Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.9 | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.g.151.9 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.236995 | + | 0.410487i | 0.0837904 | + | 0.145129i | 0.904875 | − | 0.425677i | \(-0.139964\pi\) |
−0.821085 | + | 0.570806i | \(0.806631\pi\) | |||||||
\(3\) | −2.45316 | + | 4.58061i | −0.472110 | + | 0.881540i | ||||
\(4\) | 3.88767 | − | 6.73364i | 0.485958 | − | 0.841705i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.46167 | + | 0.0785933i | −0.167495 | + | 0.00534760i | ||||
\(7\) | −4.10329 | − | 7.10710i | −0.221557 | − | 0.383747i | 0.733724 | − | 0.679447i | \(-0.237780\pi\) |
−0.955281 | + | 0.295700i | \(0.904447\pi\) | |||||||
\(8\) | 7.47735 | 0.330455 | ||||||||
\(9\) | −14.9641 | − | 22.4739i | −0.554224 | − | 0.832367i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.63291 | − | 4.56034i | −0.0721685 | − | 0.125000i | 0.827683 | − | 0.561196i | \(-0.189659\pi\) |
−0.899851 | + | 0.436196i | \(0.856325\pi\) | |||||||
\(12\) | 21.3071 | + | 34.3266i | 0.512570 | + | 0.825769i | ||||
\(13\) | −38.5171 | + | 66.7136i | −0.821748 | + | 1.42331i | 0.0826310 | + | 0.996580i | \(0.473668\pi\) |
−0.904379 | + | 0.426730i | \(0.859666\pi\) | |||||||
\(14\) | 1.94492 | − | 3.36869i | 0.0371286 | − | 0.0643087i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −29.3292 | − | 50.7997i | −0.458269 | − | 0.793746i | ||||
\(17\) | −88.9397 | −1.26888 | −0.634442 | − | 0.772970i | \(-0.718770\pi\) | ||||
−0.634442 | + | 0.772970i | \(0.718770\pi\) | |||||||
\(18\) | 5.67885 | − | 11.4688i | 0.0743622 | − | 0.150179i | ||||
\(19\) | −91.7358 | −1.10766 | −0.553832 | − | 0.832628i | \(-0.686835\pi\) | ||||
−0.553832 | + | 0.832628i | \(0.686835\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 42.6209 | − | 1.36075i | 0.442888 | − | 0.0141400i | ||||
\(22\) | 1.24798 | − | 2.16156i | 0.0120941 | − | 0.0209475i | ||||
\(23\) | 77.2204 | − | 133.750i | 0.700068 | − | 1.21255i | −0.268374 | − | 0.963315i | \(-0.586486\pi\) |
0.968442 | − | 0.249238i | \(-0.0801803\pi\) | |||||||
\(24\) | −18.3431 | + | 34.2509i | −0.156011 | + | 0.291309i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −36.5135 | −0.275418 | ||||||||
\(27\) | 139.654 | − | 13.4125i | 0.995420 | − | 0.0956017i | ||||
\(28\) | −63.8088 | −0.430669 | ||||||||
\(29\) | −84.1517 | − | 145.755i | −0.538847 | − | 0.933311i | −0.998966 | − | 0.0454539i | \(-0.985527\pi\) |
0.460119 | − | 0.887857i | \(-0.347807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.3943 | + | 63.0367i | −0.210858 | + | 0.365217i | −0.951983 | − | 0.306150i | \(-0.900959\pi\) |
0.741125 | + | 0.671367i | \(0.234292\pi\) | |||||||
\(32\) | 43.8112 | − | 75.8832i | 0.242025 | − | 0.419199i | ||||
\(33\) | 27.3481 | − | 0.873138i | 0.144264 | − | 0.00460587i | ||||
\(34\) | −21.0783 | − | 36.5086i | −0.106320 | − | 0.184152i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −209.506 | + | 13.3914i | −0.969937 | + | 0.0619972i | ||||
\(37\) | −154.836 | −0.687971 | −0.343986 | − | 0.938975i | \(-0.611777\pi\) | ||||
−0.343986 | + | 0.938975i | \(0.611777\pi\) | |||||||
\(38\) | −21.7409 | − | 37.6564i | −0.0928117 | − | 0.160754i | ||||
\(39\) | −211.101 | − | 340.091i | −0.866748 | − | 1.39636i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.97579 | + | 6.88627i | −0.0151442 | + | 0.0262306i | −0.873498 | − | 0.486827i | \(-0.838154\pi\) |
0.858354 | + | 0.513058i | \(0.171487\pi\) | |||||||
\(42\) | 10.6595 | + | 17.1728i | 0.0391618 | + | 0.0630911i | ||||
\(43\) | 11.6007 | + | 20.0930i | 0.0411416 | + | 0.0712594i | 0.885863 | − | 0.463947i | \(-0.153567\pi\) |
−0.844721 | + | 0.535206i | \(0.820234\pi\) | |||||||
\(44\) | −40.9436 | −0.140284 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 73.2034 | 0.234636 | ||||||||
\(47\) | −150.699 | − | 261.018i | −0.467696 | − | 0.810073i | 0.531623 | − | 0.846981i | \(-0.321582\pi\) |
−0.999319 | + | 0.0369081i | \(0.988249\pi\) | |||||||
\(48\) | 304.643 | − | 9.72629i | 0.916072 | − | 0.0292473i | ||||
\(49\) | 137.826 | − | 238.722i | 0.401825 | − | 0.695982i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 218.183 | − | 407.398i | 0.599053 | − | 1.11857i | ||||
\(52\) | 299.483 | + | 518.721i | 0.798671 | + | 1.38334i | ||||
\(53\) | −344.542 | −0.892952 | −0.446476 | − | 0.894796i | \(-0.647321\pi\) | ||||
−0.446476 | + | 0.894796i | \(0.647321\pi\) | |||||||
\(54\) | 38.6029 | + | 54.1473i | 0.0972812 | + | 0.136454i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −30.6817 | − | 53.1423i | −0.0732146 | − | 0.126811i | ||||
\(57\) | 225.042 | − | 420.206i | 0.522940 | − | 0.976450i | ||||
\(58\) | 39.8871 | − | 69.0864i | 0.0903005 | − | 0.156405i | ||||
\(59\) | −125.779 | + | 217.855i | −0.277542 | + | 0.480718i | −0.970773 | − | 0.239998i | \(-0.922853\pi\) |
0.693231 | + | 0.720715i | \(0.256187\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −136.451 | − | 236.340i | −0.286406 | − | 0.496069i | 0.686543 | − | 0.727089i | \(-0.259127\pi\) |
−0.972949 | + | 0.231020i | \(0.925794\pi\) | |||||||
\(62\) | −34.5010 | −0.0706715 | ||||||||
\(63\) | −98.3226 | + | 198.568i | −0.196627 | + | 0.397099i | ||||
\(64\) | −427.736 | −0.835421 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.83978 | + | 11.0191i | 0.0127563 | + | 0.0205509i | ||||
\(67\) | −417.734 | + | 723.536i | −0.761706 | + | 1.31931i | 0.180265 | + | 0.983618i | \(0.442305\pi\) |
−0.941971 | + | 0.335695i | \(0.891029\pi\) | |||||||
\(68\) | −345.768 | + | 598.887i | −0.616625 | + | 1.06803i | ||||
\(69\) | 423.222 | + | 681.825i | 0.738405 | + | 1.18960i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 351.152 | 0.586959 | 0.293479 | − | 0.955965i | \(-0.405187\pi\) | ||||
0.293479 | + | 0.955965i | \(0.405187\pi\) | |||||||
\(72\) | −111.891 | − | 168.045i | −0.183146 | − | 0.275060i | ||||
\(73\) | 522.749 | 0.838126 | 0.419063 | − | 0.907957i | \(-0.362359\pi\) | ||||
0.419063 | + | 0.907957i | \(0.362359\pi\) | |||||||
\(74\) | −36.6954 | − | 63.5584i | −0.0576454 | − | 0.0998448i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −356.638 | + | 617.715i | −0.538279 | + | 0.932326i | ||||
\(77\) | −21.6072 | + | 37.4248i | −0.0319788 | + | 0.0553889i | ||||
\(78\) | 89.5732 | − | 167.254i | 0.130028 | − | 0.242792i | ||||
\(79\) | 350.053 | + | 606.310i | 0.498533 | + | 0.863484i | 0.999999 | − | 0.00169342i | \(-0.000539032\pi\) |
−0.501466 | + | 0.865177i | \(0.667206\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −281.154 | + | 672.602i | −0.385671 | + | 0.922636i | ||||
\(82\) | −3.76897 | −0.00507577 | ||||||||
\(83\) | −120.651 | − | 208.974i | −0.159557 | − | 0.276360i | 0.775152 | − | 0.631775i | \(-0.217673\pi\) |
−0.934709 | + | 0.355414i | \(0.884340\pi\) | |||||||
\(84\) | 156.533 | − | 292.284i | 0.203323 | − | 0.379652i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.49862 | + | 9.52388i | −0.00689455 | + | 0.0119417i | ||||
\(87\) | 874.085 | − | 27.9067i | 1.07715 | − | 0.0343898i | ||||
\(88\) | −19.6872 | − | 34.0993i | −0.0238485 | − | 0.0413068i | ||||
\(89\) | 1021.39 | 1.21648 | 0.608242 | − | 0.793752i | \(-0.291875\pi\) | ||||
0.608242 | + | 0.793752i | \(0.291875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 632.187 | 0.728255 | ||||||||
\(92\) | −600.414 | − | 1039.95i | −0.680408 | − | 1.17850i | ||||
\(93\) | −199.466 | − | 321.347i | −0.222405 | − | 0.358302i | ||||
\(94\) | 71.4298 | − | 123.720i | 0.0783769 | − | 0.135753i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 240.116 | + | 386.835i | 0.255278 | + | 0.411263i | ||||
\(97\) | 194.642 | + | 337.130i | 0.203741 | + | 0.352891i | 0.949731 | − | 0.313067i | \(-0.101356\pi\) |
−0.745990 | + | 0.665958i | \(0.768023\pi\) | |||||||
\(98\) | 130.656 | 0.134676 | ||||||||
\(99\) | −63.0897 | + | 127.413i | −0.0640480 | + | 0.129348i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 432.260 | + | 748.696i | 0.425856 | + | 0.737604i | 0.996500 | − | 0.0835936i | \(-0.0266397\pi\) |
−0.570644 | + | 0.821197i | \(0.693306\pi\) | |||||||
\(102\) | 218.940 | − | 6.99006i | 0.212532 | − | 0.00678548i | ||||
\(103\) | −614.103 | + | 1063.66i | −0.587470 | + | 1.01753i | 0.407093 | + | 0.913387i | \(0.366543\pi\) |
−0.994563 | + | 0.104141i | \(0.966791\pi\) | |||||||
\(104\) | −288.006 | + | 498.841i | −0.271551 | + | 0.470340i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −81.6547 | − | 141.430i | −0.0748208 | − | 0.129593i | ||||
\(107\) | −1860.34 | −1.68080 | −0.840402 | − | 0.541963i | \(-0.817681\pi\) | ||||
−0.840402 | + | 0.541963i | \(0.817681\pi\) | |||||||
\(108\) | 452.611 | − | 992.519i | 0.403264 | − | 0.884308i | ||||
\(109\) | 1037.31 | 0.911524 | 0.455762 | − | 0.890102i | \(-0.349367\pi\) | ||||
0.455762 | + | 0.890102i | \(0.349367\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 379.838 | − | 709.246i | 0.324798 | − | 0.606474i | ||||
\(112\) | −240.692 | + | 416.892i | −0.203065 | + | 0.351719i | ||||
\(113\) | 703.867 | − | 1219.13i | 0.585967 | − | 1.01492i | −0.408787 | − | 0.912630i | \(-0.634048\pi\) |
0.994754 | − | 0.102295i | \(-0.0326185\pi\) | |||||||
\(114\) | 225.823 | − | 7.20982i | 0.185529 | − | 0.00592334i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1308.61 | −1.04743 | ||||||||
