Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [153,4,Mod(19,153)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(153, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("153.19");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 153 = 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 153.l (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.02729223088\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 145.3 | ||
Root | \(-3.86166i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 153.145 |
Dual form | 153.4.l.a.19.3 |
$q$-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 \(\left(\mathbb{Z}/153\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.43772 | − | 3.43772i | 1.21542 | − | 1.21542i | 0.246196 | − | 0.969220i | \(-0.420819\pi\) |
0.969220 | − | 0.246196i | \(-0.0791806\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 15.6358i | − | 1.95447i | ||||||
\(5\) | 7.10390 | − | 17.1503i | 0.635392 | − | 1.53397i | −0.197364 | − | 0.980330i | \(-0.563238\pi\) |
0.832755 | − | 0.553641i | \(-0.186762\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.36561 | + | 12.9537i | 0.289716 | + | 0.699436i | 0.999990 | − | 0.00448945i | \(-0.00142904\pi\) |
−0.710274 | + | 0.703925i | \(0.751429\pi\) | |||||||
\(8\) | −26.2496 | − | 26.2496i | −1.16008 | − | 1.16008i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −34.5367 | − | 83.3791i | −1.09215 | − | 2.63668i | ||||
\(11\) | −17.9963 | + | 7.45431i | −0.493281 | + | 0.204324i | −0.615435 | − | 0.788187i | \(-0.711020\pi\) |
0.122154 | + | 0.992511i | \(0.461020\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 29.9060i | 0.638033i | 0.947749 | + | 0.319016i | \(0.103352\pi\) | ||||
−0.947749 | + | 0.319016i | \(0.896648\pi\) | |||||||
\(14\) | 62.9767 | + | 26.0858i | 1.20223 | + | 0.497980i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −55.3912 | −0.865487 | ||||||||
\(17\) | 56.0566 | − | 42.0792i | 0.799748 | − | 0.600335i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.3771 | + | 32.3771i | −0.390938 | + | 0.390938i | −0.875022 | − | 0.484084i | \(-0.839153\pi\) |
0.484084 | + | 0.875022i | \(0.339153\pi\) | |||||||
\(20\) | −268.158 | − | 111.075i | −2.99810 | − | 1.24185i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −36.2404 | + | 87.4920i | −0.351203 | + | 0.847880i | ||||
\(23\) | −82.5263 | + | 34.1835i | −0.748171 | + | 0.309903i | −0.723995 | − | 0.689805i | \(-0.757696\pi\) |
−0.0241759 | + | 0.999708i | \(0.507696\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −155.280 | − | 155.280i | −1.24224 | − | 1.24224i | ||||
\(26\) | 102.808 | + | 102.808i | 0.775475 | + | 0.775475i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 202.542 | − | 83.8955i | 1.36703 | − | 0.566241i | ||||
\(29\) | 22.1603 | − | 53.4998i | 0.141899 | − | 0.342574i | −0.836913 | − | 0.547336i | \(-0.815642\pi\) |
0.978812 | + | 0.204762i | \(0.0656420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 149.621 | + | 61.9751i | 0.866863 | + | 0.359067i | 0.771388 | − | 0.636365i | \(-0.219563\pi\) |
0.0954754 | + | 0.995432i | \(0.469563\pi\) | |||||||
\(32\) | 19.5778 | − | 19.5778i | 0.108153 | − | 0.108153i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 48.0504 | − | 337.363i | 0.242370 | − | 1.70168i | ||||
\(35\) | 260.277 | 1.25700 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 125.263 | + | 51.8855i | 0.556569 | + | 0.230538i | 0.643195 | − | 0.765702i | \(-0.277608\pi\) |
−0.0866259 | + | 0.996241i | \(0.527608\pi\) | |||||||
\(38\) | 222.607i | 0.950304i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −636.664 | + | 263.715i | −2.51663 | + | 1.04242i | ||||
\(41\) | 21.7716 | + | 52.5612i | 0.0829304 | + | 0.200212i | 0.959905 | − | 0.280324i | \(-0.0904421\pi\) |
−0.876975 | + | 0.480536i | \(0.840442\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.8715 | + | 36.8715i | 0.130764 | + | 0.130764i | 0.769460 | − | 0.638695i | \(-0.220526\pi\) |
−0.638695 | + | 0.769460i | \(0.720526\pi\) | |||||||
\(44\) | 116.554 | + | 281.386i | 0.399345 | + | 0.964104i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −166.189 | + | 401.215i | −0.532678 | + | 1.28600i | ||||
\(47\) | 482.699i | 1.49806i | 0.662536 | + | 0.749030i | \(0.269480\pi\) | ||||
−0.662536 | + | 0.749030i | \(0.730520\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 103.528 | − | 103.528i | 0.301832 | − | 0.301832i | ||||
\(50\) | −1067.62 | −3.01967 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 467.603 | 1.24702 | ||||||||
\(53\) | 374.747 | − | 374.747i | 0.971234 | − | 0.971234i | −0.0283638 | − | 0.999598i | \(-0.509030\pi\) |
0.999598 | + | 0.0283638i | \(0.00902968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 361.597i | 0.886504i | ||||||||
\(56\) | 199.185 | − | 480.875i | 0.475308 | − | 1.14749i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −107.736 | − | 260.098i | −0.243904 | − | 0.588836i | ||||
\(59\) | −198.031 | − | 198.031i | −0.436973 | − | 0.436973i | 0.454019 | − | 0.890992i | \(-0.349990\pi\) |
−0.890992 | + | 0.454019i | \(0.849990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 224.504 | + | 542.000i | 0.471226 | + | 1.13764i | 0.963622 | + | 0.267268i | \(0.0861209\pi\) |
−0.492397 | + | 0.870371i | \(0.663879\pi\) | |||||||
\(62\) | 727.408 | − | 301.302i | 1.49001 | − | 0.617184i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 577.735i | − | 1.12839i | ||||||
\(65\) | 512.897 | + | 212.449i | 0.978724 | + | 0.405401i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −367.471 | −0.670056 | −0.335028 | − | 0.942208i | \(-0.608746\pi\) | ||||
−0.335028 | + | 0.942208i | \(0.608746\pi\) | |||||||
\(68\) | −657.940 | − | 876.488i | −1.17334 | − | 1.56309i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 894.759 | − | 894.759i | 1.52777 | − | 1.52777i | ||||
\(71\) | 55.9406 | + | 23.1713i | 0.0935060 | + | 0.0387314i | 0.428946 | − | 0.903330i | \(-0.358885\pi\) |
−0.335440 | + | 0.942062i | \(0.608885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −140.861 | + | 340.067i | −0.225842 | + | 0.545231i | −0.995663 | − | 0.0930283i | \(-0.970345\pi\) |
0.769821 | + | 0.638259i | \(0.220345\pi\) | |||||||
\(74\) | 608.985 | − | 252.250i | 0.956663 | − | 0.396263i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 506.241 | + | 506.241i | 0.764077 | + | 0.764077i | ||||
\(77\) | −193.122 | − | 193.122i | −0.285823 | − | 0.285823i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 201.148 | − | 83.3181i | 0.286467 | − | 0.118659i | −0.234823 | − | 0.972038i | \(-0.575451\pi\) |
0.521290 | + | 0.853380i | \(0.325451\pi\) | |||||||
\(80\) | −393.493 | + | 949.976i | −0.549923 | + | 1.32763i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 255.535 | + | 105.846i | 0.344136 | + | 0.142546i | ||||
\(83\) | −420.131 | + | 420.131i | −0.555606 | + | 0.555606i | −0.928053 | − | 0.372447i | \(-0.878519\pi\) |
0.372447 | + | 0.928053i | \(0.378519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −323.451 | − | 1260.31i | −0.412743 | − | 1.60824i | ||||
\(86\) | 253.508 | 0.317866 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 668.069 | + | 276.723i | 0.809277 | + | 0.335213i | ||||
\(89\) | − | 887.553i | − | 1.05708i | −0.848907 | − | 0.528542i | \(-0.822739\pi\) | ||
0.848907 | − | 0.528542i | \(-0.177261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −387.394 | + | 160.464i | −0.446263 | + | 0.184848i | ||||
\(92\) | 534.486 | + | 1290.36i | 0.605696 | + | 1.46228i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1659.38 | + | 1659.38i | 1.82077 | + | 1.82077i | ||||
\(95\) | 325.274 | + | 785.281i | 0.351289 | + | 0.848086i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 338.553 | − | 817.340i | 0.354380 | − | 0.855549i | −0.641688 | − | 0.766965i | \(-0.721766\pi\) |
0.996069 | − | 0.0885841i | \(-0.0282342\pi\) | |||||||
\(98\) | − | 711.801i | − | 0.733702i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2427.92 | + | 2427.92i | −2.42792 | + | 2.42792i | ||||
\(101\) | −1845.31 | −1.81798 | −0.908988 | − | 0.416822i | \(-0.863144\pi\) | ||||
−0.908988 | + | 0.416822i | \(0.863144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1823.07 | −1.74400 | −0.872002 | − | 0.489502i | \(-0.837178\pi\) | ||||
−0.872002 | + | 0.489502i | \(0.837178\pi\) | |||||||
\(104\) | 785.020 | − | 785.020i | 0.740169 | − | 0.740169i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 2576.54i | − | 2.36091i | ||||||
\(107\) | −710.011 | + | 1714.12i | −0.641490 | + | 1.54869i | 0.183181 | + | 0.983079i | \(0.441361\pi\) |
