Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1009,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.bb (of order \(6\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1099.1 | ||
Character | \(\chi\) | \(=\) | 1110.1099 |
Dual form | 1110.2.bb.d.1009.1 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −0.00835632 | − | 2.23605i | −0.00373706 | − | 0.999993i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.70065 | + | 2.13657i | 1.39871 | + | 0.807548i | 0.994258 | − | 0.107009i | \(-0.0341275\pi\) |
0.404456 | + | 0.914557i | \(0.367461\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 1.12526 | + | 1.93230i | 0.355839 | + | 0.611047i | ||||
\(11\) | −5.93869 | −1.79058 | −0.895291 | − | 0.445482i | \(-0.853032\pi\) | ||||
−0.895291 | + | 0.445482i | \(0.853032\pi\) | |||||||
\(12\) | −0.866025 | + | 0.500000i | −0.250000 | + | 0.144338i | ||||
\(13\) | −1.08299 | − | 0.625263i | −0.300367 | − | 0.173417i | 0.342241 | − | 0.939612i | \(-0.388814\pi\) |
−0.642608 | + | 0.766195i | \(0.722147\pi\) | |||||||
\(14\) | −4.27314 | −1.14205 | ||||||||
\(15\) | −1.11079 | + | 1.94066i | −0.286805 | + | 0.501075i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −6.29873 | + | 3.63657i | −1.52767 | + | 0.881998i | −0.528206 | + | 0.849116i | \(0.677135\pi\) |
−0.999459 | + | 0.0328820i | \(0.989531\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | 2.05756 | − | 3.56380i | 0.472037 | − | 0.817593i | −0.527451 | − | 0.849586i | \(-0.676852\pi\) |
0.999488 | + | 0.0319930i | \(0.0101854\pi\) | |||||||
\(20\) | −1.94066 | − | 1.11079i | −0.433944 | − | 0.248380i | ||||
\(21\) | −2.13657 | − | 3.70065i | −0.466238 | − | 0.807548i | ||||
\(22\) | 5.14305 | − | 2.96934i | 1.09650 | − | 0.633066i | ||||
\(23\) | 6.89816i | 1.43837i | 0.694820 | + | 0.719183i | \(0.255484\pi\) | ||||
−0.694820 | + | 0.719183i | \(0.744516\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −4.99986 | + | 0.0373703i | −0.999972 | + | 0.00747407i | ||||
\(26\) | 1.25053 | 0.245248 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 3.70065 | − | 2.13657i | 0.699357 | − | 0.403774i | ||||
\(29\) | 3.27314 | 0.607807 | 0.303904 | − | 0.952703i | \(-0.401710\pi\) | ||||
0.303904 | + | 0.952703i | \(0.401710\pi\) | |||||||
\(30\) | −0.00835632 | − | 2.23605i | −0.00152565 | − | 0.408245i | ||||
\(31\) | −2.68816 | −0.482808 | −0.241404 | − | 0.970425i | \(-0.577608\pi\) | ||||
−0.241404 | + | 0.970425i | \(0.577608\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 5.14305 | + | 2.96934i | 0.895291 | + | 0.516896i | ||||
\(34\) | 3.63657 | − | 6.29873i | 0.623667 | − | 1.08022i | ||||
\(35\) | 4.74656 | − | 8.29270i | 0.802315 | − | 1.40172i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.08237 | + | 5.24395i | −0.506739 | + | 0.862100i | ||||
\(38\) | 4.11513i | 0.667562i | ||||||||
\(39\) | 0.625263 | + | 1.08299i | 0.100122 | + | 0.173417i | ||||
\(40\) | 2.23605 | − | 0.00835632i | 0.353551 | − | 0.00132125i | ||||
\(41\) | −1.33327 | + | 2.30929i | −0.208222 | + | 0.360651i | −0.951154 | − | 0.308715i | \(-0.900101\pi\) |
0.742933 | + | 0.669366i | \(0.233434\pi\) | |||||||
\(42\) | 3.70065 | + | 2.13657i | 0.571023 | + | 0.329680i | ||||
\(43\) | − | 9.04279i | − | 1.37901i | −0.724280 | − | 0.689506i | \(-0.757828\pi\) | ||
0.724280 | − | 0.689506i | \(-0.242172\pi\) | |||||||
\(44\) | −2.96934 | + | 5.14305i | −0.447645 | + | 0.775345i | ||||
\(45\) | 1.93230 | − | 1.12526i | 0.288050 | − | 0.167744i | ||||
\(46\) | −3.44908 | − | 5.97399i | −0.508539 | − | 0.880816i | ||||
\(47\) | − | 4.62329i | − | 0.674377i | −0.941437 | − | 0.337188i | \(-0.890524\pi\) | ||
0.941437 | − | 0.337188i | \(-0.109476\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 5.62987 | + | 9.75123i | 0.804268 | + | 1.39303i | ||||
\(50\) | 4.31132 | − | 2.53229i | 0.609713 | − | 0.358120i | ||||
\(51\) | 7.27314 | 1.01844 | ||||||||
\(52\) | −1.08299 | + | 0.625263i | −0.150183 | + | 0.0867084i | ||||
\(53\) | −1.31601 | + | 0.759799i | −0.180768 | + | 0.104366i | −0.587653 | − | 0.809113i | \(-0.699948\pi\) |
0.406885 | + | 0.913479i | \(0.366615\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0.0496256 | + | 13.2792i | 0.00669151 | + | 1.79057i | ||||
\(56\) | −2.13657 | + | 3.70065i | −0.285511 | + | 0.494520i | ||||
\(57\) | −3.56380 | + | 2.05756i | −0.472037 | + | 0.272531i | ||||
\(58\) | −2.83462 | + | 1.63657i | −0.372204 | + | 0.214892i | ||||
\(59\) | −0.0555279 | − | 0.0961772i | −0.00722912 | − | 0.0125212i | 0.862388 | − | 0.506248i | \(-0.168968\pi\) |
−0.869617 | + | 0.493726i | \(0.835634\pi\) | |||||||
\(60\) | 1.12526 | + | 1.93230i | 0.145271 | + | 0.249459i | ||||
\(61\) | −6.14118 | + | 10.6368i | −0.786298 | + | 1.36191i | 0.141923 | + | 0.989878i | \(0.454671\pi\) |
−0.928221 | + | 0.372030i | \(0.878662\pi\) | |||||||
\(62\) | 2.32802 | − | 1.34408i | 0.295658 | − | 0.170698i | ||||
\(63\) | 4.27314i | 0.538365i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.38907 | + | 2.42684i | −0.172293 | + | 0.301013i | ||||
\(66\) | −5.93869 | −0.731002 | ||||||||
\(67\) | −4.44547 | − | 2.56660i | −0.543101 | − | 0.313560i | 0.203234 | − | 0.979130i | \(-0.434855\pi\) |
−0.746335 | + | 0.665571i | \(0.768188\pi\) | |||||||
\(68\) | 7.27314i | 0.881998i | ||||||||
\(69\) | 3.44908 | − | 5.97399i | 0.415221 | − | 0.719183i | ||||
\(70\) | 0.0357078 | + | 9.55497i | 0.00426789 | + | 1.14204i | ||||
\(71\) | −3.59953 | + | 6.23456i | −0.427185 | + | 0.739907i | −0.996622 | − | 0.0821287i | \(-0.973828\pi\) |
0.569436 | + | 0.822035i | \(0.307161\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 3.36158i | 0.393443i | 0.980459 | + | 0.196722i | \(0.0630295\pi\) | ||||
−0.980459 | + | 0.196722i | \(0.936970\pi\) | |||||||
\(74\) | 0.0474386 | − | 6.08258i | 0.00551462 | − | 0.707085i | ||||
\(75\) | 4.34869 | + | 2.46757i | 0.502144 | + | 0.284930i | ||||
\(76\) | −2.05756 | − | 3.56380i | −0.236019 | − | 0.408796i | ||||
\(77\) | −21.9770 | − | 12.6884i | −2.50451 | − | 1.44598i | ||||
\(78\) | −1.08299 | − | 0.625263i | −0.122624 | − | 0.0707971i | ||||
\(79\) | −3.41867 | + | 5.92130i | −0.384630 | + | 0.666199i | −0.991718 | − | 0.128436i | \(-0.959004\pi\) |
0.607088 | + | 0.794635i | \(0.292338\pi\) | |||||||
\(80\) | −1.93230 | + | 1.12526i | −0.216038 | + | 0.125808i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | − | 2.66654i | − | 0.294470i | ||||||
\(83\) | −6.46021 | + | 3.72981i | −0.709101 | + | 0.409399i | −0.810728 | − | 0.585423i | \(-0.800928\pi\) |
0.101627 | + | 0.994823i | \(0.467595\pi\) | |||||||
\(84\) | −4.27314 | −0.466238 | ||||||||
\(85\) | 8.18420 | + | 14.0539i | 0.887701 | + | 1.52436i | ||||
\(86\) | 4.52139 | + | 7.83128i | 0.487554 | + | 0.844469i | ||||
\(87\) | −2.83462 | − | 1.63657i | −0.303904 | − | 0.175459i | ||||
\(88\) | − | 5.93869i | − | 0.633066i | ||||||
\(89\) | 4.39703 | + | 7.61589i | 0.466085 | + | 0.807282i | 0.999250 | − | 0.0387290i | \(-0.0123309\pi\) |
−0.533165 | + | 0.846011i | \(0.678998\pi\) | |||||||
\(90\) | −1.11079 | + | 1.94066i | −0.117087 | + | 0.204563i | ||||
\(91\) | −2.67184 | − | 4.62776i | −0.280085 | − | 0.485121i | ||||
\(92\) | 5.97399 | + | 3.44908i | 0.622831 | + | 0.359592i | ||||
\(93\) | 2.32802 | + | 1.34408i | 0.241404 | + | 0.139375i | ||||
\(94\) | 2.31165 | + | 4.00389i | 0.238428 | + | 0.412970i | ||||
\(95\) | −7.98605 | − | 4.57104i | −0.819351 | − | 0.468979i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 12.1077i | 1.22935i | 0.788782 | + | 0.614673i | \(0.210712\pi\) | ||||
−0.788782 | + | 0.614673i | \(0.789288\pi\) | |||||||
\(98\) | −9.75123 | − | 5.62987i | −0.985023 | − | 0.568703i | ||||
\(99\) | −2.96934 | − | 5.14305i | −0.298430 | − | 0.516896i | ||||
\(100\) | −2.46757 | + | 4.34869i | −0.246757 | + | 0.434869i | ||||
\(101\) | −7.20776 | −0.717199 | −0.358599 | − | 0.933492i | \(-0.616746\pi\) | ||||
−0.358599 | + | 0.933492i | \(0.616746\pi\) | |||||||
\(102\) | −6.29873 | + | 3.63657i | −0.623667 | + | 0.360074i | ||||
\(103\) | − | 3.19806i | − | 0.315114i | −0.987510 | − | 0.157557i | \(-0.949638\pi\) | ||
0.987510 | − | 0.157557i | \(-0.0503618\pi\) | |||||||
\(104\) | 0.625263 | − | 1.08299i | 0.0613121 | − | 0.106196i | ||||
\(105\) | −8.25699 | + | 4.80841i | −0.805800 | + | 0.469253i | ||||
\(106\) | 0.759799 | − | 1.31601i | 0.0737982 | − | 0.127822i | ||||
\(107\) | −6.68208 | − | 3.85790i | −0.645981 | − | 0.372957i | 0.140934 | − | 0.990019i | \(-0.454990\pi\) |
−0.786915 | + | 0.617062i | \(0.788323\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −3.85417 | − | 6.67561i | −0.369162 | − | 0.639408i | 0.620273 | − | 0.784386i | \(-0.287022\pi\) |
−0.989435 | + | 0.144979i | \(0.953689\pi\) | |||||||
\(110\) | −6.68259 | − | 11.4753i | −0.637160 | − | 1.09413i | ||||
\(111\) | 5.29139 | − | 3.00021i | 0.502236 | − | 0.284767i | ||||
\(112\) | − | 4.27314i | − | 0.403774i | ||||||
\(113\) | 13.4168 | − | 7.74618i | 1.26214 | − | 0.728700i | 0.288656 | − | 0.957433i | \(-0.406792\pi\) |
0.973489 | + | 0.228733i | \(0.0734584\pi\) | |||||||
\(114\) | 2.05756 | − | 3.56380i | 0.192708 | − | 0.333781i | ||||
\(115\) | 15.4247 | − | 0.0576433i | 1.43836 | − | 0.00537526i | ||||
\(116\) | 1.63657 | − | 2.83462i | 0.151952 | − | 0.263188i | ||||
\(117\) | − | 1.25053i | − | 0.115611i | ||||||
\(118\) | 0.0961772 | + | 0.0555279i | 0.00885383 | + | 0.00511176i | ||||
\(119\) | −31.0792 | −2.84902 | ||||||||
\(120\) | −1.94066 | − | 1.11079i | −0.177157 | − | 0.101401i | ||||
\(121\) | 24.2680 | 2.20618 | ||||||||
\(122\) | − | 12.2824i | − | 1.11199i | ||||||
\(123\) | 2.30929 | − | 1.33327i | 0.208222 | − | 0.120217i | ||||
