Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(20,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.20");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 20.4 | ||
Character | \(\chi\) | \(=\) | 63.20 |
Dual form | 63.4.o.a.41.4 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.38393 | − | 1.95371i | −1.19640 | − | 0.690741i | −0.236648 | − | 0.971595i | \(-0.576049\pi\) |
−0.959750 | + | 0.280855i | \(0.909382\pi\) | |||||||
\(3\) | 4.35656 | − | 2.83202i | 0.838421 | − | 0.545023i | ||||
\(4\) | 3.63397 | + | 6.29422i | 0.454246 | + | 0.786777i | ||||
\(5\) | −5.82670 | − | 10.0921i | −0.521156 | − | 0.902668i | −0.999697 | − | 0.0246032i | \(-0.992168\pi\) |
0.478542 | − | 0.878065i | \(-0.341166\pi\) | |||||||
\(6\) | −20.2752 | + | 1.07189i | −1.37956 | + | 0.0729328i | ||||
\(7\) | 17.1417 | − | 7.01157i | 0.925565 | − | 0.378589i | ||||
\(8\) | 2.86048i | 0.126416i | ||||||||
\(9\) | 10.9593 | − | 24.6758i | 0.405900 | − | 0.913918i | ||||
\(10\) | 45.5347i | 1.43993i | ||||||||
\(11\) | −41.2999 | − | 23.8445i | −1.13203 | − | 0.653581i | −0.187589 | − | 0.982248i | \(-0.560067\pi\) |
−0.944446 | + | 0.328667i | \(0.893401\pi\) | |||||||
\(12\) | 33.6570 | + | 17.1297i | 0.809661 | + | 0.412076i | ||||
\(13\) | −60.2061 | + | 34.7600i | −1.28447 | + | 0.741591i | −0.977663 | − | 0.210179i | \(-0.932595\pi\) |
−0.306811 | + | 0.951770i | \(0.599262\pi\) | |||||||
\(14\) | −71.7048 | − | 9.76328i | −1.36885 | − | 0.186382i | ||||
\(15\) | −53.9655 | − | 27.4657i | −0.928923 | − | 0.472774i | ||||
\(16\) | 34.6603 | − | 60.0334i | 0.541567 | − | 0.938022i | ||||
\(17\) | −25.6583 | −0.366062 | −0.183031 | − | 0.983107i | \(-0.558591\pi\) | ||||
−0.183031 | + | 0.983107i | \(0.558591\pi\) | |||||||
\(18\) | −85.2948 | + | 62.0897i | −1.11690 | + | 0.813038i | ||||
\(19\) | 41.1363i | 0.496701i | 0.968670 | + | 0.248351i | \(0.0798885\pi\) | ||||
−0.968670 | + | 0.248351i | \(0.920111\pi\) | |||||||
\(20\) | 42.3481 | − | 73.3490i | 0.473466 | − | 0.820067i | ||||
\(21\) | 54.8220 | − | 79.0920i | 0.569673 | − | 0.821871i | ||||
\(22\) | 93.1705 | + | 161.376i | 0.902910 | + | 1.56389i | ||||
\(23\) | 145.611 | − | 84.0685i | 1.32009 | − | 0.762152i | 0.336344 | − | 0.941739i | \(-0.390809\pi\) |
0.983742 | + | 0.179587i | \(0.0574761\pi\) | |||||||
\(24\) | 8.10093 | + | 12.4618i | 0.0688998 | + | 0.105990i | ||||
\(25\) | −5.40080 | + | 9.35446i | −0.0432064 | + | 0.0748357i | ||||
\(26\) | 271.644 | 2.04899 | ||||||||
\(27\) | −22.1374 | − | 138.539i | −0.157791 | − | 0.987473i | ||||
\(28\) | 106.425 | + | 82.4138i | 0.718300 | + | 0.556241i | ||||
\(29\) | 28.2286 | + | 16.2978i | 0.180756 | + | 0.104360i | 0.587648 | − | 0.809117i | \(-0.300054\pi\) |
−0.406892 | + | 0.913476i | \(0.633387\pi\) | |||||||
\(30\) | 128.955 | + | 198.375i | 0.784797 | + | 1.20727i | ||||
\(31\) | 148.499 | − | 85.7361i | 0.860363 | − | 0.496731i | −0.00377092 | − | 0.999993i | \(-0.501200\pi\) |
0.864134 | + | 0.503262i | \(0.167867\pi\) | |||||||
\(32\) | −214.758 | + | 123.990i | −1.18638 | + | 0.684957i | ||||
\(33\) | −247.454 | + | 13.0821i | −1.30534 | + | 0.0690092i | ||||
\(34\) | 86.8259 | + | 50.1290i | 0.437956 | + | 0.252854i | ||||
\(35\) | −170.641 | − | 132.142i | −0.824104 | − | 0.638174i | ||||
\(36\) | 195.140 | − | 20.6908i | 0.903428 | − | 0.0957906i | ||||
\(37\) | −3.86757 | −0.0171844 | −0.00859222 | − | 0.999963i | \(-0.502735\pi\) | ||||
−0.00859222 | + | 0.999963i | \(0.502735\pi\) | |||||||
\(38\) | 80.3685 | − | 139.202i | 0.343092 | − | 0.594253i | ||||
\(39\) | −163.851 | + | 321.939i | −0.672746 | + | 1.32183i | ||||
\(40\) | 28.8683 | − | 16.6671i | 0.114112 | − | 0.0658826i | ||||
\(41\) | 168.733 | + | 292.255i | 0.642725 | + | 1.11323i | 0.984822 | + | 0.173568i | \(0.0555295\pi\) |
−0.342097 | + | 0.939665i | \(0.611137\pi\) | |||||||
\(42\) | −340.036 | + | 160.535i | −1.24926 | + | 0.589789i | ||||
\(43\) | 207.351 | − | 359.142i | 0.735364 | − | 1.27369i | −0.219199 | − | 0.975680i | \(-0.570344\pi\) |
0.954563 | − | 0.298008i | \(-0.0963223\pi\) | |||||||
\(44\) | − | 346.601i | − | 1.18755i | ||||||
\(45\) | −312.888 | + | 33.1755i | −1.03650 | + | 0.109900i | ||||
\(46\) | −656.982 | −2.10580 | ||||||||
\(47\) | 74.3856 | − | 128.840i | 0.230856 | − | 0.399855i | −0.727204 | − | 0.686421i | \(-0.759181\pi\) |
0.958060 | + | 0.286566i | \(0.0925139\pi\) | |||||||
\(48\) | −19.0161 | − | 359.698i | −0.0571821 | − | 1.08162i | ||||
\(49\) | 244.676 | − | 240.380i | 0.713340 | − | 0.700818i | ||||
\(50\) | 36.5518 | − | 21.1032i | 0.103384 | − | 0.0596888i | ||||
\(51\) | −111.782 | + | 72.6650i | −0.306914 | + | 0.199512i | ||||
\(52\) | −437.574 | − | 252.633i | −1.16693 | − | 0.673730i | ||||
\(53\) | − | 59.7358i | − | 0.154818i | −0.996999 | − | 0.0774089i | \(-0.975335\pi\) | ||
0.996999 | − | 0.0774089i | \(-0.0246647\pi\) | |||||||
\(54\) | −195.753 | + | 512.054i | −0.493307 | + | 1.29040i | ||||
\(55\) | 555.739i | 1.36247i | ||||||||
\(56\) | 20.0564 | + | 49.0334i | 0.0478599 | + | 0.117007i | ||||
\(57\) | 116.499 | + | 179.213i | 0.270714 | + | 0.416445i | ||||
\(58\) | −63.6824 | − | 110.301i | −0.144171 | − | 0.249711i | ||||
\(59\) | 282.056 | + | 488.535i | 0.622382 | + | 1.07800i | 0.989041 | + | 0.147642i | \(0.0471682\pi\) |
−0.366659 | + | 0.930355i | \(0.619498\pi\) | |||||||
\(60\) | −23.2340 | − | 439.480i | −0.0499915 | − | 0.945611i | ||||
\(61\) | −571.656 | − | 330.046i | −1.19989 | − | 0.692754i | −0.239356 | − | 0.970932i | \(-0.576936\pi\) |
−0.960530 | + | 0.278178i | \(0.910270\pi\) | |||||||
\(62\) | −670.014 | −1.37245 | ||||||||
\(63\) | 14.8451 | − | 499.827i | 0.0296874 | − | 0.999559i | ||||
\(64\) | 414.401 | 0.809377 | ||||||||
\(65\) | 701.605 | + | 405.072i | 1.33882 | + | 0.772969i | ||||
\(66\) | 862.924 | + | 439.184i | 1.60937 | + | 0.819088i | ||||
\(67\) | 145.989 | + | 252.861i | 0.266200 | + | 0.461073i | 0.967877 | − | 0.251423i | \(-0.0808984\pi\) |
−0.701677 | + | 0.712495i | \(0.747565\pi\) | |||||||
\(68\) | −93.2416 | − | 161.499i | −0.166282 | − | 0.288010i | ||||
\(69\) | 396.280 | − | 778.623i | 0.691398 | − | 1.35848i | ||||
\(70\) | 319.270 | + | 780.542i | 0.545144 | + | 1.33275i | ||||
\(71\) | − | 3.05665i | − | 0.00510927i | −0.999997 | − | 0.00255464i | \(-0.999187\pi\) | ||
0.999997 | − | 0.00255464i | \(-0.000813166\pi\) | |||||||
\(72\) | 70.5845 | + | 31.3488i | 0.115534 | + | 0.0513124i | ||||
\(73\) | − | 506.596i | − | 0.812227i | −0.913823 | − | 0.406114i | \(-0.866884\pi\) | ||
0.913823 | − | 0.406114i | \(-0.133116\pi\) | |||||||
\(74\) | 13.0876 | + | 7.55611i | 0.0205594 | + | 0.0118700i | ||||
\(75\) | 2.96311 | + | 56.0485i | 0.00456200 | + | 0.0862923i | ||||
\(76\) | −258.921 | + | 149.488i | −0.390793 | + | 0.225625i | ||||
\(77\) | −875.138 | − | 119.158i | −1.29521 | − | 0.176355i | ||||
\(78\) | 1183.43 | − | 769.302i | 1.71792 | − | 1.11675i | ||||
\(79\) | −96.6430 | + | 167.391i | −0.137635 | + | 0.238391i | −0.926601 | − | 0.376046i | \(-0.877284\pi\) |
0.788966 | + | 0.614437i | \(0.210617\pi\) | |||||||
\(80\) | −807.820 | −1.12896 | ||||||||
\(81\) | −488.788 | − | 540.858i | −0.670490 | − | 0.741918i | ||||
\(82\) | − | 1318.62i | − | 1.77583i | ||||||
\(83\) | −216.246 | + | 374.550i | −0.285977 | + | 0.495327i | −0.972846 | − | 0.231454i | \(-0.925652\pi\) |
0.686868 | + | 0.726782i | \(0.258985\pi\) | |||||||
\(84\) | 697.044 | + | 57.6436i | 0.905402 | + | 0.0748742i | ||||
\(85\) | 149.503 | + | 258.947i | 0.190775 | + | 0.330433i | ||||
\(86\) | −1403.32 | + | 810.206i | −1.75958 | + | 1.01589i | ||||
\(87\) | 169.136 | − | 8.94167i | 0.208428 | − | 0.0110189i | ||||
\(88\) | 68.2066 | − | 118.137i | 0.0826233 | − | 0.143108i | ||||
\(89\) | 924.591 | 1.10120 | 0.550598 | − | 0.834771i | \(-0.314400\pi\) | ||||
0.550598 | + | 0.834771i | \(0.314400\pi\) | |||||||
\(90\) | 1123.60 | + | 499.029i | 1.31598 | + | 0.584469i | ||||
\(91\) | −788.312 | + | 1017.98i | −0.908105 | + | 1.17268i | ||||
\(92\) | 1058.29 | + | 611.005i | 1.19929 | + | 0.692409i | ||||
\(93\) | 404.140 | − | 794.068i | 0.450617 | − | 0.885387i | ||||
\(94\) | −503.430 | + | 290.656i | −0.552392 | + | 0.318924i | ||||
\(95\) | 415.154 | − | 239.689i | 0.448356 | − | 0.258859i | ||||
\(96\) | −584.462 | + | 1148.37i | −0.621369 | + | 1.22089i | ||||
\(97\) | 943.401 | + | 544.673i | 0.987503 | + | 0.570135i | 0.904527 | − | 0.426416i | \(-0.140224\pi\) |
0.0829763 | + | 0.996552i | \(0.473557\pi\) | |||||||
\(98\) | −1297.60 | + | 335.404i | −1.33752 | + | 0.345724i | ||||
\(99\) | −1041.00 | + | 757.788i | −1.05681 | + | 0.769298i | ||||
\(100\) | −78.5053 | −0.0785053 | ||||||||
\(101\) | −168.799 | + | 292.369i | −0.166298 | + | 0.288037i | −0.937116 | − | 0.349019i | \(-0.886515\pi\) |
0.770817 | + | 0.637056i | \(0.219848\pi\) | |||||||
\(102\) | 520.229 | − | 27.5029i | 0.505003 | − | 0.0266979i | ||||
\(103\) | −183.659 | + | 106.035i | −0.175694 | + | 0.101437i | −0.585268 | − | 0.810840i | \(-0.699011\pi\) |
0.409574 | + | 0.912277i | \(0.365677\pi\) | |||||||
\(104\) | −99.4302 | − | 172.218i | −0.0937493 | − | 0.162379i | ||||
\(105\) | −1117.64 | − | 92.4256i | −1.03877 | − | 0.0859030i | ||||
\(106\) | −116.706 | + | 202.142i | −0.106939 | + | 0.185224i | ||||
\(107\) | − | 399.253i | − | 0.360722i | −0.983600 | − | 0.180361i | \(-0.942273\pi\) | ||
0.983600 | − | 0.180361i | \(-0.0577266\pi\) | |||||||
\(108\) | 791.545 | − | 642.783i | 0.705245 | − | 0.572702i | ||||
\(109\) | 1847.45 | 1.62343 | 0.811714 | − | 0.584055i | \(-0.198535\pi\) | ||||
0.811714 | + | 0.584055i | \(0.198535\pi\) | |||||||
\(110\) | 1085.75 | − | 1880.58i | 0.941113 | − | 1.63006i | ||||
\(111\) | −16.8493 | + | 10.9530i | −0.0144078 | + | 0.00936591i | ||||
\(112\) | 173.208 | − | 1272.10i | 0.146131 | − | 1.07323i | ||||
\(113\) | 1101.72 | − | 636.078i | 0.917177 | − | 0.529532i | 0.0344435 | − | 0.999407i | \(-0.489034\pi\) |
0.882733 | + | 0.469874i | \(0.155701\pi\) | |||||||
\(114\) | −44.0936 | − | 834.049i | −0.0362258 | − | 0.685227i | ||||