−0.824670 | + | 0.565613i | \(0.808639\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 530.959 | + | 1281.85i | 0.466575 | + | 1.12641i | 0.965648 | + | 0.259852i | \(0.0836739\pi\) |
−0.499073 | + | 0.866560i | \(0.666326\pi\) | |||||||
\(110\) | 1243.07 | + | 1243.07i | 1.07747 | + | 1.07747i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −297.207 | − | 717.522i | −0.250745 | − | 0.605352i | ||||
\(113\) | 566.444 | − | 234.629i | 0.471563 | − | 0.195328i | −0.134230 | − | 0.990950i | \(-0.542856\pi\) |
0.605793 | + | 0.795623i | \(0.292856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1658.19i | 1.34458i | ||||||||
\(116\) | −836.510 | − | 346.494i | −0.669552 | − | 0.277337i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1361.55 | −1.06221 | ||||||||
\(119\) | 845.860 | + | 500.362i | 0.651596 | + | 0.385446i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −672.859 | + | 672.859i | −0.505529 | + | 0.505529i | ||||
\(122\) | 2635.02 | + | 1091.46i | 1.95544 | + | 0.809970i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 969.029 | − | 2339.44i | 0.701785 | − | 1.69426i | ||||
\(125\) | −1622.40 | + | 672.020i | −1.16089 | + | 0.480858i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −78.9750 | − | 78.9750i | −0.0551803 | − | 0.0551803i | 0.678978 | − | 0.734158i | \(-0.262423\pi\) |
−0.734158 | + | 0.678978i | \(0.762423\pi\) | |||||||
\(128\) | −1829.47 | − | 1829.47i | −1.26331 | − | 1.26331i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2493.53 | − | 1032.85i | 1.68229 | − | 0.696826i | ||||
\(131\) | 815.895 | − | 1969.75i | 0.544161 | − | 1.31372i | −0.377602 | − | 0.925968i | \(-0.623251\pi\) |
0.921763 | − | 0.387753i | \(-0.126749\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −593.127 | − | 245.681i | −0.386697 | − | 0.160175i | ||||
\(134\) | −1263.26 | + | 1263.26i | −0.814397 | + | 0.814397i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2576.03 | − | 366.902i | −1.62421 | − | 0.231335i | ||||
\(137\) | −3087.68 | −1.92554 | −0.962769 | − | 0.270327i | \(-0.912868\pi\) | ||||
−0.962769 | + | 0.270327i | \(0.912868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 434.062 | + | 179.794i | 0.264868 | + | 0.109712i | 0.511165 | − | 0.859482i | \(-0.329214\pi\) |
−0.246297 | + | 0.969194i | \(0.579214\pi\) | |||||||
\(140\) | − | 4069.64i | − | 2.45677i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 271.964 | − | 112.651i | 0.160723 | − | 0.0665738i | ||||
\(143\) | −222.929 | − | 538.197i | −0.130365 | − | 0.314729i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −760.113 | − | 760.113i | −0.435338 | − | 0.435338i | ||||
\(146\) | 684.816 | + | 1653.29i | 0.388190 | + | 0.937175i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 811.270 | − | 1958.58i | 0.450581 | − | 1.08780i | ||||
\(149\) | 2209.36i | 1.21475i | 0.794416 | + | 0.607374i | \(0.207777\pi\) | ||||
−0.794416 | + | 0.607374i | \(0.792223\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 532.003 | − | 532.003i | 0.286714 | − | 0.286714i | −0.549065 | − | 0.835779i | \(-0.685016\pi\) |
0.835779 | + | 0.549065i | \(0.185016\pi\) | |||||||
\(152\) | 1699.77 | 0.907038 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1327.80 | −0.694787 | ||||||||
\(155\) | 2125.79 | − | 2125.79i | 1.10160 | − | 1.10160i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 579.544i | − | 0.294603i | −0.989092 | − | 0.147301i | \(-0.952941\pi\) | ||
0.989092 | − | 0.147301i | \(-0.0470587\pi\) | |||||||
\(158\) | 405.065 | − | 977.913i | 0.203957 | − | 0.492396i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −196.687 | − | 474.844i | −0.0971842 | − | 0.234623i | ||||
\(161\) | −885.609 | − | 885.609i | −0.433514 | − | 0.433514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 680.311 | + | 1642.42i | 0.326908 | + | 0.789227i | 0.998819 | + | 0.0485941i | \(0.0154741\pi\) |
−0.671910 | + | 0.740633i | \(0.734526\pi\) | |||||||
\(164\) | 821.835 | − | 340.415i | 0.391308 | − | 0.162085i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2888.58i | 1.35059i | ||||||||
\(167\) | −2896.21 | − | 1199.65i | −1.34201 | − | 0.555879i | −0.407953 | − | 0.913003i | \(-0.633757\pi\) |
−0.934057 | + | 0.357124i | \(0.883757\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1302.63 | 0.592914 | ||||||||
\(170\) | −5444.54 | − | 3220.67i | −2.45633 | − | 1.45302i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 576.515 | − | 576.515i | 0.255575 | − | 0.255575i | ||||
\(173\) | 1080.32 | + | 447.482i | 0.474768 | + | 0.196656i | 0.607220 | − | 0.794534i | \(-0.292285\pi\) |
−0.132451 | + | 0.991190i | \(0.542285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1178.28 | − | 2844.62i | 0.508970 | − | 1.22876i | ||||
\(176\) | 996.836 | − | 412.903i | 0.426928 | − | 0.176839i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3051.16 | − | 3051.16i | −1.28480 | − | 1.28480i | ||||
\(179\) | 1097.81 | + | 1097.81i | 0.458404 | + | 0.458404i | 0.898131 | − | 0.439727i | \(-0.144925\pi\) |
−0.439727 | + | 0.898131i | \(0.644925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1382.05 | + | 572.462i | −0.567551 | + | 0.235087i | −0.647960 | − | 0.761675i | \(-0.724377\pi\) |
0.0804087 | + | 0.996762i | \(0.474377\pi\) | |||||||
\(182\) | −780.121 | + | 1883.38i | −0.317728 | + | 0.767062i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3063.59 | + | 1268.98i | 1.22745 | + | 0.508426i | ||||
\(185\) | 1779.71 | − | 1779.71i | 0.707279 | − | 0.707279i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −695.141 | + | 1175.13i | −0.271838 | + | 0.459542i | ||||
\(188\) | 7547.37 | 2.92792 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3817.77 | + | 1581.37i | 1.45774 | + | 0.603815i | ||||
\(191\) | 3008.79i | 1.13983i | 0.821702 | + | 0.569917i | \(0.193025\pi\) | ||||
−0.821702 | + | 0.569917i | \(0.806975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3597.18 | + | 1490.00i | −1.34161 | + | 0.555713i | −0.933945 | − | 0.357418i | \(-0.883657\pi\) |
−0.407666 | + | 0.913131i | \(0.633657\pi\) | |||||||
\(194\) | −1645.93 | − | 3973.63i | −0.609129 | − | 1.47057i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1618.74 | − | 1618.74i | −0.589921 | − | 0.589921i | ||||
\(197\) | 362.277 | + | 874.614i | 0.131021 | + | 0.316313i | 0.975752 | − | 0.218878i | \(-0.0702396\pi\) |
−0.844731 | + | 0.535191i | \(0.820240\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 675.758 | − | 1631.42i | 0.240720 | − | 0.581149i | −0.756635 | − | 0.653837i | \(-0.773158\pi\) |
0.997355 | + | 0.0726889i | \(0.0231580\pi\) | |||||||
\(200\) | 8152.07i | 2.88219i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6343.66 | + | 6343.66i | −2.20960 | + | 2.20960i | ||||
\(203\) | 811.925 | 0.280719 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1056.10 | 0.359812 | ||||||||
\(206\) | −6267.19 | + | 6267.19i | −2.11969 | + | 2.11969i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1656.53i | − | 0.552209i | ||||||
\(209\) | 341.319 | − | 824.018i | 0.112964 | − | 0.272720i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −142.128 | − | 343.127i | −0.0463720 | − | 0.111952i | 0.898996 | − | 0.437956i | \(-0.144298\pi\) |
−0.945368 | + | 0.326004i | \(0.894298\pi\) | |||||||
\(212\) | −5859.45 | − | 5859.45i | −1.89825 | − | 1.89825i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3451.84 | + | 8333.47i | 1.10263 | + | 2.66198i | ||||
\(215\) | 894.290 | − | 370.427i | 0.283675 | − | 0.117502i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2270.69i | 0.710342i | ||||||||
\(218\) | 6231.92 | + | 2581.35i | 1.93614 | + | 0.801976i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5653.85 | 1.73265 | ||||||||
\(221\) | 1258.42 | + | 1676.43i | 0.383033 | + | 0.510266i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1820.02 | − | 1820.02i | 0.546536 | − | 0.546536i | −0.378901 | − | 0.925437i | \(-0.623698\pi\) |
0.925437 | + | 0.378901i | \(0.123698\pi\) | |||||||
\(224\) | 358.653 | + | 148.559i | 0.106980 | + | 0.0443125i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1140.69 | − | 2753.86i | 0.335740 | − | 0.810549i | ||||
\(227\) | 4808.47 | − | 1991.73i | 1.40594 | − | 0.582361i | 0.454657 | − | 0.890666i | \(-0.349762\pi\) |
0.951288 | + | 0.308305i | \(0.0997617\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2261.84 | − | 2261.84i | −0.652694 | − | 0.652694i | 0.300947 | − | 0.953641i | \(-0.402697\pi\) |
−0.953641 | + | 0.300947i | \(0.902697\pi\) | |||||||
\(230\) | 5700.38 | + | 5700.38i | 1.63423 | + | 1.63423i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1986.05 | + | 822.648i | −0.562027 | + | 0.232799i | ||||
\(233\) | −326.467 | + | 788.162i | −0.0917923 | + | 0.221606i | −0.963107 | − | 0.269118i | \(-0.913268\pi\) |
