Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(22,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + 5832 x^{10} - 32373 x^{9} + 52488 x^{8} - 6561 x^{7} - 40824 x^{6} + 1673055 x^{5} + \cdots + 387420489 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.5 | ||
Root | \(2.85089 + 0.934028i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.43 |
Dual form | 63.4.f.c.22.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.377604 | − | 0.654029i | 0.133503 | − | 0.231234i | −0.791522 | − | 0.611141i | \(-0.790711\pi\) |
0.925025 | + | 0.379907i | \(0.124044\pi\) | |||||||
\(3\) | 3.46745 | − | 3.86999i | 0.667311 | − | 0.744780i | ||||
\(4\) | 3.71483 | + | 6.43428i | 0.464354 | + | 0.804285i | ||||
\(5\) | 6.62462 | + | 11.4742i | 0.592524 | + | 1.02628i | 0.993891 | + | 0.110364i | \(0.0352018\pi\) |
−0.401367 | + | 0.915917i | \(0.631465\pi\) | |||||||
\(6\) | −1.22176 | − | 3.72913i | −0.0831304 | − | 0.253735i | ||||
\(7\) | −3.50000 | + | 6.06218i | −0.188982 | + | 0.327327i | ||||
\(8\) | 11.6526 | 0.514977 | ||||||||
\(9\) | −2.95361 | − | 26.8380i | −0.109393 | − | 0.993999i | ||||
\(10\) | 10.0059 | 0.316415 | ||||||||
\(11\) | 6.82672 | − | 11.8242i | 0.187121 | − | 0.324104i | −0.757168 | − | 0.653220i | \(-0.773418\pi\) |
0.944289 | + | 0.329117i | \(0.106751\pi\) | |||||||
\(12\) | 37.7816 | + | 7.93417i | 0.908883 | + | 0.190866i | ||||
\(13\) | −31.6370 | − | 54.7969i | −0.674964 | − | 1.16907i | −0.976479 | − | 0.215610i | \(-0.930826\pi\) |
0.301516 | − | 0.953461i | \(-0.402507\pi\) | |||||||
\(14\) | 2.64322 | + | 4.57820i | 0.0504594 | + | 0.0873982i | ||||
\(15\) | 67.3755 | + | 14.1489i | 1.15975 | + | 0.243549i | ||||
\(16\) | −25.3186 | + | 43.8531i | −0.395603 | + | 0.685204i | ||||
\(17\) | 46.8779 | 0.668797 | 0.334399 | − | 0.942432i | \(-0.391467\pi\) | ||||
0.334399 | + | 0.942432i | \(0.391467\pi\) | |||||||
\(18\) | −18.6681 | − | 8.20236i | −0.244451 | − | 0.107406i | ||||
\(19\) | −71.2778 | −0.860644 | −0.430322 | − | 0.902675i | \(-0.641600\pi\) | ||||
−0.430322 | + | 0.902675i | \(0.641600\pi\) | |||||||
\(20\) | −49.2187 | + | 85.2493i | −0.550282 | + | 0.953116i | ||||
\(21\) | 11.3245 | + | 34.5652i | 0.117676 | + | 0.359179i | ||||
\(22\) | −5.15559 | − | 8.92974i | −0.0499625 | − | 0.0865376i | ||||
\(23\) | −7.54915 | − | 13.0755i | −0.0684395 | − | 0.118541i | 0.829775 | − | 0.558098i | \(-0.188469\pi\) |
−0.898215 | + | 0.439557i | \(0.855135\pi\) | |||||||
\(24\) | 40.4047 | − | 45.0954i | 0.343649 | − | 0.383544i | ||||
\(25\) | −25.2712 | + | 43.7710i | −0.202169 | + | 0.350168i | ||||
\(26\) | −47.7850 | −0.360439 | ||||||||
\(27\) | −114.104 | − | 81.6288i | −0.813309 | − | 0.581832i | ||||
\(28\) | −52.0076 | −0.351019 | ||||||||
\(29\) | −50.9271 | + | 88.2083i | −0.326101 | + | 0.564823i | −0.981735 | − | 0.190256i | \(-0.939068\pi\) |
0.655634 | + | 0.755079i | \(0.272402\pi\) | |||||||
\(30\) | 34.6950 | − | 38.7228i | 0.211147 | − | 0.235659i | ||||
\(31\) | −113.589 | − | 196.742i | −0.658104 | − | 1.13987i | −0.981106 | − | 0.193471i | \(-0.938025\pi\) |
0.323002 | − | 0.946398i | \(-0.395308\pi\) | |||||||
\(32\) | 65.7311 | + | 113.850i | 0.363117 | + | 0.628937i | ||||
\(33\) | −22.0883 | − | 67.4192i | −0.116518 | − | 0.355642i | ||||
\(34\) | 17.7013 | − | 30.6595i | 0.0892865 | − | 0.154649i | ||||
\(35\) | −92.7447 | −0.447906 | ||||||||
\(36\) | 161.711 | − | 118.703i | 0.748661 | − | 0.549550i | ||||
\(37\) | −112.457 | −0.499672 | −0.249836 | − | 0.968288i | \(-0.580377\pi\) | ||||
−0.249836 | + | 0.968288i | \(0.580377\pi\) | |||||||
\(38\) | −26.9147 | + | 46.6177i | −0.114899 | + | 0.199010i | ||||
\(39\) | −321.763 | − | 67.5706i | −1.32111 | − | 0.277435i | ||||
\(40\) | 77.1940 | + | 133.704i | 0.305136 | + | 0.528511i | ||||
\(41\) | 255.235 | + | 442.080i | 0.972220 | + | 1.68393i | 0.688820 | + | 0.724933i | \(0.258129\pi\) |
0.283400 | + | 0.959002i | \(0.408538\pi\) | |||||||
\(42\) | 26.8828 | + | 5.64542i | 0.0987645 | + | 0.0207407i | ||||
\(43\) | −175.214 | + | 303.479i | −0.621392 | + | 1.07628i | 0.367835 | + | 0.929891i | \(0.380099\pi\) |
−0.989227 | + | 0.146391i | \(0.953234\pi\) | |||||||
\(44\) | 101.440 | 0.347562 | ||||||||
\(45\) | 288.377 | − | 211.682i | 0.955305 | − | 0.701236i | ||||
\(46\) | −11.4023 | −0.0365475 | ||||||||
\(47\) | 274.505 | − | 475.457i | 0.851931 | − | 1.47559i | −0.0275329 | − | 0.999621i | \(-0.508765\pi\) |
0.879464 | − | 0.475966i | \(-0.157902\pi\) | |||||||
\(48\) | 81.9200 | + | 250.041i | 0.246336 | + | 0.751881i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 19.0850 | + | 33.0561i | 0.0539805 | + | 0.0934969i | ||||
\(51\) | 162.547 | − | 181.417i | 0.446296 | − | 0.498107i | ||||
\(52\) | 235.052 | − | 407.123i | 0.626844 | − | 1.08573i | ||||
\(53\) | −43.0044 | −0.111455 | −0.0557275 | − | 0.998446i | \(-0.517748\pi\) | ||||
−0.0557275 | + | 0.998446i | \(0.517748\pi\) | |||||||
\(54\) | −96.4737 | + | 43.8040i | −0.243119 | + | 0.110388i | ||||
\(55\) | 180.898 | 0.443496 | ||||||||
\(56\) | −40.7841 | + | 70.6401i | −0.0973214 | + | 0.168566i | ||||
\(57\) | −247.152 | + | 275.844i | −0.574317 | + | 0.640990i | ||||
\(58\) | 38.4605 | + | 66.6155i | 0.0870709 | + | 0.150811i | ||||
\(59\) | −166.527 | − | 288.433i | −0.367456 | − | 0.636453i | 0.621711 | − | 0.783247i | \(-0.286438\pi\) |
−0.989167 | + | 0.146794i | \(0.953105\pi\) | |||||||
\(60\) | 159.250 | + | 486.073i | 0.342652 | + | 1.04586i | ||||
\(61\) | 214.028 | − | 370.708i | 0.449238 | − | 0.778103i | −0.549099 | − | 0.835757i | \(-0.685029\pi\) |
0.998337 | + | 0.0576548i | \(0.0183623\pi\) | |||||||
\(62\) | −171.567 | −0.351435 | ||||||||
\(63\) | 173.034 | + | 76.0275i | 0.346036 | + | 0.152041i | ||||
\(64\) | −305.816 | −0.597297 | ||||||||
\(65\) | 419.166 | − | 726.018i | 0.799865 | − | 1.38541i | ||||
\(66\) | −52.4347 | − | 11.0113i | −0.0977920 | − | 0.0205364i | ||||
\(67\) | 363.134 | + | 628.966i | 0.662147 | + | 1.14687i | 0.980050 | + | 0.198749i | \(0.0636880\pi\) |
−0.317903 | + | 0.948123i | \(0.602979\pi\) | |||||||
\(68\) | 174.143 | + | 301.625i | 0.310559 | + | 0.537903i | ||||
\(69\) | −76.7784 | − | 16.1235i | −0.133957 | − | 0.0281311i | ||||
\(70\) | −35.0207 | + | 60.6577i | −0.0597968 | + | 0.103571i | ||||
\(71\) | −775.662 | −1.29654 | −0.648269 | − | 0.761412i | \(-0.724507\pi\) | ||||
−0.648269 | + | 0.761412i | \(0.724507\pi\) | |||||||
\(72\) | −34.4172 | − | 312.732i | −0.0563348 | − | 0.511886i | ||||
\(73\) | 768.941 | 1.23285 | 0.616423 | − | 0.787416i | \(-0.288581\pi\) | ||||
0.616423 | + | 0.787416i | \(0.288581\pi\) | |||||||
\(74\) | −42.4643 | + | 73.5503i | −0.0667078 | + | 0.115541i | ||||
\(75\) | 81.7666 | + | 249.573i | 0.125888 | + | 0.384242i | ||||
\(76\) | −264.785 | − | 458.621i | −0.399643 | − | 0.692203i | ||||
\(77\) | 47.7871 | + | 82.7696i | 0.0707252 | + | 0.122500i | ||||
\(78\) | −165.692 | + | 184.927i | −0.240525 | + | 0.268447i | ||||
\(79\) | −24.4554 | + | 42.3580i | −0.0348285 | + | 0.0603247i | −0.882914 | − | 0.469534i | \(-0.844422\pi\) |
0.848086 | + | 0.529859i | \(0.177755\pi\) | |||||||
\(80\) | −670.904 | −0.937617 | ||||||||
\(81\) | −711.552 | + | 158.538i | −0.976066 | + | 0.217473i | ||||
\(82\) | 385.511 | 0.519177 | ||||||||
\(83\) | 238.505 | − | 413.103i | 0.315414 | − | 0.546313i | −0.664111 | − | 0.747634i | \(-0.731190\pi\) |
0.979525 | + | 0.201321i | \(0.0645233\pi\) | |||||||
\(84\) | −180.334 | + | 201.269i | −0.234238 | + | 0.261431i | ||||
\(85\) | 310.548 | + | 537.885i | 0.396279 | + | 0.686375i | ||||
\(86\) | 132.323 | + | 229.190i | 0.165915 | + | 0.287374i | ||||
\(87\) | 164.778 | + | 502.945i | 0.203058 | + | 0.619786i | ||||
\(88\) | 79.5490 | − | 137.783i | 0.0963631 | − | 0.166906i | ||||
\(89\) | −1255.64 | −1.49548 | −0.747740 | − | 0.663992i | \(-0.768861\pi\) | ||||
−0.747740 | + | 0.663992i | \(0.768861\pi\) | |||||||
\(90\) | −29.5536 | − | 268.538i | −0.0346136 | − | 0.314516i | ||||
\(91\) | 442.918 | 0.510225 | ||||||||
\(92\) | 56.0877 | − | 97.1467i | 0.0635603 | − | 0.110090i | ||||
\(93\) | −1155.25 | − | 242.605i | −1.28811 | − | 0.270505i | ||||
\(94\) | −207.308 | − | 359.069i | −0.227471 | − | 0.393991i | ||||
\(95\) | −472.188 | − | 817.854i | −0.509952 | − | 0.883263i | ||||
\(96\) | 668.516 | + | 140.389i | 0.710731 | + | 0.149254i | ||||
\(97\) | −842.449 | + | 1459.16i | −0.881832 | + | 1.52738i | −0.0325300 | + | 0.999471i | \(0.510356\pi\) |
−0.849302 | + | 0.527907i | \(0.822977\pi\) | |||||||
\(98\) | −37.0051 | −0.0381437 | ||||||||
\(99\) | −337.502 | − | 148.291i | −0.342628 | − | 0.150544i | ||||
\(100\) | −375.513 | −0.375513 | ||||||||
\(101\) | 675.564 | − | 1170.11i | 0.665556 | − | 1.15278i | −0.313579 | − | 0.949562i | \(-0.601528\pi\) |
0.979134 | − | 0.203214i | \(-0.0651387\pi\) | |||||||
\(102\) | −57.2736 | − | 174.814i | −0.0555974 | − | 0.169697i | ||||
\(103\) | −210.779 | − | 365.080i | −0.201638 | − | 0.349247i | 0.747419 | − | 0.664353i | \(-0.231293\pi\) |
−0.949056 | + | 0.315107i | \(0.897960\pi\) | |||||||
\(104\) | −368.653 | − | 638.526i | −0.347591 | − | 0.602045i | ||||
\(105\) | −321.587 | + | 358.921i | −0.298892 | + | 0.333591i | ||||
\(106\) | −16.2386 | + | 28.1261i | −0.0148796 | + | 0.0257722i | ||||
\(107\) | 1882.83 | 1.70112 | 0.850560 | − | 0.525878i | \(-0.176263\pi\) | ||||
0.850560 | + | 0.525878i | \(0.176263\pi\) | |||||||
\(108\) | 101.345 | − | 1037.41i | 0.0902955 | − | 0.924308i | ||||
\(109\) | −217.462 | −0.191093 | −0.0955464 | − | 0.995425i | \(-0.530460\pi\) | ||||
−0.0955464 | + | 0.995425i | \(0.530460\pi\) | |||||||
\(110\) | 68.3076 | − | 118.312i | 0.0592080 | − | 0.102551i | ||||
\(111\) | −389.940 | + | 435.209i | −0.333437 | + | 0.372146i | ||||
\(112\) | −177.230 | − | 306.972i | −0.149524 | − | 0.258983i | ||||
\(113\) | 744.858 | + | 1290.13i | 0.620091 | + | 1.07403i | 0.989468 | + | 0.144750i | \(0.0462378\pi\) |
