Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(14,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.14");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.h (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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 27.1 | ||
Character | \(\chi\) | \(=\) | 143.27 |
Dual form | 143.4.h.a.53.1 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.47502 | − | 4.53963i | −0.521497 | − | 1.60500i | −0.771141 | − | 0.636664i | \(-0.780314\pi\) |
0.249645 | − | 0.968337i | \(-0.419686\pi\) | |||||||
\(3\) | −3.70948 | − | 2.69510i | −0.713890 | − | 0.518671i | 0.170536 | − | 0.985351i | \(-0.445450\pi\) |
−0.884426 | + | 0.466680i | \(0.845450\pi\) | |||||||
\(4\) | −11.9604 | + | 8.68976i | −1.49505 | + | 1.08622i | ||||
\(5\) | −2.80173 | + | 8.62283i | −0.250594 | + | 0.771249i | 0.744072 | + | 0.668100i | \(0.232892\pi\) |
−0.994666 | + | 0.103149i | \(0.967108\pi\) | |||||||
\(6\) | −6.76320 | + | 20.8150i | −0.460177 | + | 1.41628i | ||||
\(7\) | −9.62173 | + | 6.99059i | −0.519524 | + | 0.377457i | −0.816425 | − | 0.577452i | \(-0.804047\pi\) |
0.296900 | + | 0.954908i | \(0.404047\pi\) | |||||||
\(8\) | 26.1970 | + | 19.0332i | 1.15775 | + | 0.841158i | ||||
\(9\) | −1.84675 | − | 5.68371i | −0.0683981 | − | 0.210508i | ||||
\(10\) | 43.2770 | 1.36854 | ||||||||
\(11\) | 35.7483 | − | 7.28404i | 0.979866 | − | 0.199656i | ||||
\(12\) | 67.7867 | 1.63070 | ||||||||
\(13\) | 4.01722 | + | 12.3637i | 0.0857059 | + | 0.263776i | ||||
\(14\) | 45.9269 | + | 33.3678i | 0.876749 | + | 0.636995i | ||||
\(15\) | 33.6323 | − | 24.4353i | 0.578921 | − | 0.420611i | ||||
\(16\) | 11.2150 | − | 34.5163i | 0.175235 | − | 0.539318i | ||||
\(17\) | −4.68764 | + | 14.4271i | −0.0668777 | + | 0.205828i | −0.978911 | − | 0.204288i | \(-0.934512\pi\) |
0.912033 | + | 0.410117i | \(0.134512\pi\) | |||||||
\(18\) | −23.0780 | + | 16.7671i | −0.302196 | + | 0.219558i | ||||
\(19\) | −26.6482 | − | 19.3610i | −0.321764 | − | 0.233775i | 0.415164 | − | 0.909747i | \(-0.363724\pi\) |
−0.736928 | + | 0.675972i | \(0.763724\pi\) | |||||||
\(20\) | −41.4205 | − | 127.479i | −0.463095 | − | 1.42526i | ||||
\(21\) | 54.5319 | 0.566659 | ||||||||
\(22\) | −85.7961 | − | 151.540i | −0.831445 | − | 1.46857i | ||||
\(23\) | 77.8610 | 0.705876 | 0.352938 | − | 0.935647i | \(-0.385183\pi\) | ||||
0.352938 | + | 0.935647i | \(0.385183\pi\) | |||||||
\(24\) | −45.8809 | − | 141.207i | −0.390225 | − | 1.20099i | ||||
\(25\) | 34.6237 | + | 25.1556i | 0.276989 | + | 0.201245i | ||||
\(26\) | 50.2013 | − | 36.4734i | 0.378665 | − | 0.275116i | ||||
\(27\) | −46.7238 | + | 143.801i | −0.333037 | + | 1.02498i | ||||
\(28\) | 54.3334 | − | 167.221i | 0.366716 | − | 1.12864i | ||||
\(29\) | −73.8737 | + | 53.6724i | −0.473034 | + | 0.343680i | −0.798623 | − | 0.601832i | \(-0.794438\pi\) |
0.325588 | + | 0.945512i | \(0.394438\pi\) | |||||||
\(30\) | −160.535 | − | 116.636i | −0.976987 | − | 0.709822i | ||||
\(31\) | −15.6764 | − | 48.2470i | −0.0908246 | − | 0.279529i | 0.895318 | − | 0.445427i | \(-0.146948\pi\) |
−0.986143 | + | 0.165897i | \(0.946948\pi\) | |||||||
\(32\) | 85.8164 | 0.474073 | ||||||||
\(33\) | −152.239 | − | 69.3252i | −0.803073 | − | 0.365696i | ||||
\(34\) | 72.4080 | 0.365231 | ||||||||
\(35\) | −33.3212 | − | 102.552i | −0.160923 | − | 0.495271i | ||||
\(36\) | 71.4780 | + | 51.9318i | 0.330917 | + | 0.240425i | ||||
\(37\) | 58.6818 | − | 42.6349i | 0.260736 | − | 0.189436i | −0.449735 | − | 0.893162i | \(-0.648482\pi\) |
0.710471 | + | 0.703726i | \(0.248482\pi\) | |||||||
\(38\) | −48.5855 | + | 149.531i | −0.207411 | + | 0.638344i | ||||
\(39\) | 18.4196 | − | 56.6898i | 0.0756283 | − | 0.232760i | ||||
\(40\) | −237.517 | + | 172.566i | −0.938869 | + | 0.682128i | ||||
\(41\) | 94.7024 | + | 68.8053i | 0.360733 | + | 0.262088i | 0.753358 | − | 0.657611i | \(-0.228433\pi\) |
−0.392625 | + | 0.919699i | \(0.628433\pi\) | |||||||
\(42\) | −80.4354 | − | 247.555i | −0.295511 | − | 0.909489i | ||||
\(43\) | 324.184 | 1.14971 | 0.574857 | − | 0.818254i | \(-0.305058\pi\) | ||||
0.574857 | + | 0.818254i | \(0.305058\pi\) | |||||||
\(44\) | −364.269 | + | 397.765i | −1.24808 | + | 1.36285i | ||||
\(45\) | 54.1837 | 0.179494 | ||||||||
\(46\) | −114.846 | − | 353.460i | −0.368112 | − | 1.13293i | ||||
\(47\) | 269.718 | + | 195.962i | 0.837073 | + | 0.608169i | 0.921552 | − | 0.388256i | \(-0.126922\pi\) |
−0.0844783 | + | 0.996425i | \(0.526922\pi\) | |||||||
\(48\) | −134.627 | + | 97.8121i | −0.404827 | + | 0.294124i | ||||
\(49\) | −62.2836 | + | 191.689i | −0.181585 | + | 0.558861i | ||||
\(50\) | 63.1265 | − | 194.283i | 0.178549 | − | 0.549517i | ||||
\(51\) | 56.2711 | − | 40.8834i | 0.154501 | − | 0.112251i | ||||
\(52\) | −155.486 | − | 112.967i | −0.414653 | − | 0.301263i | ||||
\(53\) | 151.077 | + | 464.969i | 0.391549 | + | 1.20506i | 0.931617 | + | 0.363442i | \(0.118398\pi\) |
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(54\) | 721.723 | 1.81878 | ||||||||
\(55\) | −37.3480 | + | 328.659i | −0.0915638 | + | 0.805753i | ||||
\(56\) | −385.114 | −0.918982 | ||||||||
\(57\) | 46.6711 | + | 143.639i | 0.108452 | + | 0.333779i | ||||
\(58\) | 352.618 | + | 256.192i | 0.798292 | + | 0.579993i | ||||
\(59\) | −199.585 | + | 145.007i | −0.440403 | + | 0.319971i | −0.785795 | − | 0.618487i | \(-0.787746\pi\) |
0.345392 | + | 0.938458i | \(0.387746\pi\) | |||||||
\(60\) | −189.920 | + | 584.513i | −0.408642 | + | 1.25767i | ||||
\(61\) | 149.575 | − | 460.343i | 0.313952 | − | 0.966245i | −0.662232 | − | 0.749299i | \(-0.730391\pi\) |
0.976184 | − | 0.216946i | \(-0.0696094\pi\) | |||||||
\(62\) | −195.900 | + | 142.330i | −0.401280 | + | 0.291547i | ||||
\(63\) | 57.5014 | + | 41.7772i | 0.114992 | + | 0.0835466i | ||||
\(64\) | −216.301 | − | 665.706i | −0.422463 | − | 1.30021i | ||||
\(65\) | −117.865 | −0.224914 | ||||||||
\(66\) | −90.1559 | + | 793.364i | −0.168143 | + | 1.47964i | ||||
\(67\) | 493.429 | 0.899731 | 0.449865 | − | 0.893096i | \(-0.351472\pi\) | ||||
0.449865 | + | 0.893096i | \(0.351472\pi\) | |||||||
\(68\) | −69.3017 | − | 213.289i | −0.123589 | − | 0.380368i | ||||
\(69\) | −288.824 | − | 209.843i | −0.503918 | − | 0.366118i | ||||
\(70\) | −416.400 | + | 302.532i | −0.710990 | + | 0.516564i | ||||
\(71\) | −272.343 | + | 838.186i | −0.455228 | + | 1.40105i | 0.415639 | + | 0.909530i | \(0.363558\pi\) |
−0.870867 | + | 0.491518i | \(0.836442\pi\) | |||||||
\(72\) | 59.8001 | − | 184.046i | 0.0978821 | − | 0.301250i | ||||
\(73\) | −107.137 | + | 77.8398i | −0.171774 | + | 0.124801i | −0.670350 | − | 0.742045i | \(-0.733856\pi\) |
0.498577 | + | 0.866846i | \(0.333856\pi\) | |||||||
\(74\) | −280.103 | − | 203.507i | −0.440018 | − | 0.319692i | ||||
\(75\) | −60.6392 | − | 186.628i | −0.0933601 | − | 0.287333i | ||||
\(76\) | 486.967 | 0.734986 | ||||||||
\(77\) | −293.041 | + | 319.987i | −0.433703 | + | 0.473583i | ||||
\(78\) | −284.520 | −0.413020 | ||||||||
\(79\) | 138.610 | + | 426.598i | 0.197403 | + | 0.607545i | 0.999940 | + | 0.0109422i | \(0.00348307\pi\) |
−0.802537 | + | 0.596602i | \(0.796517\pi\) | |||||||
\(80\) | 266.207 | + | 193.411i | 0.372035 | + | 0.270300i | ||||
\(81\) | 430.338 | − | 312.659i | 0.590313 | − | 0.428888i | ||||
\(82\) | 172.663 | − | 531.403i | 0.232530 | − | 0.715654i | ||||
\(83\) | −300.018 | + | 923.362i | −0.396763 | + | 1.22111i | 0.530818 | + | 0.847486i | \(0.321885\pi\) |
−0.927580 | + | 0.373624i | \(0.878115\pi\) | |||||||
\(84\) | −652.225 | + | 473.870i | −0.847186 | + | 0.615517i | ||||
\(85\) | −111.269 | − | 80.8415i | −0.141986 | − | 0.103159i | ||||
\(86\) | −478.177 | − | 1471.68i | −0.599571 | − | 1.84529i | ||||
\(87\) | 418.685 | 0.515951 | ||||||||
\(88\) | 1075.14 | + | 489.586i | 1.30239 | + | 0.593069i | ||||
\(89\) | −1496.56 | −1.78242 | −0.891209 | − | 0.453593i | \(-0.850142\pi\) | ||||
−0.891209 | + | 0.453593i | \(0.850142\pi\) | |||||||
\(90\) | −79.9218 | − | 245.974i | −0.0936056 | − | 0.288088i | ||||
\(91\) | −125.082 | − | 90.8777i | −0.144090 | − | 0.104688i | ||||
\(92\) | −931.252 | + | 676.594i | −1.05532 | + | 0.766737i | ||||
\(93\) | −71.8789 | + | 221.221i | −0.0801451 | + | 0.246661i | ||||
\(94\) | 491.755 | − | 1513.47i | 0.539582 | − | 1.66066i | ||||
\(95\) | 241.608 | − | 175.538i | 0.260931 | − | 0.189577i | ||||
\(96\) | −318.334 | − | 231.284i | −0.338436 | − | 0.245888i | ||||
\(97\) | 195.378 | + | 601.311i | 0.204511 | + | 0.629421i | 0.999733 | + | 0.0231026i | \(0.00735442\pi\) |
−0.795222 | + | 0.606319i | \(0.792646\pi\) | |||||||
\(98\) | 962.067 | 0.991668 | ||||||||
\(99\) | −107.419 | − | 189.731i | −0.109050 | − | 0.192613i | ||||
\(100\) | −632.710 | −0.632710 | ||||||||
\(101\) | −411.847 | − | 1267.53i | −0.405745 | − | 1.24876i | −0.920271 | − | 0.391281i | \(-0.872032\pi\) |
0.514526 | − | 0.857475i | \(-0.327968\pi\) | |||||||
\(102\) | −268.596 | − | 195.146i | −0.260735 | − | 0.189435i | ||||
\(103\) | 658.980 | − | 478.777i | 0.630400 | − | 0.458012i | −0.226139 | − | 0.974095i | \(-0.572610\pi\) |
0.856539 | + | 0.516083i | \(0.172610\pi\) | |||||||
\(104\) | −130.083 | + | 400.353i | −0.122651 | + | 0.377480i | ||||
\(105\) | −152.784 | + | 470.219i | −0.142001 | + | 0.437035i | ||||
\(106\) | 1887.94 | − | 1371.67i | 1.72994 | − | 1.25687i | ||||
\(107\) | 1386.33 | + | 1007.23i | 1.25254 | + | 0.910020i | 0.998366 | − | 0.0571394i | \(-0.0181979\pi\) |
0.254169 | + | 0.967160i | \(0.418198\pi\) | |||||||
\(108\) | −690.761 | − | 2125.94i | −0.615449 | − | 1.89416i | ||||
\(109\) | −219.748 | −0.193101 | −0.0965507 | − | 0.995328i | \(-0.530781\pi\) | ||||
−0.0965507 | + | 0.995328i | \(0.530781\pi\) | |||||||
\(110\) | 1547.08 | − | 315.231i | 1.34099 | − | 0.273238i | ||||
\(111\) | −332.584 | −0.284392 | ||||||||
\(112\) | 133.382 | + | 410.507i | 0.112530 | + | 0.346332i | ||||
\(113\) | −873.134 | − | 634.369i | −0.726881 | − | 0.528110i | 0.161694 | − | 0.986841i | \(-0.448304\pi\) |
