Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,3,Mod(6,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.6");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.p (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.77112171834\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 6.2 | ||
Character | \(\chi\) | \(=\) | 65.6 |
Dual form | 65.3.p.a.11.2 |
$q$-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 \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.947644 | − | 3.53665i | −0.473822 | − | 1.76833i | −0.625842 | − | 0.779950i | \(-0.715244\pi\) |
0.152020 | − | 0.988377i | \(-0.451422\pi\) | |||||||
\(3\) | −2.34119 | + | 4.05506i | −0.780397 | + | 1.35169i | 0.151314 | + | 0.988486i | \(0.451650\pi\) |
−0.931711 | + | 0.363201i | \(0.881684\pi\) | |||||||
\(4\) | −8.14580 | + | 4.70298i | −2.03645 | + | 1.17574i | ||||
\(5\) | 1.58114 | − | 1.58114i | 0.316228 | − | 0.316228i | ||||
\(6\) | 16.5600 | + | 4.43723i | 2.75999 | + | 0.739538i | ||||
\(7\) | −2.82701 | + | 10.5506i | −0.403859 | + | 1.50722i | 0.402291 | + | 0.915512i | \(0.368214\pi\) |
−0.806150 | + | 0.591711i | \(0.798453\pi\) | |||||||
\(8\) | 13.9961 | + | 13.9961i | 1.74951 | + | 1.74951i | ||||
\(9\) | −6.46235 | − | 11.1931i | −0.718039 | − | 1.24368i | ||||
\(10\) | −7.09030 | − | 4.09359i | −0.709030 | − | 0.409359i | ||||
\(11\) | −2.43925 | + | 0.653596i | −0.221750 | + | 0.0594178i | −0.367983 | − | 0.929832i | \(-0.619952\pi\) |
0.146233 | + | 0.989250i | \(0.453285\pi\) | |||||||
\(12\) | − | 44.0423i | − | 3.67019i | ||||||
\(13\) | −12.3990 | + | 3.90697i | −0.953770 | + | 0.300536i | ||||
\(14\) | 39.9927 | 2.85662 | ||||||||
\(15\) | 2.70987 | + | 10.1134i | 0.180658 | + | 0.674224i | ||||
\(16\) | 17.4241 | − | 30.1794i | 1.08901 | − | 1.88621i | ||||
\(17\) | −12.7859 | + | 7.38192i | −0.752109 | + | 0.434230i | −0.826455 | − | 0.563002i | \(-0.809646\pi\) |
0.0743465 | + | 0.997232i | \(0.476313\pi\) | |||||||
\(18\) | −33.4622 | + | 33.4622i | −1.85901 | + | 1.85901i | ||||
\(19\) | 9.12462 | + | 2.44493i | 0.480243 | + | 0.128681i | 0.490816 | − | 0.871263i | \(-0.336699\pi\) |
−0.0105727 | + | 0.999944i | \(0.503365\pi\) | |||||||
\(20\) | −5.44357 | + | 20.3157i | −0.272179 | + | 1.01578i | ||||
\(21\) | −36.1646 | − | 36.1646i | −1.72212 | − | 1.72212i | ||||
\(22\) | 4.62308 | + | 8.00742i | 0.210140 | + | 0.363973i | ||||
\(23\) | 9.30396 | + | 5.37165i | 0.404520 | + | 0.233550i | 0.688432 | − | 0.725300i | \(-0.258299\pi\) |
−0.283912 | + | 0.958850i | \(0.591632\pi\) | |||||||
\(24\) | −89.5224 | + | 23.9875i | −3.73010 | + | 0.999478i | ||||
\(25\) | − | 5.00000i | − | 0.200000i | ||||||
\(26\) | 25.5675 | + | 40.1486i | 0.983364 | + | 1.54418i | ||||
\(27\) | 18.3769 | 0.680627 | ||||||||
\(28\) | −26.5908 | − | 99.2381i | −0.949671 | − | 3.54422i | ||||
\(29\) | 11.5912 | − | 20.0766i | 0.399697 | − | 0.692296i | −0.593991 | − | 0.804471i | \(-0.702449\pi\) |
0.993688 | + | 0.112176i | \(0.0357820\pi\) | |||||||
\(30\) | 33.1995 | − | 19.1677i | 1.10665 | − | 0.638924i | ||||
\(31\) | −2.04450 | + | 2.04450i | −0.0659515 | + | 0.0659515i | −0.739313 | − | 0.673362i | \(-0.764850\pi\) |
0.673362 | + | 0.739313i | \(0.264850\pi\) | |||||||
\(32\) | −46.7700 | − | 12.5320i | −1.46156 | − | 0.391624i | ||||
\(33\) | 3.06038 | − | 11.4215i | 0.0927389 | − | 0.346106i | ||||
\(34\) | 38.2237 | + | 38.2237i | 1.12423 | + | 1.12423i | ||||
\(35\) | 12.2120 | + | 21.1518i | 0.348914 | + | 0.604337i | ||||
\(36\) | 105.282 | + | 60.7846i | 2.92450 | + | 1.68846i | ||||
\(37\) | 14.2806 | − | 3.82648i | 0.385963 | − | 0.103418i | −0.0606194 | − | 0.998161i | \(-0.519308\pi\) |
0.446583 | + | 0.894742i | \(0.352641\pi\) | |||||||
\(38\) | − | 34.5876i | − | 0.910199i | ||||||
\(39\) | 13.1855 | − | 59.4257i | 0.338088 | − | 1.52374i | ||||
\(40\) | 44.2595 | 1.10649 | ||||||||
\(41\) | 9.33567 | + | 34.8412i | 0.227699 | + | 0.849785i | 0.981305 | + | 0.192459i | \(0.0616461\pi\) |
−0.753606 | + | 0.657327i | \(0.771687\pi\) | |||||||
\(42\) | −93.6305 | + | 162.173i | −2.22930 | + | 3.86126i | ||||
\(43\) | 22.9642 | − | 13.2584i | 0.534052 | − | 0.308335i | −0.208613 | − | 0.977998i | \(-0.566895\pi\) |
0.742665 | + | 0.669663i | \(0.233562\pi\) | |||||||
\(44\) | 16.7958 | − | 16.7958i | 0.381723 | − | 0.381723i | ||||
\(45\) | −27.9157 | − | 7.48000i | −0.620350 | − | 0.166222i | ||||
\(46\) | 10.1808 | − | 37.9953i | 0.221322 | − | 0.825985i | ||||
\(47\) | −19.8029 | − | 19.8029i | −0.421338 | − | 0.421338i | 0.464326 | − | 0.885664i | \(-0.346297\pi\) |
−0.885664 | + | 0.464326i | \(0.846297\pi\) | |||||||
\(48\) | 81.5862 | + | 141.312i | 1.69971 | + | 2.94399i | ||||
\(49\) | −60.8871 | − | 35.1532i | −1.24259 | − | 0.717412i | ||||
\(50\) | −17.6833 | + | 4.73822i | −0.353665 | + | 0.0947644i | ||||
\(51\) | − | 69.1299i | − | 1.35549i | ||||||
\(52\) | 82.6255 | − | 90.1377i | 1.58895 | − | 1.73342i | ||||
\(53\) | 22.5331 | 0.425152 | 0.212576 | − | 0.977145i | \(-0.431815\pi\) | ||||
0.212576 | + | 0.977145i | \(0.431815\pi\) | |||||||
\(54\) | −17.4148 | − | 64.9928i | −0.322496 | − | 1.20357i | ||||
\(55\) | −2.82337 | + | 4.89022i | −0.0513340 | + | 0.0889131i | ||||
\(56\) | −187.234 | + | 108.099i | −3.34346 | + | 1.93035i | ||||
\(57\) | −31.2768 | + | 31.2768i | −0.548716 | + | 0.548716i | ||||
\(58\) | −81.9882 | − | 21.9687i | −1.41359 | − | 0.378770i | ||||
\(59\) | −29.1459 | + | 108.774i | −0.493998 | + | 1.84363i | 0.0415718 | + | 0.999136i | \(0.486763\pi\) |
−0.535570 | + | 0.844491i | \(0.679903\pi\) | |||||||
\(60\) | −69.6369 | − | 69.6369i | −1.16062 | − | 1.16062i | ||||
\(61\) | 41.4471 | + | 71.7886i | 0.679461 | + | 1.17686i | 0.975143 | + | 0.221575i | \(0.0711198\pi\) |
−0.295682 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(62\) | 9.16813 | + | 5.29322i | 0.147873 | + | 0.0853746i | ||||
\(63\) | 136.363 | − | 36.5383i | 2.16449 | − | 0.579973i | ||||
\(64\) | 37.8924i | 0.592069i | ||||||||
\(65\) | −13.4271 | + | 25.7820i | −0.206571 | + | 0.396647i | ||||
\(66\) | −43.2941 | −0.655971 | ||||||||
\(67\) | 27.5554 | + | 102.838i | 0.411275 | + | 1.53490i | 0.792181 | + | 0.610286i | \(0.208946\pi\) |
−0.380906 | + | 0.924614i | \(0.624388\pi\) | |||||||
\(68\) | 69.4340 | − | 120.263i | 1.02109 | − | 1.76858i | ||||
\(69\) | −43.5647 | + | 25.1521i | −0.631373 | + | 0.364523i | ||||
\(70\) | 63.2340 | − | 63.2340i | 0.903343 | − | 0.903343i | ||||
\(71\) | 26.4832 | + | 7.09616i | 0.373003 | + | 0.0999459i | 0.440450 | − | 0.897777i | \(-0.354819\pi\) |
−0.0674472 | + | 0.997723i | \(0.521485\pi\) | |||||||
\(72\) | 66.2122 | − | 247.107i | 0.919614 | − | 3.43205i | ||||
\(73\) | 21.9442 | + | 21.9442i | 0.300605 | + | 0.300605i | 0.841251 | − | 0.540645i | \(-0.181820\pi\) |
−0.540645 | + | 0.841251i | \(0.681820\pi\) | |||||||
\(74\) | −27.0659 | − | 46.8795i | −0.365756 | − | 0.633507i | ||||
\(75\) | 20.2753 | + | 11.7060i | 0.270337 | + | 0.156079i | ||||
\(76\) | −85.8258 | + | 22.9969i | −1.12929 | + | 0.302591i | ||||
\(77\) | − | 27.5832i | − | 0.358223i | ||||||
\(78\) | −222.663 | + | 9.68204i | −2.85466 | + | 0.124129i | ||||
\(79\) | −148.335 | −1.87765 | −0.938827 | − | 0.344388i | \(-0.888086\pi\) | ||||
−0.938827 | + | 0.344388i | \(0.888086\pi\) | |||||||
\(80\) | −20.1679 | − | 75.2677i | −0.252099 | − | 0.940847i | ||||
\(81\) | 15.1372 | − | 26.2185i | 0.186880 | − | 0.323685i | ||||
\(82\) | 114.374 | − | 66.0341i | 1.39481 | − | 0.805294i | ||||
\(83\) | 24.8736 | − | 24.8736i | 0.299682 | − | 0.299682i | −0.541208 | − | 0.840889i | \(-0.682033\pi\) |
0.840889 | + | 0.541208i | \(0.182033\pi\) | |||||||
\(84\) | 464.671 | + | 124.508i | 5.53180 | + | 1.48224i | ||||
\(85\) | −8.54437 | + | 31.8880i | −0.100522 | + | 0.375153i | ||||
\(86\) | −68.6523 | − | 68.6523i | −0.798282 | − | 0.798282i | ||||
\(87\) | 54.2745 | + | 94.0062i | 0.623845 | + | 1.08053i | ||||
\(88\) | −43.2877 | − | 24.9922i | −0.491906 | − | 0.284002i | ||||
\(89\) | 124.498 | − | 33.3591i | 1.39885 | − | 0.374822i | 0.520921 | − | 0.853605i | \(-0.325589\pi\) |
0.877933 | + | 0.478783i | \(0.158922\pi\) | |||||||
\(90\) | 105.817i | 1.17574i | ||||||||
\(91\) | −6.16855 | − | 141.862i | −0.0677862 | − | 1.55892i | ||||
\(92\) | −101.051 | −1.09838 | ||||||||
\(93\) | −3.50400 | − | 13.0771i | −0.0376774 | − | 0.140614i | ||||
\(94\) | −51.2699 | + | 88.8021i | −0.545424 | + | 0.944703i | ||||
\(95\) | 18.2931 | − | 10.5615i | 0.192559 | − | 0.111174i | ||||
\(96\) | 160.315 | − | 160.315i | 1.66995 | − | 1.66995i | ||||
\(97\) | −165.650 | − | 44.3857i | −1.70773 | − | 0.457584i | −0.732863 | − | 0.680377i | \(-0.761816\pi\) |
−0.974866 | + | 0.222792i | \(0.928483\pi\) | |||||||
\(98\) | −66.6254 | + | 248.649i | −0.679851 | + | 2.53724i | ||||
\(99\) | 23.0791 | + | 23.0791i | 0.233122 | + | 0.233122i | ||||
\(100\) | 23.5149 | + | 40.7290i | 0.235149 | + | 0.407290i | ||||
\(101\) | 70.4552 | + | 40.6773i | 0.697576 | + | 0.402746i | 0.806444 | − | 0.591311i | \(-0.201389\pi\) |
−0.108868 | + | 0.994056i | \(0.534723\pi\) | |||||||
\(102\) | −244.489 | + | 65.5105i | −2.39695 | + | 0.642260i | ||||
\(103\) | 85.9224i | 0.834198i | 0.908861 | + | 0.417099i | \(0.136953\pi\) | ||||
−0.908861 | + | 0.417099i | \(0.863047\pi\) | |||||||
\(104\) | −228.220 | − | 118.855i | −2.19442 | − | 1.14284i | ||||
\(105\) | −114.363 | −1.08917 | ||||||||
\(106\) | −21.3533 | − | 79.6916i | −0.201446 | − | 0.751808i | ||||
\(107\) | 42.0616 | − | 72.8529i | 0.393099 | − | 0.680868i | −0.599757 | − | 0.800182i | \(-0.704736\pi\) |
0.992857 | + | 0.119314i | \(0.0380695\pi\) | |||||||
\(108\) | −149.695 | + | 86.4263i | −1.38606 | + | 0.800243i | ||||
\(109\) | −29.1417 | + | 29.1417i | −0.267355 | + | 0.267355i | −0.828033 | − | 0.560679i | \(-0.810540\pi\) |
0.560679 | + | 0.828033i | \(0.310540\pi\) | |||||||
\(110\) | 19.9706 | + | 5.35110i | 0.181551 | + | 0.0486464i | ||||
\(111\) | −17.9171 | + | 66.8674i | −0.161415 | + | 0.602409i | ||||
\(112\) | 269.152 | + | 269.152i | 2.40314 | + | 2.40314i | ||||