\(115\) | −1696.86 | − | 979.684i | −1.37594 | − | 0.794400i | ||||
\(116\) | 236.903i | 0.189620i | ||||||||
\(117\) | 197.913 | + | 1866.58i | 0.156385 | + | 1.47492i | ||||
\(118\) | − | 2204.22i | − | 1.71962i | ||||||
\(119\) | −439.827 | + | 179.905i | −0.338814 | + | 0.138587i | ||||
\(120\) | 78.5650 | − | 154.367i | 0.0597664 | − | 0.117431i | ||||
\(121\) | 471.620 | + | 816.871i | 0.354335 | + | 0.613727i | ||||
\(122\) | 1289.63 | + | 2233.70i | 0.957027 | + | 1.65762i | ||||
\(123\) | 1562.77 | + | 795.370i | 1.14561 | + | 0.583058i | ||||
\(124\) | 1079.28 | + | 623.124i | 0.781633 | + | 0.451276i | ||||
\(125\) | −1330.80 | −0.952242 | ||||||||
\(126\) | −1026.75 | + | 1662.37i | −0.725954 | + | 1.17536i | ||||
\(127\) | −1835.56 | −1.28252 | −0.641259 | − | 0.767325i | \(-0.721588\pi\) | ||||
−0.641259 | + | 0.767325i | \(0.721588\pi\) | |||||||
\(128\) | 315.760 | + | 182.304i | 0.218043 | + | 0.125887i | ||||
\(129\) | −113.761 | − | 2151.85i | −0.0776444 | − | 1.46868i | ||||
\(130\) | −1582.79 | − | 2741.47i | −1.06784 | − | 1.84956i | ||||
\(131\) | 673.698 | + | 1166.88i | 0.449323 | + | 0.778250i | 0.998342 | − | 0.0575597i | \(-0.0183320\pi\) |
−0.549019 | + | 0.835810i | \(0.684999\pi\) | |||||||
\(132\) | −981.581 | − | 1509.99i | −0.647240 | − | 0.995664i | ||||
\(133\) | 288.430 | + | 705.147i | 0.188046 | + | 0.459729i | ||||
\(134\) | − | 1140.88i | − | 0.735502i | ||||||
\(135\) | −1269.16 | + | 1030.64i | −0.809126 | + | 0.657060i | ||||
\(136\) | − | 73.3951i | − | 0.0462763i | ||||||
\(137\) | −964.423 | − | 556.810i | −0.601432 | − | 0.347237i | 0.168173 | − | 0.985758i | \(-0.446213\pi\) |
−0.769605 | + | 0.638521i | \(0.779547\pi\) | |||||||
\(138\) | −2862.19 | + | 1860.59i | −1.76555 | + | 1.14771i | ||||
\(139\) | −1140.22 | + | 658.307i | −0.695772 | + | 0.401704i | −0.805771 | − | 0.592228i | \(-0.798249\pi\) |
0.109999 | + | 0.993932i | \(0.464915\pi\) | |||||||
\(140\) | 211.626 | − | 1554.25i | 0.127755 | − | 0.938274i | ||||
\(141\) | −40.8111 | − | 771.959i | −0.0243753 | − | 0.461069i | ||||
\(142\) | −5.97182 | + | 10.3435i | −0.00352918 | + | 0.00611272i | ||||
\(143\) | 3315.34 | 1.93876 | ||||||||
\(144\) | −1101.52 | − | 1513.19i | −0.637452 | − | 0.875691i | ||||
\(145\) | − | 379.850i | − | 0.217550i | ||||||
\(146\) | −989.742 | + | 1714.28i | −0.561039 | + | 0.971747i | ||||
\(147\) | 385.183 | − | 1740.16i | 0.216118 | − | 0.976367i | ||||
\(148\) | −14.0546 | − | 24.3433i | −0.00780596 | − | 0.0135203i | ||||
\(149\) | −530.202 | + | 306.112i | −0.291516 | + | 0.168307i | −0.638625 | − | 0.769518i | \(-0.720497\pi\) |
0.347110 | + | 0.937825i | \(0.387163\pi\) | |||||||
\(150\) | 99.4755 | − | 195.453i | 0.0541476 | − | 0.106391i | ||||
\(151\) | −1451.09 | + | 2513.36i | −0.782040 | + | 1.35453i | 0.148712 | + | 0.988881i | \(0.452487\pi\) |
−0.930752 | + | 0.365652i | \(0.880846\pi\) | |||||||
\(152\) | −117.670 | −0.0627912 | ||||||||
\(153\) | −281.197 | + | 633.139i | −0.148585 | + | 0.334551i | ||||
\(154\) | 2728.60 | + | 2112.99i | 1.42777 | + | 1.10565i | ||||
\(155\) | −1730.52 | − | 999.116i | −0.896766 | − | 0.517748i | ||||
\(156\) | −2621.78 | + | 138.605i | −1.34558 | + | 0.0711367i | ||||
\(157\) | −1163.43 | + | 671.708i | −0.591414 | + | 0.341453i | −0.765657 | − | 0.643250i | \(-0.777586\pi\) |
0.174242 | + | 0.984703i | \(0.444252\pi\) | |||||||
\(158\) | 654.065 | − | 377.625i | 0.329333 | − | 0.190141i | ||||
\(159\) | −169.173 | − | 260.243i | −0.0843793 | − | 0.129803i | ||||
\(160\) | 2502.66 | + | 1444.91i | 1.23658 | + | 0.713938i | ||||
\(161\) | 1906.57 | − | 2462.04i | 0.933283 | − | 1.20519i | ||||
\(162\) | 597.340 | + | 2785.17i | 0.289700 | + | 1.35076i | ||||
\(163\) | 974.519 | 0.468284 | 0.234142 | − | 0.972202i | \(-0.424772\pi\) | ||||
0.234142 | + | 0.972202i | \(0.424772\pi\) | |||||||
\(164\) | −1226.34 | + | 2124.09i | −0.583911 | + | 1.01136i | ||||
\(165\) | 1573.86 | + | 2421.11i | 0.742577 | + | 1.14232i | ||||
\(166\) | 1463.52 | − | 844.966i | 0.684286 | − | 0.395073i | ||||
\(167\) | −1421.47 | − | 2462.05i | −0.658661 | − | 1.14083i | −0.980963 | − | 0.194197i | \(-0.937790\pi\) |
0.322302 | − | 0.946637i | \(-0.395543\pi\) | |||||||
\(168\) | 226.241 | + | 156.817i | 0.103898 | + | 0.0720160i | ||||
\(169\) | 1318.01 | − | 2282.87i | 0.599916 | − | 1.03908i | ||||
\(170\) | − | 1168.34i | − | 0.527106i | ||||||
\(171\) | 1015.07 | + | 450.826i | 0.453944 | + | 0.201611i | ||||
\(172\) | 3014.02 | 1.33615 | ||||||||
\(173\) | 1990.91 | − | 3448.36i | 0.874949 | − | 1.51546i | 0.0181322 | − | 0.999836i | \(-0.494228\pi\) |
0.856817 | − | 0.515621i | \(-0.172439\pi\) | |||||||
\(174\) | −589.812 | − | 300.184i | −0.256974 | − | 0.130787i | ||||
\(175\) | −26.9894 | + | 198.219i | −0.0116583 | + | 0.0856227i | ||||
\(176\) | −2862.93 | + | 1652.91i | −1.22615 | + | 0.707916i | ||||
\(177\) | 2612.34 | + | 1329.55i | 1.10935 | + | 0.564603i | ||||
\(178\) | −3128.75 | − | 1806.38i | −1.31747 | − | 0.760641i | ||||
\(179\) | 2465.66i | 1.02956i | 0.857321 | + | 0.514782i | \(0.172127\pi\) | ||||
−0.857321 | + | 0.514782i | \(0.827873\pi\) | |||||||
\(180\) | −1345.84 | − | 1848.83i | −0.557294 | − | 0.765574i | ||||
\(181\) | 2517.90i | 1.03400i | 0.855986 | + | 0.516999i | \(0.172951\pi\) | ||||
−0.855986 | + | 0.516999i | \(0.827049\pi\) | |||||||
\(182\) | 4656.44 | − | 1904.65i | 1.89647 | − | 0.775726i | ||||
\(183\) | −3425.15 | + | 181.077i | −1.38358 | + | 0.0731454i | ||||
\(184\) | 240.476 | + | 416.517i | 0.0963485 | + | 0.166881i | ||||
\(185\) | 22.5351 | + | 39.0320i | 0.00895576 | + | 0.0155118i | ||||
\(186\) | −2918.96 | + | 1897.49i | −1.15069 | + | 0.748016i | ||||
\(187\) | 1059.69 | + | 611.810i | 0.414395 | + | 0.239251i | ||||
\(188\) | 1081.26 | 0.419462 | ||||||||
\(189\) | −1350.85 | − | 2219.57i | −0.519892 | − | 0.854232i | ||||
\(190\) | −1873.13 | −0.715217 | ||||||||
\(191\) | −399.325 | − | 230.550i | −0.151278 | − | 0.0873405i | 0.422450 | − | 0.906386i | \(-0.361170\pi\) |
−0.573728 | + | 0.819046i | \(0.694503\pi\) | |||||||
\(192\) | 1805.36 | − | 1173.59i | 0.678599 | − | 0.441129i | ||||
\(193\) | 1281.14 | + | 2219.00i | 0.477815 | + | 0.827600i | 0.999677 | − | 0.0254302i | \(-0.00809554\pi\) |
−0.521861 | + | 0.853030i | \(0.674762\pi\) | |||||||
\(194\) | −2128.27 | − | 3686.26i | −0.787632 | − | 1.36422i | ||||
\(195\) | 4203.76 | − | 222.240i | 1.54378 | − | 0.0816149i | ||||
\(196\) | 2402.15 | + | 666.508i | 0.875420 | + | 0.242896i | ||||
\(197\) | 3764.93i | 1.36162i | 0.732458 | + | 0.680812i | \(0.238373\pi\) | ||||
−0.732458 | + | 0.680812i | \(0.761627\pi\) | |||||||
\(198\) | 5003.16 | − | 530.486i | 1.79575 | − | 0.190404i | ||||
\(199\) | 958.945i | 0.341597i | 0.985306 | + | 0.170799i | \(0.0546347\pi\) | ||||
−0.985306 | + | 0.170799i | \(0.945365\pi\) | |||||||
\(200\) | −26.7582 | − | 15.4489i | −0.00946045 | − | 0.00546200i | ||||
\(201\) | 1352.12 | + | 688.159i | 0.474483 | + | 0.241488i | ||||
\(202\) | 1142.41 | − | 659.569i | 0.397918 | − | 0.229738i | ||||
\(203\) | 598.160 | + | 81.4451i | 0.206811 | + | 0.0281592i | ||||
\(204\) | −863.582 | − | 439.519i | −0.296386 | − | 0.150846i | ||||
\(205\) | 1966.32 | − | 3405.76i | 0.669919 | − | 1.16033i | ||||
\(206\) | 828.650 | 0.280266 | ||||||||
\(207\) | −478.662 | − | 4514.40i | −0.160721 | − | 1.51581i | ||||
\(208\) | 4819.17i | 1.60649i | ||||||||
\(209\) | 980.876 | − | 1698.93i | 0.324634 | − | 0.562283i | ||||
\(210\) | 3601.43 | + | 2496.30i | 1.18344 | + | 0.820292i | ||||
\(211\) | 2018.18 | + | 3495.59i | 0.658471 | + | 1.14051i | 0.981012 | + | 0.193949i | \(0.0621298\pi\) |
−0.322541 | + | 0.946556i | \(0.604537\pi\) | |||||||
\(212\) | 375.990 | − | 217.078i | 0.121807 | − | 0.0703254i | ||||
\(213\) | −8.65651 | − | 13.3165i | −0.00278467 | − | 0.00428372i | ||||
\(214\) | −780.025 | + | 1351.04i | −0.249165 | + | 0.431567i | ||||
\(215\) | −4832.68 | −1.53296 | ||||||||
\(216\) | 396.286 | − | 63.3236i | 0.124833 | − | 0.0199474i | ||||
\(217\) | 1944.38 | − | 2510.87i | 0.608265 | − | 0.785481i | ||||
\(218\) | −6251.63 | − | 3609.38i | −1.94227 | − | 1.12137i | ||||
\(219\) | −1434.69 | − | 2207.02i | −0.442682 | − | 0.680988i | ||||
\(220\) | −3497.94 | + | 2019.54i | −1.07196 | + | 0.618896i | ||||
\(221\) | 1544.79 | − | 891.884i | 0.470198 | − | 0.271469i | ||||
\(222\) | 78.4158 | − | 4.14560i | 0.0237069 | − | 0.00125331i | ||||
\(223\) | −5069.18 | − | 2926.69i | −1.52223 | − | 0.878860i | −0.999655 | − | 0.0262676i | \(-0.991638\pi\) |
−0.522576 | − | 0.852593i | \(-0.675029\pi\) | |||||||
\(224\) | −2811.95 | + | 3631.20i | −0.838754 | + | 1.08312i | ||||
\(225\) | 171.639 | + | 235.787i | 0.0508561 | + | 0.0698629i | ||||
\(226\) | −4970.85 | −1.46308 | ||||||||
\(227\) | −3038.38 | + | 5262.62i | −0.888388 | + | 1.53873i | −0.0466072 | + | 0.998913i | \(0.514841\pi\) |
−0.841781 | + | 0.539820i | \(0.818492\pi\) | |||||||
\(228\) | −704.653 | + | 1384.53i | −0.204679 | + | 0.402160i | ||||
\(229\) | 814.321 | − | 470.148i | 0.234986 | − | 0.135669i | −0.377884 | − | 0.925853i | \(-0.623348\pi\) |
0.612870 | + | 0.790184i | \(0.290015\pi\) | |||||||
\(230\) | 3828.04 | + | 6630.35i | 1.09745 | + | 1.90084i | ||||
\(231\) | −4150.05 | + | 1959.29i | −1.18205 | + | 0.558060i | ||||
\(232\) | −46.6195 | + | 80.7473i | −0.0131928 | + | 0.0228505i | ||||
\(233\) | − | 3314.66i | − | 0.931976i | −0.884791 | − | 0.465988i | \(-0.845699\pi\) | ||
0.884791 | − | 0.465988i | \(-0.154301\pi\) | |||||||
\(234\) | 2977.03 | − | 6703.02i | 0.831685 | − | 1.87261i | ||||
\(235\) | −1733.69 | −0.481248 | ||||||||
\(236\) | −2049.96 | + | 3550.64i | −0.565429 | + | 0.979352i | ||||
\(237\) | 53.0224 | + | 1002.94i | 0.0145324 | + | 0.274887i | ||||
\(238\) | 1839.83 | + | 250.510i | 0.501085 | + | 0.0682274i | ||||
\(239\) | 2213.80 | − | 1278.14i | 0.599158 | − | 0.345924i | −0.169552 | − | 0.985521i | \(-0.554232\pi\) |
0.768710 | + | 0.639597i | \(0.220899\pi\) | |||||||
\(240\) | −3519.32 | + | 2287.76i | −0.946546 | + | 0.615311i | ||||
