Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.4 | ||
Character | \(\chi\) | \(=\) | 690.47 |
Dual form | 690.2.i.e.323.4 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0.451971 | + | 1.67204i | 0.260946 | + | 0.965354i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.664484 | + | 2.13506i | 0.297166 | + | 0.954826i | ||||
\(6\) | −1.50190 | − | 0.862720i | −0.613150 | − | 0.352204i | ||||
\(7\) | 2.34139 | + | 2.34139i | 0.884961 | + | 0.884961i | 0.994034 | − | 0.109073i | \(-0.0347883\pi\) |
−0.109073 | + | 0.994034i | \(0.534788\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −2.59144 | + | 1.51143i | −0.863815 | + | 0.503809i | ||||
\(10\) | −1.97957 | − | 1.03985i | −0.625996 | − | 0.328830i | ||||
\(11\) | 4.92608i | 1.48527i | 0.669697 | + | 0.742634i | \(0.266424\pi\) | ||||
−0.669697 | + | 0.742634i | \(0.733576\pi\) | |||||||
\(12\) | 1.67204 | − | 0.451971i | 0.482677 | − | 0.130473i | ||||
\(13\) | 2.78495 | − | 2.78495i | 0.772407 | − | 0.772407i | −0.206120 | − | 0.978527i | \(-0.566084\pi\) |
0.978527 | + | 0.206120i | \(0.0660836\pi\) | |||||||
\(14\) | −3.31122 | −0.884961 | ||||||||
\(15\) | −3.26957 | + | 2.07603i | −0.844200 | + | 0.536028i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.05101 | − | 2.05101i | 0.497443 | − | 0.497443i | −0.413198 | − | 0.910641i | \(-0.635588\pi\) |
0.910641 | + | 0.413198i | \(0.135588\pi\) | |||||||
\(18\) | 0.763687 | − | 2.90117i | 0.180003 | − | 0.683812i | ||||
\(19\) | − | 3.73962i | − | 0.857927i | −0.903322 | − | 0.428963i | \(-0.858879\pi\) | ||
0.903322 | − | 0.428963i | \(-0.141121\pi\) | |||||||
\(20\) | 2.13506 | − | 0.664484i | 0.477413 | − | 0.148583i | ||||
\(21\) | −2.85666 | + | 4.97313i | −0.623373 | + | 1.08523i | ||||
\(22\) | −3.48326 | − | 3.48326i | −0.742634 | − | 0.742634i | ||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | −0.862720 | + | 1.50190i | −0.176102 | + | 0.306575i | ||||
\(25\) | −4.11692 | + | 2.83742i | −0.823384 | + | 0.567484i | ||||
\(26\) | 3.93852i | 0.772407i | ||||||||
\(27\) | −3.69843 | − | 3.64988i | −0.711763 | − | 0.702420i | ||||
\(28\) | 2.34139 | − | 2.34139i | 0.442480 | − | 0.442480i | ||||
\(29\) | 9.53664 | 1.77091 | 0.885455 | − | 0.464725i | \(-0.153847\pi\) | ||||
0.885455 | + | 0.464725i | \(0.153847\pi\) | |||||||
\(30\) | 0.843964 | − | 3.77991i | 0.154086 | − | 0.690114i | ||||
\(31\) | −2.15514 | −0.387074 | −0.193537 | − | 0.981093i | \(-0.561996\pi\) | ||||
−0.193537 | + | 0.981093i | \(0.561996\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −8.23661 | + | 2.22644i | −1.43381 | + | 0.387574i | ||||
\(34\) | 2.90057i | 0.497443i | ||||||||
\(35\) | −3.44317 | + | 6.55480i | −0.582003 | + | 1.10796i | ||||
\(36\) | 1.51143 | + | 2.59144i | 0.251905 | + | 0.431907i | ||||
\(37\) | −1.67965 | − | 1.67965i | −0.276133 | − | 0.276133i | 0.555430 | − | 0.831563i | \(-0.312554\pi\) |
−0.831563 | + | 0.555430i | \(0.812554\pi\) | |||||||
\(38\) | 2.64431 | + | 2.64431i | 0.428963 | + | 0.428963i | ||||
\(39\) | 5.91528 | + | 3.39784i | 0.947202 | + | 0.544090i | ||||
\(40\) | −1.03985 | + | 1.97957i | −0.164415 | + | 0.312998i | ||||
\(41\) | − | 5.18461i | − | 0.809700i | −0.914383 | − | 0.404850i | \(-0.867324\pi\) | ||
0.914383 | − | 0.404850i | \(-0.132676\pi\) | |||||||
\(42\) | −1.49657 | − | 5.53650i | −0.230926 | − | 0.854300i | ||||
\(43\) | 2.73681 | − | 2.73681i | 0.417359 | − | 0.417359i | −0.466933 | − | 0.884292i | \(-0.654641\pi\) |
0.884292 | + | 0.466933i | \(0.154641\pi\) | |||||||
\(44\) | 4.92608 | 0.742634 | ||||||||
\(45\) | −4.94896 | − | 4.52856i | −0.737747 | − | 0.675077i | ||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −8.67231 | + | 8.67231i | −1.26499 | + | 1.26499i | −0.316341 | + | 0.948645i | \(0.602455\pi\) |
−0.948645 | + | 0.316341i | \(0.897545\pi\) | |||||||
\(48\) | −0.451971 | − | 1.67204i | −0.0652364 | − | 0.241338i | ||||
\(49\) | 3.96417i | 0.566310i | ||||||||
\(50\) | 0.904744 | − | 4.91746i | 0.127950 | − | 0.695434i | ||||
\(51\) | 4.35637 | + | 2.50238i | 0.610014 | + | 0.350403i | ||||
\(52\) | −2.78495 | − | 2.78495i | −0.386204 | − | 0.386204i | ||||
\(53\) | −8.92096 | − | 8.92096i | −1.22539 | − | 1.22539i | −0.965690 | − | 0.259697i | \(-0.916377\pi\) |
−0.259697 | − | 0.965690i | \(-0.583623\pi\) | |||||||
\(54\) | 5.19604 | − | 0.0343279i | 0.707091 | − | 0.00467144i | ||||
\(55\) | −10.5174 | + | 3.27330i | −1.41817 | + | 0.441372i | ||||
\(56\) | 3.31122i | 0.442480i | ||||||||
\(57\) | 6.25279 | − | 1.69020i | 0.828203 | − | 0.223872i | ||||
\(58\) | −6.74342 | + | 6.74342i | −0.885455 | + | 0.885455i | ||||
\(59\) | 4.44157 | 0.578243 | 0.289122 | − | 0.957292i | \(-0.406637\pi\) | ||||
0.289122 | + | 0.957292i | \(0.406637\pi\) | |||||||
\(60\) | 2.07603 | + | 3.26957i | 0.268014 | + | 0.422100i | ||||
\(61\) | −2.83318 | −0.362752 | −0.181376 | − | 0.983414i | \(-0.558055\pi\) | ||||
−0.181376 | + | 0.983414i | \(0.558055\pi\) | |||||||
\(62\) | 1.52391 | − | 1.52391i | 0.193537 | − | 0.193537i | ||||
\(63\) | −9.60641 | − | 2.52873i | −1.21029 | − | 0.318591i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 7.79659 | + | 4.09547i | 0.967048 | + | 0.507981i | ||||
\(66\) | 4.24983 | − | 7.39849i | 0.523118 | − | 0.910692i | ||||
\(67\) | −6.60677 | − | 6.60677i | −0.807146 | − | 0.807146i | 0.177055 | − | 0.984201i | \(-0.443343\pi\) |
−0.984201 | + | 0.177055i | \(0.943343\pi\) | |||||||
\(68\) | −2.05101 | − | 2.05101i | −0.248722 | − | 0.248722i | ||||
\(69\) | −0.862720 | + | 1.50190i | −0.103859 | + | 0.180808i | ||||
\(70\) | −2.20025 | − | 7.06964i | −0.262980 | − | 0.844983i | ||||
\(71\) | 1.39093i | 0.165073i | 0.996588 | + | 0.0825365i | \(0.0263021\pi\) | ||||
−0.996588 | + | 0.0825365i | \(0.973698\pi\) | |||||||
\(72\) | −2.90117 | − | 0.763687i | −0.341906 | − | 0.0900014i | ||||
\(73\) | 7.65822 | − | 7.65822i | 0.896327 | − | 0.896327i | −0.0987822 | − | 0.995109i | \(-0.531495\pi\) |
0.995109 | + | 0.0987822i | \(0.0314947\pi\) | |||||||
\(74\) | 2.37538 | 0.276133 | ||||||||
\(75\) | −6.60501 | − | 5.60123i | −0.762681 | − | 0.646774i | ||||
\(76\) | −3.73962 | −0.428963 | ||||||||
\(77\) | −11.5338 | + | 11.5338i | −1.31440 | + | 1.31440i | ||||
\(78\) | −6.58537 | + | 1.78010i | −0.745646 | + | 0.201556i | ||||
\(79\) | − | 1.62454i | − | 0.182775i | −0.995815 | − | 0.0913877i | \(-0.970870\pi\) | ||
0.995815 | − | 0.0913877i | \(-0.0291303\pi\) | |||||||
