Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [242,4,Mod(3,242)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(242, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("242.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 242 = 2 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 242.c (of order \(5\), degree \(4\), not 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: | \(14.2784622214\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 9.2 | ||
Root | \(2.22300 - 6.84169i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 242.9 |
Dual form | 242.4.c.q.27.2 |
$q$-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 \(\left(\mathbb{Z}/242\mathbb{Z}\right)^\times\).
\(n\) | \(123\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.618034 | − | 1.90211i | 0.218508 | − | 0.672499i | ||||
\(3\) | 6.31989 | − | 4.59167i | 1.21626 | − | 0.883667i | 0.220479 | − | 0.975392i | \(-0.429238\pi\) |
0.995784 | + | 0.0917244i | \(0.0292379\pi\) | |||||||
\(4\) | −3.23607 | − | 2.35114i | −0.404508 | − | 0.293893i | ||||
\(5\) | 4.60996 | + | 14.1880i | 0.412327 | + | 1.26901i | 0.914620 | + | 0.404315i | \(0.132490\pi\) |
−0.502293 | + | 0.864698i | \(0.667510\pi\) | |||||||
\(6\) | −4.82797 | − | 14.8590i | −0.328502 | − | 1.01102i | ||||
\(7\) | 17.6106 | + | 12.7948i | 0.950881 | + | 0.690856i | 0.951015 | − | 0.309144i | \(-0.100043\pi\) |
−0.000134039 | 1.00000i | \(0.500043\pi\) | ||||||||
\(8\) | −6.47214 | + | 4.70228i | −0.286031 | + | 0.207813i | ||||
\(9\) | 10.5141 | − | 32.3592i | 0.389412 | − | 1.19849i | ||||
\(10\) | 29.8363 | 0.943506 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −31.2473 | −0.751692 | ||||||||
\(13\) | 13.6056 | − | 41.8736i | 0.290270 | − | 0.893358i | −0.694500 | − | 0.719493i | \(-0.744374\pi\) |
0.984769 | − | 0.173865i | \(-0.0556258\pi\) | |||||||
\(14\) | 35.2211 | − | 25.5896i | 0.672374 | − | 0.488509i | ||||
\(15\) | 94.2810 | + | 68.4992i | 1.62288 | + | 1.17909i | ||||
\(16\) | 4.94427 | + | 15.2169i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 7.69900 | + | 23.6951i | 0.109840 | + | 0.338053i | 0.990836 | − | 0.135071i | \(-0.0431262\pi\) |
−0.880996 | + | 0.473124i | \(0.843126\pi\) | |||||||
\(18\) | −55.0527 | − | 39.9982i | −0.720892 | − | 0.523759i | ||||
\(19\) | 17.7638 | − | 12.9061i | 0.214489 | − | 0.155835i | −0.475353 | − | 0.879795i | \(-0.657680\pi\) |
0.689842 | + | 0.723960i | \(0.257680\pi\) | |||||||
\(20\) | 18.4398 | − | 56.7520i | 0.206164 | − | 0.634506i | ||||
\(21\) | 170.046 | 1.76701 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 177.749 | 1.61145 | 0.805723 | − | 0.592293i | \(-0.201777\pi\) | ||||
0.805723 | + | 0.592293i | \(0.201777\pi\) | |||||||
\(24\) | −19.3119 | + | 59.4358i | −0.164251 | + | 0.505512i | ||||
\(25\) | −78.9203 | + | 57.3389i | −0.631362 | + | 0.458711i | ||||
\(26\) | −71.2397 | − | 51.7587i | −0.537356 | − | 0.390412i | ||||
\(27\) | −16.9569 | − | 52.1881i | −0.120865 | − | 0.371985i | ||||
\(28\) | −26.9065 | − | 82.8098i | −0.181602 | − | 0.558914i | ||||
\(29\) | −120.864 | − | 87.8130i | −0.773928 | − | 0.562292i | 0.129223 | − | 0.991616i | \(-0.458752\pi\) |
−0.903151 | + | 0.429324i | \(0.858752\pi\) | |||||||
\(30\) | 188.562 | − | 136.998i | 1.14755 | − | 0.833745i | ||||
\(31\) | 23.2207 | − | 71.4658i | 0.134534 | − | 0.414053i | −0.860983 | − | 0.508633i | \(-0.830151\pi\) |
0.995517 | + | 0.0945803i | \(0.0301509\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 49.8290 | 0.251341 | ||||||||
\(35\) | −100.349 | + | 308.842i | −0.484630 | + | 1.49154i | ||||
\(36\) | −110.105 | + | 79.9963i | −0.509748 | + | 0.370353i | ||||
\(37\) | −179.874 | − | 130.686i | −0.799219 | − | 0.580667i | 0.111466 | − | 0.993768i | \(-0.464445\pi\) |
−0.910685 | + | 0.413102i | \(0.864445\pi\) | |||||||
\(38\) | −13.5703 | − | 41.7652i | −0.0579315 | − | 0.178295i | ||||
\(39\) | −106.284 | − | 327.109i | −0.436387 | − | 1.34306i | ||||
\(40\) | −96.5522 | − | 70.1493i | −0.381656 | − | 0.277289i | ||||
\(41\) | −204.779 | + | 148.781i | −0.780029 | + | 0.566724i | −0.904988 | − | 0.425438i | \(-0.860120\pi\) |
0.124959 | + | 0.992162i | \(0.460120\pi\) | |||||||
\(42\) | 105.094 | − | 323.448i | 0.386106 | − | 1.18831i | ||||
\(43\) | −130.623 | −0.463253 | −0.231626 | − | 0.972805i | \(-0.574405\pi\) | ||||
−0.231626 | + | 0.972805i | \(0.574405\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 507.582 | 1.68146 | ||||||||
\(46\) | 109.855 | − | 338.099i | 0.352114 | − | 1.08369i | ||||
\(47\) | −403.775 | + | 293.360i | −1.25312 | + | 0.910445i | −0.998399 | − | 0.0565693i | \(-0.981984\pi\) |
−0.254722 | + | 0.967014i | \(0.581984\pi\) | |||||||
\(48\) | 101.118 | + | 73.4667i | 0.304066 | + | 0.220917i | ||||
\(49\) | 40.4316 | + | 124.436i | 0.117876 | + | 0.362786i | ||||
\(50\) | 60.2897 | + | 185.553i | 0.170525 | + | 0.524822i | ||||
\(51\) | 157.457 | + | 114.399i | 0.432321 | + | 0.314100i | ||||
\(52\) | −142.479 | + | 103.517i | −0.379968 | + | 0.276063i | ||||
\(53\) | 3.99933 | − | 12.3087i | 0.0103651 | − | 0.0319005i | −0.945740 | − | 0.324924i | \(-0.894661\pi\) |
0.956105 | + | 0.293023i | \(0.0946613\pi\) | |||||||
\(54\) | −109.748 | −0.276569 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −174.143 | −0.415550 | ||||||||
\(57\) | 53.0044 | − | 163.131i | 0.123169 | − | 0.379074i | ||||
\(58\) | −241.728 | + | 175.626i | −0.547250 | + | 0.397600i | ||||
\(59\) | −28.7697 | − | 20.9024i | −0.0634831 | − | 0.0461232i | 0.555591 | − | 0.831456i | \(-0.312492\pi\) |
−0.619074 | + | 0.785332i | \(0.712492\pi\) | |||||||
\(60\) | −144.049 | − | 443.336i | −0.309943 | − | 0.953907i | ||||
\(61\) | −166.357 | − | 511.995i | −0.349178 | − | 1.07466i | −0.959309 | − | 0.282359i | \(-0.908883\pi\) |
0.610131 | − | 0.792301i | \(-0.291117\pi\) | |||||||
\(62\) | −121.585 | − | 88.3366i | −0.249053 | − | 0.180948i | ||||
\(63\) | 599.190 | − | 435.337i | 1.19827 | − | 0.870592i | ||||
\(64\) | 19.7771 | − | 60.8676i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 656.824 | 1.25337 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −519.621 | −0.947491 | −0.473745 | − | 0.880662i | \(-0.657098\pi\) | ||||
−0.473745 | + | 0.880662i | \(0.657098\pi\) | |||||||
\(68\) | 30.7960 | − | 94.7804i | 0.0549201 | − | 0.169027i | ||||
\(69\) | 1123.35 | − | 816.165i | 1.95994 | − | 1.42398i | ||||
\(70\) | 525.434 | + | 381.750i | 0.897162 | + | 0.651826i | ||||
\(71\) | 24.2420 | + | 74.6091i | 0.0405210 | + | 0.124711i | 0.969271 | − | 0.245997i | \(-0.0791152\pi\) |
−0.928750 | + | 0.370708i | \(0.879115\pi\) | |||||||
\(72\) | 84.1131 | + | 258.873i | 0.137678 | + | 0.423730i | ||||
\(73\) | 925.571 | + | 672.467i | 1.48397 | + | 1.07817i | 0.976250 | + | 0.216648i | \(0.0695123\pi\) |
0.507722 | + | 0.861521i | \(0.330488\pi\) | |||||||
\(74\) | −359.748 | + | 261.372i | −0.565133 | + | 0.410593i | ||||
\(75\) | −235.486 | + | 724.752i | −0.362555 | + | 1.11583i | ||||
\(76\) | −87.8290 | −0.132562 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −687.886 | −0.998561 | ||||||||
\(79\) | −238.730 | + | 734.735i | −0.339990 | + | 1.04638i | 0.624222 | + | 0.781247i | \(0.285416\pi\) |
−0.964212 | + | 0.265134i | \(0.914584\pi\) | |||||||
\(80\) | −193.104 | + | 140.299i | −0.269872 | + | 0.196073i | ||||
\(81\) | 396.416 | + | 288.013i | 0.543780 | + | 0.395079i | ||||
\(82\) | 156.438 | + | 481.465i | 0.210678 | + | 0.648402i | ||||
\(83\) | −166.017 | − | 510.947i | −0.219551 | − | 0.675708i | −0.998799 | − | 0.0489926i | \(-0.984399\pi\) |
0.779248 | − | 0.626715i | \(-0.215601\pi\) | |||||||
\(84\) | −550.282 | − | 399.803i | −0.714770 | − | 0.519311i | ||||
\(85\) | −300.694 | + | 218.467i | −0.383704 | + | 0.278777i | ||||
\(86\) | −80.7296 | + | 248.460i | −0.101224 | + | 0.311537i | ||||
\(87\) | −1167.06 | −1.43818 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 667.089 | 0.794509 | 0.397255 | − | 0.917708i | \(-0.369963\pi\) | ||||
0.397255 | + | 0.917708i | \(0.369963\pi\) | |||||||
\(90\) | 313.703 | − | 965.477i | 0.367413 | − | 1.13078i | ||||
\(91\) | 775.368 | − | 563.338i | 0.893194 | − | 0.648943i | ||||
\(92\) | −575.208 | − | 417.913i | −0.651843 | − | 0.473592i | ||||
\(93\) | −181.395 | − | 558.278i | −0.202256 | − | 0.622481i | ||||
\(94\) | 308.457 | + | 949.332i | 0.338456 | + | 1.04166i | ||||
\(95\) | 265.003 | + | 192.536i | 0.286197 | + | 0.207934i | ||||
\(96\) | 202.237 | − | 146.933i | 0.215007 | − | 0.156212i | ||||
\(97\) | −55.5161 | + | 170.861i | −0.0581114 | + | 0.178848i | −0.975899 | − | 0.218224i | \(-0.929974\pi\) |
0.917787 | + | 0.397072i | \(0.129974\pi\) | |||||||
\(98\) | 261.679 | 0.269730 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 390.203 | 0.390203 | ||||||||
\(101\) | 126.924 | − | 390.633i | 0.125044 | − | 0.384846i | −0.868865 | − | 0.495049i | \(-0.835150\pi\) |
0.993909 | + | 0.110203i | \(0.0351502\pi\) | |||||||
\(102\) | 314.914 | − | 228.798i | 0.305697 | − | 0.222102i | ||||
\(103\) | −1106.46 | − | 803.890i | −1.05847 | − | 0.769026i | −0.0846679 | − | 0.996409i | \(-0.526983\pi\) |
−0.973805 | + | 0.227383i | \(0.926983\pi\) | |||||||
\(104\) | 108.845 | + | 334.989i | 0.102626 | + | 0.315850i | ||||
\(105\) | 783.907 | + | 2412.62i | 0.728586 | + | 2.24236i | ||||
\(106\) | −20.9408 | − | 15.2144i | −0.0191882 | − | 0.0139410i | ||||
\(107\) | −319.756 | + | 232.317i | −0.288897 | + | 0.209896i | −0.722789 | − | 0.691069i | \(-0.757140\pi\) |
0.433892 | + | 0.900965i | \(0.357140\pi\) | |||||||
\(108\) | −67.8277 | + | 208.752i | −0.0604326 | + | 0.185993i | ||||
\(109\) | −505.826 | −0.444490 | −0.222245 | − | 0.974991i | \(-0.571338\pi\) | ||||
−0.222245 | + | 0.974991i | \(0.571338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1736.85 | −1.48518 | ||||||||
