | \(-0.816393\pi\) |
0.0531939 | + | 0.998584i | \(0.483060\pi\) | |||||||
\(998\) | −27093.3 | + | 15642.3i | −0.859343 | + | 0.496142i | ||||
\(999\) | −6395.55 | + | 9564.77i | −0.202549 | + | 0.302919i |
(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 | 105.4.s.a.26.12 | ✓ | 32 | |
3.2 | odd | 2 | 105.4.s.b.26.5 | yes | 32 | ||
7.3 | odd | 6 | 105.4.s.b.101.5 | yes | 32 | ||
21.17 | even | 6 | inner | 105.4.s.a.101.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.s.a.26.12 | ✓ | 32 | 1.1 | even | 1 | trivial | |
105.4.s.a.101.12 | yes | 32 | 21.17 | even | 6 | inner | |
105.4.s.b.26.5 | yes | 32 | 3.2 | odd | 2 | ||
105.4.s.b.101.5 | yes | 32 | 7.3 | odd | 6 |