\(80\) | −0.664484 | − | 2.13506i | −0.0742916 | − | 0.238706i | ||||
\(81\) | 4.43117 | − | 7.83356i | 0.492352 | − | 0.870396i | ||||
\(82\) | 3.66607 | + | 3.66607i | 0.404850 | + | 0.404850i | ||||
\(83\) | −0.357742 | − | 0.357742i | −0.0392673 | − | 0.0392673i | 0.687201 | − | 0.726468i | \(-0.258839\pi\) |
−0.726468 | + | 0.687201i | \(0.758839\pi\) | |||||||
\(84\) | 4.97313 | + | 2.85666i | 0.542613 | + | 0.311687i | ||||
\(85\) | 5.74189 | + | 3.01616i | 0.622795 | + | 0.327148i | ||||
\(86\) | 3.87043i | 0.417359i | ||||||||
\(87\) | 4.31028 | + | 15.9457i | 0.462111 | + | 1.70955i | ||||
\(88\) | −3.48326 | + | 3.48326i | −0.371317 | + | 0.371317i | ||||
\(89\) | −7.92555 | −0.840106 | −0.420053 | − | 0.907499i | \(-0.637989\pi\) | ||||
−0.420053 | + | 0.907499i | \(0.637989\pi\) | |||||||
\(90\) | 6.70161 | − | 0.297267i | 0.706412 | − | 0.0313347i | ||||
\(91\) | 13.0413 | 1.36710 | ||||||||
\(92\) | 0.707107 | − | 0.707107i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | −0.974060 | − | 3.60348i | −0.101005 | − | 0.373664i | ||||
\(94\) | − | 12.2645i | − | 1.26499i | ||||||
\(95\) | 7.98429 | − | 2.48492i | 0.819171 | − | 0.254947i | ||||
\(96\) | 1.50190 | + | 0.862720i | 0.153287 | + | 0.0880510i | ||||
\(97\) | 5.52335 | + | 5.52335i | 0.560811 | + | 0.560811i | 0.929538 | − | 0.368726i | \(-0.120206\pi\) |
−0.368726 | + | 0.929538i | \(0.620206\pi\) | |||||||
\(98\) | −2.80309 | − | 2.80309i | −0.283155 | − | 0.283155i | ||||
\(99\) | −7.44541 | − | 12.7657i | −0.748292 | − | 1.28300i | ||||
\(100\) | 2.83742 | + | 4.11692i | 0.283742 | + | 0.411692i | ||||
\(101\) | 18.2907i | 1.81999i | 0.414619 | + | 0.909995i | \(0.363915\pi\) | ||||
−0.414619 | + | 0.909995i | \(0.636085\pi\) | |||||||
\(102\) | −4.84987 | + | 1.31097i | −0.480209 | + | 0.129806i | ||||
\(103\) | 8.14075 | − | 8.14075i | 0.802132 | − | 0.802132i | −0.181297 | − | 0.983428i | \(-0.558029\pi\) |
0.983428 | + | 0.181297i | \(0.0580294\pi\) | |||||||
\(104\) | 3.93852 | 0.386204 | ||||||||
\(105\) | −12.5161 | − | 2.79455i | −1.22145 | − | 0.272720i | ||||
\(106\) | 12.6161 | 1.22539 | ||||||||
\(107\) | 2.27414 | − | 2.27414i | 0.219849 | − | 0.219849i | −0.588586 | − | 0.808435i | \(-0.700315\pi\) |
0.808435 | + | 0.588586i | \(0.200315\pi\) | |||||||
\(108\) | −3.64988 | + | 3.69843i | −0.351210 | + | 0.355881i | ||||
\(109\) | 3.20141i | 0.306640i | 0.988177 | + | 0.153320i | \(0.0489965\pi\) | ||||
−0.988177 | + | 0.153320i | \(0.951003\pi\) | |||||||
\(110\) | 5.12239 | − | 9.75153i | 0.488400 | − | 0.929772i | ||||
\(111\) | 2.04929 | − | 3.56760i | 0.194510 | − | 0.338621i | ||||
\(112\) | −2.34139 | − | 2.34139i | −0.221240 | − | 0.221240i | ||||
\(113\) | −6.56397 | − | 6.56397i | −0.617486 | − | 0.617486i | 0.327400 | − | 0.944886i | \(-0.393828\pi\) |
−0.944886 | + | 0.327400i | \(0.893828\pi\) | |||||||
\(114\) | −3.22624 | + | 5.61654i | −0.302165 | + | 0.526037i | ||||
\(115\) | −1.03985 | + | 1.97957i | −0.0969666 | + | 0.184596i | ||||
\(116\) | − | 9.53664i | − | 0.885455i | ||||||
\(117\) | −3.00780 | + | 11.4263i | −0.278071 | + | 1.05636i | ||||
\(118\) | −3.14067 | + | 3.14067i | −0.289122 | + | 0.289122i | ||||
\(119\) | 9.60441 | 0.880435 | ||||||||
\(120\) | −3.77991 | − | 0.843964i | −0.345057 | − | 0.0770430i | ||||
\(121\) | −13.2663 | −1.20602 | ||||||||
\(122\) | 2.00336 | − | 2.00336i | 0.181376 | − | 0.181376i | ||||
\(123\) | 8.66888 | − | 2.34329i | 0.781647 | − | 0.211288i | ||||
\(124\) | 2.15514i | 0.193537i | ||||||||
\(125\) | −8.79368 | − | 6.90443i | −0.786531 | − | 0.617551i | ||||
\(126\) | 8.58084 | − | 5.00467i | 0.764442 | − | 0.445851i | ||||
\(127\) | 8.84885 | + | 8.84885i | 0.785209 | + | 0.785209i | 0.980705 | − | 0.195496i | \(-0.0626316\pi\) |
−0.195496 | + | 0.980705i | \(0.562632\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 5.81301 | + | 3.33910i | 0.511807 | + | 0.293991i | ||||
\(130\) | −8.40896 | + | 2.61708i | −0.737514 | + | 0.229533i | ||||
\(131\) | 0.892813i | 0.0780054i | 0.999239 | + | 0.0390027i | \(0.0124181\pi\) | ||||
−0.999239 | + | 0.0390027i | \(0.987582\pi\) | |||||||
\(132\) | 2.22644 | + | 8.23661i | 0.193787 | + | 0.716905i | ||||
\(133\) | 8.75588 | − | 8.75588i | 0.759231 | − | 0.759231i | ||||
\(134\) | 9.34339 | 0.807146 | ||||||||
\(135\) | 5.33515 | − | 10.3216i | 0.459177 | − | 0.888345i | ||||
\(136\) | 2.90057 | 0.248722 | ||||||||
\(137\) | 5.62646 | − | 5.62646i | 0.480701 | − | 0.480701i | −0.424655 | − | 0.905355i | \(-0.639604\pi\) |
0.905355 | + | 0.424655i | \(0.139604\pi\) | |||||||
\(138\) | −0.451971 | − | 1.67204i | −0.0384743 | − | 0.142334i | ||||
\(139\) | 11.0965i | 0.941196i | 0.882348 | + | 0.470598i | \(0.155962\pi\) | ||||
−0.882348 | + | 0.470598i | \(0.844038\pi\) | |||||||
\(140\) | 6.55480 | + | 3.44317i | 0.553982 | + | 0.291001i | ||||
\(141\) | −18.4201 | − | 10.5808i | −1.55125 | − | 0.891067i | ||||
\(142\) | −0.983536 | − | 0.983536i | −0.0825365 | − | 0.0825365i | ||||
\(143\) | 13.7189 | + | 13.7189i | 1.14723 | + | 1.14723i | ||||
\(144\) | 2.59144 | − | 1.51143i | 0.215954 | − | 0.125952i | ||||
\(145\) | 6.33695 | + | 20.3613i | 0.526255 | + | 1.69091i | ||||
\(146\) | 10.8304i | 0.896327i | ||||||||
\(147\) | −6.62826 | + | 1.79169i | −0.546690 | + | 0.147776i | ||||
\(148\) | −1.67965 | + | 1.67965i | −0.138066 | + | 0.138066i | ||||
\(149\) | 12.7504 | 1.04456 | 0.522278 | − | 0.852775i | \(-0.325082\pi\) | ||||
0.522278 | + | 0.852775i | \(0.325082\pi\) | |||||||
\(150\) | 8.63112 | − | 0.709781i | 0.704728 | − | 0.0579534i | ||||
\(151\) | 17.4795 | 1.42246 | 0.711230 | − | 0.702959i | \(-0.248138\pi\) | ||||
0.711230 | + | 0.702959i | \(0.248138\pi\) | |||||||
\(152\) | 2.64431 | − | 2.64431i | 0.214482 | − | 0.214482i | ||||
\(153\) | −2.21513 | + | 8.41504i | −0.179082 | + | 0.680315i | ||||
\(154\) | − | 16.3113i | − | 1.31440i | ||||||
\(155\) | −1.43206 | − | 4.60134i | −0.115025 | − | 0.369589i | ||||
\(156\) | 3.39784 | − | 5.91528i | 0.272045 | − | 0.473601i | ||||
\(157\) | 9.49292 | + | 9.49292i | 0.757617 | + | 0.757617i | 0.975888 | − | 0.218271i | \(-0.0700416\pi\) |
−0.218271 | + | 0.975888i | \(0.570042\pi\) | |||||||
\(158\) | 1.14873 | + | 1.14873i | 0.0913877 | + | 0.0913877i | ||||
\(159\) | 10.8842 | − | 18.9482i | 0.863173 | − | 1.50269i | ||||
\(160\) | 1.97957 | + | 1.03985i | 0.156499 | + | 0.0822074i | ||||
\(161\) | 3.31122i | 0.260961i | ||||||||
\(162\) | 2.40586 | + | 8.67248i | 0.189022 | + | 0.681374i | ||||