\(112\) | −107.626 | + | 331.239i | −0.0908011 | + | 0.279457i | ||||
\(113\) | −1243.96 | + | 903.793i | −1.03560 | + | 0.752404i | −0.969421 | − | 0.245404i | \(-0.921079\pi\) |
−0.0661744 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(114\) | −277.535 | − | 201.641i | −0.228013 | − | 0.165661i | ||||
\(115\) | 819.416 | + | 2521.90i | 0.664443 | + | 2.04494i | ||||
\(116\) | 184.664 | + | 568.337i | 0.147807 | + | 0.454903i | ||||
\(117\) | −1211.95 | − | 880.530i | −0.957645 | − | 0.695770i | ||||
\(118\) | −57.5395 | + | 41.8049i | −0.0448893 | + | 0.0326140i | ||||
\(119\) | −167.591 | + | 515.791i | −0.129101 | + | 0.397332i | ||||
\(120\) | −932.302 | −0.709226 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1076.69 | −0.799005 | ||||||||
\(123\) | −611.031 | + | 1880.56i | −0.447925 | + | 1.37857i | ||||
\(124\) | −243.170 | + | 176.673i | −0.176107 | + | 0.127949i | ||||
\(125\) | 331.285 | + | 240.693i | 0.237048 | + | 0.172226i | ||||
\(126\) | −457.740 | − | 1408.78i | −0.323641 | − | 0.996064i | ||||
\(127\) | 215.487 | + | 663.202i | 0.150562 | + | 0.463383i | 0.997684 | − | 0.0680154i | \(-0.0216667\pi\) |
−0.847122 | + | 0.531399i | \(0.821667\pi\) | |||||||
\(128\) | −103.554 | − | 75.2365i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | −825.525 | + | 599.779i | −0.563437 | + | 0.409361i | ||||
\(130\) | 405.940 | − | 1249.35i | 0.273871 | − | 0.842889i | ||||
\(131\) | 259.910 | 0.173347 | 0.0866735 | − | 0.996237i | \(-0.472376\pi\) | ||||
0.0866735 | + | 0.996237i | \(0.472376\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 477.962 | 0.311613 | ||||||||
\(134\) | −321.144 | + | 988.379i | −0.207034 | + | 0.637186i | ||||
\(135\) | 662.273 | − | 481.170i | 0.422218 | − | 0.306759i | ||||
\(136\) | −161.250 | − | 117.155i | −0.101670 | − | 0.0738673i | ||||
\(137\) | −643.856 | − | 1981.58i | −0.401520 | − | 1.23575i | −0.923766 | − | 0.382958i | \(-0.874906\pi\) |
0.522245 | − | 0.852795i | \(-0.325094\pi\) | |||||||
\(138\) | −858.167 | − | 2641.17i | −0.529362 | − | 1.62921i | ||||
\(139\) | 140.307 | + | 101.939i | 0.0856163 | + | 0.0622039i | 0.629770 | − | 0.776782i | \(-0.283149\pi\) |
−0.544154 | + | 0.838986i | \(0.683149\pi\) | |||||||
\(140\) | 1050.87 | − | 763.500i | 0.634389 | − | 0.460911i | ||||
\(141\) | −1204.80 | + | 3708.00i | −0.719594 | + | 2.21468i | ||||
\(142\) | 156.897 | 0.0927220 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 544.391 | 0.315041 | ||||||||
\(145\) | 688.711 | − | 2119.63i | 0.394444 | − | 1.21397i | ||||
\(146\) | 1851.14 | − | 1344.93i | 1.04933 | − | 0.762380i | ||||
\(147\) | 826.891 | + | 600.772i | 0.463951 | + | 0.337080i | ||||
\(148\) | 274.823 | + | 845.818i | 0.152637 | + | 0.469769i | ||||
\(149\) | 138.766 | + | 427.077i | 0.0762961 | + | 0.234815i | 0.981930 | − | 0.189246i | \(-0.0606042\pi\) |
−0.905634 | + | 0.424061i | \(0.860604\pi\) | |||||||
\(150\) | 1233.02 | + | 895.842i | 0.671172 | + | 0.487635i | ||||
\(151\) | 23.0859 | − | 16.7729i | 0.0124418 | − | 0.00903947i | −0.581547 | − | 0.813513i | \(-0.697552\pi\) |
0.593989 | + | 0.804473i | \(0.297552\pi\) | |||||||
\(152\) | −54.2813 | + | 167.061i | −0.0289658 | + | 0.0891474i | ||||
\(153\) | 847.702 | 0.447926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1121.00 | 0.580910 | ||||||||
\(156\) | −425.137 | + | 1308.44i | −0.218194 | + | 0.671531i | ||||
\(157\) | −1394.63 | + | 1013.26i | −0.708941 | + | 0.515076i | −0.882832 | − | 0.469689i | \(-0.844366\pi\) |
0.173891 | + | 0.984765i | \(0.444366\pi\) | |||||||
\(158\) | 1250.01 | + | 908.182i | 0.629399 | + | 0.457285i | ||||
\(159\) | −31.2420 | − | 96.1531i | −0.0155827 | − | 0.0479587i | ||||
\(160\) | 147.519 | + | 454.016i | 0.0728898 | + | 0.224332i | ||||
\(161\) | 3130.26 | + | 2274.27i | 1.53229 | + | 1.11328i | ||||
\(162\) | 792.831 | − | 576.026i | 0.384510 | − | 0.279363i | ||||
\(163\) | 1025.39 | − | 3155.82i | 0.492727 | − | 1.51646i | −0.327743 | − | 0.944767i | \(-0.606288\pi\) |
0.820470 | − | 0.571690i | \(-0.193712\pi\) | |||||||
\(164\) | 1012.49 | 0.482084 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1074.48 | −0.502386 | ||||||||
\(167\) | 931.871 | − | 2868.00i | 0.431799 | − | 1.32894i | −0.464533 | − | 0.885556i | \(-0.653778\pi\) |
0.896332 | − | 0.443384i | \(-0.146222\pi\) | |||||||
\(168\) | −1100.56 | + | 799.606i | −0.505419 | + | 0.367208i | ||||
\(169\) | 209.120 | + | 151.934i | 0.0951842 | + | 0.0691554i | ||||
\(170\) | 229.710 | + | 706.973i | 0.103635 | + | 0.318955i | ||||
\(171\) | −230.862 | − | 710.519i | −0.103242 | − | 0.317747i | ||||
\(172\) | 422.706 | + | 307.114i | 0.187390 | + | 0.136147i | ||||
\(173\) | −1787.45 | + | 1298.66i | −0.785534 | + | 0.570724i | −0.906635 | − | 0.421917i | \(-0.861357\pi\) |
0.121101 | + | 0.992640i | \(0.461357\pi\) | |||||||
\(174\) | −721.281 | + | 2219.87i | −0.314254 | + | 0.967173i | ||||
\(175\) | −2123.47 | −0.917254 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −277.799 | −0.117970 | ||||||||
\(178\) | 412.284 | − | 1268.88i | 0.173607 | − | 0.534306i | ||||
\(179\) | 1837.95 | − | 1335.35i | 0.767457 | − | 0.557590i | −0.133731 | − | 0.991018i | \(-0.542696\pi\) |
0.901189 | + | 0.433427i | \(0.142696\pi\) | |||||||
\(180\) | −1642.57 | − | 1193.40i | −0.680166 | − | 0.494169i | ||||
\(181\) | −192.961 | − | 593.873i | −0.0792413 | − | 0.243880i | 0.903586 | − | 0.428406i | \(-0.140925\pi\) |
−0.982828 | + | 0.184527i | \(0.940925\pi\) | |||||||
\(182\) | −592.328 | − | 1823.00i | −0.241243 | − | 0.742471i | ||||
\(183\) | −3402.27 | − | 2471.89i | −1.37433 | − | 0.998512i | ||||
\(184\) | −1150.42 | + | 835.826i | −0.460923 | + | 0.334880i | ||||
\(185\) | 1024.96 | − | 3154.51i | 0.407333 | − | 1.25364i | ||||
\(186\) | −1174.02 | −0.462812 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1996.37 | 0.774471 | ||||||||
\(189\) | 369.116 | − | 1136.02i | 0.142059 | − | 0.437214i | ||||
\(190\) | 530.005 | − | 385.071i | 0.202372 | − | 0.147032i | ||||
\(191\) | 1087.48 | + | 790.100i | 0.411975 | + | 0.299317i | 0.774401 | − | 0.632695i | \(-0.218051\pi\) |
−0.362426 | + | 0.932013i | \(0.618051\pi\) | |||||||
\(192\) | −154.495 | − | 475.487i | −0.0580714 | − | 0.178725i | ||||
\(193\) | −1428.82 | − | 4397.46i | −0.532895 | − | 1.64008i | −0.748154 | − | 0.663526i | \(-0.769059\pi\) |
0.215258 | − | 0.976557i | \(-0.430941\pi\) | |||||||
\(194\) | 290.686 | + | 211.196i | 0.107578 | + | 0.0781597i | ||||
\(195\) | 4151.06 | − | 3015.92i | 1.52443 | − | 1.10756i | ||||
\(196\) | 161.726 | − | 497.743i | 0.0589382 | − | 0.181393i | ||||
\(197\) | −664.691 | −0.240392 | −0.120196 | − | 0.992750i | \(-0.538352\pi\) | ||||
−0.120196 | + | 0.992750i | \(0.538352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3042.82 | −1.08392 | −0.541959 | − | 0.840405i | \(-0.682317\pi\) | ||||
−0.541959 | + | 0.840405i | \(0.682317\pi\) | |||||||
\(200\) | 241.159 | − | 742.211i | 0.0852625 | − | 0.262411i | ||||
\(201\) | −3283.95 | + | 2385.93i | −1.15240 | + | 0.837266i | ||||
\(202\) | −664.584 | − | 482.849i | −0.231485 | − | 0.168184i | ||||
\(203\) | −1004.93 | − | 3092.87i | −0.347451 | − | 1.06934i | ||||
\(204\) | −240.573 | − | 740.407i | −0.0825660 | − | 0.254112i | ||||
\(205\) | −3054.93 | − | 2219.53i | −1.04081 | − | 0.756190i | ||||
\(206\) | −2212.92 | + | 1607.78i | −0.748454 | + | 0.543783i | ||||
\(207\) | 1868.88 | − | 5751.81i | 0.627517 | − | 1.93130i | ||||
\(208\) | 704.457 | 0.234833 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 5073.55 | 1.66718 | ||||||||
\(211\) | −800.851 | + | 2464.77i | −0.261293 | + | 0.804178i | 0.731231 | + | 0.682130i | \(0.238946\pi\) |
−0.992524 | + | 0.122048i | \(0.961054\pi\) | |||||||
\(212\) | −41.8815 | + | 30.4287i | −0.0135681 | + | 0.00985779i | ||||
\(213\) | 495.787 | + | 360.210i | 0.159487 | + | 0.115874i | ||||
\(214\) | 244.272 | + | 751.792i | 0.0780285 | + | 0.240147i | ||||
\(215\) | −602.168 | − | 1853.28i | −0.191012 | − | 0.587873i | ||||
\(216\) | 355.151 | + | 258.032i | 0.111875 | + | 0.0812817i | ||||
\(217\) | 1323.32 | − | 961.449i | 0.413977 | − | 0.300772i | ||||
\(218\) | −312.618 | + | 962.139i | −0.0971245 | + | 0.298919i | ||||
\(219\) | 8937.26 | 2.75764 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1096.95 | 0.333886 | ||||||||
\(222\) | −1073.43 | + | 3303.69i | −0.324523 | + | 0.998779i | ||||
\(223\) | −2133.54 | + | 1550.11i | −0.640684 | + | 0.465484i | −0.860085 | − | 0.510150i | \(-0.829590\pi\) |
0.219401 | + | 0.975635i | \(0.429590\pi\) | |||||||
\(224\) | 563.538 | + | 409.434i | 0.168094 | + | 0.122127i | ||||
\(225\) | 1025.66 | + | 3156.66i | 0.303900 | + | 0.935308i | ||||
\(226\) | 950.304 | + | 2924.73i | 0.279705 | + | 0.860843i | ||||
\(227\) | 202.796 | + | 147.340i | 0.0592954 | + | 0.0430806i | 0.617038 | − | 0.786933i | \(-0.288332\pi\) |
−0.557743 | + | 0.830014i | \(0.688332\pi\) | |||||||
\(228\) | −555.070 | + | 403.282i | −0.161230 | + | 0.117140i | ||||
\(229\) | 556.018 | − | 1711.25i | 0.160449 | − | 0.493810i | −0.838224 | − | 0.545327i | \(-0.816406\pi\) |
0.998672 | + | 0.0515169i | \(0.0164056\pi\) | |||||||
\(230\) | 5303.37 | 1.52041 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1195.17 | 0.338219 | ||||||||
\(233\) | −982.821 | + | 3024.81i | −0.276338 | + | 0.850481i | 0.712524 | + | 0.701647i | \(0.247552\pi\) |
−0.988862 | + | 0.148833i | \(0.952448\pi\) | |||||||
\(234\) | −2423.89 | + | 1761.06i | −0.677157 | + | 0.491984i | ||||
\(235\) | −6023.57 | − | 4376.38i | −1.67206 | − | 1.21482i | ||||
\(236\) | 43.9563 | + | 135.283i | 0.0121242 | + | 0.0373144i | ||||
\(237\) | 1864.91 | + | 5739.61i | 0.511135 | + | 1.57311i | ||||
