Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(16,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(4.42514325043\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 61.7 | ||
Character | \(\chi\) | \(=\) | 75.61 |
Dual form | 75.4.g.a.16.7 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.67736 | − | 2.67176i | 1.30014 | − | 0.944610i | 0.300186 | − | 0.953881i | \(-0.402951\pi\) |
0.999957 | + | 0.00927105i | \(0.00295111\pi\) | |||||||
\(3\) | −0.927051 | + | 2.85317i | −0.178411 | + | 0.549093i | ||||
\(4\) | 3.91255 | − | 12.0416i | 0.489069 | − | 1.50520i | ||||
\(5\) | 6.73234 | − | 8.92612i | 0.602159 | − | 0.798376i | ||||
\(6\) | 4.21388 | + | 12.9690i | 0.286718 | + | 0.882428i | ||||
\(7\) | 9.62995 | 0.519969 | 0.259984 | − | 0.965613i | \(-0.416283\pi\) | ||||
0.259984 | + | 0.965613i | \(0.416283\pi\) | |||||||
\(8\) | −6.54736 | − | 20.1507i | −0.289355 | − | 0.890544i | ||||
\(9\) | −7.28115 | − | 5.29007i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0.908811 | − | 50.8118i | 0.0287391 | − | 1.60681i | ||||
\(11\) | −4.49599 | + | 3.26653i | −0.123236 | + | 0.0895359i | −0.647696 | − | 0.761899i | \(-0.724267\pi\) |
0.524460 | + | 0.851435i | \(0.324267\pi\) | |||||||
\(12\) | 30.7296 | + | 22.3263i | 0.739239 | + | 0.537088i | ||||
\(13\) | −39.0421 | − | 28.3657i | −0.832948 | − | 0.605172i | 0.0874441 | − | 0.996169i | \(-0.472130\pi\) |
−0.920392 | + | 0.390998i | \(0.872130\pi\) | |||||||
\(14\) | 35.4128 | − | 25.7289i | 0.676034 | − | 0.491167i | ||||
\(15\) | 19.2265 | + | 27.4835i | 0.330951 | + | 0.473080i | ||||
\(16\) | 4.03070 | + | 2.92847i | 0.0629797 | + | 0.0457574i | ||||
\(17\) | 29.0298 | + | 89.3445i | 0.414162 | + | 1.27466i | 0.912998 | + | 0.407963i | \(0.133761\pi\) |
−0.498836 | + | 0.866696i | \(0.666239\pi\) | |||||||
\(18\) | −40.9092 | −0.535689 | ||||||||
\(19\) | 14.5147 | + | 44.6717i | 0.175258 | + | 0.539389i | 0.999645 | − | 0.0266373i | \(-0.00847993\pi\) |
−0.824387 | + | 0.566027i | \(0.808480\pi\) | |||||||
\(20\) | −81.1441 | − | 115.992i | −0.907218 | − | 1.29683i | ||||
\(21\) | −8.92746 | + | 27.4759i | −0.0927681 | + | 0.285511i | ||||
\(22\) | −7.80600 | + | 24.0244i | −0.0756475 | + | 0.232819i | ||||
\(23\) | −143.830 | + | 104.499i | −1.30394 | + | 0.947368i | −0.999986 | − | 0.00531897i | \(-0.998307\pi\) |
−0.303954 | + | 0.952687i | \(0.598307\pi\) | |||||||
\(24\) | 63.5631 | 0.540615 | ||||||||
\(25\) | −34.3512 | − | 120.187i | −0.274809 | − | 0.961499i | ||||
\(26\) | −219.358 | −1.65460 | ||||||||
\(27\) | 21.8435 | − | 15.8702i | 0.155695 | − | 0.113119i | ||||
\(28\) | 37.6777 | − | 115.960i | 0.254300 | − | 0.782656i | ||||
\(29\) | −20.1011 | + | 61.8649i | −0.128713 | + | 0.396139i | −0.994559 | − | 0.104172i | \(-0.966781\pi\) |
0.865846 | + | 0.500311i | \(0.166781\pi\) | |||||||
\(30\) | 144.132 | + | 49.6981i | 0.877160 | + | 0.302453i | ||||
\(31\) | 37.2519 | + | 114.650i | 0.215827 | + | 0.664248i | 0.999094 | + | 0.0425619i | \(0.0135520\pi\) |
−0.783267 | + | 0.621686i | \(0.786448\pi\) | |||||||
\(32\) | 192.148 | 1.06148 | ||||||||
\(33\) | −5.15194 | − | 15.8561i | −0.0271769 | − | 0.0836420i | ||||
\(34\) | 345.460 | + | 250.991i | 1.74253 | + | 1.26602i | ||||
\(35\) | 64.8321 | − | 85.9581i | 0.313104 | − | 0.415131i | ||||
\(36\) | −92.1887 | + | 66.9790i | −0.426800 | + | 0.310088i | ||||
\(37\) | −6.32796 | − | 4.59753i | −0.0281165 | − | 0.0204278i | 0.573638 | − | 0.819109i | \(-0.305532\pi\) |
−0.601755 | + | 0.798681i | \(0.705532\pi\) | |||||||
\(38\) | 172.728 | + | 125.494i | 0.737373 | + | 0.535733i | ||||
\(39\) | 117.126 | − | 85.0971i | 0.480903 | − | 0.349396i | ||||
\(40\) | −223.947 | − | 77.2189i | −0.885227 | − | 0.305234i | ||||
\(41\) | −390.226 | − | 283.516i | −1.48641 | − | 1.07994i | −0.975418 | − | 0.220361i | \(-0.929277\pi\) |
−0.510996 | − | 0.859583i | \(-0.670723\pi\) | |||||||
\(42\) | 40.5795 | + | 124.891i | 0.149084 | + | 0.458835i | ||||
\(43\) | 421.245 | 1.49394 | 0.746968 | − | 0.664861i | \(-0.231509\pi\) | ||||
0.746968 | + | 0.664861i | \(0.231509\pi\) | |||||||
\(44\) | 21.7434 | + | 66.9193i | 0.0744987 | + | 0.229283i | ||||
\(45\) | −96.2390 | + | 29.3779i | −0.318810 | + | 0.0973199i | ||||
\(46\) | −249.720 | + | 768.558i | −0.800416 | + | 2.46343i | ||||
\(47\) | 134.747 | − | 414.710i | 0.418190 | − | 1.28706i | −0.491177 | − | 0.871060i | \(-0.663433\pi\) |
0.909366 | − | 0.415996i | \(-0.136567\pi\) | |||||||
\(48\) | −12.0921 | + | 8.78542i | −0.0363613 | + | 0.0264181i | ||||
\(49\) | −250.264 | −0.729633 | ||||||||
\(50\) | −447.433 | − | 350.194i | −1.26553 | − | 0.990499i | ||||
\(51\) | −281.827 | −0.773797 | ||||||||
\(52\) | −494.322 | + | 359.146i | −1.31827 | + | 0.957781i | ||||
\(53\) | 4.44871 | − | 13.6917i | 0.0115298 | − | 0.0354849i | −0.945126 | − | 0.326706i | \(-0.894061\pi\) |
0.956656 | + | 0.291221i | \(0.0940614\pi\) | |||||||
\(54\) | 37.9249 | − | 116.721i | 0.0955728 | − | 0.294143i | ||||
\(55\) | −1.11112 | + | 62.1231i | −0.00272407 | + | 0.152303i | ||||
\(56\) | −63.0508 | − | 194.050i | −0.150456 | − | 0.463055i | ||||
\(57\) | −140.912 | −0.327443 | ||||||||
\(58\) | 91.3691 | + | 281.205i | 0.206851 | + | 0.636621i | ||||
\(59\) | −430.331 | − | 312.654i | −0.949564 | − | 0.689899i | 0.00113944 | − | 0.999999i | \(-0.499637\pi\) |
−0.950704 | + | 0.310100i | \(0.899637\pi\) | |||||||
\(60\) | 406.170 | − | 123.987i | 0.873938 | − | 0.266778i | ||||
\(61\) | 380.377 | − | 276.360i | 0.798399 | − | 0.580071i | −0.112045 | − | 0.993703i | \(-0.535740\pi\) |
0.910444 | + | 0.413632i | \(0.135740\pi\) | |||||||
\(62\) | 443.305 | + | 322.080i | 0.908061 | + | 0.659745i | ||||
\(63\) | −70.1172 | − | 50.9431i | −0.140221 | − | 0.101877i | ||||
\(64\) | 674.352 | − | 489.946i | 1.31709 | − | 0.956925i | ||||
\(65\) | −516.040 | + | 157.526i | −0.984722 | + | 0.300596i | ||||
\(66\) | −61.3091 | − | 44.5437i | −0.114343 | − | 0.0830750i | ||||
\(67\) | 81.8767 | + | 251.990i | 0.149296 | + | 0.459486i | 0.997538 | − | 0.0701225i | \(-0.0223390\pi\) |
−0.848242 | + | 0.529608i | \(0.822339\pi\) | |||||||
\(68\) | 1189.43 | 2.12117 | ||||||||
\(69\) | −164.814 | − | 507.247i | −0.287555 | − | 0.885005i | ||||
\(70\) | 8.75181 | − | 489.315i | 0.0149434 | − | 0.835490i | ||||
\(71\) | 60.2024 | − | 185.284i | 0.100630 | − | 0.309707i | −0.888050 | − | 0.459747i | \(-0.847940\pi\) |
0.988680 | + | 0.150040i | \(0.0479403\pi\) | |||||||
\(72\) | −58.9262 | + | 181.356i | −0.0964517 | + | 0.296848i | ||||
\(73\) | −66.1027 | + | 48.0264i | −0.105983 | + | 0.0770009i | −0.639514 | − | 0.768779i | \(-0.720865\pi\) |
0.533532 | + | 0.845780i | \(0.320865\pi\) | |||||||
\(74\) | −35.5537 | −0.0558518 | ||||||||
\(75\) | 374.760 | + | 13.4101i | 0.576981 | + | 0.0206462i | ||||
\(76\) | 594.708 | 0.897602 | ||||||||
\(77\) | −43.2962 | + | 31.4565i | −0.0640786 | + | 0.0465559i | ||||
\(78\) | 203.356 | − | 625.866i | 0.295199 | − | 0.908530i | ||||
\(79\) | 379.401 | − | 1167.67i | 0.540328 | − | 1.66296i | −0.191519 | − | 0.981489i | \(-0.561341\pi\) |
0.731847 | − | 0.681469i | \(-0.238659\pi\) | |||||||
\(80\) | 53.2759 | − | 16.2630i | 0.0744554 | − | 0.0227282i | ||||
\(81\) | 25.0304 | + | 77.0356i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −2192.49 | −2.95268 | ||||||||
\(83\) | 329.978 | + | 1015.57i | 0.436383 | + | 1.34305i | 0.891662 | + | 0.452701i | \(0.149540\pi\) |
−0.455279 | + | 0.890349i | \(0.650460\pi\) | |||||||
\(84\) | 295.924 | + | 215.002i | 0.384381 | + | 0.279269i | ||||
\(85\) | 992.937 | + | 342.374i | 1.26705 | + | 0.436891i | ||||
\(86\) | 1549.07 | − | 1125.46i | 1.94233 | − | 1.41119i | ||||
\(87\) | −157.876 | − | 114.704i | −0.194553 | − | 0.141351i | ||||
\(88\) | 95.2597 | + | 69.2102i | 0.115394 | + | 0.0838390i | ||||
\(89\) | −941.245 | + | 683.855i | −1.12103 | + | 0.814477i | −0.984365 | − | 0.176140i | \(-0.943639\pi\) |
−0.136666 | + | 0.990617i | \(0.543639\pi\) | |||||||
\(90\) | −275.415 | + | 365.160i | −0.322570 | + | 0.427681i | ||||
\(91\) | −375.973 | − | 273.160i | −0.433107 | − | 0.314670i | ||||
\(92\) | 695.587 | + | 2140.80i | 0.788261 | + | 2.42602i | ||||
\(93\) | −361.649 | −0.403240 | ||||||||
\(94\) | −612.490 | − | 1885.05i | −0.672059 | − | 2.06838i | ||||
\(95\) | 496.463 | + | 171.185i | 0.536169 | + | 0.184876i | ||||
\(96\) | −178.131 | + | 548.231i | −0.189379 | + | 0.582850i | ||||
\(97\) | 351.696 | − | 1082.41i | 0.368137 | − | 1.13301i | −0.579856 | − | 0.814719i | \(-0.696891\pi\) |
0.947993 | − | 0.318291i | \(-0.103109\pi\) | |||||||
\(98\) | −920.311 | + | 668.645i | −0.948627 | + | 0.689218i | ||||
\(99\) | 50.0161 | 0.0507759 | ||||||||
\(100\) | −1581.65 | − | 56.5963i | −1.58165 | − | 0.0565963i | ||||
\(101\) | −1277.88 | −1.25895 | −0.629476 | − | 0.777020i | \(-0.716730\pi\) | ||||
−0.629476 | + | 0.777020i | \(0.716730\pi\) | |||||||
\(102\) | −1036.38 | + | 752.974i | −1.00605 | + | 0.730936i | ||||
\(103\) | −159.139 | + | 489.781i | −0.152238 | + | 0.468539i | −0.997871 | − | 0.0652256i | \(-0.979223\pi\) |
0.845633 | + | 0.533765i | \(0.179223\pi\) | |||||||
\(104\) | −315.967 | + | 972.445i | −0.297914 | + | 0.916886i | ||||
\(105\) | 185.150 | + | 264.665i | 0.172084 | + | 0.245987i | ||||
\(106\) | −20.2215 | − | 62.2352i | −0.0185291 | − | 0.0570266i | ||||
\(107\) | −330.363 | −0.298480 | −0.149240 | − | 0.988801i | \(-0.547683\pi\) | ||||
−0.149240 | + | 0.988801i | \(0.547683\pi\) | |||||||
\(108\) | −105.639 | − | 325.123i | −0.0941213 | − | 0.289676i | ||||
\(109\) | 152.898 | + | 111.087i | 0.134357 | + | 0.0976162i | 0.652934 | − | 0.757415i | \(-0.273538\pi\) |
−0.518577 | + | 0.855031i | \(0.673538\pi\) | |||||||
\(110\) | 161.892 | + | 231.418i | 0.140325 | + | 0.200589i | ||||
\(111\) | 18.9839 | − | 13.7926i | 0.0162331 | − | 0.0117940i | ||||
\(112\) | 38.8154 | + | 28.2011i | 0.0327474 | + | 0.0237924i | ||||
\(113\) | 1675.54 | + | 1217.35i | 1.39488 | + | 1.01344i | 0.995310 | + | 0.0967367i | \(0.0308405\pi\) |
0.399570 | + | 0.916703i | \(0.369160\pi\) | |||||||
