Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,3,Mod(115,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.115");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.j (of order \(4\), 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: | \(3.70573159530\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 115.7 | ||
Character | \(\chi\) | \(=\) | 136.115 |
Dual form | 136.3.j.b.123.7 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.64296 | − | 1.14047i | −0.821482 | − | 0.570235i | ||||
\(3\) | 3.48624 | + | 3.48624i | 1.16208 | + | 1.16208i | 0.984020 | + | 0.178059i | \(0.0569819\pi\) |
0.178059 | + | 0.984020i | \(0.443018\pi\) | |||||||
\(4\) | 1.39866 | + | 3.74750i | 0.349665 | + | 0.936875i | ||||
\(5\) | 5.68473 | − | 5.68473i | 1.13695 | − | 1.13695i | 0.147952 | − | 0.988995i | \(-0.452732\pi\) |
0.988995 | − | 0.147952i | \(-0.0472680\pi\) | |||||||
\(6\) | −1.75181 | − | 9.70371i | −0.291969 | − | 1.61728i | ||||
\(7\) | −3.01446 | − | 3.01446i | −0.430637 | − | 0.430637i | 0.458208 | − | 0.888845i | \(-0.348492\pi\) |
−0.888845 | + | 0.458208i | \(0.848492\pi\) | |||||||
\(8\) | 1.97596 | − | 7.75213i | 0.246995 | − | 0.969017i | ||||
\(9\) | 15.3077i | 1.70086i | ||||||||
\(10\) | −15.8231 | + | 2.85655i | −1.58231 | + | 0.285655i | ||||
\(11\) | 11.0314 | − | 11.0314i | 1.00285 | − | 1.00285i | 0.00285806 | − | 0.999996i | \(-0.499090\pi\) |
0.999996 | − | 0.00285806i | \(-0.000909751\pi\) | |||||||
\(12\) | −8.18861 | + | 17.9407i | −0.682384 | + | 1.49506i | ||||
\(13\) | 14.9872i | 1.15286i | 0.817147 | + | 0.576430i | \(0.195555\pi\) | ||||
−0.817147 | + | 0.576430i | \(0.804445\pi\) | |||||||
\(14\) | 1.51475 | + | 8.39055i | 0.108196 | + | 0.599325i | ||||
\(15\) | 39.6366 | 2.64244 | ||||||||
\(16\) | −12.0875 | + | 10.4830i | −0.755469 | + | 0.655184i | ||||
\(17\) | −11.6019 | + | 12.4256i | −0.682466 | + | 0.730918i | ||||
\(18\) | 17.4580 | − | 25.1500i | 0.969887 | − | 1.39722i | ||||
\(19\) | − | 10.2535i | − | 0.539659i | −0.962908 | − | 0.269830i | \(-0.913033\pi\) | ||
0.962908 | − | 0.269830i | \(-0.0869674\pi\) | |||||||
\(20\) | 29.2545 | + | 13.3525i | 1.46273 | + | 0.667626i | ||||
\(21\) | − | 21.0183i | − | 1.00087i | ||||||
\(22\) | −30.7051 | + | 5.54321i | −1.39569 | + | 0.251964i | ||||
\(23\) | 4.83274 | + | 4.83274i | 0.210119 | + | 0.210119i | 0.804318 | − | 0.594199i | \(-0.202531\pi\) |
−0.594199 | + | 0.804318i | \(0.702531\pi\) | |||||||
\(24\) | 33.9144 | − | 20.1371i | 1.41310 | − | 0.839046i | ||||
\(25\) | − | 39.6323i | − | 1.58529i | ||||||
\(26\) | 17.0924 | − | 24.6234i | 0.657401 | − | 0.947054i | ||||
\(27\) | −21.9901 | + | 21.9901i | −0.814449 | + | 0.814449i | ||||
\(28\) | 7.08049 | − | 15.5129i | 0.252875 | − | 0.554032i | ||||
\(29\) | −17.2924 | + | 17.2924i | −0.596288 | + | 0.596288i | −0.939323 | − | 0.343034i | \(-0.888545\pi\) |
0.343034 | + | 0.939323i | \(0.388545\pi\) | |||||||
\(30\) | −65.1216 | − | 45.2044i | −2.17072 | − | 1.50681i | ||||
\(31\) | 10.2031 | − | 10.2031i | 0.329131 | − | 0.329131i | −0.523125 | − | 0.852256i | \(-0.675234\pi\) |
0.852256 | + | 0.523125i | \(0.175234\pi\) | |||||||
\(32\) | 31.8148 | − | 3.43768i | 0.994213 | − | 0.107428i | ||||
\(33\) | 76.9161 | 2.33079 | ||||||||
\(34\) | 33.2325 | − | 7.18318i | 0.977428 | − | 0.211270i | ||||
\(35\) | −34.2728 | −0.979223 | ||||||||
\(36\) | −57.3656 | + | 21.4103i | −1.59349 | + | 0.594729i | ||||
\(37\) | −23.3247 | + | 23.3247i | −0.630398 | + | 0.630398i | −0.948168 | − | 0.317770i | \(-0.897066\pi\) |
0.317770 | + | 0.948168i | \(0.397066\pi\) | |||||||
\(38\) | −11.6938 | + | 16.8462i | −0.307732 | + | 0.443320i | ||||
\(39\) | −52.2489 | + | 52.2489i | −1.33971 | + | 1.33971i | ||||
\(40\) | −32.8360 | − | 55.3016i | −0.820900 | − | 1.38254i | ||||
\(41\) | −49.1711 | + | 49.1711i | −1.19929 | + | 1.19929i | −0.224916 | + | 0.974378i | \(0.572211\pi\) |
−0.974378 | + | 0.224916i | \(0.927789\pi\) | |||||||
\(42\) | −23.9707 | + | 34.5322i | −0.570730 | + | 0.822196i | ||||
\(43\) | 30.1982i | 0.702284i | 0.936322 | + | 0.351142i | \(0.114207\pi\) | ||||
−0.936322 | + | 0.351142i | \(0.885793\pi\) | |||||||
\(44\) | 56.7693 | + | 25.9110i | 1.29021 | + | 0.588886i | ||||
\(45\) | 87.0201 | + | 87.0201i | 1.93378 | + | 1.93378i | ||||
\(46\) | −2.42842 | − | 13.4516i | −0.0527918 | − | 0.292426i | ||||
\(47\) | − | 67.7847i | − | 1.44223i | −0.692817 | − | 0.721114i | \(-0.743630\pi\) | ||
0.692817 | − | 0.721114i | \(-0.256370\pi\) | |||||||
\(48\) | −78.6860 | − | 5.59385i | −1.63929 | − | 0.116539i | ||||
\(49\) | − | 30.8260i | − | 0.629103i | ||||||
\(50\) | −45.1995 | + | 65.1145i | −0.903989 | + | 1.30229i | ||||
\(51\) | −83.7656 | + | 2.87157i | −1.64246 | + | 0.0563053i | ||||
\(52\) | −56.1644 | + | 20.9620i | −1.08009 | + | 0.403115i | ||||
\(53\) | 14.5537 | 0.274599 | 0.137299 | − | 0.990530i | \(-0.456158\pi\) | ||||
0.137299 | + | 0.990530i | \(0.456158\pi\) | |||||||
\(54\) | 61.2081 | − | 11.0499i | 1.13348 | − | 0.204628i | ||||
\(55\) | − | 125.421i | − | 2.28038i | ||||||
\(56\) | −29.3250 | + | 17.4121i | −0.523660 | + | 0.310929i | ||||
\(57\) | 35.7462 | − | 35.7462i | 0.627127 | − | 0.627127i | ||||
\(58\) | 48.1321 | − | 8.68932i | 0.829864 | − | 0.149816i | ||||
\(59\) | 3.05796i | 0.0518299i | 0.999664 | + | 0.0259150i | \(0.00824991\pi\) | ||||
−0.999664 | + | 0.0259150i | \(0.991750\pi\) | |||||||
\(60\) | 55.4382 | + | 148.538i | 0.923969 | + | 2.47564i | ||||
\(61\) | −35.3461 | − | 35.3461i | −0.579445 | − | 0.579445i | 0.355306 | − | 0.934750i | \(-0.384377\pi\) |
−0.934750 | + | 0.355306i | \(0.884377\pi\) | |||||||
\(62\) | −28.3996 | + | 5.12699i | −0.458057 | + | 0.0826933i | ||||
\(63\) | 46.1445 | − | 46.1445i | 0.732452 | − | 0.732452i | ||||
\(64\) | −56.1912 | − | 30.6358i | −0.877987 | − | 0.478685i | ||||
\(65\) | 85.1981 | + | 85.1981i | 1.31074 | + | 1.31074i | ||||
\(66\) | −126.370 | − | 87.7205i | −1.91470 | − | 1.32910i | ||||
\(67\) | −81.9173 | −1.22265 | −0.611323 | − | 0.791381i | \(-0.709362\pi\) | ||||
−0.611323 | + | 0.791381i | \(0.709362\pi\) | |||||||
\(68\) | −62.7921 | − | 26.0990i | −0.923413 | − | 0.383809i | ||||
\(69\) | 33.6961i | 0.488350i | ||||||||
\(70\) | 56.3090 | + | 39.0871i | 0.804414 | + | 0.558387i | ||||
\(71\) | −2.72821 | + | 2.72821i | −0.0384256 | + | 0.0384256i | −0.726058 | − | 0.687633i | \(-0.758650\pi\) |
0.687633 | + | 0.726058i | \(0.258650\pi\) | |||||||
\(72\) | 118.667 | + | 30.2474i | 1.64816 | + | 0.420103i | ||||
\(73\) | −80.5918 | − | 80.5918i | −1.10400 | − | 1.10400i | −0.993923 | − | 0.110074i | \(-0.964891\pi\) |
−0.110074 | − | 0.993923i | \(-0.535109\pi\) | |||||||
\(74\) | 64.9228 | − | 11.7205i | 0.877335 | − | 0.158386i | ||||
\(75\) | 138.168 | − | 138.168i | 1.84224 | − | 1.84224i | ||||
\(76\) | 38.4251 | − | 14.3412i | 0.505593 | − | 0.188700i | ||||
\(77\) | −66.5074 | −0.863733 | ||||||||
\(78\) | 145.431 | − | 26.2548i | 1.86450 | − | 0.336599i | ||||
\(79\) | −6.63690 | − | 6.63690i | −0.0840114 | − | 0.0840114i | 0.663852 | − | 0.747864i | \(-0.268920\pi\) |
−0.747864 | + | 0.663852i | \(0.768920\pi\) | |||||||
\(80\) | −9.12145 | + | 128.307i | −0.114018 | + | 1.60384i | ||||
\(81\) | −15.5563 | −0.192054 | ||||||||
\(82\) | 136.864 | − | 24.7082i | 1.66908 | − | 0.301319i | ||||
\(83\) | 4.07312i | 0.0490737i | 0.999699 | + | 0.0245369i | \(0.00781111\pi\) | ||||
−0.999699 | + | 0.0245369i | \(0.992189\pi\) | |||||||
\(84\) | 78.7659 | − | 29.3974i | 0.937689 | − | 0.349969i | ||||
\(85\) | 4.68244 | + | 136.590i | 0.0550875 | + | 1.60694i | ||||
\(86\) | 34.4402 | − | 49.6146i | 0.400467 | − | 0.576914i | ||||
\(87\) | −120.571 | −1.38587 | ||||||||
\(88\) | −63.7192 | − | 107.314i | −0.724082 | − | 1.21948i | ||||
\(89\) | 96.0501 | 1.07922 | 0.539608 | − | 0.841917i | \(-0.318573\pi\) | ||||
0.539608 | + | 0.841917i | \(0.318573\pi\) | |||||||
\(90\) | −43.7271 | − | 242.215i | −0.485857 | − | 2.69127i | ||||
\(91\) | 45.1783 | − | 45.1783i | 0.496465 | − | 0.496465i | ||||
\(92\) | −11.3513 | + | 24.8700i | −0.123384 | + | 0.270326i | ||||
\(93\) | 71.1406 | 0.764953 | ||||||||
\(94\) | −77.3064 | + | 111.368i | −0.822408 | + | 1.18476i | ||||
\(95\) | −58.2885 | − | 58.2885i | −0.613564 | − | 0.613564i | ||||
\(96\) | 122.899 | + | 98.9294i | 1.28019 | + | 1.03051i | ||||
\(97\) | 80.8898 | + | 80.8898i | 0.833916 | + | 0.833916i | 0.988050 | − | 0.154134i | \(-0.0492588\pi\) |
−0.154134 | + | 0.988050i | \(0.549259\pi\) | |||||||
\(98\) | −35.1562 | + | 50.6461i | −0.358736 | + | 0.516797i | ||||
\(99\) | 168.865 | + | 168.865i | 1.70571 | + | 1.70571i | ||||
\(100\) | 148.522 | − | 55.4321i | 1.48522 | − | 0.554321i | ||||
\(101\) | − | 106.887i | − | 1.05829i | −0.848533 | − | 0.529143i | \(-0.822514\pi\) | ||
0.848533 | − | 0.529143i | \(-0.177486\pi\) | |||||||
\(102\) | 140.899 | + | 90.8142i | 1.38136 | + | 0.890336i | ||||
\(103\) | 195.546i | 1.89850i | 0.314522 | + | 0.949250i | \(0.398156\pi\) | ||||
−0.314522 | + | 0.949250i | \(0.601844\pi\) | |||||||
\(104\) | 116.183 | + | 29.6141i | 1.11714 | + | 0.284751i | ||||
\(105\) | −119.483 | − | 119.483i | −1.13793 | − | 1.13793i | ||||
\(106\) | −23.9112 | − | 16.5981i | −0.225578 | − | 0.156586i | ||||
\(107\) | −29.2412 | − | 29.2412i | −0.273282 | − | 0.273282i | 0.557138 | − | 0.830420i | \(-0.311900\pi\) |
−0.830420 | + | 0.557138i | \(0.811900\pi\) | |||||||
\(108\) | −113.165 | − | 51.6513i | −1.04782 | − | 0.478253i | ||||
\(109\) | −125.799 | − | 125.799i | −1.15412 | − | 1.15412i | −0.985718 | − | 0.168405i | \(-0.946138\pi\) |
−0.168405 | − | 0.985718i | \(-0.553862\pi\) | |||||||
\(110\) | −143.039 | + | 206.062i | −1.30035 | + | 1.87329i | ||||
\(111\) | −162.631 | −1.46514 | ||||||||
\(112\) | 68.0378 | + | 4.83686i | 0.607480 | + | 0.0431863i | ||||