\(238\) | 877.517 | + | 637.553i | 0.238996 | + | 0.173641i | ||||
\(239\) | 4056.25 | − | 2947.04i | 1.09781 | − | 0.797608i | 0.117111 | − | 0.993119i | \(-0.462637\pi\) |
0.980701 | + | 0.195511i | \(0.0626366\pi\) | |||||||
\(240\) | −576.194 | + | 1773.34i | −0.154972 | + | 0.476953i | ||||
\(241\) | −6074.13 | −1.62352 | −0.811761 | − | 0.583990i | \(-0.801491\pi\) | ||||
−0.811761 | + | 0.583990i | \(0.801491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5309.35 | 1.40163 | ||||||||
\(244\) | −665.429 | + | 2047.98i | −0.174589 | + | 0.537330i | ||||
\(245\) | −1579.10 | + | 1147.29i | −0.411777 | + | 0.299173i | ||||
\(246\) | 3199.40 | + | 2324.50i | 0.829212 | + | 0.602458i | ||||
\(247\) | −298.741 | − | 919.430i | −0.0769572 | − | 0.236850i | ||||
\(248\) | 185.765 | + | 571.727i | 0.0475649 | + | 0.146390i | ||||
\(249\) | −3395.31 | − | 2466.84i | −0.864132 | − | 0.627829i | ||||
\(250\) | 662.570 | − | 481.385i | 0.167618 | − | 0.121782i | ||||
\(251\) | −1721.13 | + | 5297.09i | −0.432816 | + | 1.33207i | 0.462493 | + | 0.886623i | \(0.346955\pi\) |
−0.895309 | + | 0.445447i | \(0.853045\pi\) | |||||||
\(252\) | −2962.56 | −0.740570 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1394.66 | 0.344524 | ||||||||
\(255\) | −897.224 | + | 2761.37i | −0.220339 | + | 0.678133i | ||||
\(256\) | −207.108 | + | 150.473i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 4778.90 | + | 3472.08i | 1.15992 | + | 0.842732i | 0.989768 | − | 0.142685i | \(-0.0455737\pi\) |
0.170153 | + | 0.985418i | \(0.445574\pi\) | |||||||
\(258\) | 630.645 | + | 1940.93i | 0.152179 | + | 0.468359i | ||||
\(259\) | −1495.58 | − | 4602.91i | −0.358805 | − | 1.10429i | ||||
\(260\) | −2125.53 | − | 1544.29i | −0.506998 | − | 0.368356i | ||||
\(261\) | −4112.34 | + | 2987.79i | −0.975277 | + | 0.708580i | ||||
\(262\) | 160.633 | − | 494.379i | 0.0378777 | − | 0.116576i | ||||
\(263\) | 6853.74 | 1.60692 | 0.803459 | − | 0.595360i | \(-0.202991\pi\) | ||||
0.803459 | + | 0.595360i | \(0.202991\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 193.072 | 0.0447559 | ||||||||
\(266\) | 295.397 | − | 909.138i | 0.0680900 | − | 0.209560i | ||||
\(267\) | 4215.93 | − | 3063.05i | 0.966333 | − | 0.702082i | ||||
\(268\) | 1681.53 | + | 1221.70i | 0.383268 | + | 0.278460i | ||||
\(269\) | 340.340 | + | 1047.46i | 0.0771409 | + | 0.237415i | 0.982190 | − | 0.187893i | \(-0.0601657\pi\) |
−0.905049 | + | 0.425308i | \(0.860166\pi\) | |||||||
\(270\) | −505.932 | − | 1557.10i | −0.114037 | − | 0.350970i | ||||
\(271\) | −2080.54 | − | 1511.60i | −0.466362 | − | 0.338832i | 0.329660 | − | 0.944100i | \(-0.393066\pi\) |
−0.796022 | + | 0.605268i | \(0.793066\pi\) | |||||||
\(272\) | −322.500 | + | 234.310i | −0.0718913 | + | 0.0522321i | ||||
\(273\) | 2313.58 | − | 7120.46i | 0.512909 | − | 1.57857i | ||||
\(274\) | −4167.12 | −0.918777 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5554.17 | −1.21131 | ||||||||
\(277\) | 2268.22 | − | 6980.85i | 0.492000 | − | 1.51422i | −0.329581 | − | 0.944127i | \(-0.606908\pi\) |
0.821581 | − | 0.570092i | \(-0.193092\pi\) | |||||||
\(278\) | 280.613 | − | 203.878i | 0.0605398 | − | 0.0439848i | ||||
\(279\) | −2068.43 | − | 1502.80i | −0.443848 | − | 0.322475i | ||||
\(280\) | −802.791 | − | 2470.74i | −0.171343 | − | 0.527338i | ||||
\(281\) | 2315.45 | + | 7126.21i | 0.491559 | + | 1.51286i | 0.822252 | + | 0.569124i | \(0.192718\pi\) |
−0.330693 | + | 0.943738i | \(0.607282\pi\) | |||||||
\(282\) | 6308.43 | + | 4583.34i | 1.33213 | + | 0.967852i | ||||
\(283\) | −5253.84 | + | 3817.14i | −1.10356 | + | 0.801785i | −0.981638 | − | 0.190754i | \(-0.938907\pi\) |
−0.121925 | + | 0.992539i | \(0.538907\pi\) | |||||||
\(284\) | 96.9678 | − | 298.436i | 0.0202605 | − | 0.0623554i | ||||
\(285\) | 2558.85 | 0.531835 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5509.91 | −1.13324 | ||||||||
\(288\) | 336.452 | − | 1035.49i | 0.0688390 | − | 0.211865i | ||||
\(289\) | 3472.52 | − | 2522.93i | 0.706802 | − | 0.513522i | ||||
\(290\) | −3606.14 | − | 2620.01i | −0.730206 | − | 0.530525i | ||||
\(291\) | 433.681 | + | 1334.73i | 0.0873638 | + | 0.268878i | ||||
\(292\) | −1414.15 | − | 4352.30i | −0.283413 | − | 0.872257i | ||||
\(293\) | −2172.11 | − | 1578.13i | −0.433092 | − | 0.314660i | 0.349792 | − | 0.936827i | \(-0.386252\pi\) |
−0.782884 | + | 0.622168i | \(0.786252\pi\) | |||||||
\(294\) | 1653.78 | − | 1201.54i | 0.328063 | − | 0.238352i | ||||
\(295\) | 163.936 | − | 504.544i | 0.0323551 | − | 0.0995787i | ||||
\(296\) | 1778.69 | 0.349271 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 898.110 | 0.174584 | ||||||||
\(299\) | 2418.38 | − | 7443.00i | 0.467754 | − | 1.43960i | ||||
\(300\) | 2466.04 | − | 1791.68i | 0.474590 | − | 0.344810i | ||||
\(301\) | −2300.35 | − | 1671.30i | −0.440498 | − | 0.320041i | ||||
\(302\) | −17.6361 | − | 54.2783i | −0.00336041 | − | 0.0103423i | ||||
\(303\) | −991.509 | − | 3051.55i | −0.187989 | − | 0.578571i | ||||
\(304\) | 284.221 | + | 206.498i | 0.0536223 | + | 0.0389589i | ||||
\(305\) | 6497.28 | − | 4720.55i | 1.21978 | − | 0.886223i | ||||
\(306\) | 523.909 | − | 1612.43i | 0.0978754 | − | 0.301230i | ||||
\(307\) | −8331.66 | −1.54890 | −0.774451 | − | 0.632633i | \(-0.781974\pi\) | ||||
−0.774451 | + | 0.632633i | \(0.781974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10683.9 | −1.96695 | ||||||||
\(310\) | 692.818 | − | 2132.27i | 0.126934 | − | 0.390661i | ||||
\(311\) | 4061.55 | − | 2950.89i | 0.740545 | − | 0.538037i | −0.152337 | − | 0.988329i | \(-0.548680\pi\) |
0.892882 | + | 0.450292i | \(0.148680\pi\) | |||||||
\(312\) | 2226.05 | + | 1617.32i | 0.403926 | + | 0.293470i | ||||
\(313\) | 933.873 | + | 2874.16i | 0.168644 | + | 0.519033i | 0.999286 | − | 0.0377733i | \(-0.0120265\pi\) |
−0.830642 | + | 0.556807i | \(0.812026\pi\) | |||||||
\(314\) | 1065.40 | + | 3278.98i | 0.191479 | + | 0.589310i | ||||
\(315\) | 8938.80 | + | 6494.42i | 1.59887 | + | 1.16165i | ||||
\(316\) | 2500.01 | − | 1816.36i | 0.445052 | − | 0.323350i | ||||
\(317\) | −3257.08 | + | 10024.3i | −0.577085 | + | 1.77609i | 0.0518809 | + | 0.998653i | \(0.483478\pi\) |
−0.628966 | + | 0.777433i | \(0.716522\pi\) | |||||||
\(318\) | −202.203 | −0.0356571 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 954.761 | 0.166790 | ||||||||
\(321\) | −954.104 | + | 2936.43i | −0.165897 | + | 0.510578i | ||||
\(322\) | 6260.52 | − | 4548.54i | 1.08349 | − | 0.787205i | ||||
\(323\) | 442.576 | + | 321.550i | 0.0762402 | + | 0.0553917i | ||||
\(324\) | −605.669 | − | 1864.06i | −0.103853 | − | 0.319626i | ||||
\(325\) | 1327.23 | + | 4084.81i | 0.226528 | + | 0.697183i | ||||
\(326\) | −5368.99 | − | 3900.80i | −0.912150 | − | 0.662716i | ||||
\(327\) | −3196.77 | + | 2322.59i | −0.540617 | + | 0.392781i | ||||
\(328\) | 625.750 | − | 1925.86i | 0.105339 | − | 0.324201i | ||||
\(329\) | −10864.2 | −1.82055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 309.871 | 0.0514563 | 0.0257281 | − | 0.999669i | \(-0.491810\pi\) | ||||
0.0257281 | + | 0.999669i | \(0.491810\pi\) | |||||||
\(332\) | −664.067 | + | 2043.79i | −0.109775 | + | 0.337854i | ||||
\(333\) | −6120.11 | + | 4446.52i | −1.00715 | + | 0.731736i | ||||
\(334\) | −4879.34 | − | 3545.05i | −0.799358 | − | 0.580768i | ||||
\(335\) | −2395.43 | − | 7372.39i | −0.390676 | − | 1.20238i | ||||
\(336\) | 840.756 | + | 2587.58i | 0.136509 | + | 0.420131i | ||||
\(337\) | 9032.40 | + | 6562.42i | 1.46002 | + | 1.06076i | 0.983358 | + | 0.181677i | \(0.0581525\pi\) |
0.476659 | + | 0.879088i | \(0.341848\pi\) | |||||||
\(338\) | 418.239 | − | 303.869i | 0.0673054 | − | 0.0489002i | ||||
\(339\) | −3711.80 | + | 11423.7i | −0.594682 | + | 1.83024i | ||||
\(340\) | 1486.71 | 0.237142 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1494.17 | −0.236244 | ||||||||
\(343\) | 1427.13 | − | 4392.25i | 0.224658 | − | 0.691425i | ||||
\(344\) | 845.412 | − | 614.227i | 0.132504 | − | 0.0962701i | ||||
\(345\) | 16758.4 | + | 12175.7i | 2.61519 | + | 1.90005i | ||||
\(346\) | 1365.49 | + | 4202.55i | 0.212165 | + | 0.652978i | ||||
\(347\) | −777.327 | − | 2392.37i | −0.120257 | − | 0.370112i | 0.872750 | − | 0.488167i | \(-0.162334\pi\) |
−0.993007 | + | 0.118055i | \(0.962334\pi\) | |||||||
\(348\) | 3776.67 | + | 2743.91i | 0.581756 | + | 0.422670i | ||||
\(349\) | −9203.85 | + | 6686.99i | −1.41166 | + | 1.02563i | −0.418587 | + | 0.908177i | \(0.637474\pi\) |
−0.993078 | + | 0.117457i | \(0.962526\pi\) | |||||||
\(350\) | −1312.38 | + | 4039.08i | −0.200427 | + | 0.616852i | ||||
\(351\) | −2416.01 | −0.367400 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6210.08 | 0.936343 | 0.468172 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468172 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(354\) | −171.689 | + | 528.405i | −0.0257773 | + | 0.0793344i | ||||
\(355\) | −946.799 | + | 687.889i | −0.141552 | + | 0.102843i | ||||
\(356\) | −2158.75 | − | 1568.42i | −0.321386 | − | 0.233500i | ||||
\(357\) | 1309.19 | + | 4029.27i | 0.194088 | + | 0.597343i | ||||
\(358\) | −1404.07 | − | 4321.28i | −0.207283 | − | 0.637952i | ||||
\(359\) | −2012.43 | − | 1462.12i | −0.295856 | − | 0.214952i | 0.429948 | − | 0.902854i | \(-0.358532\pi\) |
−0.725804 | + | 0.687902i | \(0.758532\pi\) | |||||||
\(360\) | −3285.14 | + | 2386.79i | −0.480950 | + | 0.349430i | ||||
\(361\) | −1970.56 | + | 6064.77i | −0.287296 | + | 0.884207i | ||||
\(362\) | −1248.87 | −0.181324 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3833.63 | −0.552024 | ||||||||
\(365\) | −5274.11 | + | 16232.0i | −0.756328 | + | 2.32774i | ||||
\(366\) | −6804.54 | + | 4943.79i | −0.971801 | + | 0.706055i | ||||