\(113\) | −95.9546 | − | 166.198i | −0.849155 | − | 1.47078i | −0.881963 | − | 0.471319i | \(-0.843778\pi\) |
0.0328077 | − | 0.999462i | \(-0.489555\pi\) | |||||||
\(114\) | 140.255 | + | 80.9761i | 1.23030 | + | 0.710316i | ||||
\(115\) | 23.2042 | − | 6.21754i | 0.201775 | − | 0.0540656i | ||||
\(116\) | 218.053i | 1.87977i | ||||||||
\(117\) | 123.858 | + | 113.535i | 1.05861 | + | 0.970388i | ||||
\(118\) | 412.316 | 3.49420 | ||||||||
\(119\) | −41.7376 | − | 155.767i | −0.350736 | − | 1.30896i | ||||
\(120\) | −103.620 | + | 179.475i | −0.863499 | + | 1.49562i | ||||
\(121\) | −99.2663 | + | 57.3114i | −0.820383 | + | 0.473648i | ||||
\(122\) | 214.614 | − | 214.614i | 1.75913 | − | 1.75913i | ||||
\(123\) | −163.140 | − | 43.7132i | −1.32634 | − | 0.355392i | ||||
\(124\) | 7.03883 | − | 26.2693i | 0.0567648 | − | 0.211849i | ||||
\(125\) | −7.90569 | − | 7.90569i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | −258.447 | − | 447.643i | −2.05116 | − | 3.55272i | ||||
\(127\) | 95.9532 | + | 55.3986i | 0.755537 | + | 0.436210i | 0.827691 | − | 0.561184i | \(-0.189654\pi\) |
−0.0721539 | + | 0.997394i | \(0.522987\pi\) | |||||||
\(128\) | −53.0675 | + | 14.2194i | −0.414590 | + | 0.111089i | ||||
\(129\) | 124.162i | 0.962494i | ||||||||
\(130\) | 103.906 | + | 23.0548i | 0.799279 | + | 0.177345i | ||||
\(131\) | 121.096 | 0.924399 | 0.462199 | − | 0.886776i | \(-0.347060\pi\) | ||||
0.462199 | + | 0.886776i | \(0.347060\pi\) | |||||||
\(132\) | 28.7858 | + | 107.430i | 0.218075 | + | 0.813865i | ||||
\(133\) | −51.5909 | + | 89.3580i | −0.387901 | + | 0.671865i | ||||
\(134\) | 337.591 | − | 194.908i | 2.51933 | − | 1.45454i | ||||
\(135\) | 29.0565 | − | 29.0565i | 0.215233 | − | 0.215233i | ||||
\(136\) | −282.270 | − | 75.6339i | −2.07551 | − | 0.556132i | ||||
\(137\) | −7.16786 | + | 26.7508i | −0.0523202 | + | 0.195262i | −0.987139 | − | 0.159863i | \(-0.948895\pi\) |
0.934819 | + | 0.355124i | \(0.115561\pi\) | |||||||
\(138\) | 130.238 | + | 130.238i | 0.943754 | + | 0.943754i | ||||
\(139\) | −75.5763 | − | 130.902i | −0.543714 | − | 0.941740i | −0.998687 | − | 0.0512350i | \(-0.983684\pi\) |
0.454973 | − | 0.890505i | \(-0.349649\pi\) | |||||||
\(140\) | −198.953 | − | 114.866i | −1.42109 | − | 0.820468i | ||||
\(141\) | 126.664 | − | 33.9396i | 0.898328 | − | 0.240706i | ||||
\(142\) | − | 100.387i | − | 0.706948i | ||||||
\(143\) | 27.6907 | − | 17.6340i | 0.193642 | − | 0.123315i | ||||
\(144\) | −450.402 | −3.12779 | ||||||||
\(145\) | −13.4165 | − | 50.0712i | −0.0925278 | − | 0.345318i | ||||
\(146\) | 56.8137 | − | 98.4043i | 0.389135 | − | 0.674002i | ||||
\(147\) | 285.097 | − | 164.601i | 1.93943 | − | 1.11973i | ||||
\(148\) | −98.3313 | + | 98.3313i | −0.664400 | + | 0.664400i | ||||
\(149\) | 50.2538 | + | 13.4655i | 0.337274 | + | 0.0903723i | 0.423481 | − | 0.905905i | \(-0.360808\pi\) |
−0.0862072 | + | 0.996277i | \(0.527475\pi\) | |||||||
\(150\) | 22.1861 | − | 82.7998i | 0.147908 | − | 0.551999i | ||||
\(151\) | 123.524 | + | 123.524i | 0.818038 | + | 0.818038i | 0.985824 | − | 0.167785i | \(-0.0536615\pi\) |
−0.167785 | + | 0.985824i | \(0.553661\pi\) | |||||||
\(152\) | 93.4894 | + | 161.928i | 0.615062 | + | 1.06532i | ||||
\(153\) | 165.253 | + | 95.4090i | 1.08009 | + | 0.623588i | ||||
\(154\) | −97.5523 | + | 26.1391i | −0.633456 | + | 0.169734i | ||||
\(155\) | 6.46527i | 0.0417114i | ||||||||
\(156\) | 172.072 | + | 546.081i | 1.10302 | + | 3.50052i | ||||
\(157\) | −71.8383 | −0.457569 | −0.228784 | − | 0.973477i | \(-0.573475\pi\) | ||||
−0.228784 | + | 0.973477i | \(0.573475\pi\) | |||||||
\(158\) | 140.568 | + | 524.609i | 0.889674 | + | 3.32031i | ||||
\(159\) | −52.7542 | + | 91.3729i | −0.331787 | + | 0.574672i | ||||
\(160\) | −93.7646 | + | 54.1350i | −0.586029 | + | 0.338344i | ||||
\(161\) | −82.9763 | + | 82.9763i | −0.515381 | + | 0.515381i | ||||
\(162\) | −107.070 | − | 28.6894i | −0.660928 | − | 0.177095i | ||||
\(163\) | 35.5385 | − | 132.632i | 0.218028 | − | 0.813691i | −0.767051 | − | 0.641586i | \(-0.778277\pi\) |
0.985079 | − | 0.172105i | \(-0.0550568\pi\) | |||||||
\(164\) | −239.904 | − | 239.904i | −1.46283 | − | 1.46283i | ||||
\(165\) | −13.2201 | − | 22.8979i | −0.0801218 | − | 0.138775i | ||||
\(166\) | −111.540 | − | 64.3979i | −0.671931 | − | 0.387939i | ||||
\(167\) | −234.457 | + | 62.8225i | −1.40393 | + | 0.376183i | −0.879756 | − | 0.475426i | \(-0.842294\pi\) |
−0.524178 | + | 0.851609i | \(0.675627\pi\) | |||||||
\(168\) | − | 1012.33i | − | 6.02575i | ||||||
\(169\) | 138.471 | − | 96.8852i | 0.819356 | − | 0.573285i | ||||
\(170\) | 120.874 | 0.711024 | ||||||||
\(171\) | −31.6000 | − | 117.933i | −0.184796 | − | 0.689666i | ||||
\(172\) | −124.708 | + | 216.000i | −0.725046 | + | 1.25582i | ||||
\(173\) | 108.612 | − | 62.7074i | 0.627818 | − | 0.362471i | −0.152089 | − | 0.988367i | \(-0.548600\pi\) |
0.779906 | + | 0.625896i | \(0.215267\pi\) | |||||||
\(174\) | 281.034 | − | 281.034i | 1.61514 | − | 1.61514i | ||||
\(175\) | 52.7528 | + | 14.1351i | 0.301445 | + | 0.0807719i | ||||
\(176\) | −22.7766 | + | 85.0035i | −0.129413 | + | 0.482974i | ||||
\(177\) | −372.849 | − | 372.849i | −2.10649 | − | 2.10649i | ||||
\(178\) | −235.960 | − | 408.694i | −1.32562 | − | 2.29603i | ||||
\(179\) | 20.9013 | + | 12.0674i | 0.116767 | + | 0.0674155i | 0.557246 | − | 0.830347i | \(-0.311858\pi\) |
−0.440479 | + | 0.897763i | \(0.645191\pi\) | |||||||
\(180\) | 262.574 | − | 70.3565i | 1.45875 | − | 0.390870i | ||||
\(181\) | 40.2664i | 0.222466i | 0.993794 | + | 0.111233i | \(0.0354800\pi\) | ||||
−0.993794 | + | 0.111233i | \(0.964520\pi\) | |||||||
\(182\) | −495.870 | + | 156.250i | −2.72456 | + | 0.858518i | ||||
\(183\) | −388.143 | −2.12100 | ||||||||
\(184\) | 55.0370 | + | 205.401i | 0.299114 | + | 1.11631i | ||||
\(185\) | 16.5295 | − | 28.6299i | 0.0893484 | − | 0.154756i | ||||
\(186\) | −42.9287 | + | 24.7849i | −0.230799 | + | 0.133252i | ||||
\(187\) | 26.3631 | − | 26.3631i | 0.140979 | − | 0.140979i | ||||
\(188\) | 254.443 | + | 68.1777i | 1.35342 | + | 0.362648i | ||||
\(189\) | −51.9518 | + | 193.887i | −0.274877 | + | 1.02586i | ||||
\(190\) | −54.6877 | − | 54.6877i | −0.287830 | − | 0.287830i | ||||
\(191\) | 70.8170 | + | 122.659i | 0.370769 | + | 0.642191i | 0.989684 | − | 0.143267i | \(-0.0457607\pi\) |
−0.618915 | + | 0.785458i | \(0.712427\pi\) | |||||||
\(192\) | −153.656 | − | 88.7134i | −0.800292 | − | 0.462049i | ||||
\(193\) | 92.0270 | − | 24.6586i | 0.476824 | − | 0.127765i | −0.0123994 | − | 0.999923i | \(-0.503947\pi\) |
0.489223 | + | 0.872159i | \(0.337280\pi\) | |||||||
\(194\) | 627.908i | 3.23664i | ||||||||
\(195\) | −73.1123 | − | 114.808i | −0.374935 | − | 0.588761i | ||||
\(196\) | 661.299 | 3.37397 | ||||||||
\(197\) | 17.3590 | + | 64.7845i | 0.0881166 | + | 0.328855i | 0.995886 | − | 0.0906138i | \(-0.0288829\pi\) |
−0.907770 | + | 0.419469i | \(0.862216\pi\) | |||||||
\(198\) | 59.7520 | − | 103.493i | 0.301778 | − | 0.522694i | ||||
\(199\) | −123.221 | + | 71.1414i | −0.619199 | + | 0.357494i | −0.776557 | − | 0.630047i | \(-0.783036\pi\) |
0.157358 | + | 0.987542i | \(0.449702\pi\) | |||||||
\(200\) | 69.9804 | − | 69.9804i | 0.349902 | − | 0.349902i | ||||
\(201\) | −481.528 | − | 129.025i | −2.39566 | − | 0.641916i | ||||
\(202\) | 77.0952 | − | 287.723i | 0.381659 | − | 1.42437i | ||||
\(203\) | 179.051 | + | 179.051i | 0.882023 | + | 0.882023i | ||||
\(204\) | 325.116 | + | 563.118i | 1.59371 | + | 2.76038i | ||||
\(205\) | 69.8498 | + | 40.3278i | 0.340731 | + | 0.196721i | ||||
\(206\) | 303.878 | − | 81.4238i | 1.47514 | − | 0.395261i | ||||
\(207\) | − | 138.854i | − | 0.670791i | ||||||
\(208\) | −98.1315 | + | 442.270i | −0.471786 | + | 2.12630i | ||||
\(209\) | −23.8552 | −0.114140 | ||||||||
\(210\) | 108.375 | + | 404.461i | 0.516071 | + | 1.92600i | ||||
\(211\) | −57.8501 | + | 100.199i | −0.274171 | + | 0.474879i | −0.969926 | − | 0.243401i | \(-0.921737\pi\) |
0.695754 | + | 0.718280i | \(0.255070\pi\) | |||||||
\(212\) | −183.550 | + | 105.972i | −0.865800 | + | 0.499870i | ||||
\(213\) | −90.7776 | + | 90.7776i | −0.426186 | + | 0.426186i | ||||
\(214\) | −297.515 | − | 79.7189i | −1.39026 | − | 0.372518i | ||||
\(215\) | 15.3463 | − | 57.2730i | 0.0713779 | − | 0.266386i | ||||
\(216\) | 257.205 | + | 257.205i | 1.19076 | + | 1.19076i | ||||
\(217\) | −15.7908 | − | 27.3504i | −0.0727685 | − | 0.126039i | ||||
\(218\) | 130.680 | + | 75.4481i | 0.599449 | + | 0.346092i | ||||
\(219\) | −140.361 | + | 37.6095i | −0.640916 | + | 0.171733i | ||||
\(220\) | − | 53.1130i | − | 0.241423i | ||||||
\(221\) | 129.691 | − | 141.482i | 0.586837 | − | 0.640192i | ||||
\(222\) | 253.466 | 1.14174 | ||||||||
\(223\) | −27.2801 | − | 101.811i | −0.122332 | − | 0.456550i | 0.877398 | − | 0.479763i | \(-0.159277\pi\) |
−0.999731 | + | 0.0232127i | \(0.992611\pi\) | |||||||
\(224\) | 264.439 | − | 458.022i | 1.18053 | − | 2.04474i | ||||
\(225\) | −55.9656 | + | 32.3117i | −0.248736 | + | 0.143608i | ||||
\(226\) | −496.855 | + | 496.855i | −2.19847 | + | 2.19847i | ||||
\(227\) | 296.431 | + | 79.4286i | 1.30587 | + | 0.349906i | 0.843665 | − | 0.536870i | \(-0.180393\pi\) |
0.462200 | + | 0.886776i | \(0.347060\pi\) | |||||||
\(228\) | 107.680 | − | 401.869i | 0.472283 | − | 1.76258i | ||||
\(229\) | 312.209 | + | 312.209i | 1.36336 | + | 1.36336i | 0.869598 | + | 0.493761i | \(0.164378\pi\) |
0.493761 | + | 0.869598i | \(0.335622\pi\) | |||||||
\(230\) | −43.9786 | − | 76.1731i | −0.191211 | − | 0.331188i | ||||
\(231\) | 111.852 | + | 64.5775i | 0.484206 | + | 0.279556i | ||||
\(232\) | 443.225 | − | 118.762i | 1.91045 | − | 0.511904i | ||||
\(233\) | − | 298.199i | − | 1.27983i | −0.768448 | − | 0.639913i | \(-0.778971\pi\) | ||
0.768448 | − | 0.639913i | \(-0.221029\pi\) | |||||||
\(234\) | 284.162 | − | 545.634i | 1.21437 | − | 2.33177i | ||||
\(235\) | −62.6222 | −0.266478 | ||||||||
\(236\) | −274.145 | − | 1023.12i | −1.16163 | − | 4.33527i | ||||
\(237\) | 347.280 | − | 601.506i | 1.46532 | − | 2.53800i | ||||
\(238\) | −511.341 | + | 295.223i | −2.14849 | + | 1.24043i | ||||