−0.369377 | + | 0.929280i | \(0.620429\pi\) | |||||||
\(114\) | 87.0844 | + | 265.804i | 0.0715457 | + | 0.218376i | ||||
\(115\) | 100.021 | − | 173.241i | 0.0811040 | − | 0.140476i | ||||
\(116\) | −756.742 | −0.605705 | ||||||||
\(117\) | −1377.19 | + | 1010.92i | −1.08822 | + | 0.798801i | ||||
\(118\) | −251.524 | −0.196226 | ||||||||
\(119\) | −164.073 | + | 284.182i | −0.126391 | + | 0.218915i | ||||
\(120\) | 785.099 | + | 164.872i | 0.597245 | + | 0.125422i | ||||
\(121\) | 572.292 | + | 991.238i | 0.429971 | + | 0.744732i | ||||
\(122\) | −161.636 | − | 279.961i | −0.119949 | − | 0.207758i | ||||
\(123\) | 2595.86 | + | 545.133i | 1.90293 | + | 0.399618i | ||||
\(124\) | 843.930 | − | 1461.73i | 0.611186 | − | 1.05861i | ||||
\(125\) | 986.507 | 0.705887 | ||||||||
\(126\) | 115.062 | − | 84.4610i | 0.0813538 | − | 0.0597173i | ||||
\(127\) | 1340.67 | 0.936733 | 0.468366 | − | 0.883534i | \(-0.344843\pi\) | ||||
0.468366 | + | 0.883534i | \(0.344843\pi\) | |||||||
\(128\) | −641.326 | + | 1110.81i | −0.442858 | + | 0.767052i | ||||
\(129\) | 566.916 | + | 1730.37i | 0.386931 | + | 1.18101i | ||||
\(130\) | −316.557 | − | 548.294i | −0.213569 | − | 0.369912i | ||||
\(131\) | 162.310 | + | 281.129i | 0.108253 | + | 0.187499i | 0.915062 | − | 0.403312i | \(-0.132141\pi\) |
−0.806810 | + | 0.590811i | \(0.798808\pi\) | |||||||
\(132\) | 351.740 | − | 392.573i | 0.231932 | − | 0.258857i | ||||
\(133\) | 249.472 | − | 432.098i | 0.162646 | − | 0.281712i | ||||
\(134\) | 548.483 | 0.353595 | ||||||||
\(135\) | 180.727 | − | 1850.01i | 0.115219 | − | 1.17943i | ||||
\(136\) | 546.249 | 0.344415 | ||||||||
\(137\) | −817.305 | + | 1415.61i | −0.509687 | + | 0.882803i | 0.490250 | + | 0.871582i | \(0.336905\pi\) |
−0.999937 | + | 0.0112217i | \(0.996428\pi\) | |||||||
\(138\) | −39.5371 | + | 44.1270i | −0.0243885 | + | 0.0272198i | ||||
\(139\) | 563.815 | + | 976.556i | 0.344044 | + | 0.595902i | 0.985180 | − | 0.171526i | \(-0.0548696\pi\) |
−0.641135 | + | 0.767428i | \(0.721536\pi\) | |||||||
\(140\) | −344.531 | − | 596.745i | −0.207987 | − | 0.360244i | ||||
\(141\) | −888.181 | − | 2710.96i | −0.530485 | − | 1.61918i | ||||
\(142\) | −292.893 | + | 507.305i | −0.173092 | + | 0.299803i | ||||
\(143\) | −863.909 | −0.505201 | ||||||||
\(144\) | 1251.71 | + | 549.974i | 0.724368 | + | 0.318272i | ||||
\(145\) | −1349.49 | −0.772890 | ||||||||
\(146\) | 290.355 | − | 502.909i | 0.164589 | − | 0.285076i | ||||
\(147\) | −249.176 | − | 52.3273i | −0.139808 | − | 0.0293597i | ||||
\(148\) | −417.760 | − | 723.582i | −0.232025 | − | 0.401879i | ||||
\(149\) | 1524.86 | + | 2641.14i | 0.838401 | + | 1.45215i | 0.891231 | + | 0.453550i | \(0.149843\pi\) |
−0.0528301 | + | 0.998604i | \(0.516824\pi\) | |||||||
\(150\) | 194.103 | + | 40.7618i | 0.105656 | + | 0.0221879i | ||||
\(151\) | 1601.59 | − | 2774.04i | 0.863150 | − | 1.49502i | −0.00572215 | − | 0.999984i | \(-0.501821\pi\) |
0.868872 | − | 0.495036i | \(-0.164845\pi\) | |||||||
\(152\) | −830.571 | −0.443212 | ||||||||
\(153\) | −138.459 | − | 1258.11i | −0.0731618 | − | 0.664784i | ||||
\(154\) | 72.1783 | 0.0377681 | ||||||||
\(155\) | 1504.97 | − | 2606.69i | 0.779885 | − | 1.35080i | ||||
\(156\) | −760.528 | − | 2321.33i | −0.390327 | − | 1.19138i | ||||
\(157\) | 234.152 | + | 405.564i | 0.119028 | + | 0.206163i | 0.919383 | − | 0.393364i | \(-0.128689\pi\) |
−0.800355 | + | 0.599527i | \(0.795355\pi\) | |||||||
\(158\) | 18.4689 | + | 31.9891i | 0.00929942 | + | 0.0161071i | ||||
\(159\) | −149.116 | + | 166.427i | −0.0743751 | + | 0.0830094i | ||||
\(160\) | −870.888 | + | 1508.42i | −0.430311 | + | 0.745320i | ||||
\(161\) | 105.688 | 0.0517354 | ||||||||
\(162\) | −164.996 | + | 525.240i | −0.0800206 | + | 0.254733i | ||||
\(163\) | −3912.57 | −1.88010 | −0.940049 | − | 0.341039i | \(-0.889221\pi\) | ||||
−0.940049 | + | 0.341039i | \(0.889221\pi\) | |||||||
\(164\) | −1896.31 | + | 3284.51i | −0.902908 | + | 1.56388i | ||||
\(165\) | 627.254 | − | 700.072i | 0.295949 | − | 0.330306i | ||||
\(166\) | −180.121 | − | 311.979i | −0.0842174 | − | 0.145869i | ||||
\(167\) | 376.475 | + | 652.074i | 0.174446 | + | 0.302150i | 0.939969 | − | 0.341259i | \(-0.110853\pi\) |
−0.765523 | + | 0.643408i | \(0.777520\pi\) | |||||||
\(168\) | 131.960 | + | 402.775i | 0.0606006 | + | 0.184969i | ||||
\(169\) | −903.302 | + | 1564.56i | −0.411152 | + | 0.712137i | ||||
\(170\) | 469.056 | 0.211618 | ||||||||
\(171\) | 210.527 | + | 1912.95i | 0.0941485 | + | 0.855479i | ||||
\(172\) | −2603.56 | −1.15418 | ||||||||
\(173\) | −585.162 | + | 1013.53i | −0.257162 | + | 0.445418i | −0.965481 | − | 0.260475i | \(-0.916121\pi\) |
0.708318 | + | 0.705893i | \(0.249454\pi\) | |||||||
\(174\) | 391.161 | + | 82.1442i | 0.170424 | + | 0.0357893i | ||||
\(175\) | −176.898 | − | 306.397i | −0.0764129 | − | 0.132351i | ||||
\(176\) | 345.686 | + | 598.746i | 0.148051 | + | 0.256433i | ||||
\(177\) | −1693.65 | − | 355.669i | −0.719224 | − | 0.151038i | ||||
\(178\) | −474.135 | + | 821.225i | −0.199651 | + | 0.345806i | ||||
\(179\) | 456.552 | 0.190638 | 0.0953192 | − | 0.995447i | \(-0.469613\pi\) | ||||
0.0953192 | + | 0.995447i | \(0.469613\pi\) | |||||||
\(180\) | 2433.29 | + | 1069.14i | 1.00759 | + | 0.442715i | ||||
\(181\) | −969.577 | −0.398166 | −0.199083 | − | 0.979983i | \(-0.563796\pi\) | ||||
−0.199083 | + | 0.979983i | \(0.563796\pi\) | |||||||
\(182\) | 167.248 | − | 289.681i | 0.0681165 | − | 0.117981i | ||||
\(183\) | −692.503 | − | 2113.70i | −0.279734 | − | 0.853819i | ||||
\(184\) | −87.9672 | − | 152.364i | −0.0352447 | − | 0.0610456i | ||||
\(185\) | −744.987 | − | 1290.36i | −0.296068 | − | 0.512805i | ||||
\(186\) | −594.899 | + | 663.961i | −0.234517 | + | 0.261742i | ||||
\(187\) | 320.022 | − | 554.295i | 0.125146 | − | 0.216760i | ||||
\(188\) | 4078.97 | 1.58239 | ||||||||
\(189\) | 894.213 | − | 406.018i | 0.344150 | − | 0.156262i | ||||
\(190\) | −713.200 | −0.272321 | ||||||||
\(191\) | 1104.66 | − | 1913.33i | 0.418484 | − | 0.724835i | −0.577303 | − | 0.816530i | \(-0.695895\pi\) |
0.995787 | + | 0.0916946i | \(0.0292283\pi\) | |||||||
\(192\) | −1060.40 | + | 1183.50i | −0.398583 | + | 0.444855i | ||||
\(193\) | −334.133 | − | 578.736i | −0.124619 | − | 0.215846i | 0.796965 | − | 0.604025i | \(-0.206437\pi\) |
−0.921584 | + | 0.388179i | \(0.873104\pi\) | |||||||
\(194\) | 636.223 | + | 1101.97i | 0.235454 | + | 0.407819i | ||||
\(195\) | −1356.24 | − | 4139.60i | −0.498064 | − | 1.52022i | ||||
\(196\) | 182.027 | − | 315.280i | 0.0663363 | − | 0.114898i | ||||
\(197\) | −1668.64 | −0.603480 | −0.301740 | − | 0.953390i | \(-0.597567\pi\) | ||||
−0.301740 | + | 0.953390i | \(0.597567\pi\) | |||||||
\(198\) | −224.429 | + | 164.741i | −0.0805527 | + | 0.0591293i | ||||
\(199\) | −1022.53 | −0.364248 | −0.182124 | − | 0.983276i | \(-0.558297\pi\) | ||||
−0.182124 | + | 0.983276i | \(0.558297\pi\) | |||||||
\(200\) | −294.475 | + | 510.045i | −0.104113 | + | 0.180328i | ||||
\(201\) | 3693.24 | + | 775.584i | 1.29603 | + | 0.272167i | ||||
\(202\) | −510.191 | − | 883.676i | −0.177707 | − | 0.307798i | ||||
\(203\) | −356.490 | − | 617.458i | −0.123254 | − | 0.213483i | ||||
\(204\) | 1771.12 | + | 371.937i | 0.607859 | + | 0.127651i | ||||
\(205\) | −3381.67 | + | 5857.23i | −1.15213 | + | 1.99554i | ||||
\(206\) | −318.364 | −0.107677 | ||||||||
\(207\) | −328.623 | + | 241.224i | −0.110342 | + | 0.0809962i | ||||
\(208\) | 3204.02 | 1.06807 | ||||||||
\(209\) | −486.594 | + | 842.805i | −0.161045 | + | 0.278938i | ||||
\(210\) | 113.312 | + | 345.857i | 0.0372346 | + | 0.113650i | ||||
\(211\) | −926.172 | − | 1604.18i | −0.302182 | − | 0.523394i | 0.674448 | − | 0.738322i | \(-0.264382\pi\) |
−0.976630 | + | 0.214928i | \(0.931048\pi\) | |||||||
\(212\) | −159.754 | − | 276.702i | −0.0517545 | − | 0.0896415i | ||||
\(213\) | −2689.57 | + | 3001.80i | −0.865193 | + | 0.965634i | ||||
\(214\) | 710.962 | − | 1231.42i | 0.227105 | − | 0.393357i | ||||
\(215\) | −4642.90 | −1.47276 | ||||||||
\(216\) | −1329.61 | − | 951.187i | −0.418835 | − | 0.299630i | ||||
\(217\) | 1590.25 | 0.497480 | ||||||||
\(218\) | −82.1146 | + | 142.227i | −0.0255115 | + | 0.0441872i | ||||
\(219\) | 2666.26 | − | 2975.79i | 0.822691 | − | 0.918198i | ||||
\(220\) | 672.005 | + | 1163.95i | 0.205939 | + | 0.356697i | ||||
\(221\) | −1483.08 | − | 2568.76i | −0.451414 | − | 0.781872i | ||||
\(222\) | 137.396 | + | 419.368i | 0.0415379 | + | 0.126784i | ||||
\(223\) | 1821.92 | − | 3155.65i | 0.547106 | − | 0.947615i | −0.451365 | − | 0.892339i | \(-0.649063\pi\) |
0.998471 | − | 0.0552757i | \(-0.0176038\pi\) | |||||||
\(224\) | −920.236 | −0.274490 | ||||||||
\(225\) | 1249.36 | + | 548.945i | 0.370182 | + | 0.162650i | ||||
\(226\) | 1125.04 | 0.331136 | ||||||||
\(227\) | −2313.26 | + | 4006.69i | −0.676373 | + | 1.17151i | 0.299692 | + | 0.954036i | \(0.403116\pi\) |
−0.976065 | + | 0.217477i | \(0.930217\pi\) | |||||||
\(228\) | −2692.98 | − | 565.530i | −0.782225 | − | 0.164268i | ||||
\(229\) | −369.370 | − | 639.768i | −0.106588 | − | 0.184616i | 0.807798 | − | 0.589460i | \(-0.200659\pi\) |
−0.914386 | + | 0.404844i | \(0.867326\pi\) | |||||||
\(230\) | −75.5362 | − | 130.833i | −0.0216553 | − | 0.0375080i | ||||
\(231\) | 486.017 | + | 102.064i | 0.138431 | + | 0.0290706i | ||||
\(232\) | −593.432 | + | 1027.86i | −0.167934 | + | 0.290871i | ||||
\(233\) | 5281.44 | 1.48497 | 0.742486 | − | 0.669861i | \(-0.233646\pi\) | ||||
0.742486 | + | 0.669861i | \(0.233646\pi\) | |||||||
\(234\) | 141.138 | + | 1282.45i | 0.0394295 | + | 0.358276i | ||||
\(235\) | 7273.98 | 2.01916 | ||||||||
\(236\) | 1237.24 | − | 2142.96i | 0.341259 | − | 0.591079i | ||||
\(237\) | 79.1272 | + | 241.517i | 0.0216872 | + | 0.0661949i | ||||
\(238\) | 123.909 | + | 214.616i | 0.0337471 | + | 0.0584517i | ||||
