Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,2,Mod(25,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.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: | \(1.00611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.121 |
Dual form | 126.2.e.b.25.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | −2.50000 | + | 4.33013i | −0.693375 | + | 1.20096i | 0.277350 | + | 0.960769i | \(0.410544\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 4.50000 | − | 2.59808i | 1.16190 | − | 0.670820i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 1.50000 | + | 2.59808i | 0.335410 | + | 0.580948i | ||||
\(21\) | −3.00000 | + | 3.46410i | −0.654654 | + | 0.755929i | ||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | − | 1.73205i | − | 0.353553i | ||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | −2.50000 | + | 4.33013i | −0.490290 | + | 0.849208i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | 1.50000 | + | 2.59808i | 0.278543 | + | 0.482451i | 0.971023 | − | 0.238987i | \(-0.0768152\pi\) |
−0.692480 | + | 0.721437i | \(0.743482\pi\) | |||||||
\(30\) | 4.50000 | − | 2.59808i | 0.821584 | − | 0.474342i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.50000 | − | 2.59808i | −0.783349 | − | 0.452267i | ||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 1.50000 | − | 7.79423i | 0.253546 | − | 1.31747i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | −2.50000 | + | 4.33013i | −0.405554 | + | 0.702439i | ||||
\(39\) | 7.50000 | + | 4.33013i | 1.20096 | + | 0.693375i | ||||
\(40\) | 1.50000 | + | 2.59808i | 0.237171 | + | 0.410792i | ||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | −3.00000 | + | 3.46410i | −0.462910 | + | 0.534522i | ||||
\(43\) | −5.50000 | − | 9.52628i | −0.838742 | − | 1.45274i | −0.890947 | − | 0.454108i | \(-0.849958\pi\) |
0.0522047 | − | 0.998636i | \(-0.483375\pi\) | |||||||
\(44\) | 1.50000 | − | 2.59808i | 0.226134 | − | 0.391675i | ||||
\(45\) | −4.50000 | − | 7.79423i | −0.670820 | − | 1.16190i | ||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | − | 1.73205i | − | 0.250000i | ||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | −4.50000 | + | 2.59808i | −0.630126 | + | 0.363803i | ||||
\(52\) | −2.50000 | + | 4.33013i | −0.346688 | + | 0.600481i | ||||
\(53\) | 1.50000 | + | 2.59808i | 0.206041 | + | 0.356873i | 0.950464 | − | 0.310835i | \(-0.100609\pi\) |
−0.744423 | + | 0.667708i | \(0.767275\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 9.00000 | 1.21356 | ||||||||
\(56\) | −2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | ||||
\(57\) | 7.50000 | + | 4.33013i | 0.993399 | + | 0.573539i | ||||
\(58\) | 1.50000 | + | 2.59808i | 0.196960 | + | 0.341144i | ||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 4.50000 | − | 2.59808i | 0.580948 | − | 0.335410i | ||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 6.00000 | + | 5.19615i | 0.755929 | + | 0.654654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −15.0000 | −1.86052 | ||||||||
\(66\) | −4.50000 | − | 2.59808i | −0.553912 | − | 0.319801i | ||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −1.50000 | − | 2.59808i | −0.181902 | − | 0.315063i | ||||
\(69\) | 4.50000 | − | 2.59808i | 0.541736 | − | 0.312772i | ||||
\(70\) | 1.50000 | − | 7.79423i | 0.179284 | − | 0.931589i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | 3.50000 | − | 6.06218i | 0.406867 | − | 0.704714i | ||||
\(75\) | 6.00000 | + | 3.46410i | 0.692820 | + | 0.400000i | ||||
\(76\) | −2.50000 | + | 4.33013i | −0.286770 | + | 0.496700i | ||||
\(77\) | −7.50000 | + | 2.59808i | −0.854704 | + | 0.296078i | ||||
\(78\) | 7.50000 | + | 4.33013i | 0.849208 | + | 0.490290i | ||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 1.50000 | + | 2.59808i | 0.167705 | + | 0.290474i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 4.50000 | − | 7.79423i | 0.496942 | − | 0.860729i | ||||
\(83\) | −1.50000 | − | 2.59808i | −0.164646 | − | 0.285176i | 0.771883 | − | 0.635764i | \(-0.219315\pi\) |
−0.936530 | + | 0.350588i | \(0.885982\pi\) | |||||||
\(84\) | −3.00000 | + | 3.46410i | −0.327327 | + | 0.377964i | ||||
\(85\) | 4.50000 | − | 7.79423i | 0.488094 | − | 0.845403i | ||||
\(86\) | −5.50000 | − | 9.52628i | −0.593080 | − | 1.02725i | ||||
\(87\) | 4.50000 | − | 2.59808i | 0.482451 | − | 0.278543i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | −4.50000 | − | 7.79423i | −0.474342 | − | 0.821584i | ||||
\(91\) | 12.5000 | − | 4.33013i | 1.31036 | − | 0.453921i | ||||
\(92\) | 1.50000 | + | 2.59808i | 0.156386 | + | 0.270868i | ||||
\(93\) | 6.92820i | 0.718421i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.0000 | −1.53897 | ||||||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | 0.500000 | + | 0.866025i | 0.0507673 | + | 0.0879316i | 0.890292 | − | 0.455389i | \(-0.150500\pi\) |
−0.839525 | + | 0.543321i | \(0.817167\pi\) | |||||||
\(98\) | 1.00000 | + | 6.92820i | 0.101015 | + | 0.699854i | ||||
\(99\) | −4.50000 | + | 7.79423i | −0.452267 | + | 0.783349i | ||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | −4.50000 | + | 2.59808i | −0.445566 | + | 0.257248i | ||||
\(103\) | −2.50000 | − | 4.33013i | −0.246332 | − | 0.426660i | 0.716173 | − | 0.697923i | \(-0.245892\pi\) |
−0.962505 | + | 0.271263i | \(0.912559\pi\) | |||||||
\(104\) | −2.50000 | + | 4.33013i | −0.245145 | + | 0.424604i | ||||
\(105\) | −13.5000 | − | 2.59808i | −1.31747 | − | 0.253546i | ||||
\(106\) | 1.50000 | + | 2.59808i | 0.145693 | + | 0.252347i | ||||
\(107\) | 7.50000 | − | 12.9904i | 0.725052 | − | 1.25583i | −0.233900 | − | 0.972261i | \(-0.575149\pi\) |
0.958952 | − | 0.283567i | \(-0.0915178\pi\) | |||||||
\(108\) | 5.19615i | 0.500000i | ||||||||
\(109\) | 3.50000 | + | 6.06218i | 0.335239 | + | 0.580651i | 0.983531 | − | 0.180741i | \(-0.0578495\pi\) |
−0.648292 | + | 0.761392i | \(0.724516\pi\) | |||||||
\(110\) | 9.00000 | 0.858116 | ||||||||
\(111\) | −10.5000 | − | 6.06218i | −0.996616 | − | 0.575396i | ||||
\(112\) | −2.00000 | − | 1.73205i | −0.188982 | − | 0.163663i | ||||
\(113\) | −7.50000 | + | 12.9904i | −0.705541 | + | 1.22203i | 0.260955 | + | 0.965351i | \(0.415962\pi\) |
−0.966496 | + | 0.256681i | \(0.917371\pi\) | |||||||
\(114\) | 7.50000 | + | 4.33013i | 0.702439 | + | 0.405554i | ||||
\(115\) | −4.50000 | + | 7.79423i | −0.419627 | + | 0.726816i | ||||
\(116\) | 1.50000 | + | 2.59808i | 0.139272 | + | 0.241225i | ||||
\(117\) | 7.50000 | − | 12.9904i | 0.693375 | − | 1.20096i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | −1.50000 | + | 7.79423i | −0.137505 | + | 0.714496i | ||||
\(120\) | 4.50000 | − | 2.59808i | 0.410792 | − | 0.237171i | ||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | −13.5000 | − | 7.79423i | −1.21725 | − | 0.702782i | ||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 6.00000 | + | 5.19615i | 0.534522 | + | 0.462910i | ||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −16.5000 | + | 9.52628i | −1.45274 | + | 0.838742i | ||||
\(130\) | −15.0000 | −1.31559 | ||||||||
\(131\) | −1.50000 | − | 2.59808i | −0.131056 | − | 0.226995i | 0.793028 | − | 0.609185i | \(-0.208503\pi\) |
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(132\) | −4.50000 | − | 2.59808i | −0.391675 | − | 0.226134i | ||||
\(133\) | 12.5000 | − | 4.33013i | 1.08389 | − | 0.375470i | ||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −13.5000 | + | 7.79423i | −1.16190 | + | 0.670820i | ||||
\(136\) | −1.50000 | − | 2.59808i | −0.128624 | − | 0.222783i | ||||
\(137\) | −1.50000 | + | 2.59808i | −0.128154 | + | 0.221969i | −0.922961 | − | 0.384893i | \(-0.874238\pi\) |
0.794808 | + | 0.606861i | \(0.207572\pi\) | |||||||
\(138\) | 4.50000 | − | 2.59808i | 0.383065 | − | 0.221163i | ||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | 1.50000 | − | 7.79423i | 0.126773 | − | 0.658733i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.50000 | + | 12.9904i | 0.627182 | + | 1.08631i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −4.50000 | + | 7.79423i | −0.373705 | + | 0.647275i | ||||
\(146\) | −5.50000 | − | 9.52628i | −0.455183 | − | 0.788400i | ||||
\(147\) | 12.0000 | − | 1.73205i | 0.989743 | − | 0.142857i | ||||
\(148\) | 3.50000 | − | 6.06218i | 0.287698 | − | 0.498308i | ||||
\(149\) | 1.50000 | + | 2.59808i | 0.122885 | + | 0.212843i | 0.920904 | − | 0.389789i | \(-0.127452\pi\) |