\(117\) | 2075.69 | − | 132.675i | 1.64015 | − | 0.104836i | ||||
\(118\) | −119.236 | −0.0930215 | ||||||||
\(119\) | 364.945 | + | 632.103i | 0.281130 | + | 0.486931i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 651.636 | − | 1128.67i | 0.489583 | − | 0.847983i | ||||
\(122\) | 64.6764 | − | 112.023i | 0.0479961 | − | 0.0831317i | ||||
\(123\) | −21.7901 | − | 35.1046i | −0.0159736 | − | 0.0257340i | ||||
\(124\) | 282.977 | + | 490.131i | 0.204937 | + | 0.354960i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −104.812 | + | 6.69943i | −0.0741060 | + | 0.00473677i | ||||
\(127\) | −198.654 | −0.138801 | −0.0694005 | − | 0.997589i | \(-0.522109\pi\) | ||||
−0.0694005 | + | 0.997589i | \(0.522109\pi\) | |||||||
\(128\) | −451.861 | − | 782.645i | −0.312025 | − | 0.540443i | ||||
\(129\) | −120.497 | + | 3.84707i | −0.0822414 | + | 0.00262570i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 726.091 | − | 1257.63i | 0.484266 | − | 0.838773i | −0.515571 | − | 0.856847i | \(-0.672420\pi\) |
0.999837 | + | 0.0180739i | \(0.00575340\pi\) | |||||||
\(132\) | 100.441 | − | 187.547i | 0.0662293 | − | 0.123666i | ||||
\(133\) | 376.418 | + | 651.975i | 0.245410 | + | 0.425063i | ||||
\(134\) | −396.003 | −0.255295 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −665.033 | −0.419310 | ||||||||
\(137\) | −318.328 | − | 551.360i | −0.198515 | − | 0.343838i | 0.749532 | − | 0.661968i | \(-0.230279\pi\) |
−0.948047 | + | 0.318130i | \(0.896945\pi\) | |||||||
\(138\) | −179.579 | + | 335.316i | −0.110774 | + | 0.206841i | ||||
\(139\) | −761.621 | + | 1319.17i | −0.464747 | + | 0.804965i | −0.999190 | − | 0.0402391i | \(-0.987188\pi\) |
0.534443 | + | 0.845204i | \(0.320521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1565.31 | − | 49.9754i | 0.934916 | − | 0.0298489i | ||||
\(142\) | 83.2213 | + | 144.143i | 0.0491815 | + | 0.0851849i | ||||
\(143\) | 405.649 | 0.237217 | ||||||||
\(144\) | −702.785 | + | 1419.31i | −0.406704 | + | 0.821362i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 123.889 | + | 214.582i | 0.0702269 | + | 0.121637i | ||||
\(147\) | 755.384 | + | 1216.95i | 0.423830 | + | 0.682805i | ||||
\(148\) | −601.952 | + | 1042.61i | −0.334325 | + | 0.579069i | ||||
\(149\) | 1051.30 | − | 1820.91i | 0.578027 | − | 1.00117i | −0.417679 | − | 0.908595i | \(-0.637156\pi\) |
0.995706 | − | 0.0925770i | \(-0.0295104\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1180.25 | + | 2044.25i | 0.636074 | + | 1.10171i | 0.986286 | + | 0.165043i | \(0.0527762\pi\) |
−0.350212 | + | 0.936670i | \(0.613891\pi\) | |||||||
\(152\) | −685.940 | −0.366034 | ||||||||
\(153\) | 1330.90 | + | 1998.82i | 0.703247 | + | 1.05618i | ||||
\(154\) | −20.4832 | −0.0107181 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3110.74 | + | 99.3160i | −1.59653 | + | 0.0509721i | ||||
\(157\) | −1002.09 | + | 1735.68i | −0.509400 | + | 0.882306i | 0.490541 | + | 0.871418i | \(0.336799\pi\) |
−0.999941 | + | 0.0108880i | \(0.996534\pi\) | |||||||
\(158\) | −165.922 | + | 287.385i | −0.0835445 | + | 0.144703i | ||||
\(159\) | 845.215 | − | 1578.21i | 0.421572 | − | 0.787173i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1267.43 | −0.620419 | ||||||||
\(162\) | −342.727 | + | 43.9931i | −0.166217 | + | 0.0213359i | ||||
\(163\) | −2772.38 | −1.33220 | −0.666102 | − | 0.745861i | \(-0.732038\pi\) | ||||
−0.666102 | + | 0.745861i | \(0.732038\pi\) | |||||||
\(164\) | 30.9131 | + | 53.5430i | 0.0147189 | + | 0.0254939i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 57.1875 | − | 99.0517i | 0.0267386 | − | 0.0463127i | ||||
\(167\) | 923.165 | − | 1598.97i | 0.427764 | − | 0.740909i | −0.568910 | − | 0.822400i | \(-0.692635\pi\) |
0.996674 | + | 0.0814904i | \(0.0259680\pi\) | |||||||
\(168\) | 318.691 | − | 10.1748i | 0.146355 | − | 0.00467263i | ||||
\(169\) | −1868.64 | − | 3236.57i | −0.850540 | − | 1.47318i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1372.74 | + | 2061.66i | 0.613895 | + | 0.921984i | ||||
\(172\) | 180.399 | 0.0799725 | ||||||||
\(173\) | −96.5861 | − | 167.292i | −0.0424469 | − | 0.0735201i | 0.844021 | − | 0.536309i | \(-0.180182\pi\) |
−0.886468 | + | 0.462789i | \(0.846849\pi\) | |||||||
\(174\) | 218.609 | + | 352.187i | 0.0952455 | + | 0.153444i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −154.443 | + | 267.503i | −0.0661452 | + | 0.114567i | ||||
\(177\) | −689.356 | − | 1110.58i | −0.292741 | − | 0.471616i | ||||
\(178\) | 242.064 | + | 419.268i | 0.101930 | + | 0.176547i | ||||
\(179\) | −3931.26 | −1.64154 | −0.820770 | − | 0.571258i | \(-0.806456\pi\) | ||||
−0.820770 | + | 0.571258i | \(0.806456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1921.32 | −0.789007 | −0.394503 | − | 0.918894i | \(-0.629083\pi\) | ||||
−0.394503 | + | 0.918894i | \(0.629083\pi\) | |||||||
\(182\) | 149.825 | + | 259.505i | 0.0610208 | + | 0.105691i | ||||
\(183\) | 1417.32 | − | 45.2504i | 0.572520 | − | 0.0182787i | ||||
\(184\) | 577.404 | − | 1000.09i | 0.231341 | − | 0.400695i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 84.6364 | − | 158.036i | 0.0333647 | − | 0.0622998i | ||||
\(187\) | 234.170 | + | 405.595i | 0.0915735 | + | 0.158610i | ||||
\(188\) | −2343.47 | −0.909123 | ||||||||
\(189\) | −668.363 | − | 937.496i | −0.257229 | − | 0.360808i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 753.915 | + | 1305.82i | 0.285609 | + | 0.494690i | 0.972757 | − | 0.231828i | \(-0.0744707\pi\) |
−0.687147 | + | 0.726518i | \(0.741137\pi\) | |||||||
\(192\) | 1049.30 | − | 1959.29i | 0.394411 | − | 0.736457i | ||||
\(193\) | 2032.83 | − | 3520.96i | 0.758166 | − | 1.31318i | −0.185619 | − | 0.982622i | \(-0.559429\pi\) |
0.943785 | − | 0.330561i | \(-0.107238\pi\) | |||||||
\(194\) | −92.2585 | + | 159.796i | −0.0341432 | + | 0.0591377i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1071.64 | − | 1856.14i | −0.390541 | − | 0.676436i | ||||
\(197\) | 3916.67 | 1.41650 | 0.708252 | − | 0.705960i | \(-0.249484\pi\) | ||||
0.708252 | + | 0.705960i | \(0.249484\pi\) | |||||||
\(198\) | −67.2534 | + | 4.29876i | −0.0241388 | + | 0.00154293i | ||||
\(199\) | 615.676 | 0.219317 | 0.109659 | − | 0.993969i | \(-0.465024\pi\) | ||||
0.109659 | + | 0.993969i | \(0.465024\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2289.47 | − | 3688.42i | −0.803418 | − | 1.29433i | ||||
\(202\) | −204.887 | + | 354.874i | −0.0713652 | + | 0.123608i | ||||
\(203\) | −690.597 | + | 1196.15i | −0.238770 | + | 0.413562i | ||||
\(204\) | −1895.05 | − | 3052.99i | −0.650392 | − | 1.04780i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −582.157 | −0.196897 | ||||||||
\(207\) | −4161.41 | + | 265.992i | −1.39728 | + | 0.0893127i | ||||
\(208\) | 4518.71 | 1.50633 | ||||||||
\(209\) | 241.532 | + | 418.346i | 0.0799385 | + | 0.138458i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1116.74 | − | 1934.26i | 0.364360 | − | 0.631089i | −0.624314 | − | 0.781174i | \(-0.714621\pi\) |
0.988673 | + | 0.150085i | \(0.0479546\pi\) | |||||||
\(212\) | −1339.46 | + | 2320.02i | −0.433938 | + | 0.751602i | ||||
\(213\) | −861.430 | + | 1608.49i | −0.277109 | + | 0.517427i | ||||
\(214\) | −440.892 | − | 763.647i | −0.140835 | − | 0.243934i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1044.24 | − | 100.290i | 0.328942 | − | 0.0315921i | ||||
\(217\) | 597.344 | 0.186868 | ||||||||
\(218\) | 245.837 | + | 425.802i | 0.0763769 | + | 0.132289i | ||||
\(219\) | −1282.39 | + | 2394.51i | −0.395687 | + | 0.738841i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3425.70 | − | 5933.49i | 1.04270 | − | 1.80602i | ||||
\(222\) | 381.156 | − | 12.1691i | 0.115232 | − | 0.00367899i | ||||
\(223\) | −2315.22 | − | 4010.08i | −0.695240 | − | 1.20419i | −0.970100 | − | 0.242707i | \(-0.921965\pi\) |
0.274860 | − | 0.961484i | \(-0.411369\pi\) | |||||||
\(224\) | −719.079 | −0.214489 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 667.252 | 0.196394 | ||||||||
\(227\) | 233.846 | + | 405.034i | 0.0683741 | + | 0.118427i | 0.898186 | − | 0.439616i | \(-0.144886\pi\) |
−0.829812 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(228\) | −1954.63 | − | 3148.97i | −0.567756 | − | 0.914675i | ||||
\(229\) | −728.574 | + | 1261.93i | −0.210242 | + | 0.364150i | −0.951790 | − | 0.306749i | \(-0.900759\pi\) |
0.741548 | + | 0.670900i | \(0.234092\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −118.423 | − | 190.783i | −0.0337300 | − | 0.0543403i | ||||
\(232\) | −629.232 | − | 1089.86i | −0.178065 | − | 0.308418i | ||||
\(233\) | 2617.43 | 0.735938 | 0.367969 | − | 0.929838i | \(-0.380053\pi\) | ||||
0.367969 | + | 0.929838i | \(0.380053\pi\) | |||||||
\(234\) | 546.389 | + | 820.601i | 0.152644 | + | 0.229249i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 977.972 | + | 1693.90i | 0.269748 | + | 0.467217i | ||||
\(237\) | −3636.01 | + | 116.086i | −0.996558 | + | 0.0318169i | ||||
\(238\) | −172.980 | + | 299.610i | −0.0471119 | + | 0.0816003i | ||||
\(239\) | 1855.58 | − | 3213.96i | 0.502207 | − | 0.869847i | −0.497790 | − | 0.867298i | \(-0.665855\pi\) |
0.999997 | − | 0.00254992i | \(-0.000811665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 922.053 | + | 1597.04i | 0.246451 | + | 0.426865i | 0.962539 | − | 0.271145i | \(-0.0874023\pi\) |
−0.716088 | + | 0.698010i | \(0.754069\pi\) | |||||||