\(163\) | −11.6062 | + | 11.6062i | −0.909072 | + | 0.909072i | −0.996197 | − | 0.0871258i | \(-0.972232\pi\) |
0.0871258 | + | 0.996197i | \(0.472232\pi\) | |||||||
\(164\) | −5.18461 | −0.404850 | ||||||||
\(165\) | −10.2267 | − | 16.1062i | −0.796146 | − | 1.25386i | ||||
\(166\) | 0.505923 | 0.0392673 | ||||||||
\(167\) | 2.96090 | − | 2.96090i | 0.229121 | − | 0.229121i | −0.583204 | − | 0.812326i | \(-0.698201\pi\) |
0.812326 | + | 0.583204i | \(0.198201\pi\) | |||||||
\(168\) | −5.53650 | + | 1.49657i | −0.427150 | + | 0.115463i | ||||
\(169\) | − | 2.51194i | − | 0.193226i | ||||||
\(170\) | −6.19287 | + | 1.92738i | −0.474972 | + | 0.147823i | ||||
\(171\) | 5.65216 | + | 9.69101i | 0.432232 | + | 0.741090i | ||||
\(172\) | −2.73681 | − | 2.73681i | −0.208680 | − | 0.208680i | ||||
\(173\) | −16.0409 | − | 16.0409i | −1.21957 | − | 1.21957i | −0.967783 | − | 0.251786i | \(-0.918982\pi\) |
−0.251786 | − | 0.967783i | \(-0.581018\pi\) | |||||||
\(174\) | −14.3231 | − | 8.22745i | −1.08583 | − | 0.623721i | ||||
\(175\) | −16.2828 | − | 2.99580i | −1.23086 | − | 0.226462i | ||||
\(176\) | − | 4.92608i | − | 0.371317i | ||||||
\(177\) | 2.00746 | + | 7.42649i | 0.150890 | + | 0.558209i | ||||
\(178\) | 5.60421 | − | 5.60421i | 0.420053 | − | 0.420053i | ||||
\(179\) | 1.42969 | 0.106860 | 0.0534301 | − | 0.998572i | \(-0.482985\pi\) | ||||
0.0534301 | + | 0.998572i | \(0.482985\pi\) | |||||||
\(180\) | −4.52856 | + | 4.94896i | −0.337539 | + | 0.368873i | ||||
\(181\) | 2.71065 | 0.201481 | 0.100740 | − | 0.994913i | \(-0.467879\pi\) | ||||
0.100740 | + | 0.994913i | \(0.467879\pi\) | |||||||
\(182\) | −9.22159 | + | 9.22159i | −0.683550 | + | 0.683550i | ||||
\(183\) | −1.28052 | − | 4.73720i | −0.0946585 | − | 0.350184i | ||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | 2.47004 | − | 4.70225i | 0.181601 | − | 0.345716i | ||||
\(186\) | 3.23681 | + | 1.85928i | 0.237334 | + | 0.136329i | ||||
\(187\) | 10.1034 | + | 10.1034i | 0.738837 | + | 0.738837i | ||||
\(188\) | 8.67231 | + | 8.67231i | 0.632493 | + | 0.632493i | ||||
\(189\) | −0.113667 | − | 17.2052i | −0.00826807 | − | 1.25150i | ||||
\(190\) | −3.88864 | + | 7.40284i | −0.282112 | + | 0.537059i | ||||
\(191\) | 2.70353i | 0.195621i | 0.995205 | + | 0.0978104i | \(0.0311839\pi\) | ||||
−0.995205 | + | 0.0978104i | \(0.968816\pi\) | |||||||
\(192\) | −1.67204 | + | 0.451971i | −0.120669 | + | 0.0326182i | ||||
\(193\) | 9.56062 | − | 9.56062i | 0.688189 | − | 0.688189i | −0.273643 | − | 0.961831i | \(-0.588229\pi\) |
0.961831 | + | 0.273643i | \(0.0882286\pi\) | |||||||
\(194\) | −7.81120 | −0.560811 | ||||||||
\(195\) | −3.32397 | + | 14.8873i | −0.238034 | + | 1.06610i | ||||
\(196\) | 3.96417 | 0.283155 | ||||||||
\(197\) | 15.6486 | − | 15.6486i | 1.11492 | − | 1.11492i | 0.122441 | − | 0.992476i | \(-0.460928\pi\) |
0.992476 | − | 0.122441i | \(-0.0390723\pi\) | |||||||
\(198\) | 14.2914 | + | 3.76198i | 1.01564 | + | 0.267352i | ||||
\(199\) | − | 2.30260i | − | 0.163227i | −0.996664 | − | 0.0816135i | \(-0.973993\pi\) | ||
0.996664 | − | 0.0816135i | \(-0.0260073\pi\) | |||||||
\(200\) | −4.91746 | − | 0.904744i | −0.347717 | − | 0.0639750i | ||||
\(201\) | 8.06073 | − | 14.0329i | 0.568560 | − | 0.989802i | ||||
\(202\) | −12.9335 | − | 12.9335i | −0.909995 | − | 0.909995i | ||||
\(203\) | 22.3290 | + | 22.3290i | 1.56719 | + | 1.56719i | ||||
\(204\) | 2.50238 | − | 4.35637i | 0.175201 | − | 0.305007i | ||||
\(205\) | 11.0694 | − | 3.44509i | 0.773123 | − | 0.240616i | ||||
\(206\) | 11.5128i | 0.802132i | ||||||||
\(207\) | −2.90117 | − | 0.763687i | −0.201645 | − | 0.0530799i | ||||
\(208\) | −2.78495 | + | 2.78495i | −0.193102 | + | 0.193102i | ||||
\(209\) | 18.4216 | 1.27425 | ||||||||
\(210\) | 10.8263 | − | 6.87418i | 0.747084 | − | 0.474364i | ||||
\(211\) | 24.4727 | 1.68477 | 0.842385 | − | 0.538875i | \(-0.181151\pi\) | ||||
0.842385 | + | 0.538875i | \(0.181151\pi\) | |||||||
\(212\) | −8.92096 | + | 8.92096i | −0.612694 | + | 0.612694i | ||||
\(213\) | −2.32569 | + | 0.628660i | −0.159354 | + | 0.0430751i | ||||
\(214\) | 3.21611i | 0.219849i | ||||||||
\(215\) | 7.66180 | + | 4.02467i | 0.522530 | + | 0.274480i | ||||
\(216\) | −0.0343279 | − | 5.19604i | −0.00233572 | − | 0.353546i | ||||
\(217\) | −5.04601 | − | 5.04601i | −0.342546 | − | 0.342546i | ||||
\(218\) | −2.26374 | − | 2.26374i | −0.153320 | − | 0.153320i | ||||
\(219\) | 16.2662 | + | 9.34357i | 1.09916 | + | 0.631380i | ||||
\(220\) | 3.27330 | + | 10.5174i | 0.220686 | + | 0.709086i | ||||
\(221\) | − | 11.4239i | − | 0.768457i | ||||||
\(222\) | 1.07360 | + | 3.97174i | 0.0720556 | + | 0.266566i | ||||
\(223\) | 17.0794 | − | 17.0794i | 1.14372 | − | 1.14372i | 0.155960 | − | 0.987763i | \(-0.450153\pi\) |
0.987763 | − | 0.155960i | \(-0.0498472\pi\) | |||||||
\(224\) | 3.31122 | 0.221240 | ||||||||
\(225\) | 6.38022 | − | 13.5754i | 0.425348 | − | 0.905030i | ||||
\(226\) | 9.28286 | 0.617486 | ||||||||
\(227\) | −4.15095 | + | 4.15095i | −0.275508 | + | 0.275508i | −0.831313 | − | 0.555805i | \(-0.812410\pi\) |
0.555805 | + | 0.831313i | \(0.312410\pi\) | |||||||
\(228\) | −1.69020 | − | 6.25279i | −0.111936 | − | 0.414101i | ||||
\(229\) | 4.18617i | 0.276630i | 0.990388 | + | 0.138315i | \(0.0441686\pi\) | ||||
−0.990388 | + | 0.138315i | \(0.955831\pi\) | |||||||
\(230\) | −0.664484 | − | 2.13506i | −0.0438148 | − | 0.140781i | ||||
\(231\) | −24.4980 | − | 14.0721i | −1.61185 | − | 0.925877i | ||||
\(232\) | 6.74342 | + | 6.74342i | 0.442727 | + | 0.442727i | ||||
\(233\) | −17.1678 | − | 17.1678i | −1.12470 | − | 1.12470i | −0.991025 | − | 0.133674i | \(-0.957322\pi\) |
−0.133674 | − | 0.991025i | \(-0.542678\pi\) | |||||||
\(234\) | −5.95279 | − | 10.2065i | −0.389146 | − | 0.667217i | ||||
\(235\) | −24.2785 | − | 12.7533i | −1.58375 | − | 0.831930i | ||||
\(236\) | − | 4.44157i | − | 0.289122i | ||||||
\(237\) | 2.71630 | − | 0.734246i | 0.176443 | − | 0.0476944i | ||||
\(238\) | −6.79135 | + | 6.79135i | −0.440218 | + | 0.440218i | ||||
\(239\) | 3.42360 | 0.221454 | 0.110727 | − | 0.993851i | \(-0.464682\pi\) | ||||
0.110727 | + | 0.993851i | \(0.464682\pi\) | |||||||
\(240\) | 3.26957 | − | 2.07603i | 0.211050 | − | 0.134007i | ||||
\(241\) | −22.1025 | −1.42375 | −0.711874 | − | 0.702307i | \(-0.752153\pi\) | ||||
−0.711874 | + | 0.702307i | \(0.752153\pi\) | |||||||
\(242\) | 9.38066 | − | 9.38066i | 0.603011 | − | 0.603011i | ||||