\(239\) | −224.142 | + | 224.142i | −0.937831 | + | 0.937831i | −0.998177 | − | 0.0603465i | \(-0.980779\pi\) |
0.0603465 | + | 0.998177i | \(0.480779\pi\) | |||||||
\(240\) | 352.432 | + | 94.4339i | 1.46847 | + | 0.393475i | ||||
\(241\) | 3.02922 | − | 11.3052i | 0.0125694 | − | 0.0469095i | −0.959356 | − | 0.282197i | \(-0.908937\pi\) |
0.971926 | + | 0.235288i | \(0.0756033\pi\) | |||||||
\(242\) | 296.760 | + | 296.760i | 1.22628 | + | 1.22628i | ||||
\(243\) | 153.575 | + | 265.999i | 0.631994 | + | 1.09465i | ||||
\(244\) | −675.240 | − | 389.850i | −2.76738 | − | 1.59775i | ||||
\(245\) | −151.853 | + | 40.6889i | −0.619809 | + | 0.166077i | ||||
\(246\) | 618.394i | 2.51379i | ||||||||
\(247\) | −122.689 | + | 5.33485i | −0.496715 | + | 0.0215986i | ||||
\(248\) | −57.2299 | −0.230766 | ||||||||
\(249\) | 42.6301 | + | 159.098i | 0.171205 | + | 0.638946i | ||||
\(250\) | −20.4679 | + | 35.4515i | −0.0818717 | + | 0.141806i | ||||
\(251\) | 97.5330 | − | 56.3107i | 0.388578 | − | 0.224345i | −0.292966 | − | 0.956123i | \(-0.594642\pi\) |
0.681544 | + | 0.731777i | \(0.261309\pi\) | |||||||
\(252\) | −938.945 | + | 938.945i | −3.72597 | + | 3.72597i | ||||
\(253\) | −26.2056 | − | 7.02177i | −0.103579 | − | 0.0277540i | ||||
\(254\) | 104.996 | − | 391.852i | 0.413371 | − | 1.54272i | ||||
\(255\) | −109.304 | − | 109.304i | −0.428643 | − | 0.428643i | ||||
\(256\) | 176.363 | + | 305.470i | 0.688918 | + | 1.19324i | ||||
\(257\) | −102.478 | − | 59.1658i | −0.398748 | − | 0.230217i | 0.287196 | − | 0.957872i | \(-0.407277\pi\) |
−0.685943 | + | 0.727655i | \(0.740610\pi\) | |||||||
\(258\) | 439.117 | − | 117.661i | 1.70201 | − | 0.456051i | ||||
\(259\) | 161.486i | 0.623499i | ||||||||
\(260\) | −11.8779 | − | 273.163i | −0.0456842 | − | 1.05063i | ||||
\(261\) | −299.626 | −1.14799 | ||||||||
\(262\) | −114.756 | − | 428.276i | −0.438000 | − | 1.63464i | ||||
\(263\) | −34.9965 | + | 60.6156i | −0.133066 | + | 0.230478i | −0.924857 | − | 0.380315i | \(-0.875816\pi\) |
0.791791 | + | 0.610792i | \(0.209149\pi\) | |||||||
\(264\) | 202.690 | − | 117.023i | 0.767764 | − | 0.443269i | ||||
\(265\) | 35.6279 | − | 35.6279i | 0.134445 | − | 0.134445i | ||||
\(266\) | 364.918 | + | 97.7796i | 1.37187 | + | 0.367592i | ||||
\(267\) | −156.200 | + | 582.947i | −0.585020 | + | 2.18332i | ||||
\(268\) | −708.107 | − | 708.107i | −2.64219 | − | 2.64219i | ||||
\(269\) | −197.380 | − | 341.872i | −0.733755 | − | 1.27090i | −0.955267 | − | 0.295744i | \(-0.904433\pi\) |
0.221512 | − | 0.975158i | \(-0.428901\pi\) | |||||||
\(270\) | −130.298 | − | 75.2275i | −0.482585 | − | 0.278620i | ||||
\(271\) | −70.7832 | + | 18.9663i | −0.261193 | + | 0.0699864i | −0.387039 | − | 0.922063i | \(-0.626502\pi\) |
0.125846 | + | 0.992050i | \(0.459835\pi\) | |||||||
\(272\) | 514.493i | 1.89152i | ||||||||
\(273\) | 589.699 | + | 307.111i | 2.16007 | + | 1.12495i | ||||
\(274\) | 101.401 | 0.370077 | ||||||||
\(275\) | 3.26798 | + | 12.1963i | 0.0118836 | + | 0.0443500i | ||||
\(276\) | 236.579 | − | 409.768i | 0.857172 | − | 1.48467i | ||||
\(277\) | 161.523 | − | 93.2551i | 0.583114 | − | 0.336661i | −0.179256 | − | 0.983802i | \(-0.557369\pi\) |
0.762370 | + | 0.647142i | \(0.224036\pi\) | |||||||
\(278\) | −391.336 | + | 391.336i | −1.40768 | + | 1.40768i | ||||
\(279\) | 36.0965 | + | 9.67204i | 0.129378 | + | 0.0346668i | ||||
\(280\) | −125.122 | + | 466.963i | −0.446865 | + | 1.66772i | ||||
\(281\) | 9.79830 | + | 9.79830i | 0.0348694 | + | 0.0348694i | 0.724326 | − | 0.689457i | \(-0.242151\pi\) |
−0.689457 | + | 0.724326i | \(0.742151\pi\) | |||||||
\(282\) | −240.065 | − | 415.805i | −0.851295 | − | 1.47449i | ||||
\(283\) | 11.8738 | + | 6.85533i | 0.0419568 | + | 0.0242238i | 0.520832 | − | 0.853659i | \(-0.325622\pi\) |
−0.478875 | + | 0.877883i | \(0.658955\pi\) | |||||||
\(284\) | −249.100 | + | 66.7462i | −0.877113 | + | 0.235022i | ||||
\(285\) | 98.9060i | 0.347039i | ||||||||
\(286\) | −88.6064 | − | 81.2218i | −0.309813 | − | 0.283992i | ||||
\(287\) | −393.986 | −1.37277 | ||||||||
\(288\) | 161.972 | + | 604.488i | 0.562403 | + | 2.09892i | ||||
\(289\) | −35.5147 | + | 61.5132i | −0.122888 | + | 0.212848i | ||||
\(290\) | −164.370 | + | 94.8993i | −0.566794 | + | 0.327239i | ||||
\(291\) | 567.804 | − | 567.804i | 1.95122 | − | 1.95122i | ||||
\(292\) | −281.956 | − | 75.5499i | −0.965602 | − | 0.258732i | ||||
\(293\) | −74.4582 | + | 277.882i | −0.254123 | + | 0.948402i | 0.714452 | + | 0.699684i | \(0.246676\pi\) |
−0.968576 | + | 0.248718i | \(0.919991\pi\) | |||||||
\(294\) | −852.306 | − | 852.306i | −2.89900 | − | 2.89900i | ||||
\(295\) | 125.903 | + | 218.070i | 0.426790 | + | 0.739222i | ||||
\(296\) | 253.429 | + | 146.317i | 0.856178 | + | 0.494315i | ||||
\(297\) | −44.8260 | + | 12.0111i | −0.150929 | + | 0.0404413i | ||||
\(298\) | − | 190.491i | − | 0.639231i | ||||||
\(299\) | −136.347 | − | 30.2528i | −0.456009 | − | 0.101180i | ||||
\(300\) | −220.211 | −0.734038 | ||||||||
\(301\) | 74.9634 | + | 279.767i | 0.249048 | + | 0.929459i | ||||
\(302\) | 319.804 | − | 553.918i | 1.05896 | − | 1.83416i | ||||
\(303\) | −329.898 | + | 190.467i | −1.08877 | + | 0.628603i | ||||
\(304\) | 232.775 | − | 232.775i | 0.765707 | − | 0.765707i | ||||
\(305\) | 179.041 | + | 47.9740i | 0.587021 | + | 0.157292i | ||||
\(306\) | 180.828 | − | 674.857i | 0.590940 | − | 2.20542i | ||||
\(307\) | 166.198 | + | 166.198i | 0.541360 | + | 0.541360i | 0.923928 | − | 0.382567i | \(-0.124960\pi\) |
−0.382567 | + | 0.923928i | \(0.624960\pi\) | |||||||
\(308\) | 129.723 | + | 224.687i | 0.421179 | + | 0.729504i | ||||
\(309\) | −348.421 | − | 201.161i | −1.12757 | − | 0.651005i | ||||
\(310\) | 22.8654 | − | 6.12677i | 0.0737594 | − | 0.0197638i | ||||
\(311\) | − | 431.405i | − | 1.38715i | −0.720382 | − | 0.693577i | \(-0.756034\pi\) | ||
0.720382 | − | 0.693577i | \(-0.243966\pi\) | |||||||
\(312\) | 1016.27 | − | 647.183i | 3.25728 | − | 2.07430i | ||||
\(313\) | 430.738 | 1.37616 | 0.688080 | − | 0.725635i | \(-0.258454\pi\) | ||||
0.688080 | + | 0.725635i | \(0.258454\pi\) | |||||||
\(314\) | 68.0771 | + | 254.067i | 0.216806 | + | 0.809131i | ||||
\(315\) | 157.836 | − | 273.381i | 0.501068 | − | 0.867875i | ||||
\(316\) | 1208.30 | − | 697.615i | 3.82375 | − | 2.20764i | ||||
\(317\) | 71.9231 | − | 71.9231i | 0.226887 | − | 0.226887i | −0.584504 | − | 0.811391i | \(-0.698711\pi\) |
0.811391 | + | 0.584504i | \(0.198711\pi\) | |||||||
\(318\) | 373.147 | + | 99.9843i | 1.17342 | + | 0.314416i | ||||
\(319\) | −15.1519 | + | 56.5478i | −0.0474982 | + | 0.177266i | ||||
\(320\) | 59.9132 | + | 59.9132i | 0.187229 | + | 0.187229i | ||||
\(321\) | 196.949 | + | 341.125i | 0.613547 | + | 1.06270i | ||||
\(322\) | 372.091 | + | 214.827i | 1.15556 | + | 0.667163i | ||||
\(323\) | −134.714 | + | 36.0966i | −0.417072 | + | 0.111754i | ||||
\(324\) | 284.760i | 0.878890i | ||||||||
\(325\) | 19.5349 | + | 61.9951i | 0.0601073 | + | 0.190754i | ||||
\(326\) | −502.750 | −1.54218 | ||||||||
\(327\) | −49.9451 | − | 186.398i | −0.152737 | − | 0.570023i | ||||
\(328\) | −356.977 | + | 618.303i | −1.08835 | + | 1.88507i | ||||
\(329\) | 264.915 | − | 152.949i | 0.805212 | − | 0.464889i | ||||
\(330\) | −68.4540 | + | 68.4540i | −0.207436 | + | 0.207436i | ||||
\(331\) | −328.526 | − | 88.0283i | −0.992525 | − | 0.265946i | −0.274214 | − | 0.961669i | \(-0.588418\pi\) |
−0.718311 | + | 0.695722i | \(0.755084\pi\) | |||||||
\(332\) | −85.6352 | + | 319.595i | −0.257937 | + | 0.962635i | ||||
\(333\) | −135.117 | − | 135.117i | −0.405756 | − | 0.405756i | ||||
\(334\) | 444.363 | + | 769.660i | 1.33043 | + | 2.30437i | ||||
\(335\) | 206.171 | + | 119.033i | 0.615435 | + | 0.355321i | ||||
\(336\) | −1721.56 | + | 461.291i | −5.12369 | + | 1.37289i | ||||
\(337\) | − | 103.737i | − | 0.307824i | −0.988085 | − | 0.153912i | \(-0.950813\pi\) | ||
0.988085 | − | 0.153912i | \(-0.0491872\pi\) | |||||||
\(338\) | −473.871 | − | 397.912i | −1.40198 | − | 1.17725i | ||||
\(339\) | 898.592 | 2.65071 | ||||||||
\(340\) | −80.3680 | − | 299.937i | −0.236376 | − | 0.882169i | ||||
\(341\) | 3.65077 | − | 6.32332i | 0.0107061 | − | 0.0185434i | ||||
\(342\) | −387.143 | + | 223.517i | −1.13200 | + | 0.653558i | ||||
\(343\) | 164.561 | − | 164.561i | 0.479770 | − | 0.479770i | ||||
\(344\) | 506.975 | + | 135.843i | 1.47376 | + | 0.394894i | ||||
\(345\) | −29.1129 | + | 108.651i | −0.0843852 | + | 0.314930i | ||||
\(346\) | −324.700 | − | 324.700i | −0.938441 | − | 0.938441i | ||||
\(347\) | −112.919 | − | 195.582i | −0.325416 | − | 0.563638i | 0.656180 | − | 0.754604i | \(-0.272171\pi\) |
−0.981597 | + | 0.190967i | \(0.938838\pi\) | |||||||
\(348\) | −884.218 | − | 510.503i | −2.54086 | − | 1.46696i | ||||
\(349\) | 495.441 | − | 132.753i | 1.41960 | − | 0.380381i | 0.534259 | − | 0.845321i | \(-0.320591\pi\) |
0.885342 | + | 0.464940i | \(0.153924\pi\) | |||||||
\(350\) | − | 199.964i | − | 0.571324i | ||||||
\(351\) | −227.856 | + | 71.7981i | −0.649162 | + | 0.204553i | ||||
\(352\) | 122.275 | 0.347371 | ||||||||
\(353\) | 60.9396 | + | 227.430i | 0.172633 | + | 0.644276i | 0.996943 | + | 0.0781366i | \(0.0248970\pi\) |
−0.824309 | + | 0.566140i | \(0.808436\pi\) | |||||||
\(354\) | −965.310 | + | 1671.97i | −2.72686 | + | 4.72307i | ||||
\(355\) | 53.0937 | − | 30.6536i | 0.149560 | − | 0.0863483i | ||||
\(356\) | −857.248 | + | 857.248i | −2.40800 | + | 2.40800i | ||||
\(357\) | 729.359 | + | 195.431i | 2.04302 | + | 0.547426i | ||||
\(358\) | 22.8712 | − | 85.3563i | 0.0638859 | − | 0.238425i | ||||
\(359\) | 66.5213 | + | 66.5213i | 0.185296 | + | 0.185296i | 0.793659 | − | 0.608363i | \(-0.208173\pi\) |
−0.608363 | + | 0.793659i | \(0.708173\pi\) | |||||||
\(360\) | −286.020 | − | 495.402i | −0.794501 | − | 1.37612i | ||||
\(361\) | −235.354 | − | 135.882i | −0.651951 | − | 0.376404i | ||||
\(362\) | 142.408 | − | 38.1582i | 0.393393 | − | 0.105409i | ||||
\(363\) | − | 536.708i | − | 1.47853i | ||||||
\(364\) | 717.420 | + | 1126.57i | 1.97093 | + | 3.09496i | ||||
\(365\) | 69.3936 | 0.190119 | ||||||||