−0.888575 | + | 0.458731i | \(0.848304\pi\) | |||||||
\(114\) | 583.226 | − | 423.739i | 0.479159 | − | 0.348130i | ||||
\(115\) | −218.145 | + | 671.382i | −0.176888 | + | 0.544406i | ||||
\(116\) | 417.161 | − | 1283.89i | 0.333900 | − | 1.02764i | ||||
\(117\) | 62.8531 | − | 45.6654i | 0.0496647 | − | 0.0360835i | ||||
\(118\) | 952.669 | + | 692.155i | 0.743223 | + | 0.539983i | ||||
\(119\) | −55.7507 | − | 171.583i | −0.0429467 | − | 0.132176i | ||||
\(120\) | 1346.15 | 1.02405 | ||||||||
\(121\) | 1224.89 | − | 520.784i | 0.920275 | − | 0.391273i | ||||
\(122\) | −2310.41 | −1.71455 | ||||||||
\(123\) | −165.860 | − | 510.464i | −0.121586 | − | 0.374203i | ||||
\(124\) | 606.751 | + | 440.830i | 0.439418 | + | 0.319256i | ||||
\(125\) | −1230.79 | + | 894.225i | −0.880685 | + | 0.639855i | ||||
\(126\) | 104.838 | − | 322.657i | 0.0741245 | − | 0.228132i | ||||
\(127\) | 218.148 | − | 671.389i | 0.152421 | − | 0.469103i | −0.845469 | − | 0.534024i | \(-0.820679\pi\) |
0.997890 | + | 0.0649202i | \(0.0206793\pi\) | |||||||
\(128\) | −2147.59 | + | 1560.32i | −1.48299 | + | 1.07745i | ||||
\(129\) | −1202.56 | − | 873.708i | −0.820769 | − | 0.596323i | ||||
\(130\) | 173.853 | + | 535.066i | 0.117292 | + | 0.360987i | ||||
\(131\) | 941.040 | 0.627626 | 0.313813 | − | 0.949485i | \(-0.398393\pi\) | ||||
0.313813 | + | 0.949485i | \(0.398393\pi\) | |||||||
\(132\) | 2423.26 | − | 493.761i | 1.59786 | − | 0.325579i | ||||
\(133\) | 391.747 | 0.255404 | ||||||||
\(134\) | −727.816 | − | 2239.99i | −0.469207 | − | 1.44407i | ||||
\(135\) | −1109.07 | − | 805.783i | −0.707060 | − | 0.513709i | ||||
\(136\) | −397.396 | + | 288.725i | −0.250562 | + | 0.182044i | ||||
\(137\) | −725.077 | + | 2231.56i | −0.452171 | + | 1.39164i | 0.422253 | + | 0.906478i | \(0.361239\pi\) |
−0.874424 | + | 0.485162i | \(0.838761\pi\) | |||||||
\(138\) | −526.589 | + | 1620.68i | −0.324828 | + | 0.999718i | ||||
\(139\) | −1666.90 | + | 1211.07i | −1.01715 | + | 0.739006i | −0.965697 | − | 0.259670i | \(-0.916386\pi\) |
−0.0514563 | + | 0.998675i | \(0.516386\pi\) | |||||||
\(140\) | 1289.69 | + | 937.015i | 0.778562 | + | 0.565659i | ||||
\(141\) | −472.379 | − | 1453.83i | −0.282138 | − | 0.868332i | ||||
\(142\) | 4206.77 | 2.48608 | ||||||||
\(143\) | 233.667 | + | 412.721i | 0.136645 | + | 0.241353i | ||||
\(144\) | −216.892 | −0.125516 | ||||||||
\(145\) | −255.834 | − | 787.375i | −0.146523 | − | 0.450951i | ||||
\(146\) | 511.393 | + | 371.549i | 0.289885 | + | 0.210614i | ||||
\(147\) | 747.661 | − | 543.207i | 0.419497 | − | 0.304782i | ||||
\(148\) | −331.373 | + | 1019.86i | −0.184045 | + | 0.566434i | ||||
\(149\) | −123.352 | + | 379.638i | −0.0678214 | + | 0.208733i | −0.979223 | − | 0.202784i | \(-0.935001\pi\) |
0.911402 | + | 0.411517i | \(0.135001\pi\) | |||||||
\(150\) | −757.779 | + | 550.559i | −0.412483 | + | 0.299686i | ||||
\(151\) | 405.961 | + | 294.948i | 0.218786 | + | 0.158957i | 0.691780 | − | 0.722108i | \(-0.256827\pi\) |
−0.472994 | + | 0.881066i | \(0.656827\pi\) | |||||||
\(152\) | −329.599 | − | 1014.40i | −0.175882 | − | 0.541308i | ||||
\(153\) | 90.6563 | 0.0479028 | ||||||||
\(154\) | 1884.86 | + | 858.311i | 0.986276 | + | 0.449121i | ||||
\(155\) | 459.946 | 0.238347 | ||||||||
\(156\) | 272.314 | + | 838.097i | 0.139760 | + | 0.430138i | ||||
\(157\) | −2287.24 | − | 1661.78i | −1.16268 | − | 0.844740i | −0.172570 | − | 0.984997i | \(-0.555207\pi\) |
−0.990115 | + | 0.140258i | \(0.955207\pi\) | |||||||
\(158\) | 1732.14 | − | 1258.48i | 0.872165 | − | 0.633665i | ||||
\(159\) | 692.716 | − | 2131.96i | 0.345509 | − | 1.06337i | ||||
\(160\) | −240.434 | + | 739.980i | −0.118800 | + | 0.365629i | ||||
\(161\) | −749.158 | + | 544.295i | −0.366720 | + | 0.266438i | ||||
\(162\) | −2054.11 | − | 1492.40i | −0.996211 | − | 0.723790i | ||||
\(163\) | 1127.35 | + | 3469.61i | 0.541721 | + | 1.66725i | 0.728661 | + | 0.684875i | \(0.240143\pi\) |
−0.186940 | + | 0.982371i | \(0.559857\pi\) | |||||||
\(164\) | −1730.58 | −0.823999 | ||||||||
\(165\) | 1024.31 | − | 1118.50i | 0.483288 | − | 0.527728i | ||||
\(166\) | 4634.25 | 2.16679 | ||||||||
\(167\) | −451.697 | − | 1390.18i | −0.209301 | − | 0.644163i | −0.999509 | − | 0.0313245i | \(-0.990027\pi\) |
0.790208 | − | 0.612839i | \(-0.209973\pi\) | |||||||
\(168\) | 1428.57 | + | 1037.92i | 0.656052 | + | 0.476650i | ||||
\(169\) | −136.724 | + | 99.3357i | −0.0622321 | + | 0.0452143i | ||||
\(170\) | −202.867 | + | 624.361i | −0.0915248 | + | 0.281684i | ||||
\(171\) | −60.8300 | + | 187.216i | −0.0272034 | + | 0.0837236i | ||||
\(172\) | −3877.39 | + | 2817.09i | −1.71888 | + | 1.24884i | ||||
\(173\) | 2628.55 | + | 1909.76i | 1.15518 | + | 0.839284i | 0.989160 | − | 0.146839i | \(-0.0469100\pi\) |
0.166015 | + | 0.986123i | \(0.446910\pi\) | |||||||
\(174\) | −617.567 | − | 1900.68i | −0.269067 | − | 0.828103i | ||||
\(175\) | −508.992 | −0.219864 | ||||||||
\(176\) | 149.501 | − | 1315.59i | 0.0640286 | − | 0.563446i | ||||
\(177\) | 1131.17 | 0.480359 | ||||||||
\(178\) | 2207.45 | + | 6793.84i | 0.929525 | + | 2.86078i | ||||
\(179\) | −938.463 | − | 681.833i | −0.391866 | − | 0.284707i | 0.374354 | − | 0.927286i | \(-0.377865\pi\) |
−0.766220 | + | 0.642579i | \(0.777865\pi\) | |||||||
\(180\) | −648.061 | + | 470.844i | −0.268353 | + | 0.194970i | ||||
\(181\) | 392.968 | − | 1209.43i | 0.161376 | − | 0.496665i | −0.837375 | − | 0.546629i | \(-0.815911\pi\) |
0.998751 | + | 0.0499642i | \(0.0159107\pi\) | |||||||
\(182\) | −228.053 | + | 701.874i | −0.0928813 | + | 0.285859i | ||||
\(183\) | −1795.51 | + | 1304.52i | −0.725291 | + | 0.526955i | ||||
\(184\) | 2039.73 | + | 1481.95i | 0.817231 | + | 0.593753i | ||||
\(185\) | 203.222 | + | 625.454i | 0.0807633 | + | 0.248564i | ||||
\(186\) | 1110.28 | 0.437687 | ||||||||
\(187\) | −62.4880 | + | 549.889i | −0.0244362 | + | 0.215037i | ||||
\(188\) | −4928.81 | −1.91208 | ||||||||
\(189\) | −555.692 | − | 1710.24i | −0.213866 | − | 0.658211i | ||||
\(190\) | −1153.25 | − | 837.888i | −0.440347 | − | 0.319930i | ||||
\(191\) | 1897.45 | − | 1378.58i | 0.718820 | − | 0.522253i | −0.167187 | − | 0.985925i | \(-0.553468\pi\) |
0.886007 | + | 0.463672i | \(0.153468\pi\) | |||||||
\(192\) | −991.776 | + | 3052.37i | −0.372788 | + | 1.14732i | ||||
\(193\) | 557.296 | − | 1715.18i | 0.207850 | − | 0.639696i | −0.791734 | − | 0.610865i | \(-0.790822\pi\) |
0.999584 | − | 0.0288307i | \(-0.00917837\pi\) | |||||||
\(194\) | 2441.54 | − | 1773.89i | 0.903570 | − | 0.656482i | ||||
\(195\) | 437.220 | + | 317.659i | 0.160564 | + | 0.116656i | ||||
\(196\) | −920.795 | − | 2833.92i | −0.335567 | − | 1.03277i | ||||
\(197\) | −1652.94 | −0.597802 | −0.298901 | − | 0.954284i | \(-0.596620\pi\) | ||||
−0.298901 | + | 0.954284i | \(0.596620\pi\) | |||||||
\(198\) | −702.866 | + | 767.497i | −0.252275 | + | 0.275473i | ||||
\(199\) | −3746.42 | −1.33456 | −0.667278 | − | 0.744809i | \(-0.732541\pi\) | ||||
−0.667278 | + | 0.744809i | \(0.732541\pi\) | |||||||
\(200\) | 428.244 | + | 1318.00i | 0.151407 | + | 0.465984i | ||||
\(201\) | −1830.37 | − | 1329.84i | −0.642309 | − | 0.466665i | ||||
\(202\) | −5146.65 | + | 3739.26i | −1.79266 | + | 1.30244i | ||||
\(203\) | 335.591 | − | 1032.84i | 0.116029 | − | 0.357100i | ||||
\(204\) | −317.760 | + | 977.965i | −0.109057 | + | 0.335643i | ||||
\(205\) | −858.627 | + | 623.829i | −0.292532 | + | 0.212537i | ||||
\(206\) | −3145.47 | − | 2285.32i | −1.06386 | − | 0.772941i | ||||
\(207\) | −143.790 | − | 442.540i | −0.0482806 | − | 0.148592i | ||||
\(208\) | 471.804 | 0.157278 | ||||||||
\(209\) | −1093.65 | − | 498.018i | −0.361960 | − | 0.164826i | ||||
\(210\) | 2359.98 | 0.775496 | ||||||||
\(211\) | −69.5810 | − | 214.148i | −0.0227021 | − | 0.0698700i | 0.939064 | − | 0.343743i | \(-0.111695\pi\) |
−0.961766 | + | 0.273873i | \(0.911695\pi\) | |||||||
\(212\) | −5847.42 | − | 4248.40i | −1.89435 | − | 1.37633i | ||||
\(213\) | 3269.24 | − | 2375.25i | 1.05167 | − | 0.764080i | ||||
\(214\) | 2527.58 | − | 7779.08i | 0.807391 | − | 2.48489i | ||||
\(215\) | −908.276 | + | 2795.39i | −0.288111 | + | 0.886715i | ||||
\(216\) | −3961.03 | + | 2877.85i | −1.24775 | + | 0.906543i | ||||
\(217\) | 488.109 | + | 354.632i | 0.152696 | + | 0.110940i | ||||
\(218\) | 324.132 | + | 997.575i | 0.100702 | + | 0.309928i | ||||
\(219\) | 607.210 | 0.187358 | ||||||||
\(220\) | −2409.27 | − | 4255.45i | −0.738333 | − | 1.30410i | ||||
\(221\) | −197.204 | −0.0600243 | ||||||||
\(222\) | 490.567 | + | 1509.81i | 0.148309 | + | 0.456449i | ||||
\(223\) | 764.872 | + | 555.712i | 0.229684 | + | 0.166875i | 0.696675 | − | 0.717387i | \(-0.254662\pi\) |
−0.466991 | + | 0.884262i | \(0.654662\pi\) | |||||||
\(224\) | −825.702 | + | 599.908i | −0.246293 | + | 0.178942i | ||||
\(225\) | 79.0357 | − | 243.247i | 0.0234180 | − | 0.0720732i | ||||
\(226\) | −1591.91 | + | 4899.41i | −0.468551 | + | 1.44205i | ||||
\(227\) | −998.279 | + | 725.292i | −0.291886 | + | 0.212067i | −0.724085 | − | 0.689711i | \(-0.757738\pi\) |
0.432199 | + | 0.901778i | \(0.357738\pi\) | |||||||
\(228\) | −1806.39 | − | 1312.42i | −0.524699 | − | 0.381216i | ||||
\(229\) | −1440.94 | − | 4434.75i | −0.415807 | − | 1.27972i | −0.911527 | − | 0.411241i | \(-0.865096\pi\) |
0.495719 | − | 0.868483i | \(-0.334904\pi\) | |||||||
\(230\) | 3369.59 | 0.966019 | ||||||||
\(231\) | 1949.43 | − | 397.213i | 0.555250 | − | 0.113137i | ||||
\(232\) | −2956.83 | −0.836747 | ||||||||
\(233\) | 755.615 | + | 2325.55i | 0.212455 | + | 0.653869i | 0.999324 | + | 0.0367498i | \(0.0117005\pi\) |
−0.786869 | + | 0.617119i | \(0.788300\pi\) | |||||||
\(234\) | −300.013 | − | 217.973i | −0.0838141 | − | 0.0608945i | ||||
\(235\) | −2445.42 | + | 1776.70i | −0.678815 | + | 0.493188i | ||||
\(236\) | 1127.05 | − | 3468.69i | 0.310867 | − | 0.956749i | ||||
\(237\) | 635.551 | − | 1956.02i | 0.174192 | − | 0.536107i | ||||