\(113\) | −53.2241 | + | 53.2241i | −0.471010 | + | 0.471010i | −0.902241 | − | 0.431232i | \(-0.858079\pi\) |
0.431232 | + | 0.902241i | \(0.358079\pi\) | |||||||
\(114\) | −99.4972 | + | 17.9623i | −0.872783 | + | 0.157564i | ||||
\(115\) | 54.9456 | 0.477788 | ||||||||
\(116\) | −88.9892 | − | 40.6170i | −0.767149 | − | 0.350146i | ||||
\(117\) | −229.419 | −1.96085 | ||||||||
\(118\) | 3.48751 | − | 5.02413i | 0.0295552 | − | 0.0425773i | ||||
\(119\) | 72.4300 | − | 2.48297i | 0.608656 | − | 0.0208653i | ||||
\(120\) | 78.3205 | − | 307.269i | 0.652671 | − | 2.56057i | ||||
\(121\) | − | 122.383i | − | 1.01143i | ||||||
\(122\) | 17.7612 | + | 98.3835i | 0.145584 | + | 0.806423i | ||||
\(123\) | −342.844 | −2.78735 | ||||||||
\(124\) | 52.5066 | + | 23.9654i | 0.423440 | + | 0.193269i | ||||
\(125\) | −83.1808 | − | 83.1808i | −0.665447 | − | 0.665447i | ||||
\(126\) | −128.440 | + | 23.1873i | −1.01937 | + | 0.184026i | ||||
\(127\) | 237.212 | 1.86781 | 0.933904 | − | 0.357523i | \(-0.116379\pi\) | ||||
0.933904 | + | 0.357523i | \(0.116379\pi\) | |||||||
\(128\) | 57.3808 | + | 114.418i | 0.448287 | + | 0.893889i | ||||
\(129\) | −105.278 | + | 105.278i | −0.816110 | + | 0.816110i | ||||
\(130\) | −42.8116 | − | 237.143i | −0.329320 | − | 1.82418i | ||||
\(131\) | 38.3249 | + | 38.3249i | 0.292556 | + | 0.292556i | 0.838089 | − | 0.545533i | \(-0.183673\pi\) |
−0.545533 | + | 0.838089i | \(0.683673\pi\) | |||||||
\(132\) | 107.579 | + | 288.243i | 0.814996 | + | 2.18366i | ||||
\(133\) | −30.9089 | + | 30.9089i | −0.232397 | + | 0.232397i | ||||
\(134\) | 134.587 | + | 93.4241i | 1.00438 | + | 0.697195i | ||||
\(135\) | 250.016i | 1.85197i | ||||||||
\(136\) | 73.4000 | + | 114.492i | 0.539706 | + | 0.841854i | ||||
\(137\) | 97.4794 | 0.711528 | 0.355764 | − | 0.934576i | \(-0.384221\pi\) | ||||
0.355764 | + | 0.934576i | \(0.384221\pi\) | |||||||
\(138\) | 38.4294 | − | 55.3615i | 0.278474 | − | 0.401170i | ||||
\(139\) | 11.3450 | + | 11.3450i | 0.0816188 | + | 0.0816188i | 0.746738 | − | 0.665119i | \(-0.231619\pi\) |
−0.665119 | + | 0.746738i | \(0.731619\pi\) | |||||||
\(140\) | −47.9360 | − | 128.437i | −0.342400 | − | 0.917409i | ||||
\(141\) | 236.314 | − | 236.314i | 1.67598 | − | 1.67598i | ||||
\(142\) | 7.59380 | − | 1.37091i | 0.0534775 | − | 0.00965431i | ||||
\(143\) | 165.329 | + | 165.329i | 1.15615 | + | 1.15615i | ||||
\(144\) | −160.470 | − | 185.032i | −1.11437 | − | 1.28494i | ||||
\(145\) | 196.605i | 1.35590i | ||||||||
\(146\) | 40.4969 | + | 224.322i | 0.277376 | + | 1.53645i | ||||
\(147\) | 107.467 | − | 107.467i | 0.731067 | − | 0.731067i | ||||
\(148\) | −120.033 | − | 54.7860i | −0.811032 | − | 0.370176i | ||||
\(149\) | 47.1261i | 0.316282i | 0.987417 | + | 0.158141i | \(0.0505501\pi\) | ||||
−0.987417 | + | 0.158141i | \(0.949450\pi\) | |||||||
\(150\) | −384.581 | + | 69.4285i | −2.56387 | + | 0.462857i | ||||
\(151\) | −98.2232 | −0.650485 | −0.325242 | − | 0.945631i | \(-0.605446\pi\) | ||||
−0.325242 | + | 0.945631i | \(0.605446\pi\) | |||||||
\(152\) | −79.4867 | − | 20.2606i | −0.522939 | − | 0.133293i | ||||
\(153\) | −190.207 | − | 177.599i | −1.24319 | − | 1.16078i | ||||
\(154\) | 109.269 | + | 75.8497i | 0.709541 | + | 0.492530i | ||||
\(155\) | − | 116.003i | − | 0.748409i | ||||||
\(156\) | −268.881 | − | 122.724i | −1.72360 | − | 0.786694i | ||||
\(157\) | 115.343i | 0.734667i | 0.930089 | + | 0.367333i | \(0.119729\pi\) | ||||
−0.930089 | + | 0.367333i | \(0.880271\pi\) | |||||||
\(158\) | 3.33500 | + | 18.4734i | 0.0211076 | + | 0.116920i | ||||
\(159\) | 50.7377 | + | 50.7377i | 0.319105 | + | 0.319105i | ||||
\(160\) | 161.316 | − | 200.401i | 1.00823 | − | 1.25251i | ||||
\(161\) | − | 29.1362i | − | 0.180970i | ||||||
\(162\) | 25.5585 | + | 17.7415i | 0.157769 | + | 0.109516i | ||||
\(163\) | 99.2678 | − | 99.2678i | 0.609005 | − | 0.609005i | −0.333681 | − | 0.942686i | \(-0.608291\pi\) |
0.942686 | + | 0.333681i | \(0.108291\pi\) | |||||||
\(164\) | −253.042 | − | 115.495i | −1.54294 | − | 0.704238i | ||||
\(165\) | 437.247 | − | 437.247i | 2.64998 | − | 2.64998i | ||||
\(166\) | 4.64527 | − | 6.69199i | 0.0279835 | − | 0.0403132i | ||||
\(167\) | 189.570 | − | 189.570i | 1.13515 | − | 1.13515i | 0.145844 | − | 0.989308i | \(-0.453410\pi\) |
0.989308 | − | 0.145844i | \(-0.0465896\pi\) | |||||||
\(168\) | −162.936 | − | 41.5313i | −0.969859 | − | 0.247210i | ||||
\(169\) | −55.6155 | −0.329086 | ||||||||
\(170\) | 148.084 | − | 229.753i | 0.871080 | − | 1.35149i | ||||
\(171\) | 156.958 | 0.917882 | ||||||||
\(172\) | −113.168 | + | 42.2370i | −0.657953 | + | 0.245564i | ||||
\(173\) | −70.0684 | + | 70.0684i | −0.405019 | + | 0.405019i | −0.879998 | − | 0.474978i | \(-0.842456\pi\) |
0.474978 | + | 0.879998i | \(0.342456\pi\) | |||||||
\(174\) | 198.093 | + | 137.507i | 1.13847 | + | 0.790270i | ||||
\(175\) | −119.470 | + | 119.470i | −0.682687 | + | 0.682687i | ||||
\(176\) | −17.7005 | + | 248.984i | −0.100571 | + | 1.41468i | ||||
\(177\) | −10.6608 | + | 10.6608i | −0.0602305 | + | 0.0602305i | ||||
\(178\) | −157.807 | − | 109.542i | −0.886556 | − | 0.615406i | ||||
\(179\) | − | 19.1662i | − | 0.107074i | −0.998566 | − | 0.0535368i | \(-0.982951\pi\) | ||
0.998566 | − | 0.0535368i | \(-0.0170494\pi\) | |||||||
\(180\) | −204.396 | + | 447.819i | −1.13554 | + | 2.48789i | ||||
\(181\) | −10.8598 | − | 10.8598i | −0.0599987 | − | 0.0599987i | 0.676471 | − | 0.736469i | \(-0.263509\pi\) |
−0.736469 | + | 0.676471i | \(0.763509\pi\) | |||||||
\(182\) | −125.751 | + | 22.7018i | −0.690938 | + | 0.124735i | ||||
\(183\) | − | 246.450i | − | 1.34672i | ||||||
\(184\) | 47.0133 | − | 27.9147i | 0.255507 | − | 0.151710i | ||||
\(185\) | 265.190i | 1.43346i | ||||||||
\(186\) | −116.881 | − | 81.1337i | −0.628395 | − | 0.436203i | ||||
\(187\) | 9.08641 | + | 265.057i | 0.0485905 | + | 1.41742i | ||||
\(188\) | 254.023 | − | 94.8077i | 1.35119 | − | 0.504296i | ||||
\(189\) | 132.577 | 0.701465 | ||||||||
\(190\) | 29.2897 | + | 162.242i | 0.154156 | + | 0.853906i | ||||
\(191\) | − | 2.88936i | − | 0.0151275i | −0.999971 | − | 0.00756377i | \(-0.997592\pi\) | ||
0.999971 | − | 0.00756377i | \(-0.00240765\pi\) | |||||||
\(192\) | −89.0919 | − | 302.699i | −0.464020 | − | 1.57656i | ||||
\(193\) | −51.3210 | + | 51.3210i | −0.265912 | + | 0.265912i | −0.827450 | − | 0.561539i | \(-0.810210\pi\) |
0.561539 | + | 0.827450i | \(0.310210\pi\) | |||||||
\(194\) | −40.6467 | − | 225.151i | −0.209519 | − | 1.16057i | ||||
\(195\) | 594.041i | 3.04637i | ||||||||
\(196\) | 115.521 | − | 43.1151i | 0.589391 | − | 0.219975i | ||||
\(197\) | 207.826 | + | 207.826i | 1.05496 | + | 1.05496i | 0.998399 | + | 0.0565569i | \(0.0180122\pi\) |
0.0565569 | + | 0.998399i | \(0.481988\pi\) | |||||||
\(198\) | −84.8538 | − | 470.025i | −0.428555 | − | 2.37386i | ||||
\(199\) | −101.314 | + | 101.314i | −0.509118 | + | 0.509118i | −0.914256 | − | 0.405138i | \(-0.867224\pi\) |
0.405138 | + | 0.914256i | \(0.367224\pi\) | |||||||
\(200\) | −307.235 | − | 78.3119i | −1.53618 | − | 0.391560i | ||||
\(201\) | −285.583 | − | 285.583i | −1.42081 | − | 1.42081i | ||||
\(202\) | −121.901 | + | 175.611i | −0.603471 | + | 0.869362i | ||||
\(203\) | 104.254 | 0.513568 | ||||||||
\(204\) | −127.921 | − | 309.895i | −0.627063 | − | 1.51909i | ||||
\(205\) | 559.049i | 2.72707i | ||||||||
\(206\) | 223.014 | − | 321.274i | 1.08259 | − | 1.55958i | ||||
\(207\) | −73.9781 | + | 73.9781i | −0.357382 | + | 0.357382i | ||||
\(208\) | −157.110 | − | 181.158i | −0.755336 | − | 0.870950i | ||||
\(209\) | −113.111 | − | 113.111i | −0.541199 | − | 0.541199i | ||||
\(210\) | 60.0396 | + | 332.573i | 0.285903 | + | 1.58368i | ||||
\(211\) | −122.098 | + | 122.098i | −0.578664 | + | 0.578664i | −0.934535 | − | 0.355871i | \(-0.884184\pi\) |
0.355871 | + | 0.934535i | \(0.384184\pi\) | |||||||
\(212\) | 20.3557 | + | 54.5401i | 0.0960175 | + | 0.257264i | ||||
\(213\) | −19.0224 | −0.0893071 | ||||||||
\(214\) | 14.6935 | + | 81.3910i | 0.0686614 | + | 0.380332i | ||||
\(215\) | 171.669 | + | 171.669i | 0.798460 | + | 0.798460i | ||||
\(216\) | 127.019 | + | 213.922i | 0.588050 | + | 0.990380i | ||||
\(217\) | −61.5135 | −0.283472 | ||||||||
\(218\) | 63.2135 | + | 350.154i | 0.289970 | + | 1.60621i | ||||
\(219\) | − | 561.924i | − | 2.56586i | ||||||
\(220\) | 470.015 | − | 175.421i | 2.13643 | − | 0.797369i | ||||
\(221\) | −186.225 | − | 173.880i | −0.842646 | − | 0.786787i | ||||
\(222\) | 267.197 | + | 185.476i | 1.20359 | + | 0.835476i | ||||
\(223\) | −192.560 | −0.863499 | −0.431749 | − | 0.901994i | \(-0.642103\pi\) | ||||
−0.431749 | + | 0.901994i | \(0.642103\pi\) | |||||||
\(224\) | −106.267 | − | 85.5418i | −0.474408 | − | 0.381883i | ||||
\(225\) | 606.680 | 2.69635 | ||||||||
\(226\) | 148.146 | − | 26.7448i | 0.655512 | − | 0.118340i | ||||
\(227\) | −88.2081 | + | 88.2081i | −0.388582 | + | 0.388582i | −0.874181 | − | 0.485599i | \(-0.838601\pi\) |
0.485599 | + | 0.874181i | \(0.338601\pi\) | |||||||
\(228\) | 183.956 | + | 83.9622i | 0.806823 | + | 0.368255i | ||||
\(229\) | 180.100 | 0.786464 | 0.393232 | − | 0.919439i | \(-0.371357\pi\) | ||||
0.393232 | + | 0.919439i | \(0.371357\pi\) | |||||||
\(230\) | −90.2736 | − | 62.6638i | −0.392494 | − | 0.272451i | ||||
\(231\) | −231.861 | − | 231.861i | −1.00373 | − | 1.00373i | ||||
\(232\) | 99.8837 | + | 168.222i | 0.430533 | + | 0.725094i | ||||
\(233\) | 161.016 | + | 161.016i | 0.691058 | + | 0.691058i | 0.962465 | − | 0.271407i | \(-0.0874889\pi\) |
−0.271407 | + | 0.962465i | \(0.587489\pi\) | |||||||
\(234\) | 376.927 | + | 261.646i | 1.61080 | + | 1.11814i | ||||
\(235\) | −385.338 | − | 385.338i | −1.63974 | − | 1.63974i | ||||
\(236\) | −11.4597 | + | 4.27705i | −0.0485581 | + | 0.0181231i | ||||
\(237\) | − | 46.2756i | − | 0.195256i | ||||||
\(238\) | −121.832 | − | 78.5248i | −0.511898 | − | 0.329936i | ||||