\(243\) | 15.1008 | + | 3.86856i | 0.968717 | + | 0.248168i | ||||
\(244\) | 2.83318i | 0.181376i | ||||||||
\(245\) | −8.46372 | + | 2.63413i | −0.540728 | + | 0.168288i | ||||
\(246\) | −4.47287 | + | 7.78678i | −0.285180 | + | 0.496467i | ||||
\(247\) | −10.4147 | − | 10.4147i | −0.662669 | − | 0.662669i | ||||
\(248\) | −1.52391 | − | 1.52391i | −0.0967686 | − | 0.0967686i | ||||
\(249\) | 0.436470 | − | 0.759848i | 0.0276602 | − | 0.0481534i | ||||
\(250\) | 11.1002 | − | 1.33590i | 0.702041 | − | 0.0844896i | ||||
\(251\) | 14.1807i | 0.895079i | 0.894264 | + | 0.447540i | \(0.147700\pi\) | ||||
−0.894264 | + | 0.447540i | \(0.852300\pi\) | |||||||
\(252\) | −2.52873 | + | 9.60641i | −0.159295 | + | 0.605147i | ||||
\(253\) | −3.48326 | + | 3.48326i | −0.218991 | + | 0.218991i | ||||
\(254\) | −12.5142 | −0.785209 | ||||||||
\(255\) | −2.44797 | + | 10.9639i | −0.153298 | + | 0.686585i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.2661 | + | 17.2661i | −1.07703 | + | 1.07703i | −0.0802573 | + | 0.996774i | \(0.525574\pi\) |
−0.996774 | + | 0.0802573i | \(0.974426\pi\) | |||||||
\(258\) | −6.47152 | + | 1.74932i | −0.402899 | + | 0.108908i | ||||
\(259\) | − | 7.86541i | − | 0.488733i | ||||||
\(260\) | 4.09547 | − | 7.79659i | 0.253990 | − | 0.483524i | ||||
\(261\) | −24.7137 | + | 14.4139i | −1.52974 | + | 0.892201i | ||||
\(262\) | −0.631314 | − | 0.631314i | −0.0390027 | − | 0.0390027i | ||||
\(263\) | 14.7411 | + | 14.7411i | 0.908978 | + | 0.908978i | 0.996190 | − | 0.0872121i | \(-0.0277958\pi\) |
−0.0872121 | + | 0.996190i | \(0.527796\pi\) | |||||||
\(264\) | −7.39849 | − | 4.24983i | −0.455346 | − | 0.261559i | ||||
\(265\) | 13.1189 | − | 24.9746i | 0.805888 | − | 1.53418i | ||||
\(266\) | 12.3827i | 0.759231i | ||||||||
\(267\) | −3.58212 | − | 13.2518i | −0.219222 | − | 0.811000i | ||||
\(268\) | −6.60677 | + | 6.60677i | −0.403573 | + | 0.403573i | ||||
\(269\) | −25.7589 | −1.57054 | −0.785272 | − | 0.619150i | \(-0.787477\pi\) | ||||
−0.785272 | + | 0.619150i | \(0.787477\pi\) | |||||||
\(270\) | 3.52598 | + | 11.0710i | 0.214584 | + | 0.673761i | ||||
\(271\) | −0.344837 | −0.0209473 | −0.0104737 | − | 0.999945i | \(-0.503334\pi\) | ||||
−0.0104737 | + | 0.999945i | \(0.503334\pi\) | |||||||
\(272\) | −2.05101 | + | 2.05101i | −0.124361 | + | 0.124361i | ||||
\(273\) | 5.89429 | + | 21.8056i | 0.356739 | + | 1.31973i | ||||
\(274\) | 7.95701i | 0.480701i | ||||||||
\(275\) | −13.9774 | − | 20.2803i | −0.842866 | − | 1.22295i | ||||
\(276\) | 1.50190 | + | 0.862720i | 0.0904040 | + | 0.0519296i | ||||
\(277\) | −21.8081 | − | 21.8081i | −1.31032 | − | 1.31032i | −0.921174 | − | 0.389150i | \(-0.872769\pi\) |
−0.389150 | − | 0.921174i | \(-0.627231\pi\) | |||||||
\(278\) | −7.84644 | − | 7.84644i | −0.470598 | − | 0.470598i | ||||
\(279\) | 5.58492 | − | 3.25734i | 0.334361 | − | 0.195012i | ||||
\(280\) | −7.06964 | + | 2.20025i | −0.422492 | + | 0.131490i | ||||
\(281\) | 7.85543i | 0.468616i | 0.972162 | + | 0.234308i | \(0.0752824\pi\) | ||||
−0.972162 | + | 0.234308i | \(0.924718\pi\) | |||||||
\(282\) | 20.5068 | − | 5.54320i | 1.22116 | − | 0.330093i | ||||
\(283\) | −8.05637 | + | 8.05637i | −0.478901 | + | 0.478901i | −0.904780 | − | 0.425879i | \(-0.859965\pi\) |
0.425879 | + | 0.904780i | \(0.359965\pi\) | |||||||
\(284\) | 1.39093 | 0.0825365 | ||||||||
\(285\) | 7.76355 | + | 12.2269i | 0.459873 | + | 0.724262i | ||||
\(286\) | −19.4015 | −1.14723 | ||||||||
\(287\) | 12.1392 | − | 12.1392i | 0.716553 | − | 0.716553i | ||||
\(288\) | −0.763687 | + | 2.90117i | −0.0450007 | + | 0.170953i | ||||
\(289\) | 8.58671i | 0.505101i | ||||||||
\(290\) | −18.8785 | − | 9.91668i | −1.10858 | − | 0.582328i | ||||
\(291\) | −6.73888 | + | 11.7317i | −0.395040 | + | 0.687723i | ||||
\(292\) | −7.65822 | − | 7.65822i | −0.448163 | − | 0.448163i | ||||
\(293\) | −21.2971 | − | 21.2971i | −1.24419 | − | 1.24419i | −0.958247 | − | 0.285941i | \(-0.907694\pi\) |
−0.285941 | − | 0.958247i | \(-0.592306\pi\) | |||||||
\(294\) | 3.41997 | − | 5.95380i | 0.199457 | − | 0.347233i | ||||
\(295\) | 2.95135 | + | 9.48300i | 0.171834 | + | 0.552122i | ||||
\(296\) | − | 2.37538i | − | 0.138066i | ||||||
\(297\) | 17.9796 | − | 18.2187i | 1.04328 | − | 1.05716i | ||||
\(298\) | −9.01592 | + | 9.01592i | −0.522278 | + | 0.522278i | ||||
\(299\) | 3.93852 | 0.227770 | ||||||||
\(300\) | −5.60123 | + | 6.60501i | −0.323387 | + | 0.381341i | ||||
\(301\) | 12.8158 | 0.738693 | ||||||||
\(302\) | −12.3599 | + | 12.3599i | −0.711230 | + | 0.711230i | ||||
\(303\) | −30.5828 | + | 8.26686i | −1.75693 | + | 0.474918i | ||||
\(304\) | 3.73962i | 0.214482i | ||||||||
\(305\) | −1.88261 | − | 6.04900i | −0.107798 | − | 0.346365i | ||||
\(306\) | −4.38400 | − | 7.51666i | −0.250617 | − | 0.429699i | ||||
\(307\) | −7.39676 | − | 7.39676i | −0.422155 | − | 0.422155i | 0.463790 | − | 0.885945i | \(-0.346489\pi\) |
−0.885945 | + | 0.463790i | \(0.846489\pi\) | |||||||
\(308\) | 11.5338 | + | 11.5338i | 0.657202 | + | 0.657202i | ||||
\(309\) | 17.2910 | + | 9.93229i | 0.983653 | + | 0.565028i | ||||
\(310\) | 4.26626 | + | 2.24102i | 0.242307 | + | 0.127282i | ||||
\(311\) | 23.2216i | 1.31678i | 0.752679 | + | 0.658388i | \(0.228761\pi\) | ||||
−0.752679 | + | 0.658388i | \(0.771239\pi\) | |||||||
\(312\) | 1.78010 | + | 6.58537i | 0.100778 | + | 0.372823i | ||||
\(313\) | −5.38747 | + | 5.38747i | −0.304518 | + | 0.304518i | −0.842779 | − | 0.538260i | \(-0.819082\pi\) |
0.538260 | + | 0.842779i | \(0.319082\pi\) | |||||||
\(314\) | −13.4250 | −0.757617 | ||||||||
\(315\) | −0.984317 | − | 22.1905i | −0.0554600 | − | 1.25029i | ||||
\(316\) | −1.62454 | −0.0913877 | ||||||||
\(317\) | 4.39344 | − | 4.39344i | 0.246760 | − | 0.246760i | −0.572879 | − | 0.819640i | \(-0.694174\pi\) |
0.819640 | + | 0.572879i | \(0.194174\pi\) | |||||||
\(318\) | 5.70213 | + | 21.0947i | 0.319759 | + | 1.18293i | ||||
\(319\) | 46.9782i | 2.63028i | ||||||||
\(320\) | −2.13506 | + | 0.664484i | −0.119353 | + | 0.0371458i | ||||
\(321\) | 4.83029 | + | 2.77461i | 0.269601 | + | 0.154863i | ||||
\(322\) | −2.34139 | − | 2.34139i | −0.130480 | − | 0.130480i | ||||
\(323\) | −7.66999 | − | 7.66999i | −0.426770 | − | 0.426770i | ||||
\(324\) | −7.83356 | − | 4.43117i | −0.435198 | − | 0.246176i | ||||
\(325\) | −3.56335 | + | 19.3675i | −0.197659 | + | 1.07432i | ||||
\(326\) | − | 16.4137i | − | 0.909072i | ||||||
\(327\) | −5.35290 | + | 1.44695i | −0.296016 | + | 0.0800163i | ||||