\(238\) | −696.690 | + | 506.175i | −0.189747 | + | 0.137859i | ||||
\(239\) | 4632.04 | + | 3365.37i | 1.25365 | + | 0.910828i | 0.998428 | − | 0.0560547i | \(-0.0178521\pi\) |
0.255220 | + | 0.966883i | \(0.417852\pi\) | |||||||
\(240\) | −466.229 | − | 1434.91i | −0.125396 | − | 0.385928i | ||||
\(241\) | 2786.65 | 0.744830 | 0.372415 | − | 0.928066i | \(-0.378530\pi\) | ||||
0.372415 | + | 0.928066i | \(0.378530\pi\) | |||||||
\(242\) | −4170.89 | − | 4792.36i | −1.10791 | − | 1.27299i | ||||
\(243\) | 1643.46 | 0.433861 | ||||||||
\(244\) | 2211.30 | + | 6805.67i | 0.580179 | + | 1.78561i | ||||
\(245\) | −1478.40 | − | 1074.12i | −0.385517 | − | 0.280094i | ||||
\(246\) | −2072.67 | + | 1505.88i | −0.537190 | + | 0.390292i | ||||
\(247\) | 132.323 | − | 407.249i | 0.0340871 | − | 0.104909i | ||||
\(248\) | 507.621 | − | 1562.30i | 0.129976 | − | 0.400024i | ||||
\(249\) | 3601.46 | − | 2616.61i | 0.916600 | − | 0.665949i | ||||
\(250\) | 5874.89 | + | 4268.36i | 1.48624 | + | 1.07982i | ||||
\(251\) | 1419.11 | + | 4367.58i | 0.356867 | + | 1.09832i | 0.954919 | + | 0.296867i | \(0.0959418\pi\) |
−0.598052 | + | 0.801458i | \(0.704058\pi\) | |||||||
\(252\) | −1050.78 | −0.262669 | ||||||||
\(253\) | 2783.40 | − | 567.143i | 0.691664 | − | 0.140933i | ||||
\(254\) | −3369.63 | −0.832399 | ||||||||
\(255\) | 194.874 | + | 599.760i | 0.0478568 | + | 0.147288i | ||||
\(256\) | 5720.74 | + | 4156.36i | 1.39666 | + | 1.01474i | ||||
\(257\) | 2758.27 | − | 2004.00i | 0.669480 | − | 0.486406i | −0.200371 | − | 0.979720i | \(-0.564215\pi\) |
0.869851 | + | 0.493315i | \(0.164215\pi\) | |||||||
\(258\) | −2192.52 | + | 6747.89i | −0.529072 | + | 1.62832i | ||||
\(259\) | −266.578 | + | 820.442i | −0.0639549 | + | 0.196833i | ||||
\(260\) | 1409.72 | − | 1024.22i | 0.336259 | − | 0.244306i | ||||
\(261\) | 441.485 | + | 320.757i | 0.104702 | + | 0.0760704i | ||||
\(262\) | −1388.05 | − | 4271.97i | −0.327305 | − | 1.00734i | ||||
\(263\) | 882.728 | 0.206963 | 0.103482 | − | 0.994631i | \(-0.467002\pi\) | ||||
0.103482 | + | 0.994631i | \(0.467002\pi\) | |||||||
\(264\) | −2668.72 | − | 4713.71i | −0.622153 | − | 1.09890i | ||||
\(265\) | −4432.62 | −1.02752 | ||||||||
\(266\) | −577.832 | − | 1778.38i | −0.133192 | − | 0.409924i | ||||
\(267\) | 5551.47 | + | 4033.38i | 1.27245 | + | 0.924490i | ||||
\(268\) | −5901.63 | + | 4287.78i | −1.34515 | + | 0.977306i | ||||
\(269\) | 867.049 | − | 2668.50i | 0.196524 | − | 0.604838i | −0.803432 | − | 0.595397i | \(-0.796995\pi\) |
0.999955 | − | 0.00944125i | \(-0.00300529\pi\) | |||||||
\(270\) | −2022.07 | + | 6223.29i | −0.455775 | + | 1.40273i | ||||
\(271\) | 5279.63 | − | 3835.88i | 1.18345 | − | 0.859827i | 0.190893 | − | 0.981611i | \(-0.438862\pi\) |
0.992557 | + | 0.121784i | \(0.0388615\pi\) | |||||||
\(272\) | 445.398 | + | 323.601i | 0.0992876 | + | 0.0721367i | ||||
\(273\) | 219.067 | + | 674.218i | 0.0485660 | + | 0.149471i | ||||
\(274\) | 11199.9 | 2.46939 | ||||||||
\(275\) | 1420.97 | + | 647.069i | 0.311592 | + | 0.141890i | ||||
\(276\) | 5277.95 | 1.15107 | ||||||||
\(277\) | −3.17145 | − | 9.76073i | −0.000687921 | − | 0.00211720i | 0.950712 | − | 0.310075i | \(-0.100354\pi\) |
−0.951400 | + | 0.307958i | \(0.900354\pi\) | |||||||
\(278\) | 7956.52 | + | 5780.75i | 1.71655 | + | 1.24714i | ||||
\(279\) | −245.271 | + | 178.200i | −0.0526309 | + | 0.0382386i | ||||
\(280\) | 1078.98 | − | 3320.77i | 0.230291 | − | 0.708764i | ||||
\(281\) | −515.358 | + | 1586.11i | −0.109408 | + | 0.336724i | −0.990740 | − | 0.135775i | \(-0.956648\pi\) |
0.881332 | + | 0.472498i | \(0.156648\pi\) | |||||||
\(282\) | −5903.10 | + | 4288.85i | −1.24654 | + | 0.905664i | ||||
\(283\) | −1194.50 | − | 867.857i | −0.250904 | − | 0.182292i | 0.455223 | − | 0.890377i | \(-0.349559\pi\) |
−0.706127 | + | 0.708085i | \(0.749559\pi\) | |||||||
\(284\) | −4026.30 | − | 12391.7i | −0.841256 | − | 2.58912i | ||||
\(285\) | −1369.33 | −0.284604 | ||||||||
\(286\) | 1528.94 | − | 1669.53i | 0.316112 | − | 0.345180i | ||||
\(287\) | −1392.19 | −0.286336 | ||||||||
\(288\) | −158.482 | − | 487.756i | −0.0324257 | − | 0.0997962i | ||||
\(289\) | 3788.53 | + | 2752.53i | 0.771124 | + | 0.560255i | ||||
\(290\) | −3197.03 | + | 2322.78i | −0.647366 | + | 0.470339i | ||||
\(291\) | 895.840 | − | 2757.11i | 0.180464 | − | 0.555412i | ||||
\(292\) | 604.999 | − | 1862.00i | 0.121250 | − | 0.373168i | ||||
\(293\) | 7754.97 | − | 5634.31i | 1.54625 | − | 1.12341i | 0.599984 | − | 0.800012i | \(-0.295174\pi\) |
0.946262 | − | 0.323401i | \(-0.104826\pi\) | |||||||
\(294\) | −3568.77 | − | 2592.86i | −0.707942 | − | 0.514350i | ||||
\(295\) | −691.188 | − | 2127.26i | −0.136415 | − | 0.419843i | ||||
\(296\) | 2348.77 | 0.461214 | ||||||||
\(297\) | −622.846 | + | 5480.99i | −0.121688 | + | 1.07084i | ||||
\(298\) | 1905.36 | 0.370385 | ||||||||
\(299\) | 312.785 | + | 962.653i | 0.0604977 | + | 0.186193i | ||||
\(300\) | 2347.03 | + | 1705.21i | 0.451685 | + | 0.328169i | ||||
\(301\) | −3119.21 | + | 2266.24i | −0.597304 | + | 0.433967i | ||||
\(302\) | 740.156 | − | 2277.96i | 0.141030 | − | 0.434047i | ||||
\(303\) | −1888.39 | + | 5811.86i | −0.358036 | + | 1.10192i | ||||
\(304\) | −967.132 | + | 702.663i | −0.182463 | + | 0.132567i | ||||
\(305\) | 3550.39 | + | 2579.51i | 0.666541 | + | 0.484270i | ||||
\(306\) | −133.719 | − | 411.546i | −0.0249811 | − | 0.0768841i | ||||
\(307\) | −6758.47 | −1.25644 | −0.628219 | − | 0.778037i | \(-0.716216\pi\) | ||||
−0.628219 | + | 0.778037i | \(0.716216\pi\) | |||||||
\(308\) | 724.284 | − | 6373.64i | 0.133993 | − | 1.17913i | ||||
\(309\) | −3734.82 | −0.687594 | ||||||||
\(310\) | −678.427 | − | 2087.98i | −0.124297 | − | 0.382547i | ||||
\(311\) | 5269.36 | + | 3828.41i | 0.960765 | + | 0.698037i | 0.953328 | − | 0.301936i | \(-0.0976328\pi\) |
0.00743680 | + | 0.999972i | \(0.497633\pi\) | |||||||
\(312\) | 1561.53 | − | 1134.52i | 0.283347 | − | 0.205864i | ||||
\(313\) | 17.3670 | − | 53.4500i | 0.00313623 | − | 0.00965231i | −0.949476 | − | 0.313839i | \(-0.898385\pi\) |
0.952612 | + | 0.304187i | \(0.0983847\pi\) | |||||||
\(314\) | −4170.14 | + | 12834.4i | −0.749473 | + | 2.30664i | ||||
\(315\) | −521.341 | + | 378.777i | −0.0932516 | + | 0.0677512i | ||||
\(316\) | −5364.87 | − | 3897.81i | −0.955056 | − | 0.693889i | ||||
\(317\) | −402.630 | − | 1239.17i | −0.0713374 | − | 0.219554i | 0.909031 | − | 0.416729i | \(-0.136823\pi\) |
−0.980368 | + | 0.197175i | \(0.936823\pi\) | |||||||
\(318\) | −10700.1 | −1.88689 | ||||||||
\(319\) | −2249.91 | + | 2456.80i | −0.394893 | + | 0.431204i | ||||
\(320\) | 6346.28 | 1.10865 | ||||||||
\(321\) | −2427.98 | − | 7472.57i | −0.422171 | − | 1.29931i | ||||
\(322\) | 3575.92 | + | 2598.06i | 0.618876 | + | 0.449640i | ||||
\(323\) | 404.241 | − | 293.698i | 0.0696364 | − | 0.0505938i | ||||
\(324\) | −2430.10 | + | 7479.07i | −0.416684 | + | 1.28242i | ||||
\(325\) | −171.926 | + | 529.133i | −0.0293438 | + | 0.0903109i | ||||
\(326\) | 14087.9 | − | 10235.5i | 2.39343 | − | 1.73893i | ||||
\(327\) | 815.151 | + | 592.242i | 0.137853 | + | 0.100156i | ||||
\(328\) | 1171.33 | + | 3604.99i | 0.197183 | + | 0.606866i | ||||
\(329\) | −3965.04 | −0.664438 | ||||||||
\(330\) | −6588.45 | − | 3000.19i | −1.09904 | − | 0.500469i | ||||
\(331\) | −5832.34 | −0.968503 | −0.484252 | − | 0.874929i | \(-0.660908\pi\) | ||||
−0.484252 | + | 0.874929i | \(0.660908\pi\) | |||||||
\(332\) | −4435.44 | − | 13650.9i | −0.733213 | − | 2.25660i | ||||
\(333\) | −350.695 | − | 254.795i | −0.0577116 | − | 0.0419299i | ||||
\(334\) | −5644.64 | + | 4101.07i | −0.924733 | + | 0.671858i | ||||
\(335\) | −1382.45 | + | 4254.75i | −0.225467 | + | 0.693917i | ||||
\(336\) | 611.578 | − | 1882.24i | 0.0992985 | − | 0.305609i | ||||
\(337\) | 8165.62 | − | 5932.67i | 1.31991 | − | 0.958971i | 0.319977 | − | 0.947425i | \(-0.396325\pi\) |
0.999933 | − | 0.0115453i | \(-0.00367506\pi\) | |||||||
\(338\) | 652.617 | + | 474.154i | 0.105023 | + | 0.0763035i | ||||
\(339\) | 1529.19 | + | 4706.36i | 0.244998 | + | 0.754025i | ||||
\(340\) | 2033.32 | 0.324329 | ||||||||
\(341\) | −911.837 | − | 1610.56i | −0.144806 | − | 0.255768i | ||||
\(342\) | 939.615 | 0.148563 | ||||||||
\(343\) | −2001.33 | − | 6159.46i | −0.315049 | − | 0.969620i | ||||
\(344\) | 8492.66 | + | 6170.28i | 1.33109 | + | 0.967090i | ||||
\(345\) | 2618.65 | − | 1902.56i | 0.408647 | − | 0.296899i | ||||
\(346\) | 4792.43 | − | 14749.6i | 0.744632 | − | 2.29174i | ||||
\(347\) | 3604.53 | − | 11093.6i | 0.557641 | − | 1.71624i | −0.131224 | − | 0.991353i | \(-0.541891\pi\) |
0.688865 | − | 0.724890i | \(-0.258109\pi\) | |||||||
\(348\) | −5007.66 | + | 3638.28i | −0.771375 | + | 0.560437i | ||||
\(349\) | −7712.73 | − | 5603.62i | −1.18296 | − | 0.859470i | −0.190457 | − | 0.981696i | \(-0.560997\pi\) |
−0.992502 | + | 0.122225i | \(0.960997\pi\) | |||||||
\(350\) | 750.771 | + | 2310.63i | 0.114658 | + | 0.352882i | ||||
\(351\) | −1965.62 | −0.298909 | ||||||||
\(352\) | 3067.79 | − | 625.090i | 0.464528 | − | 0.0946517i | ||||
\(353\) | −10578.4 | −1.59500 | −0.797499 | − | 0.603321i | \(-0.793844\pi\) | ||||
−0.797499 | + | 0.603321i | \(0.793844\pi\) | |||||||
\(354\) | −1668.49 | − | 5135.07i | −0.250506 | − | 0.770977i | ||||
\(355\) | −6464.50 | − | 4696.74i | −0.966479 | − | 0.702188i | ||||
\(356\) | 17899.5 | − | 13004.8i | 2.66481 | − | 1.93610i | ||||
\(357\) | −255.626 | + | 786.737i | −0.0378969 | + | 0.116635i | ||||
\(358\) | −1711.02 | + | 5265.99i | −0.252599 | + | 0.777419i | ||||
\(359\) | 6366.82 | − | 4625.77i | 0.936011 | − | 0.680052i | −0.0114459 | − | 0.999934i | \(-0.503643\pi\) |
0.947457 | + | 0.319882i | \(0.103643\pi\) | |||||||
\(360\) | 1419.45 | + | 1031.29i | 0.207810 | + | 0.150983i | ||||
\(361\) | −1784.27 | − | 5491.42i | −0.260136 | − | 0.800616i | ||||
\(362\) | −6070.01 | −0.881305 | ||||||||
\(363\) | −5947.25 | − | 1369.35i | −0.859917 | − | 0.197994i | ||||