\(239\) | − | 382.325i | − | 1.59969i | −0.600208 | − | 0.799844i | \(-0.704916\pi\) | ||
0.600208 | − | 0.799844i | \(-0.295084\pi\) | |||||||
\(240\) | −479.108 | + | 415.509i | −1.99628 | + | 1.73129i | ||||
\(241\) | −87.2774 | − | 87.2774i | −0.362147 | − | 0.362147i | 0.502456 | − | 0.864603i | \(-0.332430\pi\) |
−0.864603 | + | 0.502456i | \(0.832430\pi\) | |||||||
\(242\) | −139.574 | + | 201.071i | −0.576754 | + | 0.830873i | ||||
\(243\) | 143.678 | + | 143.678i | 0.591268 | + | 0.591268i | ||||
\(244\) | 83.0224 | − | 181.897i | 0.340256 | − | 0.745478i | ||||
\(245\) | −175.238 | − | 175.238i | −0.715256 | − | 0.715256i | ||||
\(246\) | 563.280 | + | 391.003i | 2.28976 | + | 1.58944i | ||||
\(247\) | 153.671 | 0.622152 | ||||||||
\(248\) | −58.9347 | − | 99.2564i | −0.237640 | − | 0.400228i | ||||
\(249\) | −14.1999 | + | 14.1999i | −0.0570275 | + | 0.0570275i | ||||
\(250\) | 41.7979 | + | 231.528i | 0.167192 | + | 0.926113i | ||||
\(251\) | 303.912 | 1.21081 | 0.605403 | − | 0.795919i | \(-0.293012\pi\) | ||||
0.605403 | + | 0.795919i | \(0.293012\pi\) | |||||||
\(252\) | 237.467 | + | 108.386i | 0.942329 | + | 0.430103i | ||||
\(253\) | 106.624 | 0.421437 | ||||||||
\(254\) | −389.730 | − | 270.533i | −1.53437 | − | 1.06509i | ||||
\(255\) | −459.861 | + | 492.509i | −1.80338 | + | 1.93141i | ||||
\(256\) | 36.2155 | − | 253.425i | 0.141467 | − | 0.989943i | ||||
\(257\) | 101.903i | 0.396510i | 0.980151 | + | 0.198255i | \(0.0635274\pi\) | ||||
−0.980151 | + | 0.198255i | \(0.936473\pi\) | |||||||
\(258\) | 293.035 | − | 52.9017i | 1.13579 | − | 0.205045i | ||||
\(259\) | 140.623 | 0.542946 | ||||||||
\(260\) | −200.117 | + | 438.443i | −0.769679 | + | 1.68632i | ||||
\(261\) | −264.706 | − | 264.706i | −1.01420 | − | 1.01420i | ||||
\(262\) | −19.2580 | − | 106.675i | −0.0735039 | − | 0.407155i | ||||
\(263\) | 196.170 | 0.745892 | 0.372946 | − | 0.927853i | \(-0.378348\pi\) | ||||
0.372946 | + | 0.927853i | \(0.378348\pi\) | |||||||
\(264\) | 151.983 | − | 596.264i | 0.575694 | − | 2.25858i | ||||
\(265\) | 82.7340 | − | 82.7340i | 0.312204 | − | 0.312204i | ||||
\(266\) | 86.0328 | − | 15.5315i | 0.323431 | − | 0.0583892i | ||||
\(267\) | 334.854 | + | 334.854i | 1.25413 | + | 1.25413i | ||||
\(268\) | −114.574 | − | 306.985i | −0.427516 | − | 1.14547i | ||||
\(269\) | −1.93426 | + | 1.93426i | −0.00719055 | + | 0.00719055i | −0.710693 | − | 0.703502i | \(-0.751618\pi\) |
0.703502 | + | 0.710693i | \(0.251618\pi\) | |||||||
\(270\) | 285.136 | − | 410.767i | 1.05606 | − | 1.52136i | ||||
\(271\) | 42.2327i | 0.155840i | 0.996960 | + | 0.0779201i | \(0.0248279\pi\) | ||||
−0.996960 | + | 0.0779201i | \(0.975172\pi\) | |||||||
\(272\) | 9.98121 | − | 271.817i | 0.0366956 | − | 0.999326i | ||||
\(273\) | 315.004 | 1.15386 | ||||||||
\(274\) | −160.155 | − | 111.172i | −0.584507 | − | 0.405738i | ||||
\(275\) | −437.200 | − | 437.200i | −1.58982 | − | 1.58982i | ||||
\(276\) | −126.276 | + | 47.1294i | −0.457522 | + | 0.170759i | ||||
\(277\) | −100.385 | + | 100.385i | −0.362401 | + | 0.362401i | −0.864696 | − | 0.502295i | \(-0.832489\pi\) |
0.502295 | + | 0.864696i | \(0.332489\pi\) | |||||||
\(278\) | −5.70081 | − | 31.5781i | −0.0205065 | − | 0.113590i | ||||
\(279\) | 156.186 | + | 156.186i | 0.559805 | + | 0.559805i | ||||
\(280\) | −67.7217 | + | 265.687i | −0.241863 | + | 0.948884i | ||||
\(281\) | − | 270.323i | − | 0.962002i | −0.876720 | − | 0.481001i | \(-0.840273\pi\) | ||
0.876720 | − | 0.481001i | \(-0.159727\pi\) | |||||||
\(282\) | −657.763 | + | 118.746i | −2.33249 | + | 0.421086i | ||||
\(283\) | 16.2495 | − | 16.2495i | 0.0574187 | − | 0.0574187i | −0.677814 | − | 0.735233i | \(-0.737073\pi\) |
0.735233 | + | 0.677814i | \(0.237073\pi\) | |||||||
\(284\) | −14.0398 | − | 6.40814i | −0.0494360 | − | 0.0225639i | ||||
\(285\) | − | 406.415i | − | 1.42602i | ||||||
\(286\) | −83.0771 | − | 460.184i | −0.290479 | − | 1.60903i | ||||
\(287\) | 296.449 | 1.03292 | ||||||||
\(288\) | 52.6230 | + | 487.012i | 0.182719 | + | 1.69101i | ||||
\(289\) | −19.7912 | − | 288.322i | −0.0684815 | − | 0.997652i | ||||
\(290\) | 224.222 | − | 323.015i | 0.773179 | − | 1.11384i | ||||
\(291\) | 564.002i | 1.93815i | ||||||||
\(292\) | 189.297 | − | 414.738i | 0.648278 | − | 1.42034i | ||||
\(293\) | 130.049i | 0.443852i | 0.975063 | + | 0.221926i | \(0.0712344\pi\) | ||||
−0.975063 | + | 0.221926i | \(0.928766\pi\) | |||||||
\(294\) | −299.127 | + | 54.0015i | −1.01744 | + | 0.183679i | ||||
\(295\) | 17.3837 | + | 17.3837i | 0.0589278 | + | 0.0589278i | ||||
\(296\) | 134.728 | + | 226.905i | 0.455161 | + | 0.766571i | ||||
\(297\) | 485.164i | 1.63355i | ||||||||
\(298\) | 53.7458 | − | 77.4264i | 0.180355 | − | 0.259820i | ||||
\(299\) | −72.4291 | + | 72.4291i | −0.242238 | + | 0.242238i | ||||
\(300\) | 711.033 | + | 324.534i | 2.37011 | + | 1.08178i | ||||
\(301\) | 91.0314 | − | 91.0314i | 0.302430 | − | 0.302430i | ||||
\(302\) | 161.377 | + | 112.021i | 0.534362 | + | 0.370929i | ||||
\(303\) | 372.633 | − | 372.633i | 1.22981 | − | 1.22981i | ||||
\(304\) | 107.487 | + | 123.940i | 0.353576 | + | 0.407696i | ||||
\(305\) | −401.866 | −1.31759 | ||||||||
\(306\) | 109.958 | + | 508.714i | 0.359340 | + | 1.66246i | ||||
\(307\) | −288.357 | −0.939273 | −0.469637 | − | 0.882860i | \(-0.655615\pi\) | ||||
−0.469637 | + | 0.882860i | \(0.655615\pi\) | |||||||
\(308\) | −93.0212 | − | 249.237i | −0.302017 | − | 0.809210i | ||||
\(309\) | −681.718 | + | 681.718i | −2.20621 | + | 2.20621i | ||||
\(310\) | −132.298 | + | 190.589i | −0.426769 | + | 0.614804i | ||||
\(311\) | 31.5824 | − | 31.5824i | 0.101551 | − | 0.101551i | −0.654506 | − | 0.756057i | \(-0.727123\pi\) |
0.756057 | + | 0.654506i | \(0.227123\pi\) | |||||||
\(312\) | 301.798 | + | 508.282i | 0.967303 | + | 1.62911i | ||||
\(313\) | 11.8712 | − | 11.8712i | 0.0379272 | − | 0.0379272i | −0.687889 | − | 0.725816i | \(-0.741462\pi\) |
0.725816 | + | 0.687889i | \(0.241462\pi\) | |||||||
\(314\) | 131.545 | − | 189.504i | 0.418932 | − | 0.603515i | ||||
\(315\) | − | 524.638i | − | 1.66552i | ||||||
\(316\) | 15.5890 | − | 34.1545i | 0.0493323 | − | 0.108084i | ||||
\(317\) | −79.1608 | − | 79.1608i | −0.249719 | − | 0.249719i | 0.571136 | − | 0.820855i | \(-0.306503\pi\) |
−0.820855 | + | 0.571136i | \(0.806503\pi\) | |||||||
\(318\) | −25.4954 | − | 141.225i | −0.0801743 | − | 0.444104i | ||||
\(319\) | 381.518i | 1.19598i | ||||||||
\(320\) | −493.588 | + | 145.275i | −1.54246 | + | 0.453985i | ||||
\(321\) | − | 203.884i | − | 0.635152i | ||||||
\(322\) | −33.2289 | + | 47.8697i | −0.103195 | + | 0.148664i | ||||
\(323\) | 127.406 | + | 118.961i | 0.394447 | + | 0.368299i | ||||
\(324\) | −21.7580 | − | 58.2974i | −0.0671544 | − | 0.179930i | ||||
\(325\) | 593.977 | 1.82762 | ||||||||
\(326\) | −276.305 | + | 49.8815i | −0.847562 | + | 0.153011i | ||||
\(327\) | − | 877.133i | − | 2.68236i | ||||||
\(328\) | 284.021 | + | 478.341i | 0.865916 | + | 1.45836i | ||||
\(329\) | −204.334 | + | 204.334i | −0.621077 | + | 0.621077i | ||||
\(330\) | −1217.05 | + | 219.714i | −3.68803 | + | 0.665801i | ||||
\(331\) | − | 70.7790i | − | 0.213834i | −0.994268 | − | 0.106917i | \(-0.965902\pi\) | ||
0.994268 | − | 0.106917i | \(-0.0340979\pi\) | |||||||
\(332\) | −15.2640 | + | 5.69691i | −0.0459759 | + | 0.0171594i | ||||
\(333\) | −357.048 | − | 357.048i | −1.07222 | − | 1.07222i | ||||
\(334\) | −527.656 | + | 95.2580i | −1.57981 | + | 0.285204i | ||||
\(335\) | −465.678 | + | 465.678i | −1.39008 | + | 1.39008i | ||||
\(336\) | 220.333 | + | 254.058i | 0.655754 | + | 0.756126i | ||||
\(337\) | 359.334 | + | 359.334i | 1.06627 | + | 1.06627i | 0.997642 | + | 0.0686301i | \(0.0218628\pi\) |
0.0686301 | + | 0.997642i | \(0.478137\pi\) | |||||||
\(338\) | 91.3743 | + | 63.4278i | 0.270338 | + | 0.187656i | ||||
\(339\) | −371.104 | −1.09470 | ||||||||
\(340\) | −505.322 | + | 208.590i | −1.48624 | + | 0.613501i | ||||
\(341\) | − | 225.108i | − | 0.660141i | ||||||
\(342\) | −257.876 | − | 179.006i | −0.754024 | − | 0.523408i | ||||
\(343\) | −240.633 | + | 240.633i | −0.701553 | + | 0.701553i | ||||
\(344\) | 234.101 | + | 59.6705i | 0.680525 | + | 0.173461i | ||||
\(345\) | 191.553 | + | 191.553i | 0.555227 | + | 0.555227i | ||||
\(346\) | 195.031 | − | 35.2090i | 0.563672 | − | 0.101760i | ||||
\(347\) | 239.694 | − | 239.694i | 0.690761 | − | 0.690761i | −0.271638 | − | 0.962399i | \(-0.587565\pi\) |
0.962399 | + | 0.271638i | \(0.0875654\pi\) | |||||||
\(348\) | −168.637 | − | 451.838i | −0.484589 | − | 1.29839i | ||||
\(349\) | 96.6762 | 0.277009 | 0.138505 | − | 0.990362i | \(-0.455770\pi\) | ||||
0.138505 | + | 0.990362i | \(0.455770\pi\) | |||||||
\(350\) | 332.537 | − | 60.0331i | 0.950106 | − | 0.171523i | ||||
\(351\) | −329.570 | − | 329.570i | −0.938946 | − | 0.938946i | ||||
\(352\) | 313.039 | − | 388.884i | 0.889316 | − | 1.10478i | ||||
\(353\) | −151.648 | −0.429597 | −0.214799 | − | 0.976658i | \(-0.568910\pi\) | ||||
−0.214799 | + | 0.976658i | \(0.568910\pi\) | |||||||
\(354\) | 29.6736 | − | 5.35699i | 0.0838237 | − | 0.0151327i | ||||
\(355\) | 31.0183i | 0.0873756i | ||||||||
\(356\) | 134.341 | + | 359.948i | 0.377364 | + | 1.01109i | ||||
\(357\) | 261.164 | + | 243.852i | 0.731553 | + | 0.683059i | ||||
\(358\) | −21.8584 | + | 31.4893i | −0.0610571 | + | 0.0879590i | ||||
\(359\) | 250.419 | 0.697545 | 0.348773 | − | 0.937207i | \(-0.386599\pi\) | ||||
0.348773 | + | 0.937207i | \(0.386599\pi\) | |||||||
\(360\) | 846.540 | − | 502.643i | 2.35150 | − | 1.39623i | ||||
\(361\) | 255.865 | 0.708768 | ||||||||
\(362\) | 5.45697 | + | 30.2274i | 0.0150745 | + | 0.0835012i | ||||
\(363\) | 426.657 | − | 426.657i | 1.17536 | − | 1.17536i | ||||
\(364\) | 232.495 | + | 106.117i | 0.638721 | + | 0.291529i | ||||
\(365\) | −916.285 | −2.51037 | ||||||||
\(366\) | −281.069 | + | 404.908i | −0.767947 | + | 1.10631i | ||||