\(367\) | −5436.21 | − | 3949.64i | −0.773209 | − | 0.561770i | 0.129724 | − | 0.991550i | \(-0.458591\pi\) |
−0.902933 | + | 0.429781i | \(0.858591\pi\) | |||||||
\(368\) | 878.840 | + | 2704.79i | 0.124491 | + | 0.383144i | ||||
\(369\) | 2661.35 | + | 8190.80i | 0.375459 | + | 1.15554i | ||||
\(370\) | −5366.77 | − | 3899.19i | −0.754068 | − | 0.547862i | ||||
\(371\) | 227.918 | − | 165.592i | 0.0318946 | − | 0.0231728i | ||||
\(372\) | −725.582 | + | 2233.11i | −0.101128 | + | 0.311240i | ||||
\(373\) | 8614.37 | 1.19580 | 0.597902 | − | 0.801569i | \(-0.296001\pi\) | ||||
0.597902 | + | 0.801569i | \(0.296001\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3198.87 | 0.440503 | ||||||||
\(376\) | 1233.83 | − | 3797.33i | 0.169228 | − | 0.520831i | ||||
\(377\) | −5321.47 | + | 3866.28i | −0.726976 | + | 0.528179i | ||||
\(378\) | −1932.72 | − | 1404.20i | −0.262985 | − | 0.191070i | ||||
\(379\) | −2474.95 | − | 7617.10i | −0.335434 | − | 1.03236i | −0.966508 | − | 0.256637i | \(-0.917386\pi\) |
0.631074 | − | 0.775723i | \(-0.282614\pi\) | |||||||
\(380\) | −404.888 | − | 1246.12i | −0.0546587 | − | 0.168222i | ||||
\(381\) | 4407.06 | + | 3201.92i | 0.592600 | + | 0.430549i | ||||
\(382\) | 2174.96 | − | 1580.20i | 0.291310 | − | 0.211649i | ||||
\(383\) | 2475.83 | − | 7619.82i | 0.330310 | − | 1.01659i | −0.638676 | − | 0.769476i | \(-0.720517\pi\) |
0.968986 | − | 0.247115i | \(-0.0794826\pi\) | |||||||
\(384\) | −999.912 | −0.132882 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9247.52 | −1.21940 | ||||||||
\(387\) | −1373.39 | + | 4226.86i | −0.180396 | + | 0.555203i | ||||
\(388\) | 581.372 | − | 422.392i | 0.0760688 | − | 0.0552672i | ||||
\(389\) | −6496.09 | − | 4719.68i | −0.846696 | − | 0.615160i | 0.0775373 | − | 0.996989i | \(-0.475294\pi\) |
−0.924233 | + | 0.381829i | \(0.875294\pi\) | |||||||
\(390\) | −3171.13 | − | 9759.72i | −0.411734 | − | 1.26719i | ||||
\(391\) | 1368.49 | + | 4211.78i | 0.177001 | + | 0.544754i | ||||
\(392\) | −846.811 | − | 615.244i | −0.109108 | − | 0.0792717i | ||||
\(393\) | 1642.60 | − | 1193.42i | 0.210836 | − | 0.153181i | ||||
\(394\) | −410.801 | + | 1264.32i | −0.0525276 | + | 0.161663i | ||||
\(395\) | −11524.9 | −1.46806 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4435.00 | 0.560670 | 0.280335 | − | 0.959902i | \(-0.409554\pi\) | ||||
0.280335 | + | 0.959902i | \(0.409554\pi\) | |||||||
\(398\) | −1880.57 | + | 5787.79i | −0.236845 | + | 0.728934i | ||||
\(399\) | 3020.67 | − | 2194.64i | 0.379004 | − | 0.275363i | ||||
\(400\) | −1262.72 | − | 917.423i | −0.157841 | − | 0.114678i | ||||
\(401\) | −1214.19 | − | 3736.90i | −0.151207 | − | 0.465366i | 0.846550 | − | 0.532309i | \(-0.178675\pi\) |
−0.997757 | + | 0.0669429i | \(0.978675\pi\) | |||||||
\(402\) | 2508.72 | + | 7721.03i | 0.311252 | + | 0.957936i | ||||
\(403\) | −2676.60 | − | 1944.67i | −0.330847 | − | 0.240374i | ||||
\(404\) | −1329.17 | + | 965.697i | −0.163685 | + | 0.118924i | ||||
\(405\) | −2258.86 | + | 6952.07i | −0.277145 | + | 0.852965i | ||||
\(406\) | −6504.07 | −0.795054 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1557.02 | −0.188931 | ||||||||
\(409\) | 4500.59 | − | 13851.4i | 0.544107 | − | 1.67459i | −0.178996 | − | 0.983850i | \(-0.557285\pi\) |
0.723103 | − | 0.690740i | \(-0.242715\pi\) | |||||||
\(410\) | −6109.85 | + | 4439.07i | −0.735961 | + | 0.534707i | ||||
\(411\) | −13167.9 | − | 9567.02i | −1.58035 | − | 1.14819i | ||||
\(412\) | 1690.52 | + | 5202.89i | 0.202150 | + | 0.622155i | ||||
\(413\) | −239.208 | − | 736.208i | −0.0285004 | − | 0.0877153i | ||||
\(414\) | −9785.57 | − | 7109.63i | −1.16168 | − | 0.844008i | ||||
\(415\) | 6483.98 | − | 4710.89i | 0.766955 | − | 0.557225i | ||||
\(416\) | 435.378 | − | 1339.96i | 0.0513129 | − | 0.157925i | ||||
\(417\) | 1354.79 | 0.159099 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4028.77 | 0.469734 | 0.234867 | − | 0.972028i | \(-0.424535\pi\) | ||||
0.234867 | + | 0.972028i | \(0.424535\pi\) | |||||||
\(420\) | 3135.63 | − | 9650.47i | 0.364293 | − | 1.12118i | ||||
\(421\) | 6898.98 | − | 5012.40i | 0.798659 | − | 0.580260i | −0.111861 | − | 0.993724i | \(-0.535681\pi\) |
0.910521 | + | 0.413464i | \(0.135681\pi\) | |||||||
\(422\) | 4193.31 | + | 3046.62i | 0.483714 | + | 0.351439i | ||||
\(423\) | 5247.54 | + | 16150.3i | 0.603177 | + | 1.85639i | ||||
\(424\) | 31.9946 | + | 98.4694i | 0.00366462 | + | 0.0112785i | ||||
\(425\) | −1966.26 | − | 1428.57i | −0.224418 | − | 0.163049i | ||||
\(426\) | 991.574 | − | 720.420i | 0.112774 | − | 0.0819354i | ||||
\(427\) | 3621.24 | − | 11145.0i | 0.410408 | − | 1.26310i | ||||
\(428\) | 1580.96 | 0.178548 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3897.31 | −0.437082 | ||||||||
\(431\) | −4145.53 | + | 12758.6i | −0.463302 | + | 1.42590i | 0.397803 | + | 0.917471i | \(0.369773\pi\) |
−0.861105 | + | 0.508427i | \(0.830227\pi\) | |||||||
\(432\) | 710.301 | − | 516.064i | 0.0791074 | − | 0.0574749i | ||||
\(433\) | −3343.11 | − | 2428.91i | −0.371038 | − | 0.269575i | 0.386603 | − | 0.922246i | \(-0.373648\pi\) |
−0.757641 | + | 0.652671i | \(0.773648\pi\) | |||||||
\(434\) | −1010.93 | − | 3111.32i | −0.111811 | − | 0.344120i | ||||
\(435\) | −5380.08 | − | 16558.2i | −0.593000 | − | 1.82507i | ||||
\(436\) | 1636.89 | + | 1189.27i | 0.179800 | + | 0.130632i | ||||
\(437\) | 3157.50 | − | 2294.06i | 0.345637 | − | 0.251120i | ||||
\(438\) | 5523.53 | − | 16999.7i | 0.602567 | − | 1.85451i | ||||
\(439\) | −3358.46 | −0.365126 | −0.182563 | − | 0.983194i | \(-0.558439\pi\) | ||||
−0.182563 | + | 0.983194i | \(0.558439\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4451.74 | 0.480698 | ||||||||
\(442\) | 677.952 | − | 2086.52i | 0.0729568 | − | 0.224538i | ||||
\(443\) | 357.383 | − | 259.654i | 0.0383290 | − | 0.0278477i | −0.568456 | − | 0.822714i | \(-0.692459\pi\) |
0.606785 | + | 0.794866i | \(0.292459\pi\) | |||||||
\(444\) | 5620.57 | + | 4083.58i | 0.600767 | + | 0.436483i | ||||
\(445\) | 3075.25 | + | 9464.66i | 0.327598 | + | 1.00824i | ||||
\(446\) | 1629.88 | + | 5016.26i | 0.173043 | + | 0.532571i | ||||
\(447\) | 2837.98 | + | 2061.91i | 0.300295 | + | 0.218177i | ||||
\(448\) | 1127.08 | − | 818.869i | 0.118860 | − | 0.0863569i | ||||
\(449\) | −126.227 | + | 388.486i | −0.0132673 | + | 0.0408325i | −0.957471 | − | 0.288530i | \(-0.906834\pi\) |
0.944204 | + | 0.329362i | \(0.106834\pi\) | |||||||
\(450\) | 6638.23 | 0.695398 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6150.49 | 0.640033 | ||||||||
\(453\) | 68.8849 | − | 212.006i | 0.00714458 | − | 0.0219888i | ||||
\(454\) | 405.592 | − | 294.680i | 0.0419282 | − | 0.0304626i | ||||
\(455\) | 11567.0 | + | 8403.95i | 1.19181 | + | 0.865897i | ||||
\(456\) | 424.036 | + | 1305.05i | 0.0435467 | + | 0.134023i | ||||
\(457\) | −470.585 | − | 1448.31i | −0.0481686 | − | 0.148248i | 0.924079 | − | 0.382201i | \(-0.124834\pi\) |
−0.972248 | + | 0.233953i | \(0.924834\pi\) | |||||||
\(458\) | −2911.35 | − | 2115.22i | −0.297027 | − | 0.215803i | ||||
\(459\) | 1106.05 | − | 803.592i | 0.112475 | − | 0.0817178i | ||||
\(460\) | 3277.66 | − | 10087.6i | 0.332221 | − | 1.02247i | ||||
\(461\) | 13861.4 | 1.40041 | 0.700203 | − | 0.713944i | \(-0.253093\pi\) | ||||
0.700203 | + | 0.713944i | \(0.253093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6502.26 | −0.652669 | −0.326334 | − | 0.945254i | \(-0.605814\pi\) | ||||
−0.326334 | + | 0.945254i | \(0.605814\pi\) | |||||||
\(464\) | 738.656 | − | 2273.35i | 0.0739036 | − | 0.227452i | ||||
\(465\) | 7084.62 | − | 5147.27i | 0.706540 | − | 0.513331i | ||||
\(466\) | 5146.12 | + | 3738.87i | 0.511565 | + | 0.371674i | ||||
\(467\) | 131.015 | + | 403.223i | 0.0129821 | + | 0.0399548i | 0.957338 | − | 0.288971i | \(-0.0933132\pi\) |
−0.944356 | + | 0.328926i | \(0.893313\pi\) | |||||||
\(468\) | 1851.69 | + | 5698.91i | 0.182894 | + | 0.562890i | ||||
\(469\) | −9150.83 | − | 6648.46i | −0.900951 | − | 0.654579i | ||||
\(470\) | −12047.1 | + | 8752.76i | −1.18233 | + | 0.859010i | ||||
\(471\) | −4161.37 | + | 12807.4i | −0.407104 | + | 1.25294i | ||||
\(472\) | 284.491 | 0.0277431 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12070.0 | 1.16960 | ||||||||
\(475\) | −661.898 | + | 2037.11i | −0.0639368 | + | 0.196777i | ||||
\(476\) | 1755.03 | − | 1275.11i | 0.168995 | − | 0.122782i | ||||
\(477\) | −356.249 | − | 258.830i | −0.0341961 | − | 0.0248449i | ||||
\(478\) | −3098.70 | − | 9536.82i | −0.296509 | − | 0.912561i | ||||
\(479\) | −1408.29 | − | 4334.29i | −0.134335 | − | 0.413442i | 0.861151 | − | 0.508350i | \(-0.169744\pi\) |
−0.995486 | + | 0.0949081i | \(0.969744\pi\) | |||||||
\(480\) | 3016.99 | + | 2191.97i | 0.286888 | + | 0.208436i | ||||
\(481\) | −7919.59 | + | 5753.92i | −0.750732 | + | 0.545439i | ||||
\(482\) | −3754.02 | + | 11553.7i | −0.354753 | + | 1.09182i | ||||
\(483\) | 30225.6 | 2.84744 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2680.10 | −0.250922 | ||||||||
\(486\) | 3281.36 | − | 10099.0i | 0.306267 | − | 0.942592i | ||||
\(487\) | 5427.63 | − | 3943.41i | 0.505030 | − | 0.366926i | −0.305905 | − | 0.952062i | \(-0.598959\pi\) |
0.810935 | + | 0.585136i | \(0.198959\pi\) | |||||||
\(488\) | 3484.23 | + | 2531.44i | 0.323204 | + | 0.234822i | ||||
\(489\) | −8010.13 | − | 24652.6i | −0.740758 | − | 2.27982i | ||||
\(490\) | 1206.33 | + | 3712.70i | 0.111217 | + | 0.342291i | ||||
\(491\) | 11753.1 | + | 8539.14i | 1.08027 | + | 0.784859i | 0.977729 | − | 0.209870i | \(-0.0673040\pi\) |
0.102537 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(492\) | 6398.80 | − | 4649.00i | 0.586341 | − | 0.426002i | ||||
\(493\) | 1150.20 | − | 3539.96i | 0.105076 | − | 0.323391i | ||||
\(494\) | −1933.49 | −0.176097 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1202.30 | 0.108840 | ||||||||