\(242\) | 617.737 | 0.164090 | ||||||||
\(243\) | −2391.22 | − | 2937.86i | −0.631261 | − | 0.775570i | ||||
\(244\) | −2121.90 | −0.556725 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.24586 | − | 17.2642i | 0.00239632 | − | 0.00447449i | ||||
\(247\) | 3533.40 | − | 6120.02i | 0.910222 | − | 1.57655i | ||||
\(248\) | −272.133 | + | 471.347i | −0.0696792 | + | 0.120688i | ||||
\(249\) | 1253.21 | − | 40.0109i | 0.318951 | − | 0.0101831i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7204.10 | −1.81163 | −0.905815 | − | 0.423674i | \(-0.860740\pi\) | ||||
−0.905815 | + | 0.423674i | \(0.860740\pi\) | |||||||
\(252\) | 954.839 | + | 1434.03i | 0.238687 | + | 0.358475i | ||||
\(253\) | −813.259 | −0.202091 | ||||||||
\(254\) | −47.0801 | − | 81.5451i | −0.0116302 | − | 0.0201441i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1496.77 | + | 2592.47i | −0.365421 | + | 0.632928i | ||||
\(257\) | −878.573 | + | 1521.73i | −0.213245 | + | 0.369351i | −0.952728 | − | 0.303824i | \(-0.901736\pi\) |
0.739484 | + | 0.673175i | \(0.235070\pi\) | |||||||
\(258\) | −30.1363 | − | 48.5506i | −0.00727210 | − | 0.0117156i | ||||
\(259\) | 635.338 | + | 1100.44i | 0.152425 | + | 0.264007i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2016.44 | + | 4072.30i | −0.478215 | + | 0.965783i | ||||
\(262\) | 688.319 | 0.162307 | ||||||||
\(263\) | 2678.45 | + | 4639.22i | 0.627987 | + | 1.08771i | 0.987955 | + | 0.154741i | \(0.0494542\pi\) |
−0.359968 | + | 0.932965i | \(0.617212\pi\) | |||||||
\(264\) | 204.491 | − | 6.52876i | 0.0476726 | − | 0.00152204i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −178.418 | + | 309.030i | −0.0411261 | + | 0.0712324i | ||||
\(267\) | −2505.63 | + | 4678.59i | −0.574314 | + | 1.07238i | ||||
\(268\) | 3248.02 | + | 5625.73i | 0.740315 | + | 1.28226i | ||||
\(269\) | −1040.60 | −0.235860 | −0.117930 | − | 0.993022i | \(-0.537626\pi\) | ||||
−0.117930 | + | 0.993022i | \(0.537626\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1531.38 | −0.343265 | −0.171632 | − | 0.985161i | \(-0.554904\pi\) | ||||
−0.171632 | + | 0.985161i | \(0.554904\pi\) | |||||||
\(272\) | 2608.53 | + | 4518.11i | 0.581491 | + | 1.00717i | ||||
\(273\) | −1550.85 | + | 2895.80i | −0.343816 | + | 0.641986i | ||||
\(274\) | 150.884 | − | 261.339i | 0.0332673 | − | 0.0576207i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6236.51 | − | 199.112i | 1.36012 | − | 0.0434244i | ||||
\(277\) | −3115.55 | − | 5396.29i | −0.675794 | − | 1.17051i | −0.976236 | − | 0.216710i | \(-0.930467\pi\) |
0.300442 | − | 0.953800i | \(-0.402866\pi\) | |||||||
\(278\) | −722.001 | −0.155765 | ||||||||
\(279\) | 1961.29 | − | 125.363i | 0.420857 | − | 0.0269007i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4556.98 | + | 7892.92i | 0.967425 | + | 1.67563i | 0.702953 | + | 0.711236i | \(0.251864\pi\) |
0.264472 | + | 0.964393i | \(0.414802\pi\) | |||||||
\(282\) | 391.486 | + | 630.697i | 0.0826689 | + | 0.133183i | ||||
\(283\) | −757.546 | + | 1312.11i | −0.159122 | + | 0.275607i | −0.934552 | − | 0.355826i | \(-0.884200\pi\) |
0.775431 | + | 0.631433i | \(0.217533\pi\) | |||||||
\(284\) | 1365.16 | − | 2364.53i | 0.285238 | − | 0.494046i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 96.1368 | + | 166.514i | 0.0198765 | + | 0.0344272i | ||||
\(287\) | 65.2552 | 0.0134212 | ||||||||
\(288\) | −2360.99 | + | 150.911i | −0.483064 | + | 0.0308768i | ||||
\(289\) | 2997.26 | 0.610067 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2021.75 | + | 64.5481i | −0.407275 | + | 0.0130030i | ||||
\(292\) | 2032.27 | − | 3520.00i | 0.407294 | − | 0.705454i | ||||
\(293\) | 692.150 | − | 1198.84i | 0.138006 | − | 0.239034i | −0.788736 | − | 0.614733i | \(-0.789264\pi\) |
0.926742 | + | 0.375699i | \(0.122597\pi\) | |||||||
\(294\) | −320.520 | + | 598.487i | −0.0635821 | + | 0.118723i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1157.77 | −0.227344 | ||||||||
\(297\) | −428.862 | − | 601.554i | −0.0837881 | − | 0.117528i | ||||
\(298\) | 996.613 | 0.193732 | ||||||||
\(299\) | 5948.61 | + | 10303.3i | 1.15056 | + | 1.99283i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 95.2020 | − | 164.895i | 0.0182304 | − | 0.0315760i | ||||
\(302\) | −559.426 | + | 968.954i | −0.106594 | + | 0.184626i | ||||
\(303\) | −4489.89 | + | 143.348i | −0.851278 | + | 0.0271786i | ||||
\(304\) | 2690.54 | + | 4660.15i | 0.507609 | + | 0.879204i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −505.075 | + | 1020.03i | −0.0943570 | + | 0.190559i | ||||
\(307\) | 1628.16 | 0.302685 | 0.151342 | − | 0.988481i | \(-0.451640\pi\) | ||||
0.151342 | + | 0.988481i | \(0.451640\pi\) | |||||||
\(308\) | 168.003 | + | 290.990i | 0.0310807 | + | 0.0538334i | ||||
\(309\) | −3365.72 | − | 5422.29i | −0.619640 | − | 0.998263i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 703.314 | − | 1218.17i | 0.128236 | − | 0.222110i | −0.794758 | − | 0.606927i | \(-0.792402\pi\) |
0.922993 | + | 0.384817i | \(0.125735\pi\) | |||||||
\(312\) | −1578.47 | − | 2542.98i | −0.286422 | − | 0.461435i | ||||
\(313\) | −2715.77 | − | 4703.85i | −0.490429 | − | 0.849448i | 0.509510 | − | 0.860465i | \(-0.329827\pi\) |
−0.999939 | + | 0.0110164i | \(0.996493\pi\) | |||||||
\(314\) | −949.964 | −0.170731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5443.56 | 0.969065 | ||||||||
\(317\) | 3840.80 | + | 6652.46i | 0.680507 | + | 1.17867i | 0.974826 | + | 0.222966i | \(0.0715738\pi\) |
−0.294319 | + | 0.955707i | \(0.595093\pi\) | |||||||
\(318\) | 848.148 | − | 27.0787i | 0.149565 | − | 0.00477515i | ||||
\(319\) | −443.128 | + | 767.521i | −0.0777756 | + | 0.134711i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4563.71 | − | 8521.51i | 0.793525 | − | 1.48170i | ||||
\(322\) | −300.374 | − | 520.264i | −0.0519851 | − | 0.0900409i | ||||
\(323\) | 8158.95 | 1.40550 | ||||||||
\(324\) | 3436.02 | + | 4508.04i | 0.589167 | + | 0.772984i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −657.039 | − | 1138.03i | −0.111626 | − | 0.193342i | ||||
\(327\) | −2544.68 | + | 4751.51i | −0.430339 | + | 0.803544i | ||||
\(328\) | −29.7284 | + | 51.4910i | −0.00500449 | + | 0.00866804i | ||||
\(329\) | −1236.72 | + | 2142.07i | −0.207242 | + | 0.358954i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2064.44 | − | 3575.71i | −0.342815 | − | 0.593773i | 0.642139 | − | 0.766588i | \(-0.278047\pi\) |
−0.984954 | + | 0.172815i | \(0.944714\pi\) | |||||||
\(332\) | −1876.21 | −0.310152 | ||||||||
\(333\) | 2316.98 | + | 3479.78i | 0.381290 | + | 0.572645i | ||||
\(334\) | 875.142 | 0.143370 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1319.16 | − | 2125.22i | −0.214185 | − | 0.345060i | ||||
\(337\) | 1312.08 | − | 2272.58i | 0.212087 | − | 0.367345i | −0.740281 | − | 0.672298i | \(-0.765307\pi\) |
0.952367 | + | 0.304953i | \(0.0986407\pi\) | |||||||
\(338\) | 885.715 | − | 1534.10i | 0.142534 | − | 0.246877i | ||||
\(339\) | 3857.69 | + | 6214.87i | 0.618055 | + | 0.995709i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 383.292 | 0.0608693 | ||||||||
\(342\) | −520.954 | + | 1052.10i | −0.0823683 | + | 0.166347i | ||||
\(343\) | −5077.01 | −0.799221 | ||||||||
\(344\) | 86.7425 | + | 150.242i | 0.0135955 | + | 0.0235480i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 45.7809 | − | 79.2948i | 0.00711328 | − | 0.0123206i | ||||
\(347\) | 3457.40 | − | 5988.40i | 0.534880 | − | 0.926439i | −0.464290 | − | 0.885683i | \(-0.653690\pi\) |
0.999169 | − | 0.0407551i | \(-0.0129763\pi\) | |||||||
\(348\) | 3210.24 | − | 5994.26i | 0.494502 | − | 0.923351i | ||||
\(349\) | 1330.20 | + | 2303.98i | 0.204024 | + | 0.353379i | 0.949821 | − | 0.312793i | \(-0.101265\pi\) |
−0.745798 | + | 0.666173i | \(0.767931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4484.25 | + | 9833.40i | −0.681914 | + | 1.49535i | ||||
\(352\) | −461.404 | −0.0698663 | ||||||||
\(353\) | −2258.75 | − | 3912.26i | −0.340569 | − | 0.589883i | 0.643969 | − | 0.765051i | \(-0.277286\pi\) |
−0.984539 | + | 0.175168i | \(0.943953\pi\) | |||||||
\(354\) | 292.504 | − | 546.173i | 0.0439164 | − | 0.0820022i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3970.82 | − | 6877.67i | 0.591161 | − | 1.02392i | ||||
\(357\) | −3790.69 | + | 121.025i | −0.561973 | + | 0.0179420i | ||||
\(358\) | −931.688 | − | 1613.73i | −0.137545 | − | 0.238236i | ||||
\(359\) | 2702.34 | 0.397281 | 0.198640 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198640 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1556.45 | 0.226921 | ||||||||
\(362\) | −455.342 | − | 788.676i | −0.0661112 | − | 0.114508i | ||||
\(363\) | 3571.42 | + | 5753.68i | 0.516394 | + | 0.831929i | ||||
\(364\) | 2457.73 | − | 4256.92i | 0.353902 | − | 0.612976i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 354.472 | + | 571.067i | 0.0506244 | + | 0.0815577i | ||||
\(367\) | −1769.15 | − | 3064.27i | −0.251632 | − | 0.435840i | 0.712343 | − | 0.701832i | \(-0.247634\pi\) |
−0.963975 | + | 0.265991i | \(0.914301\pi\) | |||||||
\(368\) | −9059.26 | −1.28328 | ||||||||
\(369\) | 214.255 | − | 13.6949i | 0.0302268 | − | 0.00193206i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1413.75 | + | 2448.69i | 0.197839 | + | 0.342668i | ||||
\(372\) | −2939.29 | + | 93.8422i | −0.409664 | + | 0.0130793i | ||||