\(114\) | −518.184 | + | 376.483i | −0.425723 | + | 0.309306i | ||||
\(115\) | −35.5457 | + | 1987.36i | −0.0288231 | + | 1.61150i | ||||
\(116\) | 666.306 | + | 484.099i | 0.533318 | + | 0.387478i | ||||
\(117\) | 134.215 | + | 413.070i | 0.106053 | + | 0.326396i | ||||
\(118\) | −2417.82 | −1.88625 | ||||||||
\(119\) | 279.555 | + | 860.383i | 0.215351 | + | 0.662783i | ||||
\(120\) | 427.929 | − | 567.372i | 0.325536 | − | 0.431614i | ||||
\(121\) | −401.758 | + | 1236.48i | −0.301847 | + | 0.928988i | ||||
\(122\) | 660.417 | − | 2032.55i | 0.490093 | − | 1.50835i | ||||
\(123\) | 1170.68 | − | 850.547i | 0.858182 | − | 0.623506i | ||||
\(124\) | 1526.31 | 1.10538 | ||||||||
\(125\) | −1304.07 | − | 502.520i | −0.933117 | − | 0.359574i | ||||
\(126\) | −393.954 | −0.278541 | ||||||||
\(127\) | 2243.28 | − | 1629.84i | 1.56739 | − | 1.13878i | 0.637795 | − | 0.770206i | \(-0.279847\pi\) |
0.929599 | − | 0.368573i | \(-0.120153\pi\) | |||||||
\(128\) | 695.804 | − | 2141.46i | 0.480476 | − | 1.47875i | ||||
\(129\) | −390.515 | + | 1201.88i | −0.266535 | + | 0.820309i | ||||
\(130\) | −1476.79 | + | 1958.02i | −0.996334 | + | 1.32100i | ||||
\(131\) | −551.639 | − | 1697.77i | −0.367915 | − | 1.13233i | −0.948135 | − | 0.317867i | \(-0.897033\pi\) |
0.580220 | − | 0.814460i | \(-0.302967\pi\) | |||||||
\(132\) | −211.089 | −0.139189 | ||||||||
\(133\) | 139.776 | + | 430.187i | 0.0911288 | + | 0.280465i | ||||
\(134\) | 974.348 | + | 707.905i | 0.628141 | + | 0.456371i | ||||
\(135\) | 5.39832 | − | 301.821i | 0.00344158 | − | 0.192419i | ||||
\(136\) | 1610.29 | − | 1169.94i | 1.01530 | − | 0.737659i | ||||
\(137\) | 490.996 | + | 356.730i | 0.306194 | + | 0.222463i | 0.730262 | − | 0.683167i | \(-0.239398\pi\) |
−0.424067 | + | 0.905631i | \(0.639398\pi\) | |||||||
\(138\) | −1961.32 | − | 1424.98i | −1.20985 | − | 0.879005i | ||||
\(139\) | −271.154 | + | 197.005i | −0.165460 | + | 0.120214i | −0.667434 | − | 0.744669i | \(-0.732607\pi\) |
0.501974 | + | 0.864883i | \(0.332607\pi\) | |||||||
\(140\) | −781.413 | − | 1117.00i | −0.471725 | − | 0.674311i | ||||
\(141\) | 1058.32 | + | 768.914i | 0.632103 | + | 0.459250i | ||||
\(142\) | −273.648 | − | 842.202i | −0.161719 | − | 0.497719i | ||||
\(143\) | 268.190 | 0.156833 | ||||||||
\(144\) | −13.8563 | − | 42.6453i | −0.00801870 | − | 0.0246790i | ||||
\(145\) | 416.886 | + | 595.921i | 0.238762 | + | 0.341300i | ||||
\(146\) | −114.768 | + | 353.221i | −0.0650569 | + | 0.200225i | ||||
\(147\) | 232.008 | − | 714.046i | 0.130175 | − | 0.400636i | ||||
\(148\) | −80.1201 | + | 58.2107i | −0.0444989 | + | 0.0323303i | ||||
\(149\) | 1749.73 | 0.962037 | 0.481019 | − | 0.876710i | \(-0.340267\pi\) | ||||
0.481019 | + | 0.876710i | \(0.340267\pi\) | |||||||
\(150\) | 1413.96 | − | 951.955i | 0.769661 | − | 0.518179i | ||||
\(151\) | −1852.06 | −0.998136 | −0.499068 | − | 0.866563i | \(-0.666324\pi\) | ||||
−0.499068 | + | 0.866563i | \(0.666324\pi\) | |||||||
\(152\) | 805.134 | − | 584.964i | 0.429638 | − | 0.312150i | ||||
\(153\) | 261.268 | − | 804.100i | 0.138054 | − | 0.424887i | ||||
\(154\) | −75.1714 | + | 231.354i | −0.0393343 | + | 0.121059i | ||||
\(155\) | 1274.17 | + | 439.345i | 0.660282 | + | 0.227671i | ||||
\(156\) | −566.443 | − | 1743.33i | −0.290716 | − | 0.894733i | ||||
\(157\) | 515.248 | 0.261919 | 0.130960 | − | 0.991388i | \(-0.458194\pi\) | ||||
0.130960 | + | 0.991388i | \(0.458194\pi\) | |||||||
\(158\) | −1724.55 | − | 5307.63i | −0.868342 | − | 2.67248i | ||||
\(159\) | 34.9406 | + | 25.3858i | 0.0174275 | + | 0.0126618i | ||||
\(160\) | 1293.61 | − | 1715.14i | 0.639179 | − | 0.847459i | ||||
\(161\) | −1385.08 | + | 1006.32i | −0.678008 | + | 0.492601i | ||||
\(162\) | 297.866 | + | 216.412i | 0.144460 | + | 0.104957i | ||||
\(163\) | 825.151 | + | 599.507i | 0.396508 | + | 0.288080i | 0.768117 | − | 0.640309i | \(-0.221194\pi\) |
−0.371609 | + | 0.928389i | \(0.621194\pi\) | |||||||
\(164\) | −4940.76 | + | 3589.67i | −2.35249 | + | 1.70918i | ||||
\(165\) | −176.218 | − | 60.7615i | −0.0831426 | − | 0.0286683i | ||||
\(166\) | 3926.80 | + | 2852.99i | 1.83602 | + | 1.33395i | ||||
\(167\) | 56.6060 | + | 174.215i | 0.0262294 | + | 0.0807257i | 0.963314 | − | 0.268376i | \(-0.0864869\pi\) |
−0.937085 | + | 0.349101i | \(0.886487\pi\) | |||||||
\(168\) | 612.110 | 0.281103 | ||||||||
\(169\) | 40.7582 | + | 125.441i | 0.0185517 | + | 0.0570964i | ||||
\(170\) | 4566.13 | − | 1393.86i | 2.06004 | − | 0.628846i | ||||
\(171\) | 130.633 | − | 402.046i | 0.0584194 | − | 0.179796i | ||||
\(172\) | 1648.14 | − | 5072.46i | 0.730637 | − | 2.24867i | ||||
\(173\) | −3203.39 | + | 2327.40i | −1.40780 | + | 1.02283i | −0.414160 | + | 0.910204i | \(0.635925\pi\) |
−0.993638 | + | 0.112621i | \(0.964075\pi\) | |||||||
\(174\) | −887.030 | −0.386469 | ||||||||
\(175\) | −330.800 | − | 1157.40i | −0.142892 | − | 0.499949i | ||||
\(176\) | −27.6879 | −0.0118583 | ||||||||
\(177\) | 1290.99 | − | 937.961i | 0.548231 | − | 0.398313i | ||||
\(178\) | −1634.20 | + | 5029.56i | −0.688139 | + | 2.11787i | ||||
\(179\) | −283.506 | + | 872.543i | −0.118381 | + | 0.364340i | −0.992637 | − | 0.121125i | \(-0.961350\pi\) |
0.874256 | + | 0.485465i | \(0.161350\pi\) | |||||||
\(180\) | −22.7832 | + | 1273.81i | −0.00943423 | + | 0.527469i | ||||
\(181\) | −297.258 | − | 914.867i | −0.122072 | − | 0.375699i | 0.871284 | − | 0.490779i | \(-0.163288\pi\) |
−0.993356 | + | 0.115080i | \(0.963288\pi\) | |||||||
\(182\) | −2112.41 | −0.860341 | ||||||||
\(183\) | 435.874 | + | 1341.48i | 0.176070 | + | 0.541886i | ||||
\(184\) | 3047.43 | + | 2214.08i | 1.22097 | + | 0.887090i | ||||
\(185\) | −83.6401 | + | 25.5320i | −0.0332397 | + | 0.0101467i | ||||
\(186\) | −1329.91 | + | 966.240i | −0.524269 | + | 0.380904i | ||||
\(187\) | −422.364 | − | 306.865i | −0.165167 | − | 0.120001i | ||||
\(188\) | −4466.56 | − | 3245.15i | −1.73275 | − | 1.25892i | ||||
\(189\) | 210.351 | − | 152.829i | 0.0809567 | − | 0.0588185i | ||||
\(190\) | 2283.04 | − | 696.920i | 0.871732 | − | 0.266105i | ||||
\(191\) | 2389.63 | + | 1736.17i | 0.905274 | + | 0.657720i | 0.939815 | − | 0.341683i | \(-0.110997\pi\) |
−0.0345412 | + | 0.999403i | \(0.510997\pi\) | |||||||
\(192\) | 772.739 | + | 2378.25i | 0.290456 | + | 0.893933i | ||||
\(193\) | −3932.89 | −1.46682 | −0.733408 | − | 0.679789i | \(-0.762071\pi\) | ||||
−0.733408 | + | 0.679789i | \(0.762071\pi\) | |||||||
\(194\) | −1598.62 | − | 4920.05i | −0.591620 | − | 1.82082i | ||||
\(195\) | 28.9462 | − | 1618.39i | 0.0106302 | − | 0.594333i | ||||
\(196\) | −979.171 | + | 3013.58i | −0.356841 | + | 1.09824i | ||||
\(197\) | 876.736 | − | 2698.32i | 0.317080 | − | 0.975873i | −0.657809 | − | 0.753185i | \(-0.728517\pi\) |
0.974890 | − | 0.222689i | \(-0.0714833\pi\) | |||||||
\(198\) | 183.927 | − | 133.631i | 0.0660159 | − | 0.0479634i | ||||
\(199\) | −1133.25 | −0.403689 | −0.201845 | − | 0.979418i | \(-0.564694\pi\) | ||||
−0.201845 | + | 0.979418i | \(0.564694\pi\) | |||||||
\(200\) | −2196.95 | + | 1479.11i | −0.776739 | + | 0.522944i | ||||
\(201\) | −794.875 | −0.278936 | ||||||||
\(202\) | −4699.24 | + | 3414.20i | −1.63682 | + | 1.18922i | ||||
\(203\) | −193.573 | + | 595.756i | −0.0669269 | + | 0.205980i | ||||
\(204\) | −1102.66 | + | 3393.65i | −0.378440 | + | 1.16472i | ||||
\(205\) | −5157.83 | + | 1574.48i | −1.75726 | + | 0.536421i | ||||
\(206\) | 723.363 | + | 2226.28i | 0.244656 | + | 0.752973i | ||||
\(207\) | 1600.05 | 0.537253 | ||||||||
\(208\) | −74.2985 | − | 228.667i | −0.0247677 | − | 0.0762270i | ||||
\(209\) | −211.179 | − | 153.431i | −0.0698928 | − | 0.0507801i | ||||
\(210\) | 1387.98 | + | 478.590i | 0.456095 | + | 0.157266i | ||||
\(211\) | 2469.17 | − | 1793.96i | 0.805614 | − | 0.585313i | −0.106942 | − | 0.994265i | \(-0.534106\pi\) |
0.912556 | + | 0.408953i | \(0.134106\pi\) | |||||||
\(212\) | −147.464 | − | 107.139i | −0.0477730 | − | 0.0347091i | ||||
\(213\) | 472.836 | + | 343.535i | 0.152104 | + | 0.110510i | ||||
\(214\) | −1214.86 | + | 882.650i | −0.388067 | + | 0.281947i | ||||
\(215\) | 2835.96 | − | 3760.08i | 0.899586 | − | 1.19272i | ||||
\(216\) | −462.813 | − | 336.253i | −0.145789 | − | 0.105922i | ||||
\(217\) | 358.734 | + | 1104.07i | 0.112223 | + | 0.345388i | ||||
\(218\) | 859.057 | 0.266893 | ||||||||
\(219\) | −75.7470 | − | 233.125i | −0.0233722 | − | 0.0719321i | ||||
\(220\) | 743.714 | + | 256.440i | 0.227914 | + | 0.0785870i | ||||
\(221\) | 1400.94 | − | 4311.64i | 0.426413 | − | 1.31236i | ||||
\(222\) | 32.9601 | − | 101.441i | 0.00996458 | − | 0.0306678i | ||||
\(223\) | 4172.02 | − | 3031.15i | 1.25282 | − | 0.910228i | 0.254439 | − | 0.967089i | \(-0.418109\pi\) |
0.998382 | + | 0.0568608i | \(0.0181091\pi\) | |||||||
\(224\) | 1850.38 | 0.551935 | ||||||||
\(225\) | −385.683 | + | 1056.82i | −0.114276 | + | 0.313133i | ||||
\(226\) | 9414.03 | 2.77085 | ||||||||
\(227\) | −1446.95 | + | 1051.27i | −0.423072 | + | 0.307380i | −0.778873 | − | 0.627182i | \(-0.784208\pi\) |
0.355801 | + | 0.934562i | \(0.384208\pi\) | |||||||
\(228\) | −551.325 | + | 1696.80i | −0.160142 | + | 0.492867i | ||||
\(229\) | −390.744 | + | 1202.59i | −0.112756 | + | 0.347027i | −0.991472 | − | 0.130317i | \(-0.958400\pi\) |
0.878717 | + | 0.477344i | \(0.158400\pi\) | |||||||
\(230\) | 5179.04 | + | 7403.22i | 1.48476 | + | 2.12241i | ||||
\(231\) | −49.6130 | − | 152.693i | −0.0141311 | − | 0.0434912i | ||||
\(232\) | 1378.23 | 0.390023 | ||||||||
\(233\) | −1342.37 | − | 4131.40i | −0.377432 | − | 1.16162i | −0.941823 | − | 0.336109i | \(-0.890889\pi\) |
0.564391 | − | 0.825508i | \(-0.309111\pi\) | |||||||
\(234\) | 1597.18 | + | 1160.42i | 0.446201 | + | 0.324184i | ||||
\(235\) | −2794.58 | − | 3994.74i | −0.775738 | − | 1.10889i | ||||
\(236\) | −5448.54 | + | 3958.60i | −1.50284 | + | 1.09188i | ||||
\(237\) | 2979.85 | + | 2164.99i | 0.816718 | + | 0.593380i | ||||
\(238\) | 3326.76 | + | 2417.03i | 0.906058 | + | 0.658290i | ||||
\(239\) | −329.291 | + | 239.244i | −0.0891216 | + | 0.0647506i | −0.631454 | − | 0.775414i | \(-0.717541\pi\) |