\(328\) | 3.66607 | − | 3.66607i | 0.202425 | − | 0.202425i | ||||
\(329\) | −40.6105 | −2.23893 | ||||||||
\(330\) | 18.6201 | + | 4.15743i | 1.02500 | + | 0.228859i | ||||
\(331\) | 5.50237 | 0.302437 | 0.151219 | − | 0.988500i | \(-0.451680\pi\) | ||||
0.151219 | + | 0.988500i | \(0.451680\pi\) | |||||||
\(332\) | −0.357742 | + | 0.357742i | −0.0196336 | + | 0.0196336i | ||||
\(333\) | 6.89139 | + | 1.81405i | 0.377646 | + | 0.0994093i | ||||
\(334\) | 4.18734i | 0.229121i | ||||||||
\(335\) | 9.71573 | − | 18.4959i | 0.530827 | − | 1.01054i | ||||
\(336\) | 2.85666 | − | 4.97313i | 0.155843 | − | 0.271307i | ||||
\(337\) | 12.2108 | + | 12.2108i | 0.665163 | + | 0.665163i | 0.956592 | − | 0.291429i | \(-0.0941309\pi\) |
−0.291429 | + | 0.956592i | \(0.594131\pi\) | |||||||
\(338\) | 1.77621 | + | 1.77621i | 0.0966129 | + | 0.0966129i | ||||
\(339\) | 8.00851 | − | 13.9420i | 0.434962 | − | 0.757223i | ||||
\(340\) | 3.01616 | − | 5.74189i | 0.163574 | − | 0.311397i | ||||
\(341\) | − | 10.6164i | − | 0.574909i | ||||||
\(342\) | −10.8493 | − | 2.85590i | −0.586661 | − | 0.154429i | ||||
\(343\) | 7.10804 | − | 7.10804i | 0.383798 | − | 0.383798i | ||||
\(344\) | 3.87043 | 0.208680 | ||||||||
\(345\) | −3.77991 | − | 0.843964i | −0.203504 | − | 0.0454375i | ||||
\(346\) | 22.6853 | 1.21957 | ||||||||
\(347\) | −20.1140 | + | 20.1140i | −1.07978 | + | 1.07978i | −0.0832466 | + | 0.996529i | \(0.526529\pi\) |
−0.996529 | + | 0.0832466i | \(0.973471\pi\) | |||||||
\(348\) | 15.9457 | − | 4.31028i | 0.854777 | − | 0.231055i | ||||
\(349\) | − | 4.04914i | − | 0.216746i | −0.994110 | − | 0.108373i | \(-0.965436\pi\) | ||
0.994110 | − | 0.108373i | \(-0.0345640\pi\) | |||||||
\(350\) | 13.6320 | − | 9.39532i | 0.728663 | − | 0.502201i | ||||
\(351\) | −20.4647 | + | 0.135201i | −1.09232 | + | 0.00721650i | ||||
\(352\) | 3.48326 | + | 3.48326i | 0.185659 | + | 0.185659i | ||||
\(353\) | 26.1786 | + | 26.1786i | 1.39335 | + | 1.39335i | 0.817692 | + | 0.575656i | \(0.195253\pi\) |
0.575656 | + | 0.817692i | \(0.304747\pi\) | |||||||
\(354\) | −6.67081 | − | 3.83183i | −0.354550 | − | 0.203660i | ||||
\(355\) | −2.96971 | + | 0.924251i | −0.157616 | + | 0.0490541i | ||||
\(356\) | 7.92555i | 0.420053i | ||||||||
\(357\) | 4.34092 | + | 16.0590i | 0.229746 | + | 0.849931i | ||||
\(358\) | −1.01094 | + | 1.01094i | −0.0534301 | + | 0.0534301i | ||||
\(359\) | 18.0793 | 0.954191 | 0.477096 | − | 0.878851i | \(-0.341690\pi\) | ||||
0.477096 | + | 0.878851i | \(0.341690\pi\) | |||||||
\(360\) | −0.297267 | − | 6.70161i | −0.0156674 | − | 0.353206i | ||||
\(361\) | 5.01527 | 0.263962 | ||||||||
\(362\) | −1.91672 | + | 1.91672i | −0.100740 | + | 0.100740i | ||||
\(363\) | −5.99596 | − | 22.1817i | −0.314706 | − | 1.16424i | ||||
\(364\) | − | 13.0413i | − | 0.683550i | ||||||
\(365\) | 21.4395 | + | 11.2620i | 1.12219 | + | 0.589478i | ||||
\(366\) | 4.25517 | + | 2.44424i | 0.222421 | + | 0.127763i | ||||
\(367\) | −8.45693 | − | 8.45693i | −0.441448 | − | 0.441448i | 0.451050 | − | 0.892498i | \(-0.351049\pi\) |
−0.892498 | + | 0.451050i | \(0.851049\pi\) | |||||||
\(368\) | −0.707107 | − | 0.707107i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | 7.83617 | + | 13.4356i | 0.407935 | + | 0.699431i | ||||
\(370\) | 1.57840 | + | 5.07157i | 0.0820573 | + | 0.263659i | ||||
\(371\) | − | 41.7748i | − | 2.16884i | ||||||
\(372\) | −3.60348 | + | 0.974060i | −0.186832 | + | 0.0505027i | ||||
\(373\) | −25.2100 | + | 25.2100i | −1.30532 | + | 1.30532i | −0.380571 | + | 0.924752i | \(0.624272\pi\) |
−0.924752 | + | 0.380571i | \(0.875728\pi\) | |||||||
\(374\) | −14.2884 | −0.738837 | ||||||||
\(375\) | 7.57001 | − | 17.8240i | 0.390914 | − | 0.920427i | ||||
\(376\) | −12.2645 | −0.632493 | ||||||||
\(377\) | 26.5591 | − | 26.5591i | 1.36786 | − | 1.36786i | ||||
\(378\) | 12.2463 | + | 12.0856i | 0.629882 | + | 0.621614i | ||||
\(379\) | 12.7386i | 0.654337i | 0.944966 | + | 0.327168i | \(0.106094\pi\) | ||||
−0.944966 | + | 0.327168i | \(0.893906\pi\) | |||||||
\(380\) | −2.48492 | − | 7.98429i | −0.127473 | − | 0.409585i | ||||
\(381\) | −10.7962 | + | 18.7951i | −0.553107 | + | 0.962901i | ||||
\(382\) | −1.91169 | − | 1.91169i | −0.0978104 | − | 0.0978104i | ||||
\(383\) | −18.8838 | − | 18.8838i | −0.964917 | − | 0.964917i | 0.0344882 | − | 0.999405i | \(-0.489020\pi\) |
−0.999405 | + | 0.0344882i | \(0.989020\pi\) | |||||||
\(384\) | 0.862720 | − | 1.50190i | 0.0440255 | − | 0.0766437i | ||||
\(385\) | −32.2895 | − | 16.9613i | −1.64562 | − | 0.864430i | ||||
\(386\) | 13.5208i | 0.688189i | ||||||||
\(387\) | −2.95580 | + | 11.2288i | −0.150252 | + | 0.570790i | ||||
\(388\) | 5.52335 | − | 5.52335i | 0.280406 | − | 0.280406i | ||||
\(389\) | −33.0424 | −1.67532 | −0.837659 | − | 0.546193i | \(-0.816076\pi\) | ||||
−0.837659 | + | 0.546193i | \(0.816076\pi\) | |||||||
\(390\) | −8.17648 | − | 12.8773i | −0.414032 | − | 0.652066i | ||||
\(391\) | 2.90057 | 0.146688 | ||||||||
\(392\) | −2.80309 | + | 2.80309i | −0.141578 | + | 0.141578i | ||||
\(393\) | −1.49282 | + | 0.403525i | −0.0753028 | + | 0.0203552i | ||||
\(394\) | 22.1305i | 1.11492i | ||||||||
\(395\) | 3.46849 | − | 1.07948i | 0.174519 | − | 0.0543147i | ||||
\(396\) | −12.7657 | + | 7.44541i | −0.641499 | + | 0.374146i | ||||
\(397\) | 9.82206 | + | 9.82206i | 0.492955 | + | 0.492955i | 0.909236 | − | 0.416281i | \(-0.136667\pi\) |
−0.416281 | + | 0.909236i | \(0.636667\pi\) | |||||||
\(398\) | 1.62818 | + | 1.62818i | 0.0816135 | + | 0.0816135i | ||||
\(399\) | 18.5976 | + | 10.6828i | 0.931045 | + | 0.534809i | ||||
\(400\) | 4.11692 | − | 2.83742i | 0.205846 | − | 0.141871i | ||||
\(401\) | 15.7059i | 0.784314i | 0.919898 | + | 0.392157i | \(0.128271\pi\) | ||||
−0.919898 | + | 0.392157i | \(0.871729\pi\) | |||||||
\(402\) | 4.22294 | + | 15.6225i | 0.210621 | + | 0.779181i | ||||
\(403\) | −6.00196 | + | 6.00196i | −0.298979 | + | 0.298979i | ||||
\(404\) | 18.2907 | 0.909995 | ||||||||
\(405\) | 19.6695 | + | 4.25551i | 0.977387 | + | 0.211458i | ||||
\(406\) | −31.5779 | −1.56719 | ||||||||
\(407\) | 8.27409 | − | 8.27409i | 0.410131 | − | 0.410131i | ||||
\(408\) | 1.31097 | + | 4.84987i | 0.0649028 | + | 0.240104i | ||||
\(409\) | − | 34.5321i | − | 1.70750i | −0.520683 | − | 0.853750i | \(-0.674323\pi\) | ||
0.520683 | − | 0.853750i | \(-0.325677\pi\) | |||||||
\(410\) | −5.39122 | + | 10.2633i | −0.266253 | + | 0.506869i | ||||
\(411\) | 11.9507 | + | 6.86468i | 0.589483 | + | 0.338609i | ||||