\(373\) | 2864.94 | − | 4962.23i | 0.397697 | − | 0.688832i | −0.595744 | − | 0.803174i | \(-0.703143\pi\) |
0.993441 | + | 0.114342i | \(0.0364760\pi\) | |||||||
\(374\) | −110.994 | + | 192.248i | −0.0153460 | + | 0.0265800i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1126.83 | − | 1951.73i | −0.154553 | − | 0.267693i | ||||
\(377\) | 12965.1 | 1.77119 | ||||||||
\(378\) | 226.432 | − | 496.536i | 0.0308105 | − | 0.0675637i | ||||
\(379\) | −8727.59 | −1.18287 | −0.591433 | − | 0.806354i | \(-0.701437\pi\) | ||||
−0.591433 | + | 0.806354i | \(0.701437\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 487.330 | − | 909.959i | 0.0655293 | − | 0.122359i | ||||
\(382\) | −357.348 | + | 618.945i | −0.0478626 | + | 0.0829005i | ||||
\(383\) | 2281.40 | − | 3951.50i | 0.304371 | − | 0.527186i | −0.672750 | − | 0.739870i | \(-0.734887\pi\) |
0.977121 | + | 0.212684i | \(0.0682204\pi\) | |||||||
\(384\) | 4693.48 | − | 149.848i | 0.623732 | − | 0.0199138i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1927.08 | 0.254108 | ||||||||
\(387\) | 277.975 | − | 561.386i | 0.0365123 | − | 0.0737386i | ||||
\(388\) | 3026.82 | 0.396039 | ||||||||
\(389\) | −6042.19 | − | 10465.4i | −0.787536 | − | 1.36405i | −0.927472 | − | 0.373891i | \(-0.878023\pi\) |
0.139937 | − | 0.990160i | \(-0.455310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6867.95 | + | 11895.6i | −0.888305 | + | 1.53859i | ||||
\(392\) | 1030.57 | − | 1785.01i | 0.132785 | − | 0.229991i | ||||
\(393\) | 3979.49 | + | 6411.09i | 0.510785 | + | 0.822893i | ||||
\(394\) | 928.232 | + | 1607.74i | 0.118689 | + | 0.205576i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 612.682 | + | 920.163i | 0.0777485 | + | 0.116767i | ||||
\(397\) | −5880.63 | −0.743426 | −0.371713 | − | 0.928348i | \(-0.621230\pi\) | ||||
−0.371713 | + | 0.928348i | \(0.621230\pi\) | |||||||
\(398\) | 145.912 | + | 252.727i | 0.0183767 | + | 0.0318293i | ||||
\(399\) | −3909.86 | + | 124.829i | −0.490571 | + | 0.0156624i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1647.56 | + | 2853.65i | −0.205175 | + | 0.355373i | −0.950188 | − | 0.311676i | \(-0.899110\pi\) |
0.745014 | + | 0.667049i | \(0.232443\pi\) | |||||||
\(402\) | 971.458 | − | 1813.94i | 0.120527 | − | 0.225052i | ||||
\(403\) | −2803.60 | − | 4855.98i | −0.346545 | − | 0.600233i | ||||
\(404\) | 6721.92 | 0.827793 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −654.672 | −0.0800267 | ||||||||
\(407\) | 407.671 | + | 706.107i | 0.0496499 | + | 0.0859961i | ||||
\(408\) | 1631.43 | − | 3046.26i | 0.197960 | − | 0.369638i | ||||
\(409\) | 3108.71 | − | 5384.45i | 0.375834 | − | 0.650963i | −0.614618 | − | 0.788825i | \(-0.710690\pi\) |
0.990451 | + | 0.137862i | \(0.0440231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3306.48 | − | 105.565i | 0.396828 | − | 0.0126695i | ||||
\(412\) | 4774.86 | + | 8270.29i | 0.570972 | + | 0.988952i | ||||
\(413\) | 2064.42 | 0.245965 | ||||||||
\(414\) | −1095.42 | − | 1645.17i | −0.130041 | − | 0.195303i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3374.96 | + | 5845.60i | 0.397767 | + | 0.688953i | ||||
\(417\) | −4174.22 | − | 6724.81i | −0.490197 | − | 0.789725i | ||||
\(418\) | −114.484 | + | 198.292i | −0.0133962 | + | 0.0232028i | ||||
\(419\) | −870.140 | + | 1507.13i | −0.101454 | + | 0.175723i | −0.912284 | − | 0.409559i | \(-0.865683\pi\) |
0.810830 | + | 0.585282i | \(0.199016\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 642.288 | + | 1112.48i | 0.0743544 | + | 0.128786i | 0.900805 | − | 0.434223i | \(-0.142977\pi\) |
−0.826451 | + | 0.563009i | \(0.809644\pi\) | |||||||
\(422\) | 1058.65 | 0.122119 | ||||||||
\(423\) | −3611.04 | + | 7292.69i | −0.415070 | + | 0.838257i | ||||
\(424\) | −2576.26 | −0.295081 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −864.420 | + | 27.5982i | −0.0983129 | + | 0.00313882i | ||||
\(427\) | −1119.79 | + | 1939.54i | −0.126910 | + | 0.219815i | ||||
\(428\) | −7232.39 | + | 12526.9i | −0.816801 | + | 1.41474i | ||||
\(429\) | −995.120 | + | 1858.12i | −0.111993 | + | 0.209117i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11917.4 | −1.33189 | −0.665943 | − | 0.746003i | \(-0.731970\pi\) | ||||
−0.665943 | + | 0.746003i | \(0.731970\pi\) | |||||||
\(432\) | −4777.28 | − | 6700.98i | −0.532054 | − | 0.746299i | ||||
\(433\) | 1603.61 | 0.177978 | 0.0889889 | − | 0.996033i | \(-0.471636\pi\) | ||||
0.0889889 | + | 0.996033i | \(0.471636\pi\) | |||||||
\(434\) | 141.568 | + | 245.202i | 0.0156577 | + | 0.0271200i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4032.71 | − | 6984.85i | 0.442963 | − | 0.767234i | ||||
\(437\) | −7083.87 | + | 12269.6i | −0.775440 | + | 1.34310i | ||||
\(438\) | −1286.84 | + | 41.0846i | −0.140382 | + | 0.00448196i | ||||
\(439\) | −908.226 | − | 1573.09i | −0.0987409 | − | 0.171024i | 0.812423 | − | 0.583069i | \(-0.198148\pi\) |
−0.911164 | + | 0.412044i | \(0.864815\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7427.45 | + | 474.754i | −0.802014 | + | 0.0512638i | ||||
\(442\) | 3247.49 | 0.349474 | ||||||||
\(443\) | 1132.64 | + | 1961.79i | 0.121475 | + | 0.210401i | 0.920350 | − | 0.391097i | \(-0.127904\pi\) |
−0.798875 | + | 0.601498i | \(0.794571\pi\) | |||||||
\(444\) | −3299.12 | − | 5315.00i | −0.352634 | − | 0.568105i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1097.39 | − | 1900.74i | 0.116509 | − | 0.201799i | ||||
\(447\) | 5761.87 | + | 9282.58i | 0.609680 | + | 0.982217i | ||||
\(448\) | 1755.12 | + | 3039.96i | 0.185093 | + | 0.320591i | ||||
\(449\) | −13259.9 | −1.39371 | −0.696854 | − | 0.717213i | \(-0.745417\pi\) | ||||
−0.696854 | + | 0.717213i | \(0.745417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.8716 | 0.00437175 | ||||||||
\(452\) | −5472.80 | − | 9479.17i | −0.569511 | − | 0.986422i | ||||
\(453\) | −12259.3 | + | 391.399i | −1.27150 | + | 0.0405950i | ||||
\(454\) | −110.841 | + | 191.982i | −0.0114582 | + | 0.0198462i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1682.72 | − | 3142.03i | 0.172808 | − | 0.322673i | ||||
\(457\) | −65.9288 | − | 114.192i | −0.00674840 | − | 0.0116886i | 0.862631 | − | 0.505833i | \(-0.168815\pi\) |
−0.869380 | + | 0.494144i | \(0.835481\pi\) | |||||||
\(458\) | −690.673 | −0.0704652 | ||||||||
\(459\) | −12420.7 | + | 1192.91i | −1.26307 | + | 0.121307i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6391.25 | − | 11070.0i | −0.645705 | − | 1.11839i | −0.984138 | − | 0.177404i | \(-0.943230\pi\) |
0.338433 | − | 0.940990i | \(-0.390103\pi\) | |||||||
\(462\) | 50.2485 | − | 93.8256i | 0.00506011 | − | 0.00944840i | ||||
\(463\) | −2310.71 | + | 4002.26i | −0.231939 | + | 0.401729i | −0.958379 | − | 0.285500i | \(-0.907840\pi\) |
0.726440 | + | 0.687230i | \(0.241174\pi\) | |||||||
\(464\) | −4936.21 | + | 8549.77i | −0.493875 | + | 0.855416i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 620.318 | + | 1074.42i | 0.0616645 | + | 0.106806i | ||||
\(467\) | −5550.68 | −0.550010 | −0.275005 | − | 0.961443i | \(-0.588680\pi\) | ||||
−0.275005 | + | 0.961443i | \(0.588680\pi\) | |||||||
\(468\) | 7176.20 | − | 14492.7i | 0.708803 | − | 1.43147i | ||||
\(469\) | 6856.32 | 0.675044 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5492.17 | − | 8848.09i | −0.537295 | − | 0.865602i | ||||
\(472\) | −940.492 | + | 1628.98i | −0.0917154 | + | 0.158856i | ||||
\(473\) | 61.0873 | − | 105.806i | 0.00593826 | − | 0.0102854i | ||||
\(474\) | −909.368 | − | 1465.02i | −0.0881195 | − | 0.141964i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5675.13 | 0.546469 | ||||||||
\(477\) | 5155.74 | + | 7743.21i | 0.494896 | + | 0.743264i | ||||
\(478\) | 1759.05 | 0.168320 | ||||||||
\(479\) | −970.694 | − | 1681.29i | −0.0925932 | − | 0.160376i | 0.816008 | − | 0.578040i | \(-0.196182\pi\) |
−0.908602 | + | 0.417664i | \(0.862849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5963.85 | − | 10329.7i | 0.565339 | − | 0.979196i | ||||
\(482\) | −437.044 | + | 756.982i | −0.0413004 | + | 0.0715344i | ||||
\(483\) | 3109.20 | − | 5805.60i | 0.292906 | − | 0.546924i | ||||
\(484\) | −5066.68 | − | 8775.75i | −0.475834 | − | 0.824169i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 639.247 | − | 1677.82i | 0.0596642 | − | 0.156600i | ||||
\(487\) | 178.136 | 0.0165752 | 0.00828761 | − | 0.999966i | \(-0.497362\pi\) | ||||
0.00828761 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(488\) | −1020.29 | − | 1767.20i | −0.0946443 | − | 0.163929i | ||||
\(489\) | 6801.07 | − | 12699.2i | 0.628947 | − | 1.17439i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2795.80 | − | 4842.46i | 0.256971 | − | 0.445086i | −0.708458 | − | 0.705753i | \(-0.750609\pi\) |
0.965429 | + | 0.260667i | \(0.0839423\pi\) | |||||||
\(492\) | −321.094 | + | 10.2515i | −0.0294229 | + | 0.000939379i | ||||
\(493\) | 7484.42 | + | 12963.4i | 0.683735 | + | 1.18426i | ||||
\(494\) | 3349.59 | 0.305071 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4269.66 | 0.386519 | ||||||||
\(497\) | −1440.88 | − | 2495.67i | −0.130045 | − | 0.225244i | ||||
\(498\) | 313.428 | + | 504.943i | 0.0282029 | + | 0.0454358i | ||||
\(499\) | −5683.52 | + | 9844.15i | −0.509879 | + | 0.883136i | 0.490056 | + | 0.871691i | \(0.336976\pi\) |