\(124\) | −1.34408 | + | 2.32802i | −0.120702 | + | 0.209062i | ||||
\(125\) | 0.125342 | + | 11.1796i | 0.0112110 | + | 0.999937i | ||||
\(126\) | −2.13657 | − | 3.70065i | −0.190341 | − | 0.329680i | ||||
\(127\) | −13.1682 | + | 7.60268i | −1.16849 | + | 0.674628i | −0.953324 | − | 0.301949i | \(-0.902363\pi\) |
−0.215167 | + | 0.976577i | \(0.569029\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −4.52139 | + | 7.83128i | −0.398086 | + | 0.689506i | ||||
\(130\) | −0.0104498 | − | 2.79624i | −0.000916508 | − | 0.245247i | ||||
\(131\) | 8.24808 | + | 14.2861i | 0.720638 | + | 1.24818i | 0.960744 | + | 0.277435i | \(0.0894844\pi\) |
−0.240106 | + | 0.970747i | \(0.577182\pi\) | |||||||
\(132\) | 5.14305 | − | 2.96934i | 0.447645 | − | 0.258448i | ||||
\(133\) | 15.2286 | − | 8.79226i | 1.32049 | − | 0.762386i | ||||
\(134\) | 5.13319 | 0.443440 | ||||||||
\(135\) | −2.23605 | + | 0.00835632i | −0.192449 | + | 0.000719198i | ||||
\(136\) | −3.63657 | − | 6.29873i | −0.311833 | − | 0.540111i | ||||
\(137\) | − | 23.0633i | − | 1.97043i | −0.171327 | − | 0.985214i | \(-0.554806\pi\) | ||
0.171327 | − | 0.985214i | \(-0.445194\pi\) | |||||||
\(138\) | 6.89816i | 0.587211i | ||||||||
\(139\) | −4.48645 | − | 7.77075i | −0.380535 | − | 0.659107i | 0.610603 | − | 0.791937i | \(-0.290927\pi\) |
−0.991139 | + | 0.132830i | \(0.957594\pi\) | |||||||
\(140\) | −4.80841 | − | 8.25699i | −0.406385 | − | 0.697843i | ||||
\(141\) | −2.31165 | + | 4.00389i | −0.194676 | + | 0.337188i | ||||
\(142\) | − | 7.19905i | − | 0.604131i | ||||||
\(143\) | 6.43152 | + | 3.71324i | 0.537831 | + | 0.310517i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | −0.0273514 | − | 7.31892i | −0.00227141 | − | 0.607803i | ||||
\(146\) | −1.68079 | − | 2.91122i | −0.139103 | − | 0.240934i | ||||
\(147\) | − | 11.2597i | − | 0.928688i | ||||||
\(148\) | 3.00021 | + | 5.29139i | 0.246615 | + | 0.434949i | ||||
\(149\) | 12.1069 | 0.991838 | 0.495919 | − | 0.868369i | \(-0.334831\pi\) | ||||
0.495919 | + | 0.868369i | \(0.334831\pi\) | |||||||
\(150\) | −4.99986 | + | 0.0373703i | −0.408237 | + | 0.00305128i | ||||
\(151\) | 4.81068 | − | 8.33235i | 0.391488 | − | 0.678077i | −0.601158 | − | 0.799130i | \(-0.705294\pi\) |
0.992646 | + | 0.121053i | \(0.0386271\pi\) | |||||||
\(152\) | 3.56380 | + | 2.05756i | 0.289063 | + | 0.166890i | ||||
\(153\) | −6.29873 | − | 3.63657i | −0.509222 | − | 0.293999i | ||||
\(154\) | 25.3769 | 2.04493 | ||||||||
\(155\) | 0.0224631 | + | 6.01087i | 0.00180428 | + | 0.482805i | ||||
\(156\) | 1.25053 | 0.100122 | ||||||||
\(157\) | −7.43290 | + | 4.29139i | −0.593210 | + | 0.342490i | −0.766366 | − | 0.642405i | \(-0.777937\pi\) |
0.173156 | + | 0.984894i | \(0.444604\pi\) | |||||||
\(158\) | − | 6.83733i | − | 0.543949i | ||||||
\(159\) | 1.51960 | 0.120512 | ||||||||
\(160\) | 1.11079 | − | 1.94066i | 0.0878156 | − | 0.153422i | ||||
\(161\) | −14.7384 | + | 25.5277i | −1.16155 | + | 2.01186i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −19.6684 | + | 11.3555i | −1.54055 | + | 0.889434i | −0.541741 | + | 0.840545i | \(0.682235\pi\) |
−0.998804 | + | 0.0488890i | \(0.984432\pi\) | |||||||
\(164\) | 1.33327 | + | 2.30929i | 0.104111 | + | 0.180325i | ||||
\(165\) | 6.59663 | − | 11.5250i | 0.513547 | − | 0.897216i | ||||
\(166\) | 3.72981 | − | 6.46021i | 0.289489 | − | 0.501410i | ||||
\(167\) | −3.96167 | − | 2.28727i | −0.306564 | − | 0.176995i | 0.338824 | − | 0.940850i | \(-0.389971\pi\) |
−0.645388 | + | 0.763855i | \(0.723304\pi\) | |||||||
\(168\) | 3.70065 | − | 2.13657i | 0.285511 | − | 0.164840i | ||||
\(169\) | −5.71809 | − | 9.90403i | −0.439853 | − | 0.761848i | ||||
\(170\) | −14.1147 | − | 8.07893i | −1.08255 | − | 0.619626i | ||||
\(171\) | 4.11513 | 0.314692 | ||||||||
\(172\) | −7.83128 | − | 4.52139i | −0.597130 | − | 0.344753i | ||||
\(173\) | 1.24331 | − | 0.717825i | 0.0945270 | − | 0.0545752i | −0.451991 | − | 0.892022i | \(-0.649286\pi\) |
0.546518 | + | 0.837447i | \(0.315953\pi\) | |||||||
\(174\) | 3.27314 | 0.248136 | ||||||||
\(175\) | −18.5826 | − | 10.5443i | −1.40471 | − | 0.797071i | ||||
\(176\) | 2.96934 | + | 5.14305i | 0.223823 | + | 0.387672i | ||||
\(177\) | 0.111056i | 0.00834747i | ||||||||
\(178\) | −7.61589 | − | 4.39703i | −0.570835 | − | 0.329572i | ||||
\(179\) | 11.3781 | 0.850437 | 0.425218 | − | 0.905091i | \(-0.360197\pi\) | ||||
0.425218 | + | 0.905091i | \(0.360197\pi\) | |||||||
\(180\) | −0.00835632 | − | 2.23605i | −0.000622843 | − | 0.166666i | ||||
\(181\) | −9.91980 | + | 17.1816i | −0.737333 | + | 1.27710i | 0.216359 | + | 0.976314i | \(0.430582\pi\) |
−0.953692 | + | 0.300784i | \(0.902752\pi\) | |||||||
\(182\) | 4.62776 | + | 2.67184i | 0.343032 | + | 0.198050i | ||||
\(183\) | 10.6368 | − | 6.14118i | 0.786298 | − | 0.453969i | ||||
\(184\) | −6.89816 | −0.508539 | ||||||||
\(185\) | 11.7515 | + | 6.84852i | 0.863987 | + | 0.503514i | ||||
\(186\) | −2.68816 | −0.197106 | ||||||||
\(187\) | 37.4062 | − | 21.5965i | 2.73541 | − | 1.57929i | ||||
\(188\) | −4.00389 | − | 2.31165i | −0.292014 | − | 0.168594i | ||||
\(189\) | 2.13657 | − | 3.70065i | 0.155413 | − | 0.269183i | ||||
\(190\) | 9.20164 | − | 0.0343873i | 0.667557 | − | 0.00249472i | ||||
\(191\) | 11.1024 | 0.803339 | 0.401670 | − | 0.915785i | \(-0.368430\pi\) | ||||
0.401670 | + | 0.915785i | \(0.368430\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 25.1326i | 1.80909i | 0.426382 | + | 0.904543i | \(0.359788\pi\) | ||||
−0.426382 | + | 0.904543i | \(0.640212\pi\) | |||||||
\(194\) | −6.05383 | − | 10.4855i | −0.434639 | − | 0.752818i | ||||
\(195\) | 2.41639 | − | 1.40717i | 0.173041 | − | 0.100770i | ||||
\(196\) | 11.2597 | 0.804268 | ||||||||
\(197\) | −0.993932 | + | 0.573847i | −0.0708148 | + | 0.0408849i | −0.534989 | − | 0.844859i | \(-0.679684\pi\) |
0.464175 | + | 0.885744i | \(0.346351\pi\) | |||||||
\(198\) | 5.14305 | + | 2.96934i | 0.365501 | + | 0.211022i | ||||
\(199\) | 6.59776 | 0.467703 | 0.233851 | − | 0.972272i | \(-0.424867\pi\) | ||||
0.233851 | + | 0.972272i | \(0.424867\pi\) | |||||||
\(200\) | −0.0373703 | − | 4.99986i | −0.00264248 | − | 0.353544i | ||||
\(201\) | 2.56660 | + | 4.44547i | 0.181034 | + | 0.313560i | ||||
\(202\) | 6.24210 | − | 3.60388i | 0.439193 | − | 0.253568i | ||||
\(203\) | 12.1128 | + | 6.99330i | 0.850149 | + | 0.490834i | ||||
\(204\) | 3.63657 | − | 6.29873i | 0.254611 | − | 0.440999i | ||||
\(205\) | 5.17484 | + | 2.96197i | 0.361427 | + | 0.206873i | ||||
\(206\) | 1.59903 | + | 2.76960i | 0.111410 | + | 0.192967i | ||||
\(207\) | −5.97399 | + | 3.44908i | −0.415221 | + | 0.239728i | ||||
\(208\) | 1.25053i | 0.0867084i | ||||||||
\(209\) | −12.2192 | + | 21.1643i | −0.845221 | + | 1.46397i | ||||
\(210\) | 4.74656 | − | 8.29270i | 0.327544 | − | 0.572251i | ||||
\(211\) | 18.6041 | 1.28076 | 0.640380 | − | 0.768058i | \(-0.278777\pi\) | ||||
0.640380 | + | 0.768058i | \(0.278777\pi\) | |||||||
\(212\) | 1.51960i | 0.104366i | ||||||||
\(213\) | 6.23456 | − | 3.59953i | 0.427185 | − | 0.246636i | ||||
\(214\) | 7.71580 | 0.527442 | ||||||||
\(215\) | −20.2201 | + | 0.0755644i | −1.37900 | + | 0.00515345i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −9.94795 | − | 5.74345i | −0.675311 | − | 0.389891i | ||||
\(218\) | 6.67561 | + | 3.85417i | 0.452129 | + | 0.261037i | ||||
\(219\) | 1.68079 | − | 2.91122i | 0.113577 | − | 0.196722i | ||||
\(220\) | 11.5250 | + | 6.59663i | 0.777012 | + | 0.444745i | ||||
\(221\) | 9.09525 | 0.611813 | ||||||||
\(222\) | −3.08237 | + | 5.24395i | −0.206875 | + | 0.351951i | ||||
\(223\) | 19.3854i | 1.29814i | 0.760727 | + | 0.649072i | \(0.224843\pi\) | ||||
−0.760727 | + | 0.649072i | \(0.775157\pi\) | |||||||
\(224\) | 2.13657 | + | 3.70065i | 0.142756 | + | 0.247260i | ||||
\(225\) | −2.53229 | − | 4.31132i | −0.168820 | − | 0.287421i | ||||
\(226\) | −7.74618 | + | 13.4168i | −0.515268 | + | 0.892471i | ||||
\(227\) | −5.15116 | − | 2.97402i | −0.341895 | − | 0.197393i | 0.319215 | − | 0.947682i | \(-0.396581\pi\) |
−0.661109 | + | 0.750289i | \(0.729914\pi\) | |||||||
\(228\) | 4.11513i | 0.272531i | ||||||||
\(229\) | 4.45902 | − | 7.72325i | 0.294660 | − | 0.510367i | −0.680246 | − | 0.732984i | \(-0.738127\pi\) |
0.974906 | + | 0.222618i | \(0.0714602\pi\) | |||||||
\(230\) | −13.3293 | + | 7.76225i | −0.878910 | + | 0.511828i | ||||
\(231\) | 12.6884 | + | 21.9770i | 0.834837 | + | 1.44598i | ||||
\(232\) | 3.27314i | 0.214892i | ||||||||
\(233\) | − | 1.91329i | − | 0.125344i | −0.998034 | − | 0.0626718i | \(-0.980038\pi\) | ||
0.998034 | − | 0.0626718i | \(-0.0199621\pi\) | |||||||
\(234\) | 0.625263 | + | 1.08299i | 0.0408747 | + | 0.0707971i | ||||
\(235\) | −10.3379 | + | 0.0386337i | −0.674372 | + | 0.00252019i | ||||
\(236\) | −0.111056 | −0.00722912 | ||||||||
\(237\) | 5.92130 | − | 3.41867i | 0.384630 | − | 0.222066i | ||||
\(238\) | 26.9154 | − | 15.5396i | 1.74466 | − | 1.00728i | ||||
\(239\) | −7.76415 | − | 13.4479i | −0.502221 | − | 0.869872i | −0.999997 | − | 0.00256635i | \(-0.999183\pi\) |
0.497776 | − | 0.867306i | \(-0.334150\pi\) | |||||||
\(240\) | 2.23605 | − | 0.00835632i | 0.144337 | − | 0.000539398i | ||||
\(241\) | −5.55610 | + | 9.62345i | −0.357900 | + | 0.619901i | −0.987610 | − | 0.156929i | \(-0.949840\pi\) |
0.629710 | + | 0.776830i | \(0.283174\pi\) | |||||||
\(242\) | −21.0167 | + | 12.1340i | −1.35101 | + | 0.780003i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 6.14118 | + | 10.6368i | 0.393149 | + | 0.680954i | ||||
\(245\) | 21.7572 | − | 12.6702i | 1.39002 | − | 0.809468i | ||||
\(246\) | −1.33327 | + | 2.30929i | −0.0850062 | + | 0.147235i | ||||