\(497\) | −527.695 | + | 1624.08i | −0.0476265 | + | 0.146579i | ||||
\(498\) | −6790.62 | + | 4933.67i | −0.611034 | + | 0.443942i | ||||
\(499\) | 7847.09 | + | 5701.24i | 0.703976 | + | 0.511468i | 0.881225 | − | 0.472698i | \(-0.156720\pi\) |
−0.177249 | + | 0.984166i | \(0.556720\pi\) | |||||||
\(500\) | −506.158 | − | 1557.79i | −0.0452722 | − | 0.139333i | ||||
\(501\) | −7279.61 | − | 22404.3i | −0.649159 | − | 1.99791i | ||||
\(502\) | 9011.95 | + | 6547.57i | 0.801241 | + | 0.582136i | ||||
\(503\) | 12707.4 | − | 9232.43i | 1.12643 | − | 0.818397i | 0.141256 | − | 0.989973i | \(-0.454886\pi\) |
0.985171 | + | 0.171576i | \(0.0548859\pi\) | |||||||
\(504\) | −1830.96 | + | 5635.12i | −0.161820 | + | 0.498032i | ||||
\(505\) | 6127.41 | 0.539933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2019.25 | 0.176879 | ||||||||
\(508\) | 861.950 | − | 2652.81i | 0.0752812 | − | 0.231692i | ||||
\(509\) | 1192.56 | − | 866.443i | 0.103849 | − | 0.0754507i | −0.534649 | − | 0.845074i | \(-0.679556\pi\) |
0.638498 | + | 0.769624i | \(0.279556\pi\) | |||||||
\(510\) | 4697.93 | + | 3413.24i | 0.407898 | + | 0.296355i | ||||
\(511\) | 7695.74 | + | 23685.0i | 0.666222 | + | 2.05042i | ||||
\(512\) | 158.217 | + | 486.941i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | −974.766 | − | 708.209i | −0.0838928 | − | 0.0609517i | ||||
\(514\) | 9557.81 | − | 6944.15i | 0.820188 | − | 0.595902i | ||||
\(515\) | 6304.85 | − | 19404.3i | 0.539466 | − | 1.66031i | ||||
\(516\) | 4081.62 | 0.348223 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −9679.57 | −0.821035 | ||||||||
\(519\) | −5333.48 | + | 16414.8i | −0.451086 | + | 1.38830i | ||||
\(520\) | −4251.05 | + | 3088.57i | −0.358502 | + | 0.260467i | ||||
\(521\) | 7501.89 | + | 5450.44i | 0.630832 | + | 0.458326i | 0.856688 | − | 0.515834i | \(-0.172518\pi\) |
−0.225856 | + | 0.974161i | \(0.572518\pi\) | |||||||
\(522\) | 3141.55 | + | 9668.69i | 0.263413 | + | 0.810703i | ||||
\(523\) | 1311.01 | + | 4034.86i | 0.109610 | + | 0.337346i | 0.990785 | − | 0.135445i | \(-0.0432464\pi\) |
−0.881174 | + | 0.472791i | \(0.843246\pi\) | |||||||
\(524\) | −841.087 | − | 611.085i | −0.0701203 | − | 0.0509454i | ||||
\(525\) | −13420.1 | + | 9750.28i | −1.11562 | + | 0.810547i | ||||
\(526\) | 4235.84 | − | 13036.6i | 0.351125 | − | 1.08065i | ||||
\(527\) | 1872.17 | 0.154749 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19427.7 | 1.59676 | ||||||||
\(530\) | 119.325 | − | 367.245i | 0.00977953 | − | 0.0300983i | ||||
\(531\) | −978.875 | + | 711.194i | −0.0799992 | + | 0.0581228i | ||||
\(532\) | −1546.72 | − | 1123.76i | −0.126050 | − | 0.0915809i | ||||
\(533\) | 3443.86 | + | 10599.1i | 0.279869 | + | 0.861348i | ||||
\(534\) | −3220.68 | − | 9912.25i | −0.260997 | − | 0.803268i | ||||
\(535\) | −4770.17 | − | 3465.73i | −0.385481 | − | 0.280068i | ||||
\(536\) | 3363.06 | − | 2443.41i | 0.271011 | − | 0.196901i | ||||
\(537\) | 5484.16 | − | 16878.5i | 0.440706 | − | 1.35635i | ||||
\(538\) | 2202.73 | 0.176517 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3274.46 | −0.260945 | ||||||||
\(541\) | 2014.87 | − | 6201.13i | 0.160122 | − | 0.492805i | −0.838522 | − | 0.544868i | \(-0.816580\pi\) |
0.998644 | + | 0.0520633i | \(0.0165798\pi\) | |||||||
\(542\) | −4161.09 | + | 3023.21i | −0.329768 | + | 0.239590i | ||||
\(543\) | −3946.36 | − | 2867.20i | −0.311887 | − | 0.226599i | ||||
\(544\) | 246.368 | + | 758.243i | 0.0194172 | + | 0.0597599i | ||||
\(545\) | −2331.84 | − | 7176.66i | −0.183275 | − | 0.564063i | ||||
\(546\) | −12114.1 | − | 8801.38i | −0.949513 | − | 0.689861i | ||||
\(547\) | 5154.07 | − | 3744.65i | 0.402874 | − | 0.292705i | −0.367836 | − | 0.929890i | \(-0.619901\pi\) |
0.770711 | + | 0.637185i | \(0.219901\pi\) | |||||||
\(548\) | −2575.42 | + | 7926.34i | −0.200760 | + | 0.617876i | ||||
\(549\) | −18316.8 | −1.42394 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3280.33 | −0.253624 | ||||||||
\(552\) | −3432.67 | + | 10564.7i | −0.264681 | + | 0.814605i | ||||
\(553\) | −13605.0 | + | 9884.59i | −1.04619 | + | 0.760100i | ||||
\(554\) | −11876.5 | − | 8628.81i | −0.910804 | − | 0.661738i | ||||
\(555\) | −8006.81 | − | 24642.4i | −0.612379 | − | 1.88471i | ||||
\(556\) | −214.370 | − | 659.762i | −0.0163513 | − | 0.0503240i | ||||
\(557\) | 4938.23 | + | 3587.84i | 0.375655 | + | 0.272929i | 0.759552 | − | 0.650447i | \(-0.225418\pi\) |
−0.383897 | + | 0.923376i | \(0.625418\pi\) | |||||||
\(558\) | −4136.86 | + | 3005.61i | −0.313848 | + | 0.228024i | ||||
\(559\) | −1777.20 | + | 5469.67i | −0.134468 | + | 0.413851i | ||||
\(560\) | −5195.77 | −0.392074 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14985.9 | 1.12481 | ||||||||
\(563\) | 4200.34 | − | 12927.3i | 0.314429 | − | 0.967711i | −0.661561 | − | 0.749892i | \(-0.730106\pi\) |
0.975989 | − | 0.217820i | \(-0.0698945\pi\) | |||||||
\(564\) | 12616.9 | − | 9166.69i | 0.941961 | − | 0.684375i | ||||
\(565\) | −18557.6 | − | 13482.9i | −1.38181 | − | 1.00395i | ||||
\(566\) | 4013.57 | + | 12352.5i | 0.298062 | + | 0.917341i | ||||
\(567\) | 3296.03 | + | 10144.1i | 0.244127 | + | 0.751347i | ||||
\(568\) | −507.730 | − | 368.888i | −0.0375068 | − | 0.0272503i | ||||
\(569\) | 13913.1 | − | 10108.5i | 1.02508 | − | 0.744761i | 0.0577589 | − | 0.998331i | \(-0.481605\pi\) |
0.967317 | + | 0.253569i | \(0.0816045\pi\) | |||||||
\(570\) | 1581.46 | − | 4867.22i | 0.116210 | − | 0.357659i | ||||
\(571\) | −2475.65 | −0.181441 | −0.0907203 | − | 0.995876i | \(-0.528917\pi\) | ||||
−0.0907203 | + | 0.995876i | \(0.528917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10500.6 | 0.765567 | ||||||||
\(574\) | −3405.31 | + | 10480.5i | −0.247622 | + | 0.762101i | ||||
\(575\) | −14028.0 | + | 10191.9i | −1.01741 | + | 0.739188i | ||||
\(576\) | −1761.69 | − | 1279.94i | −0.127437 | − | 0.0925883i | ||||
\(577\) | −6285.32 | − | 19344.2i | −0.453485 | − | 1.39568i | −0.872904 | − | 0.487892i | \(-0.837766\pi\) |
0.419419 | − | 0.907793i | \(-0.362234\pi\) | |||||||
\(578\) | −2652.77 | − | 8164.38i | −0.190901 | − | 0.587532i | ||||
\(579\) | −29221.7 | − | 21230.8i | −2.09743 | − | 1.52387i | ||||
\(580\) | −7212.27 | + | 5240.02i | −0.516333 | + | 0.375138i | ||||
\(581\) | 3613.83 | − | 11122.2i | 0.258050 | − | 0.794196i | ||||
\(582\) | 2806.85 | 0.199910 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9152.55 | −0.648519 | ||||||||
\(585\) | 6905.94 | − | 21254.3i | 0.488078 | − | 1.50215i | ||||
\(586\) | −4344.22 | + | 3156.26i | −0.306242 | + | 0.222498i | ||||
\(587\) | 11988.4 | + | 8710.07i | 0.842953 | + | 0.612441i | 0.923194 | − | 0.384334i | \(-0.125569\pi\) |
−0.0802411 | + | 0.996775i | \(0.525569\pi\) | |||||||
\(588\) | −1263.38 | − | 3888.28i | −0.0886068 | − | 0.272704i | ||||
\(589\) | −509.862 | − | 1569.19i | −0.0356681 | − | 0.109775i | ||||
\(590\) | −858.382 | − | 623.651i | −0.0598967 | − | 0.0435175i | ||||
\(591\) | −4200.77 | + | 3052.04i | −0.292380 | + | 0.212427i | ||||
\(592\) | 1099.29 | − | 3383.27i | 0.0763186 | − | 0.234885i | ||||
\(593\) | −11123.2 | −0.770281 | −0.385140 | − | 0.922858i | \(-0.625847\pi\) | ||||
−0.385140 | + | 0.922858i | \(0.625847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8090.63 | −0.557451 | ||||||||
\(596\) | 555.062 | − | 1708.31i | 0.0381481 | − | 0.117408i | ||||
\(597\) | −19230.3 | + | 13971.6i | −1.31833 | + | 0.957824i | ||||
\(598\) | −12662.8 | − | 9200.06i | −0.865920 | − | 0.629127i | ||||
\(599\) | 2560.26 | + | 7879.67i | 0.174640 | + | 0.537487i | 0.999617 | − | 0.0276796i | \(-0.00881183\pi\) |
−0.824977 | + | 0.565167i | \(0.808812\pi\) | |||||||
\(600\) | −1883.89 | − | 5798.01i | −0.128182 | − | 0.394505i | ||||
\(601\) | 22101.0 | + | 16057.3i | 1.50003 | + | 1.08984i | 0.970370 | + | 0.241625i | \(0.0776803\pi\) |
0.529660 | + | 0.848210i | \(0.322320\pi\) | |||||||
\(602\) | −4600.70 | + | 3342.60i | −0.311479 | + | 0.226303i | ||||
\(603\) | −5463.37 | + | 16814.5i | −0.368965 | + | 1.13556i | ||||
\(604\) | −114.143 | −0.00768944 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6417.18 | −0.430165 | ||||||||
\(607\) | −5045.53 | + | 15528.6i | −0.337384 | + | 1.03836i | 0.628152 | + | 0.778091i | \(0.283812\pi\) |
−0.965536 | + | 0.260270i | \(0.916188\pi\) | |||||||
\(608\) | 568.441 | − | 412.997i | 0.0379167 | − | 0.0275481i | ||||
\(609\) | −20552.5 | − | 14932.3i | −1.36754 | − | 0.993574i | ||||
\(610\) | −4963.48 | − | 15276.0i | −0.329452 | − | 1.01395i | ||||
\(611\) | 6790.45 | + | 20898.9i | 0.449611 | + | 1.38376i | ||||
\(612\) | −2743.22 | − | 1993.07i | −0.181190 | − | 0.131642i | ||||
\(613\) | −17009.8 | + | 12358.4i | −1.12075 | + | 0.814274i | −0.984323 | − | 0.176376i | \(-0.943563\pi\) |
−0.136429 | + | 0.990650i | \(0.543563\pi\) | |||||||
\(614\) | −5149.25 | + | 15847.8i | −0.338448 | + | 1.04163i | ||||
\(615\) | −29498.2 | −1.93412 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 871.824 | 0.0568854 | 0.0284427 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284427 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(618\) | −6603.02 | + | 20322.0i | −0.429793 | + | 1.32277i | ||||
\(619\) | −7602.75 | + | 5523.72i | −0.493668 | + | 0.358671i | −0.806593 | − | 0.591107i | \(-0.798691\pi\) |
0.312925 | + | 0.949778i | \(0.398691\pi\) | |||||||
\(620\) | −3627.64 | − | 2635.64i | −0.234983 | − | 0.170725i | ||||
\(621\) | −3014.08 | − | 9276.38i | −0.194768 | − | 0.599434i | ||||
\(622\) | −3102.75 | − | 9549.28i | −0.200014 | − | 0.615581i | ||||
\(623\) | 11747.8 | + | 8535.29i | 0.755484 | + | 0.548891i | ||||
\(624\) | 4452.09 | − | 3234.63i | 0.285619 | − | 0.207514i | ||||