\(241\) | −1800.75 | − | 1039.66i | −0.481312 | − | 0.277886i | 0.239651 | − | 0.970859i | \(-0.422967\pi\) |
−0.720963 | + | 0.692973i | \(0.756300\pi\) | |||||||
\(242\) | − | 3685.64i | − | 0.979016i | ||||||
\(243\) | −3661.16 | − | 972.027i | −0.966516 | − | 0.256607i | ||||
\(244\) | − | 4797.50i | − | 1.25872i | ||||||
\(245\) | −3851.60 | − | 1068.68i | −1.00437 | − | 0.278674i | ||||
\(246\) | −3734.37 | − | 5744.67i | −0.967866 | − | 1.48889i | ||||
\(247\) | −1429.90 | − | 2476.66i | −0.368349 | − | 0.638000i | ||||
\(248\) | 245.246 | + | 424.779i | 0.0627949 | + | 0.108764i | ||||
\(249\) | 118.642 | + | 2244.16i | 0.0301953 | + | 0.571157i | ||||
\(250\) | 4503.32 | + | 2600.00i | 1.13926 | + | 0.657753i | ||||
\(251\) | 4718.74 | 1.18663 | 0.593316 | − | 0.804970i | \(-0.297819\pi\) | ||||
0.593316 | + | 0.804970i | \(0.297819\pi\) | |||||||
\(252\) | 3199.96 | − | 1722.92i | 0.799916 | − | 0.430688i | ||||
\(253\) | −8018.29 | −1.99251 | ||||||||
\(254\) | 6211.40 | + | 3586.16i | 1.53440 | + | 0.885888i | ||||
\(255\) | 1384.67 | + | 704.724i | 0.340044 | + | 0.173065i | ||||
\(256\) | −2369.94 | − | 4104.86i | −0.578599 | − | 1.00216i | ||||
\(257\) | −2401.45 | − | 4159.43i | −0.582873 | − | 1.00957i | −0.995137 | − | 0.0985008i | \(-0.968595\pi\) |
0.412264 | − | 0.911064i | \(-0.364738\pi\) | |||||||
\(258\) | −3819.12 | + | 7503.94i | −0.921582 | + | 1.81076i | ||||
\(259\) | −66.2967 | + | 27.1177i | −0.0159053 | + | 0.00650584i | ||||
\(260\) | 5888.08i | 1.40447i | ||||||||
\(261\) | 711.527 | − | 517.951i | 0.168745 | − | 0.122837i | ||||
\(262\) | − | 5264.85i | − | 1.24146i | ||||||
\(263\) | 2334.00 | + | 1347.54i | 0.547227 | + | 0.315941i | 0.748003 | − | 0.663696i | \(-0.231013\pi\) |
−0.200776 | + | 0.979637i | \(0.564346\pi\) | |||||||
\(264\) | −37.4211 | − | 707.836i | −0.00872389 | − | 0.165016i | ||||
\(265\) | −602.862 | + | 348.062i | −0.139749 | + | 0.0806842i | ||||
\(266\) | 401.626 | − | 2949.67i | 0.0925762 | − | 0.679910i | ||||
\(267\) | 4028.04 | − | 2618.46i | 0.923266 | − | 0.600177i | ||||
\(268\) | −1061.04 | + | 1837.78i | −0.241841 | + | 0.418881i | ||||
\(269\) | −4182.34 | −0.947961 | −0.473981 | − | 0.880535i | \(-0.657183\pi\) | ||||
−0.473981 | + | 0.880535i | \(0.657183\pi\) | |||||||
\(270\) | 6308.31 | − | 1008.02i | 1.42190 | − | 0.227208i | ||||
\(271\) | − | 654.173i | − | 0.146635i | −0.997309 | − | 0.0733176i | \(-0.976641\pi\) | ||
0.997309 | − | 0.0733176i | \(-0.0233587\pi\) | |||||||
\(272\) | −889.325 | + | 1540.36i | −0.198247 | + | 0.343374i | ||||
\(273\) | −551.378 | + | 6667.43i | −0.122238 | + | 1.47814i | ||||
\(274\) | 2175.69 | + | 3768.40i | 0.479701 | + | 0.830867i | ||||
\(275\) | 446.105 | − | 257.559i | 0.0978223 | − | 0.0564777i | ||||
\(276\) | 6340.89 | − | 335.223i | 1.38289 | − | 0.0731089i | ||||
\(277\) | 1828.75 | − | 3167.49i | 0.396675 | − | 0.687061i | −0.596638 | − | 0.802510i | \(-0.703497\pi\) |
0.993313 | + | 0.115449i | \(0.0368306\pi\) | |||||||
\(278\) | 5144.57 | 1.10989 | ||||||||
\(279\) | −488.156 | − | 4603.94i | −0.104750 | − | 0.987924i | ||||
\(280\) | 377.989 | − | 488.115i | 0.0806756 | − | 0.104180i | ||||
\(281\) | 2453.28 | + | 1416.40i | 0.520819 | + | 0.300695i | 0.737270 | − | 0.675598i | \(-0.236115\pi\) |
−0.216450 | + | 0.976294i | \(0.569448\pi\) | |||||||
\(282\) | −1370.08 | + | 2691.99i | −0.289317 | + | 0.568459i | ||||
\(283\) | 7878.39 | − | 4548.59i | 1.65485 | − | 0.955426i | 0.679808 | − | 0.733390i | \(-0.262063\pi\) |
0.975039 | − | 0.222035i | \(-0.0712701\pi\) | |||||||
\(284\) | 19.2393 | − | 11.1078i | 0.00401986 | − | 0.00232087i | ||||
\(285\) | 1129.84 | − | 2219.94i | 0.234828 | − | 0.461397i | ||||
\(286\) | −11218.9 | − | 6477.21i | −2.31953 | − | 1.33918i | ||||
\(287\) | 4941.54 | + | 3826.66i | 1.01634 | + | 0.787040i | ||||
\(288\) | 705.966 | + | 6658.16i | 0.144442 | + | 1.36228i | ||||
\(289\) | −4254.65 | −0.865998 | ||||||||
\(290\) | −742.116 | + | 1285.38i | −0.150271 | + | 0.260277i | ||||
\(291\) | 5652.51 | − | 298.831i | 1.13868 | − | 0.0601985i | ||||
\(292\) | 3188.63 | − | 1840.95i | 0.639042 | − | 0.368951i | ||||
\(293\) | −1538.44 | − | 2664.66i | −0.306747 | − | 0.531301i | 0.670902 | − | 0.741546i | \(-0.265907\pi\) |
−0.977649 | + | 0.210245i | \(0.932574\pi\) | |||||||
\(294\) | −4703.20 | + | 5136.04i | −0.932980 | + | 1.01884i | ||||
\(295\) | 3286.91 | − | 5693.09i | 0.648716 | − | 1.12361i | ||||
\(296\) | − | 11.0631i | − | 0.00217239i | ||||||
\(297\) | −2389.11 | + | 6249.48i | −0.466768 | + | 1.22098i | ||||
\(298\) | 2392.22 | 0.465025 | ||||||||
\(299\) | −5844.44 | + | 10122.9i | −1.13041 | + | 1.95793i | ||||
\(300\) | −342.013 | + | 222.329i | −0.0658205 | + | 0.0427872i | ||||
\(301\) | 1036.19 | − | 7610.15i | 0.198423 | − | 1.45728i | ||||
\(302\) | 9820.76 | − | 5670.02i | 1.87126 | − | 1.08037i | ||||
\(303\) | 92.6103 | + | 1751.77i | 0.0175588 | + | 0.332133i | ||||
\(304\) | 2469.55 | + | 1425.80i | 0.465917 | + | 0.268997i | ||||
\(305\) | 7692.30i | 1.44413i | ||||||||
\(306\) | 2188.52 | − | 1593.12i | 0.408854 | − | 0.297622i | ||||
\(307\) | 3006.74i | 0.558970i | 0.960150 | + | 0.279485i | \(0.0901637\pi\) | ||||
−0.960150 | + | 0.279485i | \(0.909836\pi\) | |||||||
\(308\) | −2430.22 | − | 5941.32i | −0.449592 | − | 1.09915i | ||||
\(309\) | −499.826 | + | 982.076i | −0.0920198 | + | 0.180804i | ||||
\(310\) | 3903.97 | + | 6761.87i | 0.715260 | + | 1.23887i | ||||
\(311\) | 2232.53 | + | 3866.86i | 0.407059 | + | 0.705046i | 0.994559 | − | 0.104178i | \(-0.0332211\pi\) |
−0.587500 | + | 0.809224i | \(0.699888\pi\) | |||||||
\(312\) | −920.899 | − | 468.691i | −0.167101 | − | 0.0850461i | ||||
\(313\) | 6007.81 | + | 3468.61i | 1.08492 | + | 0.626382i | 0.932221 | − | 0.361890i | \(-0.117869\pi\) |
0.152704 | + | 0.988272i | \(0.451202\pi\) | |||||||
\(314\) | 5249.29 | 0.943423 | ||||||||
\(315\) | −5130.82 | + | 2762.52i | −0.917742 | + | 0.494128i | ||||
\(316\) | −1404.79 | −0.250081 | ||||||||
\(317\) | −4933.94 | − | 2848.61i | −0.874189 | − | 0.504713i | −0.00545096 | − | 0.999985i | \(-0.501735\pi\) |
−0.868738 | + | 0.495272i | \(0.835068\pi\) | |||||||
\(318\) | 64.0301 | + | 1211.16i | 0.0112913 | + | 0.213580i | ||||
\(319\) | −777.226 | − | 1346.20i | −0.136415 | − | 0.236277i | ||||
\(320\) | −2414.59 | − | 4182.19i | −0.421811 | − | 0.730599i | ||||
\(321\) | −1130.69 | − | 1739.37i | −0.196602 | − | 0.302437i | ||||
\(322\) | −11261.8 | + | 4606.48i | −1.94905 | + | 0.797233i | ||||
\(323\) | − | 1055.49i | − | 0.181824i | ||||||
\(324\) | 1628.04 | − | 5042.00i | 0.279157 | − | 0.864540i | ||||
\(325\) | − | 750.927i | − | 0.128166i | ||||||
\(326\) | −3297.70 | − | 1903.93i | −0.560254 | − | 0.323463i | ||||
\(327\) | 8048.54 | − | 5232.02i | 1.36112 | − | 0.884806i | ||||
\(328\) | −835.988 | + | 482.658i | −0.140731 | + | 0.0812510i | ||||
\(329\) | 371.727 | − | 2730.09i | 0.0622917 | − | 0.457491i | ||||
\(330\) | −595.690 | − | 11267.7i | −0.0993687 | − | 1.87960i | ||||
\(331\) | −3928.31 | + | 6804.03i | −0.652325 | + | 1.12986i | 0.330233 | + | 0.943900i | \(0.392873\pi\) |
−0.982557 | + | 0.185960i | \(0.940461\pi\) | |||||||
\(332\) | −3143.33 | −0.519617 | ||||||||
\(333\) | −42.3858 | + | 95.4352i | −0.00697516 | + | 0.0157052i | ||||
\(334\) | 11108.5i | 1.81986i | ||||||||
\(335\) | 1701.27 | − | 2946.69i | 0.277464 | − | 0.480581i | ||||
\(336\) | −2848.02 | − | 6032.50i | −0.462417 | − | 0.979464i | ||||
\(337\) | 2447.80 | + | 4239.71i | 0.395668 | + | 0.685317i | 0.993186 | − | 0.116538i | \(-0.0371798\pi\) |
−0.597518 | + | 0.801855i | \(0.703846\pi\) | |||||||
\(338\) | −8920.13 | + | 5150.04i | −1.43548 | + | 0.828773i | ||||
\(339\) | 2998.32 | − | 5891.20i | 0.480373 | − | 0.943853i | ||||
\(340\) | −1086.58 | + | 1882.01i | −0.173318 | + | 0.300196i | ||||
\(341\) | −8177.34 | −1.29861 | ||||||||
\(342\) | −2554.14 | − | 3508.72i | −0.403837 | − | 0.554765i | ||||
\(343\) | 2508.71 | − | 5836.09i | 0.394921 | − | 0.918715i | ||||
\(344\) | 1027.32 | + | 593.121i | 0.161015 | + | 0.0929621i | ||||
\(345\) | −10167.0 | + | 537.496i | −1.58658 | + | 0.0838777i | ||||
\(346\) | −13474.2 | + | 7779.33i | −2.09358 | + | 1.20873i | ||||
\(347\) | 1816.16 | − | 1048.56i | 0.280969 | − | 0.162218i | −0.352893 | − | 0.935664i | \(-0.614802\pi\) |
0.633862 | + | 0.773446i | \(0.281469\pi\) | |||||||
\(348\) | 670.914 | + | 1032.08i | 0.103347 | + | 0.158981i | ||||
\(349\) | 7325.59 | + | 4229.43i | 1.12358 | + | 0.648700i | 0.942313 | − | 0.334734i | \(-0.108647\pi\) |
0.181268 | + | 0.983434i | \(0.441980\pi\) | |||||||
\(350\) | 478.593 | − | 618.030i | 0.0730911 | − | 0.0943860i | ||||
\(351\) | 6148.41 | + | 7571.37i | 0.934979 | + | 1.15137i | ||||
\(352\) | 11826.0 | 1.79070 | ||||||||
\(353\) | 316.445 | − | 548.099i | 0.0477129 | − | 0.0826412i | −0.841183 | − | 0.540751i | \(-0.818140\pi\) |
0.888896 | + | 0.458110i | \(0.151473\pi\) | |||||||
\(354\) | −6242.40 | − | 9602.83i | −0.937232 | − | 1.44176i | ||||
\(355\) | −30.8482 | + | 17.8102i | −0.00461197 | + | 0.00266272i | ||||
\(356\) | 3359.93 | + | 5819.58i | 0.500214 | + | 0.866396i | ||||
\(357\) | −1406.64 | + | 2029.37i | −0.208536 | + | 0.300856i | ||||
\(358\) | 4817.18 | − | 8343.60i | 0.711162 | − | 1.23177i | ||||
\(359\) | 7038.13i | 1.03470i | 0.855773 | + | 0.517351i | \(0.173082\pi\) | ||||
−0.855773 | + | 0.517351i | \(0.826918\pi\) | |||||||
\(360\) | −94.8978 | − | 895.008i | −0.0138932 | − | 0.131031i | ||||
\(361\) | 5166.80 | 0.753288 | ||||||||
\(362\) | 4919.24 | − | 8520.38i | 0.714225 | − | 1.23707i | ||||
\(363\) | 4368.04 | + | 2223.11i | 0.631578 | + | 0.321441i | ||||
\(364\) | −9272.12 | − | 1262.49i | −1.33514 | − | 0.181792i | ||||
\(365\) | −5112.64 | + | 2951.78i | −0.733172 | + | 0.423297i | ||||
\(366\) | 11944.2 | + | 6079.00i | 1.70583 | + | 0.868182i | ||||
\(367\) | −591.654 | − | 341.591i | −0.0841528 | − | 0.0485856i | 0.457333 | − | 0.889295i | \(-0.348805\pi\) |
−0.541486 | + | 0.840710i | \(0.682138\pi\) | |||||||