\(247\) | −4.45663 | + | 2.57304i | −0.283569 | + | 0.163718i | ||||
\(248\) | − | 2.68816i | − | 0.170698i | ||||||
\(249\) | 7.45961 | 0.472734 | ||||||||
\(250\) | −5.69837 | − | 9.61918i | −0.360396 | − | 0.608370i | ||||
\(251\) | 13.3364 | 0.841789 | 0.420894 | − | 0.907110i | \(-0.361716\pi\) | ||||
0.420894 | + | 0.907110i | \(0.361716\pi\) | |||||||
\(252\) | 3.70065 | + | 2.13657i | 0.233119 | + | 0.134591i | ||||
\(253\) | − | 40.9660i | − | 2.57551i | ||||||
\(254\) | 7.60268 | − | 13.1682i | 0.477034 | − | 0.826248i | ||||
\(255\) | −0.0607767 | − | 16.2631i | −0.00380599 | − | 1.01844i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 21.3805 | − | 12.3440i | 1.33368 | − | 0.769999i | 0.347817 | − | 0.937563i | \(-0.386923\pi\) |
0.985861 | + | 0.167563i | \(0.0535898\pi\) | |||||||
\(258\) | − | 9.04279i | − | 0.562979i | ||||||
\(259\) | −22.6108 | + | 12.8203i | −1.40497 | + | 0.796615i | ||||
\(260\) | 1.40717 | + | 2.41639i | 0.0872690 | + | 0.149858i | ||||
\(261\) | 1.63657 | + | 2.83462i | 0.101301 | + | 0.175459i | ||||
\(262\) | −14.2861 | − | 8.24808i | −0.882598 | − | 0.509568i | ||||
\(263\) | −21.8902 | − | 12.6383i | −1.34981 | − | 0.779311i | −0.361584 | − | 0.932340i | \(-0.617764\pi\) |
−0.988222 | + | 0.153029i | \(0.951097\pi\) | |||||||
\(264\) | −2.96934 | + | 5.14305i | −0.182750 | + | 0.316533i | ||||
\(265\) | 1.70995 | + | 2.93632i | 0.105041 | + | 0.180377i | ||||
\(266\) | −8.79226 | + | 15.2286i | −0.539088 | + | 0.933728i | ||||
\(267\) | − | 8.79407i | − | 0.538188i | ||||||
\(268\) | −4.44547 | + | 2.56660i | −0.271551 | + | 0.156780i | ||||
\(269\) | −25.0272 | −1.52594 | −0.762968 | − | 0.646436i | \(-0.776259\pi\) | ||||
−0.762968 | + | 0.646436i | \(0.776259\pi\) | |||||||
\(270\) | 1.93230 | − | 1.12526i | 0.117596 | − | 0.0684813i | ||||
\(271\) | −6.67337 | − | 11.5586i | −0.405379 | − | 0.702136i | 0.588987 | − | 0.808143i | \(-0.299527\pi\) |
−0.994365 | + | 0.106006i | \(0.966194\pi\) | |||||||
\(272\) | 6.29873 | + | 3.63657i | 0.381916 | + | 0.220500i | ||||
\(273\) | 5.34368i | 0.323414i | ||||||||
\(274\) | 11.5316 | + | 19.9734i | 0.696652 | + | 1.20664i | ||||
\(275\) | 29.6926 | − | 0.221931i | 1.79053 | − | 0.0133829i | ||||
\(276\) | −3.44908 | − | 5.97399i | −0.207610 | − | 0.359592i | ||||
\(277\) | 16.1983 | + | 9.35210i | 0.973262 | + | 0.561913i | 0.900229 | − | 0.435416i | \(-0.143399\pi\) |
0.0730329 | + | 0.997330i | \(0.476732\pi\) | |||||||
\(278\) | 7.77075 | + | 4.48645i | 0.466059 | + | 0.269079i | ||||
\(279\) | −1.34408 | − | 2.32802i | −0.0804680 | − | 0.139375i | ||||
\(280\) | 8.29270 | + | 4.74656i | 0.495584 | + | 0.283661i | ||||
\(281\) | −5.15883 | − | 8.93535i | −0.307750 | − | 0.533038i | 0.670120 | − | 0.742253i | \(-0.266243\pi\) |
−0.977870 | + | 0.209214i | \(0.932909\pi\) | |||||||
\(282\) | − | 4.62329i | − | 0.275313i | ||||||
\(283\) | −5.24310 | − | 3.02711i | −0.311670 | − | 0.179943i | 0.336003 | − | 0.941861i | \(-0.390925\pi\) |
−0.647674 | + | 0.761918i | \(0.724258\pi\) | |||||||
\(284\) | 3.59953 | + | 6.23456i | 0.213593 | + | 0.369953i | ||||
\(285\) | 4.63060 | + | 7.95166i | 0.274293 | + | 0.471016i | ||||
\(286\) | −7.42648 | −0.439137 | ||||||||
\(287\) | −9.86794 | + | 5.69726i | −0.582486 | + | 0.336298i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 17.9493 | − | 31.0891i | 1.05584 | − | 1.82877i | ||||
\(290\) | 3.68315 | + | 6.32469i | 0.216282 | + | 0.371399i | ||||
\(291\) | 6.05383 | − | 10.4855i | 0.354882 | − | 0.614673i | ||||
\(292\) | 2.91122 | + | 1.68079i | 0.170366 | + | 0.0983608i | ||||
\(293\) | 4.60340 | + | 2.65778i | 0.268934 | + | 0.155269i | 0.628403 | − | 0.777888i | \(-0.283709\pi\) |
−0.359469 | + | 0.933157i | \(0.617042\pi\) | |||||||
\(294\) | 5.62987 | + | 9.75123i | 0.328341 | + | 0.568703i | ||||
\(295\) | −0.214593 | + | 0.124967i | −0.0124941 | + | 0.00727586i | ||||
\(296\) | −5.24395 | − | 3.08237i | −0.304798 | − | 0.179159i | ||||
\(297\) | 5.93869i | 0.344598i | ||||||||
\(298\) | −10.4849 | + | 6.05346i | −0.607374 | + | 0.350668i | ||||
\(299\) | 4.31317 | − | 7.47062i | 0.249437 | − | 0.432037i | ||||
\(300\) | 4.31132 | − | 2.53229i | 0.248914 | − | 0.146202i | ||||
\(301\) | 19.3206 | − | 33.4642i | 1.11362 | − | 1.92884i | ||||
\(302\) | 9.62137i | 0.553648i | ||||||||
\(303\) | 6.24210 | + | 3.60388i | 0.358599 | + | 0.207037i | ||||
\(304\) | −4.11513 | −0.236019 | ||||||||
\(305\) | 23.8358 | + | 13.6431i | 1.36484 | + | 0.781203i | ||||
\(306\) | 7.27314 | 0.415778 | ||||||||
\(307\) | − | 18.2790i | − | 1.04324i | −0.853178 | − | 0.521620i | \(-0.825328\pi\) | ||
0.853178 | − | 0.521620i | \(-0.174672\pi\) | |||||||
\(308\) | −21.9770 | + | 12.6884i | −1.25226 | + | 0.722990i | ||||
\(309\) | −1.59903 | + | 2.76960i | −0.0909656 | + | 0.157557i | ||||
\(310\) | −3.02489 | − | 5.19433i | −0.171802 | − | 0.295018i | ||||
\(311\) | −16.0222 | − | 27.7513i | −0.908537 | − | 1.57363i | −0.816098 | − | 0.577913i | \(-0.803867\pi\) |
−0.0924383 | − | 0.995718i | \(-0.529466\pi\) | |||||||
\(312\) | −1.08299 | + | 0.625263i | −0.0613121 | + | 0.0353985i | ||||
\(313\) | 7.68688 | − | 4.43802i | 0.434488 | − | 0.250852i | −0.266769 | − | 0.963761i | \(-0.585956\pi\) |
0.701257 | + | 0.712909i | \(0.252623\pi\) | |||||||
\(314\) | 4.29139 | − | 7.43290i | 0.242177 | − | 0.419463i | ||||
\(315\) | 9.55497 | − | 0.0357078i | 0.538362 | − | 0.00201190i | ||||
\(316\) | 3.41867 | + | 5.92130i | 0.192315 | + | 0.333099i | ||||
\(317\) | 3.82489 | − | 2.20830i | 0.214827 | − | 0.124031i | −0.388725 | − | 0.921354i | \(-0.627085\pi\) |
0.603553 | + | 0.797323i | \(0.293751\pi\) | |||||||
\(318\) | −1.31601 | + | 0.759799i | −0.0737982 | + | 0.0426074i | ||||
\(319\) | −19.4382 | −1.08833 | ||||||||
\(320\) | 0.00835632 | + | 2.23605i | 0.000467133 | + | 0.124999i | ||||
\(321\) | 3.85790 | + | 6.68208i | 0.215327 | + | 0.372957i | ||||
\(322\) | − | 29.4768i | − | 1.64268i | ||||||
\(323\) | 29.9299i | 1.66534i | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 5.43815 | + | 3.08576i | 0.301654 | + | 0.171167i | ||||
\(326\) | 11.3555 | − | 19.6684i | 0.628925 | − | 1.08933i | ||||
\(327\) | 7.70833i | 0.426272i | ||||||||
\(328\) | −2.30929 | − | 1.33327i | −0.127509 | − | 0.0736176i | ||||
\(329\) | 9.87800 | − | 17.1092i | 0.544592 | − | 0.943260i | ||||
\(330\) | 0.0496256 | + | 13.2792i | 0.00273180 | + | 0.730997i | ||||
\(331\) | −15.1841 | − | 26.2996i | −0.834592 | − | 1.44556i | −0.894362 | − | 0.447344i | \(-0.852370\pi\) |
0.0597696 | − | 0.998212i | \(-0.480963\pi\) | |||||||
\(332\) | 7.45961i | 0.409399i | ||||||||
\(333\) | −6.08258 | − | 0.0474386i | −0.333323 | − | 0.00259962i | ||||
\(334\) | 4.57455 | 0.250308 | ||||||||
\(335\) | −5.70189 | + | 9.96176i | −0.311528 | + | 0.544269i | ||||
\(336\) | −2.13657 | + | 3.70065i | −0.116560 | + | 0.201887i | ||||
\(337\) | −20.8921 | − | 12.0621i | −1.13807 | − | 0.657063i | −0.192115 | − | 0.981372i | \(-0.561535\pi\) |
−0.945951 | + | 0.324310i | \(0.894868\pi\) | |||||||
\(338\) | 9.90403 | + | 5.71809i | 0.538708 | + | 0.311023i | ||||
\(339\) | −15.4924 | −0.841430 | ||||||||
\(340\) | 16.2631 | − | 0.0607767i | 0.881992 | − | 0.00329608i | ||||
\(341\) | 15.9642 | 0.864507 | ||||||||
\(342\) | −3.56380 | + | 2.05756i | −0.192708 | + | 0.111260i | ||||
\(343\) | 18.2025i | 0.982843i | ||||||||
\(344\) | 9.04279 | 0.487554 | ||||||||
\(345\) | −13.3870 | − | 7.66241i | −0.720730 | − | 0.412530i | ||||
\(346\) | −0.717825 | + | 1.24331i | −0.0385905 | + | 0.0668407i | ||||
\(347\) | − | 28.8375i | − | 1.54808i | −0.633139 | − | 0.774038i | \(-0.718234\pi\) | ||
0.633139 | − | 0.774038i | \(-0.281766\pi\) | |||||||
\(348\) | −2.83462 | + | 1.63657i | −0.151952 | + | 0.0877294i | ||||
\(349\) | 11.6328 | + | 20.1486i | 0.622689 | + | 1.07853i | 0.988983 | + | 0.148029i | \(0.0472930\pi\) |
−0.366294 | + | 0.930499i | \(0.619374\pi\) | |||||||
\(350\) | 21.3651 | − | 0.159689i | 1.14201 | − | 0.00853573i | ||||
\(351\) | −0.625263 | + | 1.08299i | −0.0333741 | + | 0.0578056i | ||||
\(352\) | −5.14305 | − | 2.96934i | −0.274126 | − | 0.158267i | ||||
\(353\) | −0.169377 | + | 0.0977899i | −0.00901503 | + | 0.00520483i | −0.504501 | − | 0.863411i | \(-0.668323\pi\) |
0.495486 | + | 0.868616i | \(0.334990\pi\) | |||||||
\(354\) | −0.0555279 | − | 0.0961772i | −0.00295128 | − | 0.00511176i | ||||
\(355\) | 13.9709 | + | 7.99663i | 0.741498 | + | 0.424417i | ||||
\(356\) | 8.79407 | 0.466085 | ||||||||
\(357\) | 26.9154 | + | 15.5396i | 1.42451 | + | 0.822442i | ||||
\(358\) | −9.85370 | + | 5.68904i | −0.520784 | + | 0.300675i | ||||
\(359\) | 3.52995 | 0.186303 | 0.0931517 | − | 0.995652i | \(-0.470306\pi\) | ||||
0.0931517 | + | 0.995652i | \(0.470306\pi\) | |||||||
\(360\) | 1.12526 | + | 1.93230i | 0.0593066 | + | 0.101841i | ||||
\(361\) | 1.03287 | + | 1.78898i | 0.0543615 | + | 0.0941570i | ||||
\(362\) | − | 19.8396i | − | 1.04275i | ||||||
\(363\) | −21.0167 | − | 12.1340i | −1.10309 | − | 0.636870i | ||||
\(364\) | −5.34368 | −0.280085 | ||||||||
\(365\) | 7.51667 | − | 0.0280905i | 0.393441 | − | 0.00147032i | ||||
\(366\) | −6.14118 | + | 10.6368i | −0.321005 | + | 0.555996i | ||||
\(367\) | 1.73122 | + | 0.999522i | 0.0903691 | + | 0.0521746i | 0.544504 | − | 0.838759i | \(-0.316718\pi\) |
−0.454134 | + | 0.890933i | \(0.650051\pi\) | |||||||
\(368\) | 5.97399 | − | 3.44908i | 0.311416 | − | 0.179796i | ||||
\(369\) | −2.66654 | −0.138815 | ||||||||
\(370\) | −13.6014 | − | 0.0552472i | −0.707101 | − | 0.00287217i | ||||
\(371\) | −6.49346 | −0.337124 | ||||||||
\(372\) | 2.32802 | − | 1.34408i | 0.120702 | − | 0.0696873i | ||||