\(367\) | −220.037 | − | 220.037i | −0.599555 | − | 0.599555i | 0.340639 | − | 0.940194i | \(-0.389356\pi\) |
−0.940194 | + | 0.340639i | \(0.889356\pi\) | |||||||
\(368\) | −109.077 | − | 7.75438i | −0.296405 | − | 0.0210717i | ||||
\(369\) | −752.696 | − | 752.696i | −2.03983 | − | 2.03983i | ||||
\(370\) | 302.441 | − | 435.697i | 0.817407 | − | 1.17756i | ||||
\(371\) | −43.8716 | − | 43.8716i | −0.118252 | − | 0.118252i | ||||
\(372\) | 99.5015 | + | 266.600i | 0.267477 | + | 0.716665i | ||||
\(373\) | 366.462i | 0.982472i | 0.871027 | + | 0.491236i | \(0.163455\pi\) | ||||
−0.871027 | + | 0.491236i | \(0.836545\pi\) | |||||||
\(374\) | 287.361 | − | 445.842i | 0.768344 | − | 1.19209i | ||||
\(375\) | − | 579.976i | − | 1.54660i | ||||||
\(376\) | −525.476 | − | 133.940i | −1.39754 | − | 0.356223i | ||||
\(377\) | −259.164 | − | 259.164i | −0.687437 | − | 0.687437i | ||||
\(378\) | −217.819 | − | 151.200i | −0.576241 | − | 0.399999i | ||||
\(379\) | −353.592 | − | 353.592i | −0.932961 | − | 0.932961i | 0.0649288 | − | 0.997890i | \(-0.479318\pi\) |
−0.997890 | + | 0.0649288i | \(0.979318\pi\) | |||||||
\(380\) | 136.910 | − | 299.962i | 0.360291 | − | 0.789374i | ||||
\(381\) | 826.976 | + | 826.976i | 2.17054 | + | 2.17054i | ||||
\(382\) | −3.29523 | + | 4.74712i | −0.00862625 | + | 0.0124270i | ||||
\(383\) | 236.241 | 0.616817 | 0.308409 | − | 0.951254i | \(-0.400204\pi\) | ||||
0.308409 | + | 0.951254i | \(0.400204\pi\) | |||||||
\(384\) | −198.845 | + | 598.931i | −0.517825 | + | 1.55972i | ||||
\(385\) | −378.077 | + | 378.077i | −0.982018 | + | 0.982018i | ||||
\(386\) | 142.848 | − | 25.7885i | 0.370074 | − | 0.0668096i | ||||
\(387\) | −462.265 | −1.19448 | ||||||||
\(388\) | −189.997 | + | 416.272i | −0.489684 | + | 1.07287i | ||||
\(389\) | −708.253 | −1.82070 | −0.910350 | − | 0.413838i | \(-0.864188\pi\) | ||||
−0.910350 | + | 0.413838i | \(0.864188\pi\) | |||||||
\(390\) | 677.486 | − | 975.988i | 1.73714 | − | 2.50253i | ||||
\(391\) | −116.119 | + | 3.98066i | −0.296979 | + | 0.0101807i | ||||
\(392\) | −238.968 | − | 60.9111i | −0.609611 | − | 0.155385i | ||||
\(393\) | 267.219i | 0.679947i | ||||||||
\(394\) | −104.432 | − | 578.471i | −0.265055 | − | 1.46820i | ||||
\(395\) | −75.4580 | −0.191033 | ||||||||
\(396\) | −396.637 | + | 869.007i | −1.00161 | + | 2.19446i | ||||
\(397\) | −100.242 | − | 100.242i | −0.252498 | − | 0.252498i | 0.569496 | − | 0.821994i | \(-0.307138\pi\) |
−0.821994 | + | 0.569496i | \(0.807138\pi\) | |||||||
\(398\) | 282.002 | − | 50.9100i | 0.708548 | − | 0.127914i | ||||
\(399\) | −215.511 | −0.540128 | ||||||||
\(400\) | 415.464 | + | 479.056i | 1.03866 | + | 1.19764i | ||||
\(401\) | 264.727 | − | 264.727i | 0.660168 | − | 0.660168i | −0.295252 | − | 0.955419i | \(-0.595404\pi\) |
0.955419 | + | 0.295252i | \(0.0954036\pi\) | |||||||
\(402\) | 143.504 | + | 794.901i | 0.356975 | + | 1.97737i | ||||
\(403\) | 152.915 | + | 152.915i | 0.379442 | + | 0.379442i | ||||
\(404\) | 400.558 | − | 149.498i | 0.991481 | − | 0.370045i | ||||
\(405\) | −88.4336 | + | 88.4336i | −0.218355 | + | 0.218355i | ||||
\(406\) | −171.286 | − | 118.899i | −0.421887 | − | 0.292854i | ||||
\(407\) | 514.608i | 1.26439i | ||||||||
\(408\) | −143.257 | + | 655.036i | −0.351120 | + | 1.60548i | ||||
\(409\) | 572.788 | 1.40046 | 0.700229 | − | 0.713918i | \(-0.253081\pi\) | ||||
0.700229 | + | 0.713918i | \(0.253081\pi\) | |||||||
\(410\) | 637.578 | − | 918.496i | 1.55507 | − | 2.24024i | ||||
\(411\) | 339.836 | + | 339.836i | 0.826852 | + | 0.826852i | ||||
\(412\) | −732.807 | + | 273.502i | −1.77866 | + | 0.663839i | ||||
\(413\) | 9.21812 | − | 9.21812i | 0.0223199 | − | 0.0223199i | ||||
\(414\) | 205.913 | − | 37.1736i | 0.497374 | − | 0.0897912i | ||||
\(415\) | 23.1546 | + | 23.1546i | 0.0557942 | + | 0.0557942i | ||||
\(416\) | 51.5211 | + | 476.814i | 0.123849 | + | 1.14619i | ||||
\(417\) | 79.1028i | 0.189695i | ||||||||
\(418\) | 56.8375 | + | 314.836i | 0.135975 | + | 0.753196i | ||||
\(419\) | 285.422 | − | 285.422i | 0.681198 | − | 0.681198i | −0.279072 | − | 0.960270i | \(-0.590027\pi\) |
0.960270 | + | 0.279072i | \(0.0900268\pi\) | |||||||
\(420\) | 280.647 | − | 614.879i | 0.668207 | − | 1.46400i | ||||
\(421\) | − | 125.339i | − | 0.297717i | −0.988858 | − | 0.148859i | \(-0.952440\pi\) | ||
0.988858 | − | 0.148859i | \(-0.0475599\pi\) | |||||||
\(422\) | 339.852 | − | 61.3536i | 0.805336 | − | 0.145388i | ||||
\(423\) | 1037.63 | 2.45302 | ||||||||
\(424\) | 28.7576 | − | 112.822i | 0.0678245 | − | 0.266091i | ||||
\(425\) | 492.455 | + | 459.811i | 1.15872 | + | 1.08191i | ||||
\(426\) | 31.2531 | + | 21.6945i | 0.0733641 | + | 0.0509260i | ||||
\(427\) | 213.099i | 0.499061i | ||||||||
\(428\) | 68.6829 | − | 150.480i | 0.160474 | − | 0.351589i | ||||
\(429\) | 1152.76i | 2.68708i | ||||||||
\(430\) | −86.2626 | − | 477.829i | −0.200611 | − | 1.11123i | ||||
\(431\) | −464.382 | − | 464.382i | −1.07745 | − | 1.07745i | −0.996737 | − | 0.0807163i | \(-0.974279\pi\) |
−0.0807163 | − | 0.996737i | \(-0.525721\pi\) | |||||||
\(432\) | 35.2843 | − | 496.327i | 0.0816767 | − | 1.14891i | ||||
\(433\) | − | 10.8152i | − | 0.0249774i | −0.999922 | − | 0.0124887i | \(-0.996025\pi\) | ||
0.999922 | − | 0.0124887i | \(-0.00397537\pi\) | |||||||
\(434\) | 101.064 | + | 70.1543i | 0.232868 | + | 0.161646i | ||||
\(435\) | −685.411 | + | 685.411i | −1.57566 | + | 1.57566i | ||||
\(436\) | 295.483 | − | 647.384i | 0.677712 | − | 1.48482i | ||||
\(437\) | 49.5526 | − | 49.5526i | 0.113393 | − | 0.113393i | ||||
\(438\) | −640.857 | + | 923.221i | −1.46314 | + | 2.10781i | ||||
\(439\) | −204.530 | + | 204.530i | −0.465899 | + | 0.465899i | −0.900583 | − | 0.434684i | \(-0.856860\pi\) |
0.434684 | + | 0.900583i | \(0.356860\pi\) | |||||||
\(440\) | −972.280 | − | 247.827i | −2.20973 | − | 0.563243i | ||||
\(441\) | 471.876 | 1.07001 | ||||||||
\(442\) | 107.656 | + | 498.062i | 0.243565 | + | 1.12684i | ||||
\(443\) | −421.536 | −0.951549 | −0.475774 | − | 0.879567i | \(-0.657832\pi\) | ||||
−0.475774 | + | 0.879567i | \(0.657832\pi\) | |||||||
\(444\) | −227.465 | − | 609.460i | −0.512310 | − | 1.37266i | ||||
\(445\) | 546.019 | − | 546.019i | 1.22701 | − | 1.22701i | ||||
\(446\) | 316.369 | + | 219.609i | 0.709348 | + | 0.492397i | ||||
\(447\) | −164.293 | + | 164.293i | −0.367545 | + | 0.367545i | ||||
\(448\) | 77.0355 | + | 261.737i | 0.171954 | + | 0.584234i | ||||
\(449\) | 243.909 | − | 243.909i | 0.543227 | − | 0.543227i | −0.381247 | − | 0.924473i | \(-0.624505\pi\) |
0.924473 | + | 0.381247i | \(0.124505\pi\) | |||||||
\(450\) | −996.753 | − | 691.900i | −2.21501 | − | 1.53755i | ||||
\(451\) | 1084.85i | 2.40543i | ||||||||
\(452\) | −273.900 | − | 125.015i | −0.605972 | − | 0.276582i | ||||
\(453\) | −342.429 | − | 342.429i | −0.755915 | − | 0.755915i | ||||
\(454\) | 245.521 | − | 44.3241i | 0.540796 | − | 0.0976302i | ||||
\(455\) | − | 513.653i | − | 1.12891i | ||||||
\(456\) | −206.476 | − | 347.743i | −0.452799 | − | 0.762594i | ||||
\(457\) | 531.965i | 1.16404i | 0.813176 | + | 0.582018i | \(0.197737\pi\) | ||||
−0.813176 | + | 0.582018i | \(0.802263\pi\) | |||||||
\(458\) | −295.898 | − | 205.399i | −0.646066 | − | 0.448469i | ||||
\(459\) | −18.1130 | − | 528.368i | −0.0394618 | − | 1.15113i | ||||
\(460\) | 76.8502 | + | 205.909i | 0.167066 | + | 0.447627i | ||||
\(461\) | 867.923 | 1.88270 | 0.941348 | − | 0.337437i | \(-0.109560\pi\) | ||||
0.941348 | + | 0.337437i | \(0.109560\pi\) | |||||||
\(462\) | 116.509 | + | 645.369i | 0.252183 | + | 1.39690i | ||||
\(463\) | − | 649.150i | − | 1.40205i | −0.713135 | − | 0.701026i | \(-0.752726\pi\) | ||
0.713135 | − | 0.701026i | \(-0.247274\pi\) | |||||||
\(464\) | 27.7465 | − | 390.296i | 0.0597985 | − | 0.841156i | ||||
\(465\) | 404.415 | − | 404.415i | 0.869711 | − | 0.869711i | ||||
\(466\) | −80.9099 | − | 448.179i | −0.173626 | − | 0.961757i | ||||
\(467\) | − | 492.375i | − | 1.05434i | −0.849761 | − | 0.527168i | \(-0.823254\pi\) | ||
0.849761 | − | 0.527168i | \(-0.176746\pi\) | |||||||
\(468\) | −320.879 | − | 859.748i | −0.685640 | − | 1.83707i | ||||
\(469\) | 246.937 | + | 246.937i | 0.526517 | + | 0.526517i | ||||
\(470\) | 193.630 | + | 1072.56i | 0.411979 | + | 2.28205i | ||||
\(471\) | −402.112 | + | 402.112i | −0.853741 | + | 0.853741i | ||||
\(472\) | 23.7058 | + | 6.04242i | 0.0502240 | + | 0.0128017i | ||||
\(473\) | 333.129 | + | 333.129i | 0.704289 | + | 0.704289i | ||||
\(474\) | −52.7759 | + | 76.0291i | −0.111342 | + | 0.160399i | ||||
\(475\) | −406.371 | −0.855518 | ||||||||
\(476\) | 110.610 | + | 267.959i | 0.232374 | + | 0.562938i | ||||
\(477\) | 222.784i | 0.467052i | ||||||||
\(478\) | −436.030 | + | 628.147i | −0.912197 | + | 1.31411i | ||||
\(479\) | 476.562 | − | 476.562i | 0.994910 | − | 0.994910i | −0.00507662 | − | 0.999987i | \(-0.501616\pi\) |
0.999987 | + | 0.00507662i | \(0.00161594\pi\) | |||||||
\(480\) | 1261.03 | − | 136.258i | 2.62715 | − | 0.283871i | ||||
\(481\) | −349.572 | − | 349.572i | −0.726761 | − | 0.726761i | ||||
\(482\) | 43.8564 | + | 242.931i | 0.0909884 | + | 0.504006i | ||||
\(483\) | 101.576 | − | 101.576i | 0.210302 | − | 0.210302i | ||||
\(484\) | 458.631 | − | 171.173i | 0.947585 | − | 0.353662i | ||||
\(485\) | 919.674 | 1.89623 | ||||||||
\(486\) | −72.1974 | − | 399.918i | −0.148554 | − | 0.822877i | ||||
\(487\) | −273.707 | − | 273.707i | −0.562027 | − | 0.562027i | 0.367856 | − | 0.929883i | \(-0.380092\pi\) |
−0.929883 | + | 0.367856i | \(0.880092\pi\) | |||||||
\(488\) | −343.850 | + | 204.165i | −0.704611 | + | 0.418371i | ||||
\(489\) | 692.142 | 1.41542 | ||||||||
\(490\) | 88.0560 | + | 487.762i | 0.179706 | + | 0.995434i | ||||
\(491\) | 6.68678i | 0.0136187i | 0.999977 | + | 0.00680935i | \(0.00216750\pi\) | ||||
−0.999977 | + | 0.00680935i | \(0.997832\pi\) | |||||||