0.871315 | + | 0.490724i | \(0.163268\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8278.44 | + | 3429.04i | 2.29798 | + | 0.951855i | ||||
\(236\) | −3096.36 | + | 3096.36i | −0.854051 | + | 0.854051i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4627.93 | − | 1187.73i | 1.26044 | − | 0.323482i | ||||
\(239\) | −1892.67 | −0.512246 | −0.256123 | − | 0.966644i | \(-0.582445\pi\) | ||||
−0.256123 | + | 0.966644i | \(0.582445\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1708.64 | + | 707.742i | 0.456694 | + | 0.189169i | 0.599157 | − | 0.800631i | \(-0.295502\pi\) |
−0.142464 | + | 0.989800i | \(0.545502\pi\) | |||||||
\(242\) | 4626.19i | 1.22886i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8474.59 | − | 3510.29i | 2.22348 | − | 0.920997i | ||||
\(245\) | −1040.09 | − | 2511.00i | −0.271220 | − | 0.654783i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −968.269 | − | 968.269i | −0.249431 | − | 0.249431i | ||||
\(248\) | −2300.67 | − | 5554.32i | −0.589085 | − | 1.42218i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3267.13 | + | 7887.56i | −0.826527 | + | 1.99541i | ||||
\(251\) | − | 1026.39i | − | 0.258109i | −0.991637 | − | 0.129055i | \(-0.958806\pi\) | ||
0.991637 | − | 0.129055i | \(-0.0411942\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1230.35 | − | 1230.35i | 0.305738 | − | 0.305738i | ||||
\(254\) | −542.987 | −0.134134 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7956.49 | −1.94250 | ||||||||
\(257\) | −1849.68 | + | 1849.68i | −0.448949 | + | 0.448949i | −0.895005 | − | 0.446056i | \(-0.852828\pi\) |
0.446056 | + | 0.895005i | \(0.352828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1901.02i | 0.456075i | ||||||||
\(260\) | 3321.80 | − | 8019.54i | 0.792344 | − | 1.91289i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3966.61 | − | 9576.24i | −0.935335 | − | 2.25810i | ||||
\(263\) | −3529.99 | − | 3529.99i | −0.827637 | − | 0.827637i | 0.159553 | − | 0.987189i | \(-0.448995\pi\) |
−0.987189 | + | 0.159553i | \(0.948995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3764.86 | − | 9089.18i | −0.872731 | − | 2.10696i | ||||
\(266\) | −2883.59 | + | 1194.42i | −0.664677 | + | 0.275318i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5745.70i | 1.30961i | ||||||||
\(269\) | 3150.91 | + | 1305.15i | 0.714181 | + | 0.295823i | 0.710033 | − | 0.704168i | \(-0.248680\pi\) |
0.00414728 | + | 0.999991i | \(0.498680\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −75.0911 | −0.0168319 | −0.00841597 | − | 0.999965i | \(-0.502679\pi\) | ||||
−0.00841597 | + | 0.999965i | \(0.502679\pi\) | |||||||
\(272\) | −3105.04 | + | 2330.81i | −0.692172 | + | 0.519582i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10614.6 | + | 10614.6i | −2.34033 | + | 2.34033i | ||||
\(275\) | 3951.97 | + | 1636.96i | 0.866591 | + | 0.358954i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1317.15 | + | 3179.88i | −0.285704 | + | 0.689750i | −0.999949 | − | 0.0101463i | \(-0.996770\pi\) |
0.714245 | + | 0.699896i | \(0.246770\pi\) | |||||||
\(278\) | 2110.26 | − | 874.099i | 0.455270 | − | 0.188579i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6832.18 | − | 6832.18i | −1.45822 | − | 1.45822i | ||||
\(281\) | −1183.03 | − | 1183.03i | −0.251151 | − | 0.251151i | 0.570291 | − | 0.821443i | \(-0.306830\pi\) |
−0.821443 | + | 0.570291i | \(0.806830\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6275.19 | − | 2599.27i | 1.31810 | − | 0.545973i | 0.390860 | − | 0.920450i | \(-0.372178\pi\) |
0.927236 | + | 0.374477i | \(0.122178\pi\) | |||||||
\(284\) | 362.302 | − | 874.674i | 0.0756995 | − | 0.182755i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2616.53 | − | 1083.80i | −0.540975 | − | 0.224079i | ||||
\(287\) | −564.046 | + | 564.046i | −0.116009 | + | 0.116009i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1371.69 | − | 4717.63i | 0.279195 | − | 0.960234i | ||||
\(290\) | −5226.11 | −1.05823 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5317.22 | + | 2202.46i | 1.06564 | + | 0.441402i | ||||
\(293\) | − | 6436.90i | − | 1.28344i | −0.766939 | − | 0.641720i | \(-0.778221\pi\) | ||
0.766939 | − | 0.641720i | \(-0.221779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4803.08 | + | 1989.50i | −0.947952 | + | 0.392655i | ||||
\(296\) | −1926.12 | − | 4650.07i | −0.378221 | − | 0.913107i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7595.14 | + | 7595.14i | 1.47643 | + | 1.47643i | ||||
\(299\) | −1022.29 | − | 2468.03i | −0.197728 | − | 0.477357i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −279.786 | + | 675.462i | −0.0535767 | + | 0.129346i | ||||
\(302\) | − | 3657.75i | − | 0.696953i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1793.41 | − | 1793.41i | 0.338352 | − | 0.338352i | ||||
\(305\) | 10890.3 | 2.04452 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5129.87 | 0.953672 | 0.476836 | − | 0.878992i | \(-0.341784\pi\) | ||||
0.476836 | + | 0.878992i | \(0.341784\pi\) | |||||||
\(308\) | −3019.62 | + | 3019.62i | −0.558632 | + | 0.558632i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 14615.7i | − | 2.67779i | ||||||
\(311\) | 1309.80 | − | 3162.14i | 0.238816 | − | 0.576554i | −0.758344 | − | 0.651854i | \(-0.773991\pi\) |
0.997161 | + | 0.0753000i | \(0.0239915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1639.23 | − | 3957.46i | −0.296022 | − | 0.714661i | −0.999990 | − | 0.00442950i | \(-0.998590\pi\) |
0.703968 | − | 0.710232i | \(-0.251410\pi\) | |||||||
\(314\) | −1992.31 | − | 1992.31i | −0.358065 | − | 0.358065i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1302.74 | − | 3145.10i | −0.231915 | − | 0.559892i | ||||
\(317\) | −360.637 | + | 149.381i | −0.0638971 | + | 0.0264670i | −0.414403 | − | 0.910093i | \(-0.636010\pi\) |
0.350506 | + | 0.936560i | \(0.386010\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1127.99i | 0.197979i | ||||||||
\(320\) | −9908.34 | − | 4104.17i | −1.73092 | − | 0.716969i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6088.94 | −1.05380 | ||||||||
\(323\) | −452.549 | + | 3177.35i | −0.0779582 | + | 0.547346i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4643.79 | − | 4643.79i | 0.792589 | − | 0.792589i | ||||
\(326\) | 7984.87 | + | 3307.44i | 1.35657 | + | 0.561909i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 808.216 | − | 1951.21i | 0.136056 | − | 0.328467i | ||||
\(329\) | −6252.75 | + | 2589.97i | −1.04780 | + | 0.434012i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2704.60 | − | 2704.60i | −0.449119 | − | 0.449119i | 0.445942 | − | 0.895062i | \(-0.352869\pi\) |
−0.895062 | + | 0.445942i | \(0.852869\pi\) | |||||||
\(332\) | 6569.07 | + | 6569.07i | 1.08592 | + | 1.08592i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14080.4 | + | 5832.30i | −2.30672 | + | 0.955477i | ||||
\(335\) | −2610.48 | + | 6302.25i | −0.425748 | + | 1.02785i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2195.97 | + | 909.601i | 0.354962 | + | 0.147030i | 0.553037 | − | 0.833157i | \(-0.313469\pi\) |
−0.198075 | + | 0.980187i | \(0.563469\pi\) | |||||||
\(338\) | 4478.08 | − | 4478.08i | 0.720638 | − | 0.720638i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19706.0 | + | 5057.41i | −3.14326 | + | 0.806695i | ||||
\(341\) | −3154.61 | −0.500973 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6339.70 | + | 2625.99i | 0.997993 | + | 0.413382i | ||||
\(344\) | − | 1935.73i | − | 0.303394i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5252.13 | − | 2175.51i | 0.816059 | − | 0.338023i | ||||
\(347\) | 4562.82 | + | 11015.6i | 0.705893 | + | 1.70418i | 0.710017 | + | 0.704184i | \(0.248687\pi\) |
−0.00412480 | + | 0.999991i | \(0.501313\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5225.48 | − | 5225.48i | −0.801471 | − | 0.801471i | 0.181854 | − | 0.983326i | \(-0.441790\pi\) |
−0.983326 | + | 0.181854i | \(0.941790\pi\) | |||||||
\(350\) | −5728.41 | − | 13829.6i | −0.874847 | − | 2.11207i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −206.389 | + | 498.267i | −0.0312516 | + | 0.0754481i | ||||
\(353\) | − | 2966.18i | − | 0.447235i | −0.974677 | − | 0.223617i | \(-0.928213\pi\) | ||
0.974677 | − | 0.223617i | \(-0.0717866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 794.792 | − | 794.792i | 0.118826 | − | 0.118826i | ||||
\(356\) | −13877.6 | −2.06604 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7547.93 | 1.11430 | ||||||||
\(359\) | 4614.81 | − | 4614.81i | 0.678441 | − | 0.678441i | −0.281206 | − | 0.959647i | \(-0.590735\pi\) |
0.959647 | + | 0.281206i | \(0.0907345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4762.44i | 0.694335i | ||||||||