\(364\) | 2285.75 | 0.329136 | ||||||||
\(365\) | −371.030 | − | 1141.91i | −0.0532071 | − | 0.163755i | ||||
\(366\) | 8570.43 | + | 6226.78i | 1.22400 | + | 0.889288i | ||||
\(367\) | 5856.68 | − | 4255.12i | 0.833014 | − | 0.605220i | −0.0873968 | − | 0.996174i | \(-0.527855\pi\) |
0.920410 | + | 0.390954i | \(0.127855\pi\) | |||||||
\(368\) | 873.214 | − | 2687.48i | 0.123694 | − | 0.380691i | ||||
\(369\) | 216.178 | − | 665.328i | 0.0304980 | − | 0.0938633i | ||||
\(370\) | 2539.58 | − | 1845.11i | 0.356828 | − | 0.259250i | ||||
\(371\) | −4704.03 | − | 3417.68i | −0.658278 | − | 0.478267i | ||||
\(372\) | −1062.65 | − | 3270.50i | −0.148107 | − | 0.455827i | ||||
\(373\) | −1489.27 | −0.206733 | −0.103366 | − | 0.994643i | \(-0.532961\pi\) | ||||
−0.103366 | + | 0.994643i | \(0.532961\pi\) | |||||||
\(374\) | 2588.46 | − | 527.422i | 0.357878 | − | 0.0729207i | ||||
\(375\) | 6975.63 | 0.960587 | ||||||||
\(376\) | 3336.02 | + | 10267.2i | 0.457559 | + | 1.40822i | ||||
\(377\) | −960.358 | − | 697.741i | −0.131196 | − | 0.0953196i | ||||
\(378\) | −6944.22 | + | 5045.27i | −0.944900 | + | 0.686510i | ||||
\(379\) | −3252.72 | + | 10010.8i | −0.440847 | + | 1.35679i | 0.446127 | + | 0.894969i | \(0.352803\pi\) |
−0.886974 | + | 0.461818i | \(0.847197\pi\) | |||||||
\(380\) | −1364.35 | + | 4199.03i | −0.184183 | + | 0.566857i | ||||
\(381\) | −2618.67 | + | 1902.58i | −0.352122 | + | 0.255832i | ||||
\(382\) | −9057.00 | − | 6580.29i | −1.21308 | − | 0.881354i | ||||
\(383\) | 4292.46 | + | 13210.8i | 0.572675 | + | 1.76251i | 0.643964 | + | 0.765056i | \(0.277289\pi\) |
−0.0712891 | + | 0.997456i | \(0.522711\pi\) | |||||||
\(384\) | 12171.7 | 1.61753 | ||||||||
\(385\) | −1938.17 | − | 3423.36i | −0.256567 | − | 0.453170i | ||||
\(386\) | −8608.30 | −1.13511 | ||||||||
\(387\) | −598.688 | − | 1842.57i | −0.0786382 | − | 0.242024i | ||||
\(388\) | −7562.05 | − | 5494.15i | −0.989446 | − | 0.718874i | ||||
\(389\) | −2517.20 | + | 1828.86i | −0.328091 | + | 0.238372i | −0.739620 | − | 0.673025i | \(-0.764995\pi\) |
0.411529 | + | 0.911397i | \(0.364995\pi\) | |||||||
\(390\) | 797.147 | − | 2453.37i | 0.103500 | − | 0.318541i | ||||
\(391\) | −364.985 | + | 1123.31i | −0.0472074 | + | 0.145289i | ||||
\(392\) | −5280.11 | + | 3836.22i | −0.680321 | + | 0.494282i | ||||
\(393\) | −3490.77 | − | 2536.19i | −0.448056 | − | 0.325532i | ||||
\(394\) | 2438.11 | + | 7503.73i | 0.311752 | + | 0.959474i | ||||
\(395\) | −4066.83 | −0.518036 | ||||||||
\(396\) | 2933.49 | + | 1335.83i | 0.372256 | + | 0.169515i | ||||
\(397\) | −7136.13 | −0.902147 | −0.451073 | − | 0.892487i | \(-0.648959\pi\) | ||||
−0.451073 | + | 0.892487i | \(0.648959\pi\) | |||||||
\(398\) | 5526.03 | + | 17007.4i | 0.695966 | + | 2.14196i | ||||
\(399\) | −1453.18 | − | 1055.79i | −0.182330 | − | 0.132471i | ||||
\(400\) | 1256.58 | − | 912.962i | 0.157073 | − | 0.114120i | ||||
\(401\) | −4531.89 | + | 13947.7i | −0.564368 | + | 1.73695i | 0.105454 | + | 0.994424i | \(0.466371\pi\) |
−0.669822 | + | 0.742522i | \(0.733629\pi\) | |||||||
\(402\) | −3337.16 | + | 10270.7i | −0.414036 | + | 1.27427i | ||||
\(403\) | 533.537 | − | 387.637i | 0.0659488 | − | 0.0479146i | ||||
\(404\) | 15940.4 | + | 11581.4i | 1.96303 | + | 1.42623i | ||||
\(405\) | 1490.31 | + | 4586.72i | 0.182850 | + | 0.562755i | ||||
\(406\) | −5183.72 | −0.633655 | ||||||||
\(407\) | 1787.22 | − | 1951.57i | 0.217664 | − | 0.237679i | ||||
\(408\) | 2252.28 | 0.273295 | ||||||||
\(409\) | 1771.89 | + | 5453.33i | 0.214216 | + | 0.659290i | 0.999208 | + | 0.0397844i | \(0.0126671\pi\) |
−0.784992 | + | 0.619506i | \(0.787333\pi\) | |||||||
\(410\) | 4098.44 | + | 2977.69i | 0.493677 | + | 0.358677i | ||||
\(411\) | 8703.92 | − | 6323.76i | 1.04460 | − | 0.758950i | ||||
\(412\) | −3721.22 | + | 11452.8i | −0.444980 | + | 1.36951i | ||||
\(413\) | 906.668 | − | 2790.44i | 0.108025 | − | 0.332466i | ||||
\(414\) | −1796.87 | + | 1305.51i | −0.213313 | + | 0.154981i | ||||
\(415\) | −7121.42 | − | 5174.01i | −0.842353 | − | 0.612005i | ||||
\(416\) | 344.744 | + | 1061.01i | 0.0406309 | + | 0.125049i | ||||
\(417\) | 9447.28 | 1.10944 | ||||||||
\(418\) | −647.662 | + | 5699.37i | −0.0757852 | + | 0.666903i | ||||
\(419\) | −14210.7 | −1.65690 | −0.828448 | − | 0.560066i | \(-0.810776\pi\) | ||||
−0.828448 | + | 0.560066i | \(0.810776\pi\) | |||||||
\(420\) | −2258.74 | − | 6951.68i | −0.262417 | − | 0.807636i | ||||
\(421\) | 11180.9 | + | 8123.43i | 1.29436 | + | 0.940408i | 0.999884 | − | 0.0152502i | \(-0.00485447\pi\) |
0.294477 | + | 0.955658i | \(0.404854\pi\) | |||||||
\(422\) | −869.521 | + | 631.744i | −0.100302 | + | 0.0728739i | ||||
\(423\) | 615.688 | − | 1894.89i | 0.0707702 | − | 0.217808i | ||||
\(424\) | −4892.08 | + | 15056.3i | −0.560331 | + | 1.72452i | ||||
\(425\) | −525.225 | + | 381.598i | −0.0599463 | + | 0.0435535i | ||||
\(426\) | −15604.9 | − | 11337.6i | −1.77479 | − | 1.28946i | ||||
\(427\) | 1778.91 | + | 5474.91i | 0.201610 | + | 0.620491i | ||||
\(428\) | −25333.6 | −2.86109 | ||||||||
\(429\) | 245.541 | − | 2160.74i | 0.0276336 | − | 0.243173i | ||||
\(430\) | 14029.7 | 1.57343 | ||||||||
\(431\) | 1568.60 | + | 4827.64i | 0.175305 | + | 0.539535i | 0.999647 | − | 0.0265576i | \(-0.00845455\pi\) |
−0.824342 | + | 0.566092i | \(0.808455\pi\) | |||||||
\(432\) | 4439.48 | + | 3225.47i | 0.494432 | + | 0.359226i | ||||
\(433\) | −5502.76 | + | 3997.99i | −0.610730 | + | 0.443721i | −0.849671 | − | 0.527313i | \(-0.823200\pi\) |
0.238942 | + | 0.971034i | \(0.423200\pi\) | |||||||
\(434\) | 889.929 | − | 2738.92i | 0.0984285 | − | 0.302932i | ||||
\(435\) | −1173.04 | + | 3610.25i | −0.129294 | + | 0.397927i | ||||
\(436\) | 2628.28 | − | 1909.56i | 0.288697 | − | 0.209751i | ||||
\(437\) | −2074.86 | − | 1507.47i | −0.227125 | − | 0.165016i | ||||
\(438\) | −895.643 | − | 2756.51i | −0.0977066 | − | 0.300710i | ||||
\(439\) | 10759.7 | 1.16978 | 0.584890 | − | 0.811113i | \(-0.301138\pi\) | ||||
0.584890 | + | 0.811113i | \(0.301138\pi\) | |||||||
\(440\) | −7233.86 | + | 7899.04i | −0.783774 | + | 0.855845i | ||||
\(441\) | 1204.53 | 0.130065 | ||||||||
\(442\) | 290.879 | + | 895.233i | 0.0313025 | + | 0.0963391i | ||||
\(443\) | −7703.77 | − | 5597.12i | −0.826224 | − | 0.600287i | 0.0922646 | − | 0.995735i | \(-0.470589\pi\) |
−0.918488 | + | 0.395448i | \(0.870589\pi\) | |||||||
\(444\) | 3977.85 | − | 2890.08i | 0.425181 | − | 0.308912i | ||||
\(445\) | 4192.96 | − | 12904.6i | 0.446663 | − | 1.37469i | ||||
\(446\) | 1394.53 | − | 4291.92i | 0.148056 | − | 0.455669i | ||||
\(447\) | 1480.73 | − | 1075.82i | 0.156681 | − | 0.113835i | ||||
\(448\) | 6734.86 | + | 4893.17i | 0.710251 | + | 0.516028i | ||||
\(449\) | 367.852 | + | 1132.13i | 0.0386638 | + | 0.118995i | 0.968526 | − | 0.248914i | \(-0.0800738\pi\) |
−0.929862 | + | 0.367909i | \(0.880074\pi\) | |||||||
\(450\) | −1220.83 | −0.127890 | ||||||||
\(451\) | 3886.63 | + | 1769.86i | 0.405797 | + | 0.184788i | ||||
\(452\) | 15955.6 | 1.66037 | ||||||||
\(453\) | −710.992 | − | 2188.21i | −0.0737424 | − | 0.226956i | ||||
\(454\) | 4765.03 | + | 3462.00i | 0.492586 | + | 0.357885i | ||||
\(455\) | 1134.07 | − | 823.950i | 0.116848 | − | 0.0848953i | ||||
\(456\) | −1511.27 | + | 4651.21i | −0.155201 | + | 0.477660i | ||||
\(457\) | −5325.93 | + | 16391.5i | −0.545157 | + | 1.67782i | 0.175461 | + | 0.984486i | \(0.443858\pi\) |
−0.720617 | + | 0.693333i | \(0.756142\pi\) | |||||||
\(458\) | −18006.7 | + | 13082.7i | −1.83712 | + | 1.33474i | ||||
\(459\) | −1855.61 | − | 1348.18i | −0.188698 | − | 0.137097i | ||||
\(460\) | −3225.04 | − | 9925.65i | −0.326887 | − | 1.00606i | ||||
\(461\) | −16519.2 | −1.66893 | −0.834463 | − | 0.551064i | \(-0.814222\pi\) | ||||
−0.834463 | + | 0.551064i | \(0.814222\pi\) | |||||||
\(462\) | −4678.63 | − | 8263.77i | −0.471146 | − | 0.832177i | ||||
\(463\) | −8199.50 | −0.823030 | −0.411515 | − | 0.911403i | \(-0.635000\pi\) | ||||
−0.411515 | + | 0.911403i | \(0.635000\pi\) | |||||||
\(464\) | 1024.08 | + | 3151.79i | 0.102460 | + | 0.315341i | ||||
\(465\) | −1706.16 | − | 1239.60i | −0.170153 | − | 0.123624i | ||||
\(466\) | 9442.57 | − | 6860.43i | 0.938667 | − | 0.681981i | ||||
\(467\) | −4761.65 | + | 14654.9i | −0.471826 | + | 1.45213i | 0.378364 | + | 0.925657i | \(0.376487\pi\) |
−0.850190 | + | 0.526476i | \(0.823513\pi\) | |||||||
\(468\) | −354.928 | + | 1092.36i | −0.0350568 | + | 0.107894i | ||||
\(469\) | −4747.64 | + | 3449.36i | −0.467432 | + | 0.339609i | ||||
\(470\) | 11672.6 | + | 8480.64i | 1.14557 | + | 0.832304i | ||||
\(471\) | 4005.82 | + | 12328.7i | 0.391886 | + | 1.20610i | ||||
\(472\) | −7988.48 | −0.779025 | ||||||||
\(473\) | 11589.1 | − | 2361.37i | 1.12656 | − | 0.229547i | ||||
\(474\) | −9817.07 | −0.951294 | ||||||||
\(475\) | −435.620 | − | 1340.70i | −0.0420792 | − | 0.129506i | ||||
\(476\) | 2157.82 | + | 1567.75i | 0.207780 | + | 0.150961i | ||||
\(477\) | 2363.74 | − | 1717.36i | 0.226894 | − | 0.164848i | ||||
\(478\) | 8445.22 | − | 25991.7i | 0.808108 | − | 2.48710i | ||||
\(479\) | 4185.88 | − | 12882.8i | 0.399285 | − | 1.22887i | −0.526288 | − | 0.850306i | \(-0.676417\pi\) |
0.925574 | − | 0.378568i | \(-0.123583\pi\) | |||||||
\(480\) | 2886.20 | − | 2096.95i | 0.274451 | − | 0.199400i | ||||
\(481\) | 762.864 | + | 554.253i | 0.0723152 | + | 0.0525400i | ||||
\(482\) | −4110.35 | − | 12650.4i | −0.388426 | − | 1.19545i | ||||
\(483\) | 4245.91 | 0.399991 | ||||||||
\(484\) | −10124.7 | + | 16872.8i | −0.950852 | + | 1.58459i | ||||
\(485\) | −5732.39 | −0.536690 | ||||||||
\(486\) | −2424.13 | − | 7460.72i | −0.226257 | − | 0.696348i | ||||
\(487\) | 10874.9 | + | 7901.04i | 1.01188 | + | 0.735175i | 0.964603 | − | 0.263706i | \(-0.0849450\pi\) |
0.0472791 | + | 0.998882i | \(0.484945\pi\) | |||||||
\(488\) | 12680.2 | − | 9212.73i | 1.17624 | − | 0.854591i | ||||
\(489\) | 5169.07 | − | 15908.8i | 0.478024 | − | 1.47121i | ||||