\(625\) | −5655.84 | + | 17406.9i | −0.361974 | + | 1.11404i | ||||
\(626\) | 6044.15 | 0.385899 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6895.44 | 0.438150 | ||||||||
\(629\) | 1711.77 | − | 5268.28i | 0.108510 | − | 0.333959i | ||||
\(630\) | 17877.6 | − | 12988.8i | 1.13057 | − | 0.821409i | ||||
\(631\) | 11759.8 | + | 8544.01i | 0.741919 | + | 0.539036i | 0.893311 | − | 0.449438i | \(-0.148376\pi\) |
−0.151393 | + | 0.988474i | \(0.548376\pi\) | |||||||
\(632\) | −1909.84 | − | 5877.88i | −0.120205 | − | 0.369952i | ||||
\(633\) | 6256.10 | + | 19254.3i | 0.392824 | + | 1.20899i | ||||
\(634\) | 17054.3 | + | 12390.7i | 1.06832 | + | 0.776178i | ||||
\(635\) | −8416.12 | + | 6114.67i | −0.525958 | + | 0.382131i | ||||
\(636\) | −124.968 | + | 384.612i | −0.00779136 | + | 0.0239794i | ||||
\(637\) | 5760.67 | 0.358314 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2669.17 | 0.165244 | ||||||||
\(640\) | 590.075 | − | 1816.06i | 0.0364449 | − | 0.112166i | ||||
\(641\) | 9238.70 | − | 6712.31i | 0.569277 | − | 0.413604i | −0.265565 | − | 0.964093i | \(-0.585559\pi\) |
0.834843 | + | 0.550489i | \(0.185559\pi\) | |||||||
\(642\) | 4995.76 | + | 3629.63i | 0.307113 | + | 0.223131i | ||||
\(643\) | 7407.11 | + | 22796.7i | 0.454289 | + | 1.39816i | 0.871968 | + | 0.489563i | \(0.162844\pi\) |
−0.417679 | + | 0.908595i | \(0.637156\pi\) | |||||||
\(644\) | −4782.61 | − | 14719.4i | −0.292642 | − | 0.900659i | ||||
\(645\) | −12315.3 | − | 8947.58i | −0.751805 | − | 0.546218i | ||||
\(646\) | 885.152 | − | 643.100i | 0.0539100 | − | 0.0391679i | ||||
\(647\) | 2569.24 | − | 7907.32i | 0.156117 | − | 0.480478i | −0.842156 | − | 0.539234i | \(-0.818714\pi\) |
0.998272 | + | 0.0587569i | \(0.0187137\pi\) | |||||||
\(648\) | −3919.97 | −0.237641 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 8590.04 | 0.518353 | ||||||||
\(651\) | 3948.59 | − | 12152.5i | 0.237723 | − | 0.731635i | ||||
\(652\) | −10738.0 | + | 7801.60i | −0.644988 | + | 0.468611i | ||||
\(653\) | 24334.7 | + | 17680.2i | 1.45833 | + | 1.05954i | 0.983794 | + | 0.179303i | \(0.0573843\pi\) |
0.474536 | + | 0.880236i | \(0.342616\pi\) | |||||||
\(654\) | 2442.11 | + | 7516.05i | 0.146016 | + | 0.449390i | ||||
\(655\) | 1198.17 | + | 3687.60i | 0.0714757 | + | 0.219980i | ||||
\(656\) | −3276.47 | − | 2380.50i | −0.195007 | − | 0.141681i | ||||
\(657\) | 31492.1 | − | 22880.3i | 1.87005 | − | 1.35867i | ||||
\(658\) | −6714.44 | + | 20664.9i | −0.397806 | + | 1.22432i | ||||
\(659\) | 10041.6 | 0.593572 | 0.296786 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296786 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1402.50 | 0.0825281 | 0.0412640 | − | 0.999148i | \(-0.486862\pi\) | ||||
0.0412640 | + | 0.999148i | \(0.486862\pi\) | |||||||
\(662\) | 191.511 | − | 589.409i | 0.0112436 | − | 0.0346043i | ||||
\(663\) | 6932.60 | − | 5036.83i | 0.406093 | − | 0.295044i | ||||
\(664\) | 3477.10 | + | 2526.26i | 0.203219 | + | 0.147648i | ||||
\(665\) | 2203.39 | + | 6781.32i | 0.128487 | + | 0.395441i | ||||
\(666\) | 4675.35 | + | 14389.3i | 0.272021 | + | 0.837196i | ||||
\(667\) | −21483.5 | − | 15608.7i | −1.24714 | − | 0.906102i | ||||
\(668\) | −9758.68 | + | 7090.10i | −0.565232 | + | 0.410665i | ||||
\(669\) | −6366.17 | + | 19593.1i | −0.367908 | + | 1.13230i | ||||
\(670\) | −15503.6 | −0.893963 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5441.49 | 0.312366 | ||||||||
\(673\) | −6299.43 | + | 19387.7i | −0.360810 | + | 1.11046i | 0.591753 | + | 0.806119i | \(0.298436\pi\) |
−0.952563 | + | 0.304341i | \(0.901564\pi\) | |||||||
\(674\) | 18064.8 | − | 13124.8i | 1.03239 | − | 0.750074i | ||||
\(675\) | 4330.65 | + | 3146.40i | 0.246944 | + | 0.179415i | ||||
\(676\) | −319.507 | − | 983.340i | −0.0181786 | − | 0.0559479i | ||||
\(677\) | 2282.09 | + | 7023.55i | 0.129554 | + | 0.398725i | 0.994703 | − | 0.102789i | \(-0.0327766\pi\) |
−0.865149 | + | 0.501514i | \(0.832777\pi\) | |||||||
\(678\) | 19435.2 | + | 14120.5i | 1.10089 | + | 0.799846i | ||||
\(679\) | −3163.81 | + | 2298.64i | −0.178815 | + | 0.129917i | ||||
\(680\) | 918.838 | − | 2827.89i | 0.0518174 | − | 0.159478i | ||||
\(681\) | 1958.19 | 0.110188 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25844.0 | −1.44787 | −0.723935 | − | 0.689868i | \(-0.757668\pi\) | ||||
−0.723935 | + | 0.689868i | \(0.757668\pi\) | |||||||
\(684\) | −923.446 | + | 2842.07i | −0.0516211 | + | 0.158873i | ||||
\(685\) | 25146.5 | − | 18270.0i | 1.40263 | − | 1.01907i | ||||
\(686\) | −7472.53 | − | 5429.11i | −0.415893 | − | 0.302164i | ||||
\(687\) | −4343.51 | − | 13368.0i | −0.241216 | − | 0.742386i | ||||
\(688\) | −645.837 | − | 1987.68i | −0.0357882 | − | 0.110145i | ||||
\(689\) | −460.996 | − | 334.933i | −0.0254899 | − | 0.0185195i | ||||
\(690\) | 33516.7 | − | 24351.3i | 1.84922 | − | 1.34353i | ||||
\(691\) | 2607.73 | − | 8025.78i | 0.143564 | − | 0.441845i | −0.853259 | − | 0.521487i | \(-0.825378\pi\) |
0.996824 | + | 0.0796417i | \(0.0253776\pi\) | |||||||
\(692\) | 8837.64 | 0.485486 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5030.97 | −0.275177 | ||||||||
\(695\) | −799.499 | + | 2460.60i | −0.0436356 | + | 0.134296i | ||||
\(696\) | 7553.35 | − | 5487.83i | 0.411363 | − | 0.298873i | ||||
\(697\) | −5101.98 | − | 3706.80i | −0.277261 | − | 0.201442i | ||||
\(698\) | 7031.12 | + | 21639.6i | 0.381278 | + | 1.17345i | ||||
\(699\) | 7677.62 | + | 23629.3i | 0.415442 | + | 1.27860i | ||||
\(700\) | 6871.70 | + | 4992.58i | 0.371037 | + | 0.269574i | ||||
\(701\) | −10503.8 | + | 7631.43i | −0.565937 | + | 0.411177i | −0.833627 | − | 0.552328i | \(-0.813740\pi\) |
0.267690 | + | 0.963505i | \(0.413740\pi\) | |||||||
\(702\) | −1493.18 | + | 4595.53i | −0.0802798 | + | 0.247076i | ||||
\(703\) | −4881.90 | −0.261912 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −58163.2 | −3.10717 | ||||||||
\(706\) | 3838.04 | − | 11812.3i | 0.204598 | − | 0.629689i | ||||
\(707\) | 7233.28 | − | 5255.29i | 0.384775 | − | 0.279555i | ||||
\(708\) | 898.976 | + | 653.144i | 0.0477197 | + | 0.0346704i | ||||
\(709\) | −5537.15 | − | 17041.6i | −0.293303 | − | 0.902695i | −0.983786 | − | 0.179346i | \(-0.942602\pi\) |
0.690483 | − | 0.723349i | \(-0.257398\pi\) | |||||||
\(710\) | 723.290 | + | 2226.06i | 0.0382318 | + | 0.117665i | ||||
\(711\) | 21265.4 | + | 15450.2i | 1.12168 | + | 0.814948i | ||||
\(712\) | −4317.49 | + | 3136.84i | −0.227254 | + | 0.165110i | ||||
\(713\) | 4127.45 | − | 12703.0i | 0.216794 | − | 0.667224i | ||||
\(714\) | 8473.24 | 0.444122 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9087.33 | −0.474315 | ||||||||
\(717\) | 12103.2 | − | 37250.0i | 0.630410 | − | 1.94020i | ||||
\(718\) | −4024.87 | + | 2924.24i | −0.209202 | + | 0.151994i | ||||
\(719\) | −2845.59 | − | 2067.45i | −0.147598 | − | 0.107236i | 0.511536 | − | 0.859262i | \(-0.329077\pi\) |
−0.659133 | + | 0.752026i | \(0.729077\pi\) | |||||||
\(720\) | 2509.62 | + | 7723.82i | 0.129900 | + | 0.399791i | ||||
\(721\) | −9199.75 | − | 28313.9i | −0.475196 | − | 1.46250i | ||||
\(722\) | 10318.0 | + | 7496.47i | 0.531851 | + | 0.386412i | ||||
\(723\) | −38387.8 | + | 27890.4i | −1.97463 | + | 1.43465i | ||||
\(724\) | −771.844 | + | 2375.49i | −0.0396207 | + | 0.121940i | ||||
\(725\) | 14573.7 | 0.746559 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29438.9 | −1.50183 | −0.750913 | − | 0.660401i | \(-0.770386\pi\) | ||||
−0.750913 | + | 0.660401i | \(0.770386\pi\) | |||||||
\(728\) | −2369.31 | + | 7292.00i | −0.120622 | + | 0.371235i | ||||
\(729\) | 22851.3 | − | 16602.5i | 1.16097 | − | 0.843492i | ||||
\(730\) | 27615.6 | + | 20063.9i | 1.40014 | + | 1.01726i | ||||
\(731\) | −1005.67 | − | 3095.13i | −0.0508837 | − | 0.156604i | ||||
\(732\) | 5198.21 | + | 15998.4i | 0.262474 | + | 0.807813i | ||||
\(733\) | 2779.70 | + | 2019.57i | 0.140069 | + | 0.101766i | 0.655613 | − | 0.755097i | \(-0.272410\pi\) |
−0.515544 | + | 0.856863i | \(0.672410\pi\) | |||||||
\(734\) | −10872.4 | + | 7899.28i | −0.546742 | + | 0.397231i | ||||
\(735\) | −4711.81 | + | 14501.5i | −0.236459 | + | 0.727747i | ||||
\(736\) | 5687.97 | 0.284866 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 17224.6 | 0.859143 | ||||||||
\(739\) | 10383.5 | − | 31957.2i | 0.516866 | − | 1.59075i | −0.262995 | − | 0.964797i | \(-0.584710\pi\) |
0.779861 | − | 0.625953i | \(-0.215290\pi\) | |||||||
\(740\) | −10733.5 | + | 7798.37i | −0.533206 | + | 0.387397i | ||||
\(741\) | −6109.73 | − | 4438.98i | −0.302897 | − | 0.220067i | ||||
\(742\) | −174.114 | − | 535.867i | −0.00861444 | − | 0.0265125i | ||||
\(743\) | 368.875 | + | 1135.28i | 0.0182136 | + | 0.0560557i | 0.959750 | − | 0.280855i | \(-0.0906180\pi\) |
−0.941537 | + | 0.336911i | \(0.890618\pi\) | |||||||
\(744\) | 3799.20 | + | 2760.28i | 0.187211 | + | 0.136017i | ||||
\(745\) | −5419.66 | + | 3937.61i | −0.266525 | + | 0.193641i | ||||
\(746\) | 5323.97 | − | 16385.5i | 0.261293 | − | 0.804177i | ||||
\(747\) | −18279.4 | −0.895324 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8603.54 | −0.419715 | ||||||||
\(750\) | 1977.01 | − | 6084.60i | 0.0962535 | − | 0.296238i | ||||
\(751\) | −19828.5 | + | 14406.2i | −0.963451 | + | 0.699988i | −0.953950 | − | 0.299967i | \(-0.903024\pi\) |
−0.00950152 | + | 0.999955i | \(0.503024\pi\) | |||||||
\(752\) | −6460.40 | − | 4693.76i | −0.313280 | − | 0.227611i | ||||
\(753\) | 13445.1 | + | 41379.9i | 0.650688 | + | 2.00261i | ||||
\(754\) | 4065.25 | + | 12511.5i | 0.196349 | + | 0.604302i | ||||
\(755\) | 344.399 | + | 250.221i | 0.0166013 | + | 0.0120615i | ||||
\(756\) | −3865.43 | + | 2808.40i | −0.185958 | + | 0.135107i | ||||
\(757\) | 3338.57 | − | 10275.0i | 0.160294 | − | 0.493333i | −0.838365 | − | 0.545109i | \(-0.816488\pi\) |