\(239\) | −735.318 | − | 1273.61i | −0.199012 | − | 0.344698i | 0.749197 | − | 0.662348i | \(-0.230440\pi\) |
−0.948208 | + | 0.317650i | \(0.897106\pi\) | |||||||
\(240\) | −2326.33 | + | 2596.39i | −0.625682 | + | 0.698318i | ||||
\(241\) | 2497.89 | − | 4326.48i | 0.667650 | − | 1.15640i | −0.310910 | − | 0.950439i | \(-0.600634\pi\) |
0.978560 | − | 0.205964i | \(-0.0660329\pi\) | |||||||
\(242\) | 864.397 | 0.229610 | ||||||||
\(243\) | −1853.73 | + | 3303.42i | −0.489370 | + | 0.872076i | ||||
\(244\) | 3180.31 | 0.834421 | ||||||||
\(245\) | 324.606 | − | 562.235i | 0.0846463 | − | 0.146612i | ||||
\(246\) | 1336.74 | − | 1491.92i | 0.346452 | − | 0.386673i | ||||
\(247\) | 2255.02 | + | 3905.80i | 0.580904 | + | 1.00615i | ||||
\(248\) | −1323.61 | − | 2292.56i | −0.338908 | − | 0.587006i | ||||
\(249\) | −771.700 | − | 2355.43i | −0.196404 | − | 0.599474i | ||||
\(250\) | 372.509 | − | 645.204i | 0.0942380 | − | 0.163225i | ||||
\(251\) | 1656.71 | 0.416617 | 0.208308 | − | 0.978063i | \(-0.433204\pi\) | ||||
0.208308 | + | 0.978063i | \(0.433204\pi\) | |||||||
\(252\) | 153.610 | + | 1395.78i | 0.0383990 | + | 0.348912i | ||||
\(253\) | −206.144 | −0.0512259 | ||||||||
\(254\) | 506.241 | − | 876.835i | 0.125057 | − | 0.216604i | ||||
\(255\) | 3158.42 | + | 663.271i | 0.775639 | + | 0.162885i | ||||
\(256\) | −738.931 | − | 1279.87i | −0.180403 | − | 0.312467i | ||||
\(257\) | −1881.10 | − | 3258.16i | −0.456575 | − | 0.790811i | 0.542202 | − | 0.840248i | \(-0.317591\pi\) |
−0.998777 | + | 0.0494368i | \(0.984257\pi\) | |||||||
\(258\) | 1345.78 | + | 282.616i | 0.324747 | + | 0.0681972i | ||||
\(259\) | 393.601 | − | 681.736i | 0.0944292 | − | 0.163556i | ||||
\(260\) | 6228.53 | 1.48568 | ||||||||
\(261\) | 2517.75 | + | 1106.25i | 0.597106 | + | 0.262356i | ||||
\(262\) | 245.155 | 0.0578082 | ||||||||
\(263\) | −212.838 | + | 368.646i | −0.0499017 | + | 0.0864322i | −0.889897 | − | 0.456161i | \(-0.849224\pi\) |
0.839996 | + | 0.542593i | \(0.182557\pi\) | |||||||
\(264\) | −257.386 | − | 785.609i | −0.0600039 | − | 0.183147i | ||||
\(265\) | −284.888 | − | 493.441i | −0.0660397 | − | 0.114384i | ||||
\(266\) | −188.403 | − | 326.324i | −0.0434276 | − | 0.0752188i | ||||
\(267\) | −4353.87 | + | 4859.32i | −0.997950 | + | 1.11380i | ||||
\(268\) | −2697.96 | + | 4673.01i | −0.614941 | + | 1.06511i | ||||
\(269\) | −1371.63 | −0.310891 | −0.155446 | − | 0.987844i | \(-0.549681\pi\) | ||||
−0.155446 | + | 0.987844i | \(0.549681\pi\) | |||||||
\(270\) | −1141.72 | − | 816.771i | −0.257343 | − | 0.184100i | ||||
\(271\) | 944.084 | 0.211620 | 0.105810 | − | 0.994386i | \(-0.466256\pi\) | ||||
0.105810 | + | 0.994386i | \(0.466256\pi\) | |||||||
\(272\) | −1186.88 | + | 2055.74i | −0.264578 | + | 0.458263i | ||||
\(273\) | 1535.80 | − | 1714.09i | 0.340478 | − | 0.380005i | ||||
\(274\) | 617.235 | + | 1069.08i | 0.136089 | + | 0.235714i | ||||
\(275\) | 345.039 | + | 597.625i | 0.0756604 | + | 0.131048i | ||||
\(276\) | −181.475 | − | 553.910i | −0.0395780 | − | 0.120802i | ||||
\(277\) | −1138.54 | + | 1972.01i | −0.246961 | + | 0.427750i | −0.962681 | − | 0.270638i | \(-0.912765\pi\) |
0.715720 | + | 0.698388i | \(0.246099\pi\) | |||||||
\(278\) | 851.594 | 0.183724 | ||||||||
\(279\) | −4944.66 | + | 3629.60i | −1.06104 | + | 0.778848i | ||||
\(280\) | −1080.72 | −0.230661 | ||||||||
\(281\) | 509.924 | − | 883.214i | 0.108254 | − | 0.187502i | −0.806809 | − | 0.590813i | \(-0.798807\pi\) |
0.915063 | + | 0.403311i | \(0.132141\pi\) | |||||||
\(282\) | −2108.42 | − | 442.771i | −0.445230 | − | 0.0934987i | ||||
\(283\) | −1172.93 | − | 2031.58i | −0.246374 | − | 0.426731i | 0.716143 | − | 0.697953i | \(-0.245906\pi\) |
−0.962517 | + | 0.271222i | \(0.912572\pi\) | |||||||
\(284\) | −2881.45 | − | 4990.82i | −0.602052 | − | 1.04278i | ||||
\(285\) | −4802.37 | − | 1008.50i | −0.998133 | − | 0.209609i | ||||
\(286\) | −326.215 | + | 565.021i | −0.0674458 | + | 0.116820i | ||||
\(287\) | −3573.29 | −0.734929 | ||||||||
\(288\) | 2861.35 | − | 2100.36i | 0.585440 | − | 0.429739i | ||||
\(289\) | −2715.46 | −0.552710 | ||||||||
\(290\) | −509.572 | + | 882.605i | −0.103183 | + | 0.178718i | ||||
\(291\) | 2725.80 | + | 8319.84i | 0.549104 | + | 1.67601i | ||||
\(292\) | 2856.48 | + | 4947.58i | 0.572476 | + | 0.991558i | ||||
\(293\) | −824.163 | − | 1427.49i | −0.164328 | − | 0.284625i | 0.772088 | − | 0.635515i | \(-0.219212\pi\) |
−0.936416 | + | 0.350891i | \(0.885879\pi\) | |||||||
\(294\) | −128.313 | + | 143.209i | −0.0254537 | + | 0.0284087i | ||||
\(295\) | 2206.35 | − | 3821.51i | 0.435453 | − | 0.754227i | ||||
\(296\) | −1310.42 | −0.257320 | ||||||||
\(297\) | −1744.15 | + | 791.936i | −0.340761 | + | 0.154723i | ||||
\(298\) | 2303.18 | 0.447716 | ||||||||
\(299\) | −477.665 | + | 827.341i | −0.0923883 | + | 0.160021i | ||||
\(300\) | −1302.07 | + | 1453.23i | −0.250584 | + | 0.279674i | ||||
\(301\) | −1226.50 | − | 2124.35i | −0.234864 | − | 0.406796i | ||||
\(302\) | −1209.53 | − | 2094.97i | −0.230466 | − | 0.399179i | ||||
\(303\) | −2185.83 | − | 6671.72i | −0.414432 | − | 1.26495i | ||||
\(304\) | 1804.65 | − | 3125.75i | 0.340473 | − | 0.589717i | ||||
\(305\) | 5671.42 | 1.06474 | ||||||||
\(306\) | −875.120 | − | 384.509i | −0.163488 | − | 0.0718331i | ||||
\(307\) | −6918.79 | −1.28624 | −0.643121 | − | 0.765765i | \(-0.722361\pi\) | ||||
−0.643121 | + | 0.765765i | \(0.722361\pi\) | |||||||
\(308\) | −355.042 | + | 614.950i | −0.0656831 | + | 0.113766i | ||||
\(309\) | −2143.72 | − | 450.184i | −0.394667 | − | 0.0828804i | ||||
\(310\) | −1136.56 | − | 1968.59i | −0.208234 | − | 0.360672i | ||||
\(311\) | −242.477 | − | 419.983i | −0.0442110 | − | 0.0765757i | 0.843073 | − | 0.537799i | \(-0.180744\pi\) |
−0.887284 | + | 0.461223i | \(0.847411\pi\) | |||||||
\(312\) | −3749.37 | − | 787.372i | −0.680341 | − | 0.142872i | ||||
\(313\) | −2147.26 | + | 3719.17i | −0.387765 | + | 0.671628i | −0.992149 | − | 0.125065i | \(-0.960086\pi\) |
0.604384 | + | 0.796693i | \(0.293419\pi\) | |||||||
\(314\) | 353.667 | 0.0635624 | ||||||||
\(315\) | 273.932 | + | 2489.08i | 0.0489978 | + | 0.445218i | ||||
\(316\) | −363.391 | −0.0646910 | ||||||||
\(317\) | 912.824 | − | 1581.06i | 0.161733 | − | 0.280130i | −0.773757 | − | 0.633482i | \(-0.781625\pi\) |
0.935490 | + | 0.353353i | \(0.114958\pi\) | |||||||
\(318\) | 52.5412 | + | 160.369i | 0.00926529 | + | 0.0282800i | ||||
\(319\) | 695.330 | + | 1204.35i | 0.122041 | + | 0.211381i | ||||
\(320\) | −2025.92 | − | 3508.99i | −0.353913 | − | 0.612995i | ||||
\(321\) | 6528.61 | − | 7286.52i | 1.13518 | − | 1.26696i | ||||
\(322\) | 39.9082 | − | 69.1231i | 0.00690683 | − | 0.0119630i | ||||
\(323\) | −3341.35 | −0.575597 | ||||||||
\(324\) | −3663.37 | − | 3989.38i | −0.628150 | − | 0.684051i | ||||
\(325\) | 3198.02 | 0.545828 | ||||||||
\(326\) | −1477.40 | + | 2558.93i | −0.250999 | + | 0.434743i | ||||
\(327\) | −754.039 | + | 841.577i | −0.127518 | + | 0.142322i | ||||
\(328\) | 2974.15 | + | 5151.38i | 0.500671 | + | 0.867187i | ||||
\(329\) | 1921.54 | + | 3328.20i | 0.322000 | + | 0.557720i | ||||
\(330\) | −221.014 | − | 674.592i | −0.0368679 | − | 0.112530i | ||||
\(331\) | 4978.50 | − | 8623.02i | 0.826717 | − | 1.43192i | −0.0738835 | − | 0.997267i | \(-0.523539\pi\) |
0.900600 | − | 0.434648i | \(-0.143127\pi\) | |||||||
\(332\) | 3544.03 | 0.585855 | ||||||||
\(333\) | 332.155 | + | 3018.13i | 0.0546607 | + | 0.496674i | ||||
\(334\) | 568.633 | 0.0931563 | ||||||||
\(335\) | −4811.25 | + | 8333.33i | −0.784676 | + | 1.35910i | ||||
\(336\) | −1802.51 | − | 378.530i | −0.292664 | − | 0.0614598i | ||||
\(337\) | 609.417 | + | 1055.54i | 0.0985076 | + | 0.170620i | 0.911067 | − | 0.412258i | \(-0.135260\pi\) |
−0.812560 | + | 0.582878i | \(0.801926\pi\) | |||||||
\(338\) | 682.180 | + | 1181.57i | 0.109780 | + | 0.190145i | ||||
\(339\) | 7575.55 | + | 1590.87i | 1.21371 | + | 0.254880i | ||||
\(340\) | −2307.27 | + | 3996.31i | −0.368027 | + | 0.637441i | ||||
\(341\) | −3101.77 | −0.492581 | ||||||||
\(342\) | 1330.62 | + | 584.646i | 0.210385 | + | 0.0924387i | ||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −2041.69 | + | 3536.32i | −0.320002 | + | 0.554260i | ||||
\(345\) | −323.623 | − | 987.781i | −0.0505023 | − | 0.154146i | ||||
\(346\) | 441.919 | + | 765.426i | 0.0686639 | + | 0.118929i | ||||
\(347\) | 1130.99 | + | 1958.93i | 0.174970 | + | 0.303057i | 0.940151 | − | 0.340758i | \(-0.110684\pi\) |
−0.765181 | + | 0.643815i | \(0.777350\pi\) | |||||||
\(348\) | −2623.96 | + | 2928.58i | −0.404193 | + | 0.451116i | ||||
\(349\) | −3540.17 | + | 6131.75i | −0.542983 | + | 0.940473i | 0.455748 | + | 0.890109i | \(0.349372\pi\) |
−0.998731 | + | 0.0503647i | \(0.983962\pi\) | |||||||
\(350\) | −267.190 | −0.0408054 | ||||||||
\(351\) | −863.094 | + | 8835.04i | −0.131249 | + | 1.34353i | ||||
\(352\) | 1794.91 | 0.271787 | ||||||||
\(353\) | 3848.28 | − | 6665.41i | 0.580235 | − | 1.00500i | −0.415216 | − | 0.909723i | \(-0.636294\pi\) |
0.995451 | − | 0.0952740i | \(-0.0303727\pi\) | |||||||
\(354\) | −872.147 | + | 973.395i | −0.130944 | + | 0.146145i | ||||
\(355\) | −5138.47 | − | 8900.08i | −0.768229 | − | 1.33061i | ||||
\(356\) | −4664.50 | − | 8079.14i | −0.694432 | − | 1.20279i | ||||
\(357\) | 530.868 | + | 1620.35i | 0.0787017 | + | 0.240218i | ||||
\(358\) | 172.396 | − | 298.598i | 0.0254508 | − | 0.0440821i | ||||
\(359\) | −5452.32 | −0.801567 | −0.400784 | − | 0.916173i | \(-0.631262\pi\) | ||||
−0.400784 | + | 0.916173i | \(0.631262\pi\) | |||||||
\(360\) | 3360.34 | − | 2466.64i | 0.491960 | − | 0.361120i | ||||
\(361\) | −1778.48 | −0.259292 | ||||||||
\(362\) | −366.116 | + | 634.131i | −0.0531564 | + | 0.0920696i | ||||
\(363\) | 5820.47 | + | 1222.31i | 0.841586 | + | 0.176734i | ||||
\(364\) | 1645.37 | + | 2849.86i | 0.236925 | + | 0.410366i | ||||