\(492\) | −479.522 | − | 1284.81i | −0.974638 | − | 2.61140i | ||||
\(493\) | −14.2435 | − | 415.493i | −0.0288915 | − | 0.842784i | ||||
\(494\) | −252.477 | − | 175.258i | −0.511086 | − | 0.354772i | ||||
\(495\) | 1919.91 | 3.87860 | ||||||||
\(496\) | −16.3714 | + | 230.288i | −0.0330068 | + | 0.464290i | ||||
\(497\) | 16.4482 | 0.0330950 | ||||||||
\(498\) | 39.5244 | − | 7.13535i | 0.0793662 | − | 0.0143280i | ||||
\(499\) | −43.4592 | + | 43.4592i | −0.0870926 | + | 0.0870926i | −0.749311 | − | 0.662218i | \(-0.769615\pi\) |
0.662218 | + | 0.749311i | \(0.269615\pi\) | |||||||
\(500\) | 195.378 | − | 428.062i | 0.390757 | − | 0.856124i | ||||
\(501\) | 1321.77 | 2.63827 | ||||||||
\(502\) | −499.317 | − | 346.603i | −0.994655 | − | 0.690443i | ||||
\(503\) | 226.691 | + | 226.691i | 0.450678 | + | 0.450678i | 0.895580 | − | 0.444901i | \(-0.146761\pi\) |
−0.444901 | + | 0.895580i | \(0.646761\pi\) | |||||||
\(504\) | −266.538 | − | 448.898i | −0.528846 | − | 0.890670i | ||||
\(505\) | −607.623 | − | 607.623i | −1.20321 | − | 1.20321i | ||||
\(506\) | −175.179 | − | 121.601i | −0.346203 | − | 0.240318i | ||||
\(507\) | −193.889 | − | 193.889i | −0.382424 | − | 0.382424i | ||||
\(508\) | 331.778 | + | 888.951i | 0.653107 | + | 1.74990i | ||||
\(509\) | 896.044i | 1.76040i | 0.474601 | + | 0.880201i | \(0.342592\pi\) | ||||
−0.474601 | + | 0.880201i | \(0.657408\pi\) | |||||||
\(510\) | 1317.23 | − | 284.717i | 2.58280 | − | 0.558269i | ||||
\(511\) | 485.882i | 0.950845i | ||||||||
\(512\) | −348.525 | + | 375.066i | −0.680712 | + | 0.732551i | ||||
\(513\) | 225.476 | + | 225.476i | 0.439525 | + | 0.439525i | ||||
\(514\) | 116.217 | − | 167.423i | 0.226104 | − | 0.325725i | ||||
\(515\) | 1111.62 | + | 1111.62i | 2.15849 | + | 2.15849i | ||||
\(516\) | −541.778 | − | 247.282i | −1.04996 | − | 0.479228i | ||||
\(517\) | −747.760 | − | 747.760i | −1.44634 | − | 1.44634i | ||||
\(518\) | −231.038 | − | 160.376i | −0.446020 | − | 0.309607i | ||||
\(519\) | −488.550 | −0.941329 | ||||||||
\(520\) | 828.815 | − | 492.119i | 1.59388 | − | 0.946382i | ||||
\(521\) | 606.761 | − | 606.761i | 1.16461 | − | 1.16461i | 0.181153 | − | 0.983455i | \(-0.442017\pi\) |
0.983455 | − | 0.181153i | \(-0.0579829\pi\) | |||||||
\(522\) | 133.013 | + | 736.792i | 0.254815 | + | 1.41148i | ||||
\(523\) | 549.518 | 1.05070 | 0.525352 | − | 0.850885i | \(-0.323934\pi\) | ||||
0.525352 | + | 0.850885i | \(0.323934\pi\) | |||||||
\(524\) | −90.0190 | + | 197.226i | −0.171792 | + | 0.376385i | ||||
\(525\) | −833.002 | −1.58667 | ||||||||
\(526\) | −322.300 | − | 223.725i | −0.612737 | − | 0.425334i | ||||
\(527\) | 8.40414 | + | 245.154i | 0.0159471 | + | 0.465189i | ||||
\(528\) | −929.724 | + | 806.308i | −1.76084 | + | 1.52710i | ||||
\(529\) | − | 482.289i | − | 0.911700i | ||||||
\(530\) | −230.285 | + | 41.5734i | −0.434499 | + | 0.0784403i | ||||
\(531\) | −46.8104 | −0.0881552 | ||||||||
\(532\) | −159.062 | − | 72.6000i | −0.298989 | − | 0.136466i | ||||
\(533\) | −736.936 | − | 736.936i | −1.38262 | − | 1.38262i | ||||
\(534\) | −168.262 | − | 932.042i | −0.315097 | − | 1.74540i | ||||
\(535\) | −332.457 | −0.621415 | ||||||||
\(536\) | −161.865 | + | 635.034i | −0.301988 | + | 1.18476i | ||||
\(537\) | 66.8178 | − | 66.8178i | 0.124428 | − | 0.124428i | ||||
\(538\) | 5.38388 | − | 0.971954i | 0.0100072 | − | 0.00180661i | ||||
\(539\) | −340.054 | − | 340.054i | −0.630898 | − | 0.630898i | ||||
\(540\) | −936.935 | + | 349.687i | −1.73506 | + | 0.647569i | ||||
\(541\) | 154.714 | − | 154.714i | 0.285978 | − | 0.285978i | −0.549509 | − | 0.835488i | \(-0.685185\pi\) |
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(542\) | 48.1651 | − | 69.3868i | 0.0888655 | − | 0.128020i | ||||
\(543\) | − | 75.7194i | − | 0.139446i | ||||||
\(544\) | −326.397 | + | 435.202i | −0.599995 | + | 0.800003i | ||||
\(545\) | −1430.27 | −2.62435 | ||||||||
\(546\) | −517.541 | − | 359.253i | −0.947877 | − | 0.657972i | ||||
\(547\) | 367.807 | + | 367.807i | 0.672408 | + | 0.672408i | 0.958271 | − | 0.285863i | \(-0.0922801\pi\) |
−0.285863 | + | 0.958271i | \(0.592280\pi\) | |||||||
\(548\) | 136.340 | + | 365.304i | 0.248796 | + | 0.666613i | ||||
\(549\) | 541.068 | − | 541.068i | 0.985551 | − | 0.985551i | ||||
\(550\) | 219.690 | + | 1216.92i | 0.399437 | + | 2.21258i | ||||
\(551\) | 177.308 | + | 177.308i | 0.321793 | + | 0.321793i | ||||
\(552\) | 261.217 | + | 66.5822i | 0.473219 | + | 0.120620i | ||||
\(553\) | 40.0134i | 0.0723569i | ||||||||
\(554\) | 279.416 | − | 50.4430i | 0.504360 | − | 0.0910524i | ||||
\(555\) | −924.514 | + | 924.514i | −1.66579 | + | 1.66579i | ||||
\(556\) | −26.6476 | + | 58.3833i | −0.0479274 | + | 0.105006i | ||||
\(557\) | 245.377i | 0.440533i | 0.975440 | + | 0.220266i | \(0.0706927\pi\) | ||||
−0.975440 | + | 0.220266i | \(0.929307\pi\) | |||||||
\(558\) | −78.4823 | − | 434.732i | −0.140649 | − | 0.779089i | ||||
\(559\) | −452.586 | −0.809636 | ||||||||
\(560\) | 414.273 | − | 359.280i | 0.739773 | − | 0.641572i | ||||
\(561\) | −892.374 | + | 955.729i | −1.59068 | + | 1.70362i | ||||
\(562\) | −308.295 | + | 444.130i | −0.548567 | + | 0.790267i | ||||
\(563\) | − | 639.761i | − | 1.13634i | −0.822910 | − | 0.568171i | \(-0.807651\pi\) | ||
0.822910 | − | 0.568171i | \(-0.192349\pi\) | |||||||
\(564\) | 1216.11 | + | 555.063i | 2.15622 | + | 0.984154i | ||||
\(565\) | 605.129i | 1.07102i | ||||||||
\(566\) | −45.2294 | + | 8.16528i | −0.0799105 | + | 0.0144263i | ||||
\(567\) | 46.8940 | + | 46.8940i | 0.0827055 | + | 0.0827055i | ||||
\(568\) | 15.7586 | + | 26.5403i | 0.0277441 | + | 0.0467259i | ||||
\(569\) | 518.845i | 0.911855i | 0.890017 | + | 0.455927i | \(0.150692\pi\) | ||||
−0.890017 | + | 0.455927i | \(0.849308\pi\) | |||||||
\(570\) | −463.504 | + | 667.726i | −0.813165 | + | 1.17145i | ||||
\(571\) | 601.990 | − | 601.990i | 1.05427 | − | 1.05427i | 0.0558335 | − | 0.998440i | \(-0.482218\pi\) |
0.998440 | − | 0.0558335i | \(-0.0177816\pi\) | |||||||
\(572\) | −388.332 | + | 850.812i | −0.678903 | + | 1.48743i | ||||
\(573\) | 10.0730 | − | 10.0730i | 0.0175794 | − | 0.0175794i | ||||
\(574\) | −487.054 | − | 338.091i | −0.848527 | − | 0.589008i | ||||
\(575\) | 191.533 | − | 191.533i | 0.333100 | − | 0.333100i | ||||
\(576\) | 468.964 | − | 860.157i | 0.814174 | − | 1.49333i | ||||
\(577\) | −895.276 | −1.55160 | −0.775802 | − | 0.630976i | \(-0.782655\pi\) | ||||
−0.775802 | + | 0.630976i | \(0.782655\pi\) | |||||||
\(578\) | −296.306 | + | 496.273i | −0.512640 | + | 0.858604i | ||||
\(579\) | −357.834 | −0.618021 | ||||||||
\(580\) | −736.777 | + | 274.983i | −1.27030 | + | 0.474109i | ||||
\(581\) | 12.2783 | − | 12.2783i | 0.0211330 | − | 0.0211330i | ||||
\(582\) | 643.227 | − | 926.635i | 1.10520 | − | 1.59216i | ||||
\(583\) | 160.548 | − | 160.548i | 0.275382 | − | 0.275382i | ||||
\(584\) | −784.005 | + | 465.512i | −1.34247 | + | 0.797110i | ||||
\(585\) | −1304.19 | + | 1304.19i | −2.22938 | + | 2.22938i | ||||
\(586\) | 148.317 | − | 213.665i | 0.253100 | − | 0.364617i | ||||
\(587\) | 266.131i | 0.453374i | 0.973968 | + | 0.226687i | \(0.0727894\pi\) | ||||
−0.973968 | + | 0.226687i | \(0.927211\pi\) | |||||||
\(588\) | 553.042 | + | 252.423i | 0.940547 | + | 0.429290i | ||||
\(589\) | −104.617 | − | 104.617i | −0.177619 | − | 0.177619i | ||||
\(590\) | −8.73521 | − | 48.3864i | −0.0148054 | − | 0.0820108i | ||||
\(591\) | 1449.06i | 2.45189i | ||||||||
\(592\) | 37.4257 | − | 526.450i | 0.0632192 | − | 0.889273i | ||||
\(593\) | − | 180.986i | − | 0.305203i | −0.988288 | − | 0.152602i | \(-0.951235\pi\) | ||
0.988288 | − | 0.152602i | \(-0.0487651\pi\) | |||||||
\(594\) | 553.314 | − | 797.106i | 0.931505 | − | 1.34193i | ||||
\(595\) | 397.630 | − | 425.860i | 0.668286 | − | 0.715732i | ||||
\(596\) | −176.605 | + | 65.9133i | −0.296317 | + | 0.110593i | ||||
\(597\) | −706.413 | −1.18327 | ||||||||
\(598\) | 201.601 | − | 36.3952i | 0.337126 | − | 0.0608615i | ||||
\(599\) | 760.421i | 1.26948i | 0.772724 | + | 0.634742i | \(0.218894\pi\) | ||||
−0.772724 | + | 0.634742i | \(0.781106\pi\) | |||||||
\(600\) | −798.080 | − | 1344.11i | −1.33013 | − | 2.24018i | ||||
\(601\) | 176.857 | − | 176.857i | 0.294271 | − | 0.294271i | −0.544494 | − | 0.838765i | \(-0.683278\pi\) |
0.838765 | + | 0.544494i | \(0.183278\pi\) | |||||||
\(602\) | −253.380 | + | 45.7428i | −0.420897 | + | 0.0759847i | ||||
\(603\) | − | 1253.97i | − | 2.07954i | ||||||
\(604\) | −137.381 | − | 368.091i | −0.227452 | − | 0.609423i | ||||
\(605\) | −695.716 | − | 695.716i | −1.14994 | − | 1.14994i | ||||
\(606\) | −1037.20 | + | 187.246i | −1.71155 | + | 0.308987i | ||||
\(607\) | 671.104 | − | 671.104i | 1.10561 | − | 1.10561i | 0.111888 | − | 0.993721i | \(-0.464310\pi\) |
0.993721 | − | 0.111888i | \(-0.0356898\pi\) | |||||||
\(608\) | −35.2483 | − | 326.214i | −0.0579743 | − | 0.536536i | ||||
\(609\) | 363.455 | + | 363.455i | 0.596807 | + | 0.596807i | ||||
\(610\) | 660.252 | + | 458.316i | 1.08238 | + | 0.751338i | ||||
\(611\) | 1015.90 | 1.66269 | ||||||||
\(612\) | 399.515 | − | 961.202i | 0.652803 | − | 1.57059i | ||||
\(613\) | − | 558.893i | − | 0.911734i | −0.890048 | − | 0.455867i | \(-0.849329\pi\) | ||
0.890048 | − | 0.455867i | \(-0.150671\pi\) | |||||||
\(614\) | 473.760 | + | 328.862i | 0.771596 | + | 0.535606i | ||||
\(615\) | −1948.98 | + | 1948.98i | −3.16907 | + | 3.16907i | ||||
\(616\) | −131.416 | + | 515.575i | −0.213338 | + | 0.836972i | ||||
\(617\) | −200.067 | − | 200.067i | −0.324257 | − | 0.324257i | 0.526140 | − | 0.850398i | \(-0.323639\pi\) |
−0.850398 | + | 0.526140i | \(0.823639\pi\) | |||||||
\(618\) | 1897.52 | − | 342.560i | 3.07042 | − | 0.554303i | ||||
\(619\) | −635.439 | + | 635.439i | −1.02656 | + | 1.02656i | −0.0269190 | + | 0.999638i | \(0.508570\pi\) |