\(490\) | −2695.45 | + | 8295.74i | −0.248506 | + | 0.764823i | ||||
\(491\) | 2358.39 | − | 1713.47i | 0.216767 | − | 0.157490i | −0.474103 | − | 0.880469i | \(-0.657228\pi\) |
0.690870 | + | 0.722979i | \(0.257228\pi\) | |||||||
\(492\) | 6419.57 | + | 4664.09i | 0.588245 | + | 0.427385i | ||||
\(493\) | −428.042 | − | 1317.38i | −0.0391036 | − | 0.120348i | ||||
\(494\) | −2043.94 | −0.186156 | ||||||||
\(495\) | 1936.98 | − | 394.676i | 0.175880 | − | 0.0358371i | ||||
\(496\) | −1841.12 | −0.166671 | ||||||||
\(497\) | −3239.01 | − | 9968.64i | −0.292333 | − | 0.899708i | ||||
\(498\) | −17190.7 | − | 12489.8i | −1.54685 | − | 1.12385i | ||||
\(499\) | 2692.01 | − | 1955.86i | 0.241504 | − | 0.175463i | −0.460449 | − | 0.887686i | \(-0.652312\pi\) |
0.701953 | + | 0.712223i | \(0.252312\pi\) | |||||||
\(500\) | 6950.24 | − | 21390.6i | 0.621648 | − | 1.91324i | ||||
\(501\) | −2071.11 | + | 6374.21i | −0.184691 | + | 0.568420i | ||||
\(502\) | 17734.0 | − | 12884.5i | 1.57671 | − | 1.14555i | ||||
\(503\) | 4922.34 | + | 3576.29i | 0.436335 | + | 0.317016i | 0.784177 | − | 0.620537i | \(-0.213085\pi\) |
−0.347842 | + | 0.937553i | \(0.613085\pi\) | |||||||
\(504\) | 711.209 | + | 2188.88i | 0.0628567 | + | 0.193453i | ||||
\(505\) | 12083.6 | 1.06478 | ||||||||
\(506\) | −6680.18 | − | 11799.1i | −0.586897 | − | 1.03663i | ||||
\(507\) | 774.894 | 0.0678782 | ||||||||
\(508\) | 3225.07 | + | 9925.75i | 0.281672 | + | 0.866898i | ||||
\(509\) | 1902.84 | + | 1382.49i | 0.165701 | + | 0.120389i | 0.667545 | − | 0.744569i | \(-0.267345\pi\) |
−0.501844 | + | 0.864958i | \(0.667345\pi\) | |||||||
\(510\) | 2435.25 | − | 1769.31i | 0.211440 | − | 0.153620i | ||||
\(511\) | 486.699 | − | 1497.91i | 0.0421337 | − | 0.129674i | ||||
\(512\) | 3867.69 | − | 11903.5i | 0.333847 | − | 1.02747i | ||||
\(513\) | 4029.25 | − | 2927.42i | 0.346775 | − | 0.251947i | ||||
\(514\) | −13165.9 | − | 9565.60i | −1.12981 | − | 0.820857i | ||||
\(515\) | 2282.13 | + | 7023.67i | 0.195267 | + | 0.600970i | ||||
\(516\) | 21975.4 | 1.87483 | ||||||||
\(517\) | 11069.4 | + | 5040.67i | 0.941644 | + | 0.428798i | ||||
\(518\) | 4117.71 | 0.349270 | ||||||||
\(519\) | −4603.60 | − | 14168.4i | −0.389355 | − | 1.19831i | ||||
\(520\) | −3087.72 | − | 2243.36i | −0.260395 | − | 0.189188i | ||||
\(521\) | −6206.20 | + | 4509.07i | −0.521878 | + | 0.379167i | −0.817311 | − | 0.576197i | \(-0.804536\pi\) |
0.295433 | + | 0.955363i | \(0.404536\pi\) | |||||||
\(522\) | 804.923 | − | 2477.30i | 0.0674914 | − | 0.207717i | ||||
\(523\) | 3934.95 | − | 12110.5i | 0.328993 | − | 1.01254i | −0.640613 | − | 0.767864i | \(-0.721320\pi\) |
0.969606 | − | 0.244672i | \(-0.0786802\pi\) | |||||||
\(524\) | −11255.2 | + | 8177.41i | −0.938335 | + | 0.681740i | ||||
\(525\) | 1888.10 | + | 1371.78i | 0.156959 | + | 0.114037i | ||||
\(526\) | −1302.04 | − | 4007.26i | −0.107931 | − | 0.332176i | ||||
\(527\) | 769.548 | 0.0636092 | ||||||||
\(528\) | −4100.22 | + | 4477.24i | −0.337953 | + | 0.369029i | ||||
\(529\) | −6104.66 | −0.501739 | ||||||||
\(530\) | 6538.18 | + | 20122.5i | 0.535850 | + | 1.64918i | ||||
\(531\) | 1192.76 | + | 866.592i | 0.0974792 | + | 0.0708228i | ||||
\(532\) | −4685.46 | + | 3404.19i | −0.381843 | + | 0.277425i | ||||
\(533\) | −470.250 | + | 1447.28i | −0.0382154 | + | 0.117615i | ||||
\(534\) | 10121.5 | − | 31150.9i | 0.820228 | − | 2.52440i | ||||
\(535\) | −12569.2 | + | 9132.09i | −1.01573 | + | 0.737971i | ||||
\(536\) | 12926.4 | + | 9391.55i | 1.04167 | + | 0.756816i | ||||
\(537\) | 1643.60 | + | 5058.50i | 0.132080 | + | 0.406499i | ||||
\(538\) | −13392.9 | −1.07325 | ||||||||
\(539\) | −830.264 | + | 7306.24i | −0.0663488 | + | 0.583863i | ||||
\(540\) | 20267.0 | 1.61509 | ||||||||
\(541\) | −1851.64 | − | 5698.75i | −0.147150 | − | 0.452881i | 0.850131 | − | 0.526571i | \(-0.176522\pi\) |
−0.997281 | + | 0.0736900i | \(0.976522\pi\) | |||||||
\(542\) | −25201.0 | − | 18309.6i | −1.99719 | − | 1.45104i | ||||
\(543\) | −4717.24 | + | 3427.28i | −0.372811 | + | 0.270863i | ||||
\(544\) | −402.277 | + | 1238.08i | −0.0317049 | + | 0.0975778i | ||||
\(545\) | 615.674 | − | 1894.85i | 0.0483900 | − | 0.148929i | ||||
\(546\) | 2737.57 | − | 1988.96i | 0.214574 | − | 0.155897i | ||||
\(547\) | 3104.23 | + | 2255.35i | 0.242646 | + | 0.176292i | 0.702461 | − | 0.711722i | \(-0.252084\pi\) |
−0.459815 | + | 0.888014i | \(0.652084\pi\) | |||||||
\(548\) | −10719.5 | − | 32991.1i | −0.835607 | − | 2.57173i | ||||
\(549\) | −2892.69 | −0.224876 | ||||||||
\(550\) | 841.500 | − | 7405.13i | 0.0652394 | − | 0.574101i | ||||
\(551\) | 3007.75 | 0.232549 | ||||||||
\(552\) | −3572.33 | − | 10994.5i | −0.275450 | − | 0.847749i | ||||
\(553\) | −4315.84 | − | 3135.64i | −0.331877 | − | 0.241123i | ||||
\(554\) | −39.6322 | + | 28.7945i | −0.00303937 | + | 0.00220823i | ||||
\(555\) | 931.810 | − | 2867.82i | 0.0712669 | − | 0.219337i | ||||
\(556\) | 9412.88 | − | 28969.9i | 0.717977 | − | 2.20971i | ||||
\(557\) | −18238.1 | + | 13250.8i | −1.38739 | + | 1.00800i | −0.391241 | + | 0.920288i | \(0.627954\pi\) |
−0.996146 | + | 0.0877076i | \(0.972046\pi\) | |||||||
\(558\) | 1170.74 | + | 850.594i | 0.0888198 | + | 0.0645314i | ||||
\(559\) | 1302.32 | + | 4008.13i | 0.0985372 | + | 0.303266i | ||||
\(560\) | −3913.42 | −0.295308 | ||||||||
\(561\) | 1713.80 | − | 1871.39i | 0.128978 | − | 0.140838i | ||||
\(562\) | 7960.51 | 0.597498 | ||||||||
\(563\) | 5390.47 | + | 16590.2i | 0.403519 | + | 1.24190i | 0.922126 | + | 0.386890i | \(0.126451\pi\) |
−0.518607 | + | 0.855013i | \(0.673549\pi\) | |||||||
\(564\) | 18283.3 | + | 13283.6i | 1.36501 | + | 0.991739i | ||||
\(565\) | 7916.34 | − | 5751.56i | 0.589456 | − | 0.428265i | ||||
\(566\) | −2177.84 | + | 6702.70i | −0.161734 | + | 0.497766i | ||||
\(567\) | −1954.92 | + | 6016.64i | −0.144796 | + | 0.445635i | ||||
\(568\) | −23088.0 | + | 16774.4i | −1.70555 | + | 1.23915i | ||||
\(569\) | 9882.48 | + | 7180.04i | 0.728111 | + | 0.529004i | 0.888965 | − | 0.457975i | \(-0.151425\pi\) |
−0.160854 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(570\) | 2019.79 | + | 6216.26i | 0.148420 | + | 0.456790i | ||||
\(571\) | −15055.4 | −1.10341 | −0.551706 | − | 0.834039i | \(-0.686023\pi\) | ||||
−0.551706 | + | 0.834039i | \(0.686023\pi\) | |||||||
\(572\) | −6381.20 | − | 2905.82i | −0.466454 | − | 0.212409i | ||||
\(573\) | −10753.9 | −0.784036 | ||||||||
\(574\) | 2053.50 | + | 6320.03i | 0.149323 | + | 0.459570i | ||||
\(575\) | 2695.84 | + | 1958.64i | 0.195520 | + | 0.142054i | ||||
\(576\) | −3384.22 | + | 2458.78i | −0.244808 | + | 0.177863i | ||||
\(577\) | −2355.29 | + | 7248.84i | −0.169934 | + | 0.523004i | −0.999366 | − | 0.0356042i | \(-0.988664\pi\) |
0.829432 | + | 0.558608i | \(0.188664\pi\) | |||||||
\(578\) | 6907.33 | − | 21258.6i | 0.497071 | − | 1.52983i | ||||
\(579\) | −6689.85 | + | 4860.46i | −0.480174 | + | 0.348867i | ||||
\(580\) | 9901.98 | + | 7194.21i | 0.708892 | + | 0.515040i | ||||
\(581\) | −3568.15 | − | 10981.6i | −0.254788 | − | 0.784157i | ||||
\(582\) | −13837.6 | −0.985548 | ||||||||
\(583\) | 8787.61 | + | 15521.4i | 0.624264 | + | 1.10263i | ||||
\(584\) | −4288.22 | −0.303849 | ||||||||
\(585\) | 217.668 | + | 669.913i | 0.0153837 | + | 0.0473462i | ||||
\(586\) | −37016.4 | − | 26894.0i | −2.60944 | − | 1.89587i | ||||
\(587\) | −5810.77 | + | 4221.77i | −0.408580 | + | 0.296850i | −0.773026 | − | 0.634374i | \(-0.781258\pi\) |
0.364447 | + | 0.931224i | \(0.381258\pi\) | |||||||
\(588\) | −4222.00 | + | 12994.0i | −0.296110 | + | 0.911332i | ||||
\(589\) | −516.364 | + | 1589.20i | −0.0361229 | + | 0.111175i | ||||
\(590\) | −8637.45 | + | 6275.47i | −0.602709 | + | 0.437894i | ||||
\(591\) | 6131.55 | + | 4454.83i | 0.426765 | + | 0.310063i | ||||
\(592\) | −813.480 | − | 2503.63i | −0.0564760 | − | 0.173815i | ||||
\(593\) | −6280.73 | −0.434939 | −0.217470 | − | 0.976067i | \(-0.569780\pi\) | ||||
−0.217470 | + | 0.976067i | \(0.569780\pi\) | |||||||
\(594\) | 25800.4 | − | 5257.05i | 1.78216 | − | 0.363130i | ||||
\(595\) | 1635.73 | 0.112703 | ||||||||
\(596\) | −1823.62 | − | 5612.53i | −0.125333 | − | 0.385736i | ||||
\(597\) | 13897.3 | + | 10097.0i | 0.952726 | + | 0.692196i | ||||
\(598\) | 3908.73 | − | 2839.86i | 0.267291 | − | 0.194198i | ||||
\(599\) | −3149.71 | + | 9693.81i | −0.214848 | + | 0.661233i | 0.784317 | + | 0.620360i | \(0.213014\pi\) |
−0.999164 | + | 0.0408722i | \(0.986986\pi\) | |||||||
\(600\) | 1963.57 | − | 6043.26i | 0.133604 | − | 0.411192i | ||||
\(601\) | 13250.7 | − | 9627.16i | 0.899343 | − | 0.653411i | −0.0389539 | − | 0.999241i | \(-0.512403\pi\) |
0.938297 | + | 0.345830i | \(0.112403\pi\) | |||||||
\(602\) | 14888.8 | + | 10817.3i | 1.00801 | + | 0.732362i | ||||
\(603\) | −911.240 | − | 2804.51i | −0.0615399 | − | 0.189400i | ||||
\(604\) | −7418.49 | −0.499759 | ||||||||
\(605\) | 1058.84 | + | 12021.1i | 0.0711535 | + | 0.807812i | ||||
\(606\) | 29169.1 | 1.95530 | ||||||||
\(607\) | 765.795 | + | 2356.88i | 0.0512070 | + | 0.157599i | 0.973390 | − | 0.229155i | \(-0.0735963\pi\) |
−0.922183 | + | 0.386754i | \(0.873596\pi\) | |||||||
\(608\) | −2286.85 | − | 1661.50i | −0.152540 | − | 0.110827i | ||||
\(609\) | −4028.48 | + | 2926.86i | −0.268049 | + | 0.194749i | ||||
\(610\) | 6473.14 | − | 19922.3i | 0.429656 | − | 1.32234i | ||||
\(611\) | −1339.30 | + | 4121.95i | −0.0886781 | + | 0.272923i | ||||
\(612\) | −1084.29 | + | 787.782i | −0.0716173 | + | 0.0520330i | ||||
\(613\) | −6917.19 | − | 5025.63i | −0.455763 | − | 0.331131i | 0.336104 | − | 0.941825i | \(-0.390891\pi\) |
−0.791867 | + | 0.610694i | \(0.790891\pi\) | |||||||
\(614\) | 9968.85 | + | 30681.0i | 0.655228 | + | 2.01658i | ||||
\(615\) | 4866.34 | 0.319073 | ||||||||
\(616\) | −13767.2 | + | 2805.18i | −0.900480 | + | 0.183481i | ||||
\(617\) | −4958.66 | −0.323547 | −0.161773 | − | 0.986828i | \(-0.551721\pi\) | ||||
−0.161773 | + | 0.986828i | \(0.551721\pi\) | |||||||