\(366\) | 367.821 | + | 1372.73i | 1.00498 | + | 3.75062i | ||||
\(367\) | −236.298 | + | 409.281i | −0.643865 | + | 1.11521i | 0.340698 | + | 0.940173i | \(0.389337\pi\) |
−0.984562 | + | 0.175034i | \(0.943997\pi\) | |||||||
\(368\) | 324.226 | − | 187.192i | 0.881049 | − | 0.508674i | ||||
\(369\) | 329.651 | − | 329.651i | 0.893364 | − | 0.893364i | ||||
\(370\) | −116.918 | − | 31.3281i | −0.315995 | − | 0.0846705i | ||||
\(371\) | −63.7013 | + | 237.736i | −0.171702 | + | 0.640799i | ||||
\(372\) | 90.0443 | + | 90.0443i | 0.242055 | + | 0.242055i | ||||
\(373\) | −5.04459 | − | 8.73748i | −0.0135244 | − | 0.0234249i | 0.859184 | − | 0.511667i | \(-0.170972\pi\) |
−0.872708 | + | 0.488242i | \(0.837638\pi\) | |||||||
\(374\) | −118.220 | − | 68.2544i | −0.316097 | − | 0.182498i | ||||
\(375\) | 50.5668 | − | 13.5493i | 0.134845 | − | 0.0361316i | ||||
\(376\) | − | 554.325i | − | 1.47427i | ||||||
\(377\) | −65.2810 | + | 294.216i | −0.173159 | + | 0.780414i | ||||
\(378\) | 734.943 | 1.94429 | ||||||||
\(379\) | −138.529 | − | 516.998i | −0.365512 | − | 1.36411i | −0.866725 | − | 0.498786i | \(-0.833779\pi\) |
0.501213 | − | 0.865324i | \(-0.332887\pi\) | |||||||
\(380\) | −99.3411 | + | 172.064i | −0.261424 | + | 0.452800i | ||||
\(381\) | −449.290 | + | 259.397i | −1.17924 | + | 0.680833i | ||||
\(382\) | 366.692 | − | 366.692i | 0.959926 | − | 0.959926i | ||||
\(383\) | −720.347 | − | 193.016i | −1.88080 | − | 0.503959i | −0.999507 | − | 0.0313900i | \(-0.990007\pi\) |
−0.881294 | − | 0.472569i | \(-0.843327\pi\) | |||||||
\(384\) | 66.5807 | − | 248.482i | 0.173387 | − | 0.647090i | ||||
\(385\) | −43.6129 | − | 43.6129i | −0.113280 | − | 0.113280i | ||||
\(386\) | −174.418 | − | 302.100i | −0.451859 | − | 0.782643i | ||||
\(387\) | −296.806 | − | 171.361i | −0.766940 | − | 0.442793i | ||||
\(388\) | 1558.09 | − | 417.490i | 4.01570 | − | 1.07600i | ||||
\(389\) | − | 644.701i | − | 1.65733i | −0.559747 | − | 0.828664i | \(-0.689101\pi\) | ||
0.559747 | − | 0.828664i | \(-0.310899\pi\) | |||||||
\(390\) | −336.753 | + | 367.370i | −0.863470 | + | 0.941975i | ||||
\(391\) | −158.612 | −0.405658 | ||||||||
\(392\) | −360.174 | − | 1344.19i | −0.918811 | − | 3.42905i | ||||
\(393\) | −283.509 | + | 491.053i | −0.721398 | + | 1.24950i | ||||
\(394\) | 212.670 | − | 122.785i | 0.539773 | − | 0.311638i | ||||
\(395\) | −234.538 | + | 234.538i | −0.593767 | + | 0.593767i | ||||
\(396\) | −296.538 | − | 79.4570i | −0.748833 | − | 0.200649i | ||||
\(397\) | −57.4332 | + | 214.344i | −0.144668 | + | 0.539908i | 0.855102 | + | 0.518460i | \(0.173494\pi\) |
−0.999770 | + | 0.0214484i | \(0.993172\pi\) | |||||||
\(398\) | 368.372 | + | 368.372i | 0.925557 | + | 0.925557i | ||||
\(399\) | −241.568 | − | 418.408i | −0.605434 | − | 1.04864i | ||||
\(400\) | −150.897 | − | 87.1204i | −0.377243 | − | 0.217801i | ||||
\(401\) | 235.780 | − | 63.1769i | 0.587979 | − | 0.157548i | 0.0474496 | − | 0.998874i | \(-0.484891\pi\) |
0.540529 | + | 0.841325i | \(0.318224\pi\) | |||||||
\(402\) | 1825.27i | 4.54047i | ||||||||
\(403\) | 17.3620 | − | 33.3375i | 0.0430818 | − | 0.0827234i | ||||
\(404\) | −765.218 | −1.89410 | ||||||||
\(405\) | −17.5210 | − | 65.3891i | −0.0432616 | − | 0.161455i | ||||
\(406\) | 463.564 | − | 802.916i | 1.14178 | − | 1.97763i | ||||
\(407\) | −32.3331 | + | 18.6675i | −0.0794425 | + | 0.0458661i | ||||
\(408\) | 967.547 | − | 967.547i | 2.37144 | − | 2.37144i | ||||
\(409\) | 594.078 | + | 159.183i | 1.45251 | + | 0.389200i | 0.896897 | − | 0.442239i | \(-0.145816\pi\) |
0.555616 | + | 0.831439i | \(0.312482\pi\) | |||||||
\(410\) | 76.4327 | − | 285.251i | 0.186421 | − | 0.695734i | ||||
\(411\) | −91.6949 | − | 91.6949i | −0.223102 | − | 0.223102i | ||||
\(412\) | −404.091 | − | 699.906i | −0.980804 | − | 1.69880i | ||||
\(413\) | −1065.23 | − | 615.011i | −2.57925 | − | 1.48913i | ||||
\(414\) | −491.078 | + | 131.584i | −1.18618 | + | 0.317836i | ||||
\(415\) | − | 78.6571i | − | 0.189535i | ||||||
\(416\) | 628.864 | − | 27.3448i | 1.51169 | − | 0.0657326i | ||||
\(417\) | 707.754 | 1.69725 | ||||||||
\(418\) | 22.6063 | + | 84.3678i | 0.0540820 | + | 0.201837i | ||||
\(419\) | −207.996 | + | 360.259i | −0.496410 | + | 0.859808i | −0.999991 | − | 0.00414029i | \(-0.998682\pi\) |
0.503581 | + | 0.863948i | \(0.332015\pi\) | |||||||
\(420\) | 931.574 | − | 537.844i | 2.21803 | − | 1.28058i | ||||
\(421\) | −120.829 | + | 120.829i | −0.287004 | + | 0.287004i | −0.835894 | − | 0.548890i | \(-0.815050\pi\) |
0.548890 | + | 0.835894i | \(0.315050\pi\) | |||||||
\(422\) | 409.192 | + | 109.643i | 0.969649 | + | 0.259817i | ||||
\(423\) | −93.6828 | + | 349.629i | −0.221472 | + | 0.826546i | ||||
\(424\) | 315.374 | + | 315.374i | 0.743807 | + | 0.743807i | ||||
\(425\) | 36.9096 | + | 63.9293i | 0.0868461 | + | 0.150422i | ||||
\(426\) | 407.074 | + | 235.024i | 0.955573 | + | 0.551700i | ||||
\(427\) | −874.581 | + | 234.343i | −2.04820 | + | 0.548814i | ||||
\(428\) | 791.260i | 1.84874i | ||||||||
\(429\) | 6.67776 | + | 153.572i | 0.0155659 | + | 0.357977i | ||||
\(430\) | −217.098 | −0.504878 | ||||||||
\(431\) | −2.51445 | − | 9.38404i | −0.00583398 | − | 0.0217727i | 0.962947 | − | 0.269689i | \(-0.0869209\pi\) |
−0.968781 | + | 0.247916i | \(0.920254\pi\) | |||||||
\(432\) | 320.201 | − | 554.605i | 0.741207 | − | 1.28381i | ||||
\(433\) | 578.091 | − | 333.761i | 1.33508 | − | 0.770811i | 0.349010 | − | 0.937119i | \(-0.386518\pi\) |
0.986074 | + | 0.166308i | \(0.0531845\pi\) | |||||||
\(434\) | −81.7649 | + | 81.7649i | −0.188398 | + | 0.188398i | ||||
\(435\) | 234.452 | + | 62.8213i | 0.538971 | + | 0.144417i | ||||
\(436\) | 100.330 | − | 374.435i | 0.230114 | − | 0.858795i | ||||
\(437\) | 71.7618 | + | 71.7618i | 0.164215 | + | 0.164215i | ||||
\(438\) | 266.024 | + | 460.766i | 0.607360 | + | 1.05198i | ||||
\(439\) | 151.187 | + | 87.2881i | 0.344390 | + | 0.198834i | 0.662212 | − | 0.749317i | \(-0.269618\pi\) |
−0.317821 | + | 0.948151i | \(0.602951\pi\) | |||||||
\(440\) | −107.960 | + | 28.9278i | −0.245364 | + | 0.0657450i | ||||
\(441\) | 908.689i | 2.06052i | ||||||||
\(442\) | −623.275 | − | 324.597i | −1.41013 | − | 0.734383i | ||||
\(443\) | 332.785 | 0.751208 | 0.375604 | − | 0.926780i | \(-0.377435\pi\) | ||||
0.375604 | + | 0.926780i | \(0.377435\pi\) | |||||||
\(444\) | −168.527 | − | 628.952i | −0.379565 | − | 1.41656i | ||||
\(445\) | 144.103 | − | 249.594i | 0.323827 | − | 0.560886i | ||||
\(446\) | −334.217 | + | 192.960i | −0.749366 | + | 0.432647i | ||||
\(447\) | −172.257 | + | 172.257i | −0.385363 | + | 0.385363i | ||||
\(448\) | −399.786 | − | 107.122i | −0.892380 | − | 0.239113i | ||||
\(449\) | 55.3406 | − | 206.534i | 0.123253 | − | 0.459987i | −0.876518 | − | 0.481368i | \(-0.840140\pi\) |
0.999771 | + | 0.0213819i | \(0.00680659\pi\) | |||||||
\(450\) | 167.311 | + | 167.311i | 0.371802 | + | 0.371802i | ||||
\(451\) | −45.5441 | − | 78.8847i | −0.100985 | − | 0.174911i | ||||
\(452\) | 1563.25 | + | 902.544i | 3.45852 | + | 1.99678i | ||||
\(453\) | −790.089 | + | 211.704i | −1.74413 | + | 0.467337i | ||||
\(454\) | − | 1123.65i | − | 2.47499i | ||||||
\(455\) | −234.056 | − | 214.550i | −0.514409 | − | 0.471538i | ||||
\(456\) | −875.506 | −1.91997 | ||||||||
\(457\) | 197.982 | + | 738.880i | 0.433222 | + | 1.61681i | 0.745286 | + | 0.666745i | \(0.232313\pi\) |
−0.312064 | + | 0.950061i | \(0.601020\pi\) | |||||||
\(458\) | 808.313 | − | 1400.04i | 1.76488 | − | 3.05685i | ||||
\(459\) | −234.965 | + | 135.657i | −0.511906 | + | 0.295549i | ||||
\(460\) | −159.776 | + | 159.776i | −0.347338 | + | 0.347338i | ||||
\(461\) | 539.715 | + | 144.616i | 1.17075 | + | 0.313701i | 0.791251 | − | 0.611491i | \(-0.209430\pi\) |
0.379498 | + | 0.925193i | \(0.376097\pi\) | |||||||
\(462\) | 122.393 | − | 456.777i | 0.264920 | − | 0.988695i | ||||
\(463\) | 57.5124 | + | 57.5124i | 0.124217 | + | 0.124217i | 0.766482 | − | 0.642265i | \(-0.222005\pi\) |
−0.642265 | + | 0.766482i | \(0.722005\pi\) | |||||||
\(464\) | −403.933 | − | 699.632i | −0.870545 | − | 1.50783i | ||||
\(465\) | −26.2170 | − | 15.1364i | −0.0563808 | − | 0.0325514i | ||||
\(466\) | −1054.63 | + | 282.587i | −2.26315 | + | 0.606409i | ||||
\(467\) | − | 529.582i | − | 1.13401i | −0.823715 | − | 0.567004i | \(-0.808102\pi\) | ||
0.823715 | − | 0.567004i | \(-0.191898\pi\) | |||||||
\(468\) | −1542.88 | − | 342.335i | −3.29674 | − | 0.731485i | ||||
\(469\) | −1162.90 | −2.47953 | ||||||||
\(470\) | 59.3436 | + | 221.473i | 0.126263 | + | 0.471220i | ||||
\(471\) | 168.187 | − | 291.309i | 0.357085 | − | 0.618490i | ||||
\(472\) | −1930.34 | + | 1114.48i | −4.08970 | + | 2.36119i | ||||
\(473\) | −47.3499 | + | 47.3499i | −0.100105 | + | 0.100105i | ||||
\(474\) | −2456.42 | − | 658.195i | −5.18232 | − | 1.38860i | ||||
\(475\) | 12.2247 | − | 45.6231i | 0.0257362 | − | 0.0960486i | ||||
\(476\) | 1072.55 | + | 1072.55i | 2.25326 | + | 2.25326i | ||||
\(477\) | −145.616 | − | 252.215i | −0.305276 | − | 0.528753i | ||||
\(478\) | 1005.12 | + | 580.305i | 2.10276 | + | 1.21403i | ||||
\(479\) | 315.370 | − | 84.5031i | 0.658392 | − | 0.176416i | 0.0858717 | − | 0.996306i | \(-0.472632\pi\) |
0.572520 | + | 0.819891i | \(0.305966\pi\) | |||||||
\(480\) | − | 506.962i | − | 1.05617i | ||||||
\(481\) | −162.116 | + | 103.239i | −0.337039 | + | 0.214633i | ||||
\(482\) | −42.8532 | −0.0889070 | ||||||||
\(483\) | −142.211 | − | 530.738i | −0.294432 | − | 1.09884i | ||||
\(484\) | 539.069 | − | 933.695i | 1.11378 | − | 1.92912i | ||||
\(485\) | −332.095 | + | 191.735i | −0.684732 | + | 0.395330i | ||||
\(486\) | 795.212 | − | 795.212i | 1.63624 | − | 1.63624i | ||||
\(487\) | −426.089 | − | 114.170i | −0.874925 | − | 0.234436i | −0.206709 | − | 0.978403i | \(-0.566275\pi\) |
−0.668216 | + | 0.743967i | \(0.732942\pi\) | |||||||
\(488\) | −424.661 | + | 1584.86i | −0.870207 | + | 3.24765i | ||||
\(489\) | 454.627 | + | 454.627i | 0.929708 | + | 0.929708i | ||||
\(490\) | 287.805 | + | 498.493i | 0.587358 | + | 1.01733i | ||||
\(491\) | −71.0296 | − | 41.0089i | −0.144663 | − | 0.0835213i | 0.425921 | − | 0.904760i | \(-0.359950\pi\) |