\(373\) | 11.9568 | + | 6.90326i | 0.619099 | + | 0.357437i | 0.776518 | − | 0.630095i | \(-0.216984\pi\) |
−0.157419 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(374\) | −21.5965 | + | 37.4062i | −1.11673 | + | 1.93423i | ||||
\(375\) | 5.48127 | − | 9.74452i | 0.283052 | − | 0.503205i | ||||
\(376\) | 4.62329 | 0.238428 | ||||||||
\(377\) | −3.54477 | − | 2.04657i | −0.182565 | − | 0.105404i | ||||
\(378\) | 4.27314i | 0.219787i | ||||||||
\(379\) | −3.38018 | − | 5.85465i | −0.173628 | − | 0.300733i | 0.766057 | − | 0.642772i | \(-0.222216\pi\) |
−0.939686 | + | 0.342039i | \(0.888882\pi\) | |||||||
\(380\) | −7.95166 | + | 4.63060i | −0.407911 | + | 0.237545i | ||||
\(381\) | 15.2054 | 0.778994 | ||||||||
\(382\) | −9.61493 | + | 5.55119i | −0.491943 | + | 0.284023i | ||||
\(383\) | −12.2108 | − | 7.04991i | −0.623943 | − | 0.360233i | 0.154460 | − | 0.987999i | \(-0.450636\pi\) |
−0.778402 | + | 0.627766i | \(0.783970\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −28.1883 | + | 49.2478i | −1.43661 | + | 2.50990i | ||||
\(386\) | −12.5663 | − | 21.7655i | −0.639609 | − | 1.10783i | ||||
\(387\) | 7.83128 | − | 4.52139i | 0.398086 | − | 0.229835i | ||||
\(388\) | 10.4855 | + | 6.05383i | 0.532322 | + | 0.307336i | ||||
\(389\) | 2.87886 | − | 4.98634i | 0.145964 | − | 0.252817i | −0.783768 | − | 0.621054i | \(-0.786705\pi\) |
0.929732 | + | 0.368236i | \(0.120038\pi\) | |||||||
\(390\) | −1.38907 | + | 2.42684i | −0.0703383 | + | 0.122888i | ||||
\(391\) | −25.0857 | − | 43.4497i | −1.26864 | − | 2.19734i | ||||
\(392\) | −9.75123 | + | 5.62987i | −0.492511 | + | 0.284352i | ||||
\(393\) | − | 16.4962i | − | 0.832121i | ||||||
\(394\) | 0.573847 | − | 0.993932i | 0.0289100 | − | 0.0500736i | ||||
\(395\) | 13.2689 | + | 7.59484i | 0.667632 | + | 0.382138i | ||||
\(396\) | −5.93869 | −0.298430 | ||||||||
\(397\) | 11.8180i | 0.593130i | 0.955013 | + | 0.296565i | \(0.0958411\pi\) | ||||
−0.955013 | + | 0.296565i | \(0.904159\pi\) | |||||||
\(398\) | −5.71382 | + | 3.29888i | −0.286408 | + | 0.165358i | ||||
\(399\) | −17.5845 | −0.880327 | ||||||||
\(400\) | 2.53229 | + | 4.31132i | 0.126615 | + | 0.215566i | ||||
\(401\) | 5.04044 | 0.251708 | 0.125854 | − | 0.992049i | \(-0.459833\pi\) | ||||
0.125854 | + | 0.992049i | \(0.459833\pi\) | |||||||
\(402\) | −4.44547 | − | 2.56660i | −0.221720 | − | 0.128010i | ||||
\(403\) | 2.91124 | + | 1.68081i | 0.145019 | + | 0.0837270i | ||||
\(404\) | −3.60388 | + | 6.24210i | −0.179300 | + | 0.310556i | ||||
\(405\) | 1.94066 | + | 1.11079i | 0.0964320 | + | 0.0551956i | ||||
\(406\) | −13.9866 | −0.694144 | ||||||||
\(407\) | 18.3052 | − | 31.1422i | 0.907357 | − | 1.54366i | ||||
\(408\) | 7.27314i | 0.360074i | ||||||||
\(409\) | 1.41880 | + | 2.45743i | 0.0701549 | + | 0.121512i | 0.898969 | − | 0.438012i | \(-0.144317\pi\) |
−0.828814 | + | 0.559524i | \(0.810984\pi\) | |||||||
\(410\) | −5.96253 | + | 0.0222825i | −0.294468 | + | 0.00110045i | ||||
\(411\) | −11.5316 | + | 19.9734i | −0.568814 | + | 0.985214i | ||||
\(412\) | −2.76960 | − | 1.59903i | −0.136448 | − | 0.0787785i | ||||
\(413\) | − | 0.474557i | − | 0.0233514i | ||||||
\(414\) | 3.44908 | − | 5.97399i | 0.169513 | − | 0.293605i | ||||
\(415\) | 8.39403 | + | 14.4142i | 0.412046 | + | 0.707566i | ||||
\(416\) | −0.625263 | − | 1.08299i | −0.0306560 | − | 0.0530978i | ||||
\(417\) | 8.97289i | 0.439404i | ||||||||
\(418\) | − | 24.4384i | − | 1.19532i | ||||||
\(419\) | 2.45402 | + | 4.25048i | 0.119887 | + | 0.207650i | 0.919723 | − | 0.392569i | \(-0.128414\pi\) |
−0.799836 | + | 0.600219i | \(0.795080\pi\) | |||||||
\(420\) | 0.0357078 | + | 9.55497i | 0.00174236 | + | 0.466235i | ||||
\(421\) | −25.3784 | −1.23687 | −0.618433 | − | 0.785837i | \(-0.712232\pi\) | ||||
−0.618433 | + | 0.785837i | \(0.712232\pi\) | |||||||
\(422\) | −16.1116 | + | 9.30206i | −0.784303 | + | 0.452817i | ||||
\(423\) | 4.00389 | − | 2.31165i | 0.194676 | − | 0.112396i | ||||
\(424\) | −0.759799 | − | 1.31601i | −0.0368991 | − | 0.0639111i | ||||
\(425\) | 31.3569 | − | 18.4177i | 1.52103 | − | 0.893391i | ||||
\(426\) | −3.59953 | + | 6.23456i | −0.174398 | + | 0.302066i | ||||
\(427\) | −45.4527 | + | 26.2421i | −2.19961 | + | 1.26995i | ||||
\(428\) | −6.68208 | + | 3.85790i | −0.322991 | + | 0.186479i | ||||
\(429\) | −3.71324 | − | 6.43152i | −0.179277 | − | 0.310517i | ||||
\(430\) | 17.4734 | − | 10.1755i | 0.842641 | − | 0.490707i | ||||
\(431\) | −6.96555 | + | 12.0647i | −0.335519 | + | 0.581136i | −0.983584 | − | 0.180449i | \(-0.942245\pi\) |
0.648065 | + | 0.761585i | \(0.275578\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 22.8789i | − | 1.09949i | −0.835332 | − | 0.549746i | \(-0.814725\pi\) | ||
0.835332 | − | 0.549746i | \(-0.185275\pi\) | |||||||
\(434\) | 11.4869 | 0.551389 | ||||||||
\(435\) | −3.63577 | + | 6.35204i | −0.174322 | + | 0.304557i | ||||
\(436\) | −7.70833 | −0.369162 | ||||||||
\(437\) | 24.5837 | + | 14.1934i | 1.17600 | + | 0.678963i | ||||
\(438\) | 3.36158i | 0.160623i | ||||||||
\(439\) | −5.14932 | + | 8.91889i | −0.245764 | + | 0.425675i | −0.962346 | − | 0.271827i | \(-0.912372\pi\) |
0.716582 | + | 0.697502i | \(0.245705\pi\) | |||||||
\(440\) | −13.2792 | + | 0.0496256i | −0.633062 | + | 0.00236581i | ||||
\(441\) | −5.62987 | + | 9.75123i | −0.268089 | + | 0.464344i | ||||
\(442\) | −7.87672 | + | 4.54763i | −0.374657 | + | 0.216309i | ||||
\(443\) | − | 21.4199i | − | 1.01769i | −0.860859 | − | 0.508844i | \(-0.830073\pi\) | ||
0.860859 | − | 0.508844i | \(-0.169927\pi\) | |||||||
\(444\) | 0.0474386 | − | 6.08258i | 0.00225134 | − | 0.288666i | ||||
\(445\) | 16.9928 | − | 9.89564i | 0.805535 | − | 0.469098i | ||||
\(446\) | −9.69271 | − | 16.7883i | −0.458963 | − | 0.794947i | ||||
\(447\) | −10.4849 | − | 6.05346i | −0.495919 | − | 0.286319i | ||||
\(448\) | −3.70065 | − | 2.13657i | −0.174839 | − | 0.100944i | ||||
\(449\) | −16.3407 | + | 28.3030i | −0.771167 | + | 1.33570i | 0.165757 | + | 0.986167i | \(0.446993\pi\) |
−0.936924 | + | 0.349533i | \(0.886340\pi\) | |||||||
\(450\) | 4.34869 | + | 2.46757i | 0.204999 | + | 0.116322i | ||||
\(451\) | 7.91788 | − | 13.7142i | 0.372838 | − | 0.645775i | ||||
\(452\) | − | 15.4924i | − | 0.728700i | ||||||
\(453\) | −8.33235 | + | 4.81068i | −0.391488 | + | 0.226026i | ||||
\(454\) | 5.94805 | 0.279156 | ||||||||
\(455\) | −10.3256 | + | 6.01304i | −0.484071 | + | 0.281896i | ||||
\(456\) | −2.05756 | − | 3.56380i | −0.0963542 | − | 0.166890i | ||||
\(457\) | −9.41322 | − | 5.43472i | −0.440332 | − | 0.254226i | 0.263407 | − | 0.964685i | \(-0.415154\pi\) |
−0.703738 | + | 0.710459i | \(0.748487\pi\) | |||||||
\(458\) | 8.91804i | 0.416713i | ||||||||
\(459\) | 3.63657 | + | 6.29873i | 0.169741 | + | 0.293999i | ||||
\(460\) | 7.66241 | − | 13.3870i | 0.357262 | − | 0.624171i | ||||
\(461\) | 14.4531 | + | 25.0336i | 0.673150 | + | 1.16593i | 0.977006 | + | 0.213212i | \(0.0683925\pi\) |
−0.303856 | + | 0.952718i | \(0.598274\pi\) | |||||||
\(462\) | −21.9770 | − | 12.6884i | −1.02246 | − | 0.590319i | ||||
\(463\) | 32.1719 | + | 18.5745i | 1.49516 | + | 0.863229i | 0.999985 | − | 0.00556589i | \(-0.00177169\pi\) |
0.495172 | + | 0.868795i | \(0.335105\pi\) | |||||||
\(464\) | −1.63657 | − | 2.83462i | −0.0759759 | − | 0.131594i | ||||
\(465\) | 2.98598 | − | 5.21680i | 0.138472 | − | 0.241923i | ||||
\(466\) | 0.956644 | + | 1.65696i | 0.0443157 | + | 0.0767570i | ||||
\(467\) | − | 22.3568i | − | 1.03455i | −0.855819 | − | 0.517276i | \(-0.826946\pi\) | ||
0.855819 | − | 0.517276i | \(-0.173054\pi\) | |||||||
\(468\) | −1.08299 | − | 0.625263i | −0.0500611 | − | 0.0289028i | ||||
\(469\) | −10.9674 | − | 18.9961i | −0.506429 | − | 0.877160i | ||||
\(470\) | 8.93359 | − | 5.20242i | 0.412076 | − | 0.239970i | ||||
\(471\) | 8.58277 | 0.395473 | ||||||||
\(472\) | 0.0961772 | − | 0.0555279i | 0.00442691 | − | 0.00255588i | ||||
\(473\) | 53.7023i | 2.46923i | ||||||||
\(474\) | −3.41867 | + | 5.92130i | −0.157025 | + | 0.271975i | ||||
\(475\) | −10.1543 | + | 17.8954i | −0.465913 | + | 0.821098i | ||||
\(476\) | −15.5396 | + | 26.9154i | −0.712256 | + | 1.23366i | ||||
\(477\) | −1.31601 | − | 0.759799i | −0.0602560 | − | 0.0347888i | ||||
\(478\) | 13.4479 | + | 7.76415i | 0.615092 | + | 0.355124i | ||||
\(479\) | 5.34678 | + | 9.26089i | 0.244300 | + | 0.423141i | 0.961935 | − | 0.273279i | \(-0.0881084\pi\) |
−0.717634 | + | 0.696420i | \(0.754775\pi\) | |||||||
\(480\) | −1.93230 | + | 1.12526i | −0.0881970 | + | 0.0513610i | ||||
\(481\) | 6.61702 | − | 3.75184i | 0.301710 | − | 0.171069i | ||||
\(482\) | − | 11.1122i | − | 0.506147i | ||||||
\(483\) | 25.5277 | − | 14.7384i | 1.16155 | − | 0.670621i | ||||
\(484\) | 12.1340 | − | 21.0167i | 0.551546 | − | 0.955305i | ||||
\(485\) | 27.0733 | − | 0.101175i | 1.22934 | − | 0.00459414i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | − | 12.8937i | − | 0.584270i | −0.956377 | − | 0.292135i | \(-0.905634\pi\) | ||
0.956377 | − | 0.292135i | \(-0.0943656\pi\) | |||||||
\(488\) | −10.6368 | − | 6.14118i | −0.481507 | − | 0.277998i | ||||
\(489\) | 22.7111 | 1.02703 | ||||||||
\(490\) | −12.5072 | + | 21.8513i | −0.565018 | + | 0.987141i | ||||
\(491\) | −38.5951 | −1.74177 | −0.870885 | − | 0.491486i | \(-0.836454\pi\) | ||||
−0.870885 | + | 0.491486i | \(0.836454\pi\) | |||||||
\(492\) | − | 2.66654i | − | 0.120217i | ||||||
\(493\) | −20.6166 | + | 11.9030i | −0.928526 | + | 0.536085i | ||||
\(494\) | 2.57304 | − | 4.45663i | 0.115766 | − | 0.200513i | ||||
\(495\) | −11.4753 | + | 6.68259i | −0.515778 | + | 0.300360i | ||||
\(496\) | 1.34408 | + | 2.32802i | 0.0603510 | + | 0.104531i | ||||