\(365\) | 5093.94 | + | 8822.96i | 0.730490 | + | 1.26525i | ||||
\(366\) | −1643.91 | − | 345.223i | −0.234777 | − | 0.0493035i | ||||
\(367\) | 2855.40 | − | 4945.69i | 0.406132 | − | 0.703441i | −0.588320 | − | 0.808628i | \(-0.700211\pi\) |
0.994453 | + | 0.105187i | \(0.0335440\pi\) | |||||||
\(368\) | 764.536 | 0.108299 | ||||||||
\(369\) | 11110.7 | − | 8155.72i | 1.56747 | − | 1.15060i | ||||
\(370\) | −1125.24 | −0.158104 | ||||||||
\(371\) | 150.516 | − | 260.701i | 0.0210630 | − | 0.0364822i | ||||
\(372\) | −2730.59 | − | 8334.47i | −0.380577 | − | 1.16162i | ||||
\(373\) | −139.606 | − | 241.805i | −0.0193795 | − | 0.0335662i | 0.856173 | − | 0.516689i | \(-0.172836\pi\) |
−0.875552 | + | 0.483123i | \(0.839502\pi\) | |||||||
\(374\) | −241.683 | − | 418.607i | −0.0334148 | − | 0.0578761i | ||||
\(375\) | 3420.66 | − | 3817.77i | 0.471046 | − | 0.525730i | ||||
\(376\) | 3198.70 | − | 5540.31i | 0.438724 | − | 0.759893i | ||||
\(377\) | 6444.72 | 0.880425 | ||||||||
\(378\) | 72.1102 | − | 738.154i | 0.00981203 | − | 0.100441i | ||||
\(379\) | −4973.85 | −0.674115 | −0.337058 | − | 0.941484i | \(-0.609432\pi\) | ||||
−0.337058 | + | 0.941484i | \(0.609432\pi\) | |||||||
\(380\) | 3508.20 | − | 6076.38i | 0.473597 | − | 0.820294i | ||||
\(381\) | 4648.70 | − | 5188.37i | 0.625092 | − | 0.697659i | ||||
\(382\) | −834.247 | − | 1444.96i | −0.111738 | − | 0.193535i | ||||
\(383\) | 4909.92 | + | 8504.23i | 0.655053 | + | 1.13458i | 0.981881 | + | 0.189501i | \(0.0606869\pi\) |
−0.326828 | + | 0.945084i | \(0.605980\pi\) | |||||||
\(384\) | 2075.05 | + | 6333.60i | 0.275761 | + | 0.841693i | ||||
\(385\) | −633.142 | + | 1096.63i | −0.0838128 | + | 0.145168i | ||||
\(386\) | −504.680 | −0.0665480 | ||||||||
\(387\) | 8662.27 | + | 3806.02i | 1.13780 | + | 0.499925i | ||||
\(388\) | −12518.2 | −1.63793 | ||||||||
\(389\) | 2206.60 | − | 3821.95i | 0.287607 | − | 0.498150i | −0.685631 | − | 0.727949i | \(-0.740474\pi\) |
0.973238 | + | 0.229799i | \(0.0738070\pi\) | |||||||
\(390\) | −3219.54 | − | 676.106i | −0.418019 | − | 0.0877845i | ||||
\(391\) | −353.888 | − | 612.953i | −0.0457721 | − | 0.0792797i | ||||
\(392\) | −285.488 | − | 494.481i | −0.0367840 | − | 0.0637118i | ||||
\(393\) | 1650.77 | + | 346.663i | 0.211884 | + | 0.0444958i | ||||
\(394\) | −630.084 | + | 1091.34i | −0.0805664 | + | 0.139545i | ||||
\(395\) | −648.032 | −0.0825469 | ||||||||
\(396\) | −299.616 | − | 2722.46i | −0.0380209 | − | 0.345476i | ||||
\(397\) | −977.573 | −0.123584 | −0.0617922 | − | 0.998089i | \(-0.519682\pi\) | ||||
−0.0617922 | + | 0.998089i | \(0.519682\pi\) | |||||||
\(398\) | −386.112 | + | 668.765i | −0.0486282 | + | 0.0842265i | ||||
\(399\) | −807.184 | − | 2463.73i | −0.101278 | − | 0.309125i | ||||
\(400\) | −1279.66 | − | 2216.44i | −0.159958 | − | 0.277055i | ||||
\(401\) | 7542.21 | + | 13063.5i | 0.939251 | + | 1.62683i | 0.766871 | + | 0.641801i | \(0.221812\pi\) |
0.172380 | + | 0.985031i | \(0.444854\pi\) | |||||||
\(402\) | 1901.83 | − | 2122.62i | 0.235957 | − | 0.263350i | ||||
\(403\) | −7187.25 | + | 12448.7i | −0.888393 | + | 1.53874i | ||||
\(404\) | 10038.4 | 1.23621 | ||||||||
\(405\) | −6532.86 | − | 7114.23i | −0.801531 | − | 0.872861i | ||||
\(406\) | −538.447 | −0.0658194 | ||||||||
\(407\) | −767.715 | + | 1329.72i | −0.0934993 | + | 0.161946i | ||||
\(408\) | 1894.09 | − | 2113.98i | 0.229832 | − | 0.256513i | ||||
\(409\) | 553.615 | + | 958.890i | 0.0669304 | + | 0.115927i | 0.897549 | − | 0.440915i | \(-0.145346\pi\) |
−0.830618 | + | 0.556842i | \(0.812013\pi\) | |||||||
\(410\) | 2553.86 | + | 4423.42i | 0.307625 | + | 0.532822i | ||||
\(411\) | 2644.45 | + | 8071.53i | 0.317374 | + | 0.968708i | ||||
\(412\) | 1566.02 | − | 2712.42i | 0.187263 | − | 0.324348i | ||||
\(413\) | 2331.37 | 0.277771 | ||||||||
\(414\) | 33.6781 | + | 306.016i | 0.00399804 | + | 0.0363282i | ||||
\(415\) | 6320.03 | 0.747562 | ||||||||
\(416\) | 4159.07 | − | 7203.73i | 0.490181 | − | 0.849019i | ||||
\(417\) | 5734.26 | + | 1204.20i | 0.673400 | + | 0.141415i | ||||
\(418\) | 367.479 | + | 636.492i | 0.0430000 | + | 0.0744781i | ||||
\(419\) | −3879.30 | − | 6719.15i | −0.452306 | − | 0.783417i | 0.546223 | − | 0.837640i | \(-0.316065\pi\) |
−0.998529 | + | 0.0542226i | \(0.982732\pi\) | |||||||
\(420\) | −3504.04 | − | 735.852i | −0.407094 | − | 0.0854902i | ||||
\(421\) | −2420.37 | + | 4192.20i | −0.280194 | + | 0.485309i | −0.971432 | − | 0.237317i | \(-0.923732\pi\) |
0.691239 | + | 0.722626i | \(0.257065\pi\) | |||||||
\(422\) | −1398.90 | −0.161369 | ||||||||
\(423\) | −13571.1 | − | 5962.85i | −1.55993 | − | 0.685399i | ||||
\(424\) | −501.113 | −0.0573967 | ||||||||
\(425\) | −1184.66 | + | 2051.89i | −0.135210 | + | 0.234191i | ||||
\(426\) | 947.674 | + | 2892.54i | 0.107782 | + | 0.328977i | ||||
\(427\) | 1498.20 | + | 2594.95i | 0.169796 | + | 0.294095i | ||||
\(428\) | 6994.39 | + | 12114.6i | 0.789922 | + | 1.36818i | ||||
\(429\) | −2995.56 | + | 3343.32i | −0.337126 | + | 0.376263i | ||||
\(430\) | −1753.17 | + | 3036.59i | −0.196618 | + | 0.340552i | ||||
\(431\) | −14945.3 | −1.67027 | −0.835136 | − | 0.550043i | \(-0.814611\pi\) | ||||
−0.835136 | + | 0.550043i | \(0.814611\pi\) | |||||||
\(432\) | 6468.63 | − | 2937.09i | 0.720421 | − | 0.327108i | ||||
\(433\) | −4492.90 | −0.498649 | −0.249325 | − | 0.968420i | \(-0.580209\pi\) | ||||
−0.249325 | + | 0.968420i | \(0.580209\pi\) | |||||||
\(434\) | 600.484 | − | 1040.07i | 0.0664151 | − | 0.115034i | ||||
\(435\) | −4679.29 | + | 5222.51i | −0.515758 | + | 0.575633i | ||||
\(436\) | −807.836 | − | 1399.21i | −0.0887347 | − | 0.153693i | ||||
\(437\) | 538.087 | + | 931.994i | 0.0589020 | + | 0.102021i | ||||
\(438\) | −939.462 | − | 2867.48i | −0.102487 | − | 0.312816i | ||||
\(439\) | −1421.09 | + | 2461.40i | −0.154499 | + | 0.267600i | −0.932876 | − | 0.360197i | \(-0.882710\pi\) |
0.778378 | + | 0.627796i | \(0.216043\pi\) | |||||||
\(440\) | 2107.93 | 0.228390 | ||||||||
\(441\) | −1066.51 | + | 782.867i | −0.115162 | + | 0.0845338i | ||||
\(442\) | −2240.06 | −0.241061 | ||||||||
\(443\) | 530.564 | − | 918.964i | 0.0569026 | − | 0.0985582i | −0.836171 | − | 0.548469i | \(-0.815211\pi\) |
0.893074 | + | 0.449911i | \(0.148544\pi\) | |||||||
\(444\) | −4248.81 | − | 892.255i | −0.454144 | − | 0.0953706i | ||||
\(445\) | −8318.15 | − | 14407.5i | −0.886108 | − | 1.53478i | ||||
\(446\) | −1375.92 | − | 2383.17i | −0.146081 | − | 0.253019i | ||||
\(447\) | 15508.6 | + | 3256.82i | 1.64101 | + | 0.344613i | ||||
\(448\) | 1070.36 | − | 1853.91i | 0.112879 | − | 0.195511i | ||||
\(449\) | −11131.1 | −1.16995 | −0.584977 | − | 0.811050i | \(-0.698897\pi\) | ||||
−0.584977 | + | 0.811050i | \(0.698897\pi\) | |||||||
\(450\) | 830.790 | − | 609.837i | 0.0870307 | − | 0.0638844i | ||||
\(451\) | 6969.68 | 0.727692 | ||||||||
\(452\) | −5534.04 | + | 9585.24i | −0.575884 | + | 0.997460i | ||||
\(453\) | −5182.06 | − | 15817.0i | −0.537471 | − | 1.64050i | ||||
\(454\) | 1746.99 | + | 3025.88i | 0.180596 | + | 0.312801i | ||||
\(455\) | 2934.17 | + | 5082.12i | 0.302320 | + | 0.523634i | ||||
\(456\) | −2879.96 | + | 3214.30i | −0.295760 | + | 0.330095i | ||||
\(457\) | 5168.70 | − | 8952.45i | 0.529063 | − | 0.916363i | −0.470363 | − | 0.882473i | \(-0.655877\pi\) |
0.999426 | − | 0.0338903i | \(-0.0107897\pi\) | |||||||
\(458\) | −557.902 | −0.0569193 | ||||||||
\(459\) | −5348.96 | − | 3826.58i | −0.543939 | − | 0.389128i | ||||
\(460\) | 1486.24 | 0.150644 | ||||||||
\(461\) | −2445.94 | + | 4236.49i | −0.247112 | + | 0.428011i | −0.962723 | − | 0.270488i | \(-0.912815\pi\) |
0.715611 | + | 0.698499i | \(0.246148\pi\) | |||||||
\(462\) | 250.274 | − | 279.329i | 0.0252031 | − | 0.0281289i | ||||
\(463\) | 1886.10 | + | 3266.82i | 0.189318 | + | 0.327909i | 0.945023 | − | 0.327003i | \(-0.106039\pi\) |
−0.755705 | + | 0.654912i | \(0.772705\pi\) | |||||||
\(464\) | −2578.80 | − | 4466.62i | −0.258013 | − | 0.446891i | ||||
\(465\) | −4869.44 | − | 14862.8i | −0.485623 | − | 1.48225i | ||||
\(466\) | 1994.29 | − | 3454.21i | 0.198248 | − | 0.343376i | ||||
\(467\) | −1446.52 | −0.143334 | −0.0716669 | − | 0.997429i | \(-0.522832\pi\) | ||||
−0.0716669 | + | 0.997429i | \(0.522832\pi\) | |||||||
\(468\) | −11620.6 | − | 5105.84i | −1.14778 | − | 0.504311i | ||||
\(469\) | −5083.87 | −0.500536 | ||||||||
\(470\) | 2746.68 | − | 4757.39i | 0.269564 | − | 0.466898i | ||||
\(471\) | 2381.44 | + | 500.105i | 0.232974 | + | 0.0489249i | ||||
\(472\) | −1940.47 | − | 3360.99i | −0.189231 | − | 0.327758i | ||||
\(473\) | 2392.27 | + | 4143.54i | 0.232551 | + | 0.402791i | ||||
\(474\) | 187.837 | + | 39.4461i | 0.0182018 | + | 0.00382240i | ||||
\(475\) | 1801.27 | − | 3119.90i | 0.173996 | − | 0.301370i | ||||
\(476\) | −2438.01 | −0.234760 | ||||||||
\(477\) | 127.018 | + | 1154.15i | 0.0121924 | + | 0.110786i | ||||
\(478\) | −1110.63 | −0.106275 | ||||||||
\(479\) | −550.722 | + | 953.878i | −0.0525326 | + | 0.0909892i | −0.891096 | − | 0.453815i | \(-0.850063\pi\) |
0.838563 | + | 0.544804i | \(0.183396\pi\) | |||||||
\(480\) | 2817.82 | + | 8600.70i | 0.267948 | + | 0.817847i | ||||
\(481\) | 3557.82 | + | 6162.32i | 0.337261 | + | 0.584153i | ||||
\(482\) | −1886.43 | − | 3267.39i | −0.178266 | − | 0.308767i | ||||
\(483\) | 366.468 | − | 409.012i | 0.0345236 | − | 0.0385314i | ||||
\(484\) | −4251.93 | + | 7364.57i | −0.399318 | + | 0.691638i | ||||
\(485\) | −22323.6 | −2.09003 | ||||||||
\(486\) | 1460.56 | + | 2459.78i | 0.136321 | + | 0.229584i | ||||
\(487\) | −1543.15 | −0.143587 | −0.0717933 | − | 0.997420i | \(-0.522872\pi\) | ||||
−0.0717933 | + | 0.997420i | \(0.522872\pi\) | |||||||
\(488\) | 2493.98 | − | 4319.70i | 0.231347 | − | 0.400705i | ||||
\(489\) | −13566.6 | + | 15141.6i | −1.25461 | + | 1.40026i | ||||
\(490\) | −245.145 | − | 424.604i | −0.0226011 | − | 0.0391462i | ||||