−0.798019 | + | 0.602632i | \(0.794119\pi\) | |||||||
\(150\) | 6.00000 | + | 3.46410i | 0.489898 | + | 0.282843i | ||||
\(151\) | −5.50000 | + | 9.52628i | −0.447584 | + | 0.775238i | −0.998228 | − | 0.0595022i | \(-0.981049\pi\) |
0.550645 | + | 0.834740i | \(0.314382\pi\) | |||||||
\(152\) | −2.50000 | + | 4.33013i | −0.202777 | + | 0.351220i | ||||
\(153\) | 4.50000 | + | 7.79423i | 0.363803 | + | 0.630126i | ||||
\(154\) | −7.50000 | + | 2.59808i | −0.604367 | + | 0.209359i | ||||
\(155\) | −6.00000 | − | 10.3923i | −0.481932 | − | 0.834730i | ||||
\(156\) | 7.50000 | + | 4.33013i | 0.600481 | + | 0.346688i | ||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | 4.50000 | − | 2.59808i | 0.356873 | − | 0.206041i | ||||
\(160\) | 1.50000 | + | 2.59808i | 0.118585 | + | 0.205396i | ||||
\(161\) | 1.50000 | − | 7.79423i | 0.118217 | − | 0.614271i | ||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | −8.50000 | + | 14.7224i | −0.665771 | + | 1.15315i | 0.313304 | + | 0.949653i | \(0.398564\pi\) |
−0.979076 | + | 0.203497i | \(0.934769\pi\) | |||||||
\(164\) | 4.50000 | − | 7.79423i | 0.351391 | − | 0.608627i | ||||
\(165\) | − | 15.5885i | − | 1.21356i | ||||||
\(166\) | −1.50000 | − | 2.59808i | −0.116423 | − | 0.201650i | ||||
\(167\) | −1.50000 | + | 2.59808i | −0.116073 | + | 0.201045i | −0.918208 | − | 0.396098i | \(-0.870364\pi\) |
0.802135 | + | 0.597143i | \(0.203697\pi\) | |||||||
\(168\) | −3.00000 | + | 3.46410i | −0.231455 | + | 0.267261i | ||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 4.50000 | − | 7.79423i | 0.345134 | − | 0.597790i | ||||
\(171\) | 7.50000 | − | 12.9904i | 0.573539 | − | 0.993399i | ||||
\(172\) | −5.50000 | − | 9.52628i | −0.419371 | − | 0.726372i | ||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 4.50000 | − | 2.59808i | 0.341144 | − | 0.196960i | ||||
\(175\) | 10.0000 | − | 3.46410i | 0.755929 | − | 0.261861i | ||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | − | 20.7846i | − | 1.56227i | ||||||
\(178\) | −7.50000 | + | 12.9904i | −0.562149 | + | 0.973670i | ||||
\(179\) | −1.50000 | − | 2.59808i | −0.112115 | − | 0.194189i | 0.804508 | − | 0.593942i | \(-0.202429\pi\) |
−0.916623 | + | 0.399753i | \(0.869096\pi\) | |||||||
\(180\) | −4.50000 | − | 7.79423i | −0.335410 | − | 0.580948i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 12.5000 | − | 4.33013i | 0.926562 | − | 0.320970i | ||||
\(183\) | − | 3.46410i | − | 0.256074i | ||||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 21.0000 | 1.54395 | ||||||||
\(186\) | 6.92820i | 0.508001i | ||||||||
\(187\) | −9.00000 | −0.658145 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | − | 10.3923i | 0.654654 | − | 0.755929i | ||||
\(190\) | −15.0000 | −1.08821 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | − | 1.73205i | − | 0.125000i | ||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 0.500000 | + | 0.866025i | 0.0358979 | + | 0.0621770i | ||||
\(195\) | 25.9808i | 1.86052i | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | −4.50000 | + | 7.79423i | −0.319801 | + | 0.553912i | ||||
\(199\) | 3.50000 | + | 6.06218i | 0.248108 | + | 0.429736i | 0.963001 | − | 0.269498i | \(-0.0868577\pi\) |
−0.714893 | + | 0.699234i | \(0.753524\pi\) | |||||||
\(200\) | −2.00000 | + | 3.46410i | −0.141421 | + | 0.244949i | ||||
\(201\) | 6.92820i | 0.488678i | ||||||||
\(202\) | 1.50000 | − | 2.59808i | 0.105540 | − | 0.182800i | ||||
\(203\) | 1.50000 | − | 7.79423i | 0.105279 | − | 0.547048i | ||||
\(204\) | −4.50000 | + | 2.59808i | −0.315063 | + | 0.181902i | ||||
\(205\) | 27.0000 | 1.88576 | ||||||||
\(206\) | −2.50000 | − | 4.33013i | −0.174183 | − | 0.301694i | ||||
\(207\) | −4.50000 | − | 7.79423i | −0.312772 | − | 0.541736i | ||||
\(208\) | −2.50000 | + | 4.33013i | −0.173344 | + | 0.300240i | ||||
\(209\) | 7.50000 | + | 12.9904i | 0.518786 | + | 0.898563i | ||||
\(210\) | −13.5000 | − | 2.59808i | −0.931589 | − | 0.179284i | ||||
\(211\) | −2.50000 | + | 4.33013i | −0.172107 | + | 0.298098i | −0.939156 | − | 0.343490i | \(-0.888391\pi\) |
0.767049 | + | 0.641588i | \(0.221724\pi\) | |||||||
\(212\) | 1.50000 | + | 2.59808i | 0.103020 | + | 0.178437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.50000 | − | 12.9904i | 0.512689 | − | 0.888004i | ||||
\(215\) | 16.5000 | − | 28.5788i | 1.12529 | − | 1.94906i | ||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 8.00000 | + | 6.92820i | 0.543075 | + | 0.470317i | ||||
\(218\) | 3.50000 | + | 6.06218i | 0.237050 | + | 0.410582i | ||||
\(219\) | −16.5000 | + | 9.52628i | −1.11497 | + | 0.643726i | ||||
\(220\) | 9.00000 | 0.606780 | ||||||||
\(221\) | 15.0000 | 1.00901 | ||||||||
\(222\) | −10.5000 | − | 6.06218i | −0.704714 | − | 0.406867i | ||||
\(223\) | −8.50000 | − | 14.7224i | −0.569202 | − | 0.985887i | −0.996645 | − | 0.0818447i | \(-0.973919\pi\) |
0.427443 | − | 0.904042i | \(-0.359414\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | 6.00000 | − | 10.3923i | 0.400000 | − | 0.692820i | ||||
\(226\) | −7.50000 | + | 12.9904i | −0.498893 | + | 0.864107i | ||||
\(227\) | −4.50000 | + | 7.79423i | −0.298675 | + | 0.517321i | −0.975833 | − | 0.218517i | \(-0.929878\pi\) |
0.677158 | + | 0.735838i | \(0.263211\pi\) | |||||||
\(228\) | 7.50000 | + | 4.33013i | 0.496700 | + | 0.286770i | ||||
\(229\) | −8.50000 | − | 14.7224i | −0.561696 | − | 0.972886i | −0.997349 | − | 0.0727709i | \(-0.976816\pi\) |
0.435653 | − | 0.900115i | \(-0.356518\pi\) | |||||||
\(230\) | −4.50000 | + | 7.79423i | −0.296721 | + | 0.513936i | ||||
\(231\) | 4.50000 | + | 12.9904i | 0.296078 | + | 0.854704i | ||||
\(232\) | 1.50000 | + | 2.59808i | 0.0984798 | + | 0.170572i | ||||
\(233\) | −13.5000 | + | 23.3827i | −0.884414 | + | 1.53185i | −0.0380310 | + | 0.999277i | \(0.512109\pi\) |
−0.846383 | + | 0.532574i | \(0.821225\pi\) | |||||||
\(234\) | 7.50000 | − | 12.9904i | 0.490290 | − | 0.849208i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | − | 13.8564i | − | 0.900070i | ||||||
\(238\) | −1.50000 | + | 7.79423i | −0.0972306 | + | 0.505225i | ||||
\(239\) | −13.5000 | + | 23.3827i | −0.873242 | + | 1.51250i | −0.0146191 | + | 0.999893i | \(0.504654\pi\) |
−0.858623 | + | 0.512607i | \(0.828680\pi\) | |||||||
\(240\) | 4.50000 | − | 2.59808i | 0.290474 | − | 0.167705i | ||||
\(241\) | −11.5000 | + | 19.9186i | −0.740780 | + | 1.28307i | 0.211360 | + | 0.977408i | \(0.432211\pi\) |
−0.952141 | + | 0.305661i | \(0.901123\pi\) | |||||||
\(242\) | 1.00000 | + | 1.73205i | 0.0642824 | + | 0.111340i | ||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −16.5000 | + | 12.9904i | −1.05415 | + | 0.829925i | ||||
\(246\) | −13.5000 | − | 7.79423i | −0.860729 | − | 0.496942i | ||||
\(247\) | −12.5000 | − | 21.6506i | −0.795356 | − | 1.37760i | ||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | −4.50000 | + | 2.59808i | −0.285176 | + | 0.164646i | ||||
\(250\) | 3.00000 | 0.189737 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 6.00000 | + | 5.19615i | 0.377964 | + | 0.327327i | ||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | −16.0000 | −1.00393 | ||||||||
\(255\) | −13.5000 | − | 7.79423i | −0.845403 | − | 0.488094i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | −16.5000 | + | 9.52628i | −1.02725 | + | 0.593080i | ||||
\(259\) | −17.5000 | + | 6.06218i | −1.08740 | + | 0.376685i | ||||
\(260\) | −15.0000 | −0.930261 | ||||||||
\(261\) | −4.50000 | − | 7.79423i | −0.278543 | − | 0.482451i | ||||
\(262\) | −1.50000 | − | 2.59808i | −0.0926703 | − | 0.160510i | ||||
\(263\) | 4.50000 | − | 7.79423i | 0.277482 | − | 0.480613i | −0.693276 | − | 0.720672i | \(-0.743833\pi\) |
0.970758 | + | 0.240059i | \(0.0771668\pi\) | |||||||
\(264\) | −4.50000 | − | 2.59808i | −0.276956 | − | 0.159901i | ||||
\(265\) | −4.50000 | + | 7.79423i | −0.276433 | + | 0.478796i | ||||
\(266\) | 12.5000 | − | 4.33013i | 0.766424 | − | 0.265497i | ||||
\(267\) | 22.5000 | + | 12.9904i | 1.37698 | + | 0.794998i | ||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | −10.5000 | − | 18.1865i | −0.640196 | − | 1.10885i | −0.985389 | − | 0.170321i | \(-0.945520\pi\) |
0.345192 | − | 0.938532i | \(-0.387814\pi\) | |||||||
\(270\) | −13.5000 | + | 7.79423i | −0.821584 | + | 0.474342i | ||||
\(271\) | 6.50000 | − | 11.2583i | 0.394847 | − | 0.683895i | −0.598235 | − | 0.801321i | \(-0.704131\pi\) |
0.993082 | + | 0.117426i | \(0.0374643\pi\) | |||||||