\(362\) | −2783.12 | + | 6719.05i | −0.404082 | + | 0.975539i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2508.97 | + | 6057.20i | 0.361280 | + | 0.872208i | ||||
\(365\) | 4831.61 | + | 4831.61i | 0.692871 | + | 0.692871i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2256.50 | + | 5447.66i | 0.320949 | + | 0.774838i | 0.999199 | + | 0.0400079i | \(0.0127383\pi\) |
−0.678251 | + | 0.734831i | \(0.737262\pi\) | |||||||
\(368\) | 4571.23 | − | 1893.47i | 0.647532 | − | 0.268217i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 12236.2i | − | 1.71928i | ||||||
\(371\) | 6865.11 | + | 2843.62i | 0.960697 | + | 0.397934i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9234.98 | 1.28195 | 0.640977 | − | 0.767560i | \(-0.278529\pi\) | ||||
0.640977 | + | 0.767560i | \(0.278529\pi\) | |||||||
\(374\) | 1650.08 | + | 6429.47i | 0.228138 | + | 0.888930i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12670.6 | − | 12670.6i | 1.73787 | − | 1.73787i | ||||
\(377\) | 1599.96 | + | 662.726i | 0.218574 | + | 0.0905361i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −554.759 | + | 1339.31i | −0.0751875 | + | 0.181519i | −0.957005 | − | 0.290073i | \(-0.906320\pi\) |
0.881817 | + | 0.471592i | \(0.156320\pi\) | |||||||
\(380\) | 12278.5 | − | 5085.91i | 1.65756 | − | 0.686584i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10343.4 | + | 10343.4i | 1.38537 | + | 1.38537i | ||||
\(383\) | −5769.34 | − | 5769.34i | −0.769711 | − | 0.769711i | 0.208344 | − | 0.978056i | \(-0.433192\pi\) |
−0.978056 | + | 0.208344i | \(0.933192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4684.03 | + | 1940.19i | −0.620053 | + | 0.256834i | ||||
\(386\) | −7243.89 | + | 17488.3i | −0.955192 | + | 2.30604i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12779.7 | − | 5293.54i | −1.67215 | − | 0.692626i | ||||
\(389\) | −1037.93 | + | 1037.93i | −0.135283 | + | 0.135283i | −0.771506 | − | 0.636222i | \(-0.780496\pi\) |
0.636222 | + | 0.771506i | \(0.280496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3187.73 | + | 5388.85i | −0.412303 | + | 0.696998i | ||||
\(392\) | −5435.15 | −0.700298 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4252.08 | + | 1761.27i | 0.543697 | + | 0.225207i | ||||
\(395\) | − | 4041.63i | − | 0.514827i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5560.11 | + | 2303.07i | −0.702907 | + | 0.291154i | −0.705366 | − | 0.708843i | \(-0.749217\pi\) |
0.00245887 | + | 0.999997i | \(0.499217\pi\) | |||||||
\(398\) | −3285.31 | − | 7931.43i | −0.413763 | − | 0.998912i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8601.13 | + | 8601.13i | 1.07514 | + | 1.07514i | ||||
\(401\) | −2257.50 | − | 5450.08i | −0.281132 | − | 0.678713i | 0.718730 | − | 0.695289i | \(-0.244724\pi\) |
−0.999863 | + | 0.0165756i | \(0.994724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1853.43 | + | 4474.57i | −0.229096 | + | 0.553087i | ||||
\(404\) | 28852.9i | 3.55318i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2791.17 | − | 2791.17i | 0.341190 | − | 0.341190i | ||||
\(407\) | −2641.04 | −0.321649 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9261.09 | −1.11964 | −0.559818 | − | 0.828616i | \(-0.689129\pi\) | ||||
−0.559818 | + | 0.828616i | \(0.689129\pi\) | |||||||
\(410\) | 3630.59 | − | 3630.59i | 0.437322 | − | 0.437322i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28505.1i | 3.40861i | ||||||||
\(413\) | 1502.68 | − | 3627.79i | 0.179036 | − | 0.432232i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4220.81 | + | 10189.9i | 0.499257 | + | 1.20531i | ||||
\(416\) | 585.493 | + | 585.493i | 0.0690052 | + | 0.0690052i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1659.38 | − | 4006.10i | −0.194170 | − | 0.468767i | ||||
\(419\) | −7888.15 | + | 3267.38i | −0.919716 | + | 0.380959i | −0.791768 | − | 0.610822i | \(-0.790839\pi\) |
−0.127948 | + | 0.991781i | \(0.540839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1617.31i | − | 0.187228i | −0.995609 | − | 0.0936140i | \(-0.970158\pi\) | ||
0.995609 | − | 0.0936140i | \(-0.0298420\pi\) | |||||||
\(422\) | −1668.17 | − | 690.978i | −0.192429 | − | 0.0797068i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −19673.9 | −2.25342 | ||||||||
\(425\) | −15238.5 | − | 2170.41i | −1.73924 | − | 0.247719i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5816.32 | + | 5816.32i | −0.659184 | + | 0.659184i | ||||
\(428\) | 26801.6 | + | 11101.6i | 3.02688 | + | 1.25377i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1800.89 | − | 4347.74i | 0.201969 | − | 0.487597i | ||||
\(431\) | −2343.97 | + | 970.905i | −0.261961 | + | 0.108508i | −0.509799 | − | 0.860294i | \(-0.670280\pi\) |
0.247838 | + | 0.968802i | \(0.420280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1296.36 | − | 1296.36i | −0.143878 | − | 0.143878i | 0.631499 | − | 0.775377i | \(-0.282440\pi\) |
−0.775377 | + | 0.631499i | \(0.782440\pi\) | |||||||
\(434\) | 7805.98 | + | 7805.98i | 0.863361 | + | 0.863361i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20042.7 | − | 8301.96i | 2.20154 | − | 0.911908i | ||||
\(437\) | 1565.20 | − | 3778.73i | 0.171336 | − | 0.413641i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9607.00 | − | 3979.35i | −1.04446 | − | 0.432629i | −0.206548 | − | 0.978436i | \(-0.566223\pi\) |
−0.837911 | + | 0.545808i | \(0.816223\pi\) | |||||||
\(440\) | 9491.78 | − | 9491.78i | 1.02842 | − | 1.02842i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10089.2 | + | 1436.99i | 1.08573 | + | 0.154640i | ||||
\(443\) | 3984.14 | 0.427296 | 0.213648 | − | 0.976911i | \(-0.431465\pi\) | ||||
0.213648 | + | 0.976911i | \(0.431465\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15221.8 | − | 6305.09i | −1.62154 | − | 0.671662i | ||||
\(446\) | − | 12513.4i | − | 1.32854i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7483.82 | − | 3099.90i | 0.789235 | − | 0.326912i | ||||
\(449\) | −5045.33 | − | 12180.5i | −0.530298 | − | 1.28025i | −0.931326 | − | 0.364187i | \(-0.881347\pi\) |
0.401027 | − | 0.916066i | \(-0.368653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −783.616 | − | 783.616i | −0.0818160 | − | 0.0818160i | ||||
\(452\) | −3668.60 | − | 8856.79i | −0.381762 | − | 0.921656i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9683.14 | − | 23377.2i | 1.00100 | − | 2.41662i | ||||
\(455\) | 7783.85i | 0.802005i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11484.8 | − | 11484.8i | 1.17557 | − | 1.17557i | 0.194706 | − | 0.980862i | \(-0.437625\pi\) |
0.980862 | − | 0.194706i | \(-0.0623754\pi\) | |||||||
\(458\) | −15551.2 | −1.58659 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 25927.1 | 2.62795 | ||||||||
\(461\) | −7816.84 | + | 7816.84i | −0.789732 | + | 0.789732i | −0.981450 | − | 0.191718i | \(-0.938594\pi\) |
0.191718 | + | 0.981450i | \(0.438594\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14185.7i | − | 1.42390i | −0.702228 | − | 0.711952i | \(-0.747811\pi\) | ||
0.702228 | − | 0.711952i | \(-0.252189\pi\) | |||||||
\(464\) | −1227.49 | + | 2963.41i | −0.122812 | + | 0.296494i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1587.18 | + | 3831.78i | 0.157778 | + | 0.380909i | ||||
\(467\) | 6851.43 | + | 6851.43i | 0.678900 | + | 0.678900i | 0.959751 | − | 0.280851i | \(-0.0906167\pi\) |
−0.280851 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1971.71 | − | 4760.13i | −0.194126 | − | 0.468661i | ||||
\(470\) | 40247.0 | − | 16670.8i | 3.94990 | − | 1.63610i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10396.5i | 1.01385i | ||||||||
\(473\) | −938.404 | − | 388.699i | −0.0912217 | − | 0.0377852i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10055.0 | 0.971276 | ||||||||
\(476\) | 7823.54 | − | 13225.7i | 0.753343 | − | 1.27352i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6506.47 | + | 6506.47i | −0.622592 | + | 0.622592i | ||||
\(479\) | −12229.4 | − | 5065.58i | −1.16655 | − | 0.483199i | −0.286497 | − | 0.958081i | \(-0.592491\pi\) |
−0.880049 | + | 0.474882i | \(0.842491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1551.69 | + | 3746.10i | −0.147091 | + | 0.355109i | ||||
\(482\) | 8306.83 | − | 3440.80i | 0.784992 | − | 0.325154i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10520.7 | + | 10520.7i | 0.988042 | + | 0.988042i | ||||
\(485\) | −11612.6 | − | 11612.6i | −1.08722 | − | 1.08722i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17831.1 | − | 7385.89i | 1.65915 | − | 0.687242i | 0.661136 | − | 0.750266i | \(-0.270075\pi\) |
0.998012 | + | 0.0630247i | \(0.0200747\pi\) | |||||||