−0.999935 | + | 0.0114449i | \(0.996357\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5059.59 | + | 8151.18i | 0.451189 | + | 0.726882i | ||||
\(502\) | −1707.34 | − | 2957.19i | −0.151797 | − | 0.262920i | ||||
\(503\) | 9225.98 | 0.817825 | 0.408913 | − | 0.912574i | \(-0.365908\pi\) | ||||
0.408913 | + | 0.912574i | \(0.365908\pi\) | |||||||
\(504\) | −735.192 | + | 1484.76i | −0.0649763 | + | 0.131223i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −192.738 | − | 333.832i | −0.0169333 | − | 0.0293294i | ||||
\(507\) | 19409.6 | − | 619.685i | 1.70021 | − | 0.0542824i | ||||
\(508\) | −772.302 | + | 1337.67i | −0.0674515 | + | 0.116829i | ||||
\(509\) | 9156.72 | − | 15859.9i | 0.797376 | − | 1.38110i | −0.123944 | − | 0.992289i | \(-0.539554\pi\) |
0.921320 | − | 0.388806i | \(-0.127112\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2144.99 | − | 3715.23i | −0.185692 | − | 0.321628i | ||||
\(512\) | −8648.67 | −0.746525 | ||||||||
\(513\) | −12811.2 | + | 1230.41i | −1.10259 | + | 0.105895i | ||||
\(514\) | −832.870 | −0.0714714 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −442.546 | + | 826.337i | −0.0377558 | + | 0.0704989i | ||||
\(517\) | −793.555 | + | 1374.48i | −0.0675058 | + | 0.116924i | ||||
\(518\) | −301.144 | + | 521.596i | −0.0255434 | + | 0.0442425i | ||||
\(519\) | 1003.24 | − | 32.0303i | 0.0848505 | − | 0.00270901i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11305.4 | −0.950670 | −0.475335 | − | 0.879805i | \(-0.657673\pi\) | ||||
−0.475335 | + | 0.879805i | \(0.657673\pi\) | |||||||
\(522\) | −2149.51 | + | 137.394i | −0.180233 | + | 0.0115203i | ||||
\(523\) | −2825.92 | −0.236269 | −0.118135 | − | 0.992998i | \(-0.537691\pi\) | ||||
−0.118135 | + | 0.992998i | \(0.537691\pi\) | |||||||
\(524\) | −5645.60 | − | 9778.46i | −0.470666 | − | 0.815218i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1269.56 | + | 2198.94i | −0.105239 | + | 0.182279i | ||||
\(527\) | 3236.89 | − | 5606.46i | 0.267555 | − | 0.463418i | ||||
\(528\) | −846.455 | − | 1363.67i | −0.0697674 | − | 0.112398i | ||||
\(529\) | −5842.47 | − | 10119.5i | −0.480190 | − | 0.831714i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6778.22 | − | 433.256i | 0.553954 | − | 0.0354081i | ||||
\(532\) | 5853.55 | 0.477037 | ||||||||
\(533\) | −306.272 | − | 530.478i | −0.0248895 | − | 0.0431099i | ||||
\(534\) | −2514.32 | + | 80.2744i | −0.203756 | + | 0.00650526i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3123.54 | + | 5410.13i | −0.251710 | + | 0.435974i | ||||
\(537\) | 9643.98 | − | 18007.6i | 0.774988 | − | 1.44708i | ||||
\(538\) | −246.616 | − | 427.152i | −0.0197628 | − | 0.0342302i | ||||
\(539\) | −1451.54 | −0.115997 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20588.2 | −1.63615 | −0.818075 | − | 0.575112i | \(-0.804959\pi\) | ||||
−0.818075 | + | 0.575112i | \(0.804959\pi\) | |||||||
\(542\) | −362.929 | − | 628.612i | −0.0287623 | − | 0.0498177i | ||||
\(543\) | 4713.29 | − | 8800.80i | 0.372498 | − | 0.695541i | ||||
\(544\) | −3896.55 | + | 6749.02i | −0.307101 | + | 0.531915i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1556.24 | + | 49.6856i | −0.121979 | + | 0.00389441i | ||||
\(547\) | 2176.97 | + | 3770.63i | 0.170166 | + | 0.294736i | 0.938478 | − | 0.345340i | \(-0.112236\pi\) |
−0.768312 | + | 0.640076i | \(0.778903\pi\) | |||||||
\(548\) | −4950.21 | −0.385881 | ||||||||
\(549\) | −3269.62 | + | 6603.19i | −0.254179 | + | 0.513328i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7719.72 | + | 13370.9i | 0.596862 | + | 1.03380i | ||||
\(552\) | 3164.58 | + | 5098.25i | 0.244010 | + | 0.393108i | ||||
\(553\) | 2872.74 | − | 4975.73i | 0.220906 | − | 0.382621i | ||||
\(554\) | 1476.74 | − | 2557.79i | 0.113250 | − | 0.196155i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5921.85 | + | 10257.0i | 0.451695 | + | 0.782359i | ||||
\(557\) | −22267.5 | −1.69390 | −0.846951 | − | 0.531672i | \(-0.821564\pi\) | ||||
−0.846951 | + | 0.531672i | \(0.821564\pi\) | |||||||
\(558\) | 516.275 | + | 775.373i | 0.0391679 | + | 0.0588247i | ||||
\(559\) | −1787.30 | −0.135232 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2432.33 | + | 77.6566i | −0.183054 | + | 0.00584432i | ||||
\(562\) | −2159.96 | + | 3741.16i | −0.162122 | + | 0.280803i | ||||
\(563\) | 11505.4 | − | 19927.9i | 0.861270 | − | 1.49176i | −0.00943368 | − | 0.999956i | \(-0.503003\pi\) |
0.870704 | − | 0.491808i | \(-0.163664\pi\) | |||||||
\(564\) | 5748.90 | − | 10734.5i | 0.429206 | − | 0.801428i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −718.139 | −0.0533315 | ||||||||
\(567\) | 5933.90 | − | 761.688i | 0.439507 | − | 0.0564160i | ||||
\(568\) | 2625.69 | 0.193964 | ||||||||
\(569\) | 7121.98 | + | 12335.6i | 0.524726 | + | 0.908852i | 0.999585 | + | 0.0287902i | \(0.00916546\pi\) |
−0.474860 | + | 0.880062i | \(0.657501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2396.71 | − | 4151.22i | 0.175655 | − | 0.304244i | −0.764733 | − | 0.644348i | \(-0.777129\pi\) |
0.940388 | + | 0.340104i | \(0.110462\pi\) | |||||||
\(572\) | 1577.03 | − | 2731.49i | 0.115278 | − | 0.199667i | ||||
\(573\) | −7830.92 | + | 250.016i | −0.570928 | + | 0.0182279i | ||||
\(574\) | 15.4651 | + | 26.7864i | 0.00112457 | + | 0.00194781i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6400.66 | + | 9612.90i | 0.463011 | + | 0.695377i | ||||
\(577\) | −6617.46 | −0.477450 | −0.238725 | − | 0.971087i | \(-0.576729\pi\) | ||||
−0.238725 | + | 0.971087i | \(0.576729\pi\) | |||||||
\(578\) | 710.336 | + | 1230.34i | 0.0511178 | + | 0.0885386i | ||||
\(579\) | 11141.3 | + | 17949.1i | 0.799684 | + | 1.28832i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −990.134 | + | 1714.96i | −0.0707017 | + | 0.122459i | ||||
\(582\) | −505.641 | − | 814.606i | −0.0360129 | − | 0.0580180i | ||||
\(583\) | 907.149 | + | 1571.23i | 0.0644430 | + | 0.111619i | ||||
\(584\) | 3908.78 | 0.276963 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 656.145 | 0.0462544 | ||||||||
\(587\) | −8227.71 | − | 14250.8i | −0.578524 | − | 1.00203i | −0.995649 | − | 0.0931841i | \(-0.970295\pi\) |
0.417125 | − | 0.908849i | \(-0.363038\pi\) | |||||||
\(588\) | 11131.2 | − | 355.383i | 0.780684 | − | 0.0249247i | ||||
\(589\) | 3338.65 | − | 5782.72i | 0.233560 | − | 0.404538i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9608.21 | + | 17940.8i | −0.668746 | + | 1.24870i | ||||
\(592\) | 4541.23 | + | 7865.65i | 0.315276 | + | 0.546074i | ||||
\(593\) | −15990.1 | −1.10731 | −0.553655 | − | 0.832746i | \(-0.686767\pi\) | ||||
−0.553655 | + | 0.832746i | \(0.686767\pi\) | |||||||
\(594\) | 145.292 | − | 318.607i | 0.0100360 | − | 0.0220078i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8174.22 | − | 14158.2i | −0.561794 | − | 0.973056i | ||||
\(597\) | −1510.35 | + | 2820.17i | −0.103542 | + | 0.193337i | ||||
\(598\) | −2819.58 | + | 4883.66i | −0.192812 | + | 0.333959i | ||||
\(599\) | −10230.4 | + | 17719.6i | −0.697836 | + | 1.20869i | 0.271379 | + | 0.962473i | \(0.412520\pi\) |
−0.969215 | + | 0.246215i | \(0.920813\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 320.870 | + | 555.762i | 0.0217779 | + | 0.0377205i | 0.876709 | − | 0.481021i | \(-0.159734\pi\) |
−0.854931 | + | 0.518742i | \(0.826401\pi\) | |||||||
\(602\) | 90.2496 | 0.00611013 | ||||||||
\(603\) | 22511.7 | − | 1438.92i | 1.52031 | − | 0.0971763i | ||||
\(604\) | 18353.6 | 1.23642 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1122.92 | − | 1809.07i | −0.0752733 | − | 0.121268i | ||||
\(607\) | −9375.63 | + | 16239.1i | −0.626928 | + | 1.08587i | 0.361237 | + | 0.932474i | \(0.382355\pi\) |
−0.988165 | + | 0.153397i | \(0.950979\pi\) | |||||||
\(608\) | −4019.05 | + | 6961.20i | −0.268082 | + | 0.464332i | ||||
\(609\) | −3784.95 | − | 6097.70i | −0.251846 | − | 0.405733i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23218.0 | 1.53731 | ||||||||
\(612\) | 18633.4 | − | 1191.03i | 1.23074 | − | 0.0786673i | ||||
\(613\) | −24213.4 | −1.59538 | −0.797690 | − | 0.603067i | \(-0.793945\pi\) | ||||
−0.797690 | + | 0.603067i | \(0.793945\pi\) | |||||||
\(614\) | 385.866 | + | 668.340i | 0.0253621 | + | 0.0439284i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −161.565 | + | 279.838i | −0.0105676 | + | 0.0183036i | ||||
\(617\) | 7935.46 | − | 13744.6i | 0.517779 | − | 0.896819i | −0.482008 | − | 0.876167i | \(-0.660092\pi\) |
0.999787 | − | 0.0206523i | \(-0.00657431\pi\) | |||||||
\(618\) | 1428.12 | − | 2666.64i | 0.0929572 | − | 0.173573i | ||||
\(619\) | 12217.1 | + | 21160.6i | 0.793289 | + | 1.37402i | 0.923920 | + | 0.382585i | \(0.124966\pi\) |
−0.130631 | + | 0.991431i | \(0.541700\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8990.17 | − | 19714.3i | 0.580939 | − | 1.27393i | ||||
\(622\) | 666.727 | 0.0429796 | ||||||||
\(623\) | −4191.05 | − | 7259.12i | −0.269520 | − | 0.466822i | ||||
\(624\) | −11085.1 | + | 20698.5i | −0.711153 | + | 1.32789i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1287.25 | − | 2229.58i | 0.0821865 | − | 0.142351i | ||||
\(627\) | −2508.80 | + | 80.0980i | −0.159796 | + | 0.00510176i | ||||
\(628\) | 7791.61 | + | 13495.5i | 0.495094 | + | 0.857528i | ||||
\(629\) | 13771.1 | 0.872956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22573.7 | 1.42416 | 0.712079 | − | 0.702099i | \(-0.247754\pi\) | ||||