\(272\) | −1.50000 | − | 2.59808i | −0.0909509 | − | 0.157532i | ||||
\(273\) | −7.50000 | − | 21.6506i | −0.453921 | − | 1.31036i | ||||
\(274\) | −1.50000 | + | 2.59808i | −0.0906183 | + | 0.156956i | ||||
\(275\) | 6.00000 | + | 10.3923i | 0.361814 | + | 0.626680i | ||||
\(276\) | 4.50000 | − | 2.59808i | 0.270868 | − | 0.156386i | ||||
\(277\) | 3.50000 | − | 6.06218i | 0.210295 | − | 0.364241i | −0.741512 | − | 0.670940i | \(-0.765891\pi\) |
0.951807 | + | 0.306699i | \(0.0992243\pi\) | |||||||
\(278\) | −2.50000 | + | 4.33013i | −0.149940 | + | 0.259704i | ||||
\(279\) | 12.0000 | 0.718421 | ||||||||
\(280\) | 1.50000 | − | 7.79423i | 0.0896421 | − | 0.465794i | ||||
\(281\) | −1.50000 | − | 2.59808i | −0.0894825 | − | 0.154988i | 0.817810 | − | 0.575488i | \(-0.195188\pi\) |
−0.907293 | + | 0.420500i | \(0.861855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | 0.475551 | 0.237775 | − | 0.971320i | \(-0.423582\pi\) | ||||
0.237775 | + | 0.971320i | \(0.423582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.9808i | 1.53897i | ||||||||
\(286\) | 7.50000 | + | 12.9904i | 0.443484 | + | 0.768137i | ||||
\(287\) | −22.5000 | + | 7.79423i | −1.32813 | + | 0.460079i | ||||
\(288\) | −3.00000 | −0.176777 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | −4.50000 | + | 7.79423i | −0.264249 | + | 0.457693i | ||||
\(291\) | 1.50000 | − | 0.866025i | 0.0879316 | − | 0.0507673i | ||||
\(292\) | −5.50000 | − | 9.52628i | −0.321863 | − | 0.557483i | ||||
\(293\) | 13.5000 | − | 23.3827i | 0.788678 | − | 1.36603i | −0.138098 | − | 0.990419i | \(-0.544099\pi\) |
0.926777 | − | 0.375613i | \(-0.122568\pi\) | |||||||
\(294\) | 12.0000 | − | 1.73205i | 0.699854 | − | 0.101015i | ||||
\(295\) | 18.0000 | + | 31.1769i | 1.04800 | + | 1.81519i | ||||
\(296\) | 3.50000 | − | 6.06218i | 0.203433 | − | 0.352357i | ||||
\(297\) | 13.5000 | + | 7.79423i | 0.783349 | + | 0.452267i | ||||
\(298\) | 1.50000 | + | 2.59808i | 0.0868927 | + | 0.150503i | ||||
\(299\) | −15.0000 | −0.867472 | ||||||||
\(300\) | 6.00000 | + | 3.46410i | 0.346410 | + | 0.200000i | ||||
\(301\) | −5.50000 | + | 28.5788i | −0.317015 | + | 1.64726i | ||||
\(302\) | −5.50000 | + | 9.52628i | −0.316489 | + | 0.548176i | ||||
\(303\) | −4.50000 | − | 2.59808i | −0.258518 | − | 0.149256i | ||||
\(304\) | −2.50000 | + | 4.33013i | −0.143385 | + | 0.248350i | ||||
\(305\) | 3.00000 | + | 5.19615i | 0.171780 | + | 0.297531i | ||||
\(306\) | 4.50000 | + | 7.79423i | 0.257248 | + | 0.445566i | ||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | −7.50000 | + | 2.59808i | −0.427352 | + | 0.148039i | ||||
\(309\) | −7.50000 | + | 4.33013i | −0.426660 | + | 0.246332i | ||||
\(310\) | −6.00000 | − | 10.3923i | −0.340777 | − | 0.590243i | ||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 7.50000 | + | 4.33013i | 0.424604 | + | 0.245145i | ||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | −4.50000 | + | 23.3827i | −0.253546 | + | 1.31747i | ||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 30.0000 | 1.68497 | 0.842484 | − | 0.538721i | \(-0.181092\pi\) | ||||
0.842484 | + | 0.538721i | \(0.181092\pi\) | |||||||
\(318\) | 4.50000 | − | 2.59808i | 0.252347 | − | 0.145693i | ||||
\(319\) | 9.00000 | 0.503903 | ||||||||
\(320\) | 1.50000 | + | 2.59808i | 0.0838525 | + | 0.145237i | ||||
\(321\) | −22.5000 | − | 12.9904i | −1.25583 | − | 0.725052i | ||||
\(322\) | 1.50000 | − | 7.79423i | 0.0835917 | − | 0.434355i | ||||
\(323\) | 15.0000 | 0.834622 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | −10.0000 | − | 17.3205i | −0.554700 | − | 0.960769i | ||||
\(326\) | −8.50000 | + | 14.7224i | −0.470771 | + | 0.815400i | ||||
\(327\) | 10.5000 | − | 6.06218i | 0.580651 | − | 0.335239i | ||||
\(328\) | 4.50000 | − | 7.79423i | 0.248471 | − | 0.430364i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 15.5885i | − | 0.858116i | ||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | −1.50000 | − | 2.59808i | −0.0823232 | − | 0.142588i | ||||
\(333\) | −10.5000 | + | 18.1865i | −0.575396 | + | 0.996616i | ||||
\(334\) | −1.50000 | + | 2.59808i | −0.0820763 | + | 0.142160i | ||||
\(335\) | −6.00000 | − | 10.3923i | −0.327815 | − | 0.567792i | ||||
\(336\) | −3.00000 | + | 3.46410i | −0.163663 | + | 0.188982i | ||||
\(337\) | 12.5000 | − | 21.6506i | 0.680918 | − | 1.17939i | −0.293783 | − | 0.955872i | \(-0.594914\pi\) |
0.974701 | − | 0.223513i | \(-0.0717525\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 22.5000 | + | 12.9904i | 1.22203 | + | 0.705541i | ||||
\(340\) | 4.50000 | − | 7.79423i | 0.244047 | − | 0.422701i | ||||
\(341\) | −6.00000 | + | 10.3923i | −0.324918 | + | 0.562775i | ||||
\(342\) | 7.50000 | − | 12.9904i | 0.405554 | − | 0.702439i | ||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −5.50000 | − | 9.52628i | −0.296540 | − | 0.513623i | ||||
\(345\) | 13.5000 | + | 7.79423i | 0.726816 | + | 0.419627i | ||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | −12.0000 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(348\) | 4.50000 | − | 2.59808i | 0.241225 | − | 0.139272i | ||||
\(349\) | −2.50000 | − | 4.33013i | −0.133822 | − | 0.231786i | 0.791325 | − | 0.611396i | \(-0.209392\pi\) |
−0.925147 | + | 0.379610i | \(0.876058\pi\) | |||||||
\(350\) | 10.0000 | − | 3.46410i | 0.534522 | − | 0.185164i | ||||
\(351\) | −22.5000 | − | 12.9904i | −1.20096 | − | 0.693375i | ||||
\(352\) | 1.50000 | − | 2.59808i | 0.0799503 | − | 0.138478i | ||||
\(353\) | 4.50000 | − | 7.79423i | 0.239511 | − | 0.414845i | −0.721063 | − | 0.692869i | \(-0.756346\pi\) |
0.960574 | + | 0.278024i | \(0.0896796\pi\) | |||||||
\(354\) | − | 20.7846i | − | 1.10469i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.50000 | + | 12.9904i | −0.397499 | + | 0.688489i | ||||
\(357\) | 13.5000 | + | 2.59808i | 0.714496 | + | 0.137505i | ||||
\(358\) | −1.50000 | − | 2.59808i | −0.0792775 | − | 0.137313i | ||||
\(359\) | −7.50000 | + | 12.9904i | −0.395835 | + | 0.685606i | −0.993207 | − | 0.116358i | \(-0.962878\pi\) |
0.597372 | + | 0.801964i | \(0.296211\pi\) | |||||||
\(360\) | −4.50000 | − | 7.79423i | −0.237171 | − | 0.410792i | ||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 3.00000 | − | 1.73205i | 0.157459 | − | 0.0909091i | ||||
\(364\) | 12.5000 | − | 4.33013i | 0.655178 | − | 0.226960i | ||||
\(365\) | 16.5000 | − | 28.5788i | 0.863649 | − | 1.49588i | ||||
\(366\) | − | 3.46410i | − | 0.181071i | ||||||
\(367\) | 0.500000 | − | 0.866025i | 0.0260998 | − | 0.0452062i | −0.852680 | − | 0.522433i | \(-0.825025\pi\) |
0.878780 | + | 0.477227i | \(0.158358\pi\) | |||||||
\(368\) | 1.50000 | + | 2.59808i | 0.0781929 | + | 0.135434i | ||||
\(369\) | −13.5000 | + | 23.3827i | −0.702782 | + | 1.21725i | ||||
\(370\) | 21.0000 | 1.09174 | ||||||||
\(371\) | 1.50000 | − | 7.79423i | 0.0778761 | − | 0.404656i | ||||
\(372\) | 6.92820i | 0.359211i | ||||||||
\(373\) | −8.50000 | − | 14.7224i | −0.440113 | − | 0.762299i | 0.557584 | − | 0.830120i | \(-0.311728\pi\) |
−0.997697 | + | 0.0678218i | \(0.978395\pi\) | |||||||
\(374\) | −9.00000 | −0.465379 | ||||||||
\(375\) | − | 5.19615i | − | 0.268328i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0000 | −0.772539 | ||||||||
\(378\) | 9.00000 | − | 10.3923i | 0.462910 | − | 0.534522i | ||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | −15.0000 | −0.769484 | ||||||||
\(381\) | 27.7128i | 1.41977i | ||||||||
\(382\) | 12.0000 | 0.613973 | ||||||||
\(383\) | 7.50000 | + | 12.9904i | 0.383232 | + | 0.663777i | 0.991522 | − | 0.129937i | \(-0.0414776\pi\) |
−0.608290 | + | 0.793715i | \(0.708144\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | −18.0000 | − | 15.5885i | −0.917365 | − | 0.794461i | ||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | 16.5000 | + | 28.5788i | 0.838742 | + | 1.45274i | ||||
\(388\) | 0.500000 | + | 0.866025i | 0.0253837 | + | 0.0439658i | ||||
\(389\) | −4.50000 | + | 7.79423i | −0.228159 | + | 0.395183i | −0.957263 | − | 0.289220i | \(-0.906604\pi\) |
0.729103 | + | 0.684403i | \(0.239937\pi\) | |||||||
\(390\) | 25.9808i | 1.31559i | ||||||||
\(391\) | 4.50000 | − | 7.79423i | 0.227575 | − | 0.394171i | ||||
\(392\) | 1.00000 | + | 6.92820i | 0.0505076 | + | 0.349927i | ||||
\(393\) | −4.50000 | + | 2.59808i | −0.226995 | + | 0.131056i | ||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 12.0000 | + | 20.7846i | 0.603786 | + | 1.04579i | ||||