−0.570585 | + | 0.821239i | \(0.693283\pi\) | |||||||
\(492\) | 1534.49 | − | 411.164i | 3.11887 | − | 0.835699i | ||||
\(493\) | 342.261i | 0.694242i | ||||||||
\(494\) | 135.133 | + | 428.852i | 0.273548 | + | 0.868121i | ||||
\(495\) | 72.9824 | 0.147439 | ||||||||
\(496\) | 26.0782 | + | 97.3252i | 0.0525770 | + | 0.196220i | ||||
\(497\) | −149.737 | + | 259.352i | −0.301282 | + | 0.521835i | ||||
\(498\) | 522.275 | − | 301.536i | 1.04875 | − | 0.605493i | ||||
\(499\) | 345.948 | − | 345.948i | 0.693282 | − | 0.693282i | −0.269670 | − | 0.962953i | \(-0.586915\pi\) |
0.962953 | + | 0.269670i | \(0.0869148\pi\) | |||||||
\(500\) | 101.578 | + | 27.2179i | 0.203157 | + | 0.0544357i | ||||
\(501\) | 294.159 | − | 1097.82i | 0.587144 | − | 2.19125i | ||||
\(502\) | −291.578 | − | 291.578i | −0.580833 | − | 0.580833i | ||||
\(503\) | 360.251 | + | 623.973i | 0.716205 | + | 1.24050i | 0.962493 | + | 0.271307i | \(0.0874558\pi\) |
−0.246288 | + | 0.969197i | \(0.579211\pi\) | |||||||
\(504\) | 2419.94 | + | 1397.15i | 4.80146 | + | 2.77213i | ||||
\(505\) | 175.716 | − | 47.0829i | 0.347952 | − | 0.0932335i | ||||
\(506\) | 99.3343i | 0.196313i | ||||||||
\(507\) | 68.6880 | + | 788.336i | 0.135479 | + | 1.55490i | ||||
\(508\) | −1042.15 | −2.05148 | ||||||||
\(509\) | 9.64080 | + | 35.9799i | 0.0189407 | + | 0.0706875i | 0.974749 | − | 0.223302i | \(-0.0716836\pi\) |
−0.955809 | + | 0.293989i | \(0.905017\pi\) | |||||||
\(510\) | −282.989 | + | 490.152i | −0.554881 | + | 0.961081i | ||||
\(511\) | −293.560 | + | 169.487i | −0.574482 | + | 0.331677i | ||||
\(512\) | 757.819 | − | 757.819i | 1.48012 | − | 1.48012i | ||||
\(513\) | 167.682 | + | 44.9304i | 0.326866 | + | 0.0875836i | ||||
\(514\) | −112.136 | + | 418.498i | −0.218164 | + | 0.814198i | ||||
\(515\) | 135.855 | + | 135.855i | 0.263797 | + | 0.263797i | ||||
\(516\) | −583.930 | − | 1011.40i | −1.13165 | − | 1.96007i | ||||
\(517\) | 61.2473 | + | 35.3611i | 0.118467 | + | 0.0683968i | ||||
\(518\) | 571.121 | − | 153.031i | 1.10255 | − | 0.295428i | ||||
\(519\) | 587.240i | 1.13148i | ||||||||
\(520\) | −548.774 | + | 172.921i | −1.05533 | + | 0.332540i | ||||
\(521\) | −944.856 | −1.81354 | −0.906771 | − | 0.421623i | \(-0.861461\pi\) | ||||
−0.906771 | + | 0.421623i | \(0.861461\pi\) | |||||||
\(522\) | 283.939 | + | 1059.67i | 0.543944 | + | 2.03003i | ||||
\(523\) | 64.7636 | − | 112.174i | 0.123831 | − | 0.214482i | −0.797444 | − | 0.603393i | \(-0.793815\pi\) |
0.921275 | + | 0.388911i | \(0.127149\pi\) | |||||||
\(524\) | −986.425 | + | 569.513i | −1.88249 | + | 1.08686i | ||||
\(525\) | −180.823 | + | 180.823i | −0.344425 | + | 0.344425i | ||||
\(526\) | 247.541 | + | 66.3284i | 0.470610 | + | 0.126100i | ||||
\(527\) | 11.0483 | − | 41.2329i | 0.0209646 | − | 0.0782409i | ||||
\(528\) | −291.370 | − | 291.370i | −0.551837 | − | 0.551837i | ||||
\(529\) | −206.791 | − | 358.172i | −0.390909 | − | 0.677074i | ||||
\(530\) | −159.766 | − | 92.2410i | −0.301445 | − | 0.174040i | ||||
\(531\) | 1405.87 | − | 376.702i | 2.64759 | − | 0.709420i | ||||
\(532\) | − | 970.523i | − | 1.82429i | ||||||
\(533\) | −251.877 | − | 395.522i | −0.472564 | − | 0.742068i | ||||
\(534\) | 2209.71 | 4.13802 | ||||||||
\(535\) | −48.6853 | − | 181.696i | −0.0910005 | − | 0.339618i | ||||
\(536\) | −1053.66 | + | 1825.00i | −1.96579 | + | 3.40485i | ||||
\(537\) | −97.8679 | + | 56.5041i | −0.182249 | + | 0.105222i | ||||
\(538\) | −1022.04 | + | 1022.04i | −1.89970 | + | 1.89970i | ||||
\(539\) | 171.495 | + | 45.9520i | 0.318173 | + | 0.0852541i | ||||
\(540\) | −100.036 | + | 373.340i | −0.185252 | + | 0.691370i | ||||
\(541\) | 148.483 | + | 148.483i | 0.274460 | + | 0.274460i | 0.830893 | − | 0.556433i | \(-0.187830\pi\) |
−0.556433 | + | 0.830893i | \(0.687830\pi\) | |||||||
\(542\) | 134.155 | + | 232.362i | 0.247518 | + | 0.428713i | ||||
\(543\) | −163.283 | − | 94.2712i | −0.300704 | − | 0.173612i | ||||
\(544\) | 690.504 | − | 185.020i | 1.26931 | − | 0.340110i | ||||
\(545\) | 92.1541i | 0.169090i | ||||||||
\(546\) | 527.322 | − | 2376.60i | 0.965791 | − | 4.35274i | ||||
\(547\) | −145.986 | −0.266885 | −0.133442 | − | 0.991057i | \(-0.542603\pi\) | ||||
−0.133442 | + | 0.991057i | \(0.542603\pi\) | |||||||
\(548\) | −67.4206 | − | 251.617i | −0.123030 | − | 0.459155i | ||||
\(549\) | 535.692 | − | 927.845i | 0.975759 | − | 1.69006i | ||||
\(550\) | 40.0371 | − | 23.1154i | 0.0727947 | − | 0.0420280i | ||||
\(551\) | 154.851 | − | 154.851i | 0.281037 | − | 0.281037i | ||||
\(552\) | −961.766 | − | 257.704i | −1.74233 | − | 0.466856i | ||||
\(553\) | 419.345 | − | 1565.02i | 0.758308 | − | 2.83005i | ||||
\(554\) | −482.877 | − | 482.877i | −0.871619 | − | 0.871619i | ||||
\(555\) | 77.3972 | + | 134.056i | 0.139454 | + | 0.241542i | ||||
\(556\) | 1231.26 | + | 710.867i | 2.21449 | + | 1.27854i | ||||
\(557\) | 410.659 | − | 110.036i | 0.737269 | − | 0.197551i | 0.129405 | − | 0.991592i | \(-0.458693\pi\) |
0.607864 | + | 0.794041i | \(0.292027\pi\) | |||||||
\(558\) | − | 136.827i | − | 0.245209i | ||||||
\(559\) | −232.934 | + | 254.112i | −0.416697 | + | 0.454583i | ||||
\(560\) | 851.132 | 1.51988 | ||||||||
\(561\) | 45.1830 | + | 168.625i | 0.0805401 | + | 0.300580i | ||||
\(562\) | 25.3679 | − | 43.9385i | 0.0451386 | − | 0.0781824i | ||||
\(563\) | −22.9508 | + | 13.2506i | −0.0407652 | + | 0.0235358i | −0.520244 | − | 0.854018i | \(-0.674159\pi\) |
0.479479 | + | 0.877553i | \(0.340826\pi\) | |||||||
\(564\) | −872.164 | + | 872.164i | −1.54639 | + | 1.54639i | ||||
\(565\) | −414.500 | − | 111.065i | −0.733628 | − | 0.196575i | ||||
\(566\) | 12.9928 | − | 48.4898i | 0.0229555 | − | 0.0856711i | ||||
\(567\) | 233.826 | + | 233.826i | 0.412392 | + | 0.412392i | ||||
\(568\) | 271.343 | + | 469.980i | 0.477716 | + | 0.827429i | ||||
\(569\) | −424.944 | − | 245.342i | −0.746826 | − | 0.431180i | 0.0777197 | − | 0.996975i | \(-0.475236\pi\) |
−0.824546 | + | 0.565795i | \(0.808569\pi\) | |||||||
\(570\) | 349.797 | − | 93.7277i | 0.613678 | − | 0.164435i | ||||
\(571\) | − | 73.3411i | − | 0.128443i | −0.997936 | − | 0.0642217i | \(-0.979544\pi\) | ||
0.997936 | − | 0.0642217i | \(-0.0204565\pi\) | |||||||
\(572\) | −142.631 | + | 273.872i | −0.249354 | + | 0.478797i | ||||
\(573\) | −663.184 | −1.15739 | ||||||||
\(574\) | 373.359 | + | 1393.39i | 0.650451 | + | 2.42751i | ||||
\(575\) | 26.8582 | − | 46.5198i | 0.0467100 | − | 0.0809040i | ||||
\(576\) | 424.134 | − | 244.874i | 0.736344 | − | 0.425128i | ||||
\(577\) | 400.120 | − | 400.120i | 0.693449 | − | 0.693449i | −0.269540 | − | 0.962989i | \(-0.586872\pi\) |
0.962989 | + | 0.269540i | \(0.0868717\pi\) | |||||||
\(578\) | 251.206 | + | 67.3105i | 0.434613 | + | 0.116454i | ||||
\(579\) | −115.461 | + | 430.906i | −0.199414 | + | 0.744224i | ||||
\(580\) | 344.772 | + | 344.772i | 0.594434 | + | 0.594434i | ||||
\(581\) | 192.112 | + | 332.748i | 0.330658 | + | 0.572716i | ||||
\(582\) | −2546.20 | − | 1470.05i | −4.37492 | − | 2.52586i | ||||
\(583\) | −54.9638 | + | 14.7275i | −0.0942775 | + | 0.0252616i | ||||
\(584\) | 614.265i | 1.05182i | ||||||||
\(585\) | 375.352 | − | 16.3214i | 0.641627 | − | 0.0278998i | ||||
\(586\) | 1053.33 | 1.79749 | ||||||||
\(587\) | −216.378 | − | 807.535i | −0.368617 | − | 1.37570i | −0.862451 | − | 0.506141i | \(-0.831071\pi\) |
0.493834 | − | 0.869556i | \(-0.335595\pi\) | |||||||
\(588\) | −1548.23 | + | 2681.61i | −2.63304 | + | 4.56056i | ||||
\(589\) | −23.6539 | + | 13.6566i | −0.0401595 | + | 0.0231861i | ||||
\(590\) | 651.929 | − | 651.929i | 1.10496 | − | 1.10496i | ||||
\(591\) | −303.346 | − | 81.2813i | −0.513276 | − | 0.137532i | ||||
\(592\) | 133.346 | − | 497.654i | 0.225247 | − | 0.840632i | ||||
\(593\) | −322.211 | − | 322.211i | −0.543357 | − | 0.543357i | 0.381154 | − | 0.924512i | \(-0.375527\pi\) |
−0.924512 | + | 0.381154i | \(0.875527\pi\) | |||||||
\(594\) | 84.9581 | + | 147.152i | 0.143027 | + | 0.247730i | ||||
\(595\) | −312.282 | − | 180.296i | −0.524843 | − | 0.303018i | ||||
\(596\) | −472.685 | + | 126.656i | −0.793096 | + | 0.212509i | ||||
\(597\) | − | 666.222i | − | 1.11595i | ||||||
\(598\) | 22.2145 | + | 510.881i | 0.0371481 | + | 0.854315i | ||||
\(599\) | 466.798 | 0.779296 | 0.389648 | − | 0.920964i | \(-0.372597\pi\) | ||||
0.389648 | + | 0.920964i | \(0.372597\pi\) | |||||||
\(600\) | 119.937 | + | 447.612i | 0.199896 | + | 0.746020i | ||||
\(601\) | −167.094 | + | 289.416i | −0.278027 | + | 0.481557i | −0.970894 | − | 0.239508i | \(-0.923014\pi\) |
0.692867 | + | 0.721065i | \(0.256347\pi\) | |||||||
\(602\) | 918.401 | − | 530.239i | 1.52558 | − | 0.880796i | ||||
\(603\) | 973.008 | − | 973.008i | 1.61361 | − | 1.61361i | ||||
\(604\) | −1587.13 | − | 425.270i | −2.62770 | − | 0.704089i | ||||
\(605\) | −66.3365 | + | 247.571i | −0.109647 | + | 0.409209i | ||||
\(606\) | 986.240 | + | 986.240i | 1.62746 | + | 1.62746i | ||||
\(607\) | 415.933 | + | 720.417i | 0.685227 | + | 1.18685i | 0.973365 | + | 0.229260i | \(0.0736305\pi\) |
−0.288138 | + | 0.957589i | \(0.593036\pi\) | |||||||
\(608\) | −396.118 | − | 228.699i | −0.651511 | − | 0.376150i | ||||
\(609\) | −1145.25 | + | 306.870i | −1.88055 | + | 0.503891i | ||||
\(610\) | − | 678.670i | − | 1.11257i | ||||||
\(611\) | 322.906 | + | 168.167i | 0.528487 | + | 0.275232i | ||||
\(612\) | −1794.83 | −2.93272 | ||||||||
\(613\) | 87.3548 | + | 326.012i | 0.142504 | + | 0.531831i | 0.999854 | + | 0.0170973i | \(0.00544251\pi\) |
−0.857350 | + | 0.514734i | \(0.827891\pi\) | |||||||
\(614\) | 430.287 | − | 745.279i | 0.700794 | − | 1.21381i | ||||
\(615\) | −327.063 | + | 188.830i | −0.531810 | + | 0.307041i | ||||
\(616\) | 386.057 | − | 386.057i | 0.626715 | − | 0.626715i | ||||
\(617\) | 576.426 | + | 154.453i | 0.934239 | + | 0.250329i | 0.693661 | − | 0.720301i | \(-0.255996\pi\) |
0.240578 | + | 0.970630i | \(0.422663\pi\) | |||||||
\(618\) | −381.257 | + | 1422.87i | −0.616921 | + | 2.30238i | ||||
\(619\) | 199.728 | + | 199.728i | 0.322663 | + | 0.322663i | 0.849788 | − | 0.527125i | \(-0.176730\pi\) |