\(412\) | −8.14075 | − | 8.14075i | −0.401066 | − | 0.401066i | ||||
\(413\) | 10.3994 | + | 10.3994i | 0.511723 | + | 0.511723i | ||||
\(414\) | 2.59144 | − | 1.51143i | 0.127363 | − | 0.0742826i | ||||
\(415\) | 0.526085 | − | 1.00151i | 0.0258245 | − | 0.0491623i | ||||
\(416\) | − | 3.93852i | − | 0.193102i | ||||||
\(417\) | −18.5539 | + | 5.01531i | −0.908587 | + | 0.245601i | ||||
\(418\) | −13.0261 | + | 13.0261i | −0.637126 | + | 0.637126i | ||||
\(419\) | −27.4239 | −1.33974 | −0.669872 | − | 0.742477i | \(-0.733651\pi\) | ||||
−0.669872 | + | 0.742477i | \(0.733651\pi\) | |||||||
\(420\) | −2.79455 | + | 12.5161i | −0.136360 | + | 0.610724i | ||||
\(421\) | −31.6293 | −1.54152 | −0.770758 | − | 0.637128i | \(-0.780122\pi\) | ||||
−0.770758 | + | 0.637128i | \(0.780122\pi\) | |||||||
\(422\) | −17.3048 | + | 17.3048i | −0.842385 | + | 0.842385i | ||||
\(423\) | 9.36624 | − | 35.5814i | 0.455402 | − | 1.73003i | ||||
\(424\) | − | 12.6161i | − | 0.612694i | ||||||
\(425\) | −2.62427 | + | 14.2634i | −0.127296 | + | 0.691878i | ||||
\(426\) | 1.19998 | − | 2.08904i | 0.0581394 | − | 0.101214i | ||||
\(427\) | −6.63357 | − | 6.63357i | −0.321021 | − | 0.321021i | ||||
\(428\) | −2.27414 | − | 2.27414i | −0.109924 | − | 0.109924i | ||||
\(429\) | −16.7380 | + | 29.1391i | −0.808120 | + | 1.40685i | ||||
\(430\) | −8.26358 | + | 2.57184i | −0.398505 | + | 0.124025i | ||||
\(431\) | − | 14.2142i | − | 0.684674i | −0.939577 | − | 0.342337i | \(-0.888782\pi\) | ||
0.939577 | − | 0.342337i | \(-0.111218\pi\) | |||||||
\(432\) | 3.69843 | + | 3.64988i | 0.177941 | + | 0.175605i | ||||
\(433\) | 2.02138 | − | 2.02138i | 0.0971415 | − | 0.0971415i | −0.656866 | − | 0.754007i | \(-0.728118\pi\) |
0.754007 | + | 0.656866i | \(0.228118\pi\) | |||||||
\(434\) | 7.13614 | 0.342546 | ||||||||
\(435\) | −31.1807 | + | 19.7983i | −1.49500 | + | 0.949257i | ||||
\(436\) | 3.20141 | 0.153320 | ||||||||
\(437\) | 2.64431 | − | 2.64431i | 0.126494 | − | 0.126494i | ||||
\(438\) | −18.1088 | + | 4.89501i | −0.865272 | + | 0.233892i | ||||
\(439\) | − | 30.8475i | − | 1.47227i | −0.676833 | − | 0.736137i | \(-0.736648\pi\) | ||
0.676833 | − | 0.736137i | \(-0.263352\pi\) | |||||||
\(440\) | −9.75153 | − | 5.12239i | −0.464886 | − | 0.244200i | ||||
\(441\) | −5.99156 | − | 10.2729i | −0.285312 | − | 0.489187i | ||||
\(442\) | 8.07795 | + | 8.07795i | 0.384229 | + | 0.384229i | ||||
\(443\) | −7.69538 | − | 7.69538i | −0.365618 | − | 0.365618i | 0.500258 | − | 0.865876i | \(-0.333239\pi\) |
−0.865876 | + | 0.500258i | \(0.833239\pi\) | |||||||
\(444\) | −3.56760 | − | 2.04929i | −0.169311 | − | 0.0972550i | ||||
\(445\) | −5.26640 | − | 16.9215i | −0.249651 | − | 0.802155i | ||||
\(446\) | 24.1540i | 1.14372i | ||||||||
\(447\) | 5.76283 | + | 21.3193i | 0.272572 | + | 1.00837i | ||||
\(448\) | −2.34139 | + | 2.34139i | −0.110620 | + | 0.110620i | ||||
\(449\) | 32.2872 | 1.52373 | 0.761863 | − | 0.647738i | \(-0.224285\pi\) | ||||
0.761863 | + | 0.647738i | \(0.224285\pi\) | |||||||
\(450\) | 5.08780 | + | 14.1108i | 0.239841 | + | 0.665189i | ||||
\(451\) | 25.5398 | 1.20262 | ||||||||
\(452\) | −6.56397 | + | 6.56397i | −0.308743 | + | 0.308743i | ||||
\(453\) | 7.90022 | + | 29.2264i | 0.371185 | + | 1.37318i | ||||
\(454\) | − | 5.87033i | − | 0.275508i | ||||||
\(455\) | 8.66574 | + | 27.8439i | 0.406256 | + | 1.30534i | ||||
\(456\) | 5.61654 | + | 3.22624i | 0.263019 | + | 0.151083i | ||||
\(457\) | 12.4523 | + | 12.4523i | 0.582494 | + | 0.582494i | 0.935588 | − | 0.353094i | \(-0.114870\pi\) |
−0.353094 | + | 0.935588i | \(0.614870\pi\) | |||||||
\(458\) | −2.96007 | − | 2.96007i | −0.138315 | − | 0.138315i | ||||
\(459\) | −15.0715 | + | 0.0995704i | −0.703476 | + | 0.00464755i | ||||
\(460\) | 1.97957 | + | 1.03985i | 0.0922981 | + | 0.0484833i | ||||
\(461\) | − | 9.66933i | − | 0.450345i | −0.974319 | − | 0.225173i | \(-0.927705\pi\) | ||
0.974319 | − | 0.225173i | \(-0.0722946\pi\) | |||||||
\(462\) | 27.2732 | − | 7.37224i | 1.26886 | − | 0.342988i | ||||
\(463\) | −9.39853 | + | 9.39853i | −0.436787 | + | 0.436787i | −0.890929 | − | 0.454142i | \(-0.849946\pi\) |
0.454142 | + | 0.890929i | \(0.349946\pi\) | |||||||
\(464\) | −9.53664 | −0.442727 | ||||||||
\(465\) | 7.04638 | − | 4.47413i | 0.326768 | − | 0.207483i | ||||
\(466\) | 24.2789 | 1.12470 | ||||||||
\(467\) | 9.89416 | − | 9.89416i | 0.457847 | − | 0.457847i | −0.440101 | − | 0.897948i | \(-0.645057\pi\) |
0.897948 | + | 0.440101i | \(0.145057\pi\) | |||||||
\(468\) | 11.4263 | + | 3.00780i | 0.528181 | + | 0.139035i | ||||
\(469\) | − | 30.9380i | − | 1.42858i | ||||||
\(470\) | 26.1854 | − | 8.14957i | 1.20784 | − | 0.375912i | ||||
\(471\) | −11.5820 | + | 20.1631i | −0.533672 | + | 0.929065i | ||||
\(472\) | 3.14067 | + | 3.14067i | 0.144561 | + | 0.144561i | ||||
\(473\) | 13.4817 | + | 13.4817i | 0.619890 | + | 0.619890i | ||||
\(474\) | −1.40153 | + | 2.43991i | −0.0643742 | + | 0.112069i | ||||
\(475\) | 10.6109 | + | 15.3957i | 0.486860 | + | 0.706403i | ||||
\(476\) | − | 9.60441i | − | 0.440218i | ||||||
\(477\) | 36.6015 | + | 9.63478i | 1.67587 | + | 0.441146i | ||||
\(478\) | −2.42085 | + | 2.42085i | −0.110727 | + | 0.110727i | ||||
\(479\) | 18.0640 | 0.825365 | 0.412683 | − | 0.910875i | \(-0.364592\pi\) | ||||
0.412683 | + | 0.910875i | \(0.364592\pi\) | |||||||
\(480\) | −0.843964 | + | 3.77991i | −0.0385215 | + | 0.172529i | ||||
\(481\) | −9.35549 | −0.426574 | ||||||||
\(482\) | 15.6288 | − | 15.6288i | 0.711874 | − | 0.711874i | ||||
\(483\) | −5.53650 | + | 1.49657i | −0.251919 | + | 0.0680965i | ||||
\(484\) | 13.2663i | 0.603011i | ||||||||
\(485\) | −8.12248 | + | 15.4628i | −0.368823 | + | 0.702132i | ||||
\(486\) | −13.4134 | + | 7.94240i | −0.608443 | + | 0.360275i | ||||
\(487\) | 2.25954 | + | 2.25954i | 0.102389 | + | 0.102389i | 0.756446 | − | 0.654056i | \(-0.226934\pi\) |
−0.654056 | + | 0.756446i | \(0.726934\pi\) | |||||||
\(488\) | −2.00336 | − | 2.00336i | −0.0906880 | − | 0.0906880i | ||||
\(489\) | −24.6518 | − | 14.1604i | −1.11479 | − | 0.640357i | ||||
\(490\) | 4.12215 | − | 7.84737i | 0.186220 | − | 0.354508i | ||||
\(491\) | 4.50123i | 0.203138i | 0.994829 | + | 0.101569i | \(0.0323862\pi\) | ||||
−0.994829 | + | 0.101569i | \(0.967614\pi\) | |||||||
\(492\) | −2.34329 | − | 8.66888i | −0.105644 | − | 0.390823i | ||||
\(493\) | 19.5598 | − | 19.5598i | 0.880927 | − | 0.880927i | ||||
\(494\) | 14.7286 | 0.662669 | ||||||||