\(491\) | −8031.45 | − | 13910.9i | −0.738196 | − | 1.27859i | −0.953307 | − | 0.302003i | \(-0.902345\pi\) |
0.215111 | − | 0.976590i | \(-0.430989\pi\) | |||||||
\(492\) | 6135.64 | + | 18727.5i | 0.562228 | + | 1.71606i | ||||
\(493\) | −2387.35 | + | 4135.02i | −0.218095 | + | 0.377752i | ||||
\(494\) | 3406.01 | 0.310210 | ||||||||
\(495\) | −534.302 | − | 4854.93i | −0.0485153 | − | 0.440834i | ||||
\(496\) | 11503.7 | 1.04139 | ||||||||
\(497\) | 2714.82 | − | 4702.20i | 0.245022 | − | 0.424391i | ||||
\(498\) | −1831.91 | − | 384.704i | −0.164839 | − | 0.0346164i | ||||
\(499\) | −5280.99 | − | 9146.94i | −0.473767 | − | 0.820588i | 0.525782 | − | 0.850619i | \(-0.323773\pi\) |
−0.999549 | + | 0.0300313i | \(0.990439\pi\) | |||||||
\(500\) | 3664.71 | + | 6347.46i | 0.327781 | + | 0.567734i | ||||
\(501\) | 3828.92 | + | 804.078i | 0.341445 | + | 0.0717037i | ||||
\(502\) | 625.581 | − | 1083.54i | 0.0556196 | − | 0.0963360i | ||||
\(503\) | 11032.3 | 0.977943 | 0.488971 | − | 0.872300i | \(-0.337372\pi\) | ||||
0.488971 | + | 0.872300i | \(0.337372\pi\) | |||||||
\(504\) | 2016.30 | + | 885.918i | 0.178200 | + | 0.0782975i | ||||
\(505\) | 17901.4 | 1.57743 | ||||||||
\(506\) | −77.8407 | + | 134.824i | −0.00683882 | + | 0.0118452i | ||||
\(507\) | 2922.69 | + | 8920.81i | 0.256019 | + | 0.781434i | ||||
\(508\) | 4980.35 | + | 8626.23i | 0.434975 | + | 0.753399i | ||||
\(509\) | 3107.83 | + | 5382.92i | 0.270633 | + | 0.468750i | 0.969024 | − | 0.246967i | \(-0.0794338\pi\) |
−0.698391 | + | 0.715716i | \(0.746100\pi\) | |||||||
\(510\) | 1626.43 | − | 1815.24i | 0.141215 | − | 0.157608i | ||||
\(511\) | −2691.29 | + | 4661.46i | −0.232986 | + | 0.403543i | ||||
\(512\) | −11377.3 | −0.982053 | ||||||||
\(513\) | 8133.08 | + | 5818.32i | 0.699970 | + | 0.500750i | ||||
\(514\) | −2841.24 | −0.243817 | ||||||||
\(515\) | 2792.66 | − | 4837.03i | 0.238950 | − | 0.413874i | ||||
\(516\) | −9027.70 | + | 10075.7i | −0.770198 | + | 0.859612i | ||||
\(517\) | −3747.95 | − | 6491.63i | −0.318829 | − | 0.552228i | ||||
\(518\) | −297.250 | − | 514.852i | −0.0252132 | − | 0.0436705i | ||||
\(519\) | 1893.33 | + | 5778.94i | 0.160131 | + | 0.488761i | ||||
\(520\) | 4884.37 | − | 8459.99i | 0.411912 | − | 0.713452i | ||||
\(521\) | 11890.3 | 0.999855 | 0.499928 | − | 0.866067i | \(-0.333360\pi\) | ||||
0.499928 | + | 0.866067i | \(0.333360\pi\) | |||||||
\(522\) | 1674.23 | − | 1228.96i | 0.140381 | − | 0.103046i | ||||
\(523\) | −9534.37 | −0.797149 | −0.398574 | − | 0.917136i | \(-0.630495\pi\) | ||||
−0.398574 | + | 0.917136i | \(0.630495\pi\) | |||||||
\(524\) | −1205.91 | + | 2088.70i | −0.100535 | + | 0.174132i | ||||
\(525\) | −1799.14 | − | 377.821i | −0.149563 | − | 0.0314085i | ||||
\(526\) | 160.737 | + | 278.404i | 0.0133240 | + | 0.0230779i | ||||
\(527\) | −5324.82 | − | 9222.86i | −0.440138 | − | 0.762342i | ||||
\(528\) | 3515.79 | + | 738.319i | 0.289782 | + | 0.0608546i | ||||
\(529\) | 5969.52 | − | 10339.5i | 0.490632 | − | 0.849800i | ||||
\(530\) | −430.299 | −0.0352660 | ||||||||
\(531\) | −7249.09 | + | 5321.15i | −0.592436 | + | 0.434874i | ||||
\(532\) | 3706.99 | 0.302102 | ||||||||
\(533\) | 16149.8 | − | 27972.2i | 1.31243 | − | 2.27319i | ||||
\(534\) | 1534.09 | + | 4682.45i | 0.124320 | + | 0.379456i | ||||
\(535\) | 12473.0 | + | 21603.9i | 1.00795 | + | 1.74583i | ||||
\(536\) | 4231.45 | + | 7329.09i | 0.340990 | + | 0.590613i | ||||
\(537\) | 1583.07 | − | 1766.85i | 0.127215 | − | 0.141984i | ||||
\(538\) | −517.932 | + | 897.085i | −0.0415049 | + | 0.0718886i | ||||
\(539\) | −669.019 | −0.0534632 | ||||||||
\(540\) | 12574.8 | − | 5709.63i | 1.00210 | − | 0.455006i | ||||
\(541\) | −6195.53 | −0.492360 | −0.246180 | − | 0.969224i | \(-0.579175\pi\) | ||||
−0.246180 | + | 0.969224i | \(0.579175\pi\) | |||||||
\(542\) | 356.489 | − | 617.458i | 0.0282519 | − | 0.0489337i | ||||
\(543\) | −3361.96 | + | 3752.25i | −0.265701 | + | 0.296546i | ||||
\(544\) | 3081.34 | + | 5337.03i | 0.242851 | + | 0.420631i | ||||
\(545\) | −1440.61 | − | 2495.20i | −0.113227 | − | 0.196115i | ||||
\(546\) | −541.141 | − | 1651.70i | −0.0424152 | − | 0.129462i | ||||
\(547\) | 10611.2 | − | 18379.2i | 0.829439 | − | 1.43663i | −0.0690400 | − | 0.997614i | \(-0.521994\pi\) |
0.898479 | − | 0.439017i | \(-0.144673\pi\) | |||||||
\(548\) | −12144.6 | −0.946700 | ||||||||
\(549\) | −10581.2 | − | 4649.15i | −0.822576 | − | 0.361423i | ||||
\(550\) | 521.151 | 0.0404036 | ||||||||
\(551\) | 3629.97 | − | 6287.29i | 0.280657 | − | 0.486112i | ||||
\(552\) | −894.667 | − | 187.881i | −0.0689847 | − | 0.0144869i | ||||
\(553\) | −171.188 | − | 296.506i | −0.0131639 | − | 0.0228006i | ||||
\(554\) | 859.835 | + | 1489.28i | 0.0659402 | + | 0.114212i | ||||
\(555\) | −7576.86 | − | 1591.15i | −0.579495 | − | 0.121695i | ||||
\(556\) | −4188.95 | + | 7255.48i | −0.319517 | + | 0.553419i | ||||
\(557\) | 8798.79 | 0.669330 | 0.334665 | − | 0.942337i | \(-0.391377\pi\) | ||||
0.334665 | + | 0.942337i | \(0.391377\pi\) | |||||||
\(558\) | 506.742 | + | 4604.50i | 0.0384446 | + | 0.349326i | ||||
\(559\) | 22173.0 | 1.67767 | ||||||||
\(560\) | 2348.16 | − | 4067.14i | 0.177193 | − | 0.306907i | ||||
\(561\) | −1035.45 | − | 3160.47i | −0.0779267 | − | 0.237852i | ||||
\(562\) | −385.098 | − | 667.009i | −0.0289046 | − | 0.0500642i | ||||
\(563\) | −699.467 | − | 1211.51i | −0.0523606 | − | 0.0906912i | 0.838657 | − | 0.544660i | \(-0.183341\pi\) |
−0.891018 | + | 0.453969i | \(0.850008\pi\) | |||||||
\(564\) | 14143.6 | − | 15785.5i | 1.05595 | − | 1.17853i | ||||
\(565\) | −9868.80 | + | 17093.3i | −0.734838 | + | 1.27278i | ||||
\(566\) | −1771.62 | −0.131566 | ||||||||
\(567\) | 1529.35 | − | 4868.44i | 0.113274 | − | 0.360591i | ||||
\(568\) | −9038.47 | −0.667686 | ||||||||
\(569\) | 7119.00 | − | 12330.5i | 0.524506 | − | 0.908471i | −0.475087 | − | 0.879939i | \(-0.657583\pi\) |
0.999593 | − | 0.0285321i | \(-0.00908329\pi\) | |||||||
\(570\) | −2472.98 | + | 2760.07i | −0.181723 | + | 0.202819i | ||||
\(571\) | 6280.19 | + | 10877.6i | 0.460276 | + | 0.797221i | 0.998974 | − | 0.0452773i | \(-0.0144171\pi\) |
−0.538698 | + | 0.842499i | \(0.681084\pi\) | |||||||
\(572\) | −3209.27 | − | 5558.63i | −0.234592 | − | 0.406325i | ||||
\(573\) | −3574.20 | − | 10909.4i | −0.260584 | − | 0.795368i | ||||
\(574\) | −1349.29 | + | 2337.03i | −0.0981153 | + | 0.169941i | ||||
\(575\) | 763.104 | 0.0553455 | ||||||||
\(576\) | 903.262 | + | 8207.48i | 0.0653401 | + | 0.593713i | ||||
\(577\) | 1067.68 | 0.0770330 | 0.0385165 | − | 0.999258i | \(-0.487737\pi\) | ||||
0.0385165 | + | 0.999258i | \(0.487737\pi\) | |||||||
\(578\) | −1025.37 | + | 1775.99i | −0.0737884 | + | 0.127805i | ||||
\(579\) | −3398.29 | − | 713.645i | −0.243917 | − | 0.0512229i | ||||
\(580\) | −5013.13 | − | 8682.99i | −0.358895 | − | 0.621624i | ||||
\(581\) | 1669.54 | + | 2891.72i | 0.119215 | + | 0.206487i | ||||
\(582\) | 6470.69 | + | 1358.85i | 0.460857 | + | 0.0967804i | ||||
\(583\) | −293.579 | + | 508.494i | −0.0208556 | + | 0.0361230i | ||||
\(584\) | 8960.15 | 0.634886 | ||||||||
\(585\) | −20722.9 | − | 9105.20i | −1.46459 | − | 0.643511i | ||||
\(586\) | −1244.83 | −0.0877532 | ||||||||
\(587\) | −9690.25 | + | 16784.0i | −0.681362 | + | 1.18015i | 0.293203 | + | 0.956050i | \(0.405279\pi\) |
−0.974565 | + | 0.224103i | \(0.928055\pi\) | |||||||
\(588\) | −588.960 | − | 1797.66i | −0.0413066 | − | 0.126078i | ||||
\(589\) | 8096.39 | + | 14023.4i | 0.566393 | + | 0.981022i | ||||
\(590\) | −1666.25 | − | 2886.03i | −0.116269 | − | 0.201383i | ||||
\(591\) | −5785.92 | + | 6457.61i | −0.402709 | + | 0.449460i | ||||
\(592\) | 2847.26 | − | 4931.60i | 0.197672 | − | 0.342378i | ||||
\(593\) | 14325.4 | 0.992030 | 0.496015 | − | 0.868314i | \(-0.334796\pi\) | ||||
0.496015 | + | 0.868314i | \(0.334796\pi\) | |||||||
\(594\) | −140.650 | + | 1439.76i | −0.00971541 | + | 0.0994516i | ||||
\(595\) | −4347.67 | −0.299558 | ||||||||
\(596\) | −11329.2 | + | 19622.8i | −0.778630 | + | 1.34863i | ||||
\(597\) | −3545.57 | + | 3957.18i | −0.243067 | + | 0.271284i | ||||
\(598\) | 360.736 | + | 624.814i | 0.0246682 | + | 0.0427266i | ||||
\(599\) | −10008.6 | − | 17335.4i | −0.682703 | − | 1.18248i | −0.974153 | − | 0.225890i | \(-0.927471\pi\) |
0.291450 | − | 0.956586i | \(-0.405862\pi\) | |||||||
\(600\) | 952.793 | + | 2908.17i | 0.0648293 | + | 0.197876i | ||||
\(601\) | 11674.9 | − | 20221.6i | 0.792396 | − | 1.37247i | −0.132083 | − | 0.991239i | \(-0.542167\pi\) |
0.924479 | − | 0.381232i | \(-0.124500\pi\) | |||||||
\(602\) | −1852.52 | −0.125420 | ||||||||
\(603\) | 15807.6 | − | 11603.5i | 1.06756 | − | 0.783633i | ||||
\(604\) | 23798.6 | 1.60323 | ||||||||
\(605\) | −7582.43 | + | 13133.2i | −0.509537 | + | 0.882543i | ||||
\(606\) | −5188.88 | − | 1089.67i | −0.347828 | − | 0.0730442i | ||||
\(607\) | −9244.78 | − | 16012.4i | −0.618178 | − | 1.07072i | −0.989818 | − | 0.142338i | \(-0.954538\pi\) |
0.371640 | − | 0.928377i | \(-0.378795\pi\) | |||||||
\(608\) | −4685.17 | − | 8114.95i | −0.312514 | − | 0.541291i | ||||
\(609\) | −3625.66 | − | 761.393i | −0.241247 | − | 0.0506621i | ||||
\(610\) | 2141.55 | − | 3709.27i | 0.142146 | − | 0.246203i | ||||
\(611\) | −34738.1 | −2.30009 | ||||||||
\(612\) | 7580.65 | − | 5564.54i | 0.500702 | − | 0.367538i | ||||
\(613\) | −2325.71 | −0.153238 | −0.0766189 | − | 0.997060i | \(-0.524412\pi\) | ||||
−0.0766189 | + | 0.997060i | \(0.524412\pi\) | |||||||
\(614\) | −2612.56 | + | 4525.08i | −0.171717 | + | 0.297423i | ||||
\(615\) | 10941.6 | + | 33396.6i | 0.717413 | + | 2.18973i | ||||
\(616\) | 556.843 | + | 964.480i | 0.0364218 | + | 0.0630845i | ||||
\(617\) | −4537.18 | − | 7858.63i | −0.296045 | − | 0.512766i | 0.679182 | − | 0.733970i | \(-0.262335\pi\) |
−0.975228 | + | 0.221204i | \(0.929001\pi\) | |||||||