−0.527125 | + | 0.849788i | \(0.676730\pi\) | |||||||
\(620\) | −30.4060 | − | 52.6647i | −0.0490419 | − | 0.0849431i | ||||
\(621\) | 170.978 | + | 98.7143i | 0.275327 | + | 0.158960i | ||||
\(622\) | −1525.73 | + | 408.818i | −2.45294 | + | 0.657264i | ||||
\(623\) | 1407.83i | 2.25976i | ||||||||
\(624\) | −1563.69 | − | 1433.37i | −2.50591 | − | 2.29706i | ||||
\(625\) | −25.0000 | −0.0400000 | ||||||||
\(626\) | −408.186 | − | 1523.37i | −0.652055 | − | 2.43350i | ||||
\(627\) | 55.8497 | − | 96.7345i | 0.0890745 | − | 0.154281i | ||||
\(628\) | 585.180 | − | 337.854i | 0.931815 | − | 0.537984i | ||||
\(629\) | −154.343 | + | 154.343i | −0.245379 | + | 0.245379i | ||||
\(630\) | −1116.43 | − | 299.145i | −1.77210 | − | 0.474834i | ||||
\(631\) | 168.877 | − | 630.258i | 0.267634 | − | 0.998824i | −0.692984 | − | 0.720953i | \(-0.743704\pi\) |
0.960618 | − | 0.277871i | \(-0.0896289\pi\) | |||||||
\(632\) | −2076.10 | − | 2076.10i | −3.28498 | − | 3.28498i | ||||
\(633\) | −270.876 | − | 469.172i | −0.427925 | − | 0.741188i | ||||
\(634\) | −322.525 | − | 186.210i | −0.508714 | − | 0.293706i | ||||
\(635\) | 239.308 | − | 64.1225i | 0.376863 | − | 0.100980i | ||||
\(636\) | − | 992.407i | − | 1.56039i | ||||||
\(637\) | 892.283 | + | 197.981i | 1.40076 | + | 0.310802i | ||||
\(638\) | 214.349 | 0.335970 | ||||||||
\(639\) | −91.7157 | − | 342.288i | −0.143530 | − | 0.535661i | ||||
\(640\) | −61.4243 | + | 106.390i | −0.0959754 | + | 0.166234i | ||||
\(641\) | −122.614 | + | 70.7910i | −0.191285 | + | 0.110438i | −0.592584 | − | 0.805509i | \(-0.701892\pi\) |
0.401299 | + | 0.915947i | \(0.368559\pi\) | |||||||
\(642\) | 1019.80 | − | 1019.80i | 1.58848 | − | 1.58848i | ||||
\(643\) | 430.586 | + | 115.375i | 0.669651 | + | 0.179433i | 0.577598 | − | 0.816321i | \(-0.303990\pi\) |
0.0920537 | + | 0.995754i | \(0.470657\pi\) | |||||||
\(644\) | 285.672 | − | 1066.14i | 0.443591 | − | 1.65550i | ||||
\(645\) | 196.317 | + | 196.317i | 0.304367 | + | 0.304367i | ||||
\(646\) | 255.322 | + | 442.231i | 0.395236 | + | 0.684569i | ||||
\(647\) | 537.465 | + | 310.305i | 0.830703 | + | 0.479606i | 0.854093 | − | 0.520120i | \(-0.174113\pi\) |
−0.0233905 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(648\) | 578.818 | − | 155.094i | 0.893238 | − | 0.239342i | ||||
\(649\) | − | 284.377i | − | 0.438177i | ||||||
\(650\) | 200.743 | − | 127.837i | 0.308836 | − | 0.196673i | ||||
\(651\) | 147.877 | 0.227153 | ||||||||
\(652\) | 334.274 | + | 1247.53i | 0.512690 | + | 1.91339i | ||||
\(653\) | −77.8639 | + | 134.864i | −0.119240 | + | 0.206530i | −0.919467 | − | 0.393168i | \(-0.871379\pi\) |
0.800227 | + | 0.599698i | \(0.204713\pi\) | |||||||
\(654\) | −611.894 | + | 353.277i | −0.935617 | + | 0.540179i | ||||
\(655\) | 191.470 | − | 191.470i | 0.292321 | − | 0.292321i | ||||
\(656\) | 1214.15 | + | 325.331i | 1.85084 | + | 0.495932i | ||||
\(657\) | 103.813 | − | 387.435i | 0.158010 | − | 0.589703i | ||||
\(658\) | −791.971 | − | 791.971i | −1.20360 | − | 1.20360i | ||||
\(659\) | 173.055 | + | 299.740i | 0.262603 | + | 0.454841i | 0.966933 | − | 0.255032i | \(-0.0820859\pi\) |
−0.704330 | + | 0.709872i | \(0.748753\pi\) | |||||||
\(660\) | 215.376 | + | 124.348i | 0.326328 | + | 0.188406i | ||||
\(661\) | −542.311 | + | 145.312i | −0.820440 | + | 0.219836i | −0.644539 | − | 0.764572i | \(-0.722951\pi\) |
−0.175901 | + | 0.984408i | \(0.556284\pi\) | |||||||
\(662\) | 1245.30i | 1.88112i | ||||||||
\(663\) | 270.088 | + | 857.143i | 0.407373 | + | 1.29282i | ||||
\(664\) | 696.265 | 1.04859 | ||||||||
\(665\) | 59.7151 | + | 222.860i | 0.0897971 | + | 0.335127i | ||||
\(666\) | −349.819 | + | 605.904i | −0.525253 | + | 0.909765i | ||||
\(667\) | 215.688 | − | 124.528i | 0.323371 | − | 0.186698i | ||||
\(668\) | 1614.39 | − | 1614.39i | 2.41674 | − | 2.41674i | ||||
\(669\) | 476.716 | + | 127.736i | 0.712580 | + | 0.190935i | ||||
\(670\) | 225.601 | − | 841.955i | 0.336718 | − | 1.25665i | ||||
\(671\) | −148.021 | − | 148.021i | −0.220597 | − | 0.220597i | ||||
\(672\) | 1238.20 | + | 2144.63i | 1.84257 | + | 3.19142i | ||||
\(673\) | 719.976 | + | 415.678i | 1.06980 | + | 0.617650i | 0.928127 | − | 0.372264i | \(-0.121418\pi\) |
0.141674 | + | 0.989913i | \(0.454752\pi\) | |||||||
\(674\) | −366.881 | + | 98.3054i | −0.544334 | + | 0.145854i | ||||
\(675\) | − | 91.8846i | − | 0.136125i | ||||||
\(676\) | −672.309 | + | 1440.43i | −0.994540 | + | 2.13082i | ||||
\(677\) | 476.117 | 0.703275 | 0.351637 | − | 0.936136i | \(-0.385625\pi\) | ||||
0.351637 | + | 0.936136i | \(0.385625\pi\) | |||||||
\(678\) | −851.545 | − | 3178.01i | −1.25597 | − | 4.68733i | ||||
\(679\) | 936.588 | − | 1622.22i | 1.37936 | − | 2.38913i | ||||
\(680\) | −565.895 | + | 326.720i | −0.832199 | + | 0.480470i | ||||
\(681\) | −1016.09 | + | 1016.09i | −1.49206 | + | 1.49206i | ||||
\(682\) | −25.8230 | − | 6.91926i | −0.0378637 | − | 0.0101455i | ||||
\(683\) | −134.295 | + | 501.196i | −0.196625 | + | 0.733816i | 0.795215 | + | 0.606328i | \(0.207358\pi\) |
−0.991840 | + | 0.127488i | \(0.959309\pi\) | |||||||
\(684\) | 812.044 | + | 812.044i | 1.18720 | + | 1.18720i | ||||
\(685\) | 30.9634 | + | 53.6302i | 0.0452020 | + | 0.0782922i | ||||
\(686\) | −737.941 | − | 426.050i | −1.07572 | − | 0.621065i | ||||
\(687\) | −1996.97 | + | 535.086i | −2.90680 | + | 0.778873i | ||||
\(688\) | − | 924.062i | − | 1.34311i | ||||||
\(689\) | −279.388 | + | 88.0360i | −0.405497 | + | 0.127774i | ||||
\(690\) | 411.849 | 0.596883 | ||||||||
\(691\) | −55.0482 | − | 205.443i | −0.0796645 | − | 0.297312i | 0.914586 | − | 0.404392i | \(-0.132517\pi\) |
−0.994250 | + | 0.107080i | \(0.965850\pi\) | |||||||
\(692\) | −589.823 | + | 1021.60i | −0.852346 | + | 1.47631i | ||||
\(693\) | −308.742 | + | 178.252i | −0.445515 | + | 0.257218i | ||||
\(694\) | −584.699 | + | 584.699i | −0.842506 | + | 0.842506i | ||||
\(695\) | −326.471 | − | 87.4776i | −0.469742 | − | 0.125867i | ||||
\(696\) | −556.088 | + | 2075.35i | −0.798977 | + | 2.98182i | ||||
\(697\) | −376.559 | − | 376.559i | −0.540257 | − | 0.540257i | ||||
\(698\) | −939.002 | − | 1626.40i | −1.34528 | − | 2.33009i | ||||
\(699\) | 1209.22 | + | 698.141i | 1.72992 | + | 0.998772i | ||||
\(700\) | −496.191 | + | 132.954i | −0.708844 | + | 0.189934i | ||||
\(701\) | 309.004i | 0.440805i | 0.975409 | + | 0.220402i | \(0.0707371\pi\) | ||||
−0.975409 | + | 0.220402i | \(0.929263\pi\) | |||||||
\(702\) | 469.851 | + | 737.808i | 0.669304 | + | 1.05101i | ||||
\(703\) | 139.661 | 0.198664 | ||||||||
\(704\) | −24.7663 | − | 92.4292i | −0.0351794 | − | 0.131291i | ||||
\(705\) | 146.611 | − | 253.937i | 0.207958 | − | 0.360194i | ||||
\(706\) | 746.591 | − | 431.044i | 1.05749 | − | 0.610544i | ||||
\(707\) | −628.346 | + | 628.346i | −0.888750 | + | 0.888750i | ||||
\(708\) | 4790.65 | + | 1283.65i | 6.76646 | + | 1.81307i | ||||
\(709\) | −345.469 | + | 1289.31i | −0.487262 | + | 1.81849i | 0.0823878 | + | 0.996600i | \(0.473745\pi\) |
−0.569650 | + | 0.821887i | \(0.692921\pi\) | |||||||
\(710\) | −158.725 | − | 158.725i | −0.223557 | − | 0.223557i | ||||
\(711\) | 958.591 | + | 1660.33i | 1.34823 | + | 2.33520i | ||||
\(712\) | 2209.38 | + | 1275.59i | 3.10306 | + | 1.79155i | ||||
\(713\) | −30.0042 | + | 8.03961i | −0.0420817 | + | 0.0112757i | ||||
\(714\) | − | 2764.69i | − | 3.87212i | ||||||
\(715\) | 15.9011 | − | 71.6648i | 0.0222392 | − | 0.100230i | ||||
\(716\) | −227.010 | −0.317054 | ||||||||
\(717\) | −384.150 | − | 1433.67i | −0.535774 | − | 1.99953i | ||||
\(718\) | 172.224 | − | 298.302i | 0.239867 | − | 0.415462i | ||||
\(719\) | −318.358 | + | 183.804i | −0.442779 | + | 0.255639i | −0.704776 | − | 0.709430i | \(-0.748952\pi\) |
0.261997 | + | 0.965069i | \(0.415619\pi\) | |||||||
\(720\) | −712.148 | + | 712.148i | −0.989095 | + | 0.989095i | ||||
\(721\) | −906.530 | − | 242.904i | −1.25732 | − | 0.336899i | ||||
\(722\) | −257.535 | + | 961.134i | −0.356697 | + | 1.33121i | ||||
\(723\) | 38.7512 | + | 38.7512i | 0.0535979 | + | 0.0535979i | ||||
\(724\) | −189.372 | − | 328.002i | −0.261563 | − | 0.453041i | ||||
\(725\) | −100.383 | − | 57.9561i | −0.138459 | − | 0.0799394i | ||||
\(726\) | −1898.15 | + | 508.608i | −2.61453 | + | 0.700562i | ||||
\(727\) | 330.819i | 0.455047i | 0.973773 | + | 0.227524i | \(0.0730629\pi\) | ||||
−0.973773 | + | 0.227524i | \(0.926937\pi\) | |||||||
\(728\) | 1899.17 | − | 2071.84i | 2.60875 | − | 2.84594i | ||||
\(729\) | −1165.72 | −1.59907 | ||||||||
\(730\) | −65.7604 | − | 245.421i | −0.0900828 | − | 0.336193i | ||||
\(731\) | −195.745 | + | 339.040i | −0.267777 | + | 0.463803i | ||||
\(732\) | 3161.73 | − | 1825.43i | 4.31930 | − | 2.49375i | ||||
\(733\) | −578.323 | + | 578.323i | −0.788981 | + | 0.788981i | −0.981327 | − | 0.192346i | \(-0.938390\pi\) |
0.192346 | + | 0.981327i | \(0.438390\pi\) | |||||||
\(734\) | 1671.41 | + | 447.853i | 2.27713 | + | 0.610154i | ||||
\(735\) | 190.521 | − | 711.034i | 0.259212 | − | 0.967393i | ||||
\(736\) | −367.829 | − | 367.829i | −0.499767 | − | 0.499767i | ||||
\(737\) | −134.429 | − | 232.838i | −0.182401 | − | 0.315927i | ||||
\(738\) | −1478.25 | − | 853.470i | −2.00305 | − | 1.15646i | ||||
\(739\) | −717.792 | + | 192.332i | −0.971301 | + | 0.260259i | −0.709377 | − | 0.704829i | \(-0.751024\pi\) |
−0.261924 | + | 0.965088i | \(0.584357\pi\) | |||||||
\(740\) | 310.951i | 0.420204i | ||||||||
\(741\) | 265.604 | − | 510.000i | 0.358440 | − | 0.688259i | ||||
\(742\) | 901.158 | 1.21450 | ||||||||
\(743\) | 279.833 | + | 1044.35i | 0.376626 | + | 1.40559i | 0.850954 | + | 0.525240i | \(0.176025\pi\) |
−0.474327 | + | 0.880348i | \(0.657309\pi\) | |||||||
\(744\) | 133.986 | − | 232.071i | 0.180089 | − | 0.311923i | ||||
\(745\) | 100.749 | − | 58.1675i | 0.135234 | − | 0.0780771i | ||||
\(746\) | −26.1210 | + | 26.1210i | −0.0350147 | + | 0.0350147i | ||||
\(747\) | −439.154 | − | 117.671i | −0.587891 | − | 0.157525i | ||||
\(748\) | −90.7635 | + | 338.734i | −0.121342 | + | 0.452853i | ||||
\(749\) | 649.730 | + | 649.730i | 0.867464 | + | 0.867464i | ||||