\(497\) | −26.6412 | + | 15.3813i | −1.19502 | + | 0.689945i | ||||
\(498\) | −6.46021 | + | 3.72981i | −0.289489 | + | 0.167137i | ||||
\(499\) | −5.68234 | + | 9.84210i | −0.254376 | + | 0.440593i | −0.964726 | − | 0.263256i | \(-0.915204\pi\) |
0.710350 | + | 0.703849i | \(0.248537\pi\) | |||||||
\(500\) | 9.74452 | + | 5.48127i | 0.435788 | + | 0.245130i | ||||
\(501\) | 2.28727 | + | 3.96167i | 0.102188 | + | 0.176995i | ||||
\(502\) | −11.5497 | + | 6.66822i | −0.515488 | + | 0.297617i | ||||
\(503\) | 5.76066 | − | 3.32592i | 0.256855 | − | 0.148295i | −0.366044 | − | 0.930598i | \(-0.619288\pi\) |
0.622899 | + | 0.782302i | \(0.285955\pi\) | |||||||
\(504\) | −4.27314 | −0.190341 | ||||||||
\(505\) | 0.0602304 | + | 16.1169i | 0.00268022 | + | 0.717194i | ||||
\(506\) | 20.4830 | + | 35.4776i | 0.910581 | + | 1.57717i | ||||
\(507\) | 11.4362i | 0.507899i | ||||||||
\(508\) | 15.2054i | 0.674628i | ||||||||
\(509\) | 3.93391 | + | 6.81372i | 0.174367 | + | 0.302013i | 0.939942 | − | 0.341334i | \(-0.110879\pi\) |
−0.765575 | + | 0.643347i | \(0.777545\pi\) | |||||||
\(510\) | 8.18420 | + | 14.0539i | 0.362402 | + | 0.622317i | ||||
\(511\) | −7.18226 | + | 12.4400i | −0.317724 | + | 0.550315i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.56380 | − | 2.05756i | −0.157346 | − | 0.0908436i | ||||
\(514\) | −12.3440 | + | 21.3805i | −0.544472 | + | 0.943053i | ||||
\(515\) | −7.15103 | + | 0.0267240i | −0.315112 | + | 0.00117760i | ||||
\(516\) | 4.52139 | + | 7.83128i | 0.199043 | + | 0.344753i | ||||
\(517\) | 27.4563i | 1.20753i | ||||||||
\(518\) | 13.1714 | − | 22.4081i | 0.578719 | − | 0.984557i | ||||
\(519\) | −1.43565 | −0.0630180 | ||||||||
\(520\) | −2.42684 | − | 1.38907i | −0.106424 | − | 0.0609148i | ||||
\(521\) | 16.2960 | − | 28.2255i | 0.713941 | − | 1.23658i | −0.249425 | − | 0.968394i | \(-0.580242\pi\) |
0.963367 | − | 0.268188i | \(-0.0864249\pi\) | |||||||
\(522\) | −2.83462 | − | 1.63657i | −0.124068 | − | 0.0716308i | ||||
\(523\) | 10.8426 | + | 6.26000i | 0.474116 | + | 0.273731i | 0.717961 | − | 0.696083i | \(-0.245076\pi\) |
−0.243845 | + | 0.969814i | \(0.578409\pi\) | |||||||
\(524\) | 16.4962 | 0.720638 | ||||||||
\(525\) | 10.8209 | + | 18.4229i | 0.472261 | + | 0.804041i | ||||
\(526\) | 25.2766 | 1.10211 | ||||||||
\(527\) | 16.9320 | − | 9.77569i | 0.737569 | − | 0.425836i | ||||
\(528\) | − | 5.93869i | − | 0.258448i | ||||||
\(529\) | −24.5847 | −1.06890 | ||||||||
\(530\) | −2.94902 | − | 1.68795i | −0.128097 | − | 0.0733200i | ||||
\(531\) | 0.0555279 | − | 0.0961772i | 0.00240971 | − | 0.00417373i | ||||
\(532\) | − | 17.5845i | − | 0.762386i | ||||||
\(533\) | 2.88783 | − | 1.66729i | 0.125086 | − | 0.0722183i | ||||
\(534\) | 4.39703 | + | 7.61589i | 0.190278 | + | 0.329572i | ||||
\(535\) | −8.57063 | + | 14.9737i | −0.370541 | + | 0.647371i | ||||
\(536\) | 2.56660 | − | 4.44547i | 0.110860 | − | 0.192015i | ||||
\(537\) | −9.85370 | − | 5.68904i | −0.425218 | − | 0.245500i | ||||
\(538\) | 21.6742 | − | 12.5136i | 0.934442 | − | 0.539500i | ||||
\(539\) | −33.4341 | − | 57.9095i | −1.44011 | − | 2.49434i | ||||
\(540\) | −1.11079 | + | 1.94066i | −0.0478008 | + | 0.0835126i | ||||
\(541\) | 4.12381 | 0.177297 | 0.0886483 | − | 0.996063i | \(-0.471745\pi\) | ||||
0.0886483 | + | 0.996063i | \(0.471745\pi\) | |||||||
\(542\) | 11.5586 | + | 6.67337i | 0.496485 | + | 0.286646i | ||||
\(543\) | 17.1816 | − | 9.91980i | 0.737333 | − | 0.425699i | ||||
\(544\) | −7.27314 | −0.311833 | ||||||||
\(545\) | −14.8948 | + | 8.67390i | −0.638023 | + | 0.371549i | ||||
\(546\) | −2.67184 | − | 4.62776i | −0.114344 | − | 0.198050i | ||||
\(547\) | − | 35.3451i | − | 1.51125i | −0.655006 | − | 0.755624i | \(-0.727334\pi\) | ||
0.655006 | − | 0.755624i | \(-0.272666\pi\) | |||||||
\(548\) | −19.9734 | − | 11.5316i | −0.853221 | − | 0.492607i | ||||
\(549\) | −12.2824 | −0.524198 | ||||||||
\(550\) | −25.6036 | + | 15.0385i | −1.09174 | + | 0.641244i | ||||
\(551\) | 6.73470 | − | 11.6648i | 0.286908 | − | 0.496939i | ||||
\(552\) | 5.97399 | + | 3.44908i | 0.254270 | + | 0.146803i | ||||
\(553\) | −25.3026 | + | 14.6085i | −1.07598 | + | 0.621215i | ||||
\(554\) | −18.7042 | −0.794665 | ||||||||
\(555\) | −6.75283 | − | 11.8067i | −0.286642 | − | 0.501168i | ||||
\(556\) | −8.97289 | −0.380535 | ||||||||
\(557\) | −5.17687 | + | 2.98887i | −0.219351 | + | 0.126642i | −0.605650 | − | 0.795731i | \(-0.707087\pi\) |
0.386299 | + | 0.922374i | \(0.373753\pi\) | |||||||
\(558\) | 2.32802 | + | 1.34408i | 0.0985528 | + | 0.0568995i | ||||
\(559\) | −5.65412 | + | 9.79322i | −0.239144 | + | 0.414209i | ||||
\(560\) | −9.55497 | + | 0.0357078i | −0.403771 | + | 0.00150893i | ||||
\(561\) | −43.1929 | −1.82361 | ||||||||
\(562\) | 8.93535 | + | 5.15883i | 0.376915 | + | 0.217612i | ||||
\(563\) | 12.8905i | 0.543268i | 0.962401 | + | 0.271634i | \(0.0875641\pi\) | ||||
−0.962401 | + | 0.271634i | \(0.912436\pi\) | |||||||
\(564\) | 2.31165 | + | 4.00389i | 0.0973379 | + | 0.168594i | ||||
\(565\) | −17.4330 | − | 29.9359i | −0.733411 | − | 1.25941i | ||||
\(566\) | 6.05422 | 0.254478 | ||||||||
\(567\) | −3.70065 | + | 2.13657i | −0.155413 | + | 0.0897276i | ||||
\(568\) | −6.23456 | − | 3.59953i | −0.261597 | − | 0.151033i | ||||
\(569\) | 10.8120 | 0.453261 | 0.226631 | − | 0.973981i | \(-0.427229\pi\) | ||||
0.226631 | + | 0.973981i | \(0.427229\pi\) | |||||||
\(570\) | −7.98605 | − | 4.57104i | −0.334499 | − | 0.191460i | ||||
\(571\) | 12.4430 | + | 21.5520i | 0.520725 | + | 0.901922i | 0.999710 | + | 0.0240989i | \(0.00767165\pi\) |
−0.478985 | + | 0.877823i | \(0.658995\pi\) | |||||||
\(572\) | 6.43152 | − | 3.71324i | 0.268915 | − | 0.155258i | ||||
\(573\) | −9.61493 | − | 5.55119i | −0.401670 | − | 0.231904i | ||||
\(574\) | 5.69726 | − | 9.86794i | 0.237799 | − | 0.411880i | ||||
\(575\) | −0.257787 | − | 34.4899i | −0.0107505 | − | 1.43833i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −6.17293 | + | 3.56394i | −0.256982 | + | 0.148369i | −0.622957 | − | 0.782256i | \(-0.714069\pi\) |
0.365975 | + | 0.930625i | \(0.380736\pi\) | |||||||
\(578\) | 35.8986i | 1.49318i | ||||||||
\(579\) | 12.5663 | − | 21.7655i | 0.522238 | − | 0.904543i | ||||
\(580\) | −6.35204 | − | 3.63577i | −0.263754 | − | 0.150967i | ||||
\(581\) | −31.8760 | −1.32244 | ||||||||
\(582\) | 12.1077i | 0.501878i | ||||||||
\(583\) | 7.81538 | − | 4.51221i | 0.323680 | − | 0.186877i | ||||
\(584\) | −3.36158 | −0.139103 | ||||||||
\(585\) | −2.79624 | + | 0.0104498i | −0.115610 | + | 0.000432046i | ||||
\(586\) | −5.31555 | −0.219583 | ||||||||
\(587\) | −8.55022 | − | 4.93647i | −0.352905 | − | 0.203750i | 0.313059 | − | 0.949734i | \(-0.398646\pi\) |
−0.665964 | + | 0.745984i | \(0.731980\pi\) | |||||||
\(588\) | −9.75123 | − | 5.62987i | −0.402134 | − | 0.232172i | ||||
\(589\) | −5.53106 | + | 9.58008i | −0.227903 | + | 0.394740i | ||||
\(590\) | 0.123360 | − | 0.215521i | 0.00507864 | − | 0.00887287i | ||||
\(591\) | 1.14769 | 0.0472098 | ||||||||
\(592\) | 6.08258 | + | 0.0474386i | 0.249992 | + | 0.00194971i | ||||
\(593\) | 27.6314i | 1.13469i | 0.823481 | + | 0.567343i | \(0.192029\pi\) | ||||
−0.823481 | + | 0.567343i | \(0.807971\pi\) | |||||||
\(594\) | −2.96934 | − | 5.14305i | −0.121834 | − | 0.211022i | ||||
\(595\) | 0.259708 | + | 69.4947i | 0.0106470 | + | 2.84900i | ||||
\(596\) | 6.05346 | − | 10.4849i | 0.247959 | − | 0.429478i | ||||
\(597\) | −5.71382 | − | 3.29888i | −0.233851 | − | 0.135014i | ||||
\(598\) | 8.62633i | 0.352757i | ||||||||
\(599\) | 9.52530 | − | 16.4983i | 0.389193 | − | 0.674102i | −0.603148 | − | 0.797629i | \(-0.706087\pi\) |
0.992341 | + | 0.123527i | \(0.0394205\pi\) | |||||||
\(600\) | −2.46757 | + | 4.34869i | −0.100738 | + | 0.177535i | ||||
\(601\) | −17.3651 | − | 30.0773i | −0.708338 | − | 1.22688i | −0.965473 | − | 0.260502i | \(-0.916112\pi\) |
0.257135 | − | 0.966375i | \(-0.417221\pi\) | |||||||
\(602\) | 38.6411i | 1.57489i | ||||||||
\(603\) | − | 5.13319i | − | 0.209040i | ||||||
\(604\) | −4.81068 | − | 8.33235i | −0.195744 | − | 0.339039i | ||||
\(605\) | −0.202791 | − | 54.2645i | −0.00824464 | − | 2.20617i | ||||
\(606\) | −7.20776 | −0.292795 | ||||||||
\(607\) | −3.78634 | + | 2.18604i | −0.153683 | + | 0.0887288i | −0.574869 | − | 0.818245i | \(-0.694947\pi\) |
0.421187 | + | 0.906974i | \(0.361614\pi\) | |||||||
\(608\) | 3.56380 | − | 2.05756i | 0.144531 | − | 0.0834452i | ||||
\(609\) | −6.99330 | − | 12.1128i | −0.283383 | − | 0.490834i | ||||
\(610\) | −27.4640 | + | 0.102635i | −1.11199 | + | 0.00415559i | ||||
\(611\) | −2.89078 | + | 5.00697i | −0.116948 | + | 0.202560i | ||||
\(612\) | −6.29873 | + | 3.63657i | −0.254611 | + | 0.147000i | ||||
\(613\) | 0.371275 | − | 0.214356i | 0.0149957 | − | 0.00865775i | −0.492483 | − | 0.870322i | \(-0.663911\pi\) |
0.507479 | + | 0.861664i | \(0.330577\pi\) | |||||||
\(614\) | 9.13952 | + | 15.8301i | 0.368841 | + | 0.638851i | ||||
\(615\) | −3.00056 | − | 5.15256i | −0.120994 | − | 0.207771i | ||||
\(616\) | 12.6884 | − | 21.9770i | 0.511231 | − | 0.885479i | ||||
\(617\) | −12.3649 | + | 7.13885i | −0.497790 | + | 0.287399i | −0.727801 | − | 0.685789i | \(-0.759457\pi\) |
0.230010 | + | 0.973188i | \(0.426124\pi\) | |||||||
\(618\) | − | 3.19806i | − | 0.128645i | ||||||
\(619\) | 12.0527 | 0.484441 | 0.242220 | − | 0.970221i | \(-0.422124\pi\) | ||||
0.242220 | + | 0.970221i | \(0.422124\pi\) | |||||||
\(620\) | 5.21680 | + | 2.98598i | 0.209512 | + | 0.119920i | ||||
\(621\) | 6.89816 | 0.276814 | ||||||||
\(622\) | 27.7513 | + | 16.0222i | 1.11273 | + | 0.642432i | ||||
\(623\) | 37.5783i | 1.50554i | ||||||||