0.542332 | + | 0.840164i | \(0.317541\pi\) | |||||||
\(240\) | −2.98840 | + | 167.082i | −0.000803752 | + | 0.0449379i | ||||
\(241\) | −1381.89 | − | 1004.00i | −0.369358 | − | 0.268354i | 0.387587 | − | 0.921833i | \(-0.373309\pi\) |
−0.756945 | + | 0.653479i | \(0.773309\pi\) | |||||||
\(242\) | 1826.18 | + | 5620.40i | 0.485087 | + | 1.49295i | ||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −1839.57 | − | 5661.63i | −0.482650 | − | 1.48544i | ||||
\(245\) | −1684.86 | + | 2233.89i | −0.439355 | + | 0.582521i | ||||
\(246\) | 2032.55 | − | 6255.53i | 0.526790 | − | 1.62129i | ||||
\(247\) | 700.461 | − | 2155.80i | 0.180442 | − | 0.555344i | ||||
\(248\) | 2066.37 | − | 1501.30i | 0.529091 | − | 0.384407i | ||||
\(249\) | −3203.50 | −0.815315 | ||||||||
\(250\) | −6138.15 | + | 1636.22i | −1.55284 | + | 0.413933i | ||||
\(251\) | −5706.80 | −1.43510 | −0.717549 | − | 0.696508i | \(-0.754736\pi\) | ||||
−0.717549 | + | 0.696508i | \(0.754736\pi\) | |||||||
\(252\) | −887.773 | + | 645.005i | −0.221922 | + | 0.161236i | ||||
\(253\) | 305.310 | − | 939.649i | 0.0758684 | − | 0.233499i | ||||
\(254\) | 3894.82 | − | 11987.0i | 0.962136 | − | 2.96115i | ||||
\(255\) | −1897.36 | + | 2515.62i | −0.465949 | + | 0.617781i | ||||
\(256\) | −1102.12 | − | 3391.97i | −0.269072 | − | 0.828117i | ||||
\(257\) | −6301.59 | −1.52950 | −0.764751 | − | 0.644326i | \(-0.777138\pi\) | ||||
−0.764751 | + | 0.644326i | \(0.777138\pi\) | |||||||
\(258\) | 1775.07 | + | 5463.12i | 0.428338 | + | 1.31829i | ||||
\(259\) | −60.9380 | − | 44.2740i | −0.0146197 | − | 0.0106218i | ||||
\(260\) | −122.165 | + | 6830.28i | −0.0291399 | + | 1.62921i | ||||
\(261\) | 473.629 | − | 344.112i | 0.112325 | − | 0.0816091i | ||||
\(262\) | −6564.61 | − | 4769.47i | −1.54795 | − | 1.12465i | ||||
\(263\) | 4016.60 | + | 2918.23i | 0.941726 | + | 0.684204i | 0.948836 | − | 0.315771i | \(-0.102263\pi\) |
−0.00710931 | + | 0.999975i | \(0.502263\pi\) | |||||||
\(264\) | −285.779 | + | 207.631i | −0.0666230 | + | 0.0484045i | ||||
\(265\) | −92.2636 | − | 131.887i | −0.0213876 | − | 0.0305726i | ||||
\(266\) | 1663.36 | + | 1208.50i | 0.383411 | + | 0.278564i | ||||
\(267\) | −1078.57 | − | 3319.50i | −0.247219 | − | 0.760862i | ||||
\(268\) | 3354.71 | 0.764633 | ||||||||
\(269\) | 1917.12 | + | 5900.28i | 0.434530 | + | 1.33735i | 0.893567 | + | 0.448930i | \(0.148195\pi\) |
−0.459037 | + | 0.888417i | \(0.651805\pi\) | |||||||
\(270\) | −786.541 | − | 1124.33i | −0.177287 | − | 0.253424i | ||||
\(271\) | 421.312 | − | 1296.66i | 0.0944386 | − | 0.290652i | −0.892668 | − | 0.450714i | \(-0.851169\pi\) |
0.987107 | + | 0.160062i | \(0.0511694\pi\) | |||||||
\(272\) | −144.633 | + | 445.134i | −0.0322413 | + | 0.0992286i | ||||
\(273\) | 1127.92 | − | 819.481i | 0.250054 | − | 0.181675i | ||||
\(274\) | 2758.67 | 0.608238 | ||||||||
\(275\) | 547.038 | + | 428.152i | 0.119955 | + | 0.0938856i | ||||
\(276\) | −6752.90 | −1.47274 | ||||||||
\(277\) | −1694.73 | + | 1231.29i | −0.367604 | + | 0.267080i | −0.756216 | − | 0.654321i | \(-0.772954\pi\) |
0.388613 | + | 0.921401i | \(0.372954\pi\) | |||||||
\(278\) | −470.781 | + | 1448.91i | −0.101567 | + | 0.312590i | ||||
\(279\) | 335.267 | − | 1031.85i | 0.0719424 | − | 0.221416i | ||||
\(280\) | −2156.60 | − | 743.614i | −0.460290 | − | 0.158712i | ||||
\(281\) | −737.828 | − | 2270.80i | −0.156637 | − | 0.482081i | 0.841686 | − | 0.539968i | \(-0.181564\pi\) |
−0.998323 | + | 0.0578873i | \(0.981564\pi\) | |||||||
\(282\) | 5946.18 | 1.25564 | ||||||||
\(283\) | 773.293 | + | 2379.95i | 0.162429 | + | 0.499906i | 0.998838 | − | 0.0482007i | \(-0.0153487\pi\) |
−0.836408 | + | 0.548107i | \(0.815349\pi\) | |||||||
\(284\) | −1995.57 | − | 1449.87i | −0.416955 | − | 0.302936i | ||||
\(285\) | −948.667 | + | 1257.80i | −0.197173 | + | 0.261423i | ||||
\(286\) | 986.232 | − | 716.539i | 0.203906 | − | 0.148146i | ||||
\(287\) | −3757.85 | − | 2730.24i | −0.772889 | − | 0.561537i | ||||
\(288\) | −1399.06 | − | 1016.48i | −0.286251 | − | 0.207974i | ||||
\(289\) | −3165.00 | + | 2299.51i | −0.644210 | + | 0.468046i | ||||
\(290\) | 3125.20 | + | 1077.60i | 0.632820 | + | 0.218202i | ||||
\(291\) | 2762.25 | + | 2006.90i | 0.556448 | + | 0.404283i | ||||
\(292\) | 319.685 | + | 983.888i | 0.0640689 | + | 0.197184i | ||||
\(293\) | 4049.95 | 0.807510 | 0.403755 | − | 0.914867i | \(-0.367705\pi\) | ||||
0.403755 | + | 0.914867i | \(0.367705\pi\) | |||||||
\(294\) | −1054.58 | − | 3245.67i | −0.209199 | − | 0.643848i | ||||
\(295\) | −5687.92 | + | 1736.29i | −1.12259 | + | 0.342681i | ||||
\(296\) | −51.2121 | + | 157.615i | −0.0100562 | + | 0.0309499i | ||||
\(297\) | −46.3675 | + | 142.705i | −0.00905897 | + | 0.0278807i | ||||
\(298\) | 6434.39 | − | 4674.86i | 1.25079 | − | 0.908749i | ||||
\(299\) | 8579.59 | 1.65943 | ||||||||
\(300\) | 1627.75 | − | 4460.24i | 0.313260 | − | 0.858374i | ||||
\(301\) | 4056.57 | 0.776799 | ||||||||
\(302\) | −6810.70 | + | 4948.26i | −1.29772 | + | 0.942849i | ||||
\(303\) | 1184.66 | − | 3646.02i | 0.224611 | − | 0.691281i | ||||
\(304\) | −72.3155 | + | 222.564i | −0.0136434 | + | 0.0419899i | ||||
\(305\) | 94.0053 | − | 5255.85i | 0.0176483 | − | 0.986718i | ||||
\(306\) | −1187.59 | − | 3655.01i | −0.221862 | − | 0.682821i | ||||
\(307\) | 5937.18 | 1.10375 | 0.551877 | − | 0.833925i | \(-0.313912\pi\) | ||||
0.551877 | + | 0.833925i | \(0.313912\pi\) | |||||||
\(308\) | 209.388 | + | 644.430i | 0.0387370 | + | 0.119220i | ||||
\(309\) | −1249.90 | − | 908.104i | −0.230111 | − | 0.167185i | ||||
\(310\) | 5859.40 | − | 1788.64i | 1.07352 | − | 0.327703i | ||||
\(311\) | 333.441 | − | 242.259i | 0.0607965 | − | 0.0441713i | −0.556972 | − | 0.830531i | \(-0.688037\pi\) |
0.617768 | + | 0.786360i | \(0.288037\pi\) | |||||||
\(312\) | −2481.63 | − | 1803.01i | −0.450304 | − | 0.327165i | ||||
\(313\) | 3197.33 | + | 2323.00i | 0.577393 | + | 0.419500i | 0.837783 | − | 0.546003i | \(-0.183851\pi\) |
−0.260390 | + | 0.965503i | \(0.583851\pi\) | |||||||
\(314\) | 1894.75 | − | 1376.62i | 0.340532 | − | 0.247411i | ||||
\(315\) | −926.777 | + | 282.908i | −0.165771 | + | 0.0506033i | ||||
\(316\) | −12576.2 | − | 9137.18i | −2.23883 | − | 1.62660i | ||||
\(317\) | 315.053 | + | 969.635i | 0.0558207 | + | 0.171798i | 0.975080 | − | 0.221855i | \(-0.0712111\pi\) |
−0.919259 | + | 0.393653i | \(0.871211\pi\) | |||||||
\(318\) | 196.314 | 0.0346187 | ||||||||
\(319\) | −111.709 | − | 343.805i | −0.0196066 | − | 0.0603429i | ||||
\(320\) | 166.657 | − | 9317.83i | 0.0291138 | − | 1.62776i | ||||
\(321\) | 306.263 | − | 942.581i | 0.0532522 | − | 0.163893i | ||||
\(322\) | −2404.79 | + | 7401.18i | −0.416191 | + | 1.28091i | ||||
\(323\) | −3569.81 | + | 2593.62i | −0.614952 | + | 0.446789i | ||||
\(324\) | 1025.56 | 0.175851 | ||||||||
\(325\) | −2068.06 | + | 5666.76i | −0.352970 | + | 0.967185i | ||||
\(326\) | 4636.12 | 0.787641 | ||||||||
\(327\) | −458.693 | + | 333.260i | −0.0775712 | + | 0.0563588i | ||||
\(328\) | −3158.09 | + | 9719.60i | −0.531635 | + | 1.63620i | ||||
\(329\) | 1297.61 | − | 3993.64i | 0.217446 | − | 0.669229i | ||||
\(330\) | −810.356 | + | 247.369i | −0.135178 | + | 0.0412643i | ||||
\(331\) | 1115.39 | + | 3432.83i | 0.185219 | + | 0.570047i | 0.999952 | − | 0.00978995i | \(-0.00311629\pi\) |
−0.814733 | + | 0.579837i | \(0.803116\pi\) | |||||||
\(332\) | 13520.1 | 2.23498 | ||||||||
\(333\) | 21.7536 | + | 66.9507i | 0.00357985 | + | 0.0110176i | ||||
\(334\) | 673.622 | + | 489.415i | 0.110356 | + | 0.0801784i | ||||
\(335\) | 2800.52 | + | 965.645i | 0.456742 | + | 0.157489i | ||||
\(336\) | −116.446 | + | 84.6032i | −0.0189067 | + | 0.0137366i | ||||
\(337\) | 783.872 | + | 569.517i | 0.126707 | + | 0.0920580i | 0.649334 | − | 0.760504i | \(-0.275048\pi\) |
−0.522627 | + | 0.852562i | \(0.675048\pi\) | |||||||
\(338\) | 485.030 | + | 352.395i | 0.0780538 | + | 0.0567094i | ||||
\(339\) | −5026.62 | + | 3652.05i | −0.805334 | + | 0.585110i | ||||
\(340\) | 8007.65 | − | 10617.0i | 1.27728 | − | 1.69349i | ||||
\(341\) | −541.990 | − | 393.779i | −0.0860716 | − | 0.0625347i | ||||
\(342\) | −593.786 | − | 1827.49i | −0.0938838 | − | 0.288945i | ||||
\(343\) | −5713.10 | −0.899355 | ||||||||
\(344\) | −2758.04 | − | 8488.38i | −0.432278 | − | 1.33041i | ||||
\(345\) | −5637.33 | − | 1943.80i | −0.879721 | − | 0.303336i | ||||
\(346\) | −5561.77 | + | 17117.4i | −0.864169 | + | 2.65964i | ||||
\(347\) | −2913.92 | + | 8968.11i | −0.450799 | + | 1.38742i | 0.425198 | + | 0.905100i | \(0.360204\pi\) |
−0.875997 | + | 0.482316i | \(0.839796\pi\) | |||||||
\(348\) | −1998.92 | + | 1452.30i | −0.307912 | + | 0.223711i | ||||
\(349\) | 8291.60 | 1.27175 | 0.635873 | − | 0.771794i | \(-0.280640\pi\) | ||||
0.635873 | + | 0.771794i | \(0.280640\pi\) | |||||||
\(350\) | −4308.76 | − | 3372.35i | −0.658037 | − | 0.515028i | ||||
\(351\) | −1302.98 | −0.198143 | ||||||||
\(352\) | −863.896 | + | 627.657i | −0.130812 | + | 0.0950404i | ||||
\(353\) | 3508.98 | − | 10799.5i | 0.529076 | − | 1.62833i | −0.227035 | − | 0.973887i | \(-0.572903\pi\) |
0.756112 | − | 0.654443i | \(-0.227097\pi\) | |||||||
\(354\) | 2241.44 | − | 6898.44i | 0.336529 | − | 1.03573i | ||||
\(355\) | −1248.56 | − | 1784.77i | −0.186667 | − | 0.266833i | ||||
\(356\) | 4552.03 | + | 14009.7i | 0.677689 | + | 2.08571i | ||||
\(357\) | −2713.98 | −0.402350 | ||||||||
\(358\) | 1288.67 | + | 3966.12i | 0.190247 | + | 0.585519i | ||||
\(359\) | 5106.43 | + | 3710.04i | 0.750716 | + | 0.545427i | 0.896049 | − | 0.443956i | \(-0.146425\pi\) |
−0.145333 | + | 0.989383i | \(0.546425\pi\) | |||||||
\(360\) | 1222.10 | + | 1746.94i | 0.178917 | + | 0.255754i | ||||
\(361\) | 3764.16 | − | 2734.82i | 0.548792 | − | 0.398720i | ||||
\(362\) | −3537.43 | − | 2570.09i | −0.513600 | − | 0.373152i | ||||
\(363\) | −3155.45 | − | 2292.57i | −0.456248 | − | 0.331484i | ||||
\(364\) | −4760.30 | + | 3458.56i | −0.685460 | + | 0.498016i | ||||
\(365\) | −16.3364 | + | 913.371i | −0.00234270 | + | 0.130981i | ||||