\(368\) | − | 11655.4i | − | 1.65103i | ||||||
\(369\) | 9060.81 | − | 960.719i | 1.27828 | − | 0.135537i | ||||
\(370\) | − | 176.109i | − | 0.0247445i | ||||||
\(371\) | −418.842 | − | 1023.97i | −0.0586124 | − | 0.143294i | ||||
\(372\) | 6466.67 | − | 341.873i | 0.901293 | − | 0.0476486i | ||||
\(373\) | −4524.00 | − | 7835.79i | −0.627999 | − | 1.08773i | −0.987953 | − | 0.154756i | \(-0.950541\pi\) |
0.359954 | − | 0.932970i | \(-0.382792\pi\) | |||||||
\(374\) | −2390.60 | − | 4140.64i | −0.330521 | − | 0.572480i | ||||
\(375\) | −5797.71 | + | 3768.85i | −0.798380 | + | 0.518994i | ||||
\(376\) | 368.543 | + | 212.778i | 0.0505482 | + | 0.0291840i | ||||
\(377\) | −2266.05 | −0.309569 | ||||||||
\(378\) | 234.770 | + | 10150.0i | 0.0319452 | + | 1.38111i | ||||
\(379\) | 6790.65 | 0.920349 | 0.460175 | − | 0.887828i | \(-0.347787\pi\) | ||||
0.460175 | + | 0.887828i | \(0.347787\pi\) | |||||||
\(380\) | 3017.31 | + | 1742.04i | 0.407328 | + | 0.235171i | ||||
\(381\) | −7996.74 | + | 5198.35i | −1.07529 | + | 0.699002i | ||||
\(382\) | 900.857 | + | 1560.33i | 0.120659 | + | 0.208988i | ||||
\(383\) | −1170.59 | − | 2027.53i | −0.156174 | − | 0.270501i | 0.777312 | − | 0.629115i | \(-0.216583\pi\) |
−0.933486 | + | 0.358614i | \(0.883249\pi\) | |||||||
\(384\) | 1891.92 | − | 100.020i | 0.251423 | − | 0.0132920i | ||||
\(385\) | 3896.60 | + | 9526.31i | 0.515816 | + | 1.26105i | ||||
\(386\) | − | 10011.9i | − | 1.32019i | ||||||
\(387\) | −6589.68 | − | 9052.48i | −0.865562 | − | 1.18905i | ||||
\(388\) | 7917.29i | 1.03593i | ||||||||
\(389\) | 1522.53 | + | 879.032i | 0.198445 | + | 0.114572i | 0.595930 | − | 0.803036i | \(-0.296784\pi\) |
−0.397485 | + | 0.917609i | \(0.630117\pi\) | |||||||
\(390\) | −14659.4 | − | 7460.89i | −1.90335 | − | 0.968710i | ||||
\(391\) | −3736.13 | + | 2157.06i | −0.483234 | + | 0.278995i | ||||
\(392\) | 687.603 | + | 699.889i | 0.0885948 | + | 0.0901779i | ||||
\(393\) | 6239.64 | + | 3175.66i | 0.800886 | + | 0.407610i | ||||
\(394\) | 7355.58 | − | 12740.2i | 0.940530 | − | 1.62904i | ||||
\(395\) | 2252.44 | 0.286918 | ||||||||
\(396\) | −8552.64 | − | 3798.50i | −1.08532 | − | 0.482025i | ||||
\(397\) | 1120.19i | 0.141614i | 0.997490 | + | 0.0708071i | \(0.0225575\pi\) | ||||
−0.997490 | + | 0.0708071i | \(0.977443\pi\) | |||||||
\(398\) | 1873.50 | − | 3245.00i | 0.235955 | − | 0.408686i | ||||
\(399\) | 3253.56 | + | 2255.18i | 0.408225 | + | 0.282957i | ||||
\(400\) | 374.386 | + | 648.456i | 0.0467983 | + | 0.0810571i | ||||
\(401\) | −1528.43 | + | 882.440i | −0.190340 | + | 0.109893i | −0.592142 | − | 0.805834i | \(-0.701717\pi\) |
0.401802 | + | 0.915727i | \(0.368384\pi\) | |||||||
\(402\) | −3231.01 | − | 4970.33i | −0.400865 | − | 0.616660i | ||||
\(403\) | −5960.37 | + | 10323.7i | −0.736743 | + | 1.27608i | ||||
\(404\) | −2453.64 | −0.302162 | ||||||||
\(405\) | −2610.40 | + | 8084.33i | −0.320276 | + | 0.991885i | ||||
\(406\) | −1865.01 | − | 1444.24i | −0.227977 | − | 0.176542i | ||||
\(407\) | 159.730 | + | 92.2202i | 0.0194534 | + | 0.0112314i | ||||
\(408\) | −207.856 | − | 319.750i | −0.0252216 | − | 0.0387990i | ||||
\(409\) | 5868.28 | − | 3388.05i | 0.709456 | − | 0.409605i | −0.101403 | − | 0.994845i | \(-0.532333\pi\) |
0.810860 | + | 0.585241i | \(0.199000\pi\) | |||||||
\(410\) | −13307.7 | + | 7683.22i | −1.60298 | + | 0.925481i | ||||
\(411\) | −5778.47 | + | 305.489i | −0.693505 | + | 0.0366635i | ||||
\(412\) | −1334.82 | − | 770.659i | −0.159616 | − | 0.0921545i | ||||
\(413\) | 8260.31 | + | 6396.67i | 0.984173 | + | 0.762129i | ||||
\(414\) | −7200.06 | + | 16211.5i | −0.854744 | + | 1.92453i | ||||
\(415\) | 5040.01 | 0.596155 | ||||||||
\(416\) | 8619.81 | − | 14930.0i | 1.01592 | − | 1.75962i | ||||
\(417\) | −3103.11 | + | 6097.09i | −0.364412 | + | 0.716009i | ||||
\(418\) | −6638.42 | + | 3832.69i | −0.776784 | + | 0.448477i | ||||
\(419\) | −5353.56 | − | 9272.64i | −0.624197 | − | 1.08114i | −0.988696 | − | 0.149937i | \(-0.952093\pi\) |
0.364498 | − | 0.931204i | \(-0.381240\pi\) | |||||||
\(420\) | −3479.72 | − | 7370.53i | −0.404269 | − | 0.856298i | ||||
\(421\) | 1424.86 | − | 2467.93i | 0.164949 | − | 0.285700i | −0.771688 | − | 0.636001i | \(-0.780587\pi\) |
0.936637 | + | 0.350301i | \(0.113921\pi\) | |||||||
\(422\) | − | 15771.8i | − | 1.81933i | ||||||
\(423\) | −2364.00 | − | 3247.51i | −0.271730 | − | 0.373285i | ||||
\(424\) | 170.873 | 0.0195715 | ||||||||
\(425\) | 138.575 | − | 240.020i | 0.0158162 | − | 0.0273945i | ||||
\(426\) | 3.27639 | + | 61.9744i | 0.000372633 | + | 0.00704852i | ||||
\(427\) | −12113.3 | − | 1649.34i | −1.37284 | − | 0.186925i | ||||
\(428\) | 2512.99 | − | 1450.87i | 0.283808 | − | 0.163857i | ||||
\(429\) | 14443.5 | − | 9389.11i | 1.62550 | − | 1.05667i | ||||
\(430\) | 16353.4 | + | 9441.65i | 1.83403 | + | 1.05888i | ||||
\(431\) | − | 10469.5i | − | 1.17007i | −0.811010 | − | 0.585033i | \(-0.801082\pi\) | ||
0.811010 | − | 0.585033i | \(-0.198918\pi\) | |||||||
\(432\) | −9084.23 | − | 3472.80i | −1.01173 | − | 0.386771i | ||||
\(433\) | 5079.76i | 0.563782i | 0.959446 | + | 0.281891i | \(0.0909617\pi\) | ||||
−0.959446 | + | 0.281891i | \(0.909038\pi\) | |||||||
\(434\) | −11485.2 | + | 4697.85i | −1.27029 | + | 0.519594i | ||||
\(435\) | −1075.74 | − | 1654.84i | −0.118570 | − | 0.182399i | ||||
\(436\) | 6713.58 | + | 11628.3i | 0.737436 | + | 1.27728i | ||||
\(437\) | 3458.27 | + | 5989.90i | 0.378562 | + | 0.655689i | ||||
\(438\) | 543.015 | + | 10271.4i | 0.0592380 | + | 1.12051i | ||||
\(439\) | −6497.04 | − | 3751.07i | −0.706349 | − | 0.407811i | 0.103359 | − | 0.994644i | \(-0.467041\pi\) |
−0.809708 | + | 0.586834i | \(0.800374\pi\) | |||||||
\(440\) | −1589.68 | −0.172238 | ||||||||
\(441\) | −3250.10 | − | 8671.96i | −0.350945 | − | 0.936396i | ||||
\(442\) | −6969.93 | −0.750058 | ||||||||
\(443\) | 2388.50 | + | 1379.00i | 0.256165 | + | 0.147897i | 0.622584 | − | 0.782553i | \(-0.286083\pi\) |
−0.366419 | + | 0.930450i | \(0.619416\pi\) | |||||||
\(444\) | −130.171 | − | 66.2502i | −0.0139136 | − | 0.00708130i | ||||
\(445\) | −5387.31 | − | 9331.09i | −0.573894 | − | 0.994014i | ||||
\(446\) | 11435.8 | + | 19807.4i | 1.21413 | + | 2.10293i | ||||
\(447\) | −1442.94 | + | 2835.14i | −0.152682 | + | 0.299995i | ||||
\(448\) | 7103.54 | − | 2905.60i | 0.749131 | − | 0.306421i | ||||
\(449\) | 8061.59i | 0.847327i | 0.905820 | + | 0.423663i | \(0.139256\pi\) | ||||
−0.905820 | + | 0.423663i | \(0.860744\pi\) | |||||||
\(450\) | −120.155 | − | 1133.22i | −0.0125871 | − | 0.118712i | ||||
\(451\) | − | 16093.4i | − | 1.68029i | ||||||
\(452\) | 8007.22 | + | 4622.97i | 0.833248 | + | 0.481076i | ||||
\(453\) | 796.130 | + | 15059.1i | 0.0825727 | + | 1.56190i | ||||
\(454\) | 20563.3 | − | 11872.2i | 2.12573 | − | 1.22729i | ||||
\(455\) | 14866.9 | + | 2024.27i | 1.53180 | + | 0.208570i | ||||
\(456\) | −512.635 | + | 333.243i | −0.0526455 | + | 0.0342226i | ||||
\(457\) | 108.316 | − | 187.608i | 0.0110871 | − | 0.0192034i | −0.860429 | − | 0.509571i | \(-0.829804\pi\) |
0.871516 | + | 0.490368i | \(0.163137\pi\) | |||||||
\(458\) | −3674.14 | −0.374850 | ||||||||
\(459\) | 568.010 | + | 3554.67i | 0.0577613 | + | 0.361477i | ||||
\(460\) | − | 14240.6i | − | 1.44341i | ||||||
\(461\) | 594.431 | − | 1029.59i | 0.0600552 | − | 0.104019i | −0.834435 | − | 0.551107i | \(-0.814206\pi\) |
0.894490 | + | 0.447088i | \(0.147539\pi\) | |||||||
\(462\) | 17871.4 | + | 1477.91i | 1.79968 | + | 0.148828i | ||||
\(463\) | 2397.17 | + | 4152.02i | 0.240617 | + | 0.416761i | 0.960890 | − | 0.276929i | \(-0.0893168\pi\) |
−0.720273 | + | 0.693691i | \(0.755983\pi\) | |||||||
\(464\) | 1956.82 | − | 1129.77i | 0.195783 | − | 0.113035i | ||||
\(465\) | −10368.6 | + | 548.158i | −1.03405 | + | 0.0546671i | ||||
\(466\) | −6475.88 | + | 11216.5i | −0.643754 | + | 1.11501i | ||||
\(467\) | 2953.79 | 0.292687 | 0.146344 | − | 0.989234i | \(-0.453249\pi\) | ||||
0.146344 | + | 0.989234i | \(0.453249\pi\) | |||||||
\(468\) | −11029.4 | + | 8028.79i | −1.08939 | + | 0.793015i | ||||
\(469\) | 4275.46 | + | 3310.85i | 0.420943 | + | 0.325972i | ||||
\(470\) | 5866.67 | + | 3387.13i | 0.575765 | + | 0.332418i | ||||
\(471\) | −3166.28 | + | 6221.21i | −0.309754 | + | 0.608616i | ||||
\(472\) | −1397.44 | + | 806.814i | −0.136277 | + | 0.0786793i | ||||
\(473\) | −17127.1 | + | 9888.34i | −1.66492 | + | 0.961240i | ||||
\(474\) | 1780.04 | − | 3497.47i | 0.172489 | − | 0.338912i | ||||
\(475\) | −384.808 | − | 222.169i | −0.0371710 | − | 0.0214607i | ||||
\(476\) | −2730.68 | − | 2114.60i | −0.262942 | − | 0.203619i | ||||
\(477\) | −1474.03 | − | 654.663i | −0.141491 | − | 0.0628405i | ||||
\(478\) | −9988.44 | −0.955775 | ||||||||
\(479\) | 54.6189 | − | 94.6028i | 0.00521003 | − | 0.00902403i | −0.863409 | − | 0.504505i | \(-0.831675\pi\) |
0.868619 | + | 0.495481i | \(0.165008\pi\) | |||||||
\(480\) | 14995.0 | − | 792.739i | 1.42589 | − | 0.0753821i | ||||
\(481\) | 232.851 | − | 134.437i | 0.0220730 | − | 0.0127438i | ||||
\(482\) | 4062.39 | + | 7036.27i | 0.383894 | + | 0.664924i | ||||
\(483\) | 1333.53 | − | 16125.5i | 0.125627 | − | 1.51912i | ||||
\(484\) | −3427.71 | + | 5936.96i | −0.321911 | + | 0.557566i | ||||
\(485\) | − | 12694.6i | − | 1.18852i | ||||||
\(486\) | 10490.0 | + | 10442.1i | 0.979089 | + | 0.974616i | ||||
\(487\) | −3614.94 | −0.336363 | −0.168182 | − | 0.985756i | \(-0.553789\pi\) | ||||
−0.168182 | + | 0.985756i | \(0.553789\pi\) | |||||||
\(488\) | 944.088 | − | 1635.21i | 0.0875755 | − | 0.151685i | ||||
\(489\) | 4245.56 | − | 2759.86i | 0.392619 | − | 0.255225i | ||||
\(490\) | 10945.7 | + | 11141.2i | 1.00913 | + | 1.02716i | ||||
\(491\) | 16280.5 | − | 9399.53i | 1.49639 | − | 0.863940i | 0.496397 | − | 0.868096i | \(-0.334656\pi\) |
0.999991 | + | 0.00415517i | \(0.00132263\pi\) | |||||||
\(492\) | 672.824 | + | 12726.8i | 0.0616530 | + | 1.16619i | ||||
\(493\) | −724.300 | − | 418.175i | −0.0661680 | − | 0.0382021i | ||||
\(494\) | 11174.4i | 1.01774i | ||||||||
\(495\) | 13713.3 | + | 6090.51i | 1.24518 | + | 0.553026i | ||||