\(495\) | 22.3080 | − | 24.3789i | 1.00267 | − | 1.09575i | ||||
\(496\) | 2.15514 | 0.0967686 | ||||||||
\(497\) | −3.25670 | + | 3.25670i | −0.146083 | + | 0.146083i | ||||
\(498\) | 0.228663 | + | 0.845925i | 0.0102466 | + | 0.0379068i | ||||
\(499\) | 7.38579i | 0.330634i | 0.986241 | + | 0.165317i | \(0.0528647\pi\) | ||||
−0.986241 | + | 0.165317i | \(0.947135\pi\) | |||||||
\(500\) | −6.90443 | + | 8.79368i | −0.308776 | + | 0.393265i | ||||
\(501\) | 6.28899 | + | 3.61250i | 0.280971 | + | 0.161395i | ||||
\(502\) | −10.0273 | − | 10.0273i | −0.447540 | − | 0.447540i | ||||
\(503\) | −27.9883 | − | 27.9883i | −1.24793 | − | 1.24793i | −0.956630 | − | 0.291304i | \(-0.905911\pi\) |
−0.291304 | − | 0.956630i | \(-0.594089\pi\) | |||||||
\(504\) | −5.00467 | − | 8.58084i | −0.222926 | − | 0.382221i | ||||
\(505\) | −39.0516 | + | 12.1539i | −1.73777 | + | 0.540840i | ||||
\(506\) | − | 4.92608i | − | 0.218991i | ||||||
\(507\) | 4.20006 | − | 1.13532i | 0.186531 | − | 0.0504214i | ||||
\(508\) | 8.84885 | − | 8.84885i | 0.392604 | − | 0.392604i | ||||
\(509\) | −2.48509 | −0.110150 | −0.0550749 | − | 0.998482i | \(-0.517540\pi\) | ||||
−0.0550749 | + | 0.998482i | \(0.517540\pi\) | |||||||
\(510\) | −6.02166 | − | 9.48362i | −0.266644 | − | 0.419942i | ||||
\(511\) | 35.8617 | 1.58643 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −13.6492 | + | 13.8307i | −0.602625 | + | 0.610640i | ||||
\(514\) | − | 24.4180i | − | 1.07703i | ||||||
\(515\) | 22.7903 | + | 11.9715i | 1.00426 | + | 0.527529i | ||||
\(516\) | 3.33910 | − | 5.81301i | 0.146996 | − | 0.255904i | ||||
\(517\) | −42.7205 | − | 42.7205i | −1.87885 | − | 1.87885i | ||||
\(518\) | 5.56169 | + | 5.56169i | 0.244367 | + | 0.244367i | ||||
\(519\) | 19.5711 | − | 34.0711i | 0.859074 | − | 1.49556i | ||||
\(520\) | 2.61708 | + | 8.40896i | 0.114767 | + | 0.368757i | ||||
\(521\) | − | 23.6509i | − | 1.03617i | −0.855331 | − | 0.518083i | \(-0.826646\pi\) | ||
0.855331 | − | 0.518083i | \(-0.173354\pi\) | |||||||
\(522\) | 7.28301 | − | 27.6674i | 0.318769 | − | 1.21097i | ||||
\(523\) | −7.85518 | + | 7.85518i | −0.343483 | + | 0.343483i | −0.857675 | − | 0.514192i | \(-0.828092\pi\) |
0.514192 | + | 0.857675i | \(0.328092\pi\) | |||||||
\(524\) | 0.892813 | 0.0390027 | ||||||||
\(525\) | −2.35024 | − | 28.5795i | −0.102573 | − | 1.24731i | ||||
\(526\) | −20.8471 | −0.908978 | ||||||||
\(527\) | −4.42021 | + | 4.42021i | −0.192548 | + | 0.192548i | ||||
\(528\) | 8.23661 | − | 2.22644i | 0.358452 | − | 0.0968936i | ||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 8.38322 | + | 26.9361i | 0.364144 | + | 1.17003i | ||||
\(531\) | −11.5101 | + | 6.71312i | −0.499495 | + | 0.291324i | ||||
\(532\) | −8.75588 | − | 8.75588i | −0.379616 | − | 0.379616i | ||||
\(533\) | −14.4389 | − | 14.4389i | −0.625418 | − | 0.625418i | ||||
\(534\) | 11.9034 | + | 6.83753i | 0.515111 | + | 0.295889i | ||||
\(535\) | 6.36653 | + | 3.34428i | 0.275249 | + | 0.144586i | ||||
\(536\) | − | 9.34339i | − | 0.403573i | ||||||
\(537\) | 0.646179 | + | 2.39050i | 0.0278847 | + | 0.103158i | ||||
\(538\) | 18.2143 | − | 18.2143i | 0.785272 | − | 0.785272i | ||||
\(539\) | −19.5278 | −0.841123 | ||||||||
\(540\) | −10.3216 | − | 5.33515i | −0.444172 | − | 0.229588i | ||||
\(541\) | −11.8517 | −0.509544 | −0.254772 | − | 0.967001i | \(-0.582000\pi\) | ||||
−0.254772 | + | 0.967001i | \(0.582000\pi\) | |||||||
\(542\) | 0.243836 | − | 0.243836i | 0.0104737 | − | 0.0104737i | ||||
\(543\) | 1.22513 | + | 4.53231i | 0.0525755 | + | 0.194500i | ||||
\(544\) | − | 2.90057i | − | 0.124361i | ||||||
\(545\) | −6.83520 | + | 2.12729i | −0.292788 | + | 0.0911231i | ||||
\(546\) | −19.5868 | − | 11.2510i | −0.838237 | − | 0.481498i | ||||
\(547\) | 16.4980 | + | 16.4980i | 0.705404 | + | 0.705404i | 0.965565 | − | 0.260161i | \(-0.0837756\pi\) |
−0.260161 | + | 0.965565i | \(0.583776\pi\) | |||||||
\(548\) | −5.62646 | − | 5.62646i | −0.240350 | − | 0.240350i | ||||
\(549\) | 7.34204 | − | 4.28215i | 0.313351 | − | 0.182758i | ||||
\(550\) | 24.2238 | + | 4.45684i | 1.03291 | + | 0.190040i | ||||
\(551\) | − | 35.6634i | − | 1.51931i | ||||||
\(552\) | −1.67204 | + | 0.451971i | −0.0711668 | + | 0.0192372i | ||||
\(553\) | 3.80368 | − | 3.80368i | 0.161749 | − | 0.161749i | ||||
\(554\) | 30.8414 | 1.31032 | ||||||||
\(555\) | 8.97874 | + | 2.00474i | 0.381126 | + | 0.0850964i | ||||
\(556\) | 11.0965 | 0.470598 | ||||||||
\(557\) | 10.6327 | − | 10.6327i | 0.450523 | − | 0.450523i | −0.445005 | − | 0.895528i | \(-0.646798\pi\) |
0.895528 | + | 0.445005i | \(0.146798\pi\) | |||||||
\(558\) | −1.64585 | + | 6.25242i | −0.0696744 | + | 0.264686i | ||||
\(559\) | − | 15.2438i | − | 0.644742i | ||||||
\(560\) | 3.44317 | − | 6.55480i | 0.145501 | − | 0.276991i | ||||
\(561\) | −12.3269 | + | 21.4598i | −0.520442 | + | 0.906035i | ||||
\(562\) | −5.55463 | − | 5.55463i | −0.234308 | − | 0.234308i | ||||
\(563\) | −25.0671 | − | 25.0671i | −1.05645 | − | 1.05645i | −0.998308 | − | 0.0581420i | \(-0.981482\pi\) |
−0.0581420 | − | 0.998308i | \(-0.518518\pi\) | |||||||
\(564\) | −10.5808 | + | 18.4201i | −0.445533 | + | 0.775626i | ||||
\(565\) | 9.65279 | − | 18.3761i | 0.406096 | − | 0.773088i | ||||
\(566\) | − | 11.3934i | − | 0.478901i | ||||||
\(567\) | 28.7165 | − | 7.96632i | 1.20598 | − | 0.334554i | ||||
\(568\) | −0.983536 | + | 0.983536i | −0.0412682 | + | 0.0412682i | ||||
\(569\) | −10.7487 | −0.450610 | −0.225305 | − | 0.974288i | \(-0.572338\pi\) | ||||
−0.225305 | + | 0.974288i | \(0.572338\pi\) | |||||||
\(570\) | −14.1354 | − | 3.15610i | −0.592067 | − | 0.132195i | ||||
\(571\) | 0.866963 | 0.0362813 | 0.0181406 | − | 0.999835i | \(-0.494225\pi\) | ||||
0.0181406 | + | 0.999835i | \(0.494225\pi\) | |||||||
\(572\) | 13.7189 | − | 13.7189i | 0.573616 | − | 0.573616i | ||||
\(573\) | −4.52042 | + | 1.22192i | −0.188843 | + | 0.0510464i | ||||
\(574\) | 17.1674i | 0.716553i | ||||||||
\(575\) | −4.91746 | − | 0.904744i | −0.205072 | − | 0.0377304i | ||||
\(576\) | −1.51143 | − | 2.59144i | −0.0629762 | − | 0.107977i | ||||
\(577\) | 0.374062 | + | 0.374062i | 0.0155724 | + | 0.0155724i | 0.714850 | − | 0.699278i | \(-0.246495\pi\) |
−0.699278 | + | 0.714850i | \(0.746495\pi\) | |||||||
\(578\) | −6.07172 | − | 6.07172i | −0.252550 | − | 0.252550i | ||||
\(579\) | 20.3069 | + | 11.6646i | 0.843925 | + | 0.484766i | ||||
\(580\) | 20.3613 | − | 6.33695i | 0.845455 | − | 0.263127i | ||||