\(618\) | −1103.91 | + | 1232.06i | −0.0718540 | + | 0.0801956i | ||||
\(619\) | −11155.4 | + | 19321.7i | −0.724349 | + | 1.25461i | 0.234893 | + | 0.972021i | \(0.424526\pi\) |
−0.959241 | + | 0.282588i | \(0.908807\pi\) | |||||||
\(620\) | 22362.9 | 1.44857 | ||||||||
\(621\) | −205.950 | + | 2108.20i | −0.0133083 | + | 0.136230i | ||||
\(622\) | −366.241 | −0.0236092 | ||||||||
\(623\) | 4394.74 | − | 7611.92i | 0.282619 | − | 0.489511i | ||||
\(624\) | 11109.8 | − | 12399.5i | 0.712735 | − | 0.795477i | ||||
\(625\) | 9694.13 | + | 16790.7i | 0.620424 | + | 1.07461i | ||||
\(626\) | 1621.63 | + | 2808.74i | 0.103536 | + | 0.179329i | ||||
\(627\) | 1574.41 | + | 4805.49i | 0.100280 | + | 0.306081i | ||||
\(628\) | −1739.67 | + | 3013.20i | −0.110542 | + | 0.191465i | ||||
\(629\) | −5271.76 | −0.334180 | ||||||||
\(630\) | 1731.37 | + | 760.726i | 0.109491 | + | 0.0481080i | ||||
\(631\) | 6407.05 | 0.404217 | 0.202108 | − | 0.979363i | \(-0.435221\pi\) | ||||
0.202108 | + | 0.979363i | \(0.435221\pi\) | |||||||
\(632\) | −284.969 | + | 493.581i | −0.0179359 | + | 0.0310658i | ||||
\(633\) | −9419.60 | − | 1978.13i | −0.591462 | − | 0.124208i | ||||
\(634\) | −689.371 | − | 1194.03i | −0.0431837 | − | 0.0747963i | ||||
\(635\) | 8881.41 | + | 15383.1i | 0.555037 | + | 0.961351i | ||||
\(636\) | −1624.77 | − | 341.204i | −0.101300 | − | 0.0212730i | ||||
\(637\) | −1550.21 | + | 2685.05i | −0.0964234 | + | 0.167010i | ||||
\(638\) | 1050.24 | 0.0651713 | ||||||||
\(639\) | 2291.00 | + | 20817.2i | 0.141832 | + | 1.28876i | ||||
\(640\) | −16994.2 | −1.04962 | ||||||||
\(641\) | 6985.22 | − | 12098.8i | 0.430420 | − | 0.745510i | −0.566489 | − | 0.824069i | \(-0.691699\pi\) |
0.996909 | + | 0.0785592i | \(0.0250320\pi\) | |||||||
\(642\) | −2300.37 | − | 7021.31i | −0.141415 | − | 0.431634i | ||||
\(643\) | −3948.21 | − | 6838.51i | −0.242150 | − | 0.419416i | 0.719177 | − | 0.694827i | \(-0.244519\pi\) |
−0.961326 | + | 0.275411i | \(0.911186\pi\) | |||||||
\(644\) | 392.614 | + | 680.027i | 0.0240235 | + | 0.0416100i | ||||
\(645\) | −16099.0 | + | 17968.0i | −0.982787 | + | 1.09688i | ||||
\(646\) | −1261.71 | + | 2185.34i | −0.0768439 | + | 0.133098i | ||||
\(647\) | −4339.84 | −0.263704 | −0.131852 | − | 0.991269i | \(-0.542092\pi\) | ||||
−0.131852 | + | 0.991269i | \(0.542092\pi\) | |||||||
\(648\) | −8291.43 | + | 1847.38i | −0.502651 | + | 0.111993i | ||||
\(649\) | −4547.32 | −0.275036 | ||||||||
\(650\) | 1207.58 | − | 2091.60i | 0.0728697 | − | 0.126214i | ||||
\(651\) | 5514.11 | − | 6154.24i | 0.331974 | − | 0.370513i | ||||
\(652\) | −14534.5 | − | 25174.5i | −0.873031 | − | 1.51213i | ||||
\(653\) | 14916.5 | + | 25836.1i | 0.893917 | + | 1.54831i | 0.835139 | + | 0.550038i | \(0.185387\pi\) |
0.0587774 | + | 0.998271i | \(0.481280\pi\) | |||||||
\(654\) | 265.687 | + | 810.946i | 0.0158856 | + | 0.0484870i | ||||
\(655\) | −2150.48 | + | 3724.75i | −0.128285 | + | 0.222195i | ||||
\(656\) | −25848.8 | −1.53845 | ||||||||
\(657\) | −2271.15 | − | 20636.8i | −0.134865 | − | 1.22545i | ||||
\(658\) | 2902.32 | 0.171952 | ||||||||
\(659\) | 1546.96 | − | 2679.41i | 0.0914429 | − | 0.158384i | −0.816676 | − | 0.577097i | \(-0.804185\pi\) |
0.908118 | + | 0.418713i | \(0.137519\pi\) | |||||||
\(660\) | 6834.60 | + | 1435.27i | 0.403086 | + | 0.0846484i | ||||
\(661\) | −10745.5 | − | 18611.7i | −0.632300 | − | 1.09518i | −0.987080 | − | 0.160226i | \(-0.948778\pi\) |
0.354781 | − | 0.934950i | \(-0.384556\pi\) | |||||||
\(662\) | −3759.80 | − | 6512.16i | −0.220738 | − | 0.382330i | ||||
\(663\) | −15083.6 | − | 3167.57i | −0.883556 | − | 0.185548i | ||||
\(664\) | 2779.21 | − | 4813.72i | 0.162431 | − | 0.281338i | ||||
\(665\) | 6610.63 | 0.385488 | ||||||||
\(666\) | 2099.36 | + | 922.416i | 0.122145 | + | 0.0536680i | ||||
\(667\) | 1537.83 | 0.0892726 | ||||||||
\(668\) | −2797.08 | + | 4844.69i | −0.162009 | + | 0.280609i | ||||
\(669\) | −5894.94 | − | 17992.9i | −0.340675 | − | 1.03983i | ||||
\(670\) | 3633.49 | + | 6293.39i | 0.209513 | + | 0.362888i | ||||
\(671\) | −2922.22 | − | 5061.44i | −0.168124 | − | 0.291199i | ||||
\(672\) | −3190.87 | + | 3561.30i | −0.183170 | + | 0.204435i | ||||
\(673\) | −8644.89 | + | 14973.4i | −0.495150 | + | 0.857625i | −0.999984 | − | 0.00559099i | \(-0.998220\pi\) |
0.504834 | + | 0.863216i | \(0.331554\pi\) | |||||||
\(674\) | 920.472 | 0.0526042 | ||||||||
\(675\) | 6456.52 | − | 2931.59i | 0.368165 | − | 0.167166i | ||||
\(676\) | −13422.5 | −0.763681 | ||||||||
\(677\) | 8127.32 | − | 14076.9i | 0.461386 | − | 0.799144i | −0.537644 | − | 0.843172i | \(-0.680686\pi\) |
0.999030 | + | 0.0440278i | \(0.0140190\pi\) | |||||||
\(678\) | 3901.03 | − | 4353.90i | 0.220971 | − | 0.246623i | ||||
\(679\) | −5897.14 | − | 10214.1i | −0.333301 | − | 0.577295i | ||||
\(680\) | 3618.69 | + | 6267.76i | 0.204074 | + | 0.353467i | ||||
\(681\) | 7484.72 | + | 22845.3i | 0.421168 | + | 1.28551i | ||||
\(682\) | −1171.24 | + | 2028.65i | −0.0657611 | + | 0.113902i | ||||
\(683\) | 19985.7 | 1.11967 | 0.559833 | − | 0.828605i | \(-0.310865\pi\) | ||||
0.559833 | + | 0.828605i | \(0.310865\pi\) | |||||||
\(684\) | −11526.4 | + | 8460.87i | −0.644330 | + | 0.472967i | ||||
\(685\) | −21657.3 | −1.20801 | ||||||||
\(686\) | 129.518 | − | 224.332i | 0.00720849 | − | 0.0124855i | ||||
\(687\) | −3756.67 | − | 788.904i | −0.208626 | − | 0.0438116i | ||||
\(688\) | −8872.33 | − | 15367.3i | −0.491649 | − | 0.851561i | ||||
\(689\) | 1360.53 | + | 2356.51i | 0.0752281 | + | 0.130299i | ||||
\(690\) | −768.239 | − | 161.331i | −0.0423860 | − | 0.00890110i | ||||
\(691\) | −2469.99 | + | 4278.15i | −0.135981 | + | 0.235526i | −0.925972 | − | 0.377593i | \(-0.876752\pi\) |
0.789991 | + | 0.613119i | \(0.210085\pi\) | |||||||
\(692\) | −8695.12 | −0.477657 | ||||||||
\(693\) | 2080.22 | − | 1526.98i | 0.114028 | − | 0.0837014i | ||||
\(694\) | 1708.26 | 0.0934362 | ||||||||
\(695\) | −7470.12 | + | 12938.6i | −0.407709 | + | 0.706173i | ||||
\(696\) | 1920.09 | + | 5860.61i | 0.104570 | + | 0.319175i | ||||
\(697\) | 11964.9 | + | 20723.8i | 0.650218 | + | 1.12621i | ||||
\(698\) | 2673.56 | + | 4630.74i | 0.144980 | + | 0.251112i | ||||
\(699\) | 18313.1 | − | 20439.1i | 0.990938 | − | 1.10598i | ||||
\(700\) | 1314.29 | − | 2276.42i | 0.0709652 | − | 0.122915i | ||||
\(701\) | −22730.8 | −1.22472 | −0.612361 | − | 0.790578i | \(-0.709780\pi\) | ||||
−0.612361 | + | 0.790578i | \(0.709780\pi\) | |||||||
\(702\) | 5452.46 | + | 3900.63i | 0.293148 | + | 0.209715i | ||||
\(703\) | 8015.71 | 0.430040 | ||||||||
\(704\) | −2087.72 | + | 3616.04i | −0.111767 | + | 0.193586i | ||||
\(705\) | 25222.1 | − | 28150.2i | 1.34741 | − | 1.50383i | ||||
\(706\) | −2906.25 | − | 5033.76i | −0.154926 | − | 0.268340i | ||||
\(707\) | 4728.95 | + | 8190.78i | 0.251556 | + | 0.435709i | ||||
\(708\) | −4003.16 | − | 12218.7i | −0.212497 | − | 0.648596i | ||||
\(709\) | 14275.0 | − | 24725.0i | 0.756147 | − | 1.30969i | −0.188655 | − | 0.982043i | \(-0.560413\pi\) |
0.944802 | − | 0.327642i | \(-0.106254\pi\) | |||||||
\(710\) | −7761.21 | −0.410244 | ||||||||
\(711\) | 1209.04 | + | 531.225i | 0.0637727 | + | 0.0280204i | ||||
\(712\) | −14631.5 | −0.770137 | ||||||||
\(713\) | −1715.01 | + | 2970.48i | −0.0900806 | + | 0.156024i | ||||
\(714\) | 1260.21 | + | 264.645i | 0.0660534 | + | 0.0138713i | ||||
\(715\) | −5723.07 | − | 9912.64i | −0.299343 | − | 0.518478i | ||||
\(716\) | 1696.01 | + | 2937.58i | 0.0885237 | + | 0.153328i | ||||
\(717\) | −7478.52 | − | 1570.50i | −0.389527 | − | 0.0818010i | ||||
\(718\) | −2058.82 | + | 3565.98i | −0.107012 | + | 0.185350i | ||||
\(719\) | 27985.7 | 1.45158 | 0.725792 | − | 0.687914i | \(-0.241474\pi\) | ||||
0.725792 | + | 0.687914i | \(0.241474\pi\) | |||||||
\(720\) | 1981.59 | + | 18005.7i | 0.102569 | + | 0.931990i | ||||
\(721\) | 2950.91 | 0.152424 | ||||||||
\(722\) | −671.561 | + | 1163.18i | −0.0346162 | + | 0.0599570i | ||||
\(723\) | −8082.11 | − | 24668.7i | −0.415736 | − | 1.26893i | ||||
\(724\) | −3601.81 | − | 6238.53i | −0.184890 | − | 0.320239i | ||||
\(725\) | −2573.98 | − | 4458.26i | −0.131855 | − | 0.228380i | ||||
\(726\) | 2997.25 | − | 3345.21i | 0.153221 | − | 0.171009i | ||||
\(727\) | −4156.09 | + | 7198.55i | −0.212023 | + | 0.367235i | −0.952348 | − | 0.305015i | \(-0.901339\pi\) |
0.740325 | + | 0.672250i | \(0.234672\pi\) | |||||||
\(728\) | 5161.14 | 0.262754 | ||||||||
\(729\) | 6356.48 | + | 18628.4i | 0.322943 | + | 0.946419i | ||||
\(730\) | 7693.96 | 0.390091 | ||||||||
\(731\) | −8213.65 | + | 14226.5i | −0.415585 | + | 0.719815i | ||||
\(732\) | 11027.6 | − | 12307.8i | 0.556818 | − | 0.621460i | ||||
\(733\) | 18731.5 | + | 32443.9i | 0.943880 | + | 1.63485i | 0.757979 | + | 0.652279i | \(0.226187\pi\) |
0.185901 | + | 0.982568i | \(0.440480\pi\) | |||||||
\(734\) | −2156.42 | − | 3735.02i | −0.108440 | − | 0.187823i | ||||
\(735\) | −1050.29 | − | 3205.74i | −0.0527080 | − | 0.160878i | ||||
\(736\) | 992.429 | − | 1718.94i | 0.0497030 | − | 0.0860881i | ||||
\(737\) | 9916.06 | 0.495607 | ||||||||
\(738\) | −1138.65 | − | 10346.3i | −0.0567944 | − | 0.516061i | ||||
\(739\) | −16040.4 | −0.798452 | −0.399226 | − | 0.916853i | \(-0.630721\pi\) | ||||
−0.399226 | + | 0.916853i | \(0.630721\pi\) | |||||||
\(740\) | 5535.00 | − | 9586.91i | 0.274960 | − | 0.476246i | ||||
\(741\) | 22934.6 | + | 4816.28i | 1.13701 | + | 0.238773i | ||||
\(742\) | −113.670 | − | 196.883i | −0.00562395 | − | 0.00974097i | ||||
\(743\) | 4372.63 | + | 7573.62i | 0.215903 | + | 0.373956i | 0.953552 | − | 0.301230i | \(-0.0973971\pi\) |
−0.737648 | + | 0.675185i | \(0.764064\pi\) | |||||||
\(744\) | −13461.7 | − | 2826.97i | −0.663347 | − | 0.139304i | ||||
\(745\) | −20203.3 | + | 34993.1i | −0.993545 | + | 1.72087i | ||||
\(746\) | −210.863 | −0.0103489 | ||||||||
\(747\) | −11791.3 | − | 5180.85i | −0.577539 | − | 0.253758i | ||||