\(366\) | 5186.98 | + | 3768.56i | 0.740786 | + | 0.538213i | ||||
\(367\) | 1979.71 | + | 6092.93i | 0.281581 | + | 0.866617i | 0.987403 | + | 0.158227i | \(0.0505779\pi\) |
−0.705822 | + | 0.708389i | \(0.749422\pi\) | |||||||
\(368\) | −885.757 | −0.125471 | ||||||||
\(369\) | 1341.48 | + | 4128.64i | 0.189253 | + | 0.582462i | ||||
\(370\) | −239.360 | + | 317.357i | −0.0336317 | + | 0.0445908i | ||||
\(371\) | 42.8408 | − | 131.851i | 0.00599511 | − | 0.0184510i | ||||
\(372\) | −1414.97 | + | 4354.83i | −0.197212 | + | 0.606956i | ||||
\(373\) | −1659.80 | + | 1205.91i | −0.230405 | + | 0.167399i | −0.696998 | − | 0.717073i | \(-0.745481\pi\) |
0.466593 | + | 0.884472i | \(0.345481\pi\) | |||||||
\(374\) | −2373.05 | −0.328095 | ||||||||
\(375\) | 2642.71 | − | 3254.87i | 0.363918 | − | 0.448216i | ||||
\(376\) | −9238.93 | −1.26719 | ||||||||
\(377\) | 2539.63 | − | 1845.15i | 0.346944 | − | 0.252069i | ||||
\(378\) | 365.215 | − | 1124.02i | 0.0496948 | − | 0.152945i | ||||
\(379\) | −548.565 | + | 1688.31i | −0.0743480 | + | 0.228819i | −0.981324 | − | 0.192363i | \(-0.938385\pi\) |
0.906976 | + | 0.421183i | \(0.138385\pi\) | |||||||
\(380\) | 4003.78 | − | 5308.44i | 0.540499 | − | 0.716624i | ||||
\(381\) | 2570.57 | + | 7911.41i | 0.345655 | + | 1.06382i | ||||
\(382\) | 13426.1 | 1.79827 | ||||||||
\(383\) | 3419.50 | + | 10524.1i | 0.456209 | + | 1.40407i | 0.869710 | + | 0.493563i | \(0.164306\pi\) |
−0.413501 | + | 0.910504i | \(0.635694\pi\) | |||||||
\(384\) | 5464.92 | + | 3970.49i | 0.726251 | + | 0.527652i | ||||
\(385\) | −10.7001 | + | 598.242i | −0.00141643 | + | 0.0791929i | ||||
\(386\) | −14462.6 | + | 10507.7i | −1.90707 | + | 1.38557i | ||||
\(387\) | −3067.15 | − | 2228.41i | −0.402873 | − | 0.292704i | ||||
\(388\) | −11657.9 | − | 8469.96i | −1.52536 | − | 1.10824i | ||||
\(389\) | −7939.29 | + | 5768.23i | −1.03480 | + | 0.751828i | −0.969264 | − | 0.246022i | \(-0.920876\pi\) |
−0.0655378 | + | 0.997850i | \(0.520876\pi\) | |||||||
\(390\) | −4217.49 | − | 6028.72i | −0.547592 | − | 0.782760i | ||||
\(391\) | −13511.7 | − | 9816.84i | −1.74761 | − | 1.26972i | ||||
\(392\) | 1638.57 | + | 5043.00i | 0.211123 | + | 0.649770i | ||||
\(393\) | 5355.42 | 0.687393 | ||||||||
\(394\) | −3985.17 | − | 12265.1i | −0.509569 | − | 1.56829i | ||||
\(395\) | −7868.55 | − | 11247.8i | −1.00230 | − | 1.43275i | ||||
\(396\) | 195.691 | − | 602.274i | 0.0248329 | − | 0.0764278i | ||||
\(397\) | −824.666 | + | 2538.06i | −0.104254 | + | 0.320861i | −0.989555 | − | 0.144158i | \(-0.953953\pi\) |
0.885301 | + | 0.465019i | \(0.153953\pi\) | |||||||
\(398\) | −4167.38 | + | 3027.78i | −0.524854 | + | 0.381329i | ||||
\(399\) | −1356.97 | −0.170260 | ||||||||
\(400\) | 213.506 | − | 585.035i | 0.0266883 | − | 0.0731294i | ||||
\(401\) | 7824.21 | 0.974371 | 0.487185 | − | 0.873299i | \(-0.338024\pi\) | ||||
0.487185 | + | 0.873299i | \(0.338024\pi\) | |||||||
\(402\) | −2923.04 | + | 2123.72i | −0.362657 | + | 0.263486i | ||||
\(403\) | 1797.73 | − | 5532.84i | 0.222211 | − | 0.683896i | ||||
\(404\) | −4999.78 | + | 15387.7i | −0.615714 | + | 1.89497i | ||||
\(405\) | 856.142 | + | 295.206i | 0.105042 | + | 0.0362195i | ||||
\(406\) | 879.880 | + | 2707.99i | 0.107556 | + | 0.331023i | ||||
\(407\) | 43.4684 | 0.00529398 | ||||||||
\(408\) | 1845.22 | + | 5679.01i | 0.223902 | + | 0.689100i | ||||
\(409\) | −1645.97 | − | 1195.86i | −0.198992 | − | 0.144576i | 0.483827 | − | 0.875164i | \(-0.339246\pi\) |
−0.682819 | + | 0.730587i | \(0.739246\pi\) | |||||||
\(410\) | −14760.6 | + | 19570.4i | −1.77798 | + | 2.35735i | ||||
\(411\) | −1472.99 | + | 1070.19i | −0.176781 | + | 0.128439i | ||||
\(412\) | 5275.10 | + | 3832.59i | 0.630790 | + | 0.458296i | ||||
\(413\) | −4144.06 | − | 3010.84i | −0.493744 | − | 0.358726i | ||||
\(414\) | 5883.97 | − | 4274.95i | 0.698506 | − | 0.507494i | ||||
\(415\) | 11286.6 | + | 3891.73i | 1.33503 | + | 0.460331i | ||||
\(416\) | −7501.86 | − | 5450.42i | −0.884156 | − | 0.642377i | ||||
\(417\) | −310.714 | − | 956.280i | −0.0364886 | − | 0.112300i | ||||
\(418\) | −1186.51 | −0.138838 | ||||||||
\(419\) | 1669.11 | + | 5137.00i | 0.194610 | + | 0.598947i | 0.999981 | + | 0.00617611i | \(0.00196593\pi\) |
−0.805371 | + | 0.592771i | \(0.798034\pi\) | |||||||
\(420\) | 3911.39 | − | 1193.99i | 0.454420 | − | 0.138716i | ||||
\(421\) | −1827.80 | + | 5625.37i | −0.211594 | + | 0.651221i | 0.787783 | + | 0.615952i | \(0.211229\pi\) |
−0.999378 | + | 0.0352685i | \(0.988771\pi\) | |||||||
\(422\) | 4287.00 | − | 13194.0i | 0.494521 | − | 1.52198i | ||||
\(423\) | −3174.96 | + | 2306.74i | −0.364945 | + | 0.265148i | ||||
\(424\) | −305.025 | −0.0349371 | ||||||||
\(425\) | 9740.87 | − | 6558.10i | 1.11177 | − | 0.748505i | ||||
\(426\) | 2656.63 | 0.302146 | ||||||||
\(427\) | 3663.02 | − | 2661.34i | 0.415142 | − | 0.301619i | ||||
\(428\) | −1292.56 | + | 3978.09i | −0.145977 | + | 0.449272i | ||||
\(429\) | −248.626 | + | 765.192i | −0.0279808 | + | 0.0861161i | ||||
\(430\) | 382.832 | − | 21404.2i | 0.0429344 | − | 2.40047i | ||||
\(431\) | 225.406 | + | 693.727i | 0.0251912 | + | 0.0775305i | 0.962862 | − | 0.269995i | \(-0.0870220\pi\) |
−0.937671 | + | 0.347525i | \(0.887022\pi\) | |||||||
\(432\) | 134.520 | 0.0149817 | ||||||||
\(433\) | −5283.48 | − | 16260.9i | −0.586393 | − | 1.80473i | −0.593604 | − | 0.804757i | \(-0.702295\pi\) |
0.00721121 | − | 0.999974i | \(-0.497705\pi\) | |||||||
\(434\) | 4269.01 | + | 3101.61i | 0.472163 | + | 0.343047i | ||||
\(435\) | −2086.74 | + | 636.997i | −0.230003 | + | 0.0702108i | ||||
\(436\) | 1935.88 | − | 1406.50i | 0.212642 | − | 0.154493i | ||||
\(437\) | −6755.78 | − | 4908.36i | −0.739526 | − | 0.537297i | ||||
\(438\) | −901.403 | − | 654.908i | −0.0983350 | − | 0.0714445i | ||||
\(439\) | 8738.54 | − | 6348.92i | 0.950040 | − | 0.690245i | −0.000776050 | − | 1.00000i | \(-0.500247\pi\) |
0.950816 | + | 0.309755i | \(0.100247\pi\) | |||||||
\(440\) | 1259.10 | − | 384.352i | 0.136421 | − | 0.0416438i | ||||
\(441\) | 1822.21 | + | 1323.91i | 0.196762 | + | 0.142956i | ||||
\(442\) | −6367.92 | − | 19598.4i | −0.685273 | − | 2.10905i | ||||
\(443\) | 9357.79 | 1.00362 | 0.501808 | − | 0.864979i | \(-0.332668\pi\) | ||||
0.501808 | + | 0.864979i | \(0.332668\pi\) | |||||||
\(444\) | −91.8095 | − | 282.560i | −0.00981325 | − | 0.0302021i | ||||
\(445\) | −232.616 | + | 13005.6i | −0.0247799 | + | 1.38545i | ||||
\(446\) | 7243.52 | − | 22293.3i | 0.769037 | − | 2.36685i | ||||
\(447\) | −1622.09 | + | 4992.28i | −0.171638 | + | 0.528248i | ||||
\(448\) | 6493.98 | − | 4718.15i | 0.684848 | − | 0.497571i | ||||
\(449\) | 3875.68 | 0.407360 | 0.203680 | − | 0.979038i | \(-0.434710\pi\) | ||||
0.203680 | + | 0.979038i | \(0.434710\pi\) | |||||||
\(450\) | 1405.28 | + | 4916.77i | 0.147212 | + | 0.515064i | ||||
\(451\) | 2680.56 | 0.279873 | ||||||||
\(452\) | 21214.5 | − | 15413.2i | 2.20762 | − | 1.60393i | ||||
\(453\) | 1716.96 | − | 5284.24i | 0.178079 | − | 0.548069i | ||||
\(454\) | −2512.21 | + | 7731.80i | −0.259700 | + | 0.799276i | ||||
\(455\) | −4969.44 | + | 1516.97i | −0.512024 | + | 0.156300i | ||||
\(456\) | 922.601 | + | 2839.47i | 0.0947473 | + | 0.291602i | ||||
\(457\) | 13179.1 | 1.34899 | 0.674497 | − | 0.738277i | \(-0.264360\pi\) | ||||
0.674497 | + | 0.738277i | \(0.264360\pi\) | |||||||
\(458\) | 1776.11 | + | 5466.32i | 0.181206 | + | 0.557695i | ||||
\(459\) | 2052.03 | + | 1490.88i | 0.208672 | + | 0.151609i | ||||
\(460\) | 23791.9 | + | 8203.69i | 2.41153 | + | 0.831519i | ||||
\(461\) | 11024.5 | − | 8009.76i | 1.11380 | − | 0.809223i | 0.130542 | − | 0.991443i | \(-0.458328\pi\) |
0.983258 | + | 0.182220i | \(0.0583282\pi\) | |||||||
\(462\) | −590.404 | − | 428.954i | −0.0594547 | − | 0.0431964i | ||||
\(463\) | 5883.71 | + | 4274.77i | 0.590582 | + | 0.429083i | 0.842523 | − | 0.538660i | \(-0.181069\pi\) |
−0.251942 | + | 0.967742i | \(0.581069\pi\) | |||||||
\(464\) | −262.191 | + | 190.493i | −0.0262326 | + | 0.0190591i | ||||
\(465\) | −2434.75 | + | 3228.12i | −0.242814 | + | 0.321937i | ||||
\(466\) | −15974.5 | − | 11606.1i | −1.58799 | − | 1.15374i | ||||
\(467\) | −399.983 | − | 1231.02i | −0.0396338 | − | 0.121980i | 0.929282 | − | 0.369371i | \(-0.120427\pi\) |
−0.968916 | + | 0.247391i | \(0.920427\pi\) | |||||||
\(468\) | 5499.15 | 0.543158 | ||||||||
\(469\) | 788.468 | + | 2426.66i | 0.0776292 | + | 0.238918i | ||||
\(470\) | −20949.7 | − | 7223.64i | −2.05603 | − | 0.708940i | ||||
\(471\) | −477.661 | + | 1470.09i | −0.0467292 | + | 0.143818i | ||||
\(472\) | −3482.66 | + | 10718.5i | −0.339624 | + | 1.04525i | ||||
\(473\) | −1893.91 | + | 1376.01i | −0.184106 | + | 0.133761i | ||||
\(474\) | 16742.3 | 1.62236 | ||||||||
\(475\) | 4870.38 | − | 3279.01i | 0.470460 | − | 0.316740i | ||||
\(476\) | 11454.2 | 1.10294 | ||||||||
\(477\) | −104.822 | + | 76.1575i | −0.0100618 | + | 0.00731030i | ||||
\(478\) | −571.720 | + | 1759.57i | −0.0547068 | + | 0.168370i | ||||
\(479\) | −1286.67 | + | 3959.96i | −0.122734 | + | 0.377735i | −0.993481 | − | 0.113995i | \(-0.963635\pi\) |
0.870748 | + | 0.491730i | \(0.163635\pi\) | |||||||
\(480\) | 3694.34 | + | 5280.90i | 0.351297 | + | 0.502164i | ||||
\(481\) | 116.644 | + | 358.994i | 0.0110572 | + | 0.0340306i | ||||
\(482\) | −7764.15 | −0.733708 | ||||||||
\(483\) | −1587.16 | − | 4884.76i | −0.149520 | − | 0.460175i | ||||
\(484\) | 13317.3 | + | 9675.61i | 1.25069 | + | 0.908679i | ||||
\(485\) | −7293.97 | − | 10426.4i | −0.682891 | − | 0.976164i | ||||
\(486\) | −893.599 | + | 649.237i | −0.0834042 | + | 0.0605967i | ||||
\(487\) | −3269.87 | − | 2375.70i | −0.304255 | − | 0.221054i | 0.425173 | − | 0.905112i | \(-0.360213\pi\) |
−0.729427 | + | 0.684058i | \(0.760213\pi\) | |||||||
\(488\) | −8059.33 | − | 5855.44i | −0.747599 | − | 0.543163i | ||||
\(489\) | −2475.45 | + | 1798.52i | −0.228924 | + | 0.166323i | ||||
\(490\) | −227.443 | + | 12716.4i | −0.0209690 | + | 1.17238i | ||||
\(491\) | −6716.60 | − | 4879.90i | −0.617344 | − | 0.448527i | 0.234649 | − | 0.972080i | \(-0.424606\pi\) |