\(624\) | 0.625263 | − | 1.08299i | 0.0250306 | − | 0.0433542i | ||||
\(625\) | 24.9972 | − | 0.373693i | 0.999888 | − | 0.0149477i | ||||
\(626\) | −4.43802 | + | 7.68688i | −0.177379 | + | 0.307230i | ||||
\(627\) | 21.1643 | − | 12.2192i | 0.845221 | − | 0.487989i | ||||
\(628\) | 8.58277i | 0.342490i | ||||||||
\(629\) | 0.345028 | − | 44.2395i | 0.0137572 | − | 1.76394i | ||||
\(630\) | −8.25699 | + | 4.80841i | −0.328966 | + | 0.191572i | ||||
\(631\) | −7.44379 | − | 12.8930i | −0.296333 | − | 0.513263i | 0.678961 | − | 0.734174i | \(-0.262430\pi\) |
−0.975294 | + | 0.220911i | \(0.929097\pi\) | |||||||
\(632\) | −5.92130 | − | 3.41867i | −0.235537 | − | 0.135987i | ||||
\(633\) | −16.1116 | − | 9.30206i | −0.640380 | − | 0.369724i | ||||
\(634\) | −2.20830 | + | 3.82489i | −0.0877029 | + | 0.151906i | ||||
\(635\) | 17.1100 | + | 29.3813i | 0.678990 | + | 1.16596i | ||||
\(636\) | 0.759799 | − | 1.31601i | 0.0301280 | − | 0.0521832i | ||||
\(637\) | − | 14.0806i | − | 0.557894i | ||||||
\(638\) | 16.8339 | − | 9.71909i | 0.666462 | − | 0.384782i | ||||
\(639\) | −7.19905 | −0.284790 | ||||||||
\(640\) | −1.12526 | − | 1.93230i | −0.0444799 | − | 0.0763809i | ||||
\(641\) | −15.4399 | − | 26.7427i | −0.609840 | − | 1.05627i | −0.991266 | − | 0.131875i | \(-0.957900\pi\) |
0.381426 | − | 0.924399i | \(-0.375433\pi\) | |||||||
\(642\) | −6.68208 | − | 3.85790i | −0.263721 | − | 0.152259i | ||||
\(643\) | 6.52207i | 0.257205i | 0.991696 | + | 0.128603i | \(0.0410492\pi\) | ||||
−0.991696 | + | 0.128603i | \(0.958951\pi\) | |||||||
\(644\) | 14.7384 | + | 25.5277i | 0.580775 | + | 1.00593i | ||||
\(645\) | 17.5489 | + | 10.0446i | 0.690989 | + | 0.395507i | ||||
\(646\) | −14.9649 | − | 25.9201i | −0.588788 | − | 1.01981i | ||||
\(647\) | 19.3536 | + | 11.1738i | 0.760870 | + | 0.439288i | 0.829608 | − | 0.558346i | \(-0.188564\pi\) |
−0.0687382 | + | 0.997635i | \(0.521897\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 0.329763 | + | 0.571166i | 0.0129443 | + | 0.0224202i | ||||
\(650\) | −6.25246 | + | 0.0467326i | −0.245241 | + | 0.00183300i | ||||
\(651\) | 5.74345 | + | 9.94795i | 0.225104 | + | 0.389891i | ||||
\(652\) | 22.7111i | 0.889434i | ||||||||
\(653\) | 30.6001 | + | 17.6670i | 1.19747 | + | 0.691362i | 0.959991 | − | 0.280030i | \(-0.0903443\pi\) |
0.237483 | + | 0.971392i | \(0.423678\pi\) | |||||||
\(654\) | −3.85417 | − | 6.67561i | −0.150710 | − | 0.261037i | ||||
\(655\) | 31.8755 | − | 18.5625i | 1.24548 | − | 0.725298i | ||||
\(656\) | 2.66654 | 0.104111 | ||||||||
\(657\) | −2.91122 | + | 1.68079i | −0.113577 | + | 0.0655739i | ||||
\(658\) | 19.7560i | 0.770169i | ||||||||
\(659\) | 0.235145 | − | 0.407284i | 0.00915996 | − | 0.0158655i | −0.861409 | − | 0.507912i | \(-0.830418\pi\) |
0.870569 | + | 0.492046i | \(0.163751\pi\) | |||||||
\(660\) | −6.68259 | − | 11.4753i | −0.260119 | − | 0.446676i | ||||
\(661\) | 9.15487 | − | 15.8567i | 0.356083 | − | 0.616754i | −0.631220 | − | 0.775604i | \(-0.717445\pi\) |
0.987303 | + | 0.158850i | \(0.0507787\pi\) | |||||||
\(662\) | 26.2996 | + | 15.1841i | 1.02216 | + | 0.590146i | ||||
\(663\) | −7.87672 | − | 4.54763i | −0.305906 | − | 0.176615i | ||||
\(664\) | −3.72981 | − | 6.46021i | −0.144745 | − | 0.250705i | ||||
\(665\) | −19.7872 | − | 33.9786i | −0.767315 | − | 1.31763i | ||||
\(666\) | 5.29139 | − | 3.00021i | 0.205037 | − | 0.116256i | ||||
\(667\) | 22.5787i | 0.874250i | ||||||||
\(668\) | −3.96167 | + | 2.28727i | −0.153282 | + | 0.0884973i | ||||
\(669\) | 9.69271 | − | 16.7883i | 0.374742 | − | 0.649072i | ||||
\(670\) | −0.0428946 | − | 11.4781i | −0.00165716 | − | 0.443437i | ||||
\(671\) | 36.4706 | − | 63.1689i | 1.40793 | − | 2.43861i | ||||
\(672\) | − | 4.27314i | − | 0.164840i | ||||||
\(673\) | 2.70882 | + | 1.56394i | 0.104418 | + | 0.0602855i | 0.551299 | − | 0.834308i | \(-0.314132\pi\) |
−0.446882 | + | 0.894593i | \(0.647466\pi\) | |||||||
\(674\) | 24.1241 | 0.929227 | ||||||||
\(675\) | 0.0373703 | + | 4.99986i | 0.00143839 | + | 0.192445i | ||||
\(676\) | −11.4362 | −0.439853 | ||||||||
\(677\) | 26.3204i | 1.01157i | 0.862658 | + | 0.505787i | \(0.168798\pi\) | ||||
−0.862658 | + | 0.505787i | \(0.831202\pi\) | |||||||
\(678\) | 13.4168 | − | 7.74618i | 0.515268 | − | 0.297490i | ||||
\(679\) | −25.8689 | + | 44.8062i | −0.992756 | + | 1.71950i | ||||
\(680\) | −14.0539 | + | 8.18420i | −0.538942 | + | 0.313850i | ||||
\(681\) | 2.97402 | + | 5.15116i | 0.113965 | + | 0.197393i | ||||
\(682\) | −13.8254 | + | 7.98208i | −0.529400 | + | 0.305650i | ||||
\(683\) | −0.297050 | + | 0.171502i | −0.0113663 | + | 0.00656234i | −0.505672 | − | 0.862726i | \(-0.668756\pi\) |
0.494306 | + | 0.869288i | \(0.335422\pi\) | |||||||
\(684\) | 2.05756 | − | 3.56380i | 0.0786729 | − | 0.136265i | ||||
\(685\) | −51.5707 | + | 0.192724i | −1.97041 | + | 0.00736361i | ||||
\(686\) | −9.10125 | − | 15.7638i | −0.347487 | − | 0.601866i | ||||
\(687\) | −7.72325 | + | 4.45902i | −0.294660 | + | 0.170122i | ||||
\(688\) | −7.83128 | + | 4.52139i | −0.298565 | + | 0.172376i | ||||
\(689\) | 1.90030 | 0.0723956 | ||||||||
\(690\) | 15.4247 | − | 0.0576433i | 0.587207 | − | 0.00219444i | ||||
\(691\) | −11.6638 | − | 20.2023i | −0.443711 | − | 0.768531i | 0.554250 | − | 0.832350i | \(-0.313005\pi\) |
−0.997961 | + | 0.0638196i | \(0.979672\pi\) | |||||||
\(692\) | − | 1.43565i | − | 0.0545752i | ||||||
\(693\) | − | 25.3769i | − | 0.963987i | ||||||
\(694\) | 14.4187 | + | 24.9740i | 0.547328 | + | 0.947999i | ||||
\(695\) | −17.3383 | + | 10.0969i | −0.657680 | + | 0.382996i | ||||
\(696\) | 1.63657 | − | 2.83462i | 0.0620341 | − | 0.107446i | ||||
\(697\) | − | 19.3941i | − | 0.734605i | ||||||
\(698\) | −20.1486 | − | 11.6328i | −0.762635 | − | 0.440307i | ||||
\(699\) | −0.956644 | + | 1.65696i | −0.0361836 | + | 0.0626718i | ||||
\(700\) | −18.4229 | + | 10.8209i | −0.696320 | + | 0.408990i | ||||
\(701\) | 25.0713 | + | 43.4248i | 0.946930 | + | 1.64013i | 0.751839 | + | 0.659347i | \(0.229167\pi\) |
0.195091 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(702\) | − | 1.25053i | − | 0.0471981i | ||||||
\(703\) | 12.3462 | + | 21.7747i | 0.465647 | + | 0.821249i | ||||
\(704\) | 5.93869 | 0.223823 | ||||||||
\(705\) | 8.97223 | + | 5.13551i | 0.337914 | + | 0.193414i | ||||
\(706\) | 0.0977899 | − | 0.169377i | 0.00368037 | − | 0.00637459i | ||||
\(707\) | −26.6734 | − | 15.3999i | −1.00316 | − | 0.579173i | ||||
\(708\) | 0.0961772 | + | 0.0555279i | 0.00361456 | + | 0.00208687i | ||||
\(709\) | −39.5030 | −1.48357 | −0.741784 | − | 0.670639i | \(-0.766020\pi\) | ||||
−0.741784 | + | 0.670639i | \(0.766020\pi\) | |||||||
\(710\) | −16.0975 | + | 0.0601576i | −0.604127 | + | 0.00225768i | ||||
\(711\) | −6.83733 | −0.256420 | ||||||||
\(712\) | −7.61589 | + | 4.39703i | −0.285417 | + | 0.164786i | ||||
\(713\) | − | 18.5434i | − | 0.694455i | ||||||
\(714\) | −31.0792 | −1.16311 | ||||||||
\(715\) | 8.24926 | − | 14.4123i | 0.308505 | − | 0.538988i | ||||
\(716\) | 5.68904 | − | 9.85370i | 0.212609 | − | 0.368250i | ||||
\(717\) | 15.5283i | 0.579915i | ||||||||
\(718\) | −3.05702 | + | 1.76497i | −0.114087 | + | 0.0658682i | ||||
\(719\) | 10.0711 | + | 17.4437i | 0.375589 | + | 0.650540i | 0.990415 | − | 0.138123i | \(-0.0441070\pi\) |
−0.614826 | + | 0.788663i | \(0.710774\pi\) | |||||||
\(720\) | −1.94066 | − | 1.11079i | −0.0723240 | − | 0.0413967i | ||||
\(721\) | 6.83288 | − | 11.8349i | 0.254470 | − | 0.440754i | ||||
\(722\) | −1.78898 | − | 1.03287i | −0.0665790 | − | 0.0384394i | ||||
\(723\) | 9.62345 | − | 5.55610i | 0.357900 | − | 0.206634i | ||||
\(724\) | 9.91980 | + | 17.1816i | 0.368666 | + | 0.638549i | ||||
\(725\) | −16.3653 | + | 0.122318i | −0.607790 | + | 0.00454279i | ||||
\(726\) | 24.2680 | 0.900670 | ||||||||
\(727\) | 30.2818 | + | 17.4832i | 1.12309 | + | 0.648417i | 0.942188 | − | 0.335084i | \(-0.108765\pi\) |
0.180903 | + | 0.983501i | \(0.442098\pi\) | |||||||
\(728\) | 4.62776 | − | 2.67184i | 0.171516 | − | 0.0990249i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −6.49558 | + | 3.78266i | −0.240412 | + | 0.140003i | ||||
\(731\) | 32.8847 | + | 56.9580i | 1.21629 | + | 2.10667i | ||||
\(732\) | − | 12.2824i | − | 0.453969i | ||||||
\(733\) | −4.06319 | − | 2.34588i | −0.150077 | − | 0.0866471i | 0.423081 | − | 0.906092i | \(-0.360949\pi\) |
−0.573158 | + | 0.819445i | \(0.694282\pi\) | |||||||
\(734\) | −1.99904 | −0.0737861 | ||||||||
\(735\) | −25.1774 | + | 0.0940901i | −0.928682 | + | 0.00347056i | ||||
\(736\) | −3.44908 | + | 5.97399i | −0.127135 | + | 0.220204i | ||||
\(737\) | 26.4003 | + | 15.2422i | 0.972467 | + | 0.561454i | ||||
\(738\) | 2.30929 | − | 1.33327i | 0.0850062 | − | 0.0490784i | ||||
\(739\) | 19.3032 | 0.710079 | 0.355040 | − | 0.934851i | \(-0.384467\pi\) | ||||
0.355040 | + | 0.934851i | \(0.384467\pi\) | |||||||
\(740\) | 11.8067 | − | 6.75283i | 0.434025 | − | 0.248239i | ||||
\(741\) | 5.14607 | 0.189046 | ||||||||
\(742\) | 5.62350 | − | 3.24673i | 0.206445 | − | 0.119191i | ||||
\(743\) | −34.6971 | − | 20.0324i | −1.27291 | − | 0.734917i | −0.297378 | − | 0.954760i | \(-0.596112\pi\) |
−0.975535 | + | 0.219843i | \(0.929445\pi\) | |||||||
\(744\) | −1.34408 | + | 2.32802i | −0.0492764 | + | 0.0853492i | ||||
\(745\) | −0.101169 | − | 27.0717i | −0.00370656 | − | 0.991831i | ||||
\(746\) | −13.8065 | −0.505492 | ||||||||
\(747\) | −6.46021 | − | 3.72981i | −0.236367 | − | 0.136466i | ||||
\(748\) | − | 43.1929i | − | 1.57929i | ||||||
\(749\) | −16.4854 | − | 28.5535i | −0.602362 | − | 1.04332i | ||||
\(750\) | 0.125342 | + | 11.1796i | 0.00457686 | + | 0.408223i | ||||