\(618\) | 5508.92 | + | 16954.7i | 0.358578 | + | 1.10359i | ||||
\(619\) | −13659.0 | − | 9923.83i | −0.886915 | − | 0.644382i | 0.0481565 | − | 0.998840i | \(-0.484665\pi\) |
−0.935072 | + | 0.354458i | \(0.884665\pi\) | |||||||
\(620\) | −5501.15 | + | 3996.82i | −0.356341 | + | 0.258897i | ||||
\(621\) | −3637.97 | + | 11196.5i | −0.235083 | + | 0.723511i | ||||
\(622\) | 9607.20 | − | 29567.9i | 0.619314 | − | 1.90605i | ||||
\(623\) | 14399.5 | − | 10461.9i | 0.926010 | − | 0.672786i | ||||
\(624\) | −1750.15 | − | 1271.56i | −0.112279 | − | 0.0815754i | ||||
\(625\) | −2609.26 | − | 8030.48i | −0.166993 | − | 0.513951i | ||||
\(626\) | −268.260 | −0.0171275 | ||||||||
\(627\) | 2714.68 | + | 4794.89i | 0.172909 | + | 0.305406i | ||||
\(628\) | 41796.8 | 2.65585 | ||||||||
\(629\) | 340.017 | + | 1046.47i | 0.0215538 | + | 0.0663359i | ||||
\(630\) | 2488.49 | + | 1807.99i | 0.157371 | + | 0.114337i | ||||
\(631\) | 383.020 | − | 278.280i | 0.0241645 | − | 0.0175565i | −0.575637 | − | 0.817705i | \(-0.695246\pi\) |
0.599802 | + | 0.800149i | \(0.295246\pi\) | |||||||
\(632\) | −4488.37 | + | 13813.8i | −0.282497 | + | 0.869435i | ||||
\(633\) | −319.041 | + | 981.906i | −0.0200327 | + | 0.0616545i | ||||
\(634\) | −5031.48 | + | 3655.58i | −0.315182 | + | 0.228993i | ||||
\(635\) | 5178.08 | + | 3762.10i | 0.323600 | + | 0.235109i | ||||
\(636\) | 10241.0 | + | 31518.7i | 0.638497 | + | 1.96509i | ||||
\(637\) | −2620.20 | −0.162977 | ||||||||
\(638\) | 14471.6 | + | 6589.94i | 0.898019 | + | 0.408932i | ||||
\(639\) | 5266.96 | 0.326068 | ||||||||
\(640\) | −7437.38 | − | 22889.9i | −0.459357 | − | 1.41375i | ||||
\(641\) | 25153.1 | + | 18274.8i | 1.54990 | + | 1.12607i | 0.943720 | + | 0.330745i | \(0.107300\pi\) |
0.606183 | + | 0.795325i | \(0.292700\pi\) | |||||||
\(642\) | −30341.4 | + | 22044.3i | −1.86523 | + | 1.35517i | ||||
\(643\) | 6058.25 | − | 18645.4i | 0.371562 | − | 1.14355i | −0.574208 | − | 0.818710i | \(-0.694690\pi\) |
0.945769 | − | 0.324839i | \(-0.105310\pi\) | |||||||
\(644\) | 4230.46 | − | 13020.0i | 0.258856 | − | 0.796677i | ||||
\(645\) | 10903.1 | − | 7921.54i | 0.665593 | − | 0.483582i | ||||
\(646\) | −1929.54 | − | 1401.89i | −0.117518 | − | 0.0853820i | ||||
\(647\) | 9409.54 | + | 28959.6i | 0.571758 | + | 1.75969i | 0.646964 | + | 0.762521i | \(0.276039\pi\) |
−0.0752061 | + | 0.997168i | \(0.523961\pi\) | |||||||
\(648\) | 17224.5 | 1.04420 | ||||||||
\(649\) | −6078.60 | + | 6637.55i | −0.367651 | + | 0.401458i | ||||
\(650\) | 2655.66 | 0.160252 | ||||||||
\(651\) | −854.864 | − | 2631.00i | −0.0514666 | − | 0.158398i | ||||
\(652\) | −43633.7 | − | 31701.7i | −2.62090 | − | 1.90419i | ||||
\(653\) | 25029.2 | − | 18184.8i | 1.49995 | − | 1.08978i | 0.529549 | − | 0.848280i | \(-0.322361\pi\) |
0.970401 | − | 0.241498i | \(-0.0776387\pi\) | |||||||
\(654\) | 1486.20 | − | 4574.05i | 0.0888608 | − | 0.273486i | ||||
\(655\) | −2636.53 | + | 8114.42i | −0.157279 | + | 0.484056i | ||||
\(656\) | 3437.00 | − | 2497.13i | 0.204561 | − | 0.148623i | ||||
\(657\) | 640.275 | + | 465.187i | 0.0380206 | + | 0.0276235i | ||||
\(658\) | 5848.50 | + | 17999.8i | 0.346502 | + | 1.06642i | ||||
\(659\) | 31012.0 | 1.83317 | 0.916584 | − | 0.399842i | \(-0.130935\pi\) | ||||
0.916584 | + | 0.399842i | \(0.130935\pi\) | |||||||
\(660\) | −2531.70 | + | 22278.8i | −0.149313 | + | 1.31394i | ||||
\(661\) | 6859.42 | 0.403632 | 0.201816 | − | 0.979423i | \(-0.435316\pi\) | ||||
0.201816 | + | 0.979423i | \(0.435316\pi\) | |||||||
\(662\) | 8602.79 | + | 26476.7i | 0.505071 | + | 1.55445i | ||||
\(663\) | 731.524 | + | 531.484i | 0.0428508 | + | 0.0311329i | ||||
\(664\) | −25434.1 | + | 18479.0i | −1.48650 | + | 1.08001i | ||||
\(665\) | −1097.57 | + | 3377.96i | −0.0640027 | + | 0.196980i | ||||
\(666\) | −639.393 | + | 1967.85i | −0.0372012 | + | 0.114493i | ||||
\(667\) | −5751.88 | + | 4178.99i | −0.333904 | + | 0.242595i | ||||
\(668\) | 17482.8 | + | 12702.0i | 1.01262 | + | 0.735712i | ||||
\(669\) | −1339.58 | − | 4122.81i | −0.0774158 | − | 0.238261i | ||||
\(670\) | 21354.1 | 1.23132 | ||||||||
\(671\) | 1993.89 | − | 17546.0i | 0.114714 | − | 1.00947i | ||||
\(672\) | 4679.74 | 0.268638 | ||||||||
\(673\) | −4318.02 | − | 13289.5i | −0.247321 | − | 0.761177i | −0.995246 | − | 0.0973934i | \(-0.968950\pi\) |
0.747925 | − | 0.663784i | \(-0.231050\pi\) | |||||||
\(674\) | −38976.5 | − | 28318.1i | −2.22748 | − | 1.61836i | ||||
\(675\) | −5235.15 | + | 3803.56i | −0.298520 | + | 0.216888i | ||||
\(676\) | 772.073 | − | 2376.20i | 0.0439277 | − | 0.135195i | ||||
\(677\) | 5256.08 | − | 16176.5i | 0.298386 | − | 0.918338i | −0.683677 | − | 0.729785i | \(-0.739620\pi\) |
0.982063 | − | 0.188553i | \(-0.0603798\pi\) | |||||||
\(678\) | 19109.6 | − | 13883.9i | 1.08245 | − | 0.786443i | ||||
\(679\) | −6083.39 | − | 4419.84i | −0.343828 | − | 0.249806i | ||||
\(680\) | −1376.23 | − | 4235.61i | −0.0776119 | − | 0.238865i | ||||
\(681\) | 5657.83 | 0.318368 | ||||||||
\(682\) | −5966.37 | + | 6515.00i | −0.334992 | + | 0.365795i | ||||
\(683\) | 11464.8 | 0.642298 | 0.321149 | − | 0.947029i | \(-0.395931\pi\) | ||||
0.321149 | + | 0.947029i | \(0.395931\pi\) | |||||||
\(684\) | −899.305 | − | 2767.78i | −0.0502716 | − | 0.154720i | ||||
\(685\) | −17210.9 | − | 12504.4i | −0.959990 | − | 0.697473i | ||||
\(686\) | −25009.7 | + | 18170.6i | −1.39194 | + | 1.01131i | ||||
\(687\) | −6606.95 | + | 20334.1i | −0.366915 | + | 1.12925i | ||||
\(688\) | 3635.74 | − | 11189.7i | 0.201470 | − | 0.620061i | ||||
\(689\) | −5141.84 | + | 3735.76i | −0.284308 | + | 0.206562i | ||||
\(690\) | −12499.4 | − | 9081.38i | −0.689632 | − | 0.501047i | ||||
\(691\) | 1565.81 | + | 4819.06i | 0.0862028 | + | 0.265305i | 0.984861 | − | 0.173344i | \(-0.0554572\pi\) |
−0.898659 | + | 0.438649i | \(0.855457\pi\) | |||||||
\(692\) | −48034.0 | −2.63870 | ||||||||
\(693\) | 2359.89 | + | 1074.62i | 0.129357 | + | 0.0589056i | ||||
\(694\) | −55677.6 | −3.04538 | ||||||||
\(695\) | −5772.67 | − | 17766.5i | −0.315065 | − | 0.969669i | ||||
\(696\) | 10968.3 | + | 7968.93i | 0.597345 | + | 0.433997i | ||||
\(697\) | −1436.59 | + | 1043.75i | −0.0780700 | + | 0.0567212i | ||||
\(698\) | −14062.0 | + | 43278.4i | −0.762542 | + | 2.34686i | ||||
\(699\) | 3464.63 | − | 10663.0i | 0.187474 | − | 0.576985i | ||||
\(700\) | 6087.76 | − | 4423.02i | 0.328708 | − | 0.238821i | ||||
\(701\) | −28061.0 | − | 20387.5i | −1.51191 | − | 1.09847i | −0.965320 | − | 0.261070i | \(-0.915925\pi\) |
−0.546592 | − | 0.837399i | \(-0.684075\pi\) | |||||||
\(702\) | 2899.32 | + | 8923.19i | 0.155880 | + | 0.479749i | ||||
\(703\) | −2389.22 | −0.128181 | ||||||||
\(704\) | −12581.4 | − | 22222.3i | −0.673551 | − | 1.18968i | ||||
\(705\) | 13859.6 | 0.740402 | ||||||||
\(706\) | 15603.4 | + | 48022.2i | 0.831785 | + | 2.55997i | ||||
\(707\) | 12823.5 | + | 9316.81i | 0.682145 | + | 0.495608i | ||||
\(708\) | −13529.2 | + | 9829.56i | −0.718163 | + | 0.521776i | ||||
\(709\) | 3646.31 | − | 11222.2i | 0.193145 | − | 0.594440i | −0.806848 | − | 0.590759i | \(-0.798828\pi\) |
0.999993 | − | 0.00368076i | \(-0.00117162\pi\) | |||||||
\(710\) | −11786.2 | + | 36274.2i | −0.622998 | + | 1.91739i | ||||
\(711\) | 2168.68 | − | 1575.64i | 0.114391 | − | 0.0831098i | ||||
\(712\) | −39205.4 | − | 28484.4i | −2.06360 | − | 1.49930i | ||||
\(713\) | −1220.58 | − | 3756.56i | −0.0641109 | − | 0.197313i | ||||
\(714\) | 3948.55 | 0.206962 | ||||||||
\(715\) | −4213.49 | + | 858.536i | −0.220386 | + | 0.0449055i | ||||
\(716\) | 17149.4 | 0.895116 | ||||||||
\(717\) | −8112.46 | − | 24967.6i | −0.422546 | − | 1.30046i | ||||
\(718\) | −30390.4 | − | 22079.9i | −1.57961 | − | 1.14765i | ||||
\(719\) | 575.018 | − | 417.775i | 0.0298255 | − | 0.0216695i | −0.572773 | − | 0.819714i | \(-0.694132\pi\) |
0.602598 | + | 0.798045i | \(0.294132\pi\) | |||||||
\(720\) | 607.673 | − | 1870.22i | 0.0314536 | − | 0.0968044i | ||||
\(721\) | −2993.59 | + | 9213.32i | −0.154628 | + | 0.475897i | ||||
\(722\) | −22297.2 | + | 16199.9i | −1.14933 | + | 0.835037i | ||||
\(723\) | −10337.0 | − | 7510.29i | −0.531727 | − | 0.386322i | ||||
\(724\) | 5809.61 | + | 17880.1i | 0.298221 | + | 0.917831i | ||||
\(725\) | −3907.94 | −0.200189 | ||||||||
\(726\) | 2555.97 | + | 29018.1i | 0.130662 | + | 1.48342i | ||||
\(727\) | 10823.4 | 0.552159 | 0.276079 | − | 0.961135i | \(-0.410965\pi\) | ||||
0.276079 | + | 0.961135i | \(0.410965\pi\) | |||||||
\(728\) | −1547.09 | − | 4761.45i | −0.0787622 | − | 0.242405i | ||||
\(729\) | −17715.5 | − | 12871.1i | −0.900042 | − | 0.653919i | ||||
\(730\) | −4636.58 | + | 3368.68i | −0.235079 | + | 0.170795i | ||||
\(731\) | −1519.66 | + | 4677.04i | −0.0768902 | + | 0.236644i | ||||
\(732\) | 10139.2 | − | 31205.2i | 0.511960 | − | 1.57565i | ||||
\(733\) | −11093.6 | + | 8060.00i | −0.559008 | + | 0.406143i | −0.831096 | − | 0.556129i | \(-0.812286\pi\) |
0.272088 | + | 0.962272i | \(0.412286\pi\) | |||||||
\(734\) | −27955.4 | − | 20310.8i | −1.40579 | − | 1.02137i | ||||
\(735\) | 2589.24 | + | 7968.87i | 0.129940 | + | 0.399913i | ||||
\(736\) | 6681.76 | 0.334637 | ||||||||
\(737\) | 17639.3 | − | 3594.16i | 0.881616 | − | 0.179637i | ||||
\(738\) | −3339.21 | −0.166555 | ||||||||
\(739\) | −8871.73 | − | 27304.4i | −0.441613 | − | 1.35914i | −0.886156 | − | 0.463387i | \(-0.846634\pi\) |
0.444543 | − | 0.895757i | \(-0.353366\pi\) | |||||||
\(740\) | −7865.68 | − | 5714.75i | −0.390741 | − | 0.283890i | ||||
\(741\) | −1588.42 | + | 1154.06i | −0.0787479 | + | 0.0572137i | ||||
\(742\) | −8576.48 | + | 26395.7i | −0.424330 | + | 1.30595i | ||||
\(743\) | 8106.28 | − | 24948.6i | 0.400257 | − | 1.23186i | −0.524535 | − | 0.851389i | \(-0.675761\pi\) |
0.924791 | − | 0.380474i | \(-0.124239\pi\) | |||||||
\(744\) | −6093.55 | + | 4427.23i | −0.300270 | + | 0.218159i | ||||
\(745\) | −2927.96 | − | 2127.28i | −0.143989 | − | 0.104614i | ||||