0.712079 | + | 0.702099i | \(0.247754\pi\) | |||||||
\(632\) | 2617.47 | + | 4533.59i | 0.164743 | + | 0.285343i | ||||
\(633\) | 6120.54 | + | 9860.41i | 0.384312 | + | 0.619141i | ||||
\(634\) | −1820.50 | + | 3153.20i | −0.114040 | + | 0.197523i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7341.20 | − | 11826.9i | −0.457701 | − | 0.737372i | ||||
\(637\) | 10617.3 | + | 18389.8i | 0.660399 | + | 1.14384i | ||||
\(638\) | −420.077 | −0.0260674 | ||||||||
\(639\) | −5254.66 | − | 7891.76i | −0.325307 | − | 0.488565i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1861.15 | + | 3223.61i | 0.114682 | + | 0.198635i | 0.917653 | − | 0.397384i | \(-0.130082\pi\) |
−0.802971 | + | 0.596019i | \(0.796748\pi\) | |||||||
\(642\) | 4579.55 | − | 146.210i | 0.281527 | − | 0.00898826i | ||||
\(643\) | −1499.38 | + | 2597.00i | −0.0919593 | + | 0.159278i | −0.908335 | − | 0.418242i | \(-0.862646\pi\) |
0.816376 | + | 0.577520i | \(0.195980\pi\) | |||||||
\(644\) | −4927.34 | + | 8534.41i | −0.301498 | + | 0.522209i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1933.63 | + | 3349.15i | 0.117767 | + | 0.203979i | ||||
\(647\) | 4302.38 | 0.261428 | 0.130714 | − | 0.991420i | \(-0.458273\pi\) | ||||
0.130714 | + | 0.991420i | \(0.458273\pi\) | |||||||
\(648\) | −2102.29 | + | 5029.28i | −0.127447 | + | 0.304890i | ||||
\(649\) | 1324.66 | 0.0801193 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1465.38 | + | 2736.20i | −0.0882223 | + | 0.164732i | ||||
\(652\) | −10778.1 | + | 18668.2i | −0.647396 | + | 1.12132i | ||||
\(653\) | 400.641 | − | 693.930i | 0.0240096 | − | 0.0415859i | −0.853771 | − | 0.520649i | \(-0.825690\pi\) |
0.877781 | + | 0.479063i | \(0.159023\pi\) | |||||||
\(654\) | −2553.51 | + | 81.5254i | −0.152676 | + | 0.00487446i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 466.427 | 0.0277606 | ||||||||
\(657\) | −7822.45 | − | 11748.2i | −0.464510 | − | 0.697628i | ||||
\(658\) | −1172.39 | −0.0694596 | ||||||||
\(659\) | 3728.20 | + | 6457.43i | 0.220379 | + | 0.381708i | 0.954923 | − | 0.296853i | \(-0.0959372\pi\) |
−0.734544 | + | 0.678561i | \(0.762604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1332.53 | + | 2308.01i | −0.0784106 | + | 0.135811i | −0.902564 | − | 0.430555i | \(-0.858318\pi\) |
0.824154 | + | 0.566366i | \(0.191651\pi\) | |||||||
\(662\) | 978.524 | − | 1694.85i | 0.0574492 | − | 0.0995050i | ||||
\(663\) | 18775.2 | + | 30247.6i | 1.09980 | + | 1.77182i | ||||
\(664\) | −902.152 | − | 1562.57i | −0.0527264 | − | 0.0913247i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −879.293 | + | 1775.78i | −0.0511590 | + | 0.103319i | ||||
\(667\) | −25992.9 | −1.50892 | ||||||||
\(668\) | −7177.91 | − | 12432.5i | −0.415751 | − | 0.720102i | ||||
\(669\) | 24048.2 | − | 767.783i | 1.38977 | − | 0.0443710i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −718.527 | + | 1244.53i | −0.0413389 | + | 0.0716011i | ||||
\(672\) | 1764.01 | − | 3293.82i | 0.101262 | − | 0.189080i | ||||
\(673\) | −11774.9 | − | 20394.7i | −0.674427 | − | 1.16814i | −0.976636 | − | 0.214900i | \(-0.931058\pi\) |
0.302210 | − | 0.953242i | \(-0.402276\pi\) | |||||||
\(674\) | 1243.82 | 0.0710834 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29058.6 | −1.65331 | ||||||||
\(677\) | −4969.86 | − | 8608.04i | −0.282138 | − | 0.488677i | 0.689773 | − | 0.724025i | \(-0.257710\pi\) |
−0.971911 | + | 0.235349i | \(0.924377\pi\) | |||||||
\(678\) | −1636.87 | + | 3056.43i | −0.0927194 | + | 0.173129i | ||||
\(679\) | 1597.34 | − | 2766.68i | 0.0902805 | − | 0.156370i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2428.97 | + | 77.5491i | −0.136679 | + | 0.00436371i | ||||
\(682\) | 90.8382 | + | 157.336i | 0.00510026 | + | 0.00883391i | ||||
\(683\) | −11680.3 | −0.654371 | −0.327185 | − | 0.944960i | \(-0.606100\pi\) | ||||
−0.327185 | + | 0.944960i | \(0.606100\pi\) | |||||||
\(684\) | 19219.2 | − | 1228.47i | 1.07437 | − | 0.0686721i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1203.23 | − | 2084.05i | −0.0669671 | − | 0.115990i | ||||
\(687\) | −3993.09 | − | 6433.02i | −0.221756 | − | 0.357256i | ||||
\(688\) | 680.479 | − | 1178.63i | 0.0377079 | − | 0.0653120i | ||||
\(689\) | 13270.8 | − | 22985.6i | 0.733782 | − | 1.27095i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6178.47 | + | 10701.4i | 0.340145 | + | 0.589148i | 0.984459 | − | 0.175613i | \(-0.0561906\pi\) |
−0.644315 | + | 0.764761i | \(0.722857\pi\) | |||||||
\(692\) | −1501.98 | −0.0825096 | ||||||||
\(693\) | 1164.41 | − | 74.4278i | 0.0638274 | − | 0.00407977i | ||||
\(694\) | 3277.55 | 0.179271 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6535.84 | − | 208.668i | 0.355949 | − | 0.0113643i | ||||
\(697\) | 353.605 | − | 612.462i | 0.0192163 | − | 0.0332836i | ||||
\(698\) | −630.504 | + | 1092.06i | −0.0341904 | + | 0.0592195i | ||||
\(699\) | −6420.96 | + | 11989.4i | −0.347444 | + | 0.648759i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10659.6 | 0.574333 | 0.287167 | − | 0.957881i | \(-0.407287\pi\) | ||||
0.287167 | + | 0.957881i | \(0.407287\pi\) | |||||||
\(702\) | −5099.23 | + | 489.738i | −0.274157 | + | 0.0263305i | ||||
\(703\) | 14204.0 | 0.762042 | ||||||||
\(704\) | 1126.19 | + | 1950.62i | 0.0602911 | + | 0.104427i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1070.62 | − | 1854.37i | 0.0570729 | − | 0.0988531i | ||||
\(707\) | 3547.37 | − | 6144.22i | 0.188702 | − | 0.326842i | ||||
\(708\) | −10158.2 | + | 324.319i | −0.539221 | + | 0.0172156i | ||||
\(709\) | −9669.28 | − | 16747.7i | −0.512183 | − | 0.887126i | −0.999900 | − | 0.0141250i | \(-0.995504\pi\) |
0.487718 | − | 0.873002i | \(-0.337830\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8387.95 | − | 16939.9i | 0.442437 | − | 0.893526i | ||||
\(712\) | 7637.29 | 0.401994 | ||||||||
\(713\) | 5620.76 | + | 9735.43i | 0.295230 | + | 0.511353i | ||||
\(714\) | −948.053 | − | 1527.35i | −0.0496918 | − | 0.0800553i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15283.4 | + | 26471.6i | −0.797720 | + | 1.38169i | ||||
\(717\) | 10169.9 | + | 16384.0i | 0.529708 | + | 0.853379i | ||||
\(718\) | 640.440 | + | 1109.27i | 0.0332883 | + | 0.0576571i | ||||
\(719\) | −27300.1 | −1.41603 | −0.708013 | − | 0.706199i | \(-0.750408\pi\) | ||||
−0.708013 | + | 0.706199i | \(0.750408\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10079.4 | 0.520631 | ||||||||
\(722\) | 368.871 | + | 638.904i | 0.0190138 | + | 0.0329329i | ||||
\(723\) | −9577.37 | + | 305.775i | −0.492651 | + | 0.0157288i | ||||
\(724\) | −7469.43 | + | 12937.4i | −0.383424 | + | 0.664111i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1515.41 | + | 2829.62i | −0.0774683 | + | 0.144651i | ||||
\(727\) | −882.466 | − | 1528.48i | −0.0450191 | − | 0.0779753i | 0.842638 | − | 0.538481i | \(-0.181002\pi\) |
−0.887657 | + | 0.460505i | \(0.847668\pi\) | |||||||
\(728\) | 4727.08 | 0.240656 | ||||||||
\(729\) | 19323.2 | − | 3746.22i | 0.981721 | − | 0.190328i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1031.76 | − | 1787.06i | −0.0522040 | − | 0.0904199i | ||||
\(732\) | 5205.36 | − | 9719.62i | 0.262835 | − | 0.490775i | ||||
\(733\) | −8652.75 | + | 14987.0i | −0.436012 | + | 0.755195i | −0.997378 | − | 0.0723730i | \(-0.976943\pi\) |
0.561366 | + | 0.827568i | \(0.310276\pi\) | |||||||
\(734\) | 838.561 | − | 1452.43i | 0.0421688 | − | 0.0730384i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6766.23 | − | 11719.5i | −0.338868 | − | 0.586936i | ||||
\(737\) | 4399.43 | 0.219885 | ||||||||
\(738\) | 56.3990 | + | 84.7035i | 0.00281311 | + | 0.00422490i | ||||
\(739\) | −1456.60 | −0.0725058 | −0.0362529 | − | 0.999343i | \(-0.511542\pi\) | ||||
−0.0362529 | + | 0.999343i | \(0.511542\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19365.5 | + | 31198.5i | 0.960067 | + | 1.54670i | ||||
\(742\) | −670.105 | + | 1160.66i | −0.0331541 | + | 0.0574246i | ||||
\(743\) | −8468.55 | + | 14668.0i | −0.418144 | + | 0.724246i | −0.995753 | − | 0.0920673i | \(-0.970653\pi\) |
0.577609 | + | 0.816314i | \(0.303986\pi\) | |||||||
\(744\) | −1491.48 | − | 2402.82i | −0.0734949 | − | 0.118403i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2715.91 | 0.133293 | ||||||||
\(747\) | −2891.04 | + | 5838.61i | −0.141603 | + | 0.285975i | ||||
\(748\) | 3641.51 | 0.178004 | ||||||||
\(749\) | 7633.51 | + | 13221.6i | 0.372393 | + | 0.645004i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6467.80 | + | 11202.6i | −0.314265 | + | 0.544323i | −0.979281 | − | 0.202506i | \(-0.935091\pi\) |
0.665016 | + | 0.746829i | \(0.268425\pi\) | |||||||
\(752\) | −8839.78 | + | 15310.9i | −0.428661 | + | 0.742463i | ||||
\(753\) | 17672.8 | − | 32999.2i | 0.855288 | − | 1.59702i | ||||
\(754\) | 3072.67 | + | 5322.02i | 0.148409 | + | 0.257051i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8911.13 | + | 855.839i | −0.428696 | + | 0.0411727i | ||||
\(757\) | 37371.9 | 1.79433 | 0.897164 | − | 0.441697i | \(-0.145623\pi\) | ||||
0.897164 | + | 0.441697i | \(0.145623\pi\) | |||||||
\(758\) | −2068.39 | − | 3582.56i | −0.0991128 | − | 0.171668i | ||||
\(759\) | 1995.05 | − | 3725.22i | 0.0954094 | − | 0.178152i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6999.67 | − | 12123.8i | 0.333427 | − | 0.577513i | −0.649754 | − | 0.760144i | \(-0.725128\pi\) |