\(396\) | −4.50000 | + | 7.79423i | −0.226134 | + | 0.391675i | ||||
\(397\) | −14.5000 | + | 25.1147i | −0.727734 | + | 1.26047i | 0.230105 | + | 0.973166i | \(0.426093\pi\) |
−0.957839 | + | 0.287307i | \(0.907240\pi\) | |||||||
\(398\) | 3.50000 | + | 6.06218i | 0.175439 | + | 0.303870i | ||||
\(399\) | −7.50000 | − | 21.6506i | −0.375470 | − | 1.08389i | ||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | −13.5000 | − | 23.3827i | −0.674158 | − | 1.16768i | −0.976714 | − | 0.214544i | \(-0.931173\pi\) |
0.302556 | − | 0.953131i | \(-0.402160\pi\) | |||||||
\(402\) | 6.92820i | 0.345547i | ||||||||
\(403\) | 10.0000 | − | 17.3205i | 0.498135 | − | 0.862796i | ||||
\(404\) | 1.50000 | − | 2.59808i | 0.0746278 | − | 0.129259i | ||||
\(405\) | 13.5000 | + | 23.3827i | 0.670820 | + | 1.16190i | ||||
\(406\) | 1.50000 | − | 7.79423i | 0.0744438 | − | 0.386821i | ||||
\(407\) | −10.5000 | − | 18.1865i | −0.520466 | − | 0.901473i | ||||
\(408\) | −4.50000 | + | 2.59808i | −0.222783 | + | 0.128624i | ||||
\(409\) | −22.0000 | −1.08783 | −0.543915 | − | 0.839140i | \(-0.683059\pi\) | ||||
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | 27.0000 | 1.33343 | ||||||||
\(411\) | 4.50000 | + | 2.59808i | 0.221969 | + | 0.128154i | ||||
\(412\) | −2.50000 | − | 4.33013i | −0.123166 | − | 0.213330i | ||||
\(413\) | −24.0000 | − | 20.7846i | −1.18096 | − | 1.02274i | ||||
\(414\) | −4.50000 | − | 7.79423i | −0.221163 | − | 0.383065i | ||||
\(415\) | 4.50000 | − | 7.79423i | 0.220896 | − | 0.382604i | ||||
\(416\) | −2.50000 | + | 4.33013i | −0.122573 | + | 0.212302i | ||||
\(417\) | 7.50000 | + | 4.33013i | 0.367277 | + | 0.212047i | ||||
\(418\) | 7.50000 | + | 12.9904i | 0.366837 | + | 0.635380i | ||||
\(419\) | 1.50000 | − | 2.59808i | 0.0732798 | − | 0.126924i | −0.827057 | − | 0.562118i | \(-0.809987\pi\) |
0.900337 | + | 0.435194i | \(0.143320\pi\) | |||||||
\(420\) | −13.5000 | − | 2.59808i | −0.658733 | − | 0.126773i | ||||
\(421\) | 15.5000 | + | 26.8468i | 0.755424 | + | 1.30843i | 0.945163 | + | 0.326598i | \(0.105902\pi\) |
−0.189740 | + | 0.981834i | \(0.560764\pi\) | |||||||
\(422\) | −2.50000 | + | 4.33013i | −0.121698 | + | 0.210787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.50000 | + | 2.59808i | 0.0728464 | + | 0.126174i | ||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | − | 3.46410i | −0.193574 | − | 0.167640i | ||||
\(428\) | 7.50000 | − | 12.9904i | 0.362526 | − | 0.627914i | ||||
\(429\) | 22.5000 | − | 12.9904i | 1.08631 | − | 0.627182i | ||||
\(430\) | 16.5000 | − | 28.5788i | 0.795701 | − | 1.37819i | ||||
\(431\) | 1.50000 | + | 2.59808i | 0.0722525 | + | 0.125145i | 0.899888 | − | 0.436121i | \(-0.143648\pi\) |
−0.827636 | + | 0.561266i | \(0.810315\pi\) | |||||||
\(432\) | 5.19615i | 0.250000i | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 8.00000 | + | 6.92820i | 0.384012 | + | 0.332564i | ||||
\(435\) | 13.5000 | + | 7.79423i | 0.647275 | + | 0.373705i | ||||
\(436\) | 3.50000 | + | 6.06218i | 0.167620 | + | 0.290326i | ||||
\(437\) | −15.0000 | −0.717547 | ||||||||
\(438\) | −16.5000 | + | 9.52628i | −0.788400 | + | 0.455183i | ||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 9.00000 | 0.429058 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 15.0000 | 0.713477 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | −10.5000 | − | 6.06218i | −0.498308 | − | 0.287698i | ||||
\(445\) | −45.0000 | −2.13320 | ||||||||
\(446\) | −8.50000 | − | 14.7224i | −0.402487 | − | 0.697127i | ||||
\(447\) | 4.50000 | − | 2.59808i | 0.212843 | − | 0.122885i | ||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 6.00000 | − | 10.3923i | 0.282843 | − | 0.489898i | ||||
\(451\) | −13.5000 | − | 23.3827i | −0.635690 | − | 1.10105i | ||||
\(452\) | −7.50000 | + | 12.9904i | −0.352770 | + | 0.611016i | ||||
\(453\) | 16.5000 | + | 9.52628i | 0.775238 | + | 0.447584i | ||||
\(454\) | −4.50000 | + | 7.79423i | −0.211195 | + | 0.365801i | ||||
\(455\) | 30.0000 | + | 25.9808i | 1.40642 | + | 1.21800i | ||||
\(456\) | 7.50000 | + | 4.33013i | 0.351220 | + | 0.202777i | ||||
\(457\) | −34.0000 | −1.59045 | −0.795226 | − | 0.606313i | \(-0.792648\pi\) | ||||
−0.795226 | + | 0.606313i | \(0.792648\pi\) | |||||||
\(458\) | −8.50000 | − | 14.7224i | −0.397179 | − | 0.687934i | ||||
\(459\) | 13.5000 | − | 7.79423i | 0.630126 | − | 0.363803i | ||||
\(460\) | −4.50000 | + | 7.79423i | −0.209814 | + | 0.363408i | ||||
\(461\) | −4.50000 | − | 7.79423i | −0.209586 | − | 0.363013i | 0.741998 | − | 0.670402i | \(-0.233878\pi\) |
−0.951584 | + | 0.307388i | \(0.900545\pi\) | |||||||
\(462\) | 4.50000 | + | 12.9904i | 0.209359 | + | 0.604367i | ||||
\(463\) | −17.5000 | + | 30.3109i | −0.813294 | + | 1.40867i | 0.0972525 | + | 0.995260i | \(0.468995\pi\) |
−0.910546 | + | 0.413407i | \(0.864339\pi\) | |||||||
\(464\) | 1.50000 | + | 2.59808i | 0.0696358 | + | 0.120613i | ||||
\(465\) | −18.0000 | + | 10.3923i | −0.834730 | + | 0.481932i | ||||
\(466\) | −13.5000 | + | 23.3827i | −0.625375 | + | 1.08318i | ||||
\(467\) | 1.50000 | − | 2.59808i | 0.0694117 | − | 0.120225i | −0.829231 | − | 0.558906i | \(-0.811221\pi\) |
0.898642 | + | 0.438682i | \(0.144554\pi\) | |||||||
\(468\) | 7.50000 | − | 12.9904i | 0.346688 | − | 0.600481i | ||||
\(469\) | 8.00000 | + | 6.92820i | 0.369406 | + | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 24.2487i | − | 1.11732i | ||||||
\(472\) | 12.0000 | 0.552345 | ||||||||
\(473\) | −33.0000 | −1.51734 | ||||||||
\(474\) | − | 13.8564i | − | 0.636446i | ||||||
\(475\) | −10.0000 | − | 17.3205i | −0.458831 | − | 0.794719i | ||||
\(476\) | −1.50000 | + | 7.79423i | −0.0687524 | + | 0.357248i | ||||
\(477\) | −4.50000 | − | 7.79423i | −0.206041 | − | 0.356873i | ||||
\(478\) | −13.5000 | + | 23.3827i | −0.617476 | + | 1.06950i | ||||
\(479\) | 4.50000 | − | 7.79423i | 0.205610 | − | 0.356127i | −0.744717 | − | 0.667381i | \(-0.767415\pi\) |
0.950327 | + | 0.311253i | \(0.100749\pi\) | |||||||
\(480\) | 4.50000 | − | 2.59808i | 0.205396 | − | 0.118585i | ||||
\(481\) | 17.5000 | + | 30.3109i | 0.797931 | + | 1.38206i | ||||
\(482\) | −11.5000 | + | 19.9186i | −0.523811 | + | 0.907267i | ||||
\(483\) | −13.5000 | − | 2.59808i | −0.614271 | − | 0.118217i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | −1.50000 | + | 2.59808i | −0.0681115 | + | 0.117973i | ||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | 15.5000 | + | 26.8468i | 0.702372 | + | 1.21654i | 0.967632 | + | 0.252367i | \(0.0812090\pi\) |
−0.265260 | + | 0.964177i | \(0.585458\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | 25.5000 | + | 14.7224i | 1.15315 | + | 0.665771i | ||||
\(490\) | −16.5000 | + | 12.9904i | −0.745394 | + | 0.586846i | ||||
\(491\) | 19.5000 | − | 33.7750i | 0.880023 | − | 1.52424i | 0.0287085 | − | 0.999588i | \(-0.490861\pi\) |
0.851314 | − | 0.524656i | \(-0.175806\pi\) | |||||||
\(492\) | −13.5000 | − | 7.79423i | −0.608627 | − | 0.351391i | ||||
\(493\) | 4.50000 | − | 7.79423i | 0.202670 | − | 0.351034i | ||||
\(494\) | −12.5000 | − | 21.6506i | −0.562402 | − | 0.974108i | ||||
\(495\) | −27.0000 | −1.21356 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.50000 | + | 2.59808i | −0.201650 | + | 0.116423i | ||||
\(499\) | −5.50000 | − | 9.52628i | −0.246214 | − | 0.426455i | 0.716258 | − | 0.697835i | \(-0.245853\pi\) |
−0.962472 | + | 0.271380i | \(0.912520\pi\) | |||||||
\(500\) | 3.00000 | 0.134164 | ||||||||
\(501\) | 4.50000 | + | 2.59808i | 0.201045 | + | 0.116073i | ||||
\(502\) | 12.0000 | 0.535586 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 6.00000 | + | 5.19615i | 0.267261 | + | 0.231455i | ||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | 9.00000 | 0.400099 | ||||||||
\(507\) | −18.0000 | + | 10.3923i | −0.799408 | + | 0.461538i | ||||
\(508\) | −16.0000 | −0.709885 | ||||||||
\(509\) | 13.5000 | + | 23.3827i | 0.598377 | + | 1.03642i | 0.993061 | + | 0.117602i | \(0.0375208\pi\) |
−0.394684 | + | 0.918817i | \(0.629146\pi\) | |||||||
\(510\) | −13.5000 | − | 7.79423i | −0.597790 | − | 0.345134i | ||||
\(511\) | −5.50000 | + | 28.5788i | −0.243306 | + | 1.26425i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −22.5000 | − | 12.9904i | −0.993399 | − | 0.573539i | ||||
\(514\) | −7.50000 | − | 12.9904i | −0.330811 | − | 0.572981i | ||||