\(750\) | −95.8387 | − | 165.997i | −0.127785 | − | 0.221330i | ||||
\(751\) | −1023.66 | − | 591.009i | −1.36306 | − | 0.786963i | −0.373029 | − | 0.927819i | \(-0.621681\pi\) |
−0.990030 | + | 0.140857i | \(0.955014\pi\) | |||||||
\(752\) | −942.687 | + | 252.592i | −1.25357 | + | 0.335894i | ||||
\(753\) | 527.336i | 0.700314i | ||||||||
\(754\) | 1102.40 | − | 47.9357i | 1.46207 | − | 0.0635752i | ||||
\(755\) | 390.617 | 0.517373 | ||||||||
\(756\) | −488.657 | − | 1823.69i | −0.646371 | − | 2.41229i | ||||
\(757\) | −559.755 | + | 969.525i | −0.739439 | + | 1.28075i | 0.213309 | + | 0.976985i | \(0.431576\pi\) |
−0.952748 | + | 0.303761i | \(0.901758\pi\) | |||||||
\(758\) | −1697.17 | + | 979.860i | −2.23901 | + | 1.29269i | ||||
\(759\) | 89.8260 | − | 89.8260i | 0.118348 | − | 0.118348i | ||||
\(760\) | 403.851 | + | 108.212i | 0.531383 | + | 0.142384i | ||||
\(761\) | 354.351 | − | 1322.46i | 0.465639 | − | 1.73779i | −0.189122 | − | 0.981954i | \(-0.560564\pi\) |
0.654761 | − | 0.755836i | \(-0.272769\pi\) | |||||||
\(762\) | 1343.17 | + | 1343.17i | 1.76268 | + | 1.76268i | ||||
\(763\) | −225.077 | − | 389.845i | −0.294990 | − | 0.510937i | ||||
\(764\) | −1153.72 | − | 666.101i | −1.51011 | − | 0.871860i | ||||
\(765\) | 412.143 | − | 110.433i | 0.538749 | − | 0.144357i | ||||
\(766\) | 2730.53i | 3.56466i | ||||||||
\(767\) | −63.5963 | − | 1462.56i | −0.0829157 | − | 1.90686i | ||||
\(768\) | −1651.60 | −2.15052 | ||||||||
\(769\) | 125.630 | + | 468.857i | 0.163368 | + | 0.609697i | 0.998243 | + | 0.0592574i | \(0.0188733\pi\) |
−0.834875 | + | 0.550440i | \(0.814460\pi\) | |||||||
\(770\) | −112.914 | + | 195.573i | −0.146642 | + | 0.253991i | ||||
\(771\) | 479.842 | − | 277.037i | 0.622363 | − | 0.359321i | ||||
\(772\) | −633.665 | + | 633.665i | −0.820809 | + | 0.820809i | ||||
\(773\) | 139.892 | + | 37.4839i | 0.180973 | + | 0.0484915i | 0.348167 | − | 0.937432i | \(-0.386804\pi\) |
−0.167195 | + | 0.985924i | \(0.553471\pi\) | |||||||
\(774\) | −324.778 | + | 1212.09i | −0.419610 | + | 1.56601i | ||||
\(775\) | 10.2225 | + | 10.2225i | 0.0131903 | + | 0.0131903i | ||||
\(776\) | −1697.22 | − | 2939.67i | −2.18714 | − | 3.78824i | ||||
\(777\) | −654.837 | − | 378.070i | −0.842776 | − | 0.486577i | ||||
\(778\) | −2280.08 | + | 610.946i | −2.93070 | + | 0.785278i | ||||
\(779\) | 340.738i | 0.437404i | ||||||||
\(780\) | 1135.50 | + | 591.360i | 1.45577 | + | 0.758154i | ||||
\(781\) | −69.2373 | −0.0886521 | ||||||||
\(782\) | 150.308 | + | 560.956i | 0.192209 | + | 0.717335i | ||||
\(783\) | 213.011 | − | 368.946i | 0.272045 | − | 0.471195i | ||||
\(784\) | −2121.81 | + | 1225.03i | −2.70638 | + | 1.56253i | ||||
\(785\) | −113.586 | + | 113.586i | −0.144696 | + | 0.144696i | ||||
\(786\) | 2005.35 | + | 537.332i | 2.55134 | + | 0.683628i | ||||
\(787\) | 335.574 | − | 1252.38i | 0.426396 | − | 1.59133i | −0.334459 | − | 0.942410i | \(-0.608554\pi\) |
0.760855 | − | 0.648922i | \(-0.224780\pi\) | |||||||
\(788\) | −446.083 | − | 446.083i | −0.566095 | − | 0.566095i | ||||
\(789\) | −163.867 | − | 283.826i | −0.207689 | − | 0.359728i | ||||
\(790\) | 1051.74 | + | 607.221i | 1.33131 | + | 0.768634i | ||||
\(791\) | 2024.75 | − | 542.530i | 2.55973 | − | 0.685879i | ||||
\(792\) | 646.033i | 0.815698i | ||||||||
\(793\) | −794.380 | − | 728.175i | −1.00174 | − | 0.918253i | ||||
\(794\) | 812.485 | 1.02328 | ||||||||
\(795\) | 61.0616 | + | 227.885i | 0.0768070 | + | 0.286648i | ||||
\(796\) | 669.153 | − | 1159.01i | 0.840644 | − | 1.45604i | ||||
\(797\) | −529.868 | + | 305.919i | −0.664828 | + | 0.383839i | −0.794114 | − | 0.607769i | \(-0.792065\pi\) |
0.129286 | + | 0.991607i | \(0.458731\pi\) | |||||||
\(798\) | −1250.85 | + | 1250.85i | −1.56748 | + | 1.56748i | ||||
\(799\) | 399.380 | + | 107.014i | 0.499850 | + | 0.133934i | ||||
\(800\) | −62.6599 | + | 233.850i | −0.0783249 | + | 0.292312i | ||||
\(801\) | −1177.94 | − | 1177.94i | −1.47059 | − | 1.47059i | ||||
\(802\) | −446.870 | − | 774.002i | −0.557195 | − | 0.965089i | ||||
\(803\) | −67.8700 | − | 39.1848i | −0.0845206 | − | 0.0487980i | ||||
\(804\) | 4529.23 | − | 1213.60i | 5.63337 | − | 1.50946i | ||||
\(805\) | 262.394i | 0.325956i | ||||||||
\(806\) | −134.356 | − | 29.8111i | −0.166695 | − | 0.0369865i | ||||
\(807\) | 1848.42 | 2.29048 | ||||||||
\(808\) | 416.773 | + | 1555.42i | 0.515808 | + | 1.92502i | ||||
\(809\) | 51.8145 | − | 89.7453i | 0.0640476 | − | 0.110934i | −0.832224 | − | 0.554440i | \(-0.812932\pi\) |
0.896271 | + | 0.443507i | \(0.146266\pi\) | |||||||
\(810\) | −214.655 | + | 123.931i | −0.265006 | + | 0.153001i | ||||
\(811\) | −212.523 | + | 212.523i | −0.262050 | + | 0.262050i | −0.825887 | − | 0.563836i | \(-0.809325\pi\) |
0.563836 | + | 0.825887i | \(0.309325\pi\) | |||||||
\(812\) | −2300.58 | − | 616.439i | −2.83323 | − | 0.759161i | ||||
\(813\) | 88.8075 | − | 331.434i | 0.109234 | − | 0.407668i | ||||
\(814\) | 96.6608 | + | 96.6608i | 0.118748 | + | 0.118748i | ||||
\(815\) | −153.518 | − | 265.900i | −0.188365 | − | 0.326258i | ||||
\(816\) | −2086.30 | − | 1204.53i | −2.55674 | − | 1.47613i | ||||
\(817\) | 241.956 | − | 64.8318i | 0.296151 | − | 0.0793535i | ||||
\(818\) | − | 2251.90i | − | 2.75293i | ||||||
\(819\) | −1548.01 | + | 985.805i | −1.89012 | + | 1.20367i | ||||
\(820\) | −758.643 | −0.925174 | ||||||||
\(821\) | 246.199 | + | 918.827i | 0.299877 | + | 1.11916i | 0.937266 | + | 0.348614i | \(0.113348\pi\) |
−0.637390 | + | 0.770542i | \(0.719986\pi\) | |||||||
\(822\) | −237.399 | + | 411.187i | −0.288807 | + | 0.500228i | ||||
\(823\) | 787.502 | − | 454.664i | 0.956867 | − | 0.552448i | 0.0616599 | − | 0.998097i | \(-0.480361\pi\) |
0.895208 | + | 0.445650i | \(0.147027\pi\) | |||||||
\(824\) | −1202.58 | + | 1202.58i | −1.45944 | + | 1.45944i | ||||
\(825\) | −57.1075 | − | 15.3019i | −0.0692213 | − | 0.0185478i | ||||
\(826\) | −1165.62 | + | 4350.16i | −1.41117 | + | 5.26654i | ||||
\(827\) | 297.080 | + | 297.080i | 0.359226 | + | 0.359226i | 0.863528 | − | 0.504302i | \(-0.168250\pi\) |
−0.504302 | + | 0.863528i | \(0.668250\pi\) | |||||||
\(828\) | 653.026 | + | 1131.07i | 0.788679 | + | 1.36603i | ||||
\(829\) | 660.248 | + | 381.194i | 0.796439 | + | 0.459824i | 0.842225 | − | 0.539127i | \(-0.181246\pi\) |
−0.0457854 | + | 0.998951i | \(0.514579\pi\) | |||||||
\(830\) | −278.183 | + | 74.5389i | −0.335160 | + | 0.0898059i | ||||
\(831\) | 873.312i | 1.05092i | ||||||||
\(832\) | −148.045 | − | 469.829i | −0.177938 | − | 0.564698i | ||||
\(833\) | 1037.99 | 1.24609 | ||||||||
\(834\) | −670.698 | − | 2503.08i | −0.804195 | − | 3.00130i | ||||
\(835\) | −271.378 | + | 470.040i | −0.325003 | + | 0.562922i | ||||
\(836\) | 194.320 | − | 112.191i | 0.232440 | − | 0.134199i | ||||
\(837\) | −37.5716 | + | 37.5716i | −0.0448884 | + | 0.0448884i | ||||
\(838\) | 1471.22 | + | 394.212i | 1.75563 | + | 0.470420i | ||||
\(839\) | 90.1366 | − | 336.394i | 0.107433 | − | 0.400947i | −0.891177 | − | 0.453657i | \(-0.850119\pi\) |
0.998610 | + | 0.0527100i | \(0.0167859\pi\) | |||||||
\(840\) | −1600.63 | − | 1600.63i | −1.90551 | − | 1.90551i | ||||
\(841\) | 151.788 | + | 262.904i | 0.180485 | + | 0.312608i | ||||
\(842\) | 541.832 | + | 312.827i | 0.643506 | + | 0.371528i | ||||
\(843\) | −62.6724 | + | 16.7930i | −0.0743444 | + | 0.0199205i | ||||
\(844\) | − | 1088.27i | − | 1.28942i | ||||||
\(845\) | 65.7532 | − | 372.131i | 0.0778144 | − | 0.440392i | ||||
\(846\) | 1325.30 | 1.56654 | ||||||||
\(847\) | −324.041 | − | 1209.34i | −0.382574 | − | 1.42779i | ||||
\(848\) | 392.618 | − | 680.034i | 0.462993 | − | 0.801927i | ||||
\(849\) | −55.5975 | + | 32.0992i | −0.0654859 | + | 0.0378083i | ||||
\(850\) | 191.119 | − | 191.119i | 0.224845 | − | 0.224845i | ||||
\(851\) | 153.421 | + | 41.1090i | 0.180283 | + | 0.0483067i | ||||
\(852\) | 312.531 | − | 1166.38i | 0.366820 | − | 1.36899i | ||||
\(853\) | 648.566 | + | 648.566i | 0.760335 | + | 0.760335i | 0.976383 | − | 0.216048i | \(-0.0693167\pi\) |
−0.216048 | + | 0.976383i | \(0.569317\pi\) | |||||||
\(854\) | 1657.58 | + | 2871.02i | 1.94096 | + | 3.36185i | ||||
\(855\) | −236.432 | − | 136.504i | −0.276529 | − | 0.159654i | ||||
\(856\) | 1608.35 | − | 430.957i | 1.87892 | − | 0.503454i | ||||
\(857\) | − | 1229.01i | − | 1.43409i | −0.697028 | − | 0.717044i | \(-0.745495\pi\) | ||
0.697028 | − | 0.717044i | \(-0.254505\pi\) | |||||||
\(858\) | 536.804 | − | 169.149i | 0.625646 | − | 0.197143i | ||||
\(859\) | 239.765 | 0.279121 | 0.139561 | − | 0.990214i | \(-0.455431\pi\) | ||||
0.139561 | + | 0.990214i | \(0.455431\pi\) | |||||||
\(860\) | 144.346 | + | 538.707i | 0.167844 | + | 0.626404i | ||||
\(861\) | 922.397 | − | 1597.64i | 1.07131 | − | 1.85556i | ||||
\(862\) | −30.8053 | + | 17.7855i | −0.0357370 | + | 0.0206328i | ||||
\(863\) | 1021.57 | − | 1021.57i | 1.18374 | − | 1.18374i | 0.204972 | − | 0.978768i | \(-0.434290\pi\) |
0.978768 | − | 0.204972i | \(-0.0657104\pi\) | |||||||
\(864\) | −859.489 | − | 230.299i | −0.994778 | − | 0.266550i | ||||
\(865\) | 72.5822 | − | 270.881i | 0.0839101 | − | 0.313157i | ||||
\(866\) | −1728.22 | − | 1728.22i | −1.99564 | − | 1.99564i | ||||
\(867\) | −166.293 | − | 288.028i | −0.191803 | − | 0.332212i | ||||
\(868\) | 257.257 | + | 148.527i | 0.296379 | + | 0.171114i | ||||
\(869\) | 361.826 | − | 96.9509i | 0.416370 | − | 0.111566i | ||||
\(870\) | − | 888.709i | − | 1.02150i | ||||||
\(871\) | −743.447 | − | 1167.44i | −0.853555 | − | 1.34034i | ||||
\(872\) | −815.738 | −0.935480 | ||||||||
\(873\) | 573.672 | + | 2140.97i | 0.657127 | + | 2.45243i | ||||
\(874\) | 185.792 | − | 321.801i | 0.212577 | − | 0.368194i | ||||
\(875\) | 105.759 | − | 61.0600i | 0.120867 | − | 0.0697829i | ||||
\(876\) | 966.472 | − | 966.472i | 1.10328 | − | 1.10328i | ||||
\(877\) | 319.093 | + | 85.5007i | 0.363846 | + | 0.0974922i | 0.436110 | − | 0.899893i | \(-0.356356\pi\) |
−0.0722642 | + | 0.997386i | \(0.523022\pi\) | |||||||
\(878\) | 165.436 | − | 617.416i | 0.188424 | − | 0.703207i | ||||
\(879\) | −952.507 | − | 952.507i | −1.08363 | − | 1.08363i | ||||