−0.999638 | + | 0.0269190i | \(0.991430\pi\) | |||||||
\(620\) | 434.723 | − | 162.249i | 0.701166 | − | 0.261692i | ||||
\(621\) | −212.545 | −0.342262 | ||||||||
\(622\) | −87.9075 | + | 15.8700i | −0.141330 | + | 0.0255144i | ||||
\(623\) | −289.539 | − | 289.539i | −0.464750 | − | 0.464750i | ||||
\(624\) | 83.8360 | − | 1179.28i | 0.134353 | − | 1.88987i | ||||
\(625\) | 45.0869 | 0.0721390 | ||||||||
\(626\) | −33.0427 | + | 5.96522i | −0.0527839 | + | 0.00952910i | ||||
\(627\) | − | 788.661i | − | 1.25783i | ||||||
\(628\) | −432.247 | + | 161.325i | −0.688291 | + | 0.256887i | ||||
\(629\) | −19.2123 | − | 560.435i | −0.0305441 | − | 0.890994i | ||||
\(630\) | −598.333 | + | 861.961i | −0.949735 | + | 1.36819i | ||||
\(631\) | −28.1772 | −0.0446549 | −0.0223274 | − | 0.999751i | \(-0.507108\pi\) | ||||
−0.0223274 | + | 0.999751i | \(0.507108\pi\) | |||||||
\(632\) | −64.5644 | + | 38.3359i | −0.102159 | + | 0.0606580i | ||||
\(633\) | −851.325 | −1.34491 | ||||||||
\(634\) | 39.7779 | + | 220.339i | 0.0627411 | + | 0.347538i | ||||
\(635\) | 1348.48 | − | 1348.48i | 2.12360 | − | 2.12360i | ||||
\(636\) | −119.175 | + | 261.104i | −0.187382 | + | 0.410542i | ||||
\(637\) | 461.995 | 0.725267 | ||||||||
\(638\) | 435.109 | − | 626.820i | 0.681989 | − | 0.982476i | ||||
\(639\) | −41.7627 | − | 41.7627i | −0.0653563 | − | 0.0653563i | ||||
\(640\) | 976.629 | + | 324.240i | 1.52598 | + | 0.506625i | ||||
\(641\) | 183.204 | + | 183.204i | 0.285809 | + | 0.285809i | 0.835421 | − | 0.549611i | \(-0.185224\pi\) |
−0.549611 | + | 0.835421i | \(0.685224\pi\) | |||||||
\(642\) | −232.523 | + | 334.973i | −0.362185 | + | 0.521765i | ||||
\(643\) | 549.707 | + | 549.707i | 0.854909 | + | 0.854909i | 0.990733 | − | 0.135824i | \(-0.0433681\pi\) |
−0.135824 | + | 0.990733i | \(0.543368\pi\) | |||||||
\(644\) | 109.188 | − | 40.7516i | 0.169546 | − | 0.0632789i | ||||
\(645\) | 1196.96i | 1.85575i | ||||||||
\(646\) | −73.6530 | − | 340.751i | −0.114014 | − | 0.527478i | ||||
\(647\) | 1055.44i | 1.63128i | 0.578558 | + | 0.815641i | \(0.303616\pi\) | ||||
−0.578558 | + | 0.815641i | \(0.696384\pi\) | |||||||
\(648\) | −30.7387 | + | 120.595i | −0.0474363 | + | 0.186103i | ||||
\(649\) | 33.7336 | + | 33.7336i | 0.0519778 | + | 0.0519778i | ||||
\(650\) | −975.882 | − | 677.412i | −1.50136 | − | 1.04217i | ||||
\(651\) | −214.451 | − | 214.451i | −0.329417 | − | 0.329417i | ||||
\(652\) | 510.848 | + | 233.164i | 0.783509 | + | 0.357614i | ||||
\(653\) | 55.3972 | + | 55.3972i | 0.0848350 | + | 0.0848350i | 0.748251 | − | 0.663416i | \(-0.230894\pi\) |
−0.663416 | + | 0.748251i | \(0.730894\pi\) | |||||||
\(654\) | −1000.34 | + | 1441.10i | −1.52958 | + | 2.20351i | ||||
\(655\) | 435.733 | 0.665241 | ||||||||
\(656\) | 78.8976 | − | 1109.81i | 0.120271 | − | 1.69179i | ||||
\(657\) | 1233.67 | − | 1233.67i | 1.87774 | − | 1.87774i | ||||
\(658\) | 568.751 | − | 102.677i | 0.864363 | − | 0.156044i | ||||
\(659\) | −1077.19 | −1.63459 | −0.817293 | − | 0.576222i | \(-0.804526\pi\) | ||||
−0.817293 | + | 0.576222i | \(0.804526\pi\) | |||||||
\(660\) | 2250.14 | + | 1027.02i | 3.40931 | + | 1.55610i | ||||
\(661\) | −341.890 | −0.517231 | −0.258616 | − | 0.965980i | \(-0.583266\pi\) | ||||
−0.258616 | + | 0.965980i | \(0.583266\pi\) | |||||||
\(662\) | −80.7213 | + | 116.287i | −0.121936 | + | 0.175661i | ||||
\(663\) | −43.0367 | − | 1255.41i | −0.0649121 | − | 1.89353i | ||||
\(664\) | 31.5754 | + | 8.04833i | 0.0475533 | + | 0.0121210i | ||||
\(665\) | 351.417i | 0.528447i | ||||||||
\(666\) | 179.415 | + | 993.819i | 0.269391 | + | 1.49222i | ||||
\(667\) | −167.139 | −0.250583 | ||||||||
\(668\) | 975.559 | + | 445.270i | 1.46042 | + | 0.666572i | ||||
\(669\) | −671.310 | − | 671.310i | −1.00345 | − | 1.00345i | ||||
\(670\) | 1296.18 | − | 234.000i | 1.93460 | − | 0.349254i | ||||
\(671\) | −779.834 | −1.16220 | ||||||||
\(672\) | −72.2541 | − | 668.692i | −0.107521 | − | 0.995077i | ||||
\(673\) | 168.381 | − | 168.381i | 0.250195 | − | 0.250195i | −0.570856 | − | 0.821050i | \(-0.693388\pi\) |
0.821050 | + | 0.570856i | \(0.193388\pi\) | |||||||
\(674\) | −180.563 | − | 1000.18i | −0.267898 | − | 1.48395i | ||||
\(675\) | 871.520 | + | 871.520i | 1.29114 | + | 1.29114i | ||||
\(676\) | −77.7872 | − | 208.419i | −0.115070 | − | 0.308312i | ||||
\(677\) | −491.012 | + | 491.012i | −0.725276 | + | 0.725276i | −0.969675 | − | 0.244399i | \(-0.921409\pi\) |
0.244399 | + | 0.969675i | \(0.421409\pi\) | |||||||
\(678\) | 609.710 | + | 423.232i | 0.899277 | + | 0.624236i | ||||
\(679\) | − | 487.679i | − | 0.718231i | ||||||
\(680\) | 1068.12 | + | 233.598i | 1.57076 | + | 0.343526i | ||||
\(681\) | −615.029 | −0.903126 | ||||||||
\(682\) | −256.729 | + | 369.845i | −0.376435 | + | 0.542294i | ||||
\(683\) | −448.482 | − | 448.482i | −0.656635 | − | 0.656635i | 0.297947 | − | 0.954582i | \(-0.403698\pi\) |
−0.954582 | + | 0.297947i | \(0.903698\pi\) | |||||||
\(684\) | 219.531 | + | 588.200i | 0.320951 | + | 0.859941i | ||||
\(685\) | 554.144 | − | 554.144i | 0.808969 | − | 0.808969i | ||||
\(686\) | 669.785 | − | 120.917i | 0.976362 | − | 0.176263i | ||||
\(687\) | 627.872 | + | 627.872i | 0.913933 | + | 0.913933i | ||||
\(688\) | −316.567 | − | 365.021i | −0.460126 | − | 0.530554i | ||||
\(689\) | 218.119i | 0.316574i | ||||||||
\(690\) | −96.2545 | − | 533.176i | −0.139499 | − | 0.772719i | ||||
\(691\) | −384.355 | + | 384.355i | −0.556231 | + | 0.556231i | −0.928232 | − | 0.372002i | \(-0.878672\pi\) |
0.372002 | + | 0.928232i | \(0.378672\pi\) | |||||||
\(692\) | −360.583 | − | 164.579i | −0.521074 | − | 0.237831i | ||||
\(693\) | − | 1018.08i | − | 1.46908i | ||||||
\(694\) | −667.173 | + | 120.445i | −0.961344 | + | 0.173552i | ||||
\(695\) | 128.987 | 0.185592 | ||||||||
\(696\) | −238.243 | + | 934.679i | −0.342303 | + | 1.34293i | ||||
\(697\) | −40.5016 | − | 1181.46i | −0.0581084 | − | 1.69506i | ||||
\(698\) | −158.836 | − | 110.256i | −0.227558 | − | 0.157960i | ||||
\(699\) | 1122.68i | 1.60613i | ||||||||
\(700\) | −614.812 | − | 280.616i | −0.878303 | − | 0.400880i | ||||
\(701\) | − | 1161.37i | − | 1.65673i | −0.560187 | − | 0.828366i | \(-0.689271\pi\) | ||
0.560187 | − | 0.828366i | \(-0.310729\pi\) | |||||||
\(702\) | 165.607 | + | 917.336i | 0.235908 | + | 1.30675i | ||||
\(703\) | 239.161 | + | 239.161i | 0.340200 | + | 0.340200i | ||||
\(704\) | −957.823 | + | 281.911i | −1.36054 | + | 0.400441i | ||||
\(705\) | − | 2686.76i | − | 3.81100i | ||||||
\(706\) | 249.152 | + | 172.950i | 0.352906 | + | 0.244971i | ||||
\(707\) | −322.206 | + | 322.206i | −0.455737 | + | 0.455737i | ||||
\(708\) | −54.8621 | − | 25.0405i | −0.0774889 | − | 0.0353679i | ||||
\(709\) | −287.253 | + | 287.253i | −0.405152 | + | 0.405152i | −0.880044 | − | 0.474892i | \(-0.842487\pi\) |
0.474892 | + | 0.880044i | \(0.342487\pi\) | |||||||
\(710\) | 35.3755 | − | 50.9620i | 0.0498246 | − | 0.0717775i | ||||
\(711\) | 101.596 | − | 101.596i | 0.142891 | − | 0.142891i | ||||
\(712\) | 189.791 | − | 744.594i | 0.266561 | − | 1.04578i | ||||
\(713\) | 98.6175 | 0.138313 | ||||||||
\(714\) | −150.978 | − | 698.490i | −0.211454 | − | 0.978278i | ||||
\(715\) | 1879.71 | 2.62896 | ||||||||
\(716\) | 71.8252 | − | 26.8069i | 0.100315 | − | 0.0374399i | ||||
\(717\) | 1332.88 | − | 1332.88i | 1.85896 | − | 1.85896i | ||||
\(718\) | −411.429 | − | 285.595i | −0.573021 | − | 0.397764i | ||||
\(719\) | −60.3876 | + | 60.3876i | −0.0839884 | + | 0.0839884i | −0.747853 | − | 0.663865i | \(-0.768915\pi\) |
0.663865 | + | 0.747853i | \(0.268915\pi\) | |||||||
\(720\) | −1964.08 | − | 139.628i | −2.72789 | − | 0.193928i | ||||
\(721\) | 589.465 | − | 589.465i | 0.817565 | − | 0.817565i | ||||
\(722\) | −420.377 | − | 291.806i | −0.582240 | − | 0.404164i | ||||
\(723\) | − | 608.539i | − | 0.841686i | ||||||
\(724\) | 25.5078 | − | 55.8861i | 0.0352318 | − | 0.0771907i | ||||
\(725\) | 685.337 | + | 685.337i | 0.945292 | + | 0.945292i | ||||
\(726\) | −1187.57 | + | 214.393i | −1.63577 | + | 0.295307i | ||||
\(727\) | − | 808.751i | − | 1.11245i | −0.831032 | − | 0.556225i | \(-0.812249\pi\) | ||
0.831032 | − | 0.556225i | \(-0.187751\pi\) | |||||||
\(728\) | −260.958 | − | 439.499i | −0.358458 | − | 0.603707i | ||||
\(729\) | 1141.80i | 1.56625i | ||||||||
\(730\) | 1505.42 | + | 1045.00i | 2.06222 | + | 1.43150i | ||||
\(731\) | −375.231 | − | 350.357i | −0.513312 | − | 0.479285i | ||||
\(732\) | 923.571 | − | 344.699i | 1.26171 | − | 0.470901i | ||||
\(733\) | −795.900 | −1.08581 | −0.542906 | − | 0.839794i | \(-0.682676\pi\) | ||||
−0.542906 | + | 0.839794i | \(0.682676\pi\) | |||||||
\(734\) | 110.567 | + | 612.457i | 0.150636 | + | 0.834410i | ||||
\(735\) | − | 1221.84i | − | 1.66237i | ||||||
\(736\) | 170.366 | + | 137.139i | 0.231476 | + | 0.186330i | ||||
\(737\) | −903.662 | + | 903.662i | −1.22614 | + | 1.22614i | ||||
\(738\) | 378.225 | + | 2095.08i | 0.512501 | + | 2.83886i | ||||
\(739\) | 160.667i | 0.217411i | 0.994074 | + | 0.108705i | \(0.0346705\pi\) | ||||
−0.994074 | + | 0.108705i | \(0.965329\pi\) | |||||||
\(740\) | −993.798 | + | 370.910i | −1.34297 | + | 0.501230i | ||||
\(741\) | 535.735 | + | 535.735i | 0.722989 | + | 0.722989i | ||||
\(742\) | 22.0453 | + | 122.114i | 0.0297106 | + | 0.164574i | ||||
\(743\) | −802.608 | + | 802.608i | −1.08023 | + | 1.08023i | −0.0837376 | + | 0.996488i | \(0.526686\pi\) |
−0.996488 | + | 0.0837376i | \(0.973314\pi\) | |||||||
\(744\) | 140.571 | − | 551.492i | 0.188940 | − | 0.741252i | ||||
\(745\) | 267.899 | + | 267.899i | 0.359596 | + | 0.359596i | ||||
\(746\) | 417.939 | − | 602.084i | 0.560240 | − | 0.807083i | ||||
\(747\) | −62.3501 | −0.0834673 | ||||||||
\(748\) | −980.592 | + | 404.776i | −1.31095 | + | 0.541144i | ||||
\(749\) | 176.293i | 0.235371i | ||||||||
\(750\) | −661.445 | + | 952.880i | −0.881927 | + | 1.27051i | ||||