\(496\) | − | 11886.5i | − | 1.07605i | ||||||
\(497\) | −21.4320 | − | 52.3963i | −0.00193431 | − | 0.00472896i | ||||
\(498\) | 3982.97 | − | 7825.88i | 0.358396 | − | 0.704189i | ||||
\(499\) | −1620.89 | − | 2807.46i | −0.145413 | − | 0.251862i | 0.784114 | − | 0.620617i | \(-0.213118\pi\) |
−0.929527 | + | 0.368755i | \(0.879784\pi\) | |||||||
\(500\) | −4836.08 | − | 8376.34i | −0.432552 | − | 0.749203i | ||||
\(501\) | −13165.3 | − | 6700.46i | −1.17402 | − | 0.597514i | ||||
\(502\) | −15967.9 | − | 9219.06i | −1.41968 | − | 0.819655i | ||||
\(503\) | −4737.83 | −0.419979 | −0.209989 | − | 0.977704i | \(-0.567343\pi\) | ||||
−0.209989 | + | 0.977704i | \(0.567343\pi\) | |||||||
\(504\) | 1429.74 | + | 42.4641i | 0.126361 | + | 0.00375298i | ||||
\(505\) | 3934.16 | 0.346669 | ||||||||
\(506\) | 27133.3 | + | 15665.4i | 2.38384 | + | 1.37631i | ||||
\(507\) | −723.119 | − | 13678.1i | −0.0633429 | − | 1.19816i | ||||
\(508\) | −6670.37 | − | 11553.4i | −0.582579 | − | 1.00906i | ||||
\(509\) | −1272.38 | − | 2203.83i | −0.110800 | − | 0.191912i | 0.805293 | − | 0.592877i | \(-0.202008\pi\) |
−0.916093 | + | 0.400965i | \(0.868675\pi\) | |||||||
\(510\) | −3308.78 | − | 5089.97i | −0.287285 | − | 0.441937i | ||||
\(511\) | −3552.03 | − | 8683.92i | −0.307500 | − | 0.751769i | ||||
\(512\) | 15603.9i | 1.34687i | ||||||||
\(513\) | 5698.97 | − | 910.654i | 0.490479 | − | 0.0783749i | ||||
\(514\) | 18766.9i | 1.61046i | ||||||||
\(515\) | 2140.25 | + | 1235.67i | 0.183127 | + | 0.105729i | ||||
\(516\) | 13130.8 | − | 8535.78i | 1.12025 | − | 0.728230i | ||||
\(517\) | −6144.23 | + | 3547.37i | −0.522675 | + | 0.301767i | ||||
\(518\) | 277.323 | + | 37.7602i | 0.0235229 | + | 0.00320287i | ||||
\(519\) | −1092.30 | − | 20661.3i | −0.0923826 | − | 1.74746i | ||||
\(520\) | −1158.70 | + | 2006.93i | −0.0977160 | + | 0.169249i | ||||
\(521\) | 7623.86 | 0.641089 | 0.320545 | − | 0.947233i | \(-0.396134\pi\) | ||||
0.320545 | + | 0.947233i | \(0.396134\pi\) | |||||||
\(522\) | −3419.68 | + | 362.589i | −0.286734 | + | 0.0304025i | ||||
\(523\) | − | 20941.4i | − | 1.75087i | −0.483335 | − | 0.875435i | \(-0.660575\pi\) | ||
0.483335 | − | 0.875435i | \(-0.339425\pi\) | |||||||
\(524\) | −4896.40 | + | 8480.81i | −0.408206 | + | 0.707034i | ||||
\(525\) | 443.781 | + | 939.990i | 0.0368918 | + | 0.0781420i | ||||
\(526\) | −5265.39 | − | 9119.92i | −0.436467 | − | 0.755984i | ||||
\(527\) | −3810.24 | + | 2199.84i | −0.314946 | + | 0.181834i | ||||
\(528\) | −7791.46 | + | 15308.9i | −0.642196 | + | 1.26181i | ||||
\(529\) | 8051.53 | − | 13945.7i | 0.661752 | − | 1.14619i | ||||
\(530\) | 2720.05 | 0.222927 | ||||||||
\(531\) | 15146.1 | − | 1605.94i | 1.23783 | − | 0.131247i | ||||
\(532\) | −3390.20 | + | 4377.93i | −0.276286 | + | 0.356780i | ||||
\(533\) | −20317.5 | − | 11730.3i | −1.65113 | − | 0.953279i | ||||
\(534\) | −18746.3 | + | 991.058i | −1.51916 | + | 0.0803133i | ||||
\(535\) | −4029.32 | + | 2326.33i | −0.325612 | + | 0.187992i | ||||
\(536\) | −723.302 | + | 417.599i | −0.0582871 | + | 0.0336521i | ||||
\(537\) | 6982.80 | + | 10741.8i | 0.561136 | + | 0.863208i | ||||
\(538\) | 14152.7 | + | 8171.07i | 1.13414 | + | 0.654796i | ||||
\(539\) | −15836.8 | + | 4093.52i | −1.26557 | + | 0.327125i | ||||
\(540\) | −11099.1 | − | 4243.08i | −0.884502 | − | 0.338135i | ||||
\(541\) | −6660.29 | −0.529294 | −0.264647 | − | 0.964345i | \(-0.585255\pi\) | ||||
−0.264647 | + | 0.964345i | \(0.585255\pi\) | |||||||
\(542\) | −1278.06 | + | 2213.67i | −0.101287 | + | 0.175434i | ||||
\(543\) | 7130.74 | + | 10969.4i | 0.563553 | + | 0.866927i | ||||
\(544\) | 5510.33 | − | 3181.39i | 0.434289 | − | 0.250737i | ||||
\(545\) | −10764.5 | − | 18644.7i | −0.846059 | − | 1.46542i | ||||
\(546\) | 14892.1 | − | 21484.9i | 1.16725 | − | 1.68401i | ||||
\(547\) | −10779.8 | + | 18671.2i | −0.842616 | + | 1.45945i | 0.0450599 | + | 0.998984i | \(0.485652\pi\) |
−0.887676 | + | 0.460469i | \(0.847681\pi\) | |||||||
\(548\) | − | 8093.71i | − | 0.630924i | ||||||
\(549\) | −14409.1 | + | 10489.0i | −1.12015 | + | 0.815407i | ||||
\(550\) | −2012.78 | −0.156046 | ||||||||
\(551\) | −670.432 | + | 1161.22i | −0.0518355 | + | 0.0897818i | ||||
\(552\) | 2227.23 | + | 1133.55i | 0.171734 | + | 0.0874040i | ||||
\(553\) | −482.954 | + | 3546.98i | −0.0371380 | + | 0.272754i | ||||
\(554\) | −12376.7 | + | 7145.70i | −0.949163 | + | 0.547999i | ||||
\(555\) | 208.715 | + | 106.225i | 0.0159630 | + | 0.00812436i | ||||
\(556\) | −8287.06 | − | 4784.54i | −0.632103 | − | 0.364945i | ||||
\(557\) | − | 15772.0i | − | 1.19979i | −0.800079 | − | 0.599895i | \(-0.795209\pi\) | ||
0.800079 | − | 0.599895i | \(-0.204791\pi\) | |||||||
\(558\) | −7342.88 | + | 16533.1i | −0.557077 | + | 1.25431i | ||||
\(559\) | 28830.0i | 2.18136i | ||||||||
\(560\) | −13847.4 | + | 5664.09i | −1.04493 | + | 0.427413i | ||||
\(561\) | 6349.25 | − | 335.665i | 0.477835 | − | 0.0252617i | ||||
\(562\) | −5534.47 | − | 9585.99i | −0.415405 | − | 0.719503i | ||||
\(563\) | −5842.23 | − | 10119.0i | −0.437337 | − | 0.757489i | 0.560146 | − | 0.828394i | \(-0.310745\pi\) |
−0.997483 | + | 0.0709043i | \(0.977412\pi\) | |||||||
\(564\) | 4710.57 | − | 3062.15i | 0.351686 | − | 0.228617i | ||||
\(565\) | −12838.8 | − | 7412.46i | −0.955984 | − | 0.551937i | ||||
\(566\) | −35546.5 | −2.63981 | ||||||||
\(567\) | −12170.9 | − | 5844.06i | −0.901465 | − | 0.432853i | ||||
\(568\) | 8.74349 | 0.000645896 | ||||||||
\(569\) | −5808.93 | − | 3353.79i | −0.427984 | − | 0.247097i | 0.270503 | − | 0.962719i | \(-0.412810\pi\) |
−0.698488 | + | 0.715622i | \(0.746143\pi\) | |||||||
\(570\) | −8160.42 | + | 5304.75i | −0.599653 | + | 0.389810i | ||||
\(571\) | 9286.00 | + | 16083.8i | 0.680573 | + | 1.17879i | 0.974806 | + | 0.223053i | \(0.0716022\pi\) |
−0.294234 | + | 0.955733i | \(0.595064\pi\) | |||||||
\(572\) | 12047.8 | + | 20867.5i | 0.880674 | + | 1.52537i | ||||
\(573\) | −2392.61 | + | 126.490i | −0.174437 | + | 0.00922196i | ||||
\(574\) | −9245.63 | − | 22603.5i | −0.672308 | − | 1.64364i | ||||
\(575\) | 1816.15i | 0.131719i | ||||||||
\(576\) | 4541.54 | − | 10225.7i | 0.328526 | − | 0.739704i | ||||
\(577\) | 8147.17i | 0.587818i | 0.955833 | + | 0.293909i | \(0.0949563\pi\) | ||||
−0.955833 | + | 0.293909i | \(0.905044\pi\) | |||||||
\(578\) | 14397.4 | + | 8312.35i | 1.03608 | + | 0.598181i | ||||
\(579\) | 11865.6 | + | 6038.99i | 0.851671 | + | 0.433457i | ||||
\(580\) | 2390.86 | − | 1380.36i | 0.171164 | − | 0.0988213i | ||||
\(581\) | −1080.65 | + | 7936.65i | −0.0771650 | + | 0.566726i | ||||
\(582\) | −19711.5 | − | 10032.1i | −1.40390 | − | 0.714512i | ||||
\(583\) | −1424.37 | + | 2467.08i | −0.101186 | + | 0.175259i | ||||
\(584\) | 1449.11 | 0.102679 | ||||||||
\(585\) | 17684.6 | − | 12873.3i | 1.24986 | − | 0.909824i | ||||
\(586\) | 12022.7i | 0.847531i | ||||||||
\(587\) | −2070.04 | + | 3585.42i | −0.145553 | + | 0.252106i | −0.929579 | − | 0.368622i | \(-0.879830\pi\) |
0.784026 | + | 0.620728i | \(0.213163\pi\) | |||||||
\(588\) | 12352.7 | − | 3899.26i | 0.866354 | − | 0.273474i | ||||
\(589\) | 3526.87 | + | 6108.72i | 0.246727 | + | 0.427343i | ||||
\(590\) | −22245.3 | + | 12843.3i | −1.55224 | + | 0.896189i | ||||
\(591\) | 10662.4 | + | 16402.1i | 0.742116 | + | 1.14161i | ||||
\(592\) | −134.051 | + | 232.183i | −0.00930652 | + | 0.0161194i | ||||
\(593\) | 14381.9 | 0.995945 | 0.497973 | − | 0.867193i | \(-0.334078\pi\) | ||||
0.497973 | + | 0.867193i | \(0.334078\pi\) | |||||||
\(594\) | 20294.2 | − | 16480.2i | 1.40182 | − | 1.13837i | ||||
\(595\) | 4378.37 | + | 3390.54i | 0.301673 | + | 0.233611i | ||||
\(596\) | −3853.47 | − | 2224.80i | −0.264840 | − | 0.152905i | ||||
\(597\) | 2715.75 | + | 4177.71i | 0.186178 | + | 0.286402i | ||||
\(598\) | 39554.3 | − | 22836.7i | 2.70484 | − | 1.56164i | ||||
\(599\) | 12019.7 | − | 6939.59i | 0.819887 | − | 0.473362i | −0.0304902 | − | 0.999535i | \(-0.509707\pi\) |
0.850378 | + | 0.526173i | \(0.176374\pi\) | |||||||
\(600\) | −160.325 | + | 8.47590i | −0.0109088 | + | 0.000576712i | ||||
\(601\) | 12474.7 | + | 7202.28i | 0.846680 | + | 0.488831i | 0.859529 | − | 0.511087i | \(-0.170757\pi\) |
−0.0128495 | + | 0.999917i | \(0.504090\pi\) | |||||||
\(602\) | −18374.4 | + | 23727.8i | −1.24400 | + | 1.60643i | ||||
\(603\) | 7839.48 | − | 831.220i | 0.529433 | − | 0.0561358i | ||||
\(604\) | −21092.9 | −1.42095 | ||||||||
\(605\) | 5495.98 | − | 9519.31i | 0.369328 | − | 0.639694i | ||||
\(606\) | 3109.06 | − | 6108.78i | 0.208410 | − | 0.409492i | ||||
\(607\) | −17223.6 | + | 9944.08i | −1.15171 | + | 0.664938i | −0.949303 | − | 0.314364i | \(-0.898209\pi\) |
−0.202404 | + | 0.979302i | \(0.564876\pi\) | |||||||
\(608\) | −5100.51 | − | 8834.35i | −0.340219 | − | 0.589277i | ||||
\(609\) | 2836.58 | − | 1339.18i | 0.188742 | − | 0.0891073i | ||||
\(610\) | 15028.5 | − | 26030.2i | 0.997520 | − | 1.72776i | ||||
\(611\) | 10342.6i | 0.684804i | ||||||||
\(612\) | −5006.98 | + | 530.890i | −0.330711 | + | 0.0350653i | ||||
\(613\) | 8096.44 | 0.533462 | 0.266731 | − | 0.963771i | \(-0.414057\pi\) | ||||
0.266731 | + | 0.963771i | \(0.414057\pi\) | |||||||
\(614\) | 5874.30 | − | 10174.6i | 0.386103 | − | 0.668751i | ||||
\(615\) | −1078.80 | − | 20406.1i | −0.0707343 | − | 1.33797i | ||||
\(616\) | 340.849 | − | 2503.31i | 0.0222942 | − | 0.163736i | ||||
\(617\) | −8145.01 | + | 4702.53i | −0.531452 | + | 0.306834i | −0.741608 | − | 0.670834i | \(-0.765936\pi\) |
0.210155 | + | 0.977668i | \(0.432603\pi\) | |||||||
\(618\) | 3610.07 | − | 2346.76i | 0.234981 | − | 0.152751i | ||||
\(619\) | 467.098 | + | 269.679i | 0.0303300 | + | 0.0175110i | 0.515088 | − | 0.857137i | \(-0.327759\pi\) |
−0.484758 | + | 0.874648i | \(0.661092\pi\) | |||||||
\(620\) | − | 14523.0i | − | 0.940740i | ||||||
\(621\) | −14870.2 | − | 18311.7i | −0.960902 | − | 1.18329i | ||||
\(622\) | − | 17446.9i | − | 1.12469i | ||||||
\(623\) | 15849.1 | − | 6482.83i | 1.01923 | − | 0.416901i | ||||
\(624\) | 13648.0 | + | 20995.0i | 0.875572 | + | 1.34691i | ||||