\(488\) | 8334.15 | − | 20120.4i | 0.773093 | − | 1.86641i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12207.6 | − | 5056.56i | −1.12548 | − | 0.466188i | ||||
\(491\) | −51.1031 | + | 51.1031i | −0.00469705 | + | 0.00469705i | −0.709451 | − | 0.704754i | \(-0.751057\pi\) |
0.704754 | + | 0.709451i | \(0.251057\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1008.99 | − | 3931.50i | −0.0921760 | − | 0.359160i | ||||
\(494\) | −6657.27 | −0.606325 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8287.69 | − | 3432.87i | −0.750259 | − | 0.310767i | ||||
\(497\) | 848.967i | 0.0766225i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13678.5 | + | 5665.84i | −1.22713 | + | 0.508292i | −0.899668 | − | 0.436574i | \(-0.856192\pi\) |
−0.327457 | + | 0.944866i | \(0.606192\pi\) | |||||||
\(500\) | 10507.5 | + | 25367.5i | 0.939824 | + | 2.26894i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3528.45 | − | 3528.45i | −0.313710 | − | 0.313710i | ||||
\(503\) | −2561.65 | − | 6184.36i | −0.227074 | − | 0.548205i | 0.768745 | − | 0.639555i | \(-0.220882\pi\) |
−0.995819 | + | 0.0913508i | \(0.970882\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13108.9 | + | 31647.7i | −1.15513 | + | 2.78872i | ||||
\(506\) | − | 8459.22i | − | 0.743198i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1234.84 | + | 1234.84i | −0.107848 | + | 0.107848i | ||||
\(509\) | 4414.17 | 0.384390 | 0.192195 | − | 0.981357i | \(-0.438439\pi\) | ||||
0.192195 | + | 0.981357i | \(0.438439\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5160.94 | −0.446784 | ||||||||
\(512\) | −12716.4 | + | 12716.4i | −1.09764 | + | 1.09764i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12717.4i | 1.09132i | ||||||||
\(515\) | −12950.9 | + | 31266.2i | −1.10813 | + | 2.67525i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3598.19 | − | 8686.79i | −0.306089 | − | 0.738965i | ||||
\(518\) | 6535.15 | + | 6535.15i | 0.554321 | + | 0.554321i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7886.64 | − | 19040.0i | −0.665100 | − | 1.60569i | ||||
\(521\) | 1064.38 | − | 440.882i | 0.0895037 | − | 0.0370736i | −0.337482 | − | 0.941332i | \(-0.609575\pi\) |
0.426986 | + | 0.904258i | \(0.359575\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8548.79i | 0.714747i | 0.933962 | + | 0.357373i | \(0.116328\pi\) | ||||
−0.933962 | + | 0.357373i | \(0.883672\pi\) | |||||||
\(524\) | −30798.5 | − | 12757.2i | −2.56763 | − | 1.06355i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24270.2 | −2.01185 | ||||||||
\(527\) | 10995.1 | − | 2821.82i | 0.908833 | − | 0.233246i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2961.28 | + | 2961.28i | −0.243387 | + | 0.243387i | ||||
\(530\) | −44188.5 | − | 18303.5i | −3.62156 | − | 1.50010i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3841.42 | + | 9274.00i | −0.313058 | + | 0.755788i | ||||
\(533\) | −1571.89 | + | 651.100i | −0.127742 | + | 0.0529123i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24353.8 | + | 24353.8i | 1.96805 | + | 1.96805i | ||||
\(536\) | 9645.98 | + | 9645.98i | 0.777319 | + | 0.777319i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15318.7 | − | 6345.20i | 1.22757 | − | 0.508478i | ||||
\(539\) | −1091.39 | + | 2634.86i | −0.0872165 | + | 0.210559i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1681.96 | − | 696.690i | −0.133666 | − | 0.0553661i | 0.314848 | − | 0.949142i | \(-0.398046\pi\) |
−0.448514 | + | 0.893776i | \(0.648046\pi\) | |||||||
\(542\) | −258.142 | + | 258.142i | −0.0204578 | + | 0.0204578i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 273.647 | − | 1921.28i | 0.0215672 | − | 0.151423i | ||||
\(545\) | 25756.0 | 2.02434 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −76.4832 | − | 31.6804i | −0.00597840 | − | 0.00247633i | 0.379692 | − | 0.925113i | \(-0.376030\pi\) |
−0.385671 | + | 0.922637i | \(0.626030\pi\) | |||||||
\(548\) | 48278.3i | 3.76341i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 19213.1 | − | 7958.34i | 1.48955 | − | 0.616991i | ||||
\(551\) | 1014.68 | + | 2449.65i | 0.0784516 | + | 0.189399i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2158.56 | + | 2158.56i | 0.165988 | + | 0.165988i | ||||
\(554\) | 6403.54 | + | 15459.5i | 0.491084 | + | 1.18558i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2811.22 | − | 6786.89i | 0.214429 | − | 0.517677i | ||||
\(557\) | 12671.9i | 0.963963i | 0.876181 | + | 0.481981i | \(0.160083\pi\) | ||||
−0.876181 | + | 0.481981i | \(0.839917\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1102.68 | + | 1102.68i | −0.0834318 | + | 0.0834318i | ||||
\(560\) | −14417.1 | −1.08791 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8133.82 | −0.610506 | ||||||||
\(563\) | −3329.39 | + | 3329.39i | −0.249231 | + | 0.249231i | −0.820655 | − | 0.571424i | \(-0.806391\pi\) |
0.571424 | + | 0.820655i | \(0.306391\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 11381.5i | − | 0.847473i | ||||||
\(566\) | 12636.8 | − | 30507.9i | 0.938451 | − | 2.26562i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −860.179 | − | 2076.66i | −0.0635428 | − | 0.153406i | ||||
\(569\) | 6005.28 | + | 6005.28i | 0.442450 | + | 0.442450i | 0.892835 | − | 0.450384i | \(-0.148713\pi\) |
−0.450384 | + | 0.892835i | \(0.648713\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 431.903 | + | 1042.71i | 0.0316543 | + | 0.0764202i | 0.938916 | − | 0.344146i | \(-0.111831\pi\) |
−0.907262 | + | 0.420566i | \(0.861831\pi\) | |||||||
\(572\) | −8415.13 | + | 3485.66i | −0.615129 | + | 0.254795i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3878.06i | 0.281998i | ||||||||
\(575\) | 18122.7 | + | 7506.66i | 1.31438 | + | 0.544434i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18288.9 | −1.31955 | −0.659773 | − | 0.751465i | \(-0.729348\pi\) | ||||
−0.659773 | + | 0.751465i | \(0.729348\pi\) | |||||||
\(578\) | −11502.4 | − | 20933.3i | −0.827746 | − | 1.50642i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11885.0 | + | 11885.0i | −0.850855 | + | 0.850855i | ||||
\(581\) | −7696.52 | − | 3188.00i | −0.549579 | − | 0.227643i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3950.58 | + | 9537.53i | −0.280645 | + | 0.677537i | ||||
\(584\) | 12624.2 | − | 5229.10i | 0.894506 | − | 0.370517i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22128.2 | − | 22128.2i | −1.55991 | − | 1.55991i | ||||
\(587\) | −7997.50 | − | 7997.50i | −0.562338 | − | 0.562338i | 0.367633 | − | 0.929971i | \(-0.380168\pi\) |
−0.929971 | + | 0.367633i | \(0.880168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6850.88 | + | 2837.73i | −0.479262 | + | 0.198517i | ||||
\(590\) | −9672.28 | + | 23350.9i | −0.674918 | + | 1.62940i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6938.44 | − | 2874.00i | −0.481703 | − | 0.199528i | ||||
\(593\) | 3735.98 | − | 3735.98i | 0.258715 | − | 0.258715i | −0.565816 | − | 0.824532i | \(-0.691439\pi\) |
0.824532 | + | 0.565816i | \(0.191439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14590.3 | − | 10952.3i | 1.00528 | − | 0.754620i | ||||
\(596\) | 34545.0 | 2.37419 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11998.7 | − | 4970.04i | −0.820509 | − | 0.339866i | ||||
\(599\) | − | 22287.6i | − | 1.52028i | −0.649762 | − | 0.760138i | \(-0.725131\pi\) | ||
0.649762 | − | 0.760138i | \(-0.274869\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13901.4 | − | 5758.15i | 0.943511 | − | 0.390815i | 0.142723 | − | 0.989763i | \(-0.454414\pi\) |
0.800788 | + | 0.598947i | \(0.204414\pi\) | |||||||
\(602\) | 1360.22 | + | 3283.87i | 0.0920907 | + | 0.222326i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8318.28 | − | 8318.28i | −0.560374 | − | 0.560374i | ||||
\(605\) | 6759.83 | + | 16319.7i | 0.454258 | + | 1.09668i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4319.98 | + | 10429.4i | −0.288868 | + | 0.697388i | −0.999984 | − | 0.00568627i | \(-0.998190\pi\) |
0.711116 | + | 0.703075i | \(0.248190\pi\) | |||||||
\(608\) | 1267.75i | 0.0845623i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37437.8 | − | 37437.8i | 2.48494 | − | 2.48494i | ||||
\(611\) | −14435.6 | −0.955811 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14753.0 | 0.972054 | 0.486027 | − | 0.873944i | \(-0.338446\pi\) | ||||
0.486027 | + | 0.873944i | \(0.338446\pi\) | |||||||
\(614\) | 17635.0 | − | 17635.0i | 1.15911 | − | 1.15911i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10138.8i | 0.663154i | ||||||||
\(617\) | −2561.52 | + | 6184.04i | −0.167136 | + | 0.403501i | −0.985150 | − | 0.171697i | \(-0.945075\pi\) |