0.998659 | + | 0.0517762i | \(0.0164882\pi\) | |||||||
\(758\) | −16018.2 | −0.767555 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2620.49 | −0.125073 | ||||||||
\(761\) | −2526.49 | + | 7775.75i | −0.120349 | + | 0.370395i | −0.993025 | − | 0.117904i | \(-0.962383\pi\) |
0.872676 | + | 0.488299i | \(0.162383\pi\) | |||||||
\(762\) | 8814.12 | − | 6403.83i | 0.419031 | − | 0.304444i | ||||
\(763\) | −8907.88 | − | 6471.96i | −0.422657 | − | 0.307078i | ||||
\(764\) | −1661.52 | − | 5113.63i | −0.0786802 | − | 0.242153i | ||||
\(765\) | 3907.87 | + | 12027.2i | 0.184692 | + | 0.568424i | ||||
\(766\) | −12963.6 | − | 9418.61i | −0.611481 | − | 0.444267i | ||||
\(767\) | −1266.69 | + | 920.304i | −0.0596317 | + | 0.0433250i | ||||
\(768\) | −617.980 | + | 1901.95i | −0.0290357 | + | 0.0893627i | ||||
\(769\) | 28895.9 | 1.35502 | 0.677511 | − | 0.735513i | \(-0.263059\pi\) | ||||
0.677511 | + | 0.735513i | \(0.263059\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 46144.8 | 2.15547 | ||||||||
\(772\) | −5715.28 | + | 17589.8i | −0.266448 | + | 0.820041i | ||||
\(773\) | 14559.7 | − | 10578.3i | 0.677460 | − | 0.492203i | −0.195054 | − | 0.980792i | \(-0.562488\pi\) |
0.872514 | + | 0.488589i | \(0.162488\pi\) | |||||||
\(774\) | 7191.17 | + | 5224.69i | 0.333955 | + | 0.242633i | ||||
\(775\) | 2265.19 | + | 6971.55i | 0.104991 | + | 0.323130i | ||||
\(776\) | −444.129 | − | 1366.89i | −0.0205455 | − | 0.0632325i | ||||
\(777\) | −30586.9 | − | 22222.7i | −1.41223 | − | 1.02604i | ||||
\(778\) | −12992.2 | + | 9439.36i | −0.598704 | + | 0.434984i | ||||
\(779\) | −1717.47 | + | 5285.83i | −0.0789919 | + | 0.243112i | ||||
\(780\) | −20524.0 | −0.942148 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8857.06 | 0.405023 | ||||||||
\(783\) | −2533.30 | + | 7796.71i | −0.115623 | + | 0.355851i | ||||
\(784\) | −1693.62 | + | 1230.49i | −0.0771511 | + | 0.0560536i | ||||
\(785\) | −20805.3 | − | 15115.9i | −0.945954 | − | 0.687276i | ||||
\(786\) | −1254.84 | − | 3861.99i | −0.0569448 | − | 0.175258i | ||||
\(787\) | 4906.17 | + | 15099.6i | 0.222219 | + | 0.683918i | 0.998562 | + | 0.0536084i | \(0.0170723\pi\) |
−0.776343 | + | 0.630310i | \(0.782928\pi\) | |||||||
\(788\) | 2150.98 | + | 1562.78i | 0.0972407 | + | 0.0706495i | ||||
\(789\) | 43314.9 | − | 31470.1i | 1.95444 | − | 1.41998i | ||||
\(790\) | −7122.81 | + | 21921.7i | −0.320782 | + | 0.987267i | ||||
\(791\) | −33470.8 | −1.50453 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23702.5 | −1.06141 | ||||||||
\(794\) | 2740.98 | − | 8435.86i | 0.122511 | − | 0.377050i | ||||
\(795\) | 1220.19 | − | 886.523i | 0.0544350 | − | 0.0395494i | ||||
\(796\) | 9846.78 | + | 7154.10i | 0.438454 | + | 0.318556i | ||||
\(797\) | 5098.07 | + | 15690.2i | 0.226578 | + | 0.697336i | 0.998128 | + | 0.0611668i | \(0.0194822\pi\) |
−0.771549 | + | 0.636170i | \(0.780518\pi\) | |||||||
\(798\) | −2307.59 | − | 7102.02i | −0.102365 | − | 0.315049i | ||||
\(799\) | −10059.9 | − | 7308.91i | −0.445422 | − | 0.323618i | ||||
\(800\) | −2525.45 | + | 1834.85i | −0.111610 | + | 0.0810895i | ||||
\(801\) | 7013.87 | − | 21586.5i | 0.309392 | − | 0.952210i | ||||
\(802\) | −7858.41 | −0.345998 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 16236.7 | 0.712221 | ||||||||
\(805\) | −17836.9 | + | 54896.4i | −0.780955 | + | 2.40353i | ||||
\(806\) | −5353.21 | + | 3889.33i | −0.233944 | + | 0.169970i | ||||
\(807\) | 6960.50 | + | 5057.10i | 0.303620 | + | 0.220593i | ||||
\(808\) | 1015.39 | + | 3125.06i | 0.0442097 | + | 0.136063i | ||||
\(809\) | 2812.97 | + | 8657.42i | 0.122248 | + | 0.376241i | 0.993390 | − | 0.114791i | \(-0.0366199\pi\) |
−0.871142 | + | 0.491032i | \(0.836620\pi\) | |||||||
\(810\) | 11827.6 | + | 8593.23i | 0.513060 | + | 0.372760i | ||||
\(811\) | 29590.8 | − | 21499.0i | 1.28123 | − | 0.930865i | 0.281636 | − | 0.959521i | \(-0.409123\pi\) |
0.999589 | + | 0.0286567i | \(0.00912297\pi\) | |||||||
\(812\) | −4019.74 | + | 12371.5i | −0.173726 | + | 0.534672i | ||||
\(813\) | −20089.6 | −0.866633 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 49501.7 | 2.12757 | ||||||||
\(816\) | −962.291 | + | 2961.63i | −0.0412830 | + | 0.127056i | ||||
\(817\) | −2320.36 | + | 1685.84i | −0.0993626 | + | 0.0721912i | ||||
\(818\) | −23565.4 | − | 17121.3i | −1.00727 | − | 0.731823i | ||||
\(819\) | −10076.8 | − | 31013.3i | −0.429930 | − | 1.32319i | ||||
\(820\) | 4667.51 | + | 14365.1i | 0.198776 | + | 0.611771i | ||||
\(821\) | −2948.23 | − | 2142.01i | −0.125328 | − | 0.0910558i | 0.523356 | − | 0.852114i | \(-0.324680\pi\) |
−0.648683 | + | 0.761059i | \(0.724680\pi\) | |||||||
\(822\) | −26335.8 | + | 19134.0i | −1.11748 | + | 0.811894i | ||||
\(823\) | −5221.12 | + | 16068.9i | −0.221138 | + | 0.680593i | 0.777523 | + | 0.628855i | \(0.216476\pi\) |
−0.998661 | + | 0.0517380i | \(0.983524\pi\) | |||||||
\(824\) | 10941.3 | 0.462570 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1548.19 | −0.0652160 | ||||||||
\(827\) | 11983.1 | − | 36880.1i | 0.503860 | − | 1.55072i | −0.298817 | − | 0.954310i | \(-0.596592\pi\) |
0.802678 | − | 0.596413i | \(-0.203408\pi\) | |||||||
\(828\) | −19571.1 | + | 14219.3i | −0.821430 | + | 0.596804i | ||||
\(829\) | 10027.2 | + | 7285.20i | 0.420096 | + | 0.305218i | 0.777677 | − | 0.628665i | \(-0.216398\pi\) |
−0.357580 | + | 0.933882i | \(0.616398\pi\) | |||||||
\(830\) | −4953.32 | − | 15244.8i | −0.207147 | − | 0.637534i | ||||
\(831\) | −17718.9 | − | 54533.1i | −0.739665 | − | 2.27645i | ||||
\(832\) | −2279.67 | − | 1656.28i | −0.0949920 | − | 0.0690157i | ||||
\(833\) | −2637.23 | + | 1916.06i | −0.109694 | + | 0.0796970i | ||||
\(834\) | 837.308 | − | 2576.97i | 0.0347645 | − | 0.106994i | ||||
\(835\) | 44987.1 | 1.86448 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4123.41 | −0.170282 | ||||||||
\(838\) | 2489.92 | − | 7663.18i | 0.102641 | − | 0.315895i | ||||
\(839\) | −19872.6 | + | 14438.3i | −0.817732 | + | 0.594117i | −0.916062 | − | 0.401037i | \(-0.868650\pi\) |
0.0983299 | + | 0.995154i | \(0.468650\pi\) | |||||||
\(840\) | −16418.4 | − | 11928.6i | −0.674390 | − | 0.489973i | ||||
\(841\) | −639.584 | − | 1968.44i | −0.0262243 | − | 0.0807100i | ||||
\(842\) | −5270.35 | − | 16220.5i | −0.215711 | − | 0.663889i | ||||
\(843\) | 47354.6 | + | 34405.1i | 1.93473 | + | 1.40566i | ||||
\(844\) | 8386.62 | − | 6093.24i | 0.342037 | − | 0.248505i | ||||
\(845\) | −1191.61 | + | 3667.40i | −0.0485120 | + | 0.149305i | ||||
\(846\) | 33962.8 | 1.38022 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 207.074 | 0.00838554 | ||||||||
\(849\) | −15676.7 | + | 48247.8i | −0.633712 | + | 1.95036i | ||||
\(850\) | −3932.52 | + | 2857.14i | −0.158687 | + | 0.115293i | ||||
\(851\) | −31972.4 | − | 23229.3i | −1.28790 | − | 0.935712i | ||||
\(852\) | −757.495 | − | 2331.33i | −0.0304593 | − | 0.0937442i | ||||
\(853\) | 3772.37 | + | 11610.1i | 0.151422 | + | 0.466030i | 0.997781 | − | 0.0665834i | \(-0.0212098\pi\) |
−0.846358 | + | 0.532614i | \(0.821210\pi\) | |||||||
\(854\) | −18961.1 | − | 13776.0i | −0.759759 | − | 0.551997i | ||||
\(855\) | 9016.57 | − | 6550.92i | 0.360655 | − | 0.262031i | ||||
\(856\) | 977.089 | − | 3007.17i | 0.0390143 | − | 0.120074i | ||||
\(857\) | −7281.72 | −0.290244 | −0.145122 | − | 0.989414i | \(-0.546357\pi\) | ||||
−0.145122 | + | 0.989414i | \(0.546357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5927.39 | 0.235437 | 0.117718 | − | 0.993047i | \(-0.462442\pi\) | ||||
0.117718 | + | 0.993047i | \(0.462442\pi\) | |||||||
\(860\) | −2408.67 | + | 7413.13i | −0.0955058 | + | 0.293937i | ||||
\(861\) | −34822.0 | + | 25299.7i | −1.37832 | + | 1.00141i | ||||
\(862\) | 21706.3 | + | 15770.5i | 0.857679 | + | 0.623140i | ||||
\(863\) | −11916.3 | − | 36674.5i | −0.470028 | − | 1.44660i | −0.852547 | − | 0.522651i | \(-0.824943\pi\) |
0.382518 | − | 0.923948i | \(-0.375057\pi\) | |||||||
\(864\) | −542.622 | − | 1670.02i | −0.0213662 | − | 0.0657583i | ||||
\(865\) | −26665.4 | − | 19373.6i | −1.04815 | − | 0.761527i | ||||
\(866\) | −6686.22 | + | 4857.82i | −0.262364 | + | 0.190618i | ||||
\(867\) | 10361.5 | − | 31889.3i | 0.405875 | − | 1.24916i | ||||
\(868\) | −6542.86 | −0.255852 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −34820.6 | −1.35693 | ||||||||
\(871\) | −7069.75 | + | 21758.4i | −0.275028 | + | 0.846449i | ||||
\(872\) | 3273.78 | − | 2378.54i | 0.127138 | − | 0.0923709i | ||||
\(873\) | 4945.22 | + | 3592.91i | 0.191719 | + | 0.139292i | ||||
\(874\) | −2412.11 | − | 7423.72i | −0.0933535 | − | 0.287312i | ||||
\(875\) | 2754.49 | + | 8477.46i | 0.106422 | + | 0.327532i | ||||
\(876\) | −28921.6 | − | 21012.8i | −1.11549 | − | 0.810451i | ||||
\(877\) | 23067.2 | − | 16759.3i | 0.888170 | − | 0.645293i | −0.0472301 | − | 0.998884i | \(-0.515039\pi\) |
0.935400 | + | 0.353591i | \(0.115039\pi\) | |||||||
\(878\) | −2075.64 | + | 6388.16i | −0.0797830 | + | 0.245547i | ||||
\(879\) | −20973.7 | −0.804809 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40747.6 | 1.55826 | 0.779128 | − | 0.626865i | \(-0.215662\pi\) | ||||
0.779128 | + | 0.626865i | \(0.215662\pi\) | |||||||
\(882\) | 2751.33 | − | 8467.72i | 0.105036 | − | 0.323268i | ||||
\(883\) | 2908.89 | − | 2113.43i | 0.110863 | − | 0.0805467i | −0.530972 | − | 0.847389i | \(-0.678173\pi\) |
0.641835 | + | 0.766842i | \(0.278173\pi\) | |||||||
\(884\) | −3549.80 | − | 2579.08i | −0.135060 | − | 0.0981266i | ||||
\(885\) | −1280.64 | − | 3941.41i | −0.0486421 | − | 0.149705i | ||||
\(886\) | −273.016 | − | 840.257i | −0.0103523 | − | 0.0318612i | ||||
\(887\) | −6241.81 | − | 4534.94i | −0.236279 | − | 0.171667i | 0.463345 | − | 0.886178i | \(-0.346649\pi\) |
−0.699624 | + | 0.714511i | \(0.746649\pi\) | |||||||