−0.851993 | + | 0.523553i | \(0.824606\pi\) | |||||||
\(492\) | −5661.60 | − | 17424.6i | −0.518790 | − | 1.59667i | ||||
\(493\) | −6110.82 | −0.558251 | ||||||||
\(494\) | −3183.92 | − | 9799.11i | −0.289983 | − | 0.892475i | ||||
\(495\) | 336.726 | − | 446.450i | 0.0305751 | − | 0.0405382i | ||||
\(496\) | −185.597 | + | 571.209i | −0.0168015 | + | 0.0517098i | ||||
\(497\) | 579.746 | − | 1784.28i | 0.0523243 | − | 0.161038i | ||||
\(498\) | −11780.4 | + | 8558.97i | −1.06003 | + | 0.770154i | ||||
\(499\) | −5737.93 | −0.514760 | −0.257380 | − | 0.966310i | \(-0.582859\pi\) | ||||
−0.257380 | + | 0.966310i | \(0.582859\pi\) | |||||||
\(500\) | −11153.4 | + | 13736.9i | −0.997588 | + | 1.22867i | ||||
\(501\) | −549.542 | −0.0490055 | ||||||||
\(502\) | −20986.0 | + | 15247.2i | −1.86583 | + | 1.35561i | ||||
\(503\) | −700.467 | + | 2155.82i | −0.0620920 | + | 0.191100i | −0.977291 | − | 0.211904i | \(-0.932034\pi\) |
0.915199 | + | 0.403003i | \(0.132034\pi\) | |||||||
\(504\) | −567.457 | + | 1746.45i | −0.0501519 | + | 0.154352i | ||||
\(505\) | −8603.14 | + | 11406.5i | −0.758089 | + | 1.00512i | ||||
\(506\) | −1387.78 | − | 4271.14i | −0.121925 | − | 0.375248i | ||||
\(507\) | −395.689 | −0.0346611 | ||||||||
\(508\) | −10848.9 | − | 33389.5i | −0.947525 | − | 2.91618i | ||||
\(509\) | −5626.05 | − | 4087.57i | −0.489922 | − | 0.355949i | 0.315232 | − | 0.949015i | \(-0.397918\pi\) |
−0.805154 | + | 0.593065i | \(0.797918\pi\) | |||||||
\(510\) | −256.128 | + | 14320.1i | −0.0222383 | + | 1.24334i | ||||
\(511\) | −636.566 | + | 462.492i | −0.0551077 | + | 0.0400381i | ||||
\(512\) | 1457.70 | + | 1059.08i | 0.125824 | + | 0.0914165i | ||||
\(513\) | 1026.00 | + | 745.433i | 0.0883022 | + | 0.0641553i | ||||
\(514\) | −23173.2 | + | 16836.3i | −1.98857 | + | 1.44478i | ||||
\(515\) | 3300.46 | + | 4717.87i | 0.282399 | + | 0.403678i | ||||
\(516\) | 12944.7 | + | 9404.85i | 1.10437 | + | 0.802375i | ||||
\(517\) | 748.838 | + | 2304.69i | 0.0637019 | + | 0.196054i | ||||
\(518\) | −342.380 | −0.0290412 | ||||||||
\(519\) | −3670.76 | − | 11297.4i | −0.310459 | − | 0.955495i | ||||
\(520\) | 6552.97 | + | 9367.19i | 0.552628 | + | 0.789959i | ||||
\(521\) | 4158.12 | − | 12797.4i | 0.349656 | − | 1.07613i | −0.609388 | − | 0.792872i | \(-0.708585\pi\) |
0.959044 | − | 0.283258i | \(-0.0914153\pi\) | |||||||
\(522\) | 822.322 | − | 2530.85i | 0.0689503 | − | 0.212207i | ||||
\(523\) | −15776.8 | + | 11462.5i | −1.31906 | + | 0.958356i | −0.319121 | + | 0.947714i | \(0.603388\pi\) |
−0.999943 | + | 0.0106422i | \(0.996612\pi\) | |||||||
\(524\) | −22602.2 | −1.88431 | ||||||||
\(525\) | 3608.92 | + | 129.139i | 0.300012 | + | 0.0107354i | ||||
\(526\) | 22567.3 | 1.87069 | ||||||||
\(527\) | −9161.89 | + | 6656.51i | −0.757302 | + | 0.550212i | ||||
\(528\) | 25.6681 | − | 78.9983i | 0.00211565 | − | 0.00651129i | ||||
\(529\) | 6007.29 | − | 18488.5i | 0.493736 | − | 1.51956i | ||||
\(530\) | −691.657 | − | 238.490i | −0.0566861 | − | 0.0195459i | ||||
\(531\) | 1479.35 | + | 4552.96i | 0.120900 | + | 0.372093i | ||||
\(532\) | 5727.01 | 0.466725 | ||||||||
\(533\) | 7193.09 | + | 22138.1i | 0.584554 | + | 1.79907i | ||||
\(534\) | −12835.2 | − | 9325.32i | −1.04014 | − | 0.755704i | ||||
\(535\) | −2224.11 | + | 2948.86i | −0.179732 | + | 0.238299i | ||||
\(536\) | 4541.71 | − | 3299.74i | 0.365992 | − | 0.265909i | ||||
\(537\) | −2226.69 | − | 1617.78i | −0.178936 | − | 0.130005i | ||||
\(538\) | 22814.1 | + | 16575.4i | 1.82822 | + | 1.32828i | ||||
\(539\) | 1125.18 | − | 817.494i | 0.0899167 | − | 0.0653283i | ||||
\(540\) | −3613.28 | − | 1245.89i | −0.287946 | − | 0.0992866i | ||||
\(541\) | 13978.5 | + | 10156.0i | 1.11087 | + | 0.807096i | 0.982801 | − | 0.184669i | \(-0.0591213\pi\) |
0.128072 | + | 0.991765i | \(0.459121\pi\) | |||||||
\(542\) | −1915.06 | − | 5893.94i | −0.151769 | − | 0.467097i | ||||
\(543\) | 2885.84 | 0.228073 | ||||||||
\(544\) | 5578.02 | + | 17167.4i | 0.439624 | + | 1.35302i | ||||
\(545\) | 2020.93 | − | 616.909i | 0.158839 | − | 0.0484871i | ||||
\(546\) | 1958.31 | − | 6027.06i | 0.153494 | − | 0.472407i | ||||
\(547\) | −7017.43 | + | 21597.4i | −0.548526 | + | 1.68819i | 0.163929 | + | 0.986472i | \(0.447583\pi\) |
−0.712455 | + | 0.701718i | \(0.752417\pi\) | |||||||
\(548\) | 6216.64 | − | 4516.65i | 0.484602 | − | 0.352084i | ||||
\(549\) | −4231.55 | −0.328959 | ||||||||
\(550\) | 3155.57 | + | 112.916i | 0.244644 | + | 0.00875413i | ||||
\(551\) | −3055.38 | −0.236231 | ||||||||
\(552\) | −9142.28 | + | 6642.25i | −0.704930 | + | 0.512161i | ||||
\(553\) | 3653.61 | − | 11244.7i | 0.280953 | − | 0.864686i | ||||
\(554\) | −2942.41 | + | 9055.80i | −0.225651 | + | 0.694484i | ||||
\(555\) | 4.69162 | − | 262.309i | 0.000358825 | − | 0.0200620i | ||||
\(556\) | 1311.35 | + | 4035.91i | 0.100024 | + | 0.307843i | ||||
\(557\) | 7542.26 | 0.573745 | 0.286872 | − | 0.957969i | \(-0.407384\pi\) | ||||
0.286872 | + | 0.957969i | \(0.407384\pi\) | |||||||
\(558\) | −1523.95 | − | 4690.23i | −0.115616 | − | 0.355830i | ||||
\(559\) | −16446.3 | − | 11948.9i | −1.24437 | − | 0.904087i | ||||
\(560\) | 513.045 | − | 156.612i | 0.0387145 | − | 0.0118180i | ||||
\(561\) | 1267.09 | − | 920.595i | 0.0953594 | − | 0.0692827i | ||||
\(562\) | −8780.29 | − | 6379.26i | −0.659029 | − | 0.478813i | ||||
\(563\) | 9453.57 | + | 6868.42i | 0.707674 | + | 0.514155i | 0.882422 | − | 0.470458i | \(-0.155911\pi\) |
−0.174749 | + | 0.984613i | \(0.555911\pi\) | |||||||
\(564\) | 13399.7 | − | 9735.44i | 1.00040 | − | 0.726837i | ||||
\(565\) | 22146.5 | − | 6760.44i | 1.64905 | − | 0.503387i | ||||
\(566\) | 9202.34 | + | 6685.89i | 0.683398 | + | 0.496517i | ||||
\(567\) | 241.041 | + | 741.849i | 0.0178532 | + | 0.0549466i | ||||
\(568\) | −4127.77 | −0.304925 | ||||||||
\(569\) | −5612.42 | − | 17273.3i | −0.413506 | − | 1.27264i | −0.913580 | − | 0.406659i | \(-0.866694\pi\) |
0.500074 | − | 0.865983i | \(-0.333306\pi\) | |||||||
\(570\) | −128.062 | + | 7159.98i | −0.00941042 | + | 0.526138i | ||||
\(571\) | −1636.40 | + | 5036.33i | −0.119932 | + | 0.369114i | −0.992944 | − | 0.118586i | \(-0.962164\pi\) |
0.873011 | + | 0.487700i | \(0.162164\pi\) | |||||||
\(572\) | 1049.31 | − | 3229.44i | 0.0767023 | − | 0.236066i | ||||
\(573\) | −7168.88 | + | 5208.50i | −0.522660 | + | 0.379735i | ||||
\(574\) | −21113.5 | −1.53530 | ||||||||
\(575\) | 17500.1 | + | 13696.9i | 1.26923 | + | 0.993391i | ||||
\(576\) | −7501.91 | −0.542673 | ||||||||
\(577\) | 5077.07 | − | 3688.71i | 0.366311 | − | 0.266140i | −0.389369 | − | 0.921082i | \(-0.627307\pi\) |
0.755679 | + | 0.654942i | \(0.227307\pi\) | |||||||
\(578\) | −5495.12 | + | 16912.3i | −0.395445 | + | 1.21705i | ||||
\(579\) | 3645.99 | − | 11221.2i | 0.261696 | − | 0.805418i | ||||
\(580\) | 8806.93 | − | 2688.40i | 0.630496 | − | 0.192465i | ||||
\(581\) | 3177.67 | + | 9779.88i | 0.226906 | + | 0.698344i | ||||
\(582\) | 15519.7 | 1.10535 | ||||||||
\(583\) | 24.7230 | + | 76.0896i | 0.00175630 | + | 0.00540533i | ||||
\(584\) | 1400.56 | + | 1017.57i | 0.0992393 | + | 0.0721016i | ||||
\(585\) | 4590.69 | + | 1582.91i | 0.324447 | + | 0.111873i | ||||
\(586\) | 14893.1 | − | 10820.5i | 1.04988 | − | 0.762781i | ||||
\(587\) | −761.336 | − | 553.143i | −0.0535327 | − | 0.0388938i | 0.560697 | − | 0.828021i | \(-0.310533\pi\) |
−0.614230 | + | 0.789127i | \(0.710533\pi\) | |||||||
\(588\) | −7690.51 | − | 5587.48i | −0.539373 | − | 0.391877i | ||||
\(589\) | −4580.90 | + | 3328.22i | −0.320463 | + | 0.232830i | ||||
\(590\) | −16277.6 | + | 21581.7i | −1.13583 | + | 1.50594i | ||||
\(591\) | 6885.97 | + | 5002.95i | 0.479274 | + | 0.348213i | ||||
\(592\) | −12.0424 | − | 37.0625i | −0.000836043 | − | 0.00257308i | ||||
\(593\) | −17718.9 | −1.22703 | −0.613516 | − | 0.789682i | \(-0.710245\pi\) | ||||
−0.613516 | + | 0.789682i | \(0.710245\pi\) | |||||||
\(594\) | 210.762 | + | 648.659i | 0.0145584 | + | 0.0448060i | ||||
\(595\) | 9561.94 | + | 3297.05i | 0.658826 | + | 0.227169i | ||||
\(596\) | 6845.91 | − | 21069.5i | 0.470502 | − | 1.44806i | ||||
\(597\) | 1050.58 | − | 3233.36i | 0.0720226 | − | 0.221663i | ||||
\(598\) | 31550.3 | − | 22922.6i | 2.15750 | − | 1.56752i | ||||
\(599\) | −7231.26 | −0.493258 | −0.246629 | − | 0.969110i | \(-0.579323\pi\) | ||||
−0.246629 | + | 0.969110i | \(0.579323\pi\) | |||||||
\(600\) | −2183.47 | − | 7639.48i | −0.148566 | − | 0.519801i | ||||
\(601\) | −5488.00 | −0.372479 | −0.186240 | − | 0.982504i | \(-0.559630\pi\) | ||||
−0.186240 | + | 0.982504i | \(0.559630\pi\) | |||||||
\(602\) | 14917.5 | − | 10838.2i | 1.00995 | − | 0.733772i | ||||
\(603\) | 736.890 | − | 2267.91i | 0.0497653 | − | 0.153162i | ||||
\(604\) | −7246.28 | + | 22301.8i | −0.488157 | + | 1.50239i | ||||
\(605\) | 8332.23 | + | 11910.6i | 0.559923 | + | 0.800386i | ||||
\(606\) | −5384.85 | − | 16572.9i | −0.360964 | − | 1.11093i | ||||
\(607\) | −23649.8 | −1.58141 | −0.790704 | − | 0.612198i | \(-0.790285\pi\) | ||||
−0.790704 | + | 0.612198i | \(0.790285\pi\) | |||||||
\(608\) | 2788.98 | + | 8583.59i | 0.186033 | + | 0.572550i | ||||
\(609\) | −1520.34 | − | 1104.59i | −0.101162 | − | 0.0734981i | ||||
\(610\) | −13696.7 | − | 19578.8i | −0.909118 | − | 1.29955i | ||||
\(611\) | −17024.4 | + | 12368.9i | −1.12722 | + | 0.818974i | ||||
\(612\) | −8660.42 | − | 6292.17i | −0.572021 | − | 0.415598i | ||||
\(613\) | −3762.55 | − | 2733.65i | −0.247909 | − | 0.180116i | 0.456891 | − | 0.889523i | \(-0.348963\pi\) |
−0.704799 | + | 0.709407i | \(0.748963\pi\) | |||||||
\(614\) | 21833.1 | − | 15862.7i | 1.43504 | − | 1.04262i | ||||
\(615\) | 289.317 | − | 16175.8i | 0.0189698 | − | 1.06060i | ||||
\(616\) | 917.346 | + | 666.491i | 0.0600015 | + | 0.0435936i | ||||
\(617\) | −1505.87 | − | 4634.58i | −0.0982560 | − | 0.302401i | 0.889833 | − | 0.456287i | \(-0.150821\pi\) |
−0.988089 | + | 0.153886i | \(0.950821\pi\) | |||||||
\(618\) | −7022.56 | −0.457102 | ||||||||
\(619\) | 3764.65 | + | 11586.4i | 0.244449 | + | 0.752338i | 0.995727 | + | 0.0923509i | \(0.0294382\pi\) |