\(746\) | 2196.69 | + | 6760.72i | 0.107810 | + | 0.331807i | ||||
\(747\) | 5802.18 | 0.284191 | ||||||||
\(748\) | −4031.02 | − | 7119.92i | −0.197044 | − | 0.348035i | ||||
\(749\) | −20380.0 | −0.994216 | ||||||||
\(750\) | −10289.2 | − | 31666.8i | −0.500943 | − | 1.54174i | ||||
\(751\) | −17442.7 | − | 12672.9i | −0.847528 | − | 0.615765i | 0.0769353 | − | 0.997036i | \(-0.475487\pi\) |
−0.924463 | + | 0.381271i | \(0.875487\pi\) | |||||||
\(752\) | 9788.78 | − | 7111.97i | 0.474681 | − | 0.344876i | ||||
\(753\) | 6506.88 | − | 20026.1i | 0.314906 | − | 0.969180i | ||||
\(754\) | −1750.94 | + | 5388.85i | −0.0845697 | + | 0.260279i | ||||
\(755\) | −3680.68 | + | 2674.17i | −0.177422 | + | 0.128905i | ||||
\(756\) | 21507.9 | + | 15626.4i | 1.03470 | + | 0.751756i | ||||
\(757\) | −4906.09 | − | 15099.4i | −0.235555 | − | 0.724962i | −0.997047 | − | 0.0767891i | \(-0.975533\pi\) |
0.761493 | − | 0.648173i | \(-0.224467\pi\) | |||||||
\(758\) | 50243.3 | 2.40755 | ||||||||
\(759\) | −11853.5 | − | 5397.73i | −0.566870 | − | 0.258136i | ||||
\(760\) | 9670.46 | 0.461559 | ||||||||
\(761\) | 4799.68 | + | 14771.9i | 0.228631 | + | 0.703654i | 0.997903 | + | 0.0647319i | \(0.0206192\pi\) |
−0.769272 | + | 0.638922i | \(0.779381\pi\) | |||||||
\(762\) | 12499.6 | + | 9081.47i | 0.594241 | + | 0.431741i | ||||
\(763\) | 2114.36 | − | 1536.17i | 0.100321 | − | 0.0728874i | ||||
\(764\) | −10714.8 | + | 32976.8i | −0.507392 | + | 1.56159i | ||||
\(765\) | −253.994 | + | 781.714i | −0.0120042 | + | 0.0369450i | ||||
\(766\) | 53640.8 | − | 38972.3i | 2.53019 | − | 1.83829i | ||||
\(767\) | −2594.61 | − | 1885.09i | −0.122146 | − | 0.0887441i | ||||
\(768\) | −10019.2 | − | 30835.9i | −0.470750 | − | 1.44882i | ||||
\(769\) | 31012.1 | 1.45426 | 0.727130 | − | 0.686500i | \(-0.240854\pi\) | ||||
0.727130 | + | 0.686500i | \(0.240854\pi\) | |||||||
\(770\) | −12681.9 | + | 13848.1i | −0.593539 | + | 0.648117i | ||||
\(771\) | −15632.7 | −0.730220 | ||||||||
\(772\) | 8239.01 | + | 25357.1i | 0.384104 | + | 1.18215i | ||||
\(773\) | 9404.13 | + | 6832.50i | 0.437572 | + | 0.317915i | 0.784669 | − | 0.619914i | \(-0.212833\pi\) |
−0.347097 | + | 0.937829i | \(0.612833\pi\) | |||||||
\(774\) | −7481.52 | + | 5435.64i | −0.347439 | + | 0.252429i | ||||
\(775\) | 670.906 | − | 2064.84i | 0.0310963 | − | 0.0957046i | ||||
\(776\) | −6326.58 | + | 19471.2i | −0.292669 | + | 0.900742i | ||||
\(777\) | 3200.03 | − | 2324.96i | 0.147748 | − | 0.107346i | ||||
\(778\) | 12015.2 | + | 8729.59i | 0.553686 | + | 0.402276i | ||||
\(779\) | −1191.50 | − | 3667.07i | −0.0548011 | − | 0.168661i | ||||
\(780\) | −7989.72 | −0.366766 | ||||||||
\(781\) | −3630.44 | + | 31947.5i | −0.166334 | + | 1.46373i | ||||
\(782\) | 5637.76 | 0.257808 | ||||||||
\(783\) | −4266.49 | − | 13130.9i | −0.194728 | − | 0.599311i | ||||
\(784\) | 5917.90 | + | 4299.60i | 0.269583 | + | 0.195864i | ||||
\(785\) | 20737.4 | − | 15066.6i | 0.942866 | − | 0.685033i | ||||
\(786\) | −6364.43 | + | 19587.7i | −0.288819 | + | 0.888894i | ||||
\(787\) | −9571.94 | + | 29459.4i | −0.433549 | + | 1.33433i | 0.461018 | + | 0.887391i | \(0.347484\pi\) |
−0.894567 | + | 0.446934i | \(0.852516\pi\) | |||||||
\(788\) | 19769.9 | − | 14363.6i | 0.893747 | − | 0.649345i | ||||
\(789\) | −3274.46 | − | 2379.04i | −0.147749 | − | 0.107346i | ||||
\(790\) | 5998.63 | + | 18461.9i | 0.270154 | + | 0.831449i | ||||
\(791\) | 12835.7 | 0.576971 | ||||||||
\(792\) | 797.158 | − | 7014.92i | 0.0357648 | − | 0.314727i | ||||
\(793\) | 6292.44 | 0.281779 | ||||||||
\(794\) | 10525.9 | + | 32395.4i | 0.470467 | + | 1.44795i | ||||
\(795\) | 16442.7 | + | 11946.3i | 0.733539 | + | 0.532947i | ||||
\(796\) | 44808.8 | − | 32555.5i | 1.99523 | − | 1.44962i | ||||
\(797\) | −11696.9 | + | 35999.2i | −0.519855 | + | 1.59995i | 0.254417 | + | 0.967095i | \(0.418116\pi\) |
−0.774272 | + | 0.632853i | \(0.781884\pi\) | |||||||
\(798\) | −2649.46 | + | 8154.20i | −0.117531 | + | 0.361724i | ||||
\(799\) | −4091.50 | + | 2972.65i | −0.181160 | + | 0.131620i | ||||
\(800\) | 2971.28 | + | 2158.76i | 0.131313 | + | 0.0954047i | ||||
\(801\) | 2763.78 | + | 8506.03i | 0.121914 | + | 0.375213i | ||||
\(802\) | 70002.0 | 3.08212 | ||||||||
\(803\) | −3262.99 | + | 3563.04i | −0.143398 | + | 0.156584i | ||||
\(804\) | 33448.0 | 1.46719 | ||||||||
\(805\) | −2594.43 | − | 7984.82i | −0.113592 | − | 0.349600i | ||||
\(806\) | −2546.71 | − | 1850.29i | −0.111295 | − | 0.0808606i | ||||
\(807\) | −10408.2 | + | 7561.98i | −0.454009 | + | 0.329857i | ||||
\(808\) | 13336.1 | − | 41044.3i | 0.580647 | − | 1.78705i | ||||
\(809\) | 6116.04 | − | 18823.2i | 0.265795 | − | 0.818034i | −0.725714 | − | 0.687997i | \(-0.758490\pi\) |
0.991509 | − | 0.130037i | \(-0.0415097\pi\) | |||||||
\(810\) | 18623.8 | − | 13531.0i | 0.807867 | − | 0.586950i | ||||
\(811\) | −2178.81 | − | 1583.00i | −0.0943381 | − | 0.0685407i | 0.539616 | − | 0.841911i | \(-0.318569\pi\) |
−0.633954 | + | 0.773370i | \(0.718569\pi\) | |||||||
\(812\) | 4961.34 | + | 15269.4i | 0.214420 | + | 0.659917i | ||||
\(813\) | −29922.8 | −1.29082 | ||||||||
\(814\) | −11495.6 | − | 5234.75i | −0.494987 | − | 0.225403i | ||||
\(815\) | −33076.4 | −1.42161 | ||||||||
\(816\) | −780.061 | − | 2400.78i | −0.0334652 | − | 0.102995i | ||||
\(817\) | −8638.93 | − | 6276.55i | −0.369936 | − | 0.268774i | ||||
\(818\) | 22142.5 | − | 16087.5i | 0.946449 | − | 0.687635i | ||||
\(819\) | −285.527 | + | 878.761i | −0.0121821 | + | 0.0374925i | ||||
\(820\) | 4848.62 | − | 14922.5i | 0.206489 | − | 0.635509i | ||||
\(821\) | 2512.36 | − | 1825.34i | 0.106799 | − | 0.0775941i | −0.533104 | − | 0.846050i | \(-0.678975\pi\) |
0.639903 | + | 0.768456i | \(0.278975\pi\) | |||||||
\(822\) | −41546.0 | − | 30184.9i | −1.76287 | − | 1.28080i | ||||
\(823\) | −13040.1 | − | 40133.4i | −0.552309 | − | 1.69983i | −0.702947 | − | 0.711242i | \(-0.748133\pi\) |
0.150638 | − | 0.988589i | \(-0.451867\pi\) | |||||||
\(824\) | 26376.0 | 1.11511 | ||||||||
\(825\) | −3527.16 | − | 6229.95i | −0.148848 | − | 0.262908i | ||||
\(826\) | −14004.9 | −0.589943 | ||||||||
\(827\) | −11188.1 | − | 34433.4i | −0.470432 | − | 1.44784i | −0.852020 | − | 0.523509i | \(-0.824623\pi\) |
0.381588 | − | 0.924333i | \(-0.375377\pi\) | |||||||
\(828\) | 5565.35 | + | 4043.47i | 0.233586 | + | 0.169710i | ||||
\(829\) | −9698.64 | + | 7046.47i | −0.406330 | + | 0.295216i | −0.772114 | − | 0.635484i | \(-0.780801\pi\) |
0.365784 | + | 0.930700i | \(0.380801\pi\) | |||||||
\(830\) | −12983.9 | + | 39960.3i | −0.542985 | + | 1.67114i | ||||
\(831\) | −14.5417 | + | 44.7546i | −0.000607033 | + | 0.00186826i | ||||
\(832\) | 7361.68 | − | 5348.57i | 0.306755 | − | 0.222871i | ||||
\(833\) | −2473.55 | − | 1797.14i | −0.102885 | − | 0.0747506i | ||||
\(834\) | −13934.9 | − | 42887.1i | −0.578568 | − | 1.78065i | ||||
\(835\) | 13252.8 | 0.549260 | ||||||||
\(836\) | 17408.2 | − | 3547.08i | 0.720187 | − | 0.146744i | ||||
\(837\) | 7670.43 | 0.316761 | ||||||||
\(838\) | 20961.0 | + | 64511.4i | 0.864065 | + | 2.65932i | ||||
\(839\) | −8917.59 | − | 6479.01i | −0.366948 | − | 0.266603i | 0.388996 | − | 0.921239i | \(-0.372822\pi\) |
−0.755944 | + | 0.654636i | \(0.772822\pi\) | |||||||
\(840\) | −12952.3 | + | 9410.37i | −0.532019 | + | 0.386534i | ||||
\(841\) | −4960.02 | + | 15265.4i | −0.203371 | + | 0.625912i | ||||
\(842\) | 20385.3 | − | 62739.5i | 0.834352 | − | 2.56787i | ||||
\(843\) | 6186.43 | − | 4494.70i | 0.252754 | − | 0.183637i | ||||
\(844\) | 2693.12 | + | 1956.66i | 0.109835 | + | 0.0797999i | ||||
\(845\) | −473.492 | − | 1457.26i | −0.0192765 | − | 0.0593268i | ||||
\(846\) | −9510.26 | −0.386489 | ||||||||
\(847\) | −8144.92 | + | 13573.5i | −0.330417 | + | 0.550640i | ||||
\(848\) | 17743.3 | 0.718525 | ||||||||
\(849\) | 2092.03 | + | 6438.60i | 0.0845679 | + | 0.260273i | ||||
\(850\) | 2507.03 | + | 1821.46i | 0.101165 | + | 0.0735008i | ||||
\(851\) | 4569.03 | − | 3319.59i | 0.184047 | − | 0.133718i | ||||
\(852\) | −18461.3 | + | 56817.9i | −0.742338 | + | 2.28468i | ||||
\(853\) | −8585.93 | + | 26424.8i | −0.344639 | + | 1.06069i | 0.617138 | + | 0.786855i | \(0.288292\pi\) |
−0.961777 | + | 0.273834i | \(0.911708\pi\) | |||||||
\(854\) | 22230.2 | − | 16151.2i | 0.890750 | − | 0.647168i | ||||
\(855\) | −1443.90 | − | 1049.05i | −0.0577547 | − | 0.0419613i | ||||
\(856\) | 17146.8 | + | 52772.6i | 0.684658 | + | 2.10716i | ||||
\(857\) | −29633.9 | −1.18118 | −0.590592 | − | 0.806970i | \(-0.701106\pi\) | ||||
−0.590592 | + | 0.806970i | \(0.701106\pi\) | |||||||
\(858\) | −10171.1 | + | 2072.45i | −0.404704 | + | 0.0824620i | ||||
\(859\) | −24852.1 | −0.987126 | −0.493563 | − | 0.869710i | \(-0.664306\pi\) | ||||
−0.493563 | + | 0.869710i | \(0.664306\pi\) | |||||||
\(860\) | −13427.9 | − | 41326.7i | −0.532426 | − | 1.63864i | ||||
\(861\) | 5164.31 | + | 3752.09i | 0.204412 | + | 0.148514i | ||||
\(862\) | 19602.0 | − | 14241.7i | 0.774533 | − | 0.562731i | ||||
\(863\) | 13437.0 | − | 41354.8i | 0.530012 | − | 1.63121i | −0.224176 | − | 0.974549i | \(-0.571969\pi\) |
0.754187 | − | 0.656659i | \(-0.228031\pi\) | |||||||
\(864\) | −4009.67 | + | 12340.5i | −0.157884 | + | 0.485917i | ||||
\(865\) | −23832.0 | + | 17315.0i | −0.936777 | + | 0.680608i | ||||
\(866\) | 26266.1 | + | 19083.4i | 1.03067 | + | 0.748823i | ||||
\(867\) | −6635.16 | − | 20420.9i | −0.259910 | − | 0.799920i | ||||
\(868\) | −8919.66 | −0.348794 | ||||||||
\(869\) | 8062.43 | + | 14240.5i | 0.314729 | + | 0.555900i | ||||
\(870\) | 18119.5 | 0.706100 | ||||||||
\(871\) | 1982.21 | + | 6100.63i | 0.0771122 | + | 0.237327i | ||||
\(872\) | −5756.74 | − | 4182.52i | −0.223564 | − | 0.162429i | ||||
\(873\) | 3056.86 | − | 2220.94i | 0.118510 | − | 0.0861025i | ||||
\(874\) | −3782.92 | + | 11642.6i | −0.146406 | + | 0.450592i | ||||
\(875\) | 5591.21 | − | 17208.0i | 0.216020 | − | 0.664841i | ||||
\(876\) | −7262.49 | + | 5276.51i | −0.280110 | + | 0.203512i | ||||