\(751\) | −9.68222 | −0.353309 | −0.176655 | − | 0.984273i | \(-0.556528\pi\) | ||||
−0.176655 | + | 0.984273i | \(0.556528\pi\) | |||||||
\(752\) | −4.00389 | + | 2.31165i | −0.146007 | + | 0.0842971i | ||||
\(753\) | −11.5497 | − | 6.66822i | −0.420894 | − | 0.243003i | ||||
\(754\) | 4.09315 | 0.149064 | ||||||||
\(755\) | −18.6718 | − | 10.6873i | −0.679535 | − | 0.388951i | ||||
\(756\) | −2.13657 | − | 3.70065i | −0.0777063 | − | 0.134591i | ||||
\(757\) | −28.5617 | + | 16.4901i | −1.03809 | + | 0.599342i | −0.919292 | − | 0.393576i | \(-0.871238\pi\) |
−0.118799 | + | 0.992918i | \(0.537904\pi\) | |||||||
\(758\) | 5.85465 | + | 3.38018i | 0.212650 | + | 0.122774i | ||||
\(759\) | −20.4830 | + | 35.4776i | −0.743487 | + | 1.28776i | ||||
\(760\) | 4.57104 | − | 7.98605i | 0.165809 | − | 0.289684i | ||||
\(761\) | 24.2801 | + | 42.0544i | 0.880155 | + | 1.52447i | 0.851169 | + | 0.524893i | \(0.175894\pi\) |
0.0289860 | + | 0.999580i | \(0.490772\pi\) | |||||||
\(762\) | −13.1682 | + | 7.60268i | −0.477034 | + | 0.275416i | ||||
\(763\) | − | 32.9388i | − | 1.19246i | ||||||
\(764\) | 5.55119 | − | 9.61493i | 0.200835 | − | 0.347856i | ||||
\(765\) | −8.07893 | + | 14.1147i | −0.292094 | + | 0.510317i | ||||
\(766\) | 14.0998 | 0.509447 | ||||||||
\(767\) | 0.138878i | 0.00501460i | ||||||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | 41.0894 | 1.48172 | 0.740861 | − | 0.671659i | \(-0.234418\pi\) | ||||
0.740861 | + | 0.671659i | \(0.234418\pi\) | |||||||
\(770\) | −0.212057 | − | 56.7440i | −0.00764201 | − | 2.04491i | ||||
\(771\) | −24.6881 | −0.889119 | ||||||||
\(772\) | 21.7655 | + | 12.5663i | 0.783357 | + | 0.452272i | ||||
\(773\) | −16.2676 | − | 9.39211i | −0.585105 | − | 0.337811i | 0.178054 | − | 0.984021i | \(-0.443020\pi\) |
−0.763160 | + | 0.646210i | \(0.776353\pi\) | |||||||
\(774\) | −4.52139 | + | 7.83128i | −0.162518 | + | 0.281490i | ||||
\(775\) | 13.4404 | − | 0.100458i | 0.482795 | − | 0.00360854i | ||||
\(776\) | −12.1077 | −0.434639 | ||||||||
\(777\) | 25.9917 | + | 0.202712i | 0.932448 | + | 0.00727225i | ||||
\(778\) | 5.75772i | 0.206424i | ||||||||
\(779\) | 5.48658 | + | 9.50303i | 0.196577 | + | 0.340481i | ||||
\(780\) | −0.0104498 | − | 2.79624i | −0.000374163 | − | 0.100122i | ||||
\(781\) | 21.3765 | − | 37.0251i | 0.764910 | − | 1.32486i | ||||
\(782\) | 43.4497 | + | 25.0857i | 1.55376 | + | 0.897062i | ||||
\(783\) | − | 3.27314i | − | 0.116973i | ||||||
\(784\) | 5.62987 | − | 9.75123i | 0.201067 | − | 0.348258i | ||||
\(785\) | 9.65788 | + | 16.5845i | 0.344704 | + | 0.591926i | ||||
\(786\) | 8.24808 | + | 14.2861i | 0.294199 | + | 0.509568i | ||||
\(787\) | − | 9.59991i | − | 0.342200i | −0.985254 | − | 0.171100i | \(-0.945268\pi\) | ||
0.985254 | − | 0.171100i | \(-0.0547321\pi\) | |||||||
\(788\) | 1.14769i | 0.0408849i | ||||||||
\(789\) | 12.6383 | + | 21.8902i | 0.449935 | + | 0.779311i | ||||
\(790\) | −15.2886 | + | 0.0571350i | −0.543945 | + | 0.00203277i | ||||
\(791\) | 66.2011 | 2.35384 | ||||||||
\(792\) | 5.14305 | − | 2.96934i | 0.182750 | − | 0.105511i | ||||
\(793\) | 13.3016 | − | 7.67971i | 0.472355 | − | 0.272714i | ||||
\(794\) | −5.90901 | − | 10.2347i | −0.209703 | − | 0.363216i | ||||
\(795\) | −0.0126983 | − | 3.39790i | −0.000450361 | − | 0.120511i | ||||
\(796\) | 3.29888 | − | 5.71382i | 0.116926 | − | 0.202521i | ||||
\(797\) | −43.8239 | + | 25.3018i | −1.55232 | + | 0.896234i | −0.554371 | + | 0.832270i | \(0.687041\pi\) |
−0.997952 | + | 0.0639644i | \(0.979626\pi\) | |||||||
\(798\) | 15.2286 | − | 8.79226i | 0.539088 | − | 0.311243i | ||||
\(799\) | 16.8129 | + | 29.1209i | 0.594799 | + | 1.03022i | ||||
\(800\) | −4.34869 | − | 2.46757i | −0.153749 | − | 0.0872417i | ||||
\(801\) | −4.39703 | + | 7.61589i | −0.155362 | + | 0.269094i | ||||
\(802\) | −4.36515 | + | 2.52022i | −0.154139 | + | 0.0889921i | ||||
\(803\) | − | 19.9634i | − | 0.704493i | ||||||
\(804\) | 5.13319 | 0.181034 | ||||||||
\(805\) | 57.2044 | + | 32.7426i | 2.01619 | + | 1.15402i | ||||
\(806\) | −3.36162 | −0.118408 | ||||||||
\(807\) | 21.6742 | + | 12.5136i | 0.762968 | + | 0.440500i | ||||
\(808\) | − | 7.20776i | − | 0.253568i | ||||||
\(809\) | −16.5378 | + | 28.6443i | −0.581439 | + | 1.00708i | 0.413871 | + | 0.910336i | \(0.364177\pi\) |
−0.995309 | + | 0.0967455i | \(0.969157\pi\) | |||||||
\(810\) | −2.23605 | + | 0.00835632i | −0.0785669 | + | 0.000293611i | ||||
\(811\) | −12.6537 | + | 21.9168i | −0.444330 | + | 0.769603i | −0.998005 | − | 0.0631300i | \(-0.979892\pi\) |
0.553675 | + | 0.832733i | \(0.313225\pi\) | |||||||
\(812\) | 12.1128 | − | 6.99330i | 0.425074 | − | 0.245417i | ||||
\(813\) | 13.3467i | 0.468091i | ||||||||
\(814\) | −0.281723 | + | 36.1225i | −0.00987439 | + | 1.26609i | ||||
\(815\) | 25.5559 | + | 43.8846i | 0.895185 | + | 1.53721i | ||||
\(816\) | −3.63657 | − | 6.29873i | −0.127305 | − | 0.220500i | ||||
\(817\) | −32.2267 | − | 18.6061i | −1.12747 | − | 0.650945i | ||||
\(818\) | −2.45743 | − | 1.41880i | −0.0859219 | − | 0.0496070i | ||||
\(819\) | 2.67184 | − | 4.62776i | 0.0933616 | − | 0.161707i | ||||
\(820\) | 5.15256 | − | 3.00056i | 0.179935 | − | 0.104784i | ||||
\(821\) | 18.3900 | − | 31.8525i | 0.641816 | − | 1.11166i | −0.343211 | − | 0.939258i | \(-0.611514\pi\) |
0.985027 | − | 0.172400i | \(-0.0551522\pi\) | |||||||
\(822\) | − | 23.0633i | − | 0.804424i | ||||||
\(823\) | −22.9721 | + | 13.2629i | −0.800757 | + | 0.462317i | −0.843736 | − | 0.536759i | \(-0.819648\pi\) |
0.0429791 | + | 0.999076i | \(0.486315\pi\) | |||||||
\(824\) | 3.19806 | 0.111410 | ||||||||
\(825\) | −25.8255 | − | 14.6541i | −0.899129 | − | 0.510191i | ||||
\(826\) | 0.237279 | + | 0.410979i | 0.00825598 | + | 0.0142998i | ||||
\(827\) | 25.5843 | + | 14.7711i | 0.889653 | + | 0.513641i | 0.873829 | − | 0.486234i | \(-0.161630\pi\) |
0.0158239 | + | 0.999875i | \(0.494963\pi\) | |||||||
\(828\) | 6.89816i | 0.239728i | ||||||||
\(829\) | 7.11508 | + | 12.3237i | 0.247117 | + | 0.428019i | 0.962725 | − | 0.270483i | \(-0.0871835\pi\) |
−0.715608 | + | 0.698502i | \(0.753850\pi\) | |||||||
\(830\) | −14.4765 | − | 8.28606i | −0.502488 | − | 0.287613i | ||||
\(831\) | −9.35210 | − | 16.1983i | −0.324421 | − | 0.561913i | ||||
\(832\) | 1.08299 | + | 0.625263i | 0.0375458 | + | 0.0216771i | ||||
\(833\) | −70.9221 | − | 40.9469i | −2.45730 | − | 1.41872i | ||||
\(834\) | −4.48645 | − | 7.77075i | −0.155353 | − | 0.269079i | ||||
\(835\) | −5.08136 | + | 8.87762i | −0.175848 | + | 0.307223i | ||||
\(836\) | 12.2192 | + | 21.1643i | 0.422611 | + | 0.731983i | ||||
\(837\) | 2.68816i | 0.0929165i | ||||||||
\(838\) | −4.25048 | − | 2.45402i | −0.146831 | − | 0.0847727i | ||||
\(839\) | −1.18772 | − | 2.05719i | −0.0410045 | − | 0.0710219i | 0.844795 | − | 0.535090i | \(-0.179722\pi\) |
−0.885799 | + | 0.464069i | \(0.846389\pi\) | |||||||
\(840\) | −4.80841 | − | 8.25699i | −0.165906 | − | 0.284893i | ||||
\(841\) | −18.2865 | −0.630570 | ||||||||
\(842\) | 21.9783 | − | 12.6892i | 0.757423 | − | 0.437299i | ||||
\(843\) | 10.3177i | 0.355359i | ||||||||
\(844\) | 9.30206 | − | 16.1116i | 0.320190 | − | 0.554586i | ||||
\(845\) | −22.0981 | + | 12.8687i | −0.760199 | + | 0.442697i | ||||
\(846\) | −2.31165 | + | 4.00389i | −0.0794761 | + | 0.137657i | ||||
\(847\) | 89.8074 | + | 51.8503i | 3.08582 | + | 1.78160i | ||||
\(848\) | 1.31601 | + | 0.759799i | 0.0451920 | + | 0.0260916i | ||||
\(849\) | 3.02711 | + | 5.24310i | 0.103890 | + | 0.179943i | ||||
\(850\) | −17.9470 | + | 31.6287i | −0.615576 | + | 1.08485i | ||||
\(851\) | −36.1736 | − | 21.2627i | −1.24002 | − | 0.728876i | ||||
\(852\) | − | 7.19905i | − | 0.246636i | ||||||
\(853\) | −11.4895 | + | 6.63345i | −0.393392 | + | 0.227125i | −0.683629 | − | 0.729830i | \(-0.739599\pi\) |
0.290237 | + | 0.956955i | \(0.406266\pi\) | |||||||
\(854\) | 26.2421 | − | 45.4527i | 0.897988 | − | 1.55536i | ||||
\(855\) | −0.0343873 | − | 9.20164i | −0.00117602 | − | 0.314689i | ||||
\(856\) | 3.85790 | − | 6.68208i | 0.131860 | − | 0.228389i | ||||
\(857\) | 34.3574i | 1.17363i | 0.809723 | + | 0.586813i | \(0.199617\pi\) | ||||
−0.809723 | + | 0.586813i | \(0.800383\pi\) | |||||||
\(858\) | 6.43152 | + | 3.71324i | 0.219569 | + | 0.126768i | ||||
\(859\) | −31.1897 | −1.06418 | −0.532089 | − | 0.846689i | \(-0.678593\pi\) | ||||
−0.532089 | + | 0.846689i | \(0.678593\pi\) | |||||||
\(860\) | −10.0446 | + | 17.5489i | −0.342519 | + | 0.598414i | ||||
\(861\) | 11.3945 | 0.388324 | ||||||||
\(862\) | − | 13.9311i | − | 0.474495i | ||||||
\(863\) | 39.5069 | − | 22.8093i | 1.34483 | − | 0.776438i | 0.357319 | − | 0.933982i | \(-0.383691\pi\) |
0.987512 | + | 0.157544i | \(0.0503576\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −1.61548 | − | 2.77411i | −0.0549281 | − | 0.0943224i | ||||
\(866\) | 11.4395 | + | 19.8137i | 0.388729 | + | 0.673299i | ||||
\(867\) | −31.0891 | + | 17.9493i | −1.05584 | + | 0.609590i | ||||
\(868\) | −9.94795 | + | 5.74345i | −0.337655 | + | 0.194945i | ||||
\(869\) | 20.3024 | − | 35.1648i | 0.688712 | − | 1.19288i | ||||
\(870\) | −0.0273514 | − | 7.31892i | −0.000927300 | − | 0.248135i | ||||
\(871\) | 3.20959 | + | 5.55918i | 0.108753 | + | 0.188366i | ||||
\(872\) | 6.67561 | − | 3.85417i | 0.226065 | − | 0.130519i | ||||
\(873\) | −10.4855 | + | 6.05383i | −0.354882 | + | 0.204891i | ||||
\(874\) | −28.3868 | −0.960198 | ||||||||
\(875\) | −23.4222 | + | 41.6397i | −0.791816 | + | 1.40768i | ||||
\(876\) | −1.68079 | − | 2.91122i | −0.0567887 | − | 0.0983608i | ||||
\(877\) | − | 19.9901i | − | 0.675019i | −0.941322 | − | 0.337510i | \(-0.890415\pi\) | ||