\(515\) | 7.50000 | − | 12.9904i | 0.330489 | − | 0.572425i | ||||
\(516\) | −16.5000 | + | 9.52628i | −0.726372 | + | 0.419371i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −17.5000 | + | 6.06218i | −0.768906 | + | 0.266357i | ||||
\(519\) | − | 10.3923i | − | 0.456172i | ||||||
\(520\) | −15.0000 | −0.657794 | ||||||||
\(521\) | −1.50000 | − | 2.59808i | −0.0657162 | − | 0.113824i | 0.831295 | − | 0.555831i | \(-0.187600\pi\) |
−0.897011 | + | 0.442007i | \(0.854267\pi\) | |||||||
\(522\) | −4.50000 | − | 7.79423i | −0.196960 | − | 0.341144i | ||||
\(523\) | 3.50000 | − | 6.06218i | 0.153044 | − | 0.265081i | −0.779301 | − | 0.626650i | \(-0.784426\pi\) |
0.932345 | + | 0.361569i | \(0.117759\pi\) | |||||||
\(524\) | −1.50000 | − | 2.59808i | −0.0655278 | − | 0.113497i | ||||
\(525\) | −6.00000 | − | 17.3205i | −0.261861 | − | 0.755929i | ||||
\(526\) | 4.50000 | − | 7.79423i | 0.196209 | − | 0.339845i | ||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | −4.50000 | − | 2.59808i | −0.195837 | − | 0.113067i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | −4.50000 | + | 7.79423i | −0.195468 | + | 0.338560i | ||||
\(531\) | −36.0000 | −1.56227 | ||||||||
\(532\) | 12.5000 | − | 4.33013i | 0.541944 | − | 0.187735i | ||||
\(533\) | 22.5000 | + | 38.9711i | 0.974583 | + | 1.68803i | ||||
\(534\) | 22.5000 | + | 12.9904i | 0.973670 | + | 0.562149i | ||||
\(535\) | 45.0000 | 1.94552 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | −4.50000 | + | 2.59808i | −0.194189 | + | 0.112115i | ||||
\(538\) | −10.5000 | − | 18.1865i | −0.452687 | − | 0.784077i | ||||
\(539\) | 19.5000 | + | 7.79423i | 0.839924 | + | 0.335721i | ||||
\(540\) | −13.5000 | + | 7.79423i | −0.580948 | + | 0.335410i | ||||
\(541\) | −8.50000 | + | 14.7224i | −0.365444 | + | 0.632967i | −0.988847 | − | 0.148933i | \(-0.952416\pi\) |
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | 6.50000 | − | 11.2583i | 0.279199 | − | 0.483587i | ||||
\(543\) | 17.3205i | 0.743294i | ||||||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | −10.5000 | + | 18.1865i | −0.449771 | + | 0.779026i | ||||
\(546\) | −7.50000 | − | 21.6506i | −0.320970 | − | 0.926562i | ||||
\(547\) | −5.50000 | − | 9.52628i | −0.235163 | − | 0.407314i | 0.724157 | − | 0.689635i | \(-0.242229\pi\) |
−0.959320 | + | 0.282321i | \(0.908896\pi\) | |||||||
\(548\) | −1.50000 | + | 2.59808i | −0.0640768 | + | 0.110984i | ||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 6.00000 | + | 10.3923i | 0.255841 | + | 0.443129i | ||||
\(551\) | −15.0000 | −0.639021 | ||||||||
\(552\) | 4.50000 | − | 2.59808i | 0.191533 | − | 0.110581i | ||||
\(553\) | −16.0000 | − | 13.8564i | −0.680389 | − | 0.589234i | ||||
\(554\) | 3.50000 | − | 6.06218i | 0.148701 | − | 0.257557i | ||||
\(555\) | − | 36.3731i | − | 1.54395i | ||||||
\(556\) | −2.50000 | + | 4.33013i | −0.106024 | + | 0.183638i | ||||
\(557\) | 1.50000 | + | 2.59808i | 0.0635570 | + | 0.110084i | 0.896053 | − | 0.443947i | \(-0.146422\pi\) |
−0.832496 | + | 0.554031i | \(0.813089\pi\) | |||||||
\(558\) | 12.0000 | 0.508001 | ||||||||
\(559\) | 55.0000 | 2.32625 | ||||||||
\(560\) | 1.50000 | − | 7.79423i | 0.0633866 | − | 0.329366i | ||||
\(561\) | 15.5885i | 0.658145i | ||||||||
\(562\) | −1.50000 | − | 2.59808i | −0.0632737 | − | 0.109593i | ||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.0000 | −1.89316 | ||||||||
\(566\) | 8.00000 | 0.336265 | ||||||||
\(567\) | −18.0000 | − | 15.5885i | −0.755929 | − | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 25.9808i | 1.08821i | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 7.50000 | + | 12.9904i | 0.313591 | + | 0.543155i | ||||
\(573\) | − | 20.7846i | − | 0.868290i | ||||||
\(574\) | −22.5000 | + | 7.79423i | −0.939132 | + | 0.325325i | ||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | −5.50000 | − | 9.52628i | −0.228968 | − | 0.396584i | 0.728535 | − | 0.685009i | \(-0.240202\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | − | 24.2487i | − | 1.00774i | ||||||
\(580\) | −4.50000 | + | 7.79423i | −0.186852 | + | 0.323638i | ||||
\(581\) | −1.50000 | + | 7.79423i | −0.0622305 | + | 0.323359i | ||||
\(582\) | 1.50000 | − | 0.866025i | 0.0621770 | − | 0.0358979i | ||||
\(583\) | 9.00000 | 0.372742 | ||||||||
\(584\) | −5.50000 | − | 9.52628i | −0.227592 | − | 0.394200i | ||||
\(585\) | 45.0000 | 1.86052 | ||||||||
\(586\) | 13.5000 | − | 23.3827i | 0.557680 | − | 0.965930i | ||||
\(587\) | 16.5000 | + | 28.5788i | 0.681028 | + | 1.17957i | 0.974668 | + | 0.223659i | \(0.0718001\pi\) |
−0.293640 | + | 0.955916i | \(0.594867\pi\) | |||||||
\(588\) | 12.0000 | − | 1.73205i | 0.494872 | − | 0.0714286i | ||||
\(589\) | 10.0000 | − | 17.3205i | 0.412043 | − | 0.713679i | ||||
\(590\) | 18.0000 | + | 31.1769i | 0.741048 | + | 1.28353i | ||||
\(591\) | 10.3923i | 0.427482i | ||||||||
\(592\) | 3.50000 | − | 6.06218i | 0.143849 | − | 0.249154i | ||||
\(593\) | 10.5000 | − | 18.1865i | 0.431183 | − | 0.746831i | −0.565792 | − | 0.824548i | \(-0.691430\pi\) |
0.996976 | + | 0.0777165i | \(0.0247629\pi\) | |||||||
\(594\) | 13.5000 | + | 7.79423i | 0.553912 | + | 0.319801i | ||||
\(595\) | −22.5000 | + | 7.79423i | −0.922410 | + | 0.319532i | ||||
\(596\) | 1.50000 | + | 2.59808i | 0.0614424 | + | 0.106421i | ||||
\(597\) | 10.5000 | − | 6.06218i | 0.429736 | − | 0.248108i | ||||
\(598\) | −15.0000 | −0.613396 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 6.00000 | + | 3.46410i | 0.244949 | + | 0.141421i | ||||
\(601\) | 0.500000 | + | 0.866025i | 0.0203954 | + | 0.0353259i | 0.876043 | − | 0.482233i | \(-0.160174\pi\) |
−0.855648 | + | 0.517559i | \(0.826841\pi\) | |||||||
\(602\) | −5.50000 | + | 28.5788i | −0.224163 | + | 1.16479i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | −5.50000 | + | 9.52628i | −0.223792 | + | 0.387619i | ||||
\(605\) | −3.00000 | + | 5.19615i | −0.121967 | + | 0.211254i | ||||
\(606\) | −4.50000 | − | 2.59808i | −0.182800 | − | 0.105540i | ||||
\(607\) | 21.5000 | + | 37.2391i | 0.872658 | + | 1.51149i | 0.859237 | + | 0.511578i | \(0.170939\pi\) |
0.0134214 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(608\) | −2.50000 | + | 4.33013i | −0.101388 | + | 0.175610i | ||||
\(609\) | −13.5000 | − | 2.59808i | −0.547048 | − | 0.105279i | ||||
\(610\) | 3.00000 | + | 5.19615i | 0.121466 | + | 0.210386i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.50000 | + | 7.79423i | 0.181902 | + | 0.315063i | ||||
\(613\) | 15.5000 | + | 26.8468i | 0.626039 | + | 1.08433i | 0.988339 | + | 0.152270i | \(0.0486583\pi\) |
−0.362300 | + | 0.932062i | \(0.618008\pi\) | |||||||
\(614\) | −28.0000 | −1.12999 | ||||||||
\(615\) | − | 46.7654i | − | 1.88576i | ||||||
\(616\) | −7.50000 | + | 2.59808i | −0.302184 | + | 0.104679i | ||||
\(617\) | −1.50000 | + | 2.59808i | −0.0603877 | + | 0.104595i | −0.894639 | − | 0.446790i | \(-0.852567\pi\) |
0.834251 | + | 0.551385i | \(0.185900\pi\) | |||||||
\(618\) | −7.50000 | + | 4.33013i | −0.301694 | + | 0.174183i | ||||
\(619\) | 9.50000 | − | 16.4545i | 0.381837 | − | 0.661361i | −0.609488 | − | 0.792796i | \(-0.708625\pi\) |
0.991325 | + | 0.131434i | \(0.0419582\pi\) | |||||||
\(620\) | −6.00000 | − | 10.3923i | −0.240966 | − | 0.417365i | ||||
\(621\) | −13.5000 | + | 7.79423i | −0.541736 | + | 0.312772i | ||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | 37.5000 | − | 12.9904i | 1.50241 | − | 0.520449i | ||||
\(624\) | 7.50000 | + | 4.33013i | 0.300240 | + | 0.173344i | ||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 14.0000 | 0.559553 | ||||||||
\(627\) | 22.5000 | − | 12.9904i | 0.898563 | − | 0.518786i | ||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | −4.50000 | + | 23.3827i | −0.179284 | + | 0.931589i | ||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 8.00000 | 0.318223 | ||||||||
\(633\) | 7.50000 | + | 4.33013i | 0.298098 | + | 0.172107i | ||||
\(634\) | 30.0000 | 1.19145 | ||||||||
\(635\) | −24.0000 | − | 41.5692i | −0.952411 | − | 1.64962i | ||||
\(636\) | 4.50000 | − | 2.59808i | 0.178437 | − | 0.103020i | ||||
\(637\) | −32.5000 | − | 12.9904i | −1.28770 | − | 0.514698i | ||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.50000 | + | 2.59808i | 0.0592927 | + | 0.102698i | ||||
\(641\) | 22.5000 | − | 38.9711i | 0.888697 | − | 1.53927i | 0.0472793 | − | 0.998882i | \(-0.484945\pi\) |