\(751\) | −581.158 | + | 581.158i | −0.773845 | + | 0.773845i | −0.978776 | − | 0.204931i | \(-0.934303\pi\) |
0.204931 | + | 0.978776i | \(0.434303\pi\) | |||||||
\(752\) | 710.584 | + | 819.348i | 0.944925 | + | 1.08956i | ||||
\(753\) | 1059.51 | + | 1059.51i | 1.40705 | + | 1.40705i | ||||
\(754\) | 130.228 | + | 721.365i | 0.172717 | + | 0.956717i | ||||
\(755\) | −558.373 | + | 558.373i | −0.739566 | + | 0.739566i | ||||
\(756\) | 185.430 | + | 496.832i | 0.245278 | + | 0.657185i | ||||
\(757\) | 366.621 | 0.484308 | 0.242154 | − | 0.970238i | \(-0.422146\pi\) | ||||
0.242154 | + | 0.970238i | \(0.422146\pi\) | |||||||
\(758\) | 177.678 | + | 984.200i | 0.234404 | + | 1.29842i | ||||
\(759\) | 371.715 | + | 371.715i | 0.489743 | + | 0.489743i | ||||
\(760\) | −567.036 | + | 336.685i | −0.746101 | + | 0.443006i | ||||
\(761\) | −268.301 | −0.352564 | −0.176282 | − | 0.984340i | \(-0.556407\pi\) | ||||
−0.176282 | + | 0.984340i | \(0.556407\pi\) | |||||||
\(762\) | −415.551 | − | 2301.83i | −0.545342 | − | 3.02078i | ||||
\(763\) | 758.435i | 0.994017i | ||||||||
\(764\) | 10.8279 | − | 4.04123i | 0.0141726 | − | 0.00528957i | ||||
\(765\) | −2090.88 | + | 71.6774i | −2.73317 | + | 0.0936959i | ||||
\(766\) | −388.136 | − | 269.426i | −0.506704 | − | 0.351731i | ||||
\(767\) | −45.8303 | −0.0597526 | ||||||||
\(768\) | 1009.76 | − | 757.245i | 1.31479 | − | 0.985997i | ||||
\(769\) | −133.881 | −0.174097 | −0.0870486 | − | 0.996204i | \(-0.527744\pi\) | ||||
−0.0870486 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(770\) | 1052.35 | − | 189.981i | 1.36669 | − | 0.246729i | ||||
\(771\) | −355.258 | + | 355.258i | −0.460776 | + | 0.460776i | ||||
\(772\) | −264.106 | − | 120.545i | −0.342106 | − | 0.156146i | ||||
\(773\) | −122.049 | −0.157890 | −0.0789449 | − | 0.996879i | \(-0.525155\pi\) | ||||
−0.0789449 | + | 0.996879i | \(0.525155\pi\) | |||||||
\(774\) | 759.485 | + | 527.200i | 0.981247 | + | 0.681136i | ||||
\(775\) | −404.371 | − | 404.371i | −0.521770 | − | 0.521770i | ||||
\(776\) | 786.904 | − | 467.234i | 1.01405 | − | 0.602105i | ||||
\(777\) | 490.245 | + | 490.245i | 0.630946 | + | 0.630946i | ||||
\(778\) | 1163.63 | + | 807.740i | 1.49567 | + | 1.03823i | ||||
\(779\) | 504.177 | + | 504.177i | 0.647210 | + | 0.647210i | ||||
\(780\) | −2226.17 | + | 830.862i | −2.85406 | + | 1.06521i | ||||
\(781\) | 60.1920i | 0.0770705i | ||||||||
\(782\) | 195.319 | + | 125.890i | 0.249768 | + | 0.160984i | ||||
\(783\) | − | 760.523i | − | 0.971293i | ||||||
\(784\) | 323.148 | + | 372.610i | 0.412178 | + | 0.475268i | ||||
\(785\) | 655.692 | + | 655.692i | 0.835277 | + | 0.835277i | ||||
\(786\) | 304.755 | − | 439.031i | 0.387729 | − | 0.558564i | ||||
\(787\) | −109.668 | − | 109.668i | −0.139349 | − | 0.139349i | 0.633991 | − | 0.773340i | \(-0.281416\pi\) |
−0.773340 | + | 0.633991i | \(0.781416\pi\) | |||||||
\(788\) | −488.151 | + | 1069.51i | −0.619481 | + | 1.35724i | ||||
\(789\) | 683.894 | + | 683.894i | 0.866786 | + | 0.866786i | ||||
\(790\) | 123.975 | + | 86.0575i | 0.156930 | + | 0.108934i | ||||
\(791\) | 320.884 | 0.405669 | ||||||||
\(792\) | 1642.74 | − | 975.395i | 2.07416 | − | 1.23156i | ||||
\(793\) | 529.739 | − | 529.739i | 0.668018 | − | 0.668018i | ||||
\(794\) | 50.3709 | + | 279.016i | 0.0634394 | + | 0.351406i | ||||
\(795\) | 576.861 | 0.725611 | ||||||||
\(796\) | −521.380 | − | 237.972i | −0.655001 | − | 0.298959i | ||||
\(797\) | 1240.03 | 1.55587 | 0.777935 | − | 0.628345i | \(-0.216267\pi\) | ||||
0.777935 | + | 0.628345i | \(0.216267\pi\) | |||||||
\(798\) | 354.077 | + | 245.784i | 0.443706 | + | 0.308000i | ||||
\(799\) | 842.266 | + | 786.432i | 1.05415 | + | 0.984271i | ||||
\(800\) | −136.243 | − | 1260.90i | −0.170304 | − | 1.57612i | ||||
\(801\) | 1470.31i | 1.83559i | ||||||||
\(802\) | −736.850 | + | 133.024i | −0.918766 | + | 0.165865i | ||||
\(803\) | −1778.08 | −2.21430 | ||||||||
\(804\) | 670.789 | − | 1469.66i | 0.834315 | − | 1.82793i | ||||
\(805\) | −165.631 | − | 165.631i | −0.205753 | − | 0.205753i | ||||
\(806\) | −76.8390 | − | 425.629i | −0.0953338 | − | 0.528076i | ||||
\(807\) | −13.4866 | −0.0167120 | ||||||||
\(808\) | −828.601 | − | 211.204i | −1.02550 | − | 0.261391i | ||||
\(809\) | 57.3128 | − | 57.3128i | 0.0708440 | − | 0.0708440i | −0.670797 | − | 0.741641i | \(-0.734048\pi\) |
0.741641 | + | 0.670797i | \(0.234048\pi\) | |||||||
\(810\) | 246.149 | − | 44.4374i | 0.303888 | − | 0.0548610i | ||||
\(811\) | −525.988 | − | 525.988i | −0.648568 | − | 0.648568i | 0.304079 | − | 0.952647i | \(-0.401651\pi\) |
−0.952647 | + | 0.304079i | \(0.901651\pi\) | |||||||
\(812\) | 145.816 | + | 390.693i | 0.179577 | + | 0.481149i | ||||
\(813\) | −147.233 | + | 147.233i | −0.181099 | + | 0.181099i | ||||
\(814\) | 586.895 | − | 845.483i | 0.721001 | − | 1.03868i | ||||
\(815\) | − | 1128.62i | − | 1.38481i | ||||||
\(816\) | 982.415 | − | 912.821i | 1.20394 | − | 1.11865i | ||||
\(817\) | 309.638 | 0.378994 | ||||||||
\(818\) | −941.069 | − | 653.247i | −1.15045 | − | 0.798590i | ||||
\(819\) | 691.575 | + | 691.575i | 0.844415 | + | 0.844415i | ||||
\(820\) | −2095.03 | + | 781.919i | −2.55492 | + | 0.953559i | ||||
\(821\) | −687.511 | + | 687.511i | −0.837406 | + | 0.837406i | −0.988517 | − | 0.151110i | \(-0.951715\pi\) |
0.151110 | + | 0.988517i | \(0.451715\pi\) | |||||||
\(822\) | −170.766 | − | 945.911i | −0.207744 | − | 1.15074i | ||||
\(823\) | −896.180 | − | 896.180i | −1.08892 | − | 1.08892i | −0.995640 | − | 0.0932781i | \(-0.970265\pi\) |
−0.0932781 | − | 0.995640i | \(-0.529735\pi\) | |||||||
\(824\) | 1515.90 | + | 386.390i | 1.83968 | + | 0.468920i | ||||
\(825\) | − | 3048.36i | − | 3.69499i | ||||||
\(826\) | −25.6580 | + | 4.63205i | −0.0310630 | + | 0.00560781i | ||||
\(827\) | −740.614 | + | 740.614i | −0.895542 | + | 0.895542i | −0.995038 | − | 0.0994957i | \(-0.968277\pi\) |
0.0994957 | + | 0.995038i | \(0.468277\pi\) | |||||||
\(828\) | −380.703 | − | 173.763i | −0.459786 | − | 0.209858i | ||||
\(829\) | 630.248i | 0.760251i | 0.924935 | + | 0.380125i | \(0.124119\pi\) | ||||
−0.924935 | + | 0.380125i | \(0.875881\pi\) | |||||||
\(830\) | −11.6350 | − | 64.4492i | −0.0140181 | − | 0.0776497i | ||||
\(831\) | −699.933 | −0.842278 | ||||||||
\(832\) | 459.145 | − | 842.147i | 0.551857 | − | 1.01220i | ||||
\(833\) | 383.032 | + | 357.641i | 0.459822 | + | 0.429341i | ||||
\(834\) | 90.2144 | − | 129.963i | 0.108171 | − | 0.155831i | ||||
\(835\) | − | 2155.31i | − | 2.58121i | ||||||
\(836\) | 265.679 | − | 582.086i | 0.317798 | − | 0.696275i | ||||
\(837\) | 448.734i | 0.536121i | ||||||||
\(838\) | −794.453 | + | 143.423i | −0.948035 | + | 0.171149i | ||||
\(839\) | 903.926 | + | 903.926i | 1.07739 | + | 1.07739i | 0.996743 | + | 0.0806419i | \(0.0256970\pi\) |
0.0806419 | + | 0.996743i | \(0.474303\pi\) | |||||||
\(840\) | −1162.34 | + | 690.155i | −1.38374 | + | 0.821613i | ||||
\(841\) | 242.948i | 0.288880i | ||||||||
\(842\) | −142.945 | + | 205.927i | −0.169769 | + | 0.244569i | ||||
\(843\) | 942.409 | − | 942.409i | 1.11792 | − | 1.11792i | ||||
\(844\) | −628.336 | − | 286.789i | −0.744474 | − | 0.339797i | ||||
\(845\) | −316.159 | + | 316.159i | −0.374153 | + | 0.374153i | ||||
\(846\) | −1704.78 | − | 1183.38i | −2.01511 | − | 1.39880i | ||||
\(847\) | −368.920 | + | 368.920i | −0.435561 | + | 0.435561i | ||||
\(848\) | −175.918 | + | 152.566i | −0.207451 | + | 0.179913i | ||||
\(849\) | 113.299 | 0.133450 | ||||||||
\(850\) | −284.686 | − | 1317.08i | −0.334925 | − | 1.54951i | ||||
\(851\) | −225.444 | −0.264917 | ||||||||
\(852\) | −26.6059 | − | 71.2865i | −0.0312275 | − | 0.0836696i | ||||
\(853\) | 48.9309 | − | 48.9309i | 0.0573633 | − | 0.0573633i | −0.677843 | − | 0.735207i | \(-0.737085\pi\) |
0.735207 | + | 0.677843i | \(0.237085\pi\) | |||||||
\(854\) | 243.033 | − | 350.114i | 0.284582 | − | 0.409970i | ||||
\(855\) | 892.263 | − | 892.263i | 1.04358 | − | 1.04358i | ||||
\(856\) | −284.461 | + | 168.902i | −0.332315 | + | 0.197316i | ||||
\(857\) | 995.128 | − | 995.128i | 1.16118 | − | 1.16118i | 0.176958 | − | 0.984218i | \(-0.443374\pi\) |
0.984218 | − | 0.176958i | \(-0.0566258\pi\) | |||||||
\(858\) | 1314.68 | − | 1893.94i | 1.53226 | − | 2.20738i | ||||
\(859\) | 622.629i | 0.724830i | 0.932017 | + | 0.362415i | \(0.118048\pi\) | ||||
−0.932017 | + | 0.362415i | \(0.881952\pi\) | |||||||
\(860\) | −403.223 | + | 883.435i | −0.468863 | + | 1.02725i | ||||
\(861\) | 1033.49 | + | 1033.49i | 1.20034 | + | 1.20034i | ||||
\(862\) | 233.350 | + | 1292.58i | 0.270707 | + | 1.49951i | ||||
\(863\) | − | 465.128i | − | 0.538967i | −0.963005 | − | 0.269483i | \(-0.913147\pi\) | ||
0.963005 | − | 0.269483i | \(-0.0868529\pi\) | |||||||
\(864\) | −624.017 | + | 775.207i | −0.722242 | + | 0.897230i | ||||
\(865\) | 796.640i | 0.920971i | ||||||||
\(866\) | −12.3344 | + | 17.7690i | −0.0142430 | + | 0.0205185i | ||||
\(867\) | 936.161 | − | 1074.15i | 1.07977 | − | 1.23893i | ||||
\(868\) | −86.0365 | − | 230.522i | −0.0991204 | − | 0.265578i | ||||
\(869\) | −146.428 | −0.168502 | ||||||||
\(870\) | 1907.80 | − | 344.415i | 2.19287 | − | 0.395880i | ||||
\(871\) | − | 1227.71i | − | 1.40954i | ||||||
\(872\) | −1223.79 | + | 726.639i | −1.40343 | + | 0.833301i | ||||
\(873\) | −1238.24 | + | 1238.24i | −1.41837 | + | 1.41837i | ||||
\(874\) | −137.926 | + | 24.8999i | −0.157810 | + | 0.0284896i | ||||
\(875\) | 501.491i | 0.573132i | ||||||||
\(876\) | 2105.81 | − | 785.941i | 2.40389 | − | 0.897192i | ||||
\(877\) | 579.229 | + | 579.229i | 0.660466 | + | 0.660466i | 0.955490 | − | 0.295024i | \(-0.0953276\pi\) |
−0.295024 | + | 0.955490i | \(0.595328\pi\) | |||||||
\(878\) | 569.295 | − | 102.775i | 0.648400 | − | 0.117056i | ||||
\(879\) | −453.381 | + | 453.381i | −0.515791 | + | 0.515791i | ||||
\(880\) | 1314.78 | + | 1516.03i | 1.49407 | + | 1.72276i | ||||