0.818014 | + | 0.575198i | \(0.195075\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 491.884 | + | 1187.51i | 0.0319394 | + | 0.0771085i | 0.939044 | − | 0.343796i | \(-0.111713\pi\) |
−0.907105 | + | 0.420904i | \(0.861713\pi\) | |||||||
\(620\) | −33238.3 | − | 33238.3i | −2.15304 | − | 2.15304i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6367.81 | − | 15373.2i | −0.410492 | − | 0.991014i | ||||
\(623\) | 11497.1 | − | 4762.27i | 0.739362 | − | 0.306254i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5148.78i | 0.329522i | ||||||||
\(626\) | −19239.9 | − | 7969.41i | −1.22840 | − | 0.508820i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9061.61 | −0.575792 | ||||||||
\(629\) | 9205.10 | − | 2362.42i | 0.583516 | − | 0.149755i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19224.0 | − | 19224.0i | 1.21283 | − | 1.21283i | 0.242734 | − | 0.970093i | \(-0.421956\pi\) |
0.970093 | − | 0.242734i | \(-0.0780442\pi\) | |||||||
\(632\) | −7467.12 | − | 3092.98i | −0.469978 | − | 0.194671i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −726.238 | + | 1753.29i | −0.0454931 | + | 0.109830i | ||||
\(635\) | −1915.48 | + | 793.417i | −0.119706 | + | 0.0495839i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3096.11 | + | 3096.11i | 0.192578 | + | 0.192578i | ||||
\(638\) | 3877.70 | + | 3877.70i | 0.240626 | + | 0.240626i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −44372.3 | + | 18379.6i | −2.74057 | + | 1.13518i | ||||
\(641\) | 4715.24 | − | 11383.6i | 0.290547 | − | 0.701442i | −0.709448 | − | 0.704758i | \(-0.751055\pi\) |
0.999995 | + | 0.00331580i | \(0.00105545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23630.2 | − | 9787.93i | −1.44927 | − | 0.600308i | −0.487246 | − | 0.873265i | \(-0.661999\pi\) |
−0.962026 | + | 0.272956i | \(0.911999\pi\) | |||||||
\(644\) | −13847.2 | + | 13847.2i | −0.847290 | + | 0.847290i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9367.10 | + | 12478.6i | 0.570501 | + | 0.760004i | ||||
\(647\) | 28275.5 | 1.71812 | 0.859062 | − | 0.511872i | \(-0.171048\pi\) | ||||
0.859062 | + | 0.511872i | \(0.171048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5040.00 | + | 2087.64i | 0.304834 | + | 0.126266i | ||||
\(650\) | − | 31928.1i | − | 1.92665i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 25680.4 | − | 10637.2i | 1.54252 | − | 0.638933i | ||||
\(653\) | −900.910 | − | 2174.99i | −0.0539898 | − | 0.130343i | 0.894583 | − | 0.446902i | \(-0.147473\pi\) |
−0.948573 | + | 0.316559i | \(0.897473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27985.7 | − | 27985.7i | −1.66945 | − | 1.66945i | ||||
\(656\) | −1205.95 | − | 2911.43i | −0.0717752 | − | 0.173281i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12591.6 | + | 30398.8i | −0.746004 | + | 1.80101i | ||||
\(659\) | − | 21272.6i | − | 1.25745i | −0.777626 | − | 0.628727i | \(-0.783576\pi\) | ||
0.777626 | − | 0.628727i | \(-0.216424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11753.0 | − | 11753.0i | 0.691587 | − | 0.691587i | −0.270994 | − | 0.962581i | \(-0.587352\pi\) |
0.962581 | + | 0.270994i | \(0.0873525\pi\) | |||||||
\(662\) | −18595.3 | −1.09173 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22056.5 | 1.28910 | ||||||||
\(665\) | −8427.03 | + | 8427.03i | −0.491408 | + | 0.491408i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5172.66i | 0.300279i | ||||||||
\(668\) | −18757.5 | + | 45284.5i | −1.08645 | + | 2.62292i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12691.3 | + | 30639.4i | 0.731801 | + | 1.76672i | ||||
\(671\) | −8080.48 | − | 8080.48i | −0.464893 | − | 0.464893i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −87.5115 | − | 211.271i | −0.00501236 | − | 0.0121009i | 0.921354 | − | 0.388726i | \(-0.127085\pi\) |
−0.926366 | + | 0.376625i | \(0.877085\pi\) | |||||||
\(674\) | 10676.1 | − | 4422.17i | 0.610129 | − | 0.252724i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 20367.7i | − | 1.15883i | ||||||
\(677\) | −9216.32 | − | 3817.52i | −0.523208 | − | 0.216720i | 0.105417 | − | 0.994428i | \(-0.466382\pi\) |
−0.628625 | + | 0.777708i | \(0.716382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12404.1 | 0.701071 | ||||||||
\(680\) | −24592.3 | + | 41573.2i | −1.38687 | + | 2.34450i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10844.7 | + | 10844.7i | −0.608890 | + | 0.608890i | ||||
\(683\) | 28742.6 | + | 11905.6i | 1.61026 | + | 0.666990i | 0.992819 | − | 0.119630i | \(-0.0381709\pi\) |
0.617437 | + | 0.786620i | \(0.288171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21934.6 | + | 52954.8i | −1.22347 | + | 2.95372i | ||||
\(686\) | 30821.5 | − | 12766.7i | 1.71541 | − | 0.710545i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2042.36 | − | 2042.36i | −0.113175 | − | 0.113175i | ||||
\(689\) | 11207.2 | + | 11207.2i | 0.619679 | + | 0.619679i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4720.02 | + | 1955.10i | −0.259852 | + | 0.107634i | −0.508807 | − | 0.860881i | \(-0.669913\pi\) |
0.248954 | + | 0.968515i | \(0.419913\pi\) | |||||||
\(692\) | 6996.72 | − | 16891.6i | 0.384358 | − | 0.927921i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 53554.2 | + | 22182.9i | 2.92924 | + | 1.21333i | ||||
\(695\) | 6167.06 | − | 6167.06i | 0.336590 | − | 0.336590i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3432.17 | + | 2030.27i | 0.186518 | + | 0.110333i | ||||
\(698\) | −35927.4 | −1.94824 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −44477.9 | − | 18423.3i | −2.40158 | − | 0.994767i | ||||
\(701\) | 11204.5i | 0.603691i | 0.953357 | + | 0.301846i | \(0.0976027\pi\) | ||||
−0.953357 | + | 0.301846i | \(0.902397\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5735.55 | + | 2375.74i | −0.307710 | + | 0.127458i | ||||
\(704\) | 4306.62 | + | 10397.1i | 0.230557 | + | 0.556613i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10196.9 | − | 10196.9i | −0.543576 | − | 0.543576i | ||||
\(707\) | −9901.24 | − | 23903.7i | −0.526696 | − | 1.27156i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12992.1 | − | 31365.7i | 0.688193 | − | 1.66144i | −0.0601983 | − | 0.998186i | \(-0.519173\pi\) |
0.748391 | − | 0.663258i | \(-0.230827\pi\) | |||||||
\(710\) | − | 5464.54i | − | 0.288846i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23297.9 | + | 23297.9i | −1.22630 | + | 1.22630i | ||||
\(713\) | −14466.2 | −0.759838 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10813.9 | −0.565619 | ||||||||
\(716\) | 17165.1 | − | 17165.1i | 0.895937 | − | 0.895937i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 31728.8i | − | 1.64918i | ||||||
\(719\) | −2384.53 | + | 5756.76i | −0.123683 | + | 0.298596i | −0.973578 | − | 0.228355i | \(-0.926665\pi\) |
0.849895 | + | 0.526952i | \(0.176665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9781.88 | − | 23615.6i | −0.505265 | − | 1.21982i | ||||
\(722\) | 16371.9 | + | 16371.9i | 0.843906 | + | 0.843906i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8950.89 | + | 21609.4i | 0.459471 | + | 1.10926i | ||||
\(725\) | −11748.5 | + | 4866.38i | −0.601831 | + | 0.249287i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5206.88i | − | 0.265629i | −0.991141 | − | 0.132815i | \(-0.957598\pi\) | ||
0.991141 | − | 0.132815i | \(-0.0424015\pi\) | |||||||
\(728\) | 14381.0 | + | 5956.82i | 0.732139 | + | 0.303262i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 33219.4 | 1.68425 | ||||||||
\(731\) | 3618.42 | + | 515.369i | 0.183081 | + | 0.0260761i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2699.43 | − | 2699.43i | 0.136024 | − | 0.136024i | −0.635816 | − | 0.771840i | \(-0.719336\pi\) |
0.771840 | + | 0.635816i | \(0.219336\pi\) | |||||||
\(734\) | 26484.7 | + | 10970.3i | 1.33184 | + | 0.551665i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −946.446 | + | 2284.92i | −0.0474001 | + | 0.114434i | ||||
\(737\) | 6613.13 | − | 2739.25i | 0.330526 | − | 0.136908i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6513.44 | + | 6513.44i | 0.324223 | + | 0.324223i | 0.850385 | − | 0.526162i | \(-0.176369\pi\) |
−0.526162 | + | 0.850385i | \(0.676369\pi\) | |||||||
\(740\) | −27827.1 | − | 27827.1i | −1.38236 | − | 1.38236i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 33375.9 | − | 13824.7i | 1.65130 | − | 0.683992i | ||||
\(743\) | −8854.88 | + | 21377.6i | −0.437219 | + | 1.05554i | 0.539686 | + | 0.841867i | \(0.318543\pi\) |
−0.976905 | + | 0.213674i | \(0.931457\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37891.2 | + | 15695.0i | 1.86339 | + | 0.771841i | ||||
\(746\) | 31747.2 | − | 31747.2i | 1.55811 | − | 1.55811i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18374.1 | + | 10869.1i | 0.898161 | + | 0.531300i | ||||