\(888\) | 11241.1 | − | 8167.16i | 0.424806 | − | 0.308640i | ||||
\(889\) | −4690.70 | + | 14436.5i | −0.176964 | + | 0.544639i | ||||
\(890\) | 19903.5 | 0.749624 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10548.8 | 0.395965 | ||||||||
\(893\) | −3386.43 | + | 10422.4i | −0.126901 | + | 0.390561i | ||||
\(894\) | 5675.96 | − | 4123.82i | 0.212341 | − | 0.154274i | ||||
\(895\) | 27418.8 | + | 19920.9i | 1.02403 | + | 0.744003i | ||||
\(896\) | −861.009 | − | 2649.91i | −0.0321030 | − | 0.0988029i | ||||
\(897\) | −18891.9 | − | 58143.4i | −0.703214 | − | 2.16427i | ||||
\(898\) | 660.932 | + | 480.195i | 0.0245608 | + | 0.0178445i | ||||
\(899\) | −9082.17 | + | 6598.58i | −0.336938 | + | 0.244800i | ||||
\(900\) | 4102.65 | − | 12626.7i | 0.151950 | − | 0.467654i | ||||
\(901\) | 322.446 | 0.0119226 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22212.0 | −0.818571 | ||||||||
\(904\) | 3801.21 | − | 11698.9i | 0.139852 | − | 0.430421i | ||||
\(905\) | 7536.32 | − | 5475.46i | 0.276813 | − | 0.201117i | ||||
\(906\) | −360.686 | − | 262.054i | −0.0132263 | − | 0.00960944i | ||||
\(907\) | −10418.1 | − | 32063.6i | −0.381398 | − | 1.17382i | −0.939060 | − | 0.343753i | \(-0.888302\pi\) |
0.557662 | − | 0.830068i | \(-0.311698\pi\) | |||||||
\(908\) | −309.845 | − | 953.605i | −0.0113244 | − | 0.0348530i | ||||
\(909\) | −11306.1 | − | 8214.33i | −0.412539 | − | 0.299727i | ||||
\(910\) | 23134.1 | − | 16807.9i | 0.842733 | − | 0.612282i | ||||
\(911\) | 4644.75 | − | 14295.1i | 0.168922 | − | 0.519887i | −0.830382 | − | 0.557194i | \(-0.811878\pi\) |
0.999304 | + | 0.0373070i | \(0.0118780\pi\) | |||||||
\(912\) | 2744.42 | 0.0996455 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3045.69 | −0.110222 | ||||||||
\(915\) | 19386.9 | − | 59666.7i | 0.700449 | − | 2.15576i | ||||
\(916\) | −5822.70 | + | 4230.44i | −0.210030 | + | 0.152596i | ||||
\(917\) | 4577.16 | + | 3325.50i | 0.164832 | + | 0.119758i | ||||
\(918\) | −844.947 | − | 2600.48i | −0.0303784 | − | 0.0934952i | ||||
\(919\) | 5281.31 | + | 16254.2i | 0.189570 | + | 0.583435i | 0.999997 | − | 0.00240379i | \(-0.000765151\pi\) |
−0.810428 | + | 0.585839i | \(0.800765\pi\) | |||||||
\(920\) | −17162.1 | − | 12469.0i | −0.615018 | − | 0.446837i | ||||
\(921\) | −52655.2 | + | 38256.3i | −1.88387 | + | 1.36871i | ||||
\(922\) | 8566.79 | − | 26365.9i | 0.306000 | − | 0.941771i | ||||
\(923\) | 3453.98 | 0.123173 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21689.1 | 0.770955 | ||||||||
\(926\) | −4018.62 | + | 12368.0i | −0.142613 | + | 0.438919i | ||||
\(927\) | −37646.7 | + | 27351.9i | −1.33385 | + | 0.969099i | ||||
\(928\) | −3867.65 | − | 2810.01i | −0.136812 | − | 0.0994001i | ||||
\(929\) | 4066.74 | + | 12516.1i | 0.143623 | + | 0.442025i | 0.996831 | − | 0.0795446i | \(-0.0253466\pi\) |
−0.853209 | + | 0.521570i | \(0.825347\pi\) | |||||||
\(930\) | −5412.16 | − | 16656.9i | −0.190830 | − | 0.587314i | ||||
\(931\) | 2324.20 | + | 1688.63i | 0.0818182 | + | 0.0594444i | ||||
\(932\) | 10292.2 | − | 7477.75i | 0.361731 | − | 0.262813i | ||||
\(933\) | 12119.0 | − | 37298.6i | 0.425252 | − | 1.30879i | ||||
\(934\) | 847.946 | 0.0297063 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11984.4 | 0.418506 | ||||||||
\(937\) | −1253.46 | + | 3857.76i | −0.0437021 | + | 0.134501i | −0.970527 | − | 0.240993i | \(-0.922527\pi\) |
0.926825 | + | 0.375494i | \(0.122527\pi\) | |||||||
\(938\) | −18301.7 | + | 13296.9i | −0.637068 | + | 0.462857i | ||||
\(939\) | 19099.2 | + | 13876.4i | 0.663768 | + | 0.482256i | ||||
\(940\) | 9203.20 | + | 28324.5i | 0.319335 | + | 0.982813i | ||||
\(941\) | −10320.4 | − | 31763.0i | −0.357531 | − | 1.10037i | −0.954527 | − | 0.298123i | \(-0.903639\pi\) |
0.596996 | − | 0.802244i | \(-0.296361\pi\) | |||||||
\(942\) | 21789.2 | + | 15830.8i | 0.753643 | + | 0.547553i | ||||
\(943\) | −36399.3 | + | 26445.7i | −1.25697 | + | 0.913245i | ||||
\(944\) | 175.825 | − | 541.134i | 0.00606209 | − | 0.0186572i | ||||
\(945\) | 17819.5 | 0.613405 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25660.8 | 0.880533 | 0.440267 | − | 0.897867i | \(-0.354884\pi\) | ||||
0.440267 | + | 0.897867i | \(0.354884\pi\) | |||||||
\(948\) | 7459.65 | − | 22958.4i | 0.255568 | − | 0.786557i | ||||
\(949\) | 40751.6 | − | 29607.8i | 1.39394 | − | 1.01276i | ||||
\(950\) | 3465.74 | + | 2518.01i | 0.118362 | + | 0.0859948i | ||||
\(951\) | 25443.7 | + | 78307.8i | 0.867581 | + | 2.67014i | ||||
\(952\) | −1340.73 | − | 4126.33i | −0.0456441 | − | 0.140478i | ||||
\(953\) | 39522.7 | + | 28714.9i | 1.34341 | + | 0.976042i | 0.999311 | + | 0.0371079i | \(0.0118145\pi\) |
0.344096 | + | 0.938935i | \(0.388185\pi\) | |||||||
\(954\) | −712.498 | + | 517.660i | −0.0241803 | + | 0.0175680i | ||||
\(955\) | −6196.70 | + | 19071.5i | −0.209969 | + | 0.646218i | ||||
\(956\) | −20055.2 | −0.678485 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9114.68 | −0.307392 | ||||||||
\(959\) | 14015.4 | − | 43134.8i | 0.471929 | − | 1.45245i | ||||
\(960\) | 6033.98 | − | 4383.95i | 0.202860 | − | 0.147387i | ||||
\(961\) | 19533.3 | + | 14191.7i | 0.655677 | + | 0.476377i | ||||
\(962\) | 6050.03 | + | 18620.1i | 0.202766 | + | 0.624049i | ||||
\(963\) | 4155.61 | + | 12789.7i | 0.139058 | + | 0.427976i | ||||
\(964\) | 19656.3 | + | 14281.1i | 0.656728 | + | 0.477141i | ||||
\(965\) | 55804.3 | − | 40544.2i | 1.86156 | − | 1.35250i | ||||
\(966\) | 18680.4 | − | 57492.5i | 0.622188 | − | 1.91490i | ||||
\(967\) | 48861.8 | 1.62491 | 0.812456 | − | 0.583023i | \(-0.198130\pi\) | ||||
0.812456 | + | 0.583023i | \(0.198130\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4273.48 | 0.141676 | ||||||||
\(970\) | −1656.39 | + | 5097.85i | −0.0548284 | + | 0.168745i | ||||
\(971\) | −28224.6 | + | 20506.4i | −0.932822 | + | 0.677735i | −0.946682 | − | 0.322169i | \(-0.895588\pi\) |
0.0138603 | + | 0.999904i | \(0.495588\pi\) | |||||||
\(972\) | −17181.4 | − | 12483.0i | −0.566970 | − | 0.411928i | ||||
\(973\) | 1166.59 | + | 3590.40i | 0.0384370 | + | 0.118297i | ||||
\(974\) | −4146.34 | − | 12761.1i | −0.136404 | − | 0.419808i | ||||
\(975\) | 27144.1 | + | 19721.3i | 0.891596 | + | 0.647782i | ||||
\(976\) | 6968.46 | − | 5062.88i | 0.228540 | − | 0.166044i | ||||
\(977\) | −5875.16 | + | 18081.9i | −0.192388 | + | 0.592109i | 0.807609 | + | 0.589718i | \(0.200761\pi\) |
−0.999997 | + | 0.00239112i | \(0.999239\pi\) | |||||||
\(978\) | −51842.7 | −1.69504 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 7807.52 | 0.254492 | ||||||||
\(981\) | −5318.33 | + | 16368.1i | −0.173090 | + | 0.532716i | ||||
\(982\) | 23506.2 | − | 17078.3i | 0.763864 | − | 0.554979i | ||||
\(983\) | 6025.47 | + | 4377.76i | 0.195506 | + | 0.142044i | 0.681232 | − | 0.732068i | \(-0.261445\pi\) |
−0.485726 | + | 0.874111i | \(0.661445\pi\) | |||||||
\(984\) | −4888.24 | − | 15044.5i | −0.158365 | − | 0.487399i | ||||
\(985\) | −3064.20 | − | 9430.63i | −0.0991202 | − | 0.305061i | ||||
\(986\) | −6022.54 | − | 4375.63i | −0.194520 | − | 0.141327i | ||||
\(987\) | −68660.5 | + | 49884.8i | −2.21427 | + | 1.60876i | ||||
\(988\) | −1194.96 | + | 3677.72i | −0.0384786 | + | 0.118425i | ||||
\(989\) | −23218.2 | −0.746506 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5313.37 | 0.170318 | 0.0851588 | − | 0.996367i | \(-0.472860\pi\) | ||||
0.0851588 | + | 0.996367i | \(0.472860\pi\) | |||||||
\(992\) | 743.061 | − | 2286.91i | 0.0237825 | − | 0.0731949i | ||||
\(993\) | 1958.35 | − | 1422.82i | 0.0625844 | − | 0.0454702i | ||||
\(994\) | 2763.05 | + | 2007.47i | 0.0881676 | + | 0.0640575i | ||||
\(995\) | −14027.3 | − | 43171.5i | −0.446929 | − | 1.37551i | ||||
\(996\) | 5187.57 | + | 15965.7i | 0.165035 | + | 0.507924i | ||||
\(997\) | 43301.8 | + | 31460.6i | 1.37551 | + | 0.999365i | 0.997284 | + | 0.0736504i | \(0.0234649\pi\) |
0.378223 | + | 0.925714i | \(0.376535\pi\) | |||||||
\(998\) | 15694.2 | − | 11402.5i | 0.497786 | − | 0.361663i | ||||
\(999\) | −3770.14 | + | 11603.3i | −0.119401 | + | 0.367480i |
(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 | 242.4.c.q.9.2 | 8 | ||
11.2 | odd | 10 | 242.4.c.r.3.1 | 8 | |||
11.3 | even | 5 | 242.4.c.n.81.1 | 8 | |||
11.4 | even | 5 | 242.4.a.o.1.1 | 4 | |||
11.5 | even | 5 | inner | 242.4.c.q.27.2 | 8 | ||
11.6 | odd | 10 | 22.4.c.b.5.2 | ✓ | 8 | ||
11.7 | odd | 10 | 242.4.a.n.1.1 | 4 | |||
11.8 | odd | 10 | 242.4.c.r.81.1 | 8 | |||
11.9 | even | 5 | 242.4.c.n.3.1 | 8 | |||
11.10 | odd | 2 | 22.4.c.b.9.2 | yes | 8 | ||
33.17 | even | 10 | 198.4.f.d.181.1 | 8 | |||
33.26 | odd | 10 | 2178.4.a.bt.1.1 | 4 | |||
33.29 | even | 10 | 2178.4.a.by.1.1 | 4 | |||
33.32 | even | 2 | 198.4.f.d.163.1 | 8 | |||
44.7 | even | 10 | 1936.4.a.bn.1.4 | 4 | |||
44.15 | odd | 10 | 1936.4.a.bm.1.4 | 4 | |||
44.39 | even | 10 | 176.4.m.b.49.1 | 8 | |||
44.43 | even | 2 | 176.4.m.b.97.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.4.c.b.5.2 | ✓ | 8 | 11.6 | odd | 10 | ||
22.4.c.b.9.2 | yes | 8 | 11.10 | odd | 2 | ||
176.4.m.b.49.1 | 8 | 44.39 | even | 10 | |||
176.4.m.b.97.1 | 8 | 44.43 | even | 2 | |||
198.4.f.d.163.1 | 8 | 33.32 | even | 2 | |||
198.4.f.d.181.1 | 8 | 33.17 | even | 10 | |||
242.4.a.n.1.1 | 4 | 11.7 | odd | 10 | |||
242.4.a.o.1.1 | 4 | 11.4 | even | 5 | |||
242.4.c.n.3.1 | 8 | 11.9 | even | 5 | |||
242.4.c.n.81.1 | 8 | 11.3 | even | 5 | |||
242.4.c.q.9.2 | 8 | 1.1 | even | 1 | trivial | ||
242.4.c.q.27.2 | 8 | 11.5 | even | 5 | inner | ||
242.4.c.r.3.1 | 8 | 11.2 | odd | 10 | |||
242.4.c.r.81.1 | 8 | 11.8 | odd | 10 | |||
1936.4.a.bm.1.4 | 4 | 44.15 | odd | 10 | |||
1936.4.a.bn.1.4 | 4 | 44.7 | even | 10 | |||
2178.4.a.bt.1.1 | 4 | 33.26 | odd | 10 | |||
2178.4.a.by.1.1 | 4 | 33.29 | even | 10 |