\(748\) | 4755.32 | 0.232449 | ||||||||
\(749\) | −6589.90 | + | 11414.0i | −0.321481 | + | 0.556822i | ||||
\(750\) | −1205.28 | − | 3678.81i | −0.0586806 | − | 0.179108i | ||||
\(751\) | −4637.53 | − | 8032.44i | −0.225334 | − | 0.390290i | 0.731085 | − | 0.682286i | \(-0.239014\pi\) |
−0.956420 | + | 0.291996i | \(0.905681\pi\) | |||||||
\(752\) | 13900.2 | + | 24075.8i | 0.674053 | + | 1.16749i | ||||
\(753\) | 5744.57 | − | 6411.46i | 0.278013 | − | 0.310288i | ||||
\(754\) | 2433.55 | − | 4215.03i | 0.117539 | − | 0.203584i | ||||
\(755\) | 42439.7 | 2.04575 | ||||||||
\(756\) | 5934.28 | + | 4245.32i | 0.285487 | + | 0.204234i | ||||
\(757\) | 26200.4 | 1.25795 | 0.628975 | − | 0.777425i | \(-0.283475\pi\) | ||||
0.628975 | + | 0.777425i | \(0.283475\pi\) | |||||||
\(758\) | −1878.14 | + | 3253.04i | −0.0899964 | + | 0.155878i | ||||
\(759\) | −714.793 | + | 797.775i | −0.0341836 | + | 0.0381520i | ||||
\(760\) | −5502.21 | − | 9530.11i | −0.262614 | − | 0.454860i | ||||
\(761\) | 18128.8 | + | 31400.1i | 0.863560 | + | 1.49573i | 0.868470 | + | 0.495743i | \(0.165104\pi\) |
−0.00490907 | + | 0.999988i | \(0.501563\pi\) | |||||||
\(762\) | −1637.98 | − | 4999.53i | −0.0778709 | − | 0.237682i | ||||
\(763\) | 761.118 | − | 1318.30i | 0.0361132 | − | 0.0625498i | ||||
\(764\) | 16414.5 | 0.777298 | ||||||||
\(765\) | 13518.5 | − | 9923.18i | 0.638905 | − | 0.468985i | ||||
\(766\) | 7416.01 | 0.349806 | ||||||||
\(767\) | −10536.8 | + | 18250.3i | −0.496039 | + | 0.859165i | ||||
\(768\) | −7515.27 | − | 1578.21i | −0.353104 | − | 0.0741522i | ||||
\(769\) | 2312.94 | + | 4006.14i | 0.108462 | + | 0.187861i | 0.915147 | − | 0.403120i | \(-0.132074\pi\) |
−0.806686 | + | 0.590981i | \(0.798741\pi\) | |||||||
\(770\) | 478.154 | + | 828.186i | 0.0223785 | + | 0.0387607i | ||||
\(771\) | −19131.7 | − | 4017.67i | −0.893657 | − | 0.187669i | ||||
\(772\) | 2482.50 | − | 4299.81i | 0.115735 | − | 0.200458i | ||||
\(773\) | 33492.2 | 1.55838 | 0.779192 | − | 0.626785i | \(-0.215630\pi\) | ||||
0.779192 | + | 0.626785i | \(0.215630\pi\) | |||||||
\(774\) | 5760.15 | − | 4228.21i | 0.267499 | − | 0.196356i | ||||
\(775\) | 11482.1 | 0.532194 | ||||||||
\(776\) | −9816.71 | + | 17003.0i | −0.454123 | + | 0.786564i | ||||
\(777\) | −1273.52 | − | 3887.12i | −0.0587997 | − | 0.179472i | ||||
\(778\) | −1666.44 | − | 2886.36i | −0.0767928 | − | 0.133009i | ||||
\(779\) | −18192.6 | − | 31510.5i | −0.836735 | − | 1.44927i | ||||
\(780\) | 21597.1 | − | 24104.3i | 0.991411 | − | 1.10650i | ||||
\(781\) | −5295.23 | + | 9171.61i | −0.242610 | + | 0.420212i | ||||
\(782\) | −534.518 | −0.0244429 | ||||||||
\(783\) | 13011.3 | − | 5907.81i | 0.593853 | − | 0.269640i | ||||
\(784\) | 2481.22 | 0.113029 | ||||||||
\(785\) | −3102.34 | + | 5373.41i | −0.141054 | + | 0.244313i | ||||
\(786\) | 850.063 | − | 948.748i | 0.0385760 | − | 0.0430544i | ||||
\(787\) | 197.498 | + | 342.077i | 0.00894542 | + | 0.0154939i | 0.870463 | − | 0.492233i | \(-0.163819\pi\) |
−0.861518 | + | 0.507727i | \(0.830486\pi\) | |||||||
\(788\) | −6198.71 | − | 10736.5i | −0.280228 | − | 0.485370i | ||||
\(789\) | 688.651 | + | 2101.94i | 0.0310730 | + | 0.0948429i | ||||
\(790\) | −244.699 | + | 423.831i | −0.0110203 | + | 0.0190876i | ||||
\(791\) | −10428.0 | −0.468745 | ||||||||
\(792\) | −3932.77 | − | 1727.98i | −0.176446 | − | 0.0775265i | ||||
\(793\) | −27084.9 | −1.21288 | ||||||||
\(794\) | −369.135 | + | 639.361i | −0.0164989 | + | 0.0285769i | ||||
\(795\) | −2897.44 | − | 608.466i | −0.129260 | − | 0.0271447i | ||||
\(796\) | −3798.53 | − | 6579.25i | −0.169140 | − | 0.292959i | ||||
\(797\) | −21709.0 | − | 37601.0i | −0.964831 | − | 1.67114i | −0.710068 | − | 0.704133i | \(-0.751336\pi\) |
−0.254763 | − | 0.967003i | \(-0.581998\pi\) | |||||||
\(798\) | −1916.15 | − | 402.393i | −0.0850011 | − | 0.0178503i | ||||
\(799\) | 12868.2 | − | 22288.4i | 0.569769 | − | 0.986869i | ||||
\(800\) | −6644.41 | −0.293644 | ||||||||
\(801\) | 3708.68 | + | 33698.9i | 0.163595 | + | 1.48650i | ||||
\(802\) | 11391.9 | 0.501572 | ||||||||
\(803\) | 5249.35 | − | 9092.13i | 0.230692 | − | 0.399570i | ||||
\(804\) | 8729.44 | + | 26644.5i | 0.382915 | + | 1.16875i | ||||
\(805\) | 700.144 | + | 1212.68i | 0.0306544 | + | 0.0530951i | ||||
\(806\) | 5427.86 | + | 9401.33i | 0.237206 | + | 0.410853i | ||||
\(807\) | −4756.05 | + | 5308.19i | −0.207461 | + | 0.231545i | ||||
\(808\) | 7872.07 | − | 13634.8i | 0.342746 | − | 0.593653i | ||||
\(809\) | 934.793 | 0.0406249 | 0.0203125 | − | 0.999794i | \(-0.493534\pi\) | ||||
0.0203125 | + | 0.999794i | \(0.493534\pi\) | |||||||
\(810\) | −7119.74 | + | 1586.32i | −0.308842 | + | 0.0688117i | ||||
\(811\) | −8844.71 | −0.382959 | −0.191480 | − | 0.981497i | \(-0.561329\pi\) | ||||
−0.191480 | + | 0.981497i | \(0.561329\pi\) | |||||||
\(812\) | 2648.60 | − | 4587.50i | 0.114467 | − | 0.198263i | ||||
\(813\) | 3273.56 | − | 3653.59i | 0.141216 | − | 0.157610i | ||||
\(814\) | 579.784 | + | 1004.22i | 0.0249649 | + | 0.0432404i | ||||
\(815\) | −25919.3 | − | 44893.5i | −1.11400 | − | 1.92951i | ||||
\(816\) | 3840.24 | + | 11721.4i | 0.164749 | + | 0.502856i | ||||
\(817\) | 12488.8 | − | 21631.3i | 0.534797 | − | 0.926296i | ||||
\(818\) | 836.189 | 0.0357416 | ||||||||
\(819\) | −1308.21 | − | 11887.0i | −0.0558150 | − | 0.507163i | ||||
\(820\) | −50249.3 | −2.13998 | ||||||||
\(821\) | −5033.13 | + | 8717.64i | −0.213956 | + | 0.370582i | −0.952949 | − | 0.303131i | \(-0.901968\pi\) |
0.738993 | + | 0.673713i | \(0.235301\pi\) | |||||||
\(822\) | 6277.56 | + | 1318.29i | 0.266369 | + | 0.0559377i | ||||
\(823\) | 14839.3 | + | 25702.5i | 0.628513 | + | 1.08862i | 0.987850 | + | 0.155409i | \(0.0496695\pi\) |
−0.359337 | + | 0.933208i | \(0.616997\pi\) | |||||||
\(824\) | −2456.12 | − | 4254.13i | −0.103839 | − | 0.179854i | ||||
\(825\) | 3509.20 | + | 736.936i | 0.148091 | + | 0.0310992i | ||||
\(826\) | 880.334 | − | 1524.78i | 0.0370832 | − | 0.0642300i | ||||
\(827\) | −2344.57 | −0.0985837 | −0.0492919 | − | 0.998784i | \(-0.515696\pi\) | ||||
−0.0492919 | + | 0.998784i | \(0.515696\pi\) | |||||||
\(828\) | −2772.88 | − | 1218.35i | −0.116382 | − | 0.0511358i | ||||
\(829\) | −15019.6 | −0.629255 | −0.314627 | − | 0.949215i | \(-0.601880\pi\) | ||||
−0.314627 | + | 0.949215i | \(0.601880\pi\) | |||||||
\(830\) | 2386.47 | − | 4133.48i | 0.0998017 | − | 0.172862i | ||||
\(831\) | 3683.83 | + | 11244.0i | 0.153779 | + | 0.469374i | ||||
\(832\) | 9675.11 | + | 16757.8i | 0.403154 | + | 0.698283i | ||||
\(833\) | −1148.51 | − | 1989.27i | −0.0477712 | − | 0.0827422i | ||||
\(834\) | 2952.86 | − | 3295.66i | 0.122601 | − | 0.136834i | ||||
\(835\) | −4988.01 | + | 8639.48i | −0.206727 | + | 0.358062i | ||||
\(836\) | −7230.45 | −0.299127 | ||||||||
\(837\) | −3098.84 | + | 31721.2i | −0.127971 | + | 1.30997i | ||||
\(838\) | −5859.35 | −0.241537 | ||||||||
\(839\) | −13994.2 | + | 24238.7i | −0.575845 | + | 0.997392i | 0.420105 | + | 0.907476i | \(0.361993\pi\) |
−0.995949 | + | 0.0899166i | \(0.971340\pi\) | |||||||
\(840\) | −3747.33 | + | 4182.36i | −0.153923 | + | 0.171792i | ||||
\(841\) | 7007.36 | + | 12137.1i | 0.287317 | + | 0.497647i | ||||
\(842\) | 1827.88 | + | 3165.98i | 0.0748134 | + | 0.129581i | ||||
\(843\) | −1649.89 | − | 5035.90i | −0.0674084 | − | 0.205748i | ||||
\(844\) | 6881.15 | − | 11918.5i | 0.280638 | − | 0.486080i | ||||
\(845\) | −23936.1 | −0.974471 | ||||||||
\(846\) | −9024.37 | + | 6624.29i | −0.366742 | + | 0.269205i | ||||
\(847\) | −8012.08 | −0.325028 | ||||||||
\(848\) | 1088.81 | − | 1885.88i | 0.0440919 | − | 0.0763694i | ||||
\(849\) | −11929.3 | − | 2505.16i | −0.482229 | − | 0.101269i | ||||
\(850\) | 894.663 | + | 1549.60i | 0.0361020 | + | 0.0625305i | ||||
\(851\) | 848.958 | + | 1470.44i | 0.0341973 | + | 0.0592315i | ||||
\(852\) | −29305.7 | − | 6154.23i | −1.17840 | − | 0.247465i | ||||
\(853\) | −14095.8 | + | 24414.6i | −0.565804 | + | 0.980001i | 0.431171 | + | 0.902270i | \(0.358101\pi\) |
−0.996974 | + | 0.0777305i | \(0.975233\pi\) | |||||||
\(854\) | 2262.90 | 0.0906731 | ||||||||
\(855\) | −20554.9 | + | 15088.2i | −0.822177 | + | 0.603515i | ||||
\(856\) | 21939.8 | 0.876037 | ||||||||
\(857\) | 9885.20 | − | 17121.7i | 0.394016 | − | 0.682457i | −0.598959 | − | 0.800780i | \(-0.704419\pi\) |
0.992975 | + | 0.118323i | \(0.0377520\pi\) | |||||||
\(858\) | 1055.49 | + | 3221.63i | 0.0419975 | + | 0.128187i | ||||
\(859\) | −9981.80 | − | 17289.0i | −0.396478 | − | 0.686720i | 0.596811 | − | 0.802382i | \(-0.296434\pi\) |
−0.993289 | + | 0.115662i | \(0.963101\pi\) | |||||||
\(860\) | −17247.6 | − | 29873.7i | −0.683881 | − | 1.18452i | ||||
\(861\) | −12390.2 | + | 13828.6i | −0.490426 | + | 0.547360i | ||||
\(862\) | −5643.38 | + | 9774.62i | −0.222986 | + | 0.386224i | ||||
\(863\) | 31276.4 | 1.23368 | 0.616838 | − | 0.787090i | \(-0.288413\pi\) | ||||
0.616838 | + | 0.787090i | \(0.288413\pi\) | |||||||
\(864\) | 1793.22 | − | 18356.3i | 0.0706095 | − | 0.722793i | ||||
\(865\) | −15505.9 | −0.609499 | ||||||||
\(866\) | −1696.54 | + | 2938.49i | −0.0665712 | + | 0.115305i | ||||
\(867\) | −9415.73 | + | 10508.8i | −0.368829 | + | 0.411647i | ||||
\(868\) | 5907.51 | + | 10232.1i | 0.231007 | + | 0.400115i | ||||
\(869\) | 333.901 | + | 578.333i | 0.0130343 | + | 0.0225761i | ||||
\(870\) | 1648.76 | + | 5032.43i | 0.0642506 | + | 0.196109i | ||||
\(871\) | 22976.9 | − | 39797.2i | 0.893851 | − | 1.54820i | ||||
\(872\) | −2534.00 | −0.0984083 | ||||||||
\(873\) | 41649.3 | + | 18299.8i | 1.61468 | + | 0.709455i | ||||
\(874\) | 812.734 | 0.0314544 | ||||||||
\(875\) | −3452.77 | + | 5980.38i | −0.133400 | + | 0.231056i | ||||
\(876\) | 29051.8 | + | 6100.90i | 1.12051 | + | 0.235309i | ||||
\(877\) | −10282.8 | − | 17810.4i | −0.395925 | − | 0.685762i | 0.597294 | − | 0.802023i | \(-0.296243\pi\) |