\(749\) | −26013.9 | −1.26906 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28770.9 | + | 11917.3i | 1.39796 | + | 0.579053i | 0.949221 | − | 0.314612i | \(-0.101874\pi\) |
0.448736 | + | 0.893664i | \(0.351874\pi\) | |||||||
\(752\) | − | 26737.2i | − | 1.29655i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7778.48 | − | 3221.95i | 0.375697 | − | 0.155619i | ||||
\(755\) | −5344.73 | − | 12903.3i | −0.257635 | − | 0.621986i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21914.1 | + | 21914.1i | 1.05216 | + | 1.05216i | 0.998563 | + | 0.0535946i | \(0.0170679\pi\) |
0.0535946 | + | 0.998563i | \(0.482932\pi\) | |||||||
\(758\) | 2697.05 | + | 6511.26i | 0.129237 | + | 0.312005i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12075.0 | − | 29151.6i | 0.576324 | − | 1.39137i | ||||
\(761\) | 14150.5i | 0.674053i | 0.941495 | + | 0.337026i | \(0.109421\pi\) | ||||
−0.941495 | + | 0.337026i | \(0.890579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13755.8 | + | 13755.8i | −0.652679 | + | 0.652679i | ||||
\(764\) | 47044.7 | 2.22777 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −39666.7 | −1.87104 | ||||||||
\(767\) | 5922.30 | − | 5922.30i | 0.278803 | − | 0.278803i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 619.823i | 0.0290655i | 0.999894 | + | 0.0145328i | \(0.00462608\pi\) | ||||
−0.999894 | + | 0.0145328i | \(0.995374\pi\) | |||||||
\(770\) | −9432.55 | + | 22772.2i | −0.441462 | + | 1.06578i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23297.3 | + | 56244.7i | 1.08613 | + | 2.62214i | ||||
\(773\) | 7209.95 | + | 7209.95i | 0.335477 | + | 0.335477i | 0.854662 | − | 0.519185i | \(-0.173764\pi\) |
−0.519185 | + | 0.854662i | \(0.673764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13609.7 | − | 32856.6i | −0.630805 | − | 1.52290i | ||||
\(776\) | −30341.7 | + | 12568.0i | −1.40361 | + | 0.581396i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7136.23i | 0.328851i | ||||||||
\(779\) | −2406.68 | − | 996.880i | −0.110691 | − | 0.0458497i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1179.45 | −0.0540385 | ||||||||
\(782\) | 7566.83 | + | 29483.9i | 0.346022 | + | 1.34826i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5734.55 | + | 5734.55i | −0.261231 | + | 0.261231i | ||||
\(785\) | −9939.36 | − | 4117.02i | −0.451912 | − | 0.187188i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12707.6 | − | 30679.0i | 0.575577 | − | 1.38956i | −0.321171 | − | 0.947021i | \(-0.604076\pi\) |
0.896747 | − | 0.442543i | \(-0.145924\pi\) | |||||||
\(788\) | 13675.3 | − | 5664.48i | 0.618225 | − | 0.256077i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13894.0 | − | 13894.0i | −0.625729 | − | 0.625729i | ||||
\(791\) | 6078.64 | + | 6078.64i | 0.273238 | + | 0.273238i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16209.0 | + | 6714.00i | −0.725851 | + | 0.300657i | ||||
\(794\) | −11196.8 | + | 27031.4i | −0.500452 | + | 1.20820i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25508.6 | − | 10566.0i | −1.13584 | − | 0.470480i | ||||
\(797\) | −3077.08 | + | 3077.08i | −0.136757 | + | 0.136757i | −0.772172 | − | 0.635414i | \(-0.780829\pi\) |
0.635414 | + | 0.772172i | \(0.280829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20311.6 | + | 27058.4i | 0.899338 | + | 1.19807i | ||||
\(800\) | −6080.08 | −0.268704 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26496.5 | − | 10975.2i | −1.16661 | − | 0.483226i | ||||
\(803\) | − | 7169.98i | − | 0.315097i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21479.7 | + | 8897.20i | −0.940449 | + | 0.389547i | ||||
\(806\) | 9010.73 | + | 21753.8i | 0.393784 | + | 0.950678i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 48438.8 | + | 48438.8i | 2.10900 | + | 2.10900i | ||||
\(809\) | 5172.06 | + | 12486.4i | 0.224771 | + | 0.542645i | 0.995526 | − | 0.0944862i | \(-0.0301208\pi\) |
−0.770755 | + | 0.637132i | \(0.780121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2203.64 | + | 5320.06i | −0.0954135 | + | 0.230348i | −0.964379 | − | 0.264524i | \(-0.914785\pi\) |
0.868966 | + | 0.494872i | \(0.164785\pi\) | |||||||
\(812\) | − | 12695.1i | − | 0.548657i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9079.13 | + | 9079.13i | −0.390938 | + | 0.390938i | ||||
\(815\) | 33000.8 | 1.41837 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2387.59 | −0.102241 | ||||||||
\(818\) | −31837.0 | + | 31837.0i | −1.36082 | + | 1.36082i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 16513.0i | − | 0.703243i | ||||||
\(821\) | 10698.4 | − | 25828.3i | 0.454783 | − | 1.09794i | −0.515699 | − | 0.856770i | \(-0.672468\pi\) |
0.970482 | − | 0.241174i | \(-0.0775325\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14557.5 | − | 35144.9i | −0.616576 | − | 1.48855i | −0.855655 | − | 0.517547i | \(-0.826845\pi\) |
0.239078 | − | 0.971000i | \(-0.423155\pi\) | |||||||
\(824\) | 47854.9 | + | 47854.9i | 2.02318 | + | 2.02318i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7305.52 | − | 17637.1i | −0.307738 | − | 0.742946i | ||||
\(827\) | −13366.2 | + | 5536.47i | −0.562018 | + | 0.232795i | −0.645561 | − | 0.763709i | \(-0.723376\pi\) |
0.0835432 | + | 0.996504i | \(0.473376\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24519.4i | − | 1.02726i | −0.858013 | − | 0.513628i | \(-0.828301\pi\) | ||
0.858013 | − | 0.513628i | \(-0.171699\pi\) | |||||||
\(830\) | 49540.1 | + | 20520.2i | 2.07176 | + | 0.858151i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17277.7 | 0.719949 | ||||||||
\(833\) | 1447.06 | − | 10159.8i | 0.0601892 | − | 0.422590i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41148.8 | + | 41148.8i | −1.70540 | + | 1.70540i | ||||
\(836\) | −12884.2 | − | 5336.79i | −0.533024 | − | 0.220786i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15884.9 | + | 38349.5i | −0.654814 | + | 1.58086i | ||||
\(839\) | −35168.5 | + | 14567.3i | −1.44714 | + | 0.599426i | −0.961518 | − | 0.274741i | \(-0.911408\pi\) |
−0.485625 | + | 0.874167i | \(0.661408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14874.5 | + | 14874.5i | 0.609885 | + | 0.609885i | ||||
\(842\) | −5559.86 | − | 5559.86i | −0.227560 | − | 0.227560i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5365.06 | + | 2222.28i | −0.218807 | + | 0.0906327i | ||||
\(845\) | 9253.77 | − | 22340.6i | 0.376733 | − | 0.909514i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12326.3 | − | 5105.73i | −0.500045 | − | 0.207125i | ||||
\(848\) | −20757.6 | + | 20757.6i | −0.840590 | + | 0.840590i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −59846.9 | + | 44924.4i | −2.41498 | + | 1.81282i | ||||
\(851\) | −12111.1 | −0.487853 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34565.1 | + | 14317.3i | 1.38744 | + | 0.574696i | 0.946460 | − | 0.322821i | \(-0.104631\pi\) |
0.440979 | + | 0.897517i | \(0.354631\pi\) | |||||||
\(854\) | 39989.7i | 1.60237i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 63632.5 | − | 26357.4i | 2.54079 | − | 1.05243i | ||||
\(857\) | −11132.3 | − | 26875.7i | −0.443723 | − | 1.07124i | −0.974632 | − | 0.223814i | \(-0.928149\pi\) |
0.530908 | − | 0.847429i | \(-0.321851\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30775.9 | − | 30775.9i | −1.22242 | − | 1.22242i | −0.966769 | − | 0.255651i | \(-0.917710\pi\) |
−0.255651 | − | 0.966769i | \(-0.582290\pi\) | |||||||
\(860\) | −5791.91 | − | 13982.9i | −0.229654 | − | 0.554434i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4720.21 | + | 11395.6i | −0.186509 | + | 0.450274i | ||||
\(863\) | − | 15659.4i | − | 0.617672i | −0.951115 | − | 0.308836i | \(-0.900061\pi\) | ||
0.951115 | − | 0.308836i | \(-0.0999394\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15348.9 | − | 15348.9i | 0.603328 | − | 0.603328i | ||||
\(866\) | −8913.05 | −0.349743 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 35503.9 | 1.38834 | ||||||||
\(869\) | −2998.84 | + | 2998.84i | −0.117064 | + | 0.117064i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10989.6i | − | 0.427518i | ||||||
\(872\) | 19710.6 | − | 47585.5i | 0.765463 | − | 1.84799i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7609.48 | − | 18370.9i | −0.294502 | − | 0.710990i | ||||
\(875\) | −17410.3 | − | 17410.3i | −0.672659 | − | 0.672659i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11056.4 | + | 26692.6i | 0.425712 | + | 1.02776i | 0.980633 | + | 0.195856i | \(0.0627485\pi\) |
−0.554921 | + | 0.831903i | \(0.687252\pi\) | |||||||
\(878\) | −46706.0 | + | 19346.3i | −1.79528 | + | 0.743627i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 20029.3i | − | 0.767258i | ||||||