0.841417 | − | 0.540386i | \(-0.181722\pi\) | |||||||
\(642\) | −22.5000 | − | 12.9904i | −0.888004 | − | 0.512689i | ||||
\(643\) | −14.5000 | + | 25.1147i | −0.571824 | + | 0.990429i | 0.424555 | + | 0.905402i | \(0.360431\pi\) |
−0.996379 | + | 0.0850262i | \(0.972903\pi\) | |||||||
\(644\) | 1.50000 | − | 7.79423i | 0.0591083 | − | 0.307136i | ||||
\(645\) | −49.5000 | − | 28.5788i | −1.94906 | − | 1.12529i | ||||
\(646\) | 15.0000 | 0.590167 | ||||||||
\(647\) | 1.50000 | + | 2.59808i | 0.0589711 | + | 0.102141i | 0.894004 | − | 0.448059i | \(-0.147885\pi\) |
−0.835033 | + | 0.550200i | \(0.814551\pi\) | |||||||
\(648\) | 9.00000 | 0.353553 | ||||||||
\(649\) | 18.0000 | − | 31.1769i | 0.706562 | − | 1.22380i | ||||
\(650\) | −10.0000 | − | 17.3205i | −0.392232 | − | 0.679366i | ||||
\(651\) | 12.0000 | − | 13.8564i | 0.470317 | − | 0.543075i | ||||
\(652\) | −8.50000 | + | 14.7224i | −0.332886 | + | 0.576575i | ||||
\(653\) | −4.50000 | − | 7.79423i | −0.176099 | − | 0.305012i | 0.764442 | − | 0.644692i | \(-0.223014\pi\) |
−0.940541 | + | 0.339680i | \(0.889681\pi\) | |||||||
\(654\) | 10.5000 | − | 6.06218i | 0.410582 | − | 0.237050i | ||||
\(655\) | 4.50000 | − | 7.79423i | 0.175830 | − | 0.304546i | ||||
\(656\) | 4.50000 | − | 7.79423i | 0.175695 | − | 0.304314i | ||||
\(657\) | 16.5000 | + | 28.5788i | 0.643726 | + | 1.11497i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5000 | − | 33.7750i | −0.759612 | − | 1.31569i | −0.943049 | − | 0.332655i | \(-0.892055\pi\) |
0.183436 | − | 0.983032i | \(-0.441278\pi\) | |||||||
\(660\) | − | 15.5885i | − | 0.606780i | ||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | 20.0000 | 0.777322 | ||||||||
\(663\) | − | 25.9808i | − | 1.00901i | ||||||
\(664\) | −1.50000 | − | 2.59808i | −0.0582113 | − | 0.100825i | ||||
\(665\) | 30.0000 | + | 25.9808i | 1.16335 | + | 1.00749i | ||||
\(666\) | −10.5000 | + | 18.1865i | −0.406867 | + | 0.704714i | ||||
\(667\) | −4.50000 | + | 7.79423i | −0.174241 | + | 0.301794i | ||||
\(668\) | −1.50000 | + | 2.59808i | −0.0580367 | + | 0.100523i | ||||
\(669\) | −25.5000 | + | 14.7224i | −0.985887 | + | 0.569202i | ||||
\(670\) | −6.00000 | − | 10.3923i | −0.231800 | − | 0.401490i | ||||
\(671\) | 3.00000 | − | 5.19615i | 0.115814 | − | 0.200595i | ||||
\(672\) | −3.00000 | + | 3.46410i | −0.115728 | + | 0.133631i | ||||
\(673\) | −5.50000 | − | 9.52628i | −0.212009 | − | 0.367211i | 0.740334 | − | 0.672239i | \(-0.234667\pi\) |
−0.952343 | + | 0.305028i | \(0.901334\pi\) | |||||||
\(674\) | 12.5000 | − | 21.6506i | 0.481482 | − | 0.833951i | ||||
\(675\) | −18.0000 | − | 10.3923i | −0.692820 | − | 0.400000i | ||||
\(676\) | −6.00000 | − | 10.3923i | −0.230769 | − | 0.399704i | ||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 22.5000 | + | 12.9904i | 0.864107 | + | 0.498893i | ||||
\(679\) | 0.500000 | − | 2.59808i | 0.0191882 | − | 0.0997050i | ||||
\(680\) | 4.50000 | − | 7.79423i | 0.172567 | − | 0.298895i | ||||
\(681\) | 13.5000 | + | 7.79423i | 0.517321 | + | 0.298675i | ||||
\(682\) | −6.00000 | + | 10.3923i | −0.229752 | + | 0.397942i | ||||
\(683\) | 16.5000 | + | 28.5788i | 0.631355 | + | 1.09354i | 0.987275 | + | 0.159022i | \(0.0508342\pi\) |
−0.355920 | + | 0.934516i | \(0.615832\pi\) | |||||||
\(684\) | 7.50000 | − | 12.9904i | 0.286770 | − | 0.496700i | ||||
\(685\) | −9.00000 | −0.343872 | ||||||||
\(686\) | 10.0000 | − | 15.5885i | 0.381802 | − | 0.595170i | ||||
\(687\) | −25.5000 | + | 14.7224i | −0.972886 | + | 0.561696i | ||||
\(688\) | −5.50000 | − | 9.52628i | −0.209686 | − | 0.363186i | ||||
\(689\) | −15.0000 | −0.571454 | ||||||||
\(690\) | 13.5000 | + | 7.79423i | 0.513936 | + | 0.296721i | ||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 22.5000 | − | 7.79423i | 0.854704 | − | 0.296078i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −15.0000 | −0.568982 | ||||||||
\(696\) | 4.50000 | − | 2.59808i | 0.170572 | − | 0.0984798i | ||||
\(697\) | −27.0000 | −1.02270 | ||||||||
\(698\) | −2.50000 | − | 4.33013i | −0.0946264 | − | 0.163898i | ||||
\(699\) | 40.5000 | + | 23.3827i | 1.53185 | + | 0.884414i | ||||
\(700\) | 10.0000 | − | 3.46410i | 0.377964 | − | 0.130931i | ||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | −22.5000 | − | 12.9904i | −0.849208 | − | 0.490290i | ||||
\(703\) | 17.5000 | + | 30.3109i | 0.660025 | + | 1.14320i | ||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.50000 | − | 7.79423i | 0.169360 | − | 0.293340i | ||||
\(707\) | −7.50000 | + | 2.59808i | −0.282067 | + | 0.0977107i | ||||
\(708\) | − | 20.7846i | − | 0.781133i | ||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.0000 | −0.900070 | ||||||||
\(712\) | −7.50000 | + | 12.9904i | −0.281074 | + | 0.486835i | ||||
\(713\) | −6.00000 | − | 10.3923i | −0.224702 | − | 0.389195i | ||||
\(714\) | 13.5000 | + | 2.59808i | 0.505225 | + | 0.0972306i | ||||
\(715\) | −22.5000 | + | 38.9711i | −0.841452 | + | 1.45744i | ||||
\(716\) | −1.50000 | − | 2.59808i | −0.0560576 | − | 0.0970947i | ||||
\(717\) | 40.5000 | + | 23.3827i | 1.51250 | + | 0.873242i | ||||
\(718\) | −7.50000 | + | 12.9904i | −0.279898 | + | 0.484797i | ||||
\(719\) | −19.5000 | + | 33.7750i | −0.727227 | + | 1.25959i | 0.230823 | + | 0.972996i | \(0.425858\pi\) |
−0.958051 | + | 0.286599i | \(0.907475\pi\) | |||||||
\(720\) | −4.50000 | − | 7.79423i | −0.167705 | − | 0.290474i | ||||
\(721\) | −2.50000 | + | 12.9904i | −0.0931049 | + | 0.483787i | ||||
\(722\) | −3.00000 | − | 5.19615i | −0.111648 | − | 0.193381i | ||||
\(723\) | 34.5000 | + | 19.9186i | 1.28307 | + | 0.740780i | ||||
\(724\) | −10.0000 | −0.371647 | ||||||||
\(725\) | −12.0000 | −0.445669 | ||||||||
\(726\) | 3.00000 | − | 1.73205i | 0.111340 | − | 0.0642824i | ||||
\(727\) | −2.50000 | − | 4.33013i | −0.0927199 | − | 0.160596i | 0.815935 | − | 0.578144i | \(-0.196223\pi\) |
−0.908655 | + | 0.417548i | \(0.862889\pi\) | |||||||
\(728\) | 12.5000 | − | 4.33013i | 0.463281 | − | 0.160485i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 16.5000 | − | 28.5788i | 0.610692 | − | 1.05775i | ||||
\(731\) | −16.5000 | + | 28.5788i | −0.610275 | + | 1.05703i | ||||
\(732\) | − | 3.46410i | − | 0.128037i | ||||||
\(733\) | −20.5000 | − | 35.5070i | −0.757185 | − | 1.31148i | −0.944281 | − | 0.329141i | \(-0.893241\pi\) |
0.187096 | − | 0.982342i | \(-0.440092\pi\) | |||||||
\(734\) | 0.500000 | − | 0.866025i | 0.0184553 | − | 0.0319656i | ||||
\(735\) | 22.5000 | + | 28.5788i | 0.829925 | + | 1.05415i | ||||
\(736\) | 1.50000 | + | 2.59808i | 0.0552907 | + | 0.0957664i | ||||
\(737\) | −6.00000 | + | 10.3923i | −0.221013 | + | 0.382805i | ||||
\(738\) | −13.5000 | + | 23.3827i | −0.496942 | + | 0.860729i | ||||
\(739\) | −23.5000 | − | 40.7032i | −0.864461 | − | 1.49729i | −0.867581 | − | 0.497296i | \(-0.834326\pi\) |
0.00311943 | − | 0.999995i | \(-0.499007\pi\) | |||||||
\(740\) | 21.0000 | 0.771975 | ||||||||
\(741\) | −37.5000 | + | 21.6506i | −1.37760 | + | 0.795356i | ||||
\(742\) | 1.50000 | − | 7.79423i | 0.0550667 | − | 0.286135i | ||||
\(743\) | −1.50000 | + | 2.59808i | −0.0550297 | + | 0.0953142i | −0.892228 | − | 0.451585i | \(-0.850859\pi\) |
0.837198 | + | 0.546899i | \(0.184192\pi\) | |||||||
\(744\) | 6.92820i | 0.254000i | ||||||||
\(745\) | −4.50000 | + | 7.79423i | −0.164867 | + | 0.285558i | ||||
\(746\) | −8.50000 | − | 14.7224i | −0.311207 | − | 0.539027i | ||||
\(747\) | 4.50000 | + | 7.79423i | 0.164646 | + | 0.285176i | ||||
\(748\) | −9.00000 | −0.329073 | ||||||||
\(749\) | −37.5000 | + | 12.9904i | −1.37022 | + | 0.474658i | ||||
\(750\) | − | 5.19615i | − | 0.189737i | ||||||
\(751\) | −14.5000 | − | 25.1147i | −0.529113 | − | 0.916450i | −0.999424 | − | 0.0339490i | \(-0.989192\pi\) |
0.470311 | − | 0.882501i | \(-0.344142\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 20.7846i | − | 0.757433i | ||||||
\(754\) | −15.0000 | −0.546268 | ||||||||
\(755\) | −33.0000 | −1.20099 | ||||||||
\(756\) | 9.00000 | − | 10.3923i | 0.327327 | − | 0.377964i | ||||
\(757\) | 14.0000 | 0.508839 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(758\) | −16.0000 | −0.581146 | ||||||||
\(759\) | − | 15.5885i | − | 0.565825i | ||||||
\(760\) | −15.0000 | −0.544107 | ||||||||
\(761\) | −1.50000 | − | 2.59808i | −0.0543750 | − | 0.0941802i | 0.837557 | − | 0.546350i | \(-0.183983\pi\) |
−0.891932 | + | 0.452170i | \(0.850650\pi\) | |||||||