0.983181 | + | 0.182632i | \(0.0584616\pi\) | |||||||
\(762\) | 489.021 | − | 15.6129i | 0.0232485 | − | 0.000742251i | ||||
\(763\) | −4256.37 | − | 7372.25i | −0.201954 | − | 0.349795i | ||||
\(764\) | 11723.9 | 0.555177 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2162.72 | 0.102013 | ||||||||
\(767\) | −9689.27 | − | 16782.3i | −0.456140 | − | 0.790058i | ||||
\(768\) | −8203.32 | − | 13215.8i | −0.385432 | − | 0.620945i | ||||
\(769\) | 5221.26 | − | 9043.49i | 0.244842 | − | 0.424079i | −0.717245 | − | 0.696821i | \(-0.754597\pi\) |
0.962087 | + | 0.272742i | \(0.0879306\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4815.20 | − | 7757.45i | −0.224922 | − | 0.362358i | ||||
\(772\) | −15805.9 | − | 27376.6i | −0.736874 | − | 1.27630i | ||||
\(773\) | 23092.7 | 1.07450 | 0.537249 | − | 0.843424i | \(-0.319463\pi\) | ||||
0.537249 | + | 0.843424i | \(0.319463\pi\) | |||||||
\(774\) | 296.321 | − | 18.9405i | 0.0137610 | − | 0.000879587i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1455.41 | + | 2520.84i | 0.0673274 | + | 0.116615i | ||||
\(777\) | −6599.26 | + | 210.693i | −0.304694 | + | 0.00972791i | ||||
\(778\) | 2863.94 | − | 4960.49i | 0.131976 | − | 0.228589i | ||||
\(779\) | 364.722 | − | 631.717i | 0.0167747 | − | 0.0290547i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −924.553 | − | 1601.37i | −0.0423599 | − | 0.0733696i | ||||
\(782\) | −6510.68 | −0.297726 | ||||||||
\(783\) | −13707.0 | − | 19226.5i | −0.625605 | − | 0.877522i | ||||
\(784\) | −16169.3 | −0.736577 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1688.55 | + | 3152.93i | −0.0766269 | + | 0.143080i | ||||
\(787\) | 4258.12 | − | 7375.28i | 0.192866 | − | 0.334054i | −0.753333 | − | 0.657639i | \(-0.771555\pi\) |
0.946199 | + | 0.323586i | \(0.104888\pi\) | |||||||
\(788\) | 15226.7 | − | 26373.4i | 0.688362 | − | 1.19228i | ||||
\(789\) | −27821.1 | + | 888.240i | −1.25533 | + | 0.0400788i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11552.7 | −0.519299 | ||||||||
\(792\) | −471.744 | + | 952.712i | −0.0211650 | + | 0.0427439i | ||||
\(793\) | 21022.8 | 0.941413 | ||||||||
\(794\) | −1393.68 | − | 2413.92i | −0.0622920 | − | 0.107893i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2393.54 | − | 4145.74i | 0.106579 | − | 0.184600i | ||||
\(797\) | −14701.1 | + | 25463.1i | −0.653376 | + | 1.13168i | 0.328922 | + | 0.944357i | \(0.393315\pi\) |
−0.982298 | + | 0.187324i | \(0.940019\pi\) | |||||||
\(798\) | −977.858 | − | 1575.36i | −0.0433782 | − | 0.0698838i | ||||
\(799\) | 13403.1 | + | 23214.9i | 0.593452 | + | 1.02789i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15284.1 | − | 22954.6i | −0.674205 | − | 1.01256i | ||||
\(802\) | −1561.85 | −0.0687667 | ||||||||
\(803\) | −1376.35 | − | 2383.91i | −0.0604863 | − | 0.104765i | ||||
\(804\) | −33737.2 | + | 1077.12i | −1.47988 | + | 0.0472477i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1328.88 | − | 2301.69i | 0.0580742 | − | 0.100587i | ||||
\(807\) | 2552.75 | − | 4766.58i | 0.111352 | − | 0.207920i | ||||
\(808\) | 3232.16 | + | 5598.26i | 0.140726 | + | 0.243745i | ||||
\(809\) | −7358.17 | −0.319777 | −0.159888 | − | 0.987135i | \(-0.551113\pi\) | ||||
−0.159888 | + | 0.987135i | \(0.551113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14069.2 | 0.609168 | 0.304584 | − | 0.952485i | \(-0.401483\pi\) | ||||
0.304584 | + | 0.952485i | \(0.401483\pi\) | |||||||
\(812\) | 5369.62 | + | 9300.45i | 0.232065 | + | 0.401948i | ||||
\(813\) | 3756.71 | − | 7014.66i | 0.162059 | − | 0.302601i | ||||
\(814\) | −193.232 | + | 334.688i | −0.00832036 | + | 0.0144113i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −27094.9 | + | 865.052i | −1.16239 | + | 0.0371114i | ||||
\(817\) | −1064.20 | − | 1843.25i | −0.0455711 | − | 0.0789315i | ||||
\(818\) | 2947.00 | 0.125965 | ||||||||
\(819\) | −9460.08 | − | 14207.7i | −0.403617 | − | 0.606176i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13340.0 | − | 23105.6i | −0.567076 | − | 0.982205i | −0.996853 | − | 0.0792696i | \(-0.974741\pi\) |
0.429777 | − | 0.902935i | \(-0.358592\pi\) | |||||||
\(822\) | 826.951 | + | 1332.25i | 0.0350891 | + | 0.0565298i | ||||
\(823\) | 3807.19 | − | 6594.24i | 0.161252 | − | 0.279296i | −0.774066 | − | 0.633105i | \(-0.781780\pi\) |
0.935318 | + | 0.353809i | \(0.115114\pi\) | |||||||
\(824\) | −4591.86 | + | 7953.34i | −0.194132 | + | 0.336247i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 489.258 | + | 847.420i | 0.0206095 | + | 0.0356968i | ||||
\(827\) | 24854.1 | 1.04505 | 0.522527 | − | 0.852623i | \(-0.324989\pi\) | ||||
0.522527 | + | 0.852623i | \(0.324989\pi\) | |||||||
\(828\) | −14387.1 | + | 29055.5i | −0.603847 | + | 1.21950i | ||||
\(829\) | −17292.6 | −0.724482 | −0.362241 | − | 0.932084i | \(-0.617988\pi\) | ||||
−0.362241 | + | 0.932084i | \(0.617988\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32361.2 | − | 1033.19i | 1.35090 | − | 0.0431300i | ||||
\(832\) | 16475.1 | − | 28535.8i | 0.686506 | − | 1.18906i | ||||
\(833\) | −12258.2 | + | 21231.8i | −0.509870 | + | 0.883121i | ||||
\(834\) | 1771.18 | − | 3307.21i | 0.0735384 | − | 0.137313i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3755.99 | 0.155387 | ||||||||
\(837\) | −4237.10 | + | 9291.44i | −0.174977 | + | 0.383703i | ||||
\(838\) | −824.876 | −0.0340034 | ||||||||
\(839\) | −3524.59 | − | 6104.77i | −0.145033 | − | 0.251204i | 0.784352 | − | 0.620315i | \(-0.212995\pi\) |
−0.929385 | + | 0.369111i | \(0.879662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1968.51 | + | 3409.56i | −0.0807131 | + | 0.139799i | ||||
\(842\) | −304.438 | + | 527.302i | −0.0124604 | + | 0.0215820i | ||||
\(843\) | −47333.4 | + | 1511.20i | −1.93386 | + | 0.0617421i | ||||
\(844\) | −8683.06 | − | 15039.5i | −0.354127 | − | 0.613366i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3849.36 | + | 246.046i | −0.156434 | + | 0.00999910i | ||||
\(847\) | −10695.4 | −0.433882 | ||||||||
\(848\) | 10105.1 | + | 17502.6i | 0.409213 | + | 0.708777i | ||||
\(849\) | −4151.88 | − | 6688.83i | −0.167835 | − | 0.270389i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11956.5 | + | 20709.3i | −0.481627 | + | 0.834202i | ||||
\(852\) | 7482.04 | + | 12053.8i | 0.300858 | + | 0.484692i | ||||
\(853\) | 5634.57 | + | 9759.36i | 0.226171 | + | 0.391740i | 0.956670 | − | 0.291174i | \(-0.0940458\pi\) |
−0.730499 | + | 0.682914i | \(0.760712\pi\) | |||||||
\(854\) | −1061.54 | −0.0425354 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13910.4 | −0.555431 | ||||||||
\(857\) | 17077.0 | + | 29578.3i | 0.680676 | + | 1.17897i | 0.974775 | + | 0.223191i | \(0.0716474\pi\) |
−0.294098 | + | 0.955775i | \(0.595019\pi\) | |||||||
\(858\) | −998.574 | + | 31.8813i | −0.0397328 | + | 0.00126854i | ||||
\(859\) | 21367.1 | − | 37008.9i | 0.848704 | − | 1.47000i | −0.0336608 | − | 0.999433i | \(-0.510717\pi\) |
0.882365 | − | 0.470566i | \(-0.155950\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −160.081 | + | 298.909i | −0.00633629 | + | 0.0118313i | ||||
\(862\) | −2824.37 | − | 4891.96i | −0.111599 | − | 0.193295i | ||||
\(863\) | 6893.93 | 0.271926 | 0.135963 | − | 0.990714i | \(-0.456587\pi\) | ||||
0.135963 | + | 0.990714i | \(0.456587\pi\) | |||||||
\(864\) | 5100.60 | − | 11185.0i | 0.200840 | − | 0.440417i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 380.047 | + | 658.260i | 0.0149128 | + | 0.0258298i | ||||
\(867\) | −7352.75 | + | 13729.3i | −0.288019 | + | 0.537799i | ||||
\(868\) | 2322.27 | − | 4022.30i | 0.0908101 | − | 0.157288i | ||||
\(869\) | 1843.32 | − | 3192.73i | 0.0719567 | − | 0.124633i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32179.8 | − | 55737.0i | −1.25186 | − | 2.16829i | ||||
\(872\) | 7756.32 | 0.301218 | ||||||||
\(873\) | 4664.00 | − | 9419.21i | 0.180816 | − | 0.365168i | ||||
\(874\) | −6715.37 | −0.259898 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11138.3 | + | 17944.2i | 0.429598 | + | 0.692098i | ||||
\(877\) | 23969.2 | − | 41515.9i | 0.922900 | − | 1.59851i | 0.127995 | − | 0.991775i | \(-0.459146\pi\) |
0.794905 | − | 0.606734i | \(-0.207521\pi\) | |||||||
\(878\) | 430.490 | − | 745.630i | 0.0165471 | − | 0.0286604i | ||||
\(879\) | 3793.47 | + | 6111.41i | 0.145564 | + | 0.234508i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35033.8 | 1.33975 | 0.669875 | − | 0.742474i | \(-0.266348\pi\) | ||||
0.669875 | + | 0.742474i | \(0.266348\pi\) | |||||||
\(882\) | −1955.15 | − | 2936.36i | −0.0746409 | − | 0.112100i | ||||
\(883\) | −155.057 | −0.00590951 | −0.00295475 | − | 0.999996i | \(-0.500941\pi\) | ||||
−0.00295475 | + | 0.999996i | \(0.500941\pi\) | |||||||
\(884\) | −26636.0 | − | 46134.8i | −1.01342 | − | 1.75530i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −536.861 | + | 929.870i | −0.0203569 | + | 0.0352591i | ||||
\(887\) | −2238.25 | + | 3876.76i | −0.0847272 | + | 0.146752i | −0.905275 | − | 0.424826i | \(-0.860335\pi\) |
0.820548 | + | 0.571578i | \(0.193669\pi\) | |||||||
\(888\) | 2840.18 | − | 5303.28i | 0.107331 | − | 0.200413i | ||||
\(889\) | 815.135 | + | 1411.86i | 0.0307523 | + | 0.0532645i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3807.55 | − | 488.745i | 0.143162 | − | 0.0183766i | ||||
\(892\) | −36003.2 | −1.35143 | ||||||||
\(893\) | 13824.5 | + | 23944.7i | 0.518050 | + | 0.897289i | ||||