\(625\) | 8429.26 | + | 14599.9i | 0.539473 | + | 0.934394i | ||||
\(626\) | −13553.3 | − | 23475.0i | −0.865335 | − | 1.49880i | ||||
\(627\) | −538.150 | − | 10179.3i | −0.0342769 | − | 0.648363i | ||||
\(628\) | −8455.76 | − | 4881.93i | −0.537295 | − | 0.310208i | ||||
\(629\) | 99.2353 | 0.00629057 | ||||||||
\(630\) | 22759.5 | + | 675.968i | 1.43930 | + | 0.0427479i | ||||
\(631\) | −14096.7 | −0.889349 | −0.444675 | − | 0.895692i | \(-0.646681\pi\) | ||||
−0.444675 | + | 0.895692i | \(0.646681\pi\) | |||||||
\(632\) | −478.817 | − | 276.445i | −0.0301366 | − | 0.0173994i | ||||
\(633\) | 18691.9 | + | 9513.24i | 1.17368 | + | 0.597342i | ||||
\(634\) | 11130.7 | + | 19279.0i | 0.697252 | + | 1.20768i | ||||
\(635\) | 10695.3 | + | 18524.7i | 0.668391 | + | 1.15769i | ||||
\(636\) | 1023.26 | − | 2010.53i | 0.0637967 | − | 0.125350i | ||||
\(637\) | −6375.34 | + | 22977.3i | −0.396547 | + | 1.42919i | ||||
\(638\) | 6073.90i | 0.376909i | ||||||||
\(639\) | −75.4253 | − | 33.4988i | −0.00466945 | − | 0.00207385i | ||||
\(640\) | − | 4248.92i | − | 0.262427i | ||||||
\(641\) | 18973.7 | + | 10954.5i | 1.16914 | + | 0.675002i | 0.953477 | − | 0.301466i | \(-0.0974761\pi\) |
0.215661 | + | 0.976468i | \(0.430809\pi\) | |||||||
\(642\) | 427.955 | + | 8094.95i | 0.0263085 | + | 0.497636i | ||||
\(643\) | −14525.7 | + | 8386.40i | −0.890881 | + | 0.514350i | −0.874231 | − | 0.485511i | \(-0.838634\pi\) |
−0.0166504 | + | 0.999861i | \(0.505300\pi\) | |||||||
\(644\) | 22425.0 | + | 3053.38i | 1.37216 | + | 0.186832i | ||||
\(645\) | −21053.9 | + | 13686.2i | −1.28526 | + | 0.835497i | ||||
\(646\) | −2062.12 | + | 3571.70i | −0.125593 | + | 0.217534i | ||||
\(647\) | 7088.41 | 0.430717 | 0.215359 | − | 0.976535i | \(-0.430908\pi\) | ||||
0.215359 | + | 0.976535i | \(0.430908\pi\) | |||||||
\(648\) | 1547.11 | − | 1398.17i | 0.0937906 | − | 0.0847610i | ||||
\(649\) | − | 26901.9i | − | 1.62711i | ||||||
\(650\) | −1467.09 | + | 2541.08i | −0.0885295 | + | 0.153338i | ||||
\(651\) | 1359.98 | − | 16445.3i | 0.0818770 | − | 0.990082i | ||||
\(652\) | 3541.37 | + | 6133.84i | 0.212716 | + | 0.368435i | ||||
\(653\) | 3166.83 | − | 1828.37i | 0.189782 | − | 0.109571i | −0.402098 | − | 0.915596i | \(-0.631719\pi\) |
0.591881 | + | 0.806026i | \(0.298386\pi\) | |||||||
\(654\) | −37457.5 | + | 1980.26i | −2.23961 | + | 0.118401i | ||||
\(655\) | 7850.87 | − | 13598.1i | 0.468334 | − | 0.811179i | ||||
\(656\) | 23393.4 | 1.39231 | ||||||||
\(657\) | −12500.6 | − | 5551.94i | −0.742309 | − | 0.329683i | ||||
\(658\) | −6591.70 | + | 8512.17i | −0.390534 | + | 0.504314i | ||||
\(659\) | −6740.56 | − | 3891.66i | −0.398444 | − | 0.230042i | 0.287368 | − | 0.957820i | \(-0.407220\pi\) |
−0.685813 | + | 0.727778i | \(0.740553\pi\) | |||||||
\(660\) | −9519.63 | + | 18704.5i | −0.561441 | + | 1.10314i | ||||
\(661\) | 6895.85 | − | 3981.32i | 0.405775 | − | 0.234274i | −0.283198 | − | 0.959062i | \(-0.591395\pi\) |
0.688973 | + | 0.724787i | \(0.258062\pi\) | |||||||
\(662\) | 26586.2 | − | 15349.6i | 1.56088 | − | 0.901175i | ||||
\(663\) | 4204.13 | − | 8260.42i | 0.246267 | − | 0.483874i | ||||
\(664\) | −1071.39 | − | 618.568i | −0.0626175 | − | 0.0361522i | ||||
\(665\) | 5435.84 | − | 7019.56i | 0.316982 | − | 0.409333i | ||||
\(666\) | 329.883 | − | 240.136i | 0.0191933 | − | 0.0139716i | ||||
\(667\) | 5480.53 | 0.318151 | ||||||||
\(668\) | 10331.1 | − | 17894.0i | 0.598388 | − | 1.03644i | ||||
\(669\) | −30372.7 | + | 1605.71i | −1.75527 | + | 0.0927956i | ||||
\(670\) | −11513.9 | + | 6647.58i | −0.663914 | + | 0.383311i | ||||
\(671\) | 15739.5 | + | 27261.7i | 0.905542 | + | 1.56844i | ||||
\(672\) | −1966.79 | + | 23783.0i | −0.112903 | + | 1.36525i | ||||
\(673\) | −494.666 | + | 856.786i | −0.0283328 | + | 0.0490738i | −0.879844 | − | 0.475262i | \(-0.842353\pi\) |
0.851511 | + | 0.524336i | \(0.175686\pi\) | |||||||
\(674\) | − | 19129.2i | − | 1.09322i | ||||||
\(675\) | 1415.51 | + | 541.135i | 0.0807157 | + | 0.0308567i | ||||
\(676\) | 19158.5 | 1.09004 | ||||||||
\(677\) | −11083.3 | + | 19196.9i | −0.629198 | + | 1.08980i | 0.358515 | + | 0.933524i | \(0.383283\pi\) |
−0.987713 | + | 0.156279i | \(0.950050\pi\) | |||||||
\(678\) | −21655.8 | + | 14077.5i | −1.22668 | + | 0.797411i | ||||
\(679\) | 19990.5 | + | 2721.89i | 1.12985 | + | 0.153839i | ||||
\(680\) | −740.713 | + | 427.651i | −0.0417721 | + | 0.0241171i | ||||
\(681\) | 1666.98 | + | 31531.7i | 0.0938016 | + | 1.77430i | ||||
\(682\) | 27671.5 | + | 15976.1i | 1.55366 | + | 0.897006i | ||||
\(683\) | − | 2458.98i | − | 0.137760i | −0.997625 | − | 0.0688802i | \(-0.978057\pi\) | ||
0.997625 | − | 0.0688802i | \(-0.0219426\pi\) | |||||||
\(684\) | 851.142 | + | 8027.37i | 0.0475793 | + | 0.448734i | ||||
\(685\) | 12977.4i | 0.723858i | ||||||||
\(686\) | −19891.3 | + | 14847.6i | −1.10708 | + | 0.826361i | ||||
\(687\) | 2216.17 | − | 4354.41i | 0.123075 | − | 0.241821i | ||||
\(688\) | −14373.7 | − | 24895.9i | −0.796498 | − | 1.37958i | ||||
\(689\) | 2076.42 | + | 3596.46i | 0.114812 | + | 0.198859i | ||||
\(690\) | 35454.4 | + | 18044.5i | 1.95612 | + | 0.995567i | ||||
\(691\) | −21148.3 | − | 12210.0i | −1.16428 | − | 0.672200i | −0.211958 | − | 0.977279i | \(-0.567984\pi\) |
−0.952327 | + | 0.305079i | \(0.901317\pi\) | |||||||
\(692\) | 28939.6 | 1.58977 | ||||||||
\(693\) | −12531.2 | + | 20288.8i | −0.686900 | + | 1.11213i | ||||
\(694\) | −8194.32 | −0.448202 | ||||||||
\(695\) | 13287.4 | + | 7671.51i | 0.725211 | + | 0.418701i | ||||
\(696\) | 25.5774 | + | 483.808i | 0.00139297 | + | 0.0263487i | ||||
\(697\) | −4329.42 | − | 7498.77i | −0.235277 | − | 0.407512i | ||||
\(698\) | −16526.2 | − | 28624.1i | −0.896167 | − | 1.55221i | ||||
\(699\) | −9387.18 | − | 14440.5i | −0.507948 | − | 0.781388i | ||||
\(700\) | −1345.71 | + | 550.446i | −0.0726618 | + | 0.0297213i | ||||
\(701\) | − | 6521.09i | − | 0.351353i | −0.984448 | − | 0.175676i | \(-0.943789\pi\) | ||
0.984448 | − | 0.175676i | \(-0.0562112\pi\) | |||||||
\(702\) | −6013.50 | − | 37633.2i | −0.323312 | − | 2.02332i | ||||
\(703\) | − | 159.098i | − | 0.00853553i | ||||||
\(704\) | −17114.7 | − | 9881.18i | −0.916243 | − | 0.528993i | ||||
\(705\) | −7552.92 | + | 4909.84i | −0.403489 | + | 0.262291i | ||||
\(706\) | −2141.65 | + | 1236.48i | −0.114167 | + | 0.0659145i | ||||
\(707\) | −843.540 | + | 6195.24i | −0.0448721 | + | 0.329556i | ||||
\(708\) | 1124.70 | + | 21274.1i | 0.0597016 | + | 1.12928i | ||||
\(709\) | 5031.46 | − | 8714.75i | 0.266517 | − | 0.461621i | −0.701443 | − | 0.712726i | \(-0.747461\pi\) |
0.967960 | + | 0.251105i | \(0.0807939\pi\) | |||||||
\(710\) | 139.184 | 0.00735701 | ||||||||
\(711\) | 3071.35 | + | 4219.22i | 0.162004 | + | 0.222550i | ||||
\(712\) | 2644.77i | 0.139209i | ||||||||
\(713\) | 14415.4 | − | 24968.2i | 0.757169 | − | 1.31145i | ||||
\(714\) | 8724.77 | − | 4119.07i | 0.457306 | − | 0.215899i | ||||
\(715\) | −19317.5 | − | 33458.9i | −1.01040 | − | 1.75006i | ||||
\(716\) | −15519.4 | + | 8960.12i | −0.810037 | + | 0.467675i | ||||
\(717\) | 6024.84 | − | 11837.8i | 0.313810 | − | 0.616585i | ||||
\(718\) | 13750.5 | − | 23816.5i | 0.714711 | − | 1.23792i | ||||
\(719\) | −3449.87 | −0.178941 | −0.0894704 | − | 0.995989i | \(-0.528517\pi\) | ||||
−0.0894704 | + | 0.995989i | \(0.528517\pi\) | |||||||
\(720\) | −8853.14 | + | 19933.6i | −0.458246 | + | 1.03178i | ||||
\(721\) | −2404.75 | + | 3105.36i | −0.124213 | + | 0.160402i | ||||
\(722\) | −17484.1 | − | 10094.4i | −0.901232 | − | 0.520327i | ||||
\(723\) | −10789.4 | + | 570.402i | −0.554997 | + | 0.0293409i | ||||
\(724\) | −15848.2 | + | 9149.96i | −0.813527 | + | 0.469690i | ||||
\(725\) | −304.914 | + | 176.042i | −0.0156196 | + | 0.00901800i | ||||
\(726\) | −10437.8 | − | 16056.7i | −0.533586 | − | 0.820828i | ||||
\(727\) | 18318.1 | + | 10575.9i | 0.934497 | + | 0.539532i | 0.888231 | − | 0.459397i | \(-0.151935\pi\) |
0.0462657 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(728\) | −2911.92 | − | 2254.95i | −0.148246 | − | 0.114799i | ||||
\(729\) | −18702.9 | + | 6133.78i | −0.950204 | + | 0.311628i | ||||
\(730\) | 23067.7 | 1.16955 | ||||||||
\(731\) | −5320.27 | + | 9214.98i | −0.269189 | + | 0.466249i | ||||
\(732\) | −13586.6 | − | 20900.6i | −0.686033 | − | 1.05534i | ||||
\(733\) | 8853.40 | − | 5111.51i | 0.446122 | − | 0.257569i | −0.260069 | − | 0.965590i | \(-0.583745\pi\) |
0.706191 | + | 0.708021i | \(0.250412\pi\) | |||||||
\(734\) | 1334.74 | + | 2311.84i | 0.0671202 | + | 0.116256i | ||||
\(735\) | −19806.3 | + | 6252.07i | −0.993967 | + | 0.313757i | ||||
\(736\) | −20847.4 | + | 36108.7i | −1.04408 | + | 1.80840i | ||||
\(737\) | − | 13924.2i | − | 0.695934i | ||||||
\(738\) | −32538.1 | − | 14451.2i | −1.62296 | − | 0.720808i | ||||
\(739\) | −38602.2 | −1.92152 | −0.960761 | − | 0.277378i | \(-0.910534\pi\) | ||||
−0.960761 | + | 0.277378i | \(0.910534\pi\) | |||||||
\(740\) | −163.784 | + | 283.682i | −0.00813624 | + | 0.0140924i | ||||
\(741\) | −13243.4 | − | 6740.21i | −0.656557 | − | 0.334154i | ||||
\(742\) | −583.218 | + | 4283.35i | −0.0288552 | + | 0.211923i | ||||
\(743\) | 12936.5 | − | 7468.90i | 0.638755 | − | 0.368785i | −0.145380 | − | 0.989376i | \(-0.546440\pi\) |
0.784135 | + | 0.620591i | \(0.213107\pi\) | |||||||
\(744\) | 2271.41 | + | 1156.03i | 0.111927 | + | 0.0569653i | ||||
\(745\) | 6178.65 | + | 3567.25i | 0.303850 | + | 0.175428i | ||||
\(746\) | 35354.3i | 1.73514i | ||||||||
\(747\) | 6872.40 | + | 9440.85i | 0.336610 | + | 0.462413i | ||||
\(748\) | 8893.20i | 0.434716i | ||||||||
\(749\) | −2799.39 | − | 6843.88i | −0.136565 | − | 0.333872i | ||||
\(750\) | 26982.3 | − | 1426.47i | 1.31367 | − | 0.0694497i | ||||
\(751\) | 12330.2 | + | 21356.5i | 0.599113 | + | 1.03769i | 0.992952 | + | 0.118515i | \(0.0378135\pi\) |
−0.393839 | + | 0.919180i | \(0.628853\pi\) | |||||||
\(752\) | −5156.45 | − | 8931.23i | −0.250048 | − | 0.433097i | ||||
\(753\) | 20557.5 | − | 13363.6i | 0.994897 | − | 0.646741i | ||||