0.941322 | − | 0.337510i | \(-0.109585\pi\) | |||||||
\(878\) | − | 10.2986i | − | 0.347562i | ||||||
\(879\) | −2.65778 | − | 4.60340i | −0.0896446 | − | 0.155269i | ||||
\(880\) | 11.4753 | − | 6.68259i | 0.386833 | − | 0.225270i | ||||
\(881\) | −23.3579 | + | 40.4571i | −0.786948 | + | 1.36303i | 0.140881 | + | 0.990027i | \(0.455007\pi\) |
−0.927829 | + | 0.373007i | \(0.878327\pi\) | |||||||
\(882\) | − | 11.2597i | − | 0.379135i | ||||||
\(883\) | 1.18063 | + | 0.681638i | 0.0397314 | + | 0.0229389i | 0.519734 | − | 0.854328i | \(-0.326031\pi\) |
−0.480003 | + | 0.877267i | \(0.659364\pi\) | |||||||
\(884\) | 4.54763 | − | 7.87672i | 0.152953 | − | 0.264923i | ||||
\(885\) | 0.248327 | 0.000928018i | 0.00834741 | 3.11950e-5i | ||||||
\(886\) | 10.7099 | + | 18.5501i | 0.359807 | + | 0.623204i | ||||
\(887\) | 17.3078i | 0.581139i | 0.956854 | + | 0.290569i | \(0.0938447\pi\) | ||||
−0.956854 | + | 0.290569i | \(0.906155\pi\) | |||||||
\(888\) | 3.00021 | + | 5.29139i | 0.100680 | + | 0.177567i | ||||
\(889\) | −64.9746 | −2.17918 | ||||||||
\(890\) | −9.76836 | + | 17.0663i | −0.327436 | + | 0.572062i | ||||
\(891\) | 2.96934 | − | 5.14305i | 0.0994768 | − | 0.172299i | ||||
\(892\) | 16.7883 | + | 9.69271i | 0.562113 | + | 0.324536i | ||||
\(893\) | −16.4765 | − | 9.51272i | −0.551366 | − | 0.318331i | ||||
\(894\) | 12.1069 | 0.404916 | ||||||||
\(895\) | −0.0950788 | − | 25.4420i | −0.00317813 | − | 0.850431i | ||||
\(896\) | 4.27314 | 0.142756 | ||||||||
\(897\) | −7.47062 | + | 4.31317i | −0.249437 | + | 0.144012i | ||||
\(898\) | − | 32.6815i | − | 1.09059i | ||||||
\(899\) | −8.79874 | −0.293454 | ||||||||
\(900\) | −4.99986 | + | 0.0373703i | −0.166662 | + | 0.00124568i | ||||
\(901\) | 5.52613 | − | 9.57153i | 0.184102 | − | 0.318874i | ||||
\(902\) | 15.8358i | 0.527273i | ||||||||
\(903\) | −33.4642 | + | 19.3206i | −1.11362 | + | 0.642948i | ||||
\(904\) | 7.74618 | + | 13.4168i | 0.257634 | + | 0.446236i | ||||
\(905\) | 38.5018 | + | 22.0376i | 1.27984 | + | 0.732555i | ||||
\(906\) | 4.81068 | − | 8.33235i | 0.159824 | − | 0.276824i | ||||
\(907\) | 18.0725 | + | 10.4341i | 0.600087 | + | 0.346460i | 0.769076 | − | 0.639158i | \(-0.220717\pi\) |
−0.168989 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(908\) | −5.15116 | + | 2.97402i | −0.170947 | + | 0.0986964i | ||||
\(909\) | −3.60388 | − | 6.24210i | −0.119533 | − | 0.207037i | ||||
\(910\) | 5.93570 | − | 10.3702i | 0.196766 | − | 0.343770i | ||||
\(911\) | 45.8100 | 1.51775 | 0.758877 | − | 0.651234i | \(-0.225748\pi\) | ||||
0.758877 | + | 0.651234i | \(0.225748\pi\) | |||||||
\(912\) | 3.56380 | + | 2.05756i | 0.118009 | + | 0.0681327i | ||||
\(913\) | 38.3652 | − | 22.1502i | 1.26970 | − | 0.733063i | ||||
\(914\) | 10.8694 | 0.359529 | ||||||||
\(915\) | −13.8209 | − | 23.7332i | −0.456904 | − | 0.784596i | ||||
\(916\) | −4.45902 | − | 7.72325i | −0.147330 | − | 0.255183i | ||||
\(917\) | 70.4904i | 2.32780i | ||||||||
\(918\) | −6.29873 | − | 3.63657i | −0.207889 | − | 0.120025i | ||||
\(919\) | 48.7717 | 1.60883 | 0.804415 | − | 0.594068i | \(-0.202479\pi\) | ||||
0.804415 | + | 0.594068i | \(0.202479\pi\) | |||||||
\(920\) | 0.0576433 | + | 15.4247i | 0.00190044 | + | 0.508536i | ||||
\(921\) | −9.13952 | + | 15.8301i | −0.301157 | + | 0.521620i | ||||
\(922\) | −25.0336 | − | 14.4531i | −0.824437 | − | 0.475989i | ||||
\(923\) | 7.79648 | − | 4.50130i | 0.256624 | − | 0.148162i | ||||
\(924\) | 25.3769 | 0.834837 | ||||||||
\(925\) | 15.2155 | − | 26.3342i | 0.500281 | − | 0.865863i | ||||
\(926\) | −37.1489 | −1.22079 | ||||||||
\(927\) | 2.76960 | − | 1.59903i | 0.0909656 | − | 0.0525190i | ||||
\(928\) | 2.83462 | + | 1.63657i | 0.0930511 | + | 0.0537231i | ||||
\(929\) | −21.4366 | + | 37.1293i | −0.703312 | + | 1.21817i | 0.263985 | + | 0.964527i | \(0.414963\pi\) |
−0.967297 | + | 0.253645i | \(0.918370\pi\) | |||||||
\(930\) | 0.0224631 | + | 6.01087i | 0.000736596 | + | 0.197104i | ||||
\(931\) | 46.3353 | 1.51858 | ||||||||
\(932\) | −1.65696 | − | 0.956644i | −0.0542754 | − | 0.0313359i | ||||
\(933\) | 32.0444i | 1.04909i | ||||||||
\(934\) | 11.1784 | + | 19.3616i | 0.365769 | + | 0.633531i | ||||
\(935\) | −48.6034 | − | 83.4617i | −1.58950 | − | 2.72949i | ||||
\(936\) | 1.25053 | 0.0408747 | ||||||||
\(937\) | 47.5708 | − | 27.4650i | 1.55407 | − | 0.897242i | 0.556265 | − | 0.831005i | \(-0.312234\pi\) |
0.997804 | − | 0.0662376i | \(-0.0210995\pi\) | |||||||
\(938\) | 18.9961 | + | 10.9674i | 0.620246 | + | 0.358099i | ||||
\(939\) | −8.87605 | −0.289659 | ||||||||
\(940\) | −5.13551 | + | 8.97223i | −0.167502 | + | 0.292642i | ||||
\(941\) | 11.3474 | + | 19.6542i | 0.369913 | + | 0.640709i | 0.989552 | − | 0.144179i | \(-0.0460540\pi\) |
−0.619638 | + | 0.784888i | \(0.712721\pi\) | |||||||
\(942\) | −7.43290 | + | 4.29139i | −0.242177 | + | 0.139821i | ||||
\(943\) | −15.9299 | − | 9.19712i | −0.518748 | − | 0.299500i | ||||
\(944\) | −0.0555279 | + | 0.0961772i | −0.00180728 | + | 0.00313030i | ||||
\(945\) | −8.29270 | − | 4.74656i | −0.269762 | − | 0.154406i | ||||
\(946\) | −26.8511 | − | 46.5075i | −0.873006 | − | 1.51209i | ||||
\(947\) | −6.95546 | + | 4.01574i | −0.226022 | + | 0.130494i | −0.608736 | − | 0.793373i | \(-0.708323\pi\) |
0.382713 | + | 0.923867i | \(0.374990\pi\) | |||||||
\(948\) | − | 6.83733i | − | 0.222066i | ||||||
\(949\) | 2.10187 | − | 3.64055i | 0.0682297 | − | 0.118177i | ||||
\(950\) | −0.153784 | − | 20.5751i | −0.00498940 | − | 0.667543i | ||||
\(951\) | −4.41661 | −0.143218 | ||||||||
\(952\) | − | 31.0792i | − | 1.00728i | ||||||
\(953\) | 40.2906 | − | 23.2618i | 1.30514 | − | 0.753524i | 0.323860 | − | 0.946105i | \(-0.395019\pi\) |
0.981281 | + | 0.192581i | \(0.0616859\pi\) | |||||||
\(954\) | 1.51960 | 0.0491988 | ||||||||
\(955\) | −0.0927750 | − | 24.8255i | −0.00300213 | − | 0.803334i | ||||
\(956\) | −15.5283 | −0.502221 | ||||||||
\(957\) | 16.8339 | + | 9.71909i | 0.544164 | + | 0.314173i | ||||
\(958\) | −9.26089 | − | 5.34678i | −0.299206 | − | 0.172746i | ||||
\(959\) | 49.2763 | − | 85.3491i | 1.59122 | − | 2.75607i | ||||
\(960\) | 1.11079 | − | 1.94066i | 0.0358506 | − | 0.0626344i | ||||
\(961\) | −23.7738 | −0.766896 | ||||||||
\(962\) | −3.85459 | + | 6.55769i | −0.124277 | + | 0.211428i | ||||
\(963\) | − | 7.71580i | − | 0.248638i | ||||||
\(964\) | 5.55610 | + | 9.62345i | 0.178950 | + | 0.309950i | ||||
\(965\) | 56.1979 | − | 0.210016i | 1.80907 | − | 0.00676067i | ||||
\(966\) | −14.7384 | + | 25.5277i | −0.474201 | + | 0.821340i | ||||
\(967\) | 32.0985 | + | 18.5321i | 1.03222 | + | 0.595951i | 0.917619 | − | 0.397461i | \(-0.130109\pi\) |
0.114598 | + | 0.993412i | \(0.463442\pi\) | |||||||
\(968\) | 24.2680i | 0.780003i | ||||||||
\(969\) | 14.9649 | − | 25.9201i | 0.480743 | − | 0.832672i | ||||
\(970\) | −23.3956 | + | 13.6243i | −0.751188 | + | 0.437450i | ||||
\(971\) | 2.81026 | + | 4.86752i | 0.0901856 | + | 0.156206i | 0.907589 | − | 0.419859i | \(-0.137921\pi\) |
−0.817404 | + | 0.576066i | \(0.804587\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 38.3424i | − | 1.22920i | ||||||
\(974\) | 6.44686 | + | 11.1663i | 0.206571 | + | 0.357791i | ||||
\(975\) | −3.16670 | − | 5.39142i | −0.101416 | − | 0.172664i | ||||
\(976\) | 12.2824 | 0.393149 | ||||||||
\(977\) | 36.1619 | − | 20.8781i | 1.15692 | − | 0.667948i | 0.206357 | − | 0.978477i | \(-0.433839\pi\) |
0.950564 | + | 0.310528i | \(0.100506\pi\) | |||||||
\(978\) | −19.6684 | + | 11.3555i | −0.628925 | + | 0.363110i | ||||
\(979\) | −26.1126 | − | 45.2284i | −0.834563 | − | 1.44550i | ||||
\(980\) | −0.0940901 | − | 25.1774i | −0.00300560 | − | 0.804262i | ||||
\(981\) | 3.85417 | − | 6.67561i | 0.123054 | − | 0.213136i | ||||
\(982\) | 33.4243 | − | 19.2975i | 1.06661 | − | 0.615809i | ||||
\(983\) | 33.0554 | − | 19.0845i | 1.05430 | − | 0.608702i | 0.130452 | − | 0.991455i | \(-0.458357\pi\) |
0.923851 | + | 0.382753i | \(0.125024\pi\) | |||||||
\(984\) | 1.33327 | + | 2.30929i | 0.0425031 | + | 0.0736176i | ||||
\(985\) | 1.29146 | + | 2.21769i | 0.0411493 | + | 0.0706615i | ||||
\(986\) | 11.9030 | − | 20.6166i | 0.379069 | − | 0.656567i | ||||
\(987\) | −17.1092 | + | 9.87800i | −0.544592 | + | 0.314420i | ||||
\(988\) | 5.14607i | 0.163718i | ||||||||
\(989\) | 62.3786 | 1.98352 | ||||||||
\(990\) | 6.59663 | − | 11.5250i | 0.209655 | − | 0.366287i | ||||
\(991\) | −10.2413 | −0.325325 | −0.162662 | − | 0.986682i | \(-0.552008\pi\) | ||||
−0.162662 | + | 0.986682i | \(0.552008\pi\) | |||||||
\(992\) | −2.32802 | − | 1.34408i | −0.0739146 | − | 0.0426746i | ||||
\(993\) | 30.3682i | 0.963704i | ||||||||
\(994\) | 15.3813 | − | 26.6412i | 0.487865 | − | 0.845007i | ||||
\(995\) | −0.0551330 | − | 14.7529i | −0.00174783 | − | 0.467699i | ||||
\(996\) | 3.72981 | − | 6.46021i | 0.118183 | − | 0.204700i | ||||
\(997\) | −42.0769 | + | 24.2931i | −1.33259 | + | 0.769371i | −0.985696 | − | 0.168534i | \(-0.946097\pi\) |
−0.346893 | + | 0.937905i | \(0.612763\pi\) | |||||||
\(998\) | − | 11.3647i | − | 0.359743i | ||||||
\(999\) | 5.24395 | + | 3.08237i | 0.165911 | + | 0.0975219i |
(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 | 1110.2.bb.d.1099.1 | yes | 28 | |
5.4 | even | 2 | inner | 1110.2.bb.d.1099.14 | yes | 28 | |
37.10 | even | 3 | inner | 1110.2.bb.d.1009.14 | yes | 28 | |
185.84 | even | 6 | inner | 1110.2.bb.d.1009.1 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.bb.d.1009.1 | ✓ | 28 | 185.84 | even | 6 | inner | |
1110.2.bb.d.1009.14 | yes | 28 | 37.10 | even | 3 | inner | |
1110.2.bb.d.1099.1 | yes | 28 | 1.1 | even | 1 | trivial | |
1110.2.bb.d.1099.14 | yes | 28 | 5.4 | even | 2 | inner |