−0.751277 | + | 0.659987i | \(0.770562\pi\) | |||||||
\(620\) | 10275.7 | − | 13624.1i | 0.665614 | − | 0.882509i | ||||
\(621\) | −1483.33 | + | 4565.22i | −0.0958518 | + | 0.295002i | ||||
\(622\) | 578.925 | − | 1781.75i | 0.0373196 | − | 0.114858i | ||||
\(623\) | −9064.15 | + | 6585.49i | −0.582901 | + | 0.423502i | ||||
\(624\) | 721.305 | 0.0462745 | ||||||||
\(625\) | −13265.0 | + | 8257.15i | −0.848960 | + | 0.528458i | ||||
\(626\) | 17964.2 | 1.14696 | ||||||||
\(627\) | 633.538 | − | 460.293i | 0.0403526 | − | 0.0293179i | ||||
\(628\) | 2015.94 | − | 6204.41i | 0.128096 | − | 0.394240i | ||||
\(629\) | 227.065 | − | 698.834i | 0.0143937 | − | 0.0442994i | ||||
\(630\) | −2652.23 | + | 3516.48i | −0.167726 | + | 0.222381i | ||||
\(631\) | −3757.85 | − | 11565.5i | −0.237080 | − | 0.729659i | −0.996839 | − | 0.0794528i | \(-0.974683\pi\) |
0.759758 | − | 0.650206i | \(-0.225317\pi\) | |||||||
\(632\) | −26013.5 | −1.63728 | ||||||||
\(633\) | 2829.41 | + | 8708.04i | 0.177661 | + | 0.546783i | ||||
\(634\) | 3749.19 | + | 2723.95i | 0.234857 | + | 0.170634i | ||||
\(635\) | 554.398 | − | 30996.4i | 0.0346466 | − | 1.93710i | ||||
\(636\) | 442.393 | − | 321.417i | 0.0275818 | − | 0.0200393i | ||||
\(637\) | 9770.82 | + | 7098.92i | 0.607746 | + | 0.441553i | ||||
\(638\) | −1329.36 | − | 965.835i | −0.0824919 | − | 0.0599338i | ||||
\(639\) | −1418.51 | + | 1030.61i | −0.0878174 | + | 0.0638031i | ||||
\(640\) | −14430.6 | − | 20627.9i | −0.891279 | − | 1.27405i | ||||
\(641\) | 8768.13 | + | 6370.42i | 0.540281 | + | 0.392537i | 0.824190 | − | 0.566314i | \(-0.191631\pi\) |
−0.283908 | + | 0.958851i | \(0.591631\pi\) | |||||||
\(642\) | −1392.11 | − | 4284.47i | −0.0855797 | − | 0.263387i | ||||
\(643\) | −15336.9 | −0.940632 | −0.470316 | − | 0.882498i | \(-0.655860\pi\) | ||||
−0.470316 | + | 0.882498i | \(0.655860\pi\) | |||||||
\(644\) | 6698.47 | + | 20615.8i | 0.409871 | + | 1.26145i | ||||
\(645\) | 8099.06 | + | 11577.3i | 0.494419 | + | 0.706751i | ||||
\(646\) | −6197.96 | + | 19075.4i | −0.377485 | + | 1.16178i | ||||
\(647\) | 2347.69 | − | 7225.46i | 0.142654 | − | 0.439045i | −0.854048 | − | 0.520195i | \(-0.825859\pi\) |
0.996702 | + | 0.0811500i | \(0.0258593\pi\) | |||||||
\(648\) | 1388.44 | − | 1008.76i | 0.0841713 | − | 0.0611540i | ||||
\(649\) | 2956.05 | 0.178791 | ||||||||
\(650\) | 7535.21 | + | 26364.1i | 0.454700 | + | 1.59090i | ||||
\(651\) | −3482.67 | −0.209672 | ||||||||
\(652\) | 10447.5 | − | 7590.53i | 0.627538 | − | 0.455933i | ||||
\(653\) | 5843.81 | − | 17985.4i | 0.350208 | − | 1.07783i | −0.608528 | − | 0.793533i | \(-0.708240\pi\) |
0.958736 | − | 0.284298i | \(-0.0917605\pi\) | |||||||
\(654\) | −796.389 | + | 2451.03i | −0.0476166 | + | 0.146549i | ||||
\(655\) | −18868.3 | − | 6505.97i | −1.12557 | − | 0.388106i | ||||
\(656\) | −742.614 | − | 2285.53i | −0.0441985 | − | 0.136029i | ||||
\(657\) | 735.367 | 0.0436673 | ||||||||
\(658\) | −5898.25 | − | 18152.9i | −0.349449 | − | 1.07549i | ||||
\(659\) | 10574.2 | + | 7682.64i | 0.625059 | + | 0.454132i | 0.854685 | − | 0.519147i | \(-0.173750\pi\) |
−0.229626 | + | 0.973279i | \(0.573750\pi\) | |||||||
\(660\) | −1421.13 | + | 1884.21i | −0.0838140 | + | 0.111125i | ||||
\(661\) | −3910.79 | + | 2841.36i | −0.230124 | + | 0.167195i | −0.696872 | − | 0.717195i | \(-0.745426\pi\) |
0.466748 | + | 0.884390i | \(0.345426\pi\) | |||||||
\(662\) | 13273.4 | + | 9643.70i | 0.779284 | + | 0.566183i | ||||
\(663\) | 11003.1 | + | 7994.22i | 0.644533 | + | 0.468280i | ||||
\(664\) | 18303.9 | − | 13298.6i | 1.06977 | − | 0.777237i | ||||
\(665\) | 4780.92 | + | 1648.50i | 0.278791 | + | 0.0961297i | ||||
\(666\) | 258.872 | + | 188.081i | 0.0150617 | + | 0.0109430i | ||||
\(667\) | −3573.65 | − | 10998.6i | −0.207455 | − | 0.638480i | ||||
\(668\) | 2319.30 | 0.134336 | ||||||||
\(669\) | 4780.71 | + | 14713.5i | 0.276282 | + | 0.850310i | ||||
\(670\) | 12878.5 | − | 3931.29i | 0.742596 | − | 0.226685i | ||||
\(671\) | −807.434 | + | 2485.03i | −0.0464540 | + | 0.142971i | ||||
\(672\) | −1715.39 | + | 5279.44i | −0.0984714 | + | 0.303064i | ||||
\(673\) | −13291.3 | + | 9656.72i | −0.761283 | + | 0.553104i | −0.899304 | − | 0.437325i | \(-0.855926\pi\) |
0.138021 | + | 0.990429i | \(0.455926\pi\) | |||||||
\(674\) | 4404.19 | 0.251696 | ||||||||
\(675\) | −2657.75 | − | 2080.15i | −0.151551 | − | 0.118615i | ||||
\(676\) | 1669.98 | 0.0950146 | ||||||||
\(677\) | 17003.8 | − | 12354.0i | 0.965304 | − | 0.701334i | 0.0109275 | − | 0.999940i | \(-0.496522\pi\) |
0.954377 | + | 0.298606i | \(0.0965216\pi\) | |||||||
\(678\) | −8727.28 | + | 26859.8i | −0.494350 | + | 1.52145i | ||||
\(679\) | 3386.81 | − | 10423.5i | 0.191420 | − | 0.589129i | ||||
\(680\) | 397.961 | − | 22250.0i | 0.0224428 | − | 1.25478i | ||||
\(681\) | −1658.06 | − | 5102.97i | −0.0932993 | − | 0.287146i | ||||
\(682\) | −3045.18 | −0.170976 | ||||||||
\(683\) | −2500.26 | − | 7695.01i | −0.140073 | − | 0.431100i | 0.856272 | − | 0.516526i | \(-0.172775\pi\) |
−0.996345 | + | 0.0854256i | \(0.972775\pi\) | |||||||
\(684\) | −4330.16 | − | 3146.05i | −0.242058 | − | 0.175866i | ||||
\(685\) | 6489.77 | − | 1981.06i | 0.361987 | − | 0.110500i | ||||
\(686\) | −21009.1 | + | 15264.0i | −1.16929 | + | 0.849539i | ||||
\(687\) | −3068.94 | − | 2229.72i | −0.170433 | − | 0.123827i | ||||
\(688\) | 1697.91 | + | 1233.60i | 0.0940875 | + | 0.0683586i | ||||
\(689\) | −562.062 | + | 408.362i | −0.0310782 | + | 0.0225796i | ||||
\(690\) | −25923.9 | + | 7913.52i | −1.43030 | + | 0.436612i | ||||
\(691\) | −24064.9 | − | 17484.2i | −1.32485 | − | 0.962561i | −0.999858 | − | 0.0168450i | \(-0.994638\pi\) |
−0.324994 | − | 0.945716i | \(-0.605362\pi\) | |||||||
\(692\) | 15492.2 | + | 47680.0i | 0.851045 | + | 2.61925i | ||||
\(693\) | 481.653 | 0.0264019 | ||||||||
\(694\) | 13245.1 | + | 40764.3i | 0.724464 | + | 2.22967i | ||||
\(695\) | −67.0120 | + | 3746.65i | −0.00365743 | + | 0.204487i | ||||
\(696\) | −1277.69 | + | 3932.33i | −0.0695844 | + | 0.214159i | ||||
\(697\) | 14002.4 | − | 43094.9i | 0.760944 | − | 2.34194i | ||||
\(698\) | 30491.2 | − | 22153.2i | 1.65345 | − | 1.20130i | ||||
\(699\) | 13032.0 | 0.705173 | ||||||||
\(700\) | −15231.2 | − | 545.020i | −0.822407 | − | 0.0294283i | ||||
\(701\) | −24612.8 | −1.32612 | −0.663061 | − | 0.748565i | \(-0.730743\pi\) | ||||
−0.663061 | + | 0.748565i | \(0.730743\pi\) | |||||||
\(702\) | −4791.54 | + | 3481.26i | −0.257614 | + | 0.187168i | ||||
\(703\) | 113.531 | − | 349.413i | 0.00609091 | − | 0.0187459i | ||||
\(704\) | −1431.46 | + | 4405.58i | −0.0766338 | + | 0.235855i | ||||
\(705\) | 13988.4 | − | 4270.09i | 0.747281 | − | 0.228115i | ||||
\(706\) | −15949.9 | − | 49088.9i | −0.850260 | − | 2.61683i | ||||
\(707\) | −12306.0 | −0.654615 | ||||||||
\(708\) | −6243.47 | − | 19215.4i | −0.331418 | − | 1.02000i | ||||
\(709\) | −21821.6 | − | 15854.3i | −1.15589 | − | 0.839805i | −0.166639 | − | 0.986018i | \(-0.553291\pi\) |
−0.989253 | + | 0.146213i | \(0.953291\pi\) | |||||||
\(710\) | −9359.89 | − | 3227.38i | −0.494747 | − | 0.170593i | ||||
\(711\) | −8939.55 | + | 6494.97i | −0.471532 | + | 0.342588i | ||||
\(712\) | 19942.8 | + | 14489.3i | 1.04970 | + | 0.762654i | ||||
\(713\) | −17338.7 | − | 12597.3i | −0.910713 | − | 0.661671i | ||||
\(714\) | −9980.28 | + | 7251.10i | −0.523113 | + | 0.380064i | ||||
\(715\) | 1805.55 | − | 2393.90i | 0.0944386 | − | 0.125212i | ||||
\(716\) | 9397.57 | + | 6827.74i | 0.490508 | + | 0.356375i | ||||
\(717\) | −377.334 | − | 1161.31i | −0.0196538 | − | 0.0604882i | ||||
\(718\) | 28690.5 | 1.49125 | ||||||||
\(719\) | −1029.02 | − | 3167.00i | −0.0533742 | − | 0.164269i | 0.920816 | − | 0.389997i | \(-0.127524\pi\) |
−0.974190 | + | 0.225728i | \(0.927524\pi\) | |||||||
\(720\) | −473.943 | − | 163.420i | −0.0245317 | − | 0.00845875i | ||||
\(721\) | −1532.51 | + | 4716.57i | −0.0791588 | + | 0.243626i | ||||
\(722\) | 6535.39 | − | 20113.9i | 0.336873 | − | 1.03679i | ||||
\(723\) | 4145.66 | − | 3012.00i | 0.213249 | − | 0.154934i | ||||
\(724\) | −12179.5 | −0.625203 | ||||||||
\(725\) | 8125.88 | + | 290.770i | 0.416259 | + | 0.0148950i | ||||
\(726\) | −17728.9 | −0.906310 | ||||||||
\(727\) | −8000.88 | + | 5812.98i | −0.408165 | + | 0.296550i | −0.772859 | − | 0.634578i | \(-0.781174\pi\) |
0.364693 | + | 0.931128i | \(0.381174\pi\) | |||||||
\(728\) | −3042.74 | + | 9364.60i | −0.154906 | + | 0.476752i | ||||
\(729\) | 225.273 | − | 693.320i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 2380.23 | + | 3402.44i | 0.120680 | + | 0.172507i | ||||
\(731\) | 12228.6 | + | 37635.9i | 0.618731 | + | 1.90426i | ||||
\(732\) | 17859.0 | 0.901757 | ||||||||
\(733\) | 3623.64 | + | 11152.4i | 0.182595 | + | 0.561970i | 0.999899 | − | 0.0142375i | \(-0.00453208\pi\) |
−0.817304 | + | 0.576207i | \(0.804532\pi\) | |||||||
\(734\) | 23559.0 | + | 17116.6i | 1.18471 | + | 0.860742i | ||||
\(735\) | −4811.70 | − | 6878.13i | −0.241473 | − | 0.345175i | ||||
\(736\) | −27636.7 | + | 20079.2i | −1.38410 | + | 1.00561i | ||||
\(737\) | −1191.25 | − | 865.494i | −0.0595390 | − | 0.0432576i | ||||
\(738\) | 15963.8 | + | 11598.4i | 0.796255 | + | 0.578513i | ||||
\(739\) | 23869.9 | − | 17342.5i | 1.18819 | − | 0.863267i | 0.195114 | − | 0.980781i | \(-0.437492\pi\) |
0.993071 | + | 0.117513i | \(0.0374923\pi\) | |||||||
\(740\) | −19.8006 | + | 1107.06i | −0.000983629 | + | 0.0549948i | ||||
\(741\) | 5501.49 | + | 3997.07i | 0.272743 | + | 0.198159i | ||||
\(742\) | −194.732 | − | 599.322i | −0.00963453 | − | 0.0296520i | ||||
\(743\) | −18171.7 | −0.897249 | −0.448625 | − | 0.893720i | \(-0.648086\pi\) | ||||
−0.448625 | + | 0.893720i | \(0.648086\pi\) | |||||||
\(744\) | 2367.85 | + | 7287.49i | 0.116679 | + | 0.359102i | ||||
\(745\) | 11779.8 | − | 15618.3i | 0.579299 | − | 0.768068i | ||||
\(746\) | −2881.76 | + | 8869.15i | −0.141433 | + | 0.435285i | ||||
\(747\) | 2969.80 | − | 9140.12i | 0.145461 | − | 0.447683i | ||||