\(881\) | −20413.0 | − | 8455.34i | −0.780625 | − | 0.323346i | −0.0434576 | − | 0.999055i | \(-0.513837\pi\) |
−0.737168 | + | 0.675710i | \(0.763837\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40158.3 | −1.53050 | −0.765252 | − | 0.643731i | \(-0.777385\pi\) | ||||
−0.765252 | + | 0.643731i | \(0.777385\pi\) | |||||||
\(884\) | 26212.2 | − | 19676.3i | 0.997299 | − | 0.748628i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13696.3 | − | 13696.3i | 0.519343 | − | 0.519343i | ||||
\(887\) | 25685.4 | + | 10639.3i | 0.972303 | + | 0.402741i | 0.811569 | − | 0.584257i | \(-0.198614\pi\) |
0.160734 | + | 0.986998i | \(0.448614\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 599.272 | − | 1446.77i | 0.0226085 | − | 0.0545817i | ||||
\(890\) | −74003.4 | + | 30653.2i | −2.78719 | + | 1.15449i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28457.4 | − | 28457.4i | −1.06819 | − | 1.06819i | ||||
\(893\) | −15628.4 | − | 15628.4i | −0.585648 | − | 0.585648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26626.6 | − | 11029.1i | 0.994444 | − | 0.411912i | ||||
\(896\) | 13882.2 | − | 33514.6i | 0.517603 | − | 1.24960i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −59217.5 | − | 24528.7i | −2.20057 | − | 0.911507i | ||||
\(899\) | 6631.31 | − | 6631.31i | 0.246014 | − | 0.246014i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5237.99 | − | 36776.0i | 0.193677 | − | 1.35981i | ||||
\(902\) | −5387.70 | −0.198881 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21027.8 | − | 8710.02i | −0.773646 | − | 0.320455i | ||||
\(905\) | 27769.3i | 1.01998i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17011.7 | + | 7046.48i | −0.622783 | + | 0.257965i | −0.671683 | − | 0.740839i | \(-0.734428\pi\) |
0.0489002 | + | 0.998804i | \(0.484428\pi\) | |||||||
\(908\) | −31142.3 | − | 75184.2i | −1.13821 | − | 2.74788i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 26758.6 | + | 26758.6i | 0.974770 | + | 0.974770i | ||||
\(911\) | 12349.9 | + | 29815.2i | 0.449143 | + | 1.08433i | 0.972644 | + | 0.232302i | \(0.0746258\pi\) |
−0.523501 | + | 0.852025i | \(0.675374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4429.01 | − | 10692.6i | 0.160547 | − | 0.387594i | ||||
\(914\) | − | 78962.7i | − | 2.85761i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35365.7 | + | 35365.7i | −1.27567 | + | 1.27567i | ||||
\(917\) | 29893.3 | 1.07652 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19185.3 | 0.688643 | 0.344322 | − | 0.938852i | \(-0.388109\pi\) | ||||
0.344322 | + | 0.938852i | \(0.388109\pi\) | |||||||
\(920\) | 43526.8 | − | 43526.8i | 1.55982 | − | 1.55982i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 53744.2i | 1.91971i | ||||||||
\(923\) | −692.961 | + | 1672.96i | −0.0247119 | + | 0.0596599i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11394.0 | − | 27507.5i | −0.405008 | − | 0.977775i | ||||
\(926\) | −48766.6 | − | 48766.6i | −1.73064 | − | 1.73064i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −613.557 | − | 1481.26i | −0.0217037 | − | 0.0523973i | ||||
\(929\) | 19238.6 | − | 7968.89i | 0.679438 | − | 0.281433i | −0.0161538 | − | 0.999870i | \(-0.505142\pi\) |
0.695592 | + | 0.718437i | \(0.255142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6703.89i | 0.235995i | ||||||||
\(932\) | 12323.5 | + | 5104.57i | 0.433123 | + | 0.179405i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 47106.5 | 1.65029 | ||||||||
\(935\) | 15215.7 | + | 20269.9i | 0.532200 | + | 0.708981i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14900.1 | − | 14900.1i | 0.519495 | − | 0.519495i | −0.397924 | − | 0.917418i | \(-0.630269\pi\) |
0.917418 | + | 0.397924i | \(0.130269\pi\) | |||||||
\(938\) | −23142.1 | − | 9585.78i | −0.805562 | − | 0.333675i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 53615.7 | − | 129440.i | 1.86037 | − | 4.49134i | ||||
\(941\) | 10307.2 | − | 4269.37i | 0.357071 | − | 0.147904i | −0.196935 | − | 0.980417i | \(-0.563099\pi\) |
0.554006 | + | 0.832513i | \(0.313099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3593.46 | − | 3593.46i | −0.124092 | − | 0.124092i | ||||
\(944\) | 10969.1 | + | 10969.1i | 0.378194 | + | 0.378194i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4562.20 | + | 1889.73i | −0.156797 | + | 0.0649475i | ||||
\(947\) | 1165.49 | − | 2813.74i | 0.0399929 | − | 0.0965514i | −0.902621 | − | 0.430436i | \(-0.858360\pi\) |
0.942614 | + | 0.333885i | \(0.108360\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10170.0 | − | 4212.57i | −0.347875 | − | 0.144095i | ||||
\(950\) | 34566.3 | − | 34566.3i | 1.18050 | − | 1.18050i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9069.20 | − | 35337.8i | −0.308755 | − | 1.20305i | ||||
\(953\) | −6037.53 | −0.205220 | −0.102610 | − | 0.994722i | \(-0.532719\pi\) | ||||
−0.102610 | + | 0.994722i | \(0.532719\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51601.7 | + | 21374.1i | 1.74847 | + | 0.724241i | ||||
\(956\) | 29593.4i | 1.00117i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −59455.2 | + | 24627.2i | −2.00513 | + | 0.830551i | ||||
\(959\) | −16567.3 | − | 39997.0i | −0.557858 | − | 1.34679i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2519.83 | − | 2519.83i | −0.0845836 | − | 0.0845836i | ||||
\(962\) | 7543.77 | + | 18212.3i | 0.252829 | + | 0.610382i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11066.1 | − | 26715.9i | 0.369725 | − | 0.892595i | ||||
\(965\) | 72277.6i | 2.41109i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7884.94 | − | 7884.94i | 0.262216 | − | 0.262216i | −0.563738 | − | 0.825954i | \(-0.690637\pi\) |
0.825954 | + | 0.563738i | \(0.190637\pi\) | |||||||
\(968\) | 35324.6 | 1.17291 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −79841.6 | −2.64284 | ||||||||
\(971\) | −20542.5 | + | 20542.5i | −0.678930 | + | 0.678930i | −0.959758 | − | 0.280828i | \(-0.909391\pi\) |
0.280828 | + | 0.959758i | \(0.409391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6587.43i | 0.217043i | ||||||||
\(974\) | 35907.7 | − | 86688.9i | 1.18127 | − | 2.85184i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12435.5 | − | 30022.0i | −0.407839 | − | 0.984612i | ||||
\(977\) | 1718.38 | + | 1718.38i | 0.0562700 | + | 0.0562700i | 0.734682 | − | 0.678412i | \(-0.237331\pi\) |
−0.678412 | + | 0.734682i | \(0.737331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6616.10 | + | 15972.7i | 0.215987 | + | 0.521439i | ||||
\(980\) | −39261.4 | + | 16262.6i | −1.27975 | + | 0.530091i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 351.356i | 0.0114177i | ||||||||
\(983\) | 2002.34 | + | 829.397i | 0.0649693 | + | 0.0269112i | 0.414931 | − | 0.909853i | \(-0.363806\pi\) |
−0.349962 | + | 0.936764i | \(0.613806\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17573.5 | 0.568465 | ||||||||
\(986\) | −16984.0 | − | 10046.8i | −0.548561 | − | 0.324497i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15139.6 | + | 15139.6i | −0.487506 | + | 0.487506i | ||||
\(989\) | −4303.27 | − | 1782.47i | −0.138358 | − | 0.0573098i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7474.99 | − | 18046.2i | 0.239607 | − | 0.578463i | −0.757635 | − | 0.652679i | \(-0.773645\pi\) |
0.997242 | + | 0.0742153i | \(0.0236452\pi\) | |||||||
\(992\) | 4142.59 | − | 1715.92i | 0.132588 | − | 0.0549198i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2918.51 | + | 2918.51i | 0.0931282 | + | 0.0931282i | ||||
\(995\) | −23178.9 | − | 23178.9i | −0.738514 | − | 0.738514i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8215.19 | + | 3402.84i | −0.260961 | + | 0.108093i | −0.509328 | − | 0.860572i | \(-0.670106\pi\) |
0.248367 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(998\) | −27545.4 | + | 66500.5i | −0.873682 | + | 2.10925i | ||||
\(999\) | 0 | 0 |
(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 | 153.4.l.a.145.3 | 12 | ||
3.2 | odd | 2 | 17.4.d.a.9.1 | yes | 12 | ||
17.2 | even | 8 | inner | 153.4.l.a.19.3 | 12 | ||
51.2 | odd | 8 | 17.4.d.a.2.1 | ✓ | 12 | ||
51.11 | even | 16 | 289.4.a.g.1.2 | 12 | |||
51.23 | even | 16 | 289.4.a.g.1.1 | 12 | |||
51.41 | even | 16 | 289.4.b.e.288.12 | 12 | |||
51.44 | even | 16 | 289.4.b.e.288.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.2.1 | ✓ | 12 | 51.2 | odd | 8 | ||
17.4.d.a.9.1 | yes | 12 | 3.2 | odd | 2 | ||
153.4.l.a.19.3 | 12 | 17.2 | even | 8 | inner | ||
153.4.l.a.145.3 | 12 | 1.1 | even | 1 | trivial | ||
289.4.a.g.1.1 | 12 | 51.23 | even | 16 | |||
289.4.a.g.1.2 | 12 | 51.11 | even | 16 | |||
289.4.b.e.288.11 | 12 | 51.44 | even | 16 | |||
289.4.b.e.288.12 | 12 | 51.41 | even | 16 |