\(880\) | 98.3893 | + | 170.415i | 0.111806 | + | 0.193654i | ||||
\(881\) | 355.957 | + | 205.512i | 0.404037 | + | 0.233271i | 0.688225 | − | 0.725498i | \(-0.258390\pi\) |
−0.284187 | + | 0.958769i | \(0.591724\pi\) | |||||||
\(882\) | 3213.72 | − | 861.113i | 3.64367 | − | 0.976319i | ||||
\(883\) | − | 629.821i | − | 0.713274i | −0.934243 | − | 0.356637i | \(-0.883923\pi\) | ||
0.934243 | − | 0.356637i | \(-0.116077\pi\) | |||||||
\(884\) | −391.048 | + | 1762.42i | −0.442362 | + | 1.99369i | ||||
\(885\) | −1179.05 | −1.33226 | ||||||||
\(886\) | −315.362 | − | 1176.95i | −0.355939 | − | 1.32838i | ||||
\(887\) | −791.643 | + | 1371.17i | −0.892494 | + | 1.54585i | −0.0556192 | + | 0.998452i | \(0.517713\pi\) |
−0.836875 | + | 0.547394i | \(0.815620\pi\) | |||||||
\(888\) | −1186.65 | + | 685.112i | −1.33632 | + | 0.771523i | ||||
\(889\) | −855.748 | + | 855.748i | −0.962596 | + | 0.962596i | ||||
\(890\) | −1019.29 | − | 273.117i | −1.14527 | − | 0.306873i | ||||
\(891\) | −19.7873 | + | 73.8471i | −0.0222079 | + | 0.0828811i | ||||
\(892\) | 701.031 | + | 701.031i | 0.785909 | + | 0.785909i | ||||
\(893\) | −132.277 | − | 229.111i | −0.148127 | − | 0.256563i | ||||
\(894\) | 772.452 | + | 445.975i | 0.864040 | + | 0.498854i | ||||
\(895\) | 52.1281 | − | 13.9677i | 0.0582437 | − | 0.0156063i | ||||
\(896\) | − | 600.091i | − | 0.669744i | ||||||
\(897\) | 441.891 | − | 482.067i | 0.492632 | − | 0.537422i | ||||
\(898\) | −782.882 | −0.871807 | ||||||||
\(899\) | 17.3483 | + | 64.7447i | 0.0192973 | + | 0.0720186i | ||||
\(900\) | 303.923 | − | 526.410i | 0.337692 | − | 0.584900i | ||||
\(901\) | −288.104 | + | 166.337i | −0.319761 | + | 0.184614i | ||||
\(902\) | −235.828 | + | 235.828i | −0.261451 | + | 0.261451i | ||||
\(903\) | −1309.98 | − | 351.007i | −1.45069 | − | 0.388712i | ||||
\(904\) | 983.135 | − | 3669.11i | 1.08754 | − | 4.05875i | ||||
\(905\) | 63.6667 | + | 63.6667i | 0.0703499 | + | 0.0703499i | ||||
\(906\) | 1497.45 | + | 2593.65i | 1.65281 | + | 2.86275i | ||||
\(907\) | −1369.09 | − | 790.442i | −1.50947 | − | 0.871491i | −0.999939 | − | 0.0110368i | \(-0.996487\pi\) |
−0.509528 | − | 0.860454i | \(-0.670180\pi\) | |||||||
\(908\) | −2788.22 | + | 747.101i | −3.07073 | + | 0.822799i | ||||
\(909\) | − | 1051.48i | − | 1.15675i | ||||||
\(910\) | −536.986 | + | 1031.09i | −0.590095 | + | 1.13307i | ||||
\(911\) | −528.136 | −0.579733 | −0.289866 | − | 0.957067i | \(-0.593611\pi\) | ||||
−0.289866 | + | 0.957067i | \(0.593611\pi\) | |||||||
\(912\) | 398.946 | + | 1488.89i | 0.437441 | + | 1.63255i | ||||
\(913\) | −44.4156 | + | 76.9301i | −0.0486480 | + | 0.0842608i | ||||
\(914\) | 2425.55 | − | 1400.39i | 2.65377 | − | 1.53216i | ||||
\(915\) | −613.707 | + | 613.707i | −0.670718 | + | 0.670718i | ||||
\(916\) | −4011.50 | − | 1074.88i | −4.37937 | − | 1.17345i | ||||
\(917\) | −342.341 | + | 1277.63i | −0.373327 | + | 1.39328i | ||||
\(918\) | 702.434 | + | 702.434i | 0.765179 | + | 0.765179i | ||||
\(919\) | −553.271 | − | 958.293i | −0.602036 | − | 1.04276i | −0.992512 | − | 0.122143i | \(-0.961023\pi\) |
0.390477 | − | 0.920613i | \(-0.372310\pi\) | |||||||
\(920\) | 411.789 | + | 237.746i | 0.447596 | + | 0.258420i | ||||
\(921\) | −1063.04 | + | 284.841i | −1.15423 | + | 0.309274i | ||||
\(922\) | − | 2045.83i | − | 2.21891i | ||||||
\(923\) | −356.090 | + | 15.4838i | −0.385797 | + | 0.0167755i | ||||
\(924\) | −1214.83 | −1.31475 | ||||||||
\(925\) | −19.1324 | − | 71.4032i | −0.0206837 | − | 0.0771926i | ||||
\(926\) | 148.900 | − | 257.903i | 0.160799 | − | 0.278513i | ||||
\(927\) | 961.739 | − | 555.260i | 1.03747 | − | 0.598986i | ||||
\(928\) | −793.720 | + | 793.720i | −0.855302 | + | 0.855302i | ||||
\(929\) | −1081.05 | − | 289.667i | −1.16367 | − | 0.311805i | −0.375241 | − | 0.926927i | \(-0.622440\pi\) |
−0.788432 | + | 0.615122i | \(0.789107\pi\) | |||||||
\(930\) | −28.6879 | + | 107.065i | −0.0308472 | + | 0.115123i | ||||
\(931\) | −469.625 | − | 469.625i | −0.504430 | − | 0.504430i | ||||
\(932\) | 1402.42 | + | 2429.07i | 1.50475 | + | 2.60630i | ||||
\(933\) | 1749.37 | + | 1010.00i | 1.87500 | + | 1.08253i | ||||
\(934\) | −1872.95 | + | 501.855i | −2.00530 | + | 0.537318i | ||||
\(935\) | − | 83.3675i | − | 0.0891631i | ||||||
\(936\) | 144.475 | + | 3322.58i | 0.154354 | + | 3.54976i | ||||
\(937\) | 1085.83 | 1.15883 | 0.579416 | − | 0.815032i | \(-0.303280\pi\) | ||||
0.579416 | + | 0.815032i | \(0.303280\pi\) | |||||||
\(938\) | 1102.02 | + | 4112.78i | 1.17486 | + | 4.38463i | ||||
\(939\) | −1008.44 | + | 1746.67i | −1.07395 | + | 1.86014i | ||||
\(940\) | 510.108 | − | 294.511i | 0.542668 | − | 0.313309i | ||||
\(941\) | 361.172 | − | 361.172i | 0.383817 | − | 0.383817i | −0.488658 | − | 0.872475i | \(-0.662513\pi\) |
0.872475 | + | 0.488658i | \(0.162513\pi\) | |||||||
\(942\) | −1189.64 | − | 318.763i | −1.26289 | − | 0.338390i | ||||
\(943\) | −100.296 | + | 374.309i | −0.106358 | + | 0.396934i | ||||
\(944\) | 2774.89 | + | 2774.89i | 2.93951 | + | 2.93951i | ||||
\(945\) | 224.419 | + | 388.705i | 0.237480 | + | 0.411328i | ||||
\(946\) | 212.331 | + | 122.589i | 0.224451 | + | 0.129587i | ||||
\(947\) | 1343.80 | − | 360.069i | 1.41900 | − | 0.380221i | 0.533874 | − | 0.845564i | \(-0.320736\pi\) |
0.885130 | + | 0.465343i | \(0.154069\pi\) | |||||||
\(948\) | 6533.00i | 6.89135i | ||||||||
\(949\) | −357.822 | − | 186.351i | −0.377051 | − | 0.196366i | ||||
\(950\) | −172.938 | −0.182040 | ||||||||
\(951\) | 123.267 | + | 460.038i | 0.129618 | + | 0.483742i | ||||
\(952\) | 1595.96 | − | 2764.29i | 1.67643 | − | 2.90366i | ||||
\(953\) | −45.4101 | + | 26.2175i | −0.0476497 | + | 0.0275105i | −0.523636 | − | 0.851942i | \(-0.675425\pi\) |
0.475986 | + | 0.879453i | \(0.342091\pi\) | |||||||
\(954\) | −754.005 | + | 754.005i | −0.790362 | + | 0.790362i | ||||
\(955\) | 305.912 | + | 81.9688i | 0.320326 | + | 0.0858312i | ||||
\(956\) | 771.679 | − | 2879.94i | 0.807195 | − | 3.01249i | ||||
\(957\) | −193.831 | − | 193.831i | −0.202540 | − | 0.202540i | ||||
\(958\) | −597.716 | − | 1035.27i | −0.623921 | − | 1.08066i | ||||
\(959\) | −261.973 | − | 151.250i | −0.273173 | − | 0.157716i | ||||
\(960\) | −383.220 | + | 102.683i | −0.399187 | + | 0.106962i | ||||
\(961\) | 952.640i | 0.991301i | ||||||||
\(962\) | 518.748 | + | 475.514i | 0.539239 | + | 0.494298i | ||||
\(963\) | −1087.27 | −1.12904 | ||||||||
\(964\) | 28.4927 | + | 106.336i | 0.0295567 | + | 0.110307i | ||||
\(965\) | 106.519 | − | 184.496i | 0.110382 | − | 0.191188i | ||||
\(966\) | −1742.27 | + | 1005.90i | −1.80359 | + | 1.04130i | ||||
\(967\) | 206.749 | − | 206.749i | 0.213805 | − | 0.213805i | −0.592077 | − | 0.805882i | \(-0.701692\pi\) |
0.805882 | + | 0.592077i | \(0.201692\pi\) | |||||||
\(968\) | −2191.47 | − | 587.204i | −2.26392 | − | 0.606615i | ||||
\(969\) | 169.018 | − | 630.784i | 0.174425 | − | 0.650964i | ||||
\(970\) | 992.809 | + | 992.809i | 1.02351 | + | 1.02351i | ||||
\(971\) | 623.155 | + | 1079.34i | 0.641766 | + | 1.11157i | 0.985038 | + | 0.172335i | \(0.0551312\pi\) |
−0.343273 | + | 0.939236i | \(0.611535\pi\) | |||||||
\(972\) | −2501.97 | − | 1444.52i | −2.57405 | − | 1.48613i | ||||
\(973\) | 1594.74 | − | 427.310i | 1.63900 | − | 0.439168i | ||||
\(974\) | 1615.12i | 1.65823i | ||||||||
\(975\) | −297.129 | − | 65.9273i | −0.304747 | − | 0.0676177i | ||||
\(976\) | 2888.71 | 2.95975 | ||||||||
\(977\) | −76.9509 | − | 287.185i | −0.0787625 | − | 0.293946i | 0.915298 | − | 0.402778i | \(-0.131955\pi\) |
−0.994060 | + | 0.108833i | \(0.965289\pi\) | |||||||
\(978\) | 1177.03 | − | 2038.68i | 1.20351 | − | 2.08454i | ||||
\(979\) | −281.879 | + | 162.743i | −0.287925 | + | 0.166234i | ||||
\(980\) | 1045.61 | − | 1045.61i | 1.06694 | − | 1.06694i | ||||
\(981\) | 514.510 | + | 137.862i | 0.524475 | + | 0.140533i | ||||
\(982\) | −77.7237 | + | 290.069i | −0.0791484 | + | 0.295386i | ||||
\(983\) | −603.497 | − | 603.497i | −0.613934 | − | 0.613934i | 0.330035 | − | 0.943969i | \(-0.392940\pi\) |
−0.943969 | + | 0.330035i | \(0.892940\pi\) | |||||||
\(984\) | −1671.50 | − | 2895.13i | −1.69868 | − | 2.94221i | ||||
\(985\) | 129.880 | + | 74.9864i | 0.131858 | + | 0.0761283i | ||||
\(986\) | 1210.46 | − | 324.342i | 1.22765 | − | 0.328947i | ||||
\(987\) | 1432.33i | 1.45119i | ||||||||
\(988\) | 974.307 | − | 620.458i | 0.986140 | − | 0.627994i | ||||
\(989\) | 284.878 | 0.288046 | ||||||||
\(990\) | −69.1613 | − | 258.114i | −0.0698599 | − | 0.260721i | ||||
\(991\) | 880.059 | − | 1524.31i | 0.888051 | − | 1.53815i | 0.0458750 | − | 0.998947i | \(-0.485392\pi\) |
0.842176 | − | 0.539203i | \(-0.181274\pi\) | |||||||
\(992\) | 121.243 | − | 69.9995i | 0.122220 | − | 0.0705640i | ||||
\(993\) | 1126.10 | − | 1126.10i | 1.13404 | − | 1.13404i | ||||
\(994\) | 1059.14 | + | 283.795i | 1.06553 | + | 0.285508i | ||||
\(995\) | −82.3443 | + | 307.313i | −0.0827581 | + | 0.308857i | ||||
\(996\) | −1095.49 | − | 1095.49i | −1.09989 | − | 1.09989i | ||||
\(997\) | −16.6111 | − | 28.7713i | −0.0166611 | − | 0.0288579i | 0.857575 | − | 0.514360i | \(-0.171970\pi\) |
−0.874236 | + | 0.485502i | \(0.838637\pi\) | |||||||
\(998\) | −1551.33 | − | 895.663i | −1.55444 | − | 0.897458i | ||||
\(999\) | 262.434 | − | 70.3190i | 0.262697 | − | 0.0703894i |
(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 | 65.3.p.a.6.2 | ✓ | 40 | |
5.2 | odd | 4 | 325.3.w.e.149.9 | 40 | |||
5.3 | odd | 4 | 325.3.w.f.149.2 | 40 | |||
5.4 | even | 2 | 325.3.t.d.201.9 | 40 | |||
13.11 | odd | 12 | inner | 65.3.p.a.11.2 | yes | 40 | |
65.24 | odd | 12 | 325.3.t.d.76.9 | 40 | |||
65.37 | even | 12 | 325.3.w.f.24.2 | 40 | |||
65.63 | even | 12 | 325.3.w.e.24.9 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.3.p.a.6.2 | ✓ | 40 | 1.1 | even | 1 | trivial | |
65.3.p.a.11.2 | yes | 40 | 13.11 | odd | 12 | inner | |
325.3.t.d.76.9 | 40 | 65.24 | odd | 12 | |||
325.3.t.d.201.9 | 40 | 5.4 | even | 2 | |||
325.3.w.e.24.9 | 40 | 65.63 | even | 12 | |||
325.3.w.e.149.9 | 40 | 5.2 | odd | 4 | |||
325.3.w.f.24.2 | 40 | 65.37 | even | 12 | |||
325.3.w.f.149.2 | 40 | 5.3 | odd | 4 |