\(754\) | 7668.13 | + | 4427.20i | 0.370367 | + | 0.213832i | ||||
\(755\) | 33820.2 | 1.63026 | ||||||||
\(756\) | 9061.51 | − | 16568.4i | 0.435931 | − | 0.797071i | ||||
\(757\) | 31078.1 | 1.49214 | 0.746071 | − | 0.665867i | \(-0.231938\pi\) | ||||
0.746071 | + | 0.665867i | \(0.231938\pi\) | |||||||
\(758\) | −22979.1 | − | 13267.0i | −1.10110 | − | 0.635723i | ||||
\(759\) | −34932.2 | + | 22708.0i | −1.67056 | + | 1.08596i | ||||
\(760\) | 685.625 | + | 1187.54i | 0.0327240 | + | 0.0566796i | ||||
\(761\) | 1863.73 | + | 3228.07i | 0.0887780 | + | 0.153768i | 0.906995 | − | 0.421142i | \(-0.138370\pi\) |
−0.818217 | + | 0.574910i | \(0.805037\pi\) | |||||||
\(762\) | 37216.5 | − | 1967.52i | 1.76930 | − | 0.0935376i | ||||
\(763\) | 31668.4 | − | 12953.5i | 1.50259 | − | 0.614612i | ||||
\(764\) | − | 3351.25i | − | 0.158696i | ||||||
\(765\) | 8028.18 | − | 851.228i | 0.379424 | − | 0.0402304i | ||||
\(766\) | 9148.01i | 0.431503i | ||||||||
\(767\) | −33962.9 | − | 19608.5i | −1.59887 | − | 0.923106i | ||||
\(768\) | −21949.9 | − | 11171.4i | −1.03131 | − | 0.524885i | ||||
\(769\) | −5266.10 | + | 3040.38i | −0.246944 | + | 0.142573i | −0.618364 | − | 0.785892i | \(-0.712204\pi\) |
0.371420 | + | 0.928465i | \(0.378871\pi\) | |||||||
\(770\) | 5425.83 | − | 39849.1i | 0.253940 | − | 1.86502i | ||||
\(771\) | −22241.7 | − | 11319.9i | −1.03893 | − | 0.528762i | ||||
\(772\) | −9311.23 | + | 16127.5i | −0.434091 | + | 0.751868i | ||||
\(773\) | −34364.4 | −1.59897 | −0.799483 | − | 0.600688i | \(-0.794893\pi\) | ||||
−0.799483 | + | 0.600688i | \(0.794893\pi\) | |||||||
\(774\) | 4613.08 | + | 43507.2i | 0.214229 | + | 2.02046i | ||||
\(775\) | 1852.17i | 0.0858478i | ||||||||
\(776\) | −1558.02 | + | 2698.58i | −0.0720745 | + | 0.124837i | ||||
\(777\) | −212.028 | + | 305.894i | −0.00978951 | + | 0.0141234i | ||||
\(778\) | −3434.75 | − | 5949.16i | −0.158280 | − | 0.274149i | ||||
\(779\) | −12022.3 | + | 6941.07i | −0.552944 | + | 0.319242i | ||||
\(780\) | 16675.2 | + | 25651.8i | 0.765470 | + | 1.17754i | ||||
\(781\) | −72.8844 | + | 126.239i | −0.00333932 | + | 0.00578387i | ||||
\(782\) | 16857.1 | 0.770854 | ||||||||
\(783\) | 1632.96 | − | 4271.55i | 0.0745305 | − | 0.194959i | ||||
\(784\) | −5950.32 | − | 23020.4i | −0.271061 | − | 1.04867i | ||||
\(785\) | 13557.9 | + | 7827.68i | 0.616438 | + | 0.355900i | ||||
\(786\) | −14910.2 | − | 22936.6i | −0.676626 | − | 1.04087i | ||||
\(787\) | 3382.03 | − | 1952.61i | 0.153185 | − | 0.0884411i | −0.421448 | − | 0.906852i | \(-0.638478\pi\) |
0.574633 | + | 0.818411i | \(0.305145\pi\) | |||||||
\(788\) | −23697.3 | + | 13681.6i | −1.07129 | + | 0.618512i | ||||
\(789\) | 13984.5 | − | 739.315i | 0.631002 | − | 0.0333591i | ||||
\(790\) | −7622.08 | − | 4400.61i | −0.343268 | − | 0.198186i | ||||
\(791\) | 14425.4 | − | 18628.2i | 0.648431 | − | 0.837350i | ||||
\(792\) | −2167.63 | − | 2977.75i | −0.0972519 | − | 0.133598i | ||||
\(793\) | 45889.5 | 2.05496 | ||||||||
\(794\) | 2188.53 | − | 3790.65i | 0.0978188 | − | 0.169427i | ||||
\(795\) | −1640.69 | + | 3223.67i | −0.0731939 | + | 0.143814i | ||||
\(796\) | −6035.81 | + | 3484.78i | −0.268761 | + | 0.155169i | ||||
\(797\) | −2261.24 | − | 3916.59i | −0.100499 | − | 0.174069i | 0.811392 | − | 0.584503i | \(-0.198710\pi\) |
−0.911890 | + | 0.410434i | \(0.865377\pi\) | |||||||
\(798\) | −6603.83 | − | 13987.9i | −0.292949 | − | 0.620507i | ||||
\(799\) | −1908.61 | + | 3305.81i | −0.0845078 | + | 0.146372i | ||||
\(800\) | − | 2678.59i | − | 0.118378i | ||||||
\(801\) | 10132.9 | − | 22815.0i | 0.446975 | − | 1.00640i | ||||
\(802\) | 6896.13 | 0.303629 | ||||||||
\(803\) | −12079.5 | + | 20922.4i | −0.530856 | + | 0.919470i | ||||
\(804\) | 582.132 | + | 11011.3i | 0.0255351 | + | 0.483007i | ||||
\(805\) | −35956.2 | − | 4895.78i | −1.57427 | − | 0.214352i | ||||
\(806\) | 40338.9 | − | 23289.7i | 1.76288 | − | 1.01780i | ||||
\(807\) | −18220.6 | + | 11844.5i | −0.794791 | + | 0.516661i | ||||
\(808\) | −836.313 | − | 482.846i | −0.0364126 | − | 0.0210228i | ||||
\(809\) | 20951.2i | 0.910513i | 0.890360 | + | 0.455256i | \(0.150452\pi\) | ||||
−0.890360 | + | 0.455256i | \(0.849548\pi\) | |||||||
\(810\) | 24627.8 | − | 22256.8i | 1.06831 | − | 0.965462i | ||||
\(811\) | − | 22578.2i | − | 0.977592i | −0.872398 | − | 0.488796i | \(-0.837436\pi\) | ||
0.872398 | − | 0.488796i | \(-0.162564\pi\) | |||||||
\(812\) | 1661.06 | + | 4060.92i | 0.0717880 | + | 0.175505i | ||||
\(813\) | −1852.63 | − | 2849.94i | −0.0799196 | − | 0.122942i | ||||
\(814\) | −360.343 | − | 624.133i | −0.0155160 | − | 0.0268745i | ||||
\(815\) | −5678.23 | − | 9834.98i | −0.244049 | − | 0.422705i | ||||
\(816\) | 487.922 | + | 9229.25i | 0.0209322 | + | 0.395942i | ||||
\(817\) | 14773.8 | + | 8529.64i | 0.632643 | + | 0.365256i | ||||
\(818\) | −26477.1 | −1.13172 | ||||||||
\(819\) | 16480.2 | + | 30608.6i | 0.703132 | + | 1.30592i | ||||
\(820\) | 28582.1 | 1.21723 | ||||||||
\(821\) | 35093.8 | + | 20261.4i | 1.49182 | + | 0.861300i | 0.999956 | − | 0.00937459i | \(-0.00298407\pi\) |
0.491859 | + | 0.870675i | \(0.336317\pi\) | |||||||
\(822\) | 20150.7 | + | 10255.7i | 0.855034 | + | 0.435168i | ||||
\(823\) | 15823.1 | + | 27406.4i | 0.670181 | + | 1.16079i | 0.977853 | + | 0.209295i | \(0.0671168\pi\) |
−0.307672 | + | 0.951493i | \(0.599550\pi\) | |||||||
\(824\) | −303.312 | − | 525.352i | −0.0128233 | − | 0.0222105i | ||||
\(825\) | 1214.07 | − | 2385.45i | 0.0512346 | − | 0.100667i | ||||
\(826\) | −15455.1 | − | 37784.1i | −0.651029 | − | 1.59162i | ||||
\(827\) | 19924.2i | 0.837766i | 0.908040 | + | 0.418883i | \(0.137578\pi\) | ||||
−0.908040 | + | 0.418883i | \(0.862422\pi\) | |||||||
\(828\) | 26675.1 | − | 19418.0i | 1.11960 | − | 0.815001i | ||||
\(829\) | 27088.6i | 1.13489i | 0.823410 | + | 0.567447i | \(0.192069\pi\) | ||||
−0.823410 | + | 0.567447i | \(0.807931\pi\) | |||||||
\(830\) | −17055.0 | − | 9846.72i | −0.713239 | − | 0.411789i | ||||
\(831\) | −1003.33 | − | 18978.4i | −0.0418835 | − | 0.792244i | ||||
\(832\) | −24949.5 | + | 14404.6i | −1.03962 | + | 0.600227i | ||||
\(833\) | −6277.97 | + | 6167.76i | −0.261127 | + | 0.256543i | ||||
\(834\) | 22412.6 | − | 14569.5i | 0.930559 | − | 0.604918i | ||||
\(835\) | −16564.9 | + | 28691.3i | −0.686529 | + | 1.18910i | ||||
\(836\) | 14257.9 | 0.589856 | ||||||||
\(837\) | −15165.1 | − | 18674.9i | −0.626265 | − | 0.771205i | ||||
\(838\) | 41837.2i | 1.72463i | ||||||||
\(839\) | 2785.92 | − | 4825.35i | 0.114637 | − | 0.198557i | −0.802997 | − | 0.595982i | \(-0.796763\pi\) |
0.917635 | + | 0.397425i | \(0.130096\pi\) | |||||||
\(840\) | 264.381 | − | 3196.98i | 0.0108595 | − | 0.131317i | ||||
\(841\) | −11663.3 | − | 20201.4i | −0.478218 | − | 0.828298i | ||||
\(842\) | −9643.25 | + | 5567.53i | −0.394689 | + | 0.227874i | ||||
\(843\) | 14699.1 | − | 777.097i | 0.600552 | − | 0.0317493i | ||||
\(844\) | −14668.0 | + | 25405.8i | −0.598216 | + | 1.03614i | ||||
\(845\) | −30718.7 | −1.25060 | ||||||||
\(846\) | 1654.91 | + | 15607.9i | 0.0672541 | + | 0.634292i | ||||
\(847\) | 13811.9 | + | 10695.7i | 0.560311 | + | 0.433896i | ||||
\(848\) | −3586.14 | − | 2070.46i | −0.145222 | − | 0.0838442i | ||||
\(849\) | 21441.0 | − | 42128.0i | 0.866729 | − | 1.70298i | ||||
\(850\) | −937.858 | + | 541.473i | −0.0378450 | + | 0.0218498i | ||||
\(851\) | −563.160 | + | 325.141i | −0.0226849 | + | 0.0130972i | ||||
\(852\) | 52.3595 | − | 102.878i | 0.00210541 | − | 0.00413678i | ||||
\(853\) | −14771.1 | − | 8528.09i | −0.592910 | − | 0.342317i | 0.173337 | − | 0.984863i | \(-0.444545\pi\) |
−0.766247 | + | 0.642546i | \(0.777878\pi\) | |||||||
\(854\) | 37768.1 | + | 29247.1i | 1.51335 | + | 1.17191i | ||||
\(855\) | −1364.72 | − | 12871.1i | −0.0545876 | − | 0.514832i | ||||
\(856\) | 1142.05 | 0.0456012 | ||||||||
\(857\) | 3095.62 | − | 5361.77i | 0.123389 | − | 0.213716i | −0.797713 | − | 0.603037i | \(-0.793957\pi\) |
0.921102 | + | 0.389321i | \(0.127290\pi\) | |||||||
\(858\) | −67219.3 | + | 3553.67i | −2.67463 | + | 0.141399i | ||||
\(859\) | 4145.84 | − | 2393.60i | 0.164673 | − | 0.0950740i | −0.415399 | − | 0.909640i | \(-0.636358\pi\) |
0.580072 | + | 0.814565i | \(0.303025\pi\) | |||||||
\(860\) | −17561.8 | − | 30417.9i | −0.696340 | − | 1.20610i | ||||
\(861\) | 32365.3 | + | 2676.52i | 1.28108 | + | 0.105941i | ||||
\(862\) | −20454.4 | + | 35428.0i | −0.808212 | + | 1.39986i | ||||
\(863\) | 20578.3i | 0.811694i | 0.913941 | + | 0.405847i | \(0.133024\pi\) | ||||
−0.913941 | + | 0.405847i | \(0.866976\pi\) | |||||||
\(864\) | 21931.6 | + | 27007.4i | 0.863576 | + | 1.06344i | ||||
\(865\) | −46401.8 | −1.82394 | ||||||||
\(866\) | 9924.38 | − | 17189.5i | 0.389427 | − | 0.674508i | ||||
\(867\) | −18535.7 | + | 12049.3i | −0.726071 | + | 0.471989i | ||||
\(868\) | 22869.8 | + | 3113.94i | 0.894300 | + | 0.121767i | ||||
\(869\) | 7982.69 | − | 4608.81i | 0.311616 | − | 0.179911i | ||||
\(870\) | 407.156 | + | 7701.54i | 0.0158665 | + | 0.300123i | ||||
\(871\) | −17578.9 | − | 10149.2i | −0.683855 | − | 0.394824i | ||||
\(872\) | 5284.59i | 0.205228i | ||||||||
\(873\) | 23779.2 | − | 17309.9i | 0.921884 | − | 0.671079i | ||||
\(874\) | − | 27025.8i | − | 1.04595i | ||||||
\(875\) | −22812.2 | + | 9330.99i | −0.881362 | + | 0.360509i | ||||
\(876\) | 8677.83 | − | 17050.5i | 0.334699 | − | 0.657629i | ||||
\(877\) | −18325.1 | − | 31740.0i | −0.705581 | − | 1.22210i | −0.966482 | − | 0.256736i | \(-0.917353\pi\) |
0.260901 | − | 0.965366i | \(-0.415980\pi\) | |||||||
\(878\) | 14657.0 | + | 25386.7i | 0.563383 | + | 0.975808i | ||||
\(879\) | −14248.7 | − | 7251.87i | −0.546755 | − | 0.278270i | ||||
\(880\) | 33362.9 | + | 19262.1i | 1.27803 | + | 0.737868i | ||||
\(881\) | −13272.5 | −0.507561 | −0.253780 | − | 0.967262i | \(-0.581674\pi\) | ||||
−0.253780 | + | 0.967262i | \(0.581674\pi\) | |||||||
\(882\) | −5944.41 | + | 35695.0i | −0.226937 | + | 1.36271i | ||||
\(883\) | 7209.05 | 0.274750 | 0.137375 | − | 0.990519i | \(-0.456134\pi\) | ||||
0.137375 | + | 0.990519i | \(0.456134\pi\) | |||||||