−0.993219 | + | 0.116260i | \(0.962909\pi\) | |||||||
\(878\) | 1073.22 | + | 1858.87i | 0.0412521 | + | 0.0714507i | ||||
\(879\) | −8382.12 | − | 1760.25i | −0.321640 | − | 0.0675448i | ||||
\(880\) | −4580.08 | + | 7932.93i | −0.175448 | + | 0.303885i | ||||
\(881\) | −10408.7 | −0.398045 | −0.199022 | − | 0.979995i | \(-0.563777\pi\) | ||||
−0.199022 | + | 0.979995i | \(0.563777\pi\) | |||||||
\(882\) | 109.299 | + | 993.143i | 0.00417266 | + | 0.0379148i | ||||
\(883\) | 23371.7 | 0.890737 | 0.445369 | − | 0.895347i | \(-0.353073\pi\) | ||||
0.445369 | + | 0.895347i | \(0.353073\pi\) | |||||||
\(884\) | 11018.8 | − | 19085.0i | 0.419232 | − | 0.726131i | ||||
\(885\) | −7138.80 | − | 21789.4i | −0.271150 | − | 0.827620i | ||||
\(886\) | −400.686 | − | 694.008i | −0.0151933 | − | 0.0263156i | ||||
\(887\) | −18388.0 | − | 31849.0i | −0.696065 | − | 1.20562i | −0.969820 | − | 0.243820i | \(-0.921599\pi\) |
0.273755 | − | 0.961799i | \(-0.411734\pi\) | |||||||
\(888\) | −4543.81 | + | 5071.31i | −0.171712 | + | 0.191646i | ||||
\(889\) | −4692.34 | + | 8127.37i | −0.177026 | + | 0.306618i | ||||
\(890\) | −12563.8 | −0.473192 | ||||||||
\(891\) | −2982.98 | + | 9495.85i | −0.112159 | + | 0.357040i | ||||
\(892\) | 27072.5 | 1.01620 | ||||||||
\(893\) | −19566.1 | + | 33889.5i | −0.733209 | + | 1.26996i | ||||
\(894\) | 7986.14 | − | 8913.27i | 0.298766 | − | 0.333450i | ||||
\(895\) | 3024.48 | + | 5238.56i | 0.112958 | + | 0.195649i | ||||
\(896\) | −4489.28 | − | 7775.67i | −0.167384 | − | 0.289918i | ||||
\(897\) | 1545.52 | + | 4717.32i | 0.0575288 | + | 0.175593i | ||||
\(898\) | −4203.15 | + | 7280.06i | −0.156192 | + | 0.270533i | ||||
\(899\) | 23139.1 | 0.858433 | ||||||||
\(900\) | 1109.12 | + | 10078.0i | 0.0410785 | + | 0.373259i | ||||
\(901\) | −2015.96 | −0.0745408 | ||||||||
\(902\) | 2631.77 | − | 4558.37i | 0.0971491 | − | 0.168267i | ||||
\(903\) | −12474.0 | − | 2619.56i | −0.459701 | − | 0.0965377i | ||||
\(904\) | 8679.52 | + | 15033.4i | 0.319332 | + | 0.553100i | ||||
\(905\) | −6423.08 | − | 11125.1i | −0.235923 | − | 0.408631i | ||||
\(906\) | −12301.5 | − | 2583.33i | −0.451093 | − | 0.0947300i | ||||
\(907\) | 8993.19 | − | 15576.7i | 0.329233 | − | 0.570248i | −0.653127 | − | 0.757248i | \(-0.726543\pi\) |
0.982360 | + | 0.187001i | \(0.0598766\pi\) | |||||||
\(908\) | −34373.5 | −1.25631 | ||||||||
\(909\) | −33398.8 | − | 14674.7i | −1.21867 | − | 0.535456i | ||||
\(910\) | 4431.80 | 0.161443 | ||||||||
\(911\) | 19270.2 | − | 33377.0i | 0.700823 | − | 1.21386i | −0.267354 | − | 0.963598i | \(-0.586149\pi\) |
0.968178 | − | 0.250263i | \(-0.0805172\pi\) | |||||||
\(912\) | −5839.07 | − | 17822.4i | −0.212008 | − | 0.647102i | ||||
\(913\) | −3256.42 | − | 5640.29i | −0.118041 | − | 0.204454i | ||||
\(914\) | −3903.44 | − | 6760.96i | −0.141263 | − | 0.244675i | ||||
\(915\) | 19665.4 | − | 21948.3i | 0.710510 | − | 0.792994i | ||||
\(916\) | 2744.30 | − | 4753.26i | 0.0989892 | − | 0.171454i | ||||
\(917\) | −2272.34 | −0.0818313 | ||||||||
\(918\) | −4522.48 | + | 2053.44i | −0.162597 | + | 0.0738274i | ||||
\(919\) | 10755.6 | 0.386066 | 0.193033 | − | 0.981192i | \(-0.438168\pi\) | ||||
0.193033 | + | 0.981192i | \(0.438168\pi\) | |||||||
\(920\) | 1165.50 | − | 2018.70i | 0.0417667 | − | 0.0723420i | ||||
\(921\) | −23990.5 | + | 26775.6i | −0.858322 | + | 0.957966i | ||||
\(922\) | 1847.19 | + | 3199.43i | 0.0659804 | + | 0.114281i | ||||
\(923\) | 24539.6 | + | 42503.9i | 0.875116 | + | 1.51574i | ||||
\(924\) | 1148.76 | + | 3506.32i | 0.0408999 | + | 0.124837i | ||||
\(925\) | 2841.93 | − | 4922.37i | 0.101018 | − | 0.174969i | ||||
\(926\) | 2848.79 | 0.101098 | ||||||||
\(927\) | −9175.45 | + | 6735.19i | −0.325093 | + | 0.238633i | ||||
\(928\) | −13390.0 | −0.473650 | ||||||||
\(929\) | −19864.7 | + | 34406.6i | −0.701549 | + | 1.21512i | 0.266374 | + | 0.963870i | \(0.414174\pi\) |
−0.967923 | + | 0.251248i | \(0.919159\pi\) | |||||||
\(930\) | −11559.4 | − | 2427.48i | −0.407578 | − | 0.0855918i | ||||
\(931\) | 1746.31 | + | 3024.69i | 0.0614746 | + | 0.106477i | ||||
\(932\) | 19619.7 | + | 33982.2i | 0.689553 | + | 1.19434i | ||||
\(933\) | −2466.11 | − | 517.885i | −0.0865345 | − | 0.0181723i | ||||
\(934\) | −546.210 | + | 946.064i | −0.0191355 | + | 0.0331436i | ||||
\(935\) | 8480.11 | 0.296609 | ||||||||
\(936\) | −16047.9 | + | 11779.9i | −0.560407 | + | 0.411364i | ||||
\(937\) | 20261.6 | 0.706422 | 0.353211 | − | 0.935544i | \(-0.385090\pi\) | ||||
0.353211 | + | 0.935544i | \(0.385090\pi\) | |||||||
\(938\) | −1919.69 | + | 3325.00i | −0.0668231 | + | 0.115741i | ||||
\(939\) | 6947.61 | + | 21205.9i | 0.241455 | + | 0.736984i | ||||
\(940\) | 27021.6 | + | 46802.8i | 0.937604 | + | 1.62398i | ||||
\(941\) | −25892.5 | − | 44847.1i | −0.896993 | − | 1.55364i | −0.831319 | − | 0.555796i | \(-0.812413\pi\) |
−0.0656744 | − | 0.997841i | \(-0.520920\pi\) | |||||||
\(942\) | 1226.32 | − | 1368.69i | 0.0424159 | − | 0.0473400i | ||||
\(943\) | 3853.62 | − | 6674.66i | 0.133076 | − | 0.230495i | ||||
\(944\) | 16864.9 | 0.581467 | ||||||||
\(945\) | 10582.5 | + | 7570.64i | 0.364286 | + | 0.260606i | ||||
\(946\) | 3613.32 | 0.124185 | ||||||||
\(947\) | −4413.81 | + | 7644.94i | −0.151457 | + | 0.262331i | −0.931763 | − | 0.363067i | \(-0.881730\pi\) |
0.780306 | + | 0.625397i | \(0.215063\pi\) | |||||||
\(948\) | −1260.04 | + | 1406.32i | −0.0431690 | + | 0.0481805i | ||||
\(949\) | −24327.0 | − | 42135.6i | −0.832126 | − | 1.44128i | ||||
\(950\) | −1360.33 | − | 2356.17i | −0.0464580 | − | 0.0804676i | ||||
\(951\) | −2953.50 | − | 9014.86i | −0.100709 | − | 0.307389i | ||||
\(952\) | −1911.87 | + | 3311.46i | −0.0650883 | + | 0.112736i | ||||
\(953\) | −6211.21 | −0.211123 | −0.105562 | − | 0.994413i | \(-0.533664\pi\) | ||||
−0.105562 | + | 0.994413i | \(0.533664\pi\) | |||||||
\(954\) | 802.810 | + | 352.738i | 0.0272452 | + | 0.0119710i | ||||
\(955\) | 29271.8 | 0.991847 | ||||||||
\(956\) | 5463.16 | − | 9462.48i | 0.184824 | − | 0.320124i | ||||
\(957\) | 7071.83 | + | 1485.09i | 0.238871 | + | 0.0501632i | ||||
\(958\) | 415.909 | + | 720.376i | 0.0140265 | + | 0.0242947i | ||||
\(959\) | −5721.14 | − | 9909.30i | −0.192643 | − | 0.333668i | ||||
\(960\) | −20604.5 | − | 4326.97i | −0.692716 | − | 0.145471i | ||||
\(961\) | −10909.5 | + | 18895.8i | −0.366202 | + | 0.634280i | ||||
\(962\) | 5373.77 | 0.180101 | ||||||||
\(963\) | −5561.14 | − | 50531.3i | −0.186091 | − | 1.69091i | ||||
\(964\) | 37117.0 | 1.24010 | ||||||||
\(965\) | 4427.01 | − | 7667.81i | 0.147679 | − | 0.255788i | ||||
\(966\) | −129.126 | − | 394.125i | −0.00430078 | − | 0.0131271i | ||||
\(967\) | 9791.42 | + | 16959.2i | 0.325616 | + | 0.563984i | 0.981637 | − | 0.190759i | \(-0.0610949\pi\) |
−0.656021 | + | 0.754743i | \(0.727762\pi\) | |||||||
\(968\) | 6668.68 | + | 11550.5i | 0.221425 | + | 0.383520i | ||||
\(969\) | −11586.0 | + | 12931.0i | −0.384102 | + | 0.428693i | ||||
\(970\) | −8429.47 | + | 14600.3i | −0.279025 | + | 0.483285i | ||||
\(971\) | 20509.6 | 0.677842 | 0.338921 | − | 0.940815i | \(-0.389938\pi\) | ||||
0.338921 | + | 0.940815i | \(0.389938\pi\) | |||||||
\(972\) | −28141.4 | + | 344.230i | −0.928638 | + | 0.0113592i | ||||
\(973\) | −7893.41 | −0.260073 | ||||||||
\(974\) | −582.698 | + | 1009.26i | −0.0191693 | + | 0.0332021i | ||||
\(975\) | 11089.0 | − | 12376.3i | 0.364237 | − | 0.406522i | ||||
\(976\) | 10837.8 | + | 18771.6i | 0.355440 | + | 0.615639i | ||||
\(977\) | −6343.27 | − | 10986.9i | −0.207717 | − | 0.359776i | 0.743278 | − | 0.668982i | \(-0.233270\pi\) |
−0.950995 | + | 0.309207i | \(0.899937\pi\) | |||||||
\(978\) | 4780.23 | + | 14590.5i | 0.156293 | + | 0.477047i | ||||
\(979\) | −8571.92 | + | 14847.0i | −0.279836 | + | 0.484690i | ||||
\(980\) | 4823.43 | 0.157223 | ||||||||
\(981\) | 642.299 | + | 5836.25i | 0.0209042 | + | 0.189946i | ||||
\(982\) | −12130.8 | −0.394205 | ||||||||
\(983\) | 16788.1 | − | 29077.8i | 0.544716 | − | 0.943476i | −0.453909 | − | 0.891048i | \(-0.649971\pi\) |
0.998625 | − | 0.0524278i | \(-0.0166959\pi\) | |||||||
\(984\) | 30248.5 | + | 6352.21i | 0.979966 | + | 0.205794i | ||||
\(985\) | −11054.1 | − | 19146.3i | −0.357576 | − | 0.619341i | ||||
\(986\) | 1802.95 | + | 3122.79i | 0.0582328 | + | 0.100862i | ||||
\(987\) | 19542.9 | + | 4104.04i | 0.630252 | + | 0.132354i | ||||
\(988\) | −16754.0 | + | 29018.8i | −0.539490 | + | 0.934424i | ||||
\(989\) | 5290.86 | 0.170111 | ||||||||
\(990\) | −3377.02 | − | 1483.79i | −0.108413 | − | 0.0476343i | ||||
\(991\) | 47127.7 | 1.51066 | 0.755329 | − | 0.655346i | \(-0.227477\pi\) | ||||
0.755329 | + | 0.655346i | \(0.227477\pi\) | |||||||
\(992\) | 14932.7 | − | 25864.2i | 0.477937 | − | 0.827811i | ||||
\(993\) | −16108.3 | − | 49166.6i | −0.514784 | − | 1.57125i | ||||
\(994\) | −2050.25 | − | 3551.14i | −0.0654225 | − | 0.113315i | ||||
\(995\) | −6773.88 | − | 11732.7i | −0.215826 | − | 0.373821i | ||||
\(996\) | 12288.7 | − | 13715.3i | 0.390947 | − | 0.436333i | ||||
\(997\) | 19952.6 | − | 34559.0i | 0.633808 | − | 1.09779i | −0.352958 | − | 0.935639i | \(-0.614824\pi\) |
0.986766 | − | 0.162148i | \(-0.0518424\pi\) | |||||||
\(998\) | −7976.48 | −0.252997 | ||||||||
\(999\) | 12831.8 | + | 9179.76i | 0.406388 | + | 0.290725i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 63.4.f.c.43.5 | yes | 18 | |
3.2 | odd | 2 | 189.4.f.c.127.5 | 18 | |||
9.2 | odd | 6 | 567.4.a.k.1.5 | 9 | |||
9.4 | even | 3 | inner | 63.4.f.c.22.5 | ✓ | 18 | |
9.5 | odd | 6 | 189.4.f.c.64.5 | 18 | |||
9.7 | even | 3 | 567.4.a.j.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.c.22.5 | ✓ | 18 | 9.4 | even | 3 | inner | |
63.4.f.c.43.5 | yes | 18 | 1.1 | even | 1 | trivial | |
189.4.f.c.64.5 | 18 | 9.5 | odd | 6 | |||
189.4.f.c.127.5 | 18 | 3.2 | odd | 2 | |||
567.4.a.j.1.5 | 9 | 9.7 | even | 3 | |||
567.4.a.k.1.5 | 9 | 9.2 | odd | 6 |