\(877\) | 14957.8 | + | 10867.5i | 0.575928 | + | 0.418437i | 0.837254 | − | 0.546814i | \(-0.184160\pi\) |
−0.261326 | + | 0.965251i | \(0.584160\pi\) | |||||||
\(878\) | −15870.7 | − | 48845.1i | −0.610036 | − | 1.87750i | ||||
\(879\) | −43951.9 | −1.68653 | ||||||||
\(880\) | 10925.3 | + | 4975.05i | 0.418512 | + | 0.190578i | ||||
\(881\) | 14831.7 | 0.567189 | 0.283594 | − | 0.958944i | \(-0.408473\pi\) | ||||
0.283594 | + | 0.958944i | \(0.408473\pi\) | |||||||
\(882\) | −1776.70 | − | 5468.11i | −0.0678283 | − | 0.208754i | ||||
\(883\) | −3371.26 | − | 2449.36i | −0.128485 | − | 0.0933495i | 0.521687 | − | 0.853137i | \(-0.325303\pi\) |
−0.650171 | + | 0.759788i | \(0.725303\pi\) | |||||||
\(884\) | 2358.64 | − | 1713.66i | 0.0897396 | − | 0.0651996i | ||||
\(885\) | −3169.21 | + | 9753.84i | −0.120375 | + | 0.370477i | ||||
\(886\) | −14045.7 | + | 43228.1i | −0.532588 | + | 1.63914i | ||||
\(887\) | 27259.9 | − | 19805.5i | 1.03190 | − | 0.749722i | 0.0632153 | − | 0.998000i | \(-0.479865\pi\) |
0.968689 | + | 0.248278i | \(0.0798645\pi\) | |||||||
\(888\) | −8712.71 | − | 6330.15i | −0.329256 | − | 0.239218i | ||||
\(889\) | 2594.45 | + | 7984.90i | 0.0978798 | + | 0.301243i | ||||
\(890\) | −64766.7 | −2.43931 | ||||||||
\(891\) | 13106.5 | − | 14311.6i | 0.492798 | − | 0.538112i | ||||
\(892\) | −13977.2 | −0.524654 | ||||||||
\(893\) | −3393.48 | − | 10444.0i | −0.127165 | − | 0.391374i | ||||
\(894\) | −7067.91 | − | 5135.13i | −0.264414 | − | 0.192108i | ||||
\(895\) | 8508.65 | − | 6181.89i | 0.317779 | − | 0.230880i | ||||
\(896\) | 9756.01 | − | 30025.9i | 0.363756 | − | 1.11953i | ||||
\(897\) | 1434.17 | − | 4413.93i | 0.0533842 | − | 0.164300i | ||||
\(898\) | 4596.88 | − | 3339.83i | 0.170824 | − | 0.124111i | ||||
\(899\) | 3747.60 | + | 2722.79i | 0.139032 | + | 0.101012i | ||||
\(900\) | 1168.46 | + | 3596.14i | 0.0432762 | + | 0.133190i | ||||
\(901\) | −7416.34 | −0.274222 | ||||||||
\(902\) | 2301.67 | − | 20254.4i | 0.0849635 | − | 0.747671i | ||||
\(903\) | 17678.4 | 0.651496 | ||||||||
\(904\) | −10799.4 | − | 33237.1i | −0.397326 | − | 1.22284i | ||||
\(905\) | 9327.73 | + | 6776.99i | 0.342612 | + | 0.248923i | ||||
\(906\) | −8884.93 | + | 6455.28i | −0.325808 | + | 0.236713i | ||||
\(907\) | −1484.93 | + | 4570.16i | −0.0543621 | + | 0.167309i | −0.974551 | − | 0.224165i | \(-0.928035\pi\) |
0.920189 | + | 0.391474i | \(0.128035\pi\) | |||||||
\(908\) | 5637.23 | − | 17349.6i | 0.206033 | − | 0.634104i | ||||
\(909\) | −6443.72 | + | 4681.63i | −0.235121 | + | 0.170825i | ||||
\(910\) | −5413.20 | − | 3932.92i | −0.197193 | − | 0.143269i | ||||
\(911\) | −9.69861 | − | 29.8493i | −0.000352722 | − | 0.00108557i | 0.950880 | − | 0.309560i | \(-0.100182\pi\) |
−0.951233 | + | 0.308474i | \(0.900182\pi\) | |||||||
\(912\) | 5481.30 | 0.199018 | ||||||||
\(913\) | −3999.36 | + | 35194.0i | −0.144972 | + | 1.27574i | ||||
\(914\) | 82267.3 | 2.97720 | ||||||||
\(915\) | −6218.09 | − | 19137.3i | −0.224660 | − | 0.691431i | ||||
\(916\) | 55771.2 | + | 40520.1i | 2.01172 | + | 1.46160i | ||||
\(917\) | −9054.43 | + | 6578.42i | −0.326067 | + | 0.236902i | ||||
\(918\) | −3383.18 | + | 10412.4i | −0.121636 | + | 0.374356i | ||||
\(919\) | −723.403 | + | 2226.40i | −0.0259661 | + | 0.0799155i | −0.963200 | − | 0.268786i | \(-0.913377\pi\) |
0.937234 | + | 0.348702i | \(0.113377\pi\) | |||||||
\(920\) | −18493.3 | + | 13436.2i | −0.662725 | + | 0.481498i | ||||
\(921\) | 25070.4 | + | 18214.7i | 0.896958 | + | 0.651678i | ||||
\(922\) | 24366.0 | + | 74991.0i | 0.870339 | + | 2.67863i | ||||
\(923\) | −11457.2 | −0.408578 | ||||||||
\(924\) | −19864.3 | + | 21690.9i | −0.707237 | + | 0.772270i | ||||
\(925\) | 3104.28 | 0.110344 | ||||||||
\(926\) | 12094.4 | + | 37222.7i | 0.429208 | + | 1.32097i | ||||
\(927\) | −3938.20 | − | 2861.27i | −0.139533 | − | 0.101377i | ||||
\(928\) | −6339.58 | + | 4605.97i | −0.224253 | + | 0.162929i | ||||
\(929\) | −720.206 | + | 2216.57i | −0.0254351 | + | 0.0782811i | −0.962968 | − | 0.269615i | \(-0.913104\pi\) |
0.937533 | + | 0.347896i | \(0.113104\pi\) | |||||||
\(930\) | −3110.71 | + | 9573.77i | −0.109682 | + | 0.337566i | ||||
\(931\) | 5371.05 | − | 3902.29i | 0.189075 | − | 0.137371i | ||||
\(932\) | −29245.9 | − | 21248.4i | −1.02788 | − | 0.746797i | ||||
\(933\) | −9228.65 | − | 28402.9i | −0.323829 | − | 0.996643i | ||||
\(934\) | 73551.1 | 2.57673 | ||||||||
\(935\) | −4566.52 | − | 2079.46i | −0.159723 | − | 0.0727334i | ||||
\(936\) | 2515.72 | 0.0878515 | ||||||||
\(937\) | 5036.56 | + | 15501.0i | 0.175600 | + | 0.540442i | 0.999660 | − | 0.0260604i | \(-0.00829623\pi\) |
−0.824060 | + | 0.566502i | \(0.808296\pi\) | |||||||
\(938\) | 22661.7 | + | 16464.7i | 0.788838 | + | 0.573124i | ||||
\(939\) | −208.475 | + | 151.466i | −0.00724530 | + | 0.00526402i | ||||
\(940\) | 13809.2 | − | 42500.2i | 0.479155 | − | 1.47469i | ||||
\(941\) | −7515.64 | + | 23130.8i | −0.260364 | + | 0.801319i | 0.732361 | + | 0.680917i | \(0.238418\pi\) |
−0.992725 | + | 0.120402i | \(0.961582\pi\) | |||||||
\(942\) | 50058.9 | − | 36369.9i | 1.73143 | − | 1.25796i | ||||
\(943\) | 7373.63 | + | 5357.26i | 0.254632 | + | 0.185001i | ||||
\(944\) | 2766.76 | + | 8515.21i | 0.0953923 | + | 0.293587i | ||||
\(945\) | 16304.0 | 0.561238 | ||||||||
\(946\) | −27813.8 | − | 49126.9i | −0.955924 | − | 1.68843i | ||||
\(947\) | 39588.2 | 1.35844 | 0.679221 | − | 0.733934i | \(-0.262318\pi\) | ||||
0.679221 | + | 0.733934i | \(0.262318\pi\) | |||||||
\(948\) | 9395.93 | + | 28917.7i | 0.321905 | + | 0.990720i | ||||
\(949\) | −1392.79 | − | 1011.92i | −0.0476414 | − | 0.0346135i | ||||
\(950\) | −5443.74 | + | 3955.11i | −0.185914 | + | 0.135074i | ||||
\(951\) | −1846.13 | + | 5681.80i | −0.0629493 | + | 0.193738i | ||||
\(952\) | 1805.28 | − | 5556.07i | 0.0614594 | − | 0.189153i | ||||
\(953\) | 20291.1 | − | 14742.3i | 0.689708 | − | 0.501102i | −0.186856 | − | 0.982387i | \(-0.559830\pi\) |
0.876564 | + | 0.481285i | \(0.159830\pi\) | |||||||
\(954\) | −11282.7 | − | 8197.39i | −0.382906 | − | 0.278197i | ||||
\(955\) | 6571.10 | + | 20223.8i | 0.222655 | + | 0.685262i | ||||
\(956\) | −84645.5 | −2.86363 | ||||||||
\(957\) | 14967.3 | − | 3049.72i | 0.505563 | − | 0.103013i | ||||
\(958\) | −64657.4 | −2.18057 | ||||||||
\(959\) | −8623.41 | − | 26540.1i | −0.290370 | − | 0.893666i | ||||
\(960\) | −23541.4 | − | 17103.8i | −0.791454 | − | 0.575025i | ||||
\(961\) | 22019.4 | − | 15998.0i | 0.739129 | − | 0.537009i | ||||
\(962\) | 1390.87 | − | 4280.65i | 0.0466147 | − | 0.143465i | ||||
\(963\) | 3164.58 | − | 9739.58i | 0.105895 | − | 0.325912i | ||||
\(964\) | −33329.6 | + | 24215.3i | −1.11356 | + | 0.809049i | ||||
\(965\) | 13228.3 | + | 9610.93i | 0.441279 | + | 0.320608i | ||||
\(966\) | −6262.79 | − | 19274.9i | −0.208594 | − | 0.641986i | ||||
\(967\) | −14890.4 | −0.495185 | −0.247593 | − | 0.968864i | \(-0.579639\pi\) | ||||
−0.247593 | + | 0.968864i | \(0.579639\pi\) | |||||||
\(968\) | 42000.5 | + | 9670.55i | 1.39457 | + | 0.321099i | ||||
\(969\) | −2291.07 | −0.0759543 | ||||||||
\(970\) | 8455.37 | + | 26022.9i | 0.279882 | + | 0.861388i | ||||
\(971\) | 9411.82 | + | 6838.08i | 0.311060 | + | 0.225999i | 0.732351 | − | 0.680927i | \(-0.238423\pi\) |
−0.421291 | + | 0.906926i | \(0.638423\pi\) | |||||||
\(972\) | −19656.5 | + | 14281.3i | −0.648646 | + | 0.471269i | ||||
\(973\) | 7572.32 | − | 23305.2i | 0.249494 | − | 0.767863i | ||||
\(974\) | 19827.2 | − | 61022.0i | 0.652264 | − | 2.00746i | ||||
\(975\) | 2063.82 | − | 1499.45i | 0.0677899 | − | 0.0492523i | ||||
\(976\) | −14211.9 | − | 10325.5i | −0.466098 | − | 0.338640i | ||||
\(977\) | −10247.2 | − | 31537.5i | −0.335553 | − | 1.03273i | −0.966449 | − | 0.256859i | \(-0.917312\pi\) |
0.630896 | − | 0.775868i | \(-0.282688\pi\) | |||||||
\(978\) | −79844.4 | −2.61057 | ||||||||
\(979\) | −53499.6 | + | 10901.0i | −1.74653 | + | 0.355871i | ||||
\(980\) | 27016.2 | 0.880612 | ||||||||
\(981\) | 405.820 | + | 1248.98i | 0.0132078 | + | 0.0406493i | ||||
\(982\) | −11257.2 | − | 8178.82i | −0.365816 | − | 0.265781i | ||||
\(983\) | 7269.76 | − | 5281.79i | 0.235879 | − | 0.171376i | −0.463566 | − | 0.886062i | \(-0.653430\pi\) |
0.699445 | + | 0.714686i | \(0.253430\pi\) | |||||||
\(984\) | 5370.75 | − | 16529.5i | 0.173997 | − | 0.535509i | ||||
\(985\) | 4631.08 | − | 14253.0i | 0.149806 | − | 0.461054i | ||||
\(986\) | −5349.04 | + | 3886.31i | −0.172767 | + | 0.125523i | ||||
\(987\) | 14708.3 | + | 10686.2i | 0.474335 | + | 0.344625i | ||||
\(988\) | 1956.25 | + | 6020.73i | 0.0629926 | + | 0.193871i | ||||
\(989\) | 25241.3 | 0.811555 | ||||||||
\(990\) | −4648.76 | − | 8211.01i | −0.149240 | − | 0.263599i | ||||
\(991\) | 22624.0 | 0.725202 | 0.362601 | − | 0.931944i | \(-0.381889\pi\) | ||||
0.362601 | + | 0.931944i | \(0.381889\pi\) | |||||||
\(992\) | −1345.29 | − | 4140.38i | −0.0430575 | − | 0.132517i | ||||
\(993\) | 21635.0 | + | 15718.7i | 0.691405 | + | 0.502335i | ||||
\(994\) | −40476.4 | + | 29407.8i | −1.29158 | + | 0.938389i | ||||
\(995\) | 10496.4 | − | 32304.7i | 0.334432 | − | 1.02928i | ||||
\(996\) | −20337.3 | + | 62591.7i | −0.646999 | + | 1.99126i | ||||
\(997\) | −22496.1 | + | 16344.4i | −0.714604 | + | 0.519190i | −0.884656 | − | 0.466245i | \(-0.845606\pi\) |
0.170052 | + | 0.985435i | \(0.445606\pi\) | |||||||
\(998\) | −12849.6 | − | 9335.79i | −0.407563 | − | 0.296111i | ||||
\(999\) | 3389.10 | + | 10430.6i | 0.107334 | + | 0.330339i |
(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 | 143.4.h.a.27.1 | ✓ | 68 | |
11.3 | even | 5 | 1573.4.a.o.1.2 | 34 | |||
11.8 | odd | 10 | 1573.4.a.p.1.33 | 34 | |||
11.9 | even | 5 | inner | 143.4.h.a.53.1 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.h.a.27.1 | ✓ | 68 | 1.1 | even | 1 | trivial | |
143.4.h.a.53.1 | yes | 68 | 11.9 | even | 5 | inner | |
1573.4.a.o.1.2 | 34 | 11.3 | even | 5 | |||
1573.4.a.p.1.33 | 34 | 11.8 | odd | 10 |