\(894\) | −2444.85 | + | 4565.10i | −0.0914630 | + | 0.170783i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3708.23 | + | 6422.84i | −0.138262 | + | 0.239478i | ||||
\(897\) | −61788.3 | + | 1972.70i | −2.29995 | + | 0.0734300i | ||||
\(898\) | −3142.54 | − | 5443.03i | −0.116779 | − | 0.202268i | ||||
\(899\) | 12250.6 | 0.454481 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30643.4 | 1.13305 | ||||||||
\(902\) | 9.92337 | + | 17.1878i | 0.000366310 | + | 0.000634468i | ||||
\(903\) | 521.774 | + | 840.596i | 0.0192287 | + | 0.0309782i | ||||
\(904\) | 5263.06 | − | 9115.89i | 0.193636 | − | 0.335387i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3066.05 | − | 4939.51i | −0.112431 | − | 0.181130i | ||||
\(907\) | 6294.11 | + | 10901.7i | 0.230422 | + | 0.399102i | 0.957932 | − | 0.286994i | \(-0.0926561\pi\) |
−0.727511 | + | 0.686096i | \(0.759323\pi\) | |||||||
\(908\) | 3636.47 | 0.132908 | ||||||||
\(909\) | 10357.8 | − | 20918.1i | 0.377938 | − | 0.763266i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19956.5 | − | 34565.7i | −0.725784 | − | 1.25709i | −0.958651 | − | 0.284586i | \(-0.908144\pi\) |
0.232867 | − | 0.972509i | \(-0.425189\pi\) | |||||||
\(912\) | −27946.7 | + | 892.248i | −1.01470 | + | 0.0323962i | ||||
\(913\) | −635.329 | + | 1100.42i | −0.0230299 | + | 0.0398890i | ||||
\(914\) | 31.2496 | − | 54.1259i | 0.00113090 | − | 0.00195878i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5664.90 | + | 9811.90i | 0.204338 | + | 0.353924i | ||||
\(917\) | −11917.4 | −0.429169 | ||||||||
\(918\) | −3433.33 | − | 4815.84i | −0.123439 | − | 0.173144i | ||||
\(919\) | −36540.8 | −1.31161 | −0.655804 | − | 0.754931i | \(-0.727670\pi\) | ||||
−0.655804 | + | 0.754931i | \(0.727670\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3994.14 | + | 7457.99i | −0.142900 | + | 0.266828i | ||||
\(922\) | 3029.39 | − | 5247.05i | 0.108208 | − | 0.187421i | ||||
\(923\) | −13525.4 | + | 23426.6i | −0.482332 | + | 0.835424i | ||||
\(924\) | −1745.05 | + | 55.7139i | −0.0621298 | + | 0.00198361i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2190.50 | −0.0777369 | ||||||||
\(927\) | 33094.0 | − | 2115.33i | 1.17255 | − | 0.0749477i | ||||
\(928\) | −14747.1 | −0.521658 | ||||||||
\(929\) | −9366.27 | − | 16222.8i | −0.330783 | − | 0.572933i | 0.651883 | − | 0.758320i | \(-0.273979\pi\) |
−0.982666 | + | 0.185387i | \(0.940646\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12643.6 | + | 21899.3i | −0.445088 | + | 0.770915i | ||||
\(932\) | 10175.7 | − | 17624.8i | 0.357635 | − | 0.619442i | ||||
\(933\) | 3854.65 | + | 6209.98i | 0.135258 | + | 0.217905i | ||||
\(934\) | −1315.48 | − | 2278.48i | −0.0460856 | − | 0.0798226i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15520.7 | − | 992.061i | 0.541996 | − | 0.0346437i | ||||
\(937\) | 41501.3 | 1.44695 | 0.723473 | − | 0.690353i | \(-0.242545\pi\) | ||||
0.723473 | + | 0.690353i | \(0.242545\pi\) | |||||||
\(938\) | 1624.91 | + | 2814.43i | 0.0565622 | + | 0.0979686i | ||||
\(939\) | 28208.7 | − | 900.615i | 0.980359 | − | 0.0312997i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13683.3 | + | 23700.1i | −0.474029 | + | 0.821043i | −0.999558 | − | 0.0297333i | \(-0.990534\pi\) |
0.525529 | + | 0.850776i | \(0.323868\pi\) | |||||||
\(942\) | 2330.41 | − | 4351.42i | 0.0806039 | − | 0.150506i | ||||
\(943\) | 614.024 | + | 1063.52i | 0.0212040 | + | 0.0367264i | ||||
\(944\) | 14756.0 | 0.508757 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57.9095 | 0.00199028 | ||||||||
\(947\) | 25943.9 | + | 44936.1i | 0.890245 | + | 1.54195i | 0.839581 | + | 0.543234i | \(0.182800\pi\) |
0.0506637 | + | 0.998716i | \(0.483866\pi\) | |||||||
\(948\) | −13353.9 | + | 24934.9i | −0.457505 | + | 0.854269i | ||||
\(949\) | −20134.8 | + | 34874.5i | −0.688728 | + | 1.19291i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39894.4 | + | 1273.70i | −1.36032 | + | 0.0434307i | ||||
\(952\) | 2728.82 | + | 4726.45i | 0.0929008 | + | 0.160909i | ||||
\(953\) | −10624.9 | −0.361150 | −0.180575 | − | 0.983561i | \(-0.557796\pi\) | ||||
−0.180575 | + | 0.983561i | \(0.557796\pi\) | |||||||
\(954\) | −1956.60 | + | 3951.47i | −0.0664018 | + | 0.134102i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14427.7 | − | 24989.6i | −0.488103 | − | 0.845419i | ||||
\(957\) | −2428.65 | − | 3912.65i | −0.0820347 | − | 0.132161i | ||||
\(958\) | 460.099 | − | 796.915i | 0.0155168 | − | 0.0268760i | ||||
\(959\) | −2612.38 | + | 4524.78i | −0.0879647 | + | 0.152359i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12246.4 | + | 21211.4i | 0.411078 | + | 0.712008i | ||||
\(962\) | 5653.61 | 0.189480 | ||||||||
\(963\) | 27838.3 | + | 41809.2i | 0.931543 | + | 1.39905i | ||||
\(964\) | 14338.5 | 0.479059 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3119.99 | − | 99.6114i | 0.103917 | − | 0.00331775i | ||||
\(967\) | −11229.2 | + | 19449.5i | −0.373429 | + | 0.646797i | −0.990090 | − | 0.140431i | \(-0.955151\pi\) |
0.616662 | + | 0.787228i | \(0.288485\pi\) | |||||||
\(968\) | 4872.51 | − | 8439.43i | 0.161785 | − | 0.280221i | ||||
\(969\) | −20015.2 | + | 37373.0i | −0.663550 | + | 1.23900i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42186.8 | 1.39427 | 0.697137 | − | 0.716938i | \(-0.254457\pi\) | ||||
0.697137 | + | 0.716938i | \(0.254457\pi\) | |||||||
\(972\) | −29078.7 | + | 4680.17i | −0.959568 | + | 0.154441i | ||||
\(973\) | 12500.6 | 0.411871 | ||||||||
\(974\) | 42.2174 | + | 73.1228i | 0.00138884 | + | 0.00240555i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8004.00 | + | 13863.3i | −0.262502 | + | 0.454667i | ||||
\(977\) | 14339.7 | − | 24837.1i | 0.469568 | − | 0.813315i | −0.529827 | − | 0.848106i | \(-0.677743\pi\) |
0.999395 | + | 0.0347907i | \(0.0110765\pi\) | |||||||
\(978\) | 6824.67 | − | 217.890i | 0.223138 | − | 0.00712409i | ||||
\(979\) | −2689.23 | − | 4657.88i | −0.0877918 | − | 0.152060i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15522.3 | − | 23312.4i | −0.505189 | − | 0.758723i | ||||
\(982\) | 2650.36 | 0.0861267 | ||||||||
\(983\) | −26691.2 | − | 46230.6i | −0.866041 | − | 1.50003i | −0.866010 | − | 0.500027i | \(-0.833323\pi\) |
−3.14809e−5 | − | 1.00000i | \(-0.500010\pi\) | |||||||
\(984\) | −162.932 | − | 262.490i | −0.00527855 | − | 0.00850393i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3547.54 | + | 6144.52i | −0.114581 | + | 0.198460i | ||||
\(987\) | −6778.10 | − | 10919.8i | −0.218591 | − | 0.352158i | ||||
\(988\) | −27473.3 | − | 47585.2i | −0.884659 | − | 1.53228i | ||||
\(989\) | 3583.24 | 0.115208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1505.90 | −0.0482708 | −0.0241354 | − | 0.999709i | \(-0.507683\pi\) | ||||
−0.0241354 | + | 0.999709i | \(0.507683\pi\) | |||||||
\(992\) | 3188.95 | + | 5523.42i | 0.102066 | + | 0.176783i | ||||
\(993\) | 21443.4 | − | 684.618i | 0.685281 | − | 0.0218788i | ||||
\(994\) | 682.961 | − | 1182.92i | 0.0217930 | − | 0.0377465i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4602.63 | − | 8594.19i | 0.146426 | − | 0.273411i | ||||
\(997\) | −17760.5 | − | 30762.1i | −0.564174 | − | 0.977178i | −0.997126 | − | 0.0757610i | \(-0.975861\pi\) |
0.432952 | − | 0.901417i | \(-0.357472\pi\) | |||||||
\(998\) | −5387.87 | −0.170892 | ||||||||
\(999\) | −21623.4 | + | 2076.75i | −0.684820 | + | 0.0657712i |
(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 | 225.4.e.g.76.9 | 32 | ||
5.2 | odd | 4 | 45.4.j.a.4.8 | ✓ | 32 | ||
5.3 | odd | 4 | 45.4.j.a.4.9 | yes | 32 | ||
5.4 | even | 2 | inner | 225.4.e.g.76.8 | 32 | ||
9.4 | even | 3 | 2025.4.a.bk.1.8 | 16 | |||
9.5 | odd | 6 | 2025.4.a.bl.1.9 | 16 | |||
9.7 | even | 3 | inner | 225.4.e.g.151.9 | 32 | ||
15.2 | even | 4 | 135.4.j.a.64.9 | 32 | |||
15.8 | even | 4 | 135.4.j.a.64.8 | 32 | |||
45.2 | even | 12 | 135.4.j.a.19.8 | 32 | |||
45.4 | even | 6 | 2025.4.a.bk.1.9 | 16 | |||
45.7 | odd | 12 | 45.4.j.a.34.9 | yes | 32 | ||
45.13 | odd | 12 | 405.4.b.e.244.9 | 16 | |||
45.14 | odd | 6 | 2025.4.a.bl.1.8 | 16 | |||
45.22 | odd | 12 | 405.4.b.e.244.8 | 16 | |||
45.23 | even | 12 | 405.4.b.f.244.8 | 16 | |||
45.32 | even | 12 | 405.4.b.f.244.9 | 16 | |||
45.34 | even | 6 | inner | 225.4.e.g.151.8 | 32 | ||
45.38 | even | 12 | 135.4.j.a.19.9 | 32 | |||
45.43 | odd | 12 | 45.4.j.a.34.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.j.a.4.8 | ✓ | 32 | 5.2 | odd | 4 | ||
45.4.j.a.4.9 | yes | 32 | 5.3 | odd | 4 | ||
45.4.j.a.34.8 | yes | 32 | 45.43 | odd | 12 | ||
45.4.j.a.34.9 | yes | 32 | 45.7 | odd | 12 | ||
135.4.j.a.19.8 | 32 | 45.2 | even | 12 | |||
135.4.j.a.19.9 | 32 | 45.38 | even | 12 | |||
135.4.j.a.64.8 | 32 | 15.8 | even | 4 | |||
135.4.j.a.64.9 | 32 | 15.2 | even | 4 | |||
225.4.e.g.76.8 | 32 | 5.4 | even | 2 | inner | ||
225.4.e.g.76.9 | 32 | 1.1 | even | 1 | trivial | ||
225.4.e.g.151.8 | 32 | 45.34 | even | 6 | inner | ||
225.4.e.g.151.9 | 32 | 9.7 | even | 3 | inner | ||
405.4.b.e.244.8 | 16 | 45.22 | odd | 12 | |||
405.4.b.e.244.9 | 16 | 45.13 | odd | 12 | |||
405.4.b.f.244.8 | 16 | 45.23 | even | 12 | |||
405.4.b.f.244.9 | 16 | 45.32 | even | 12 | |||
2025.4.a.bk.1.8 | 16 | 9.4 | even | 3 | |||
2025.4.a.bk.1.9 | 16 | 45.4 | even | 6 | |||
2025.4.a.bl.1.8 | 16 | 45.14 | odd | 6 | |||
2025.4.a.bl.1.9 | 16 | 9.5 | odd | 6 |