\(762\) | 27.7128i | 1.00393i | ||||||||
\(763\) | 3.50000 | − | 18.1865i | 0.126709 | − | 0.658397i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | −13.5000 | + | 23.3827i | −0.488094 | + | 0.845403i | ||||
\(766\) | 7.50000 | + | 12.9904i | 0.270986 | + | 0.469362i | ||||
\(767\) | −30.0000 | + | 51.9615i | −1.08324 | + | 1.87622i | ||||
\(768\) | − | 1.73205i | − | 0.0625000i | ||||||
\(769\) | 0.500000 | − | 0.866025i | 0.0180305 | − | 0.0312297i | −0.856869 | − | 0.515534i | \(-0.827594\pi\) |
0.874900 | + | 0.484304i | \(0.160927\pi\) | |||||||
\(770\) | −18.0000 | − | 15.5885i | −0.648675 | − | 0.561769i | ||||
\(771\) | −22.5000 | + | 12.9904i | −0.810318 | + | 0.467837i | ||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | −10.5000 | − | 18.1865i | −0.377659 | − | 0.654124i | 0.613062 | − | 0.790034i | \(-0.289937\pi\) |
−0.990721 | + | 0.135910i | \(0.956604\pi\) | |||||||
\(774\) | 16.5000 | + | 28.5788i | 0.593080 | + | 1.02725i | ||||
\(775\) | 8.00000 | − | 13.8564i | 0.287368 | − | 0.497737i | ||||
\(776\) | 0.500000 | + | 0.866025i | 0.0179490 | + | 0.0310885i | ||||
\(777\) | 10.5000 | + | 30.3109i | 0.376685 | + | 1.08740i | ||||
\(778\) | −4.50000 | + | 7.79423i | −0.161333 | + | 0.279437i | ||||
\(779\) | 22.5000 | + | 38.9711i | 0.806146 | + | 1.39629i | ||||
\(780\) | 25.9808i | 0.930261i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.50000 | − | 7.79423i | 0.160920 | − | 0.278721i | ||||
\(783\) | −13.5000 | + | 7.79423i | −0.482451 | + | 0.278543i | ||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 21.0000 | + | 36.3731i | 0.749522 | + | 1.29821i | ||||
\(786\) | −4.50000 | + | 2.59808i | −0.160510 | + | 0.0926703i | ||||
\(787\) | 44.0000 | 1.56843 | 0.784215 | − | 0.620489i | \(-0.213066\pi\) | ||||
0.784215 | + | 0.620489i | \(0.213066\pi\) | |||||||
\(788\) | −6.00000 | −0.213741 | ||||||||
\(789\) | −13.5000 | − | 7.79423i | −0.480613 | − | 0.277482i | ||||
\(790\) | 12.0000 | + | 20.7846i | 0.426941 | + | 0.739483i | ||||
\(791\) | 37.5000 | − | 12.9904i | 1.33335 | − | 0.461885i | ||||
\(792\) | −4.50000 | + | 7.79423i | −0.159901 | + | 0.276956i | ||||
\(793\) | −5.00000 | + | 8.66025i | −0.177555 | + | 0.307535i | ||||
\(794\) | −14.5000 | + | 25.1147i | −0.514586 | + | 0.891289i | ||||
\(795\) | 13.5000 | + | 7.79423i | 0.478796 | + | 0.276433i | ||||
\(796\) | 3.50000 | + | 6.06218i | 0.124054 | + | 0.214868i | ||||
\(797\) | 13.5000 | − | 23.3827i | 0.478195 | − | 0.828257i | −0.521493 | − | 0.853256i | \(-0.674625\pi\) |
0.999687 | + | 0.0249984i | \(0.00795805\pi\) | |||||||
\(798\) | −7.50000 | − | 21.6506i | −0.265497 | − | 0.766424i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2.00000 | + | 3.46410i | −0.0707107 | + | 0.122474i | ||||
\(801\) | 22.5000 | − | 38.9711i | 0.794998 | − | 1.37698i | ||||
\(802\) | −13.5000 | − | 23.3827i | −0.476702 | − | 0.825671i | ||||
\(803\) | −33.0000 | −1.16454 | ||||||||
\(804\) | 6.92820i | 0.244339i | ||||||||
\(805\) | 22.5000 | − | 7.79423i | 0.793021 | − | 0.274710i | ||||
\(806\) | 10.0000 | − | 17.3205i | 0.352235 | − | 0.610089i | ||||
\(807\) | −31.5000 | + | 18.1865i | −1.10885 | + | 0.640196i | ||||
\(808\) | 1.50000 | − | 2.59808i | 0.0527698 | − | 0.0914000i | ||||
\(809\) | −19.5000 | − | 33.7750i | −0.685583 | − | 1.18747i | −0.973253 | − | 0.229736i | \(-0.926214\pi\) |
0.287670 | − | 0.957730i | \(-0.407120\pi\) | |||||||
\(810\) | 13.5000 | + | 23.3827i | 0.474342 | + | 0.821584i | ||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 1.50000 | − | 7.79423i | 0.0526397 | − | 0.273524i | ||||
\(813\) | −19.5000 | − | 11.2583i | −0.683895 | − | 0.394847i | ||||
\(814\) | −10.5000 | − | 18.1865i | −0.368025 | − | 0.637438i | ||||
\(815\) | −51.0000 | −1.78645 | ||||||||
\(816\) | −4.50000 | + | 2.59808i | −0.157532 | + | 0.0909509i | ||||
\(817\) | 55.0000 | 1.92421 | ||||||||
\(818\) | −22.0000 | −0.769212 | ||||||||
\(819\) | −37.5000 | + | 12.9904i | −1.31036 | + | 0.453921i | ||||
\(820\) | 27.0000 | 0.942881 | ||||||||
\(821\) | −54.0000 | −1.88461 | −0.942306 | − | 0.334751i | \(-0.891348\pi\) | ||||
−0.942306 | + | 0.334751i | \(0.891348\pi\) | |||||||
\(822\) | 4.50000 | + | 2.59808i | 0.156956 | + | 0.0906183i | ||||
\(823\) | −40.0000 | −1.39431 | −0.697156 | − | 0.716919i | \(-0.745552\pi\) | ||||
−0.697156 | + | 0.716919i | \(0.745552\pi\) | |||||||
\(824\) | −2.50000 | − | 4.33013i | −0.0870916 | − | 0.150847i | ||||
\(825\) | 18.0000 | − | 10.3923i | 0.626680 | − | 0.361814i | ||||
\(826\) | −24.0000 | − | 20.7846i | −0.835067 | − | 0.723189i | ||||
\(827\) | −24.0000 | −0.834562 | −0.417281 | − | 0.908778i | \(-0.637017\pi\) | ||||
−0.417281 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(828\) | −4.50000 | − | 7.79423i | −0.156386 | − | 0.270868i | ||||
\(829\) | −20.5000 | − | 35.5070i | −0.711994 | − | 1.23321i | −0.964107 | − | 0.265513i | \(-0.914459\pi\) |
0.252113 | − | 0.967698i | \(-0.418875\pi\) | |||||||
\(830\) | 4.50000 | − | 7.79423i | 0.156197 | − | 0.270542i | ||||
\(831\) | −10.5000 | − | 6.06218i | −0.364241 | − | 0.210295i | ||||
\(832\) | −2.50000 | + | 4.33013i | −0.0866719 | + | 0.150120i | ||||
\(833\) | 16.5000 | − | 12.9904i | 0.571691 | − | 0.450090i | ||||
\(834\) | 7.50000 | + | 4.33013i | 0.259704 | + | 0.149940i | ||||
\(835\) | −9.00000 | −0.311458 | ||||||||
\(836\) | 7.50000 | + | 12.9904i | 0.259393 | + | 0.449282i | ||||
\(837\) | − | 20.7846i | − | 0.718421i | ||||||
\(838\) | 1.50000 | − | 2.59808i | 0.0518166 | − | 0.0897491i | ||||
\(839\) | 19.5000 | + | 33.7750i | 0.673215 | + | 1.16604i | 0.976987 | + | 0.213298i | \(0.0684204\pi\) |
−0.303773 | + | 0.952745i | \(0.598246\pi\) | |||||||
\(840\) | −13.5000 | − | 2.59808i | −0.465794 | − | 0.0896421i | ||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 15.5000 | + | 26.8468i | 0.534165 | + | 0.925201i | ||||
\(843\) | −4.50000 | + | 2.59808i | −0.154988 | + | 0.0894825i | ||||
\(844\) | −2.50000 | + | 4.33013i | −0.0860535 | + | 0.149049i | ||||
\(845\) | 18.0000 | − | 31.1769i | 0.619219 | − | 1.07252i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | − | 5.19615i | 0.0343604 | − | 0.178542i | ||||
\(848\) | 1.50000 | + | 2.59808i | 0.0515102 | + | 0.0892183i | ||||
\(849\) | − | 13.8564i | − | 0.475551i | ||||||
\(850\) | 12.0000 | 0.411597 | ||||||||
\(851\) | 21.0000 | 0.719871 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.50000 | − | 14.7224i | −0.291034 | − | 0.504086i | 0.683020 | − | 0.730400i | \(-0.260666\pi\) |
−0.974055 | + | 0.226313i | \(0.927333\pi\) | |||||||
\(854\) | −4.00000 | − | 3.46410i | −0.136877 | − | 0.118539i | ||||
\(855\) | 45.0000 | 1.53897 | ||||||||
\(856\) | 7.50000 | − | 12.9904i | 0.256345 | − | 0.444002i | ||||
\(857\) | 16.5000 | − | 28.5788i | 0.563629 | − | 0.976235i | −0.433546 | − | 0.901131i | \(-0.642738\pi\) |
0.997176 | − | 0.0751033i | \(-0.0239287\pi\) | |||||||
\(858\) | 22.5000 | − | 12.9904i | 0.768137 | − | 0.443484i | ||||
\(859\) | −5.50000 | − | 9.52628i | −0.187658 | − | 0.325032i | 0.756811 | − | 0.653633i | \(-0.226756\pi\) |
−0.944469 | + | 0.328601i | \(0.893423\pi\) | |||||||
\(860\) | 16.5000 | − | 28.5788i | 0.562645 | − | 0.974530i | ||||
\(861\) | 13.5000 | + | 38.9711i | 0.460079 | + | 1.32813i | ||||
\(862\) | 1.50000 | + | 2.59808i | 0.0510902 | + | 0.0884908i | ||||
\(863\) | −7.50000 | + | 12.9904i | −0.255303 | + | 0.442198i | −0.964978 | − | 0.262332i | \(-0.915509\pi\) |
0.709675 | + | 0.704529i | \(0.248842\pi\) | |||||||
\(864\) | 5.19615i | 0.176777i | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 14.0000 | 0.475739 | ||||||||
\(867\) | −12.0000 | − | 6.92820i | −0.407541 | − | 0.235294i | ||||
\(868\) | 8.00000 | + | 6.92820i | 0.271538 | + | 0.235159i | ||||
\(869\) | 12.0000 | − | 20.7846i | 0.407072 | − | 0.705070i | ||||
\(870\) | 13.5000 | + | 7.79423i | 0.457693 | + | 0.264249i | ||||
\(871\) | 10.0000 | − | 17.3205i | 0.338837 | − | 0.586883i | ||||
\(872\) | 3.50000 | + | 6.06218i | 0.118525 | + | 0.205291i | ||||
\(873\) | −1.50000 | − | 2.59808i | −0.0507673 | − | 0.0879316i | ||||
\(874\) | −15.0000 | −0.507383 | ||||||||
\(875\) | −6.00000 | − | 5.19615i | −0.202837 | − | 0.175662i | ||||
\(876\) | −16.5000 | + | 9.52628i | −0.557483 | + | 0.321863i | ||||
\(877\) | 21.5000 | + | 37.2391i | 0.726003 | + | 1.25747i | 0.958560 | + | 0.284892i | \(0.0919577\pi\) |