\(881\) | −612.670 | − | 612.670i | −0.695426 | − | 0.695426i | 0.267995 | − | 0.963420i | \(-0.413639\pi\) |
−0.963420 | + | 0.267995i | \(0.913639\pi\) | |||||||
\(882\) | −775.275 | − | 538.160i | −0.878996 | − | 0.610158i | ||||
\(883\) | −157.228 | −0.178061 | −0.0890307 | − | 0.996029i | \(-0.528377\pi\) | ||||
−0.0890307 | + | 0.996029i | \(0.528377\pi\) | |||||||
\(884\) | 391.150 | − | 941.076i | 0.442478 | − | 1.06457i | ||||
\(885\) | 121.207i | 0.136958i | ||||||||
\(886\) | 692.569 | + | 480.749i | 0.781680 | + | 0.542606i | ||||
\(887\) | 326.409 | − | 326.409i | 0.367992 | − | 0.367992i | −0.498753 | − | 0.866744i | \(-0.666208\pi\) |
0.866744 | + | 0.498753i | \(0.166208\pi\) | |||||||
\(888\) | −321.353 | + | 1260.74i | −0.361884 | + | 1.41975i | ||||
\(889\) | −715.066 | − | 715.066i | −0.804348 | − | 0.804348i | ||||
\(890\) | −1519.81 | + | 274.372i | −1.70765 | + | 0.308283i | ||||
\(891\) | −171.608 | + | 171.608i | −0.192602 | + | 0.192602i | ||||
\(892\) | −269.326 | − | 721.619i | −0.301935 | − | 0.808990i | ||||
\(893\) | −695.032 | −0.778312 | ||||||||
\(894\) | 457.298 | − | 82.5561i | 0.511519 | − | 0.0923447i | ||||
\(895\) | −108.955 | − | 108.955i | −0.121737 | − | 0.121737i | ||||
\(896\) | 171.936 | − | 517.880i | 0.191893 | − | 0.577992i | ||||
\(897\) | −505.010 | −0.562999 | ||||||||
\(898\) | −678.904 | + | 122.563i | −0.756018 | + | 0.136484i | ||||
\(899\) | 352.870i | 0.392514i | ||||||||
\(900\) | 848.538 | + | 2273.53i | 0.942820 | + | 2.52615i | ||||
\(901\) | −168.851 | + | 180.839i | −0.187404 | + | 0.200709i | ||||
\(902\) | 1237.24 | − | 1782.37i | 1.37166 | − | 1.97602i | ||||
\(903\) | 634.714 | 0.702895 | ||||||||
\(904\) | 307.431 | + | 517.769i | 0.340079 | + | 0.572753i | ||||
\(905\) | −123.470 | −0.136431 | ||||||||
\(906\) | 172.069 | + | 953.129i | 0.189921 | + | 1.05202i | ||||
\(907\) | −851.844 | + | 851.844i | −0.939188 | + | 0.939188i | −0.998254 | − | 0.0590658i | \(-0.981188\pi\) |
0.0590658 | + | 0.998254i | \(0.481188\pi\) | |||||||
\(908\) | −453.933 | − | 207.187i | −0.499926 | − | 0.228179i | ||||
\(909\) | 1636.19 | 1.79999 | ||||||||
\(910\) | −585.805 | + | 843.913i | −0.643742 | + | 0.927377i | ||||
\(911\) | −174.997 | − | 174.997i | −0.192094 | − | 0.192094i | 0.604507 | − | 0.796600i | \(-0.293370\pi\) |
−0.796600 | + | 0.604507i | \(0.793370\pi\) | |||||||
\(912\) | −57.3567 | + | 806.808i | −0.0628911 | + | 0.884658i | ||||
\(913\) | 44.9322 | + | 44.9322i | 0.0492138 | + | 0.0492138i | ||||
\(914\) | 606.690 | − | 873.999i | 0.663774 | − | 0.956235i | ||||
\(915\) | −1401.00 | − | 1401.00i | −1.53115 | − | 1.53115i | ||||
\(916\) | 251.899 | + | 674.925i | 0.274999 | + | 0.736818i | ||||
\(917\) | − | 231.058i | − | 0.251971i | ||||||
\(918\) | −572.829 | + | 888.747i | −0.623997 | + | 0.968134i | ||||
\(919\) | 1063.06i | 1.15676i | 0.815767 | + | 0.578381i | \(0.196315\pi\) | ||||
−0.815767 | + | 0.578381i | \(0.803685\pi\) | |||||||
\(920\) | 108.570 | − | 425.946i | 0.118011 | − | 0.462984i | ||||
\(921\) | −1005.28 | − | 1005.28i | −1.09151 | − | 1.09151i | ||||
\(922\) | −1425.97 | − | 989.839i | −1.54660 | − | 1.07358i | ||||
\(923\) | −40.8882 | − | 40.8882i | −0.0442993 | − | 0.0442993i | ||||
\(924\) | 544.604 | − | 1193.19i | 0.589398 | − | 1.29133i | ||||
\(925\) | 924.413 | + | 924.413i | 0.999365 | + | 0.999365i | ||||
\(926\) | −740.336 | + | 1066.53i | −0.799499 | + | 1.15176i | ||||
\(927\) | −2993.35 | −3.22907 | ||||||||
\(928\) | −490.708 | + | 609.599i | −0.528780 | + | 0.656895i | ||||
\(929\) | −1032.78 | + | 1032.78i | −1.11171 | + | 1.11171i | −0.118788 | + | 0.992920i | \(0.537901\pi\) |
−0.992920 | + | 0.118788i | \(0.962099\pi\) | |||||||
\(930\) | −1125.66 | + | 203.216i | −1.21039 | + | 0.218512i | ||||
\(931\) | −316.076 | −0.339501 | ||||||||
\(932\) | −378.202 | + | 828.616i | −0.405796 | + | 0.889073i | ||||
\(933\) | 220.207 | 0.236021 | ||||||||
\(934\) | −561.538 | + | 808.954i | −0.601219 | + | 0.866117i | ||||
\(935\) | 1558.43 | + | 1455.12i | 1.66677 | + | 1.55628i | ||||
\(936\) | −453.324 | + | 1778.49i | −0.484320 | + | 1.90009i | ||||
\(937\) | 1076.22i | 1.14858i | 0.818652 | + | 0.574290i | \(0.194722\pi\) | ||||
−0.818652 | + | 0.574290i | \(0.805278\pi\) | |||||||
\(938\) | −124.084 | − | 687.331i | −0.132286 | − | 0.732763i | ||||
\(939\) | 82.7717 | 0.0881488 | ||||||||
\(940\) | 905.097 | − | 1983.01i | 0.962869 | − | 2.10958i | ||||
\(941\) | 228.432 | + | 228.432i | 0.242754 | + | 0.242754i | 0.817989 | − | 0.575234i | \(-0.195089\pi\) |
−0.575234 | + | 0.817989i | \(0.695089\pi\) | |||||||
\(942\) | 1119.25 | − | 202.059i | 1.18817 | − | 0.214500i | ||||
\(943\) | −475.262 | −0.503989 | ||||||||
\(944\) | −32.0565 | − | 36.9632i | −0.0339582 | − | 0.0391559i | ||||
\(945\) | 753.664 | − | 753.664i | 0.797528 | − | 0.797528i | ||||
\(946\) | −167.395 | − | 927.241i | −0.176951 | − | 0.980170i | ||||
\(947\) | −384.173 | − | 384.173i | −0.405673 | − | 0.405673i | 0.474553 | − | 0.880227i | \(-0.342610\pi\) |
−0.880227 | + | 0.474553i | \(0.842610\pi\) | |||||||
\(948\) | 173.418 | − | 64.7238i | 0.182930 | − | 0.0682741i | ||||
\(949\) | 1207.84 | − | 1207.84i | 1.27275 | − | 1.27275i | ||||
\(950\) | 667.653 | + | 463.454i | 0.702793 | + | 0.487846i | ||||
\(951\) | − | 551.947i | − | 0.580386i | ||||||
\(952\) | 123.871 | − | 566.394i | 0.130116 | − | 0.594951i | ||||
\(953\) | −938.109 | −0.984375 | −0.492187 | − | 0.870489i | \(-0.663802\pi\) | ||||
−0.492187 | + | 0.870489i | \(0.663802\pi\) | |||||||
\(954\) | 254.078 | − | 366.026i | 0.266329 | − | 0.383675i | ||||
\(955\) | −16.4252 | − | 16.4252i | −0.0171992 | − | 0.0171992i | ||||
\(956\) | 1432.76 | − | 534.743i | 1.49871 | − | 0.559354i | ||||
\(957\) | −1330.06 | + | 1330.06i | −1.38982 | + | 1.38982i | ||||
\(958\) | −1326.48 | + | 239.470i | −1.38463 | + | 0.249968i | ||||
\(959\) | −293.848 | − | 293.848i | −0.306411 | − | 0.306411i | ||||
\(960\) | −2227.23 | − | 1214.30i | −2.32003 | − | 1.26490i | ||||
\(961\) | 752.795i | 0.783345i | ||||||||
\(962\) | 175.658 | + | 973.010i | 0.182597 | + | 1.01144i | ||||
\(963\) | 447.616 | − | 447.616i | 0.464814 | − | 0.464814i | ||||
\(964\) | 205.001 | − | 449.143i | 0.212656 | − | 0.465916i | ||||
\(965\) | 583.492i | 0.604655i | ||||||||
\(966\) | −282.729 | + | 51.0412i | −0.292680 | + | 0.0528377i | ||||
\(967\) | 1780.84 | 1.84162 | 0.920808 | − | 0.390016i | \(-0.127530\pi\) | ||||
0.920808 | + | 0.390016i | \(0.127530\pi\) | |||||||
\(968\) | −948.732 | − | 241.825i | −0.980095 | − | 0.249819i | ||||
\(969\) | 29.4437 | + | 858.893i | 0.0303857 | + | 0.886370i | ||||
\(970\) | −1510.99 | − | 1048.86i | −1.55772 | − | 1.08130i | ||||
\(971\) | 359.300i | 0.370030i | 0.982736 | + | 0.185015i | \(0.0592334\pi\) | ||||
−0.982736 | + | 0.185015i | \(0.940767\pi\) | |||||||
\(972\) | −337.477 | + | 739.390i | −0.347198 | + | 0.760690i | ||||
\(973\) | − | 68.3982i | − | 0.0702962i | ||||||
\(974\) | 137.536 | + | 761.846i | 0.141208 | + | 0.782183i | ||||
\(975\) | 2070.74 | + | 2070.74i | 2.12384 | + | 2.12384i | ||||
\(976\) | 797.778 | + | 56.7147i | 0.817395 | + | 0.0581093i | ||||
\(977\) | 1584.03i | 1.62132i | 0.585515 | + | 0.810662i | \(0.300892\pi\) | ||||
−0.585515 | + | 0.810662i | \(0.699108\pi\) | |||||||
\(978\) | −1137.16 | − | 789.367i | −1.16275 | − | 0.807124i | ||||
\(979\) | 1059.57 | − | 1059.57i | 1.08230 | − | 1.08230i | ||||
\(980\) | 411.605 | − | 901.801i | 0.420005 | − | 0.920205i | ||||
\(981\) | 1925.70 | − | 1925.70i | 1.96300 | − | 1.96300i | ||||
\(982\) | 7.62607 | − | 10.9861i | 0.00776586 | − | 0.0111875i | ||||
\(983\) | 1150.62 | − | 1150.62i | 1.17051 | − | 1.17051i | 0.188427 | − | 0.982087i | \(-0.439661\pi\) |
0.982087 | − | 0.188427i | \(-0.0603388\pi\) | |||||||
\(984\) | −677.447 | + | 2657.77i | −0.688462 | + | 2.70099i | ||||
\(985\) | 2362.87 | 2.39886 | ||||||||
\(986\) | −450.455 | + | 698.883i | −0.456851 | + | 0.708807i | ||||
\(987\) | −1424.72 | −1.44348 | ||||||||
\(988\) | 214.934 | + | 575.884i | 0.217545 | + | 0.582878i | ||||
\(989\) | −145.940 | + | 145.940i | −0.147563 | + | 0.147563i | ||||
\(990\) | −3154.34 | − | 2189.59i | −3.18620 | − | 2.21171i | ||||
\(991\) | 582.041 | − | 582.041i | 0.587327 | − | 0.587327i | −0.349580 | − | 0.936907i | \(-0.613676\pi\) |
0.936907 | + | 0.349580i | \(0.113676\pi\) | |||||||
\(992\) | 289.534 | − | 359.684i | 0.291869 | − | 0.362584i | ||||
\(993\) | 246.752 | − | 246.752i | 0.248492 | − | 0.248492i | ||||
\(994\) | −27.0238 | − | 18.7587i | −0.0271869 | − | 0.0188719i | ||||
\(995\) | 1151.89i | 1.15768i | ||||||||
\(996\) | −73.0747 | − | 33.3532i | −0.0733682 | − | 0.0334871i | ||||
\(997\) | −658.998 | − | 658.998i | −0.660981 | − | 0.660981i | 0.294630 | − | 0.955611i | \(-0.404804\pi\) |
−0.955611 | + | 0.294630i | \(0.904804\pi\) | |||||||
\(998\) | 120.966 | − | 21.8380i | 0.121208 | − | 0.0218818i | ||||
\(999\) | − | 1025.83i | − | 1.02685i |
(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 | 136.3.j.b.115.7 | ✓ | 64 | |
4.3 | odd | 2 | 544.3.n.b.47.1 | 64 | |||
8.3 | odd | 2 | inner | 136.3.j.b.115.26 | yes | 64 | |
8.5 | even | 2 | 544.3.n.b.47.2 | 64 | |||
17.4 | even | 4 | inner | 136.3.j.b.123.26 | yes | 64 | |
68.55 | odd | 4 | 544.3.n.b.463.2 | 64 | |||
136.21 | even | 4 | 544.3.n.b.463.1 | 64 | |||
136.123 | odd | 4 | inner | 136.3.j.b.123.7 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.3.j.b.115.7 | ✓ | 64 | 1.1 | even | 1 | trivial | |
136.3.j.b.115.26 | yes | 64 | 8.3 | odd | 2 | inner | |
136.3.j.b.123.7 | yes | 64 | 136.123 | odd | 4 | inner | |
136.3.j.b.123.26 | yes | 64 | 17.4 | even | 4 | inner | |
544.3.n.b.47.1 | 64 | 4.3 | odd | 2 | |||
544.3.n.b.47.2 | 64 | 8.5 | even | 2 | |||
544.3.n.b.463.1 | 64 | 136.21 | even | 4 | |||
544.3.n.b.463.2 | 64 | 68.55 | odd | 4 |