\(884\) | 11227.4 | + | 6482.15i | 0.427171 | + | 0.246627i | ||||
\(885\) | −1803.34 | − | 34110.9i | −0.0684955 | − | 1.29562i | ||||
\(886\) | −5388.34 | − | 9332.88i | −0.204317 | − | 0.353888i | ||||
\(887\) | −12074.4 | − | 20913.5i | −0.457068 | − | 0.791666i | 0.541736 | − | 0.840549i | \(-0.317767\pi\) |
−0.998805 | + | 0.0488828i | \(0.984434\pi\) | |||||||
\(888\) | −31.3309 | − | 48.1970i | −0.00118400 | − | 0.00182138i | ||||
\(889\) | −31464.7 | + | 12870.2i | −1.18705 | + | 0.485547i | ||||
\(890\) | 42101.0i | 1.58565i | ||||||||
\(891\) | 7290.37 | + | 33992.3i | 0.274115 | + | 1.27810i | ||||
\(892\) | − | 42542.0i | − | 1.59688i | ||||||
\(893\) | 5299.99 | + | 3059.95i | 0.198608 | + | 0.114667i | ||||
\(894\) | 10421.9 | − | 6774.82i | 0.389887 | − | 0.253449i | ||||
\(895\) | 24883.8 | − | 14366.6i | 0.929354 | − | 0.536563i | ||||
\(896\) | 6690.90 | + | 911.028i | 0.249472 | + | 0.0339680i | ||||
\(897\) | 3206.51 | + | 60652.5i | 0.119356 | + | 2.25767i | ||||
\(898\) | 15750.0 | − | 27279.8i | 0.585283 | − | 1.01374i | ||||
\(899\) | 5589.24 | 0.207354 | ||||||||
\(900\) | −860.363 | + | 1937.18i | −0.0318653 | + | 0.0717474i | ||||
\(901\) | 1532.72i | 0.0566730i | ||||||||
\(902\) | −31441.9 | + | 54459.0i | −1.16065 | + | 2.01030i | ||||
\(903\) | −17037.9 | − | 36088.6i | −0.627890 | − | 1.32996i | ||||
\(904\) | 1819.48 | + | 3151.44i | 0.0669416 | + | 0.115946i | ||||
\(905\) | 25411.0 | − | 14671.0i | 0.933358 | − | 0.538874i | ||||
\(906\) | 26727.2 | − | 52514.4i | 0.980078 | − | 1.92569i | ||||
\(907\) | 14615.6 | − | 25315.0i | 0.535064 | − | 0.926758i | −0.464096 | − | 0.885785i | \(-0.653621\pi\) |
0.999160 | − | 0.0409733i | \(-0.0130459\pi\) | |||||||
\(908\) | −44165.4 | −1.61419 | ||||||||
\(909\) | 5364.50 | + | 7369.40i | 0.195742 | + | 0.268897i | ||||
\(910\) | −46353.6 | − | 35895.6i | −1.68858 | − | 1.30761i | ||||
\(911\) | −29195.6 | − | 16856.1i | −1.06179 | − | 0.613027i | −0.135866 | − | 0.990727i | \(-0.543382\pi\) |
−0.925928 | + | 0.377700i | \(0.876715\pi\) | |||||||
\(912\) | 14796.7 | − | 782.253i | 0.537244 | − | 0.0284024i | ||||
\(913\) | 17861.9 | − | 10312.6i | 0.647473 | − | 0.373819i | ||||
\(914\) | −733.065 | + | 423.235i | −0.0265291 | + | 0.0153166i | ||||
\(915\) | 21784.8 | + | 33512.0i | 0.787085 | + | 1.21079i | ||||
\(916\) | 5918.43 | + | 3417.01i | 0.213483 | + | 0.123255i | ||||
\(917\) | 19730.0 | + | 15278.6i | 0.710515 | + | 0.550212i | ||||
\(918\) | 5022.69 | − | 13138.5i | 0.180581 | − | 0.472368i | ||||
\(919\) | 12924.3 | 0.463912 | 0.231956 | − | 0.972726i | \(-0.425488\pi\) | ||||
0.231956 | + | 0.972726i | \(0.425488\pi\) | |||||||
\(920\) | 2802.36 | − | 4853.83i | 0.100425 | − | 0.173941i | ||||
\(921\) | 8515.15 | + | 13099.1i | 0.304651 | + | 0.468652i | ||||
\(922\) | −4023.02 | + | 2322.69i | −0.143700 | + | 0.0829651i | ||||
\(923\) | 106.249 | + | 184.029i | 0.00378899 | + | 0.00656273i | ||||
\(924\) | −27413.4 | − | 19001.3i | −0.976010 | − | 0.676513i | ||||
\(925\) | 20.8879 | − | 36.1790i | 0.000742477 | − | 0.00128601i | ||||
\(926\) | − | 18733.5i | − | 0.664817i | ||||||
\(927\) | 603.735 | + | 5694.00i | 0.0213908 | + | 0.201743i | ||||
\(928\) | −8083.09 | −0.285927 | ||||||||
\(929\) | −14691.7 | + | 25446.8i | −0.518859 | + | 0.898690i | 0.480901 | + | 0.876775i | \(0.340310\pi\) |
−0.999760 | + | 0.0219154i | \(0.993024\pi\) | |||||||
\(930\) | 36157.7 | + | 18402.4i | 1.27490 | + | 0.648858i | ||||
\(931\) | 9888.38 | + | 10065.1i | 0.348097 | + | 0.354317i | ||||
\(932\) | 20863.2 | − | 12045.4i | 0.733257 | − | 0.423346i | ||||
\(933\) | 20677.2 | + | 10523.6i | 0.725553 | + | 0.369269i | ||||
\(934\) | −9995.40 | − | 5770.85i | −0.350171 | − | 0.202171i | ||||
\(935\) | − | 14259.3i | − | 0.498749i | ||||||
\(936\) | −5339.30 | + | 566.126i | −0.186453 | + | 0.0197697i | ||||
\(937\) | − | 42385.1i | − | 1.47776i | −0.673837 | − | 0.738880i | \(-0.735355\pi\) | ||
0.673837 | − | 0.738880i | \(-0.264645\pi\) | |||||||
\(938\) | −7999.38 | − | 19556.7i | −0.278453 | − | 0.680755i | ||||
\(939\) | 35996.6 | − | 1903.03i | 1.25102 | − | 0.0661373i | ||||
\(940\) | −6300.17 | − | 10912.2i | −0.218605 | − | 0.378635i | ||||
\(941\) | 16870.2 | + | 29220.1i | 0.584436 | + | 1.01227i | 0.994946 | + | 0.100416i | \(0.0320174\pi\) |
−0.410510 | + | 0.911856i | \(0.634649\pi\) | |||||||
\(942\) | 22868.9 | − | 14866.1i | 0.790986 | − | 0.514187i | ||||
\(943\) | 49138.8 | + | 28370.3i | 1.69690 | + | 0.979708i | ||||
\(944\) | 39104.5 | 1.34825 | ||||||||
\(945\) | −14529.2 | + | 26565.7i | −0.500143 | + | 0.914478i | ||||
\(946\) | 77275.8 | 2.65587 | ||||||||
\(947\) | 26763.4 | + | 15451.8i | 0.918366 | + | 0.530219i | 0.883113 | − | 0.469160i | \(-0.155443\pi\) |
0.0352526 | + | 0.999378i | \(0.488776\pi\) | |||||||
\(948\) | −6120.06 | + | 3978.40i | −0.209673 | + | 0.136300i | ||||
\(949\) | 17609.3 | + | 30500.2i | 0.602341 | + | 1.04328i | ||||
\(950\) | 868.108 | + | 1503.61i | 0.0296475 | + | 0.0513510i | ||||
\(951\) | −29562.4 | + | 1562.87i | −1.00802 | + | 0.0532908i | ||||
\(952\) | −514.615 | − | 1258.12i | −0.0175197 | − | 0.0428317i | ||||
\(953\) | 14796.1i | 0.502931i | 0.967866 | + | 0.251465i | \(0.0809125\pi\) | ||||
−0.967866 | + | 0.251465i | \(0.919088\pi\) | |||||||
\(954\) | 3708.98 | + | 5095.15i | 0.125873 | + | 0.172916i | ||||
\(955\) | 5373.39i | 0.182072i | ||||||||
\(956\) | 16089.7 | + | 9289.42i | 0.544330 | + | 0.314269i | ||||
\(957\) | −7198.49 | − | 3663.66i | −0.243150 | − | 0.123751i | ||||
\(958\) | −369.653 | + | 213.419i | −0.0124665 | + | 0.00719756i | ||||
\(959\) | −20436.0 | − | 2782.55i | −0.688124 | − | 0.0936946i | ||||
\(960\) | −22363.4 | − | 11381.8i | −0.751849 | − | 0.382653i | ||||
\(961\) | −194.153 | + | 336.283i | −0.00651716 | + | 0.0112881i | ||||
\(962\) | −1050.60 | −0.0352107 | ||||||||
\(963\) | −9851.88 | − | 4375.53i | −0.329670 | − | 0.146417i | ||||
\(964\) | − | 15112.4i | − | 0.504914i | ||||||
\(965\) | 14929.6 | − | 25858.8i | 0.498032 | − | 0.862617i | ||||
\(966\) | −36017.1 | + | 51962.1i | −1.19962 | + | 1.73070i | ||||
\(967\) | −9085.95 | − | 15737.3i | −0.302156 | − | 0.523349i | 0.674468 | − | 0.738304i | \(-0.264373\pi\) |
−0.976624 | + | 0.214955i | \(0.931040\pi\) | |||||||
\(968\) | −2336.64 | + | 1349.06i | −0.0775851 | + | 0.0447938i | ||||
\(969\) | −2989.17 | − | 4598.31i | −0.0990981 | − | 0.152445i | ||||
\(970\) | −24801.5 | + | 42957.5i | −0.820957 | + | 1.42194i | ||||
\(971\) | −36450.4 | −1.20468 | −0.602342 | − | 0.798238i | \(-0.705766\pi\) | ||||
−0.602342 | + | 0.798238i | \(0.705766\pi\) | |||||||
\(972\) | −7186.38 | − | 26576.4i | −0.237143 | − | 0.876996i | ||||
\(973\) | −14929.6 | + | 19279.2i | −0.491901 | + | 0.635215i | ||||
\(974\) | 12232.7 | + | 7062.56i | 0.402424 | + | 0.232340i | ||||
\(975\) | −2126.64 | − | 3271.46i | −0.0698534 | − | 0.107457i | ||||
\(976\) | −39627.5 | + | 22879.0i | −1.29964 | + | 0.750346i | ||||
\(977\) | 4369.47 | − | 2522.71i | 0.143083 | − | 0.0826088i | −0.426750 | − | 0.904370i | \(-0.640341\pi\) |
0.569832 | + | 0.821761i | \(0.307008\pi\) | |||||||
\(978\) | −19758.6 | + | 1044.58i | −0.646023 | + | 0.0341532i | ||||
\(979\) | −38185.5 | − | 22046.4i | −1.24659 | − | 0.719720i | ||||
\(980\) | −7270.12 | − | 28126.4i | −0.236975 | − | 0.916800i | ||||
\(981\) | 20246.8 | − | 45587.3i | 0.658949 | − | 1.48368i | ||||
\(982\) | −73455.8 | −2.38704 | ||||||||
\(983\) | −24464.8 | + | 42374.3i | −0.793802 | + | 1.37491i | 0.129795 | + | 0.991541i | \(0.458568\pi\) |
−0.923597 | + | 0.383364i | \(0.874765\pi\) | |||||||
\(984\) | −2275.14 | + | 4470.26i | −0.0737080 | + | 0.144824i | ||||
\(985\) | 37996.2 | − | 21937.1i | 1.22909 | − | 0.709618i | ||||
\(986\) | 1633.98 | + | 2830.14i | 0.0527755 | + | 0.0914099i | ||||
\(987\) | −6112.22 | − | 12946.5i | −0.197117 | − | 0.417521i | ||||
\(988\) | 10392.4 | − | 18000.2i | 0.334643 | − | 0.579618i | ||||
\(989\) | − | 69726.6i | − | 2.24184i | ||||||
\(990\) | −34505.6 | − | 47401.6i | −1.10774 | − | 1.52174i | ||||
\(991\) | −41118.3 | −1.31803 | −0.659014 | − | 0.752131i | \(-0.729026\pi\) | ||||
−0.659014 | + | 0.752131i | \(0.729026\pi\) | |||||||
\(992\) | −21260.9 | + | 36825.0i | −0.680478 | + | 1.17862i | ||||
\(993\) | 2155.24 | + | 40767.3i | 0.0688766 | + | 1.30283i | ||||
\(994\) | −29.8430 | + | 219.177i | −0.000952276 | + | 0.00699383i | ||||
\(995\) | 9677.80 | − | 5587.48i | 0.308349 | − | 0.178025i | ||||
\(996\) | −13694.1 | + | 8901.98i | −0.435657 | + | 0.283203i | ||||
\(997\) | −20713.0 | − | 11958.7i | −0.657962 | − | 0.379874i | 0.133538 | − | 0.991044i | \(-0.457366\pi\) |
−0.791500 | + | 0.611169i | \(0.790699\pi\) | |||||||
\(998\) | 12667.0i | 0.401770i | ||||||||
\(999\) | 85.6181 | + | 535.807i | 0.00271155 | + | 0.0169692i |
(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 | 63.4.o.a.20.4 | yes | 44 | |
3.2 | odd | 2 | 189.4.o.a.62.20 | 44 | |||
7.6 | odd | 2 | inner | 63.4.o.a.20.3 | ✓ | 44 | |
9.2 | odd | 6 | 567.4.c.c.566.35 | 44 | |||
9.4 | even | 3 | 189.4.o.a.125.19 | 44 | |||
9.5 | odd | 6 | inner | 63.4.o.a.41.3 | yes | 44 | |
9.7 | even | 3 | 567.4.c.c.566.10 | 44 | |||
21.20 | even | 2 | 189.4.o.a.62.19 | 44 | |||
63.13 | odd | 6 | 189.4.o.a.125.20 | 44 | |||
63.20 | even | 6 | 567.4.c.c.566.9 | 44 | |||
63.34 | odd | 6 | 567.4.c.c.566.36 | 44 | |||
63.41 | even | 6 | inner | 63.4.o.a.41.4 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.o.a.20.3 | ✓ | 44 | 7.6 | odd | 2 | inner | |
63.4.o.a.20.4 | yes | 44 | 1.1 | even | 1 | trivial | |
63.4.o.a.41.3 | yes | 44 | 9.5 | odd | 6 | inner | |
63.4.o.a.41.4 | yes | 44 | 63.41 | even | 6 | inner | |
189.4.o.a.62.19 | 44 | 21.20 | even | 2 | |||
189.4.o.a.62.20 | 44 | 3.2 | odd | 2 | |||
189.4.o.a.125.19 | 44 | 9.4 | even | 3 | |||
189.4.o.a.125.20 | 44 | 63.13 | odd | 6 | |||
567.4.c.c.566.9 | 44 | 63.20 | even | 6 | |||
567.4.c.c.566.10 | 44 | 9.7 | even | 3 | |||
567.4.c.c.566.35 | 44 | 9.2 | odd | 6 | |||
567.4.c.c.566.36 | 44 | 63.34 | odd | 6 |