−0.232556 | + | 0.972583i | \(0.574709\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | −40.5000 | − | 23.3827i | −1.36603 | − | 0.788678i | ||||
\(880\) | 9.00000 | 0.303390 | ||||||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | −3.00000 | − | 20.7846i | −0.101015 | − | 0.699854i | ||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 15.0000 | 0.504505 | ||||||||
\(885\) | 54.0000 | − | 31.1769i | 1.81519 | − | 1.04800i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.5000 | + | 33.7750i | 0.654746 | + | 1.13405i | 0.981957 | + | 0.189102i | \(0.0605577\pi\) |
−0.327212 | + | 0.944951i | \(0.606109\pi\) | |||||||
\(888\) | −10.5000 | − | 6.06218i | −0.352357 | − | 0.203433i | ||||
\(889\) | 32.0000 | + | 27.7128i | 1.07325 | + | 0.929458i | ||||
\(890\) | −45.0000 | −1.50840 | ||||||||
\(891\) | 13.5000 | − | 23.3827i | 0.452267 | − | 0.783349i | ||||
\(892\) | −8.50000 | − | 14.7224i | −0.284601 | − | 0.492943i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 4.50000 | − | 2.59808i | 0.150503 | − | 0.0868927i | ||||
\(895\) | 4.50000 | − | 7.79423i | 0.150418 | − | 0.260532i | ||||
\(896\) | −2.00000 | − | 1.73205i | −0.0668153 | − | 0.0578638i | ||||
\(897\) | 25.9808i | 0.867472i | ||||||||
\(898\) | 30.0000 | 1.00111 | ||||||||
\(899\) | −6.00000 | − | 10.3923i | −0.200111 | − | 0.346603i | ||||
\(900\) | 6.00000 | − | 10.3923i | 0.200000 | − | 0.346410i | ||||
\(901\) | 4.50000 | − | 7.79423i | 0.149917 | − | 0.259663i | ||||
\(902\) | −13.5000 | − | 23.3827i | −0.449501 | − | 0.778558i | ||||
\(903\) | 49.5000 | + | 9.52628i | 1.64726 | + | 0.317015i | ||||
\(904\) | −7.50000 | + | 12.9904i | −0.249446 | + | 0.432054i | ||||
\(905\) | −15.0000 | − | 25.9808i | −0.498617 | − | 0.863630i | ||||
\(906\) | 16.5000 | + | 9.52628i | 0.548176 | + | 0.316489i | ||||
\(907\) | −8.50000 | + | 14.7224i | −0.282238 | + | 0.488850i | −0.971936 | − | 0.235247i | \(-0.924410\pi\) |
0.689698 | + | 0.724097i | \(0.257743\pi\) | |||||||
\(908\) | −4.50000 | + | 7.79423i | −0.149338 | + | 0.258661i | ||||
\(909\) | −4.50000 | + | 7.79423i | −0.149256 | + | 0.258518i | ||||
\(910\) | 30.0000 | + | 25.9808i | 0.994490 | + | 0.861254i | ||||
\(911\) | −4.50000 | − | 7.79423i | −0.149092 | − | 0.258234i | 0.781800 | − | 0.623529i | \(-0.214302\pi\) |
−0.930892 | + | 0.365295i | \(0.880968\pi\) | |||||||
\(912\) | 7.50000 | + | 4.33013i | 0.248350 | + | 0.143385i | ||||
\(913\) | −9.00000 | −0.297857 | ||||||||
\(914\) | −34.0000 | −1.12462 | ||||||||
\(915\) | 9.00000 | − | 5.19615i | 0.297531 | − | 0.171780i | ||||
\(916\) | −8.50000 | − | 14.7224i | −0.280848 | − | 0.486443i | ||||
\(917\) | −1.50000 | + | 7.79423i | −0.0495344 | + | 0.257388i | ||||
\(918\) | 13.5000 | − | 7.79423i | 0.445566 | − | 0.257248i | ||||
\(919\) | 0.500000 | − | 0.866025i | 0.0164935 | − | 0.0285675i | −0.857661 | − | 0.514216i | \(-0.828083\pi\) |
0.874154 | + | 0.485648i | \(0.161416\pi\) | |||||||
\(920\) | −4.50000 | + | 7.79423i | −0.148361 | + | 0.256968i | ||||
\(921\) | 48.4974i | 1.59804i | ||||||||
\(922\) | −4.50000 | − | 7.79423i | −0.148200 | − | 0.256689i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.50000 | + | 12.9904i | 0.148039 | + | 0.427352i | ||||
\(925\) | 14.0000 | + | 24.2487i | 0.460317 | + | 0.797293i | ||||
\(926\) | −17.5000 | + | 30.3109i | −0.575086 | + | 0.996078i | ||||
\(927\) | 7.50000 | + | 12.9904i | 0.246332 | + | 0.426660i | ||||
\(928\) | 1.50000 | + | 2.59808i | 0.0492399 | + | 0.0852860i | ||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | −18.0000 | + | 10.3923i | −0.590243 | + | 0.340777i | ||||
\(931\) | −32.5000 | − | 12.9904i | −1.06514 | − | 0.425743i | ||||
\(932\) | −13.5000 | + | 23.3827i | −0.442207 | + | 0.765925i | ||||
\(933\) | 41.5692i | 1.36092i | ||||||||
\(934\) | 1.50000 | − | 2.59808i | 0.0490815 | − | 0.0850117i | ||||
\(935\) | −13.5000 | − | 23.3827i | −0.441497 | − | 0.764696i | ||||
\(936\) | 7.50000 | − | 12.9904i | 0.245145 | − | 0.424604i | ||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 8.00000 | + | 6.92820i | 0.261209 | + | 0.226214i | ||||
\(939\) | − | 24.2487i | − | 0.791327i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.0000 | 1.76035 | 0.880175 | − | 0.474650i | \(-0.157425\pi\) | ||||
0.880175 | + | 0.474650i | \(0.157425\pi\) | |||||||
\(942\) | − | 24.2487i | − | 0.790066i | ||||||
\(943\) | 27.0000 | 0.879241 | ||||||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 40.5000 | + | 7.79423i | 1.31747 | + | 0.253546i | ||||
\(946\) | −33.0000 | −1.07292 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | − | 13.8564i | − | 0.450035i | ||||||
\(949\) | 55.0000 | 1.78538 | ||||||||
\(950\) | −10.0000 | − | 17.3205i | −0.324443 | − | 0.561951i | ||||
\(951\) | − | 51.9615i | − | 1.68497i | ||||||
\(952\) | −1.50000 | + | 7.79423i | −0.0486153 | + | 0.252612i | ||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | −4.50000 | − | 7.79423i | −0.145693 | − | 0.252347i | ||||
\(955\) | 18.0000 | + | 31.1769i | 0.582466 | + | 1.00886i | ||||
\(956\) | −13.5000 | + | 23.3827i | −0.436621 | + | 0.756250i | ||||
\(957\) | − | 15.5885i | − | 0.503903i | ||||||
\(958\) | 4.50000 | − | 7.79423i | 0.145388 | − | 0.251820i | ||||
\(959\) | 7.50000 | − | 2.59808i | 0.242188 | − | 0.0838963i | ||||
\(960\) | 4.50000 | − | 2.59808i | 0.145237 | − | 0.0838525i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 17.5000 | + | 30.3109i | 0.564223 | + | 0.977262i | ||||
\(963\) | −22.5000 | + | 38.9711i | −0.725052 | + | 1.25583i | ||||
\(964\) | −11.5000 | + | 19.9186i | −0.370390 | + | 0.641534i | ||||
\(965\) | 21.0000 | + | 36.3731i | 0.676014 | + | 1.17089i | ||||
\(966\) | −13.5000 | − | 2.59808i | −0.434355 | − | 0.0835917i | ||||
\(967\) | 24.5000 | − | 42.4352i | 0.787867 | − | 1.36463i | −0.139404 | − | 0.990236i | \(-0.544519\pi\) |
0.927271 | − | 0.374390i | \(-0.122148\pi\) | |||||||
\(968\) | 1.00000 | + | 1.73205i | 0.0321412 | + | 0.0556702i | ||||
\(969\) | − | 25.9808i | − | 0.834622i | ||||||
\(970\) | −1.50000 | + | 2.59808i | −0.0481621 | + | 0.0834192i | ||||
\(971\) | 13.5000 | − | 23.3827i | 0.433236 | − | 0.750386i | −0.563914 | − | 0.825833i | \(-0.690705\pi\) |
0.997150 | + | 0.0754473i | \(0.0240385\pi\) | |||||||
\(972\) | − | 15.5885i | − | 0.500000i | ||||||
\(973\) | 12.5000 | − | 4.33013i | 0.400732 | − | 0.138817i | ||||
\(974\) | 15.5000 | + | 26.8468i | 0.496652 | + | 0.860227i | ||||
\(975\) | −30.0000 | + | 17.3205i | −0.960769 | + | 0.554700i | ||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 6.00000 | 0.191957 | 0.0959785 | − | 0.995383i | \(-0.469402\pi\) | ||||
0.0959785 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(978\) | 25.5000 | + | 14.7224i | 0.815400 | + | 0.470771i | ||||
\(979\) | 22.5000 | + | 38.9711i | 0.719103 | + | 1.24552i | ||||
\(980\) | −16.5000 | + | 12.9904i | −0.527073 | + | 0.414963i | ||||
\(981\) | −10.5000 | − | 18.1865i | −0.335239 | − | 0.580651i | ||||
\(982\) | 19.5000 | − | 33.7750i | 0.622270 | − | 1.07780i | ||||
\(983\) | 10.5000 | − | 18.1865i | 0.334898 | − | 0.580060i | −0.648567 | − | 0.761157i | \(-0.724631\pi\) |
0.983465 | + | 0.181097i | \(0.0579648\pi\) | |||||||
\(984\) | −13.5000 | − | 7.79423i | −0.430364 | − | 0.248471i | ||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | 4.50000 | − | 7.79423i | 0.143309 | − | 0.248219i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.5000 | − | 21.6506i | −0.397678 | − | 0.688798i | ||||
\(989\) | 16.5000 | − | 28.5788i | 0.524669 | − | 0.908754i | ||||
\(990\) | −27.0000 | −0.858116 | ||||||||
\(991\) | −14.5000 | − | 25.1147i | −0.460608 | − | 0.797796i | 0.538384 | − | 0.842700i | \(-0.319035\pi\) |
−0.998991 | + | 0.0449040i | \(0.985702\pi\) | |||||||
\(992\) | −4.00000 | −0.127000 | ||||||||
\(993\) | − | 34.6410i | − | 1.09930i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.5000 | + | 18.1865i | −0.332872 | + | 0.576552i | ||||
\(996\) | −4.50000 | + | 2.59808i | −0.142588 | + | 0.0823232i | ||||
\(997\) | −20.5000 | + | 35.5070i | −0.649242 | + | 1.12452i | 0.334063 | + | 0.942551i | \(0.391580\pi\) |
−0.983304 | + | 0.181968i | \(0.941753\pi\) | |||||||
\(998\) | −5.50000 | − | 9.52628i | −0.174099 | − | 0.301549i | ||||
\(999\) | 31.5000 | + | 18.1865i | 0.996616 | + | 0.575396i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))