\(748\) | −5347.66 | + | 3885.31i | −0.261404 | + | 0.189921i | ||||
\(749\) | −3181.38 | −0.155200 | ||||||||
\(750\) | 1021.98 | − | 19030.0i | 0.0497564 | − | 0.926505i | ||||
\(751\) | −31181.1 | −1.51507 | −0.757534 | − | 0.652796i | \(-0.773596\pi\) | ||||
−0.757534 | + | 0.652796i | \(0.773596\pi\) | |||||||
\(752\) | 1757.59 | − | 1276.97i | 0.0852298 | − | 0.0619231i | ||||
\(753\) | 5290.49 | − | 16282.5i | 0.256037 | − | 0.788002i | ||||
\(754\) | 4409.35 | − | 13570.6i | 0.212969 | − | 0.655453i | ||||
\(755\) | −12468.7 | + | 16531.7i | −0.601037 | + | 0.796888i | ||||
\(756\) | −1017.30 | − | 3130.92i | −0.0489401 | − | 0.150622i | ||||
\(757\) | 23324.8 | 1.11989 | 0.559943 | − | 0.828531i | \(-0.310823\pi\) | ||||
0.559943 | + | 0.828531i | \(0.310823\pi\) | |||||||
\(758\) | 2493.48 | + | 7674.15i | 0.119482 | + | 0.367728i | ||||
\(759\) | 2397.94 | + | 1742.20i | 0.114677 | + | 0.0833176i | ||||
\(760\) | 198.978 | − | 11124.9i | 0.00949697 | − | 0.530977i | ||||
\(761\) | −5535.02 | + | 4021.43i | −0.263659 | + | 0.191559i | −0.711758 | − | 0.702424i | \(-0.752101\pi\) |
0.448100 | + | 0.893984i | \(0.352101\pi\) | |||||||
\(762\) | 30590.3 | + | 22225.2i | 1.45429 | + | 1.05660i | ||||
\(763\) | 1472.40 | + | 1069.76i | 0.0698615 | + | 0.0507574i | ||||
\(764\) | 30255.7 | − | 21982.1i | 1.43274 | − | 1.04095i | ||||
\(765\) | −5418.55 | − | 7745.58i | −0.256089 | − | 0.366068i | ||||
\(766\) | 40692.6 | + | 29564.9i | 1.91943 | + | 1.39455i | ||||
\(767\) | 7932.36 | + | 24413.3i | 0.373430 | + | 1.14930i | ||||
\(768\) | 10699.6 | 0.502719 | ||||||||
\(769\) | −2150.40 | − | 6618.26i | −0.100839 | − | 0.310352i | 0.887892 | − | 0.460052i | \(-0.152169\pi\) |
−0.988731 | + | 0.149700i | \(0.952169\pi\) | |||||||
\(770\) | 1559.01 | + | 2228.54i | 0.0729648 | + | 0.104300i | ||||
\(771\) | 5841.89 | − | 17979.5i | 0.272880 | − | 0.839839i | ||||
\(772\) | −15387.6 | + | 47358.2i | −0.717374 | + | 2.20785i | ||||
\(773\) | 19308.2 | − | 14028.2i | 0.898405 | − | 0.652729i | −0.0396508 | − | 0.999214i | \(-0.512625\pi\) |
0.938056 | + | 0.346484i | \(0.112625\pi\) | |||||||
\(774\) | −17232.8 | −0.800284 | ||||||||
\(775\) | 12499.8 | − | 8415.56i | 0.579362 | − | 0.390059i | ||||
\(776\) | −24114.0 | −1.11552 | ||||||||
\(777\) | 182.814 | − | 132.822i | 0.00844069 | − | 0.00613252i | ||||
\(778\) | −13784.3 | + | 42423.7i | −0.635207 | + | 1.95497i | ||||
\(779\) | 7001.11 | − | 21547.2i | 0.322004 | − | 0.991025i | ||||
\(780\) | −19374.7 | − | 6680.57i | −0.889391 | − | 0.306670i | ||||
\(781\) | 334.566 | + | 1029.69i | 0.0153287 | + | 0.0471768i | ||||
\(782\) | −75915.7 | −3.47153 | ||||||||
\(783\) | 542.731 | + | 1670.35i | 0.0247709 | + | 0.0762370i | ||||
\(784\) | −1008.74 | − | 732.892i | −0.0459520 | − | 0.0333861i | ||||
\(785\) | 3468.83 | − | 4599.17i | 0.157717 | − | 0.209110i | ||||
\(786\) | 19693.8 | − | 14308.4i | 0.893709 | − | 0.649318i | ||||
\(787\) | 33192.1 | + | 24115.5i | 1.50339 | + | 1.09228i | 0.969005 | + | 0.247039i | \(0.0794577\pi\) |
0.534388 | + | 0.845240i | \(0.320542\pi\) | |||||||
\(788\) | −29061.7 | − | 21114.6i | −1.31381 | − | 0.954538i | ||||
\(789\) | −12049.8 | + | 8754.69i | −0.543706 | + | 0.395025i | ||||
\(790\) | −58986.8 | − | 20339.2i | −2.65653 | − | 0.915995i | ||||
\(791\) | 16135.4 | + | 11723.0i | 0.725294 | + | 0.526957i | ||||
\(792\) | −327.474 | − | 1007.86i | −0.0146923 | − | 0.0452181i | ||||
\(793\) | −22689.9 | −1.01607 | ||||||||
\(794\) | 3748.49 | + | 11536.7i | 0.167543 | + | 0.515644i | ||||
\(795\) | 461.829 | − | 140.978i | 0.0206030 | − | 0.00628927i | ||||
\(796\) | −4433.91 | + | 13646.2i | −0.197432 | + | 0.607633i | ||||
\(797\) | −1082.46 | + | 3331.47i | −0.0481088 | + | 0.148064i | −0.972225 | − | 0.234048i | \(-0.924803\pi\) |
0.924116 | + | 0.382111i | \(0.124803\pi\) | |||||||
\(798\) | −4990.09 | + | 3625.51i | −0.221362 | + | 0.160829i | ||||
\(799\) | 40963.7 | 1.81376 | ||||||||
\(800\) | −6600.51 | − | 23093.8i | −0.291704 | − | 1.02061i | ||||
\(801\) | 10471.0 | 0.461890 | ||||||||
\(802\) | 28772.5 | − | 20904.4i | 1.26682 | − | 0.920400i | ||||
\(803\) | 140.317 | − | 431.853i | 0.00616649 | − | 0.0189785i | ||||
\(804\) | −3109.99 | + | 9571.57i | −0.136419 | + | 0.419855i | ||||
\(805\) | −342.303 | + | 19138.2i | −0.0149871 | + | 0.837930i | ||||
\(806\) | −8171.51 | − | 25149.3i | −0.357108 | − | 1.09907i | ||||
\(807\) | −18611.8 | −0.811852 | ||||||||
\(808\) | 8366.76 | + | 25750.2i | 0.364284 | + | 1.12115i | ||||
\(809\) | −31071.6 | − | 22574.8i | −1.35033 | − | 0.981074i | −0.998995 | − | 0.0448251i | \(-0.985727\pi\) |
−0.351338 | − | 0.936249i | \(-0.614273\pi\) | |||||||
\(810\) | 3937.06 | − | 1201.83i | 0.170783 | − | 0.0521332i | ||||
\(811\) | 30978.5 | − | 22507.2i | 1.34131 | − | 0.974520i | 0.341917 | − | 0.939730i | \(-0.388924\pi\) |
0.999395 | − | 0.0347900i | \(-0.0110762\pi\) | |||||||
\(812\) | 6416.49 | + | 4661.85i | 0.277309 | + | 0.201477i | ||||
\(813\) | 3309.02 | + | 2404.15i | 0.142746 | + | 0.103711i | ||||
\(814\) | 159.849 | − | 116.137i | 0.00688293 | − | 0.00500074i | ||||
\(815\) | 10906.5 | − | 3329.31i | 0.468757 | − | 0.143093i | ||||
\(816\) | −1135.96 | − | 825.323i | −0.0487335 | − | 0.0354070i | ||||
\(817\) | 6114.25 | + | 18817.7i | 0.261824 | + | 0.805813i | ||||
\(818\) | −9247.87 | −0.395286 | ||||||||
\(819\) | 1292.48 | + | 3977.85i | 0.0551440 | + | 0.169716i | ||||
\(820\) | −1221.04 | + | 68268.7i | −0.0520008 | + | 2.90737i | ||||
\(821\) | −11356.6 | + | 34952.0i | −0.482762 | + | 1.48579i | 0.352434 | + | 0.935837i | \(0.385354\pi\) |
−0.835196 | + | 0.549953i | \(0.814646\pi\) | |||||||
\(822\) | −2557.42 | + | 7870.94i | −0.108516 | + | 0.333979i | ||||
\(823\) | −21125.5 | + | 15348.6i | −0.894761 | + | 0.650082i | −0.937115 | − | 0.349020i | \(-0.886514\pi\) |
0.0423536 | + | 0.999103i | \(0.486514\pi\) | |||||||
\(824\) | 10911.4 | 0.461305 | ||||||||
\(825\) | −1728.72 | + | 1163.87i | −0.0729532 | + | 0.0491162i | ||||
\(826\) | −23283.5 | −0.980793 | ||||||||
\(827\) | −24442.5 | + | 17758.5i | −1.02775 | + | 0.746705i | −0.967857 | − | 0.251500i | \(-0.919076\pi\) |
−0.0598941 | + | 0.998205i | \(0.519076\pi\) | |||||||
\(828\) | 6260.29 | − | 19267.2i | 0.262754 | − | 0.808672i | ||||
\(829\) | −4787.44 | + | 14734.2i | −0.200572 | + | 0.617299i | 0.799294 | + | 0.600941i | \(0.205207\pi\) |
−0.999866 | + | 0.0163581i | \(0.994793\pi\) | |||||||
\(830\) | 51902.7 | − | 15843.8i | 2.17057 | − | 0.662587i | ||||
\(831\) | −1941.98 | − | 5976.81i | −0.0810669 | − | 0.249498i | ||||
\(832\) | −40225.8 | −1.67618 | ||||||||
\(833\) | −7265.11 | − | 22359.7i | −0.302186 | − | 0.930033i | ||||
\(834\) | −3697.56 | − | 2686.43i | −0.153520 | − | 0.111539i | ||||
\(835\) | 1936.16 | + | 667.605i | 0.0802437 | + | 0.0276688i | ||||
\(836\) | −2673.80 | + | 1942.63i | −0.110616 | + | 0.0803676i | ||||
\(837\) | 2633.22 | + | 1913.15i | 0.108743 | + | 0.0790061i | ||||
\(838\) | 19862.7 | + | 14431.1i | 0.818791 | + | 0.594887i | ||||
\(839\) | 5434.83 | − | 3948.64i | 0.223637 | − | 0.162482i | −0.470325 | − | 0.882493i | \(-0.655863\pi\) |
0.693962 | + | 0.720011i | \(0.255863\pi\) | |||||||
\(840\) | 4120.93 | − | 5463.76i | 0.169269 | − | 0.224426i | ||||
\(841\) | 16307.9 | + | 11848.4i | 0.668658 | + | 0.485808i | ||||
\(842\) | 8308.18 | + | 25570.0i | 0.340046 | + | 1.04655i | ||||
\(843\) | 7162.98 | 0.292653 | ||||||||
\(844\) | −11941.3 | − | 36751.6i | −0.487011 | − | 1.49887i | ||||
\(845\) | 1394.10 | + | 480.698i | 0.0567555 | + | 0.0195698i | ||||
\(846\) | −5512.41 | + | 16965.4i | −0.224020 | + | 0.689461i | ||||
\(847\) | −3868.91 | + | 11907.3i | −0.156951 | + | 0.483045i | ||||
\(848\) | 58.0272 | − | 42.1592i | 0.00234984 | − | 0.00170726i | ||||
\(849\) | −7507.29 | −0.303474 | ||||||||
\(850\) | 18299.0 | − | 50141.7i | 0.738413 | − | 2.02335i | ||||
\(851\) | 1390.59 | 0.0560149 | ||||||||
\(852\) | 5986.71 | − | 4349.60i | 0.240729 | − | 0.174900i | ||||
\(853\) | −6181.47 | + | 19024.6i | −0.248124 | + | 0.763646i | 0.746983 | + | 0.664843i | \(0.231501\pi\) |
−0.995107 | + | 0.0988032i | \(0.968499\pi\) | |||||||
\(854\) | 6359.78 | − | 19573.4i | 0.254833 | − | 0.784295i | ||||
\(855\) | −2709.24 | − | 3872.75i | −0.108367 | − | 0.154907i | ||||
\(856\) | 2163.00 | + | 6657.04i | 0.0863668 | + | 0.265810i | ||||
\(857\) | −48267.5 | −1.92391 | −0.961953 | − | 0.273214i | \(-0.911913\pi\) | ||||
−0.961953 | + | 0.273214i | \(0.911913\pi\) | |||||||
\(858\) | 1130.12 | + | 3478.15i | 0.0449670 | + | 0.138394i | ||||
\(859\) | −1154.15 | − | 838.539i | −0.0458429 | − | 0.0333068i | 0.564628 | − | 0.825346i | \(-0.309020\pi\) |
−0.610471 | + | 0.792039i | \(0.709020\pi\) | |||||||
\(860\) | −34181.5 | − | 48861.0i | −1.35532 | − | 1.93738i | ||||
\(861\) | 11273.6 | − | 8190.72i | 0.446228 | − | 0.324203i | ||||
\(862\) | 2682.37 | + | 1948.86i | 0.105988 | + | 0.0770050i | ||||
\(863\) | 18910.4 | + | 13739.2i | 0.745905 | + | 0.541932i | 0.894555 | − | 0.446958i | \(-0.147493\pi\) |
−0.148650 | + | 0.988890i | \(0.547493\pi\) | |||||||
\(864\) | 4197.18 | − | 3049.43i | 0.165267 | − | 0.120074i | ||||
\(865\) | −791.675 | + | 44262.7i | −0.0311188 | + | 1.73986i | ||||
\(866\) | −62874.5 | − | 45681.0i | −2.46716 | − | 1.79250i | ||||
\(867\) | −3626.77 | − | 11162.1i | −0.142066 | − | 0.437236i | ||||
\(868\) | 14698.3 | 0.574763 | ||||||||
\(869\) | 2108.46 | + | 6489.18i | 0.0823068 | + | 0.253314i | ||||
\(870\) | −5971.79 | + | 7917.73i | −0.232716 | + | 0.308547i | ||||
\(871\) | 3951.26 | − | 12160.7i | 0.153712 | − | 0.473077i | ||||
\(872\) | 1237.40 | − | 3808.32i | 0.0480546 | − | 0.147897i | ||||
\(873\) | −8286.76 | + | 6020.69i | −0.321265 | + | 0.233413i | ||||
\(874\) | −37957.4 | −1.46903 | ||||||||
\(875\) | −12558.1 | − | 4839.24i | −0.485191 | − | 0.186967i | ||||
\(876\) | −3103.56 | −0.119703 | ||||||||
\(877\) | −9849.32 | + | 7155.95i | −0.379234 | + | 0.275529i | −0.761029 | − | 0.648717i | \(-0.775306\pi\) |
0.381796 | + | 0.924247i | \(0.375306\pi\) | |||||||
\(878\) | 15172.0 | − | 46694.5i | 0.583177 | − | 1.79483i | ||||
\(879\) | −3754.51 | + | 11555.2i | −0.144069 | + | 0.443398i | ||||
\(880\) | −186.404 | + | 247.146i | −0.00714056 | + | 0.00946736i | ||||
\(881\) | 5210.38 | + | 16035.9i | 0.199253 | + | 0.613239i | 0.999901 | + | 0.0141028i | \(0.00448922\pi\) |
−0.800647 | + | 0.599136i | \(0.795511\pi\) | |||||||
\(882\) | 10238.1 | 0.390856 | ||||||||
\(883\) | 7204.01 | + | 22171.7i | 0.274557 | + | 0.845001i | 0.989336 | + | 0.145650i | \(0.0465274\pi\) |
−0.714779 | + | 0.699351i | \(0.753473\pi\) | |||||||
\(884\) | −46437.8 | − | 33739.0i | −1.76682 | − | 1.28367i | ||||
\(885\) | 319.052 | − | 17838.2i | 0.0121184 | − | 0.677543i | ||||
\(886\) | 34412.0 | − | 25001.8i | 1.30484 | − | 0.948025i | ||||
\(887\) | 8788.66 | + | 6385.33i | 0.332688 | + | 0.241712i | 0.741570 | − | 0.670875i | \(-0.234081\pi\) |
−0.408882 | + | 0.912587i | \(0.634081\pi\) | |||||||
\(888\) | −402.225 | − | 292.234i | −0.0152002 | − | 0.0110436i | ||||
\(889\) | 21602.7 | − | 15695.3i | 0.814996 | − | 0.592129i | ||||
\(890\) | 33892.4 | + | 48447.8i | 1.27649 | + | 1.82469i | ||||
\(891\) | −364.175 | − | 264.589i | −0.0136928 | − | 0.00994843i | ||||
\(892\) | −20176.6 | − | 62097.3i | −0.757358 | − | 2.33091i | ||||
\(893\) | 20481.6 | 0.767515 | ||||||||
\(894\) | 7373.16 | + | 22692.2i | 0.275834 | + | 0.848929i | ||||
\(895\) | 5879.76 | + | 8404.87i | 0.219596 | + | 0.313904i | ||||
\(896\) | 6700.56 | − | 20622.2i | 0.249833 | − | 0.768906i | ||||
\(897\) | −7953.72 | + | 24479.0i | −0.296061 | + | 0.911183i | ||||
\(898\) | 14252.3 | − | 10354.9i | 0.529627 | − | 0.384796i | ||||
\(899\) | −7841.60 | −0.290914 | ||||||||
\(900\) | 11216.8 | + | 8779.11i | 0.415438 | + | 0.325152i | ||||
\(901\) | 1352.42 | 0.0500064 | ||||||||
\(902\) | 9857.39 | − | 7161.81i | 0.363875 | − | 0.264371i | ||||
\(903\) | −3760.64 | + | 11574.1i | −0.138590 | + | 0.426535i | ||||
\(904\) | 13560.1 | − | 41733.7i | 0.498896 | − | 1.53545i | ||||
\(905\) | −10167.5 | − | 3505.83i | −0.373456 | − | 0.128771i | ||||
\(906\) | −7804.36 | − | 24019.4i | −0.286184 | − | 0.880784i | ||||
\(907\) | 21465.3 | 0.785825 | 0.392913 | − | 0.919576i | \(-0.371468\pi\) | ||||
0.392913 | + | 0.919576i | \(0.371468\pi\) | |||||||
\(908\) | 6997.70 | + | 21536.7i | 0.255757 | + | 0.787138i | ||||
\(909\) | 9304.46 | + | 6760.09i | 0.339504 | + | 0.246664i | ||||
\(910\) | −14221.5 | + | 18855.6i | −0.518062 | + | 0.686876i | ||||
\(911\) | 29140.5 | − | 21171.8i | 1.05979 | − | 0.769981i | 0.0857393 | − | 0.996318i | \(-0.472675\pi\) |
0.974049 | + | 0.226336i | \(0.0726748\pi\) | |||||||
\(912\) | −567.973 | − | 412.657i | −0.0206222 | − | 0.0149829i | ||||
\(913\) | −4800.96 | − | 3488.10i | −0.174029 | − | 0.126440i | ||||
\(914\) | 48464.2 | − | 35211.3i | 1.75389 | − | 1.27427i | ||||
\(915\) | 14908.7 | + | 5140.65i | 0.538651 | + | 0.185732i | ||||
\(916\) | 12952.3 | + | 9410.36i | 0.467199 | + | 0.339440i | ||||
\(917\) | −5312.26 | − | 16349.4i | −0.191304 | − | 0.588774i | ||||
\(918\) | 11529.3 | 0.414514 | ||||||||
\(919\) | 3005.90 | + | 9251.22i | 0.107895 | + | 0.332067i | 0.990399 | − | 0.138238i | \(-0.0441439\pi\) |
−0.882504 | + | 0.470305i | \(0.844144\pi\) | |||||||
\(920\) | 40279.5 | − | 12295.7i | 1.44345 | − | 0.440628i | ||||
\(921\) | −5504.07 | + | 16939.8i | −0.196922 | + | 0.606064i | ||||
\(922\) | 19140.9 | − | 58909.6i | 0.683700 | − | 2.10421i | ||||
\(923\) | −7606.14 | + | 5526.18i | −0.271245 | + | 0.197071i | ||||
\(924\) | −2032.78 | −0.0723740 | ||||||||
\(925\) | −335.192 | + | 918.472i | −0.0119147 | + | 0.0326477i | ||||
\(926\) | 33057.7 | 1.17316 | ||||||||
\(927\) | 3749.69 | − | 2724.31i | 0.132854 | − | 0.0965244i | ||||
\(928\) | −3862.40 | + | 11887.2i | −0.136626 | + | 0.420493i | ||||
\(929\) | −5837.99 | + | 17967.5i | −0.206177 | + | 0.634547i | 0.793486 | + | 0.608588i | \(0.208264\pi\) |
−0.999663 | + | 0.0259588i | \(0.991736\pi\) | |||||||
\(930\) | −328.671 | + | 18376.0i | −0.0115888 | + | 0.647929i | ||||
\(931\) | −3632.51 | − | 11179.7i | −0.127874 | − | 0.393556i | ||||
\(932\) | −55000.7 | −1.93305 | ||||||||
\(933\) | 382.090 | + | 1175.95i | 0.0134073 | + | 0.0412636i | ||||
\(934\) | −4759.87 | − | 3458.25i | −0.166753 | − | 0.121153i | ||||
\(935\) | −5582.61 | + | 1704.15i | −0.195263 | + | 0.0596059i | ||||
\(936\) | 7444.90 | − | 5409.04i | 0.259983 | − | 0.188889i | ||||
\(937\) | −29538.6 | − | 21461.0i | −1.02986 | − | 0.748240i | −0.0615828 | − | 0.998102i | \(-0.519615\pi\) |
−0.968282 | + | 0.249862i | \(0.919615\pi\) | |||||||
\(938\) | 9382.92 | + | 6817.09i | 0.326613 | + | 0.237298i | ||||
\(939\) | −9592.00 | + | 6969.00i | −0.333358 | + | 0.242199i | ||||
\(940\) | −59037.0 | + | 18021.6i | −2.04848 | + | 0.625319i | ||||
\(941\) | 14935.2 | + | 10851.1i | 0.517401 | + | 0.375914i | 0.815624 | − | 0.578582i | \(-0.196394\pi\) |
−0.298223 | + | 0.954496i | \(0.596394\pi\) | |||||||
\(942\) | 2171.19 | + | 6682.25i | 0.0750970 | + | 0.231125i | ||||
\(943\) | 85753.1 | 2.96130 | ||||||||
\(944\) | −818.936 | − | 2520.43i | −0.0282353 | − | 0.0868992i | ||||
\(945\) | 51.9856 | − | 2906.52i | 0.00178951 | − | 0.100052i | ||||
\(946\) | −3288.24 | + | 10120.1i | −0.113012 | + | 0.347817i | ||||
\(947\) | 1026.02 | − | 3157.77i | 0.0352072 | − | 0.108357i | −0.931908 | − | 0.362694i | \(-0.881857\pi\) |
0.967116 | + | 0.254337i | \(0.0818572\pi\) | |||||||
\(948\) | 37728.7 | − | 27411.5i | 1.29259 | − | 0.939119i | ||||
\(949\) | 3943.09 | 0.134877 | ||||||||
\(950\) | 9149.41 | − | 25070.6i | 0.312470 | − | 0.856208i | ||||
\(951\) | −3058.60 | −0.104292 | ||||||||
\(952\) | 15507.0 | − | 11266.5i | 0.527924 | − | 0.383559i | ||||
\(953\) | 7939.69 | − | 24435.8i | 0.269876 | − | 0.830593i | −0.720654 | − | 0.693295i | \(-0.756158\pi\) |
0.990530 | − | 0.137298i | \(-0.0438417\pi\) | |||||||
\(954\) | −181.993 | + | 560.117i | −0.00617636 | + | 0.0190089i | ||||
\(955\) | 31585.0 | − | 9641.63i | 1.07023 | − | 0.326697i | ||||
\(956\) | 1592.51 | + | 4901.24i | 0.0538760 | + | 0.165813i | ||||
\(957\) | 1084.49 | 0.0366319 | ||||||||
\(958\) | 5848.51 | + | 17999.9i | 0.197241 | + | 0.607045i | ||||
\(959\) | 4728.27 | + | 3435.29i | 0.159211 | + | 0.115674i | ||||
\(960\) | 26430.9 | + | 9113.61i | 0.888596 | + | 0.306396i | ||||
\(961\) | 12344.6 | − | 8968.87i | 0.414373 | − | 0.301060i | ||||
\(962\) | 1388.09 | + | 1008.51i | 0.0465216 | + | 0.0337999i | ||||
\(963\) | 2405.42 | + | 1747.64i | 0.0804918 | + | 0.0584807i | ||||
\(964\) | −17496.5 | + | 12711.9i | −0.584568 | + | 0.424713i | ||||
\(965\) | −26477.5 | + | 35105.4i | −0.883256 | + | 1.17107i | ||||
\(966\) | −18887.4 | − | 13722.5i | −0.629083 | − | 0.457055i | ||||
\(967\) | 7324.06 | + | 22541.2i | 0.243564 | + | 0.749612i | 0.995869 | + | 0.0907977i | \(0.0289417\pi\) |
−0.752306 | + | 0.658814i | \(0.771058\pi\) | |||||||
\(968\) | 27546.5 | 0.914646 | ||||||||
\(969\) | −4090.64 | − | 12589.7i | −0.135614 | − | 0.417378i | ||||
\(970\) | −54679.4 | − | 18854.0i | −1.80995 | − | 0.624088i | ||||
\(971\) | 2678.45 | − | 8243.43i | 0.0885228 | − | 0.272445i | −0.896989 | − | 0.442053i | \(-0.854250\pi\) |
0.985512 | + | 0.169608i | \(0.0542502\pi\) | |||||||
\(972\) | −950.750 | + | 2926.11i | −0.0313738 | + | 0.0965586i | ||||
\(973\) | −2611.20 | + | 1897.14i | −0.0860340 | + | 0.0625074i | ||||
\(974\) | −18371.8 | −0.604384 | ||||||||
\(975\) | −14251.0 | − | 11153.9i | −0.468100 | − | 0.366370i | ||||
\(976\) | 2342.50 | 0.0768255 | ||||||||
\(977\) | 33990.8 | − | 24695.8i | 1.11306 | − | 0.808688i | 0.129920 | − | 0.991524i | \(-0.458528\pi\) |
0.983143 | + | 0.182836i | \(0.0585278\pi\) | |||||||
\(978\) | −4297.92 | + | 13227.6i | −0.140524 | + | 0.432488i | ||||
\(979\) | 1998.00 | − | 6149.21i | 0.0652261 | − | 0.200745i | ||||
\(980\) | 20307.4 | + | 29028.6i | 0.661936 | + | 0.946210i | ||||
\(981\) | −525.615 | − | 1617.68i | −0.0171066 | − | 0.0526488i | ||||
\(982\) | −37737.3 | −1.22632 | ||||||||
\(983\) | −1249.89 | − | 3846.78i | −0.0405548 | − | 0.124815i | 0.928729 | − | 0.370758i | \(-0.120902\pi\) |
−0.969284 | + | 0.245944i | \(0.920902\pi\) | |||||||
\(984\) | −24804.0 | − | 18021.1i | −0.803579 | − | 0.583834i | ||||
\(985\) | −18183.0 | − | 25991.8i | −0.588181 | − | 0.840780i | ||||
\(986\) | −22471.7 | + | 16326.6i | −0.725806 | + | 0.527329i | ||||
\(987\) | 10191.6 | + | 7404.61i | 0.328674 | + | 0.238796i | ||||
\(988\) | −23218.6 | − | 16869.3i | −0.747655 | − | 0.543203i | ||||
\(989\) | −60587.6 | + | 44019.5i | −1.94800 | + | 1.41531i | ||||
\(990\) | 45.4552 | − | 2541.41i | 0.00145925 | − | 0.0815871i | ||||
\(991\) | −10409.7 | − | 7563.08i | −0.333678 | − | 0.242431i | 0.408312 | − | 0.912843i | \(-0.366118\pi\) |
−0.741990 | + | 0.670411i | \(0.766118\pi\) | |||||||
\(992\) | 7157.89 | + | 22029.7i | 0.229096 | + | 0.705085i | ||||
\(993\) | −10828.5 | −0.346054 | ||||||||
\(994\) | −2635.22 | − | 8110.37i | −0.0840886 | − | 0.258798i | ||||
\(995\) | −7629.44 | + | 10115.5i | −0.243085 | + | 0.322296i | ||||
\(996\) | −12533.8 | + | 38575.2i | −0.398745 | + | 1.22721i | ||||
\(997\) | 2451.22 | − | 7544.06i | 0.0778644 | − | 0.239642i | −0.904546 | − | 0.426376i | \(-0.859790\pi\) |
0.982411 | + | 0.186734i | \(0.0597902\pi\) | |||||||
\(998\) | −21100.4 | + | 15330.4i | −0.669261 | + | 0.486247i | ||||
\(999\) | −211.188 | −0.00668839 |
(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 | 75.4.g.a.61.7 | yes | 28 | |
3.2 | odd | 2 | 225.4.h.c.136.1 | 28 | |||
25.4 | even | 10 | 1875.4.a.e.1.14 | 14 | |||
25.16 | even | 5 | inner | 75.4.g.a.16.7 | ✓ | 28 | |
25.21 | even | 5 | 1875.4.a.h.1.1 | 14 | |||
75.41 | odd | 10 | 225.4.h.c.91.1 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.a.16.7 | ✓ | 28 | 25.16 | even | 5 | inner | |
75.4.g.a.61.7 | yes | 28 | 1.1 | even | 1 | trivial | |
225.4.h.c.91.1 | 28 | 75.41 | odd | 10 | |||
225.4.h.c.136.1 | 28 | 3.2 | odd | 2 | |||
1875.4.a.e.1.14 | 14 | 25.4 | even | 10 | |||
1875.4.a.h.1.1 | 14 | 25.21 | even | 5 |