\(581\) | − | 1.67522i | − | 0.0695000i | ||||||
\(582\) | −3.53044 | − | 13.0606i | −0.146341 | − | 0.541381i | ||||
\(583\) | 43.9453 | − | 43.9453i | 1.82003 | − | 1.82003i | ||||
\(584\) | 10.8304 | 0.448163 | ||||||||
\(585\) | −26.3944 | + | 1.17079i | −1.09128 | + | 0.0484063i | ||||
\(586\) | 30.1186 | 1.24419 | ||||||||
\(587\) | 14.5522 | − | 14.5522i | 0.600635 | − | 0.600635i | −0.339846 | − | 0.940481i | \(-0.610375\pi\) |
0.940481 | + | 0.339846i | \(0.110375\pi\) | |||||||
\(588\) | 1.79169 | + | 6.62826i | 0.0738881 | + | 0.273345i | ||||
\(589\) | 8.05939i | 0.332081i | ||||||||
\(590\) | −8.79242 | − | 4.61857i | −0.361978 | − | 0.190144i | ||||
\(591\) | 33.2378 | + | 19.0924i | 1.36722 | + | 0.785356i | ||||
\(592\) | 1.67965 | + | 1.67965i | 0.0690332 | + | 0.0690332i | ||||
\(593\) | 9.41542 | + | 9.41542i | 0.386645 | + | 0.386645i | 0.873489 | − | 0.486844i | \(-0.161852\pi\) |
−0.486844 | + | 0.873489i | \(0.661852\pi\) | |||||||
\(594\) | 0.169102 | + | 25.5961i | 0.00693834 | + | 1.05022i | ||||
\(595\) | 6.38198 | + | 20.5060i | 0.261636 | + | 0.840662i | ||||
\(596\) | − | 12.7504i | − | 0.522278i | ||||||
\(597\) | 3.85004 | − | 1.04071i | 0.157572 | − | 0.0425934i | ||||
\(598\) | −2.78495 | + | 2.78495i | −0.113885 | + | 0.113885i | ||||
\(599\) | −25.4679 | −1.04059 | −0.520294 | − | 0.853987i | \(-0.674178\pi\) | ||||
−0.520294 | + | 0.853987i | \(0.674178\pi\) | |||||||
\(600\) | −0.709781 | − | 8.63112i | −0.0289767 | − | 0.352364i | ||||
\(601\) | 33.4525 | 1.36456 | 0.682278 | − | 0.731093i | \(-0.260989\pi\) | ||||
0.682278 | + | 0.731093i | \(0.260989\pi\) | |||||||
\(602\) | −9.06217 | + | 9.06217i | −0.369346 | + | 0.369346i | ||||
\(603\) | 27.1068 | + | 7.13543i | 1.10387 | + | 0.290577i | ||||
\(604\) | − | 17.4795i | − | 0.711230i | ||||||
\(605\) | −8.81521 | − | 28.3242i | −0.358389 | − | 1.15154i | ||||
\(606\) | 15.7797 | − | 27.4708i | 0.641008 | − | 1.11593i | ||||
\(607\) | 15.2508 | + | 15.2508i | 0.619012 | + | 0.619012i | 0.945278 | − | 0.326266i | \(-0.105791\pi\) |
−0.326266 | + | 0.945278i | \(0.605791\pi\) | |||||||
\(608\) | −2.64431 | − | 2.64431i | −0.107241 | − | 0.107241i | ||||
\(609\) | −27.2429 | + | 47.4270i | −1.10394 | + | 1.92184i | ||||
\(610\) | 5.60849 | + | 2.94609i | 0.227081 | + | 0.119284i | ||||
\(611\) | 48.3040i | 1.95417i | ||||||||
\(612\) | 8.41504 | + | 2.21513i | 0.340158 | + | 0.0895411i | ||||
\(613\) | 7.09175 | − | 7.09175i | 0.286433 | − | 0.286433i | −0.549235 | − | 0.835668i | \(-0.685081\pi\) |
0.835668 | + | 0.549235i | \(0.185081\pi\) | |||||||
\(614\) | 10.4606 | 0.422155 | ||||||||
\(615\) | 10.7634 | + | 16.9515i | 0.434022 | + | 0.683549i | ||||
\(616\) | −16.3113 | −0.657202 | ||||||||
\(617\) | 1.76987 | − | 1.76987i | 0.0712523 | − | 0.0712523i | −0.670583 | − | 0.741835i | \(-0.733956\pi\) |
0.741835 | + | 0.670583i | \(0.233956\pi\) | |||||||
\(618\) | −19.2498 | + | 5.20343i | −0.774341 | + | 0.209313i | ||||
\(619\) | 49.0210i | 1.97032i | 0.171638 | + | 0.985160i | \(0.445094\pi\) | ||||
−0.171638 | + | 0.985160i | \(0.554906\pi\) | |||||||
\(620\) | −4.60134 | + | 1.43206i | −0.184794 | + | 0.0575127i | ||||
\(621\) | −0.0343279 | − | 5.19604i | −0.00137753 | − | 0.208510i | ||||
\(622\) | −16.4202 | − | 16.4202i | −0.658388 | − | 0.658388i | ||||
\(623\) | −18.5568 | − | 18.5568i | −0.743461 | − | 0.743461i | ||||
\(624\) | −5.91528 | − | 3.39784i | −0.236801 | − | 0.136022i | ||||
\(625\) | 8.89809 | − | 23.3629i | 0.355923 | − | 0.934515i | ||||
\(626\) | − | 7.61904i | − | 0.304518i | ||||||
\(627\) | 8.32605 | + | 30.8017i | 0.332510 | + | 1.23010i | ||||
\(628\) | 9.49292 | − | 9.49292i | 0.378809 | − | 0.378809i | ||||
\(629\) | −6.88996 | −0.274721 | ||||||||
\(630\) | 16.3871 | + | 14.9950i | 0.652877 | + | 0.597417i | ||||
\(631\) | −3.87479 | −0.154253 | −0.0771264 | − | 0.997021i | \(-0.524575\pi\) | ||||
−0.0771264 | + | 0.997021i | \(0.524575\pi\) | |||||||
\(632\) | 1.14873 | − | 1.14873i | 0.0456938 | − | 0.0456938i | ||||
\(633\) | 11.0610 | + | 40.9194i | 0.439633 | + | 1.62640i | ||||
\(634\) | 6.21327i | 0.246760i | ||||||||
\(635\) | −13.0129 | + | 24.7727i | −0.516400 | + | 0.983075i | ||||
\(636\) | −18.9482 | − | 10.8842i | −0.751346 | − | 0.431586i | ||||
\(637\) | 11.0400 | + | 11.0400i | 0.437422 | + | 0.437422i | ||||
\(638\) | −33.2186 | − | 33.2186i | −1.31514 | − | 1.31514i | ||||
\(639\) | −2.10229 | − | 3.60452i | −0.0831653 | − | 0.142592i | ||||
\(640\) | 1.03985 | − | 1.97957i | 0.0411037 | − | 0.0782495i | ||||
\(641\) | 17.1790i | 0.678532i | 0.940691 | + | 0.339266i | \(0.110179\pi\) | ||||
−0.940691 | + | 0.339266i | \(0.889821\pi\) | |||||||
\(642\) | −5.37747 | + | 1.45359i | −0.212232 | + | 0.0573686i | ||||
\(643\) | −3.69628 | + | 3.69628i | −0.145767 | + | 0.145767i | −0.776224 | − | 0.630457i | \(-0.782867\pi\) |
0.630457 | + | 0.776224i | \(0.282867\pi\) | |||||||
\(644\) | 3.31122 | 0.130480 | ||||||||
\(645\) | −3.26650 | + | 14.6299i | −0.128618 | + | 0.576051i | ||||
\(646\) | 10.8470 | 0.426770 | ||||||||
\(647\) | 11.5427 | − | 11.5427i | 0.453790 | − | 0.453790i | −0.442820 | − | 0.896610i | \(-0.646022\pi\) |
0.896610 | + | 0.442820i | \(0.146022\pi\) | |||||||
\(648\) | 8.67248 | − | 2.40586i | 0.340687 | − | 0.0945110i | ||||
\(649\) | 21.8795i | 0.858847i | ||||||||
\(650\) | −11.1752 | − | 16.2146i | −0.438329 | − | 0.635988i | ||||
\(651\) | 6.15649 | − | 10.7178i | 0.241292 | − | 0.420063i | ||||
\(652\) | 11.6062 | + | 11.6062i | 0.454536 | + | 0.454536i | ||||
\(653\) | 15.6907 | + | 15.6907i | 0.614025 | + | 0.614025i | 0.943992 | − | 0.329967i | \(-0.107038\pi\) |
−0.329967 | + | 0.943992i | \(0.607038\pi\) | |||||||
\(654\) | 2.76192 | − | 4.80822i | 0.108000 | − | 0.188016i | ||||
\(655\) | −1.90620 | + | 0.593260i | −0.0744816 | + | 0.0231806i | ||||
\(656\) | 5.18461i | 0.202425i | ||||||||
\(657\) | −8.27100 | + | 31.4207i | −0.322683 | + | 1.22584i | ||||
\(658\) | 28.7159 | − | 28.7159i | 1.11946 | − | 1.11946i | ||||
\(659\) | −3.17418 | −0.123649 | −0.0618243 | − | 0.998087i | \(-0.519692\pi\) | ||||
−0.0618243 | + | 0.998087i | \(0.519692\pi\) | |||||||
\(660\) | −16.1062 | + | 10.2267i | −0.626932 | + | 0.398073i | ||||
\(661\) | −12.5898 | −0.489687 | −0.244843 | − | 0.969563i | \(-0.578737\pi\) | ||||
−0.244843 | + | 0.969563i | \(0.578737\pi\) | |||||||
\(662\) | −3.89076 | + | 3.89076i | −0.151219 | + | 0.151219i | ||||
\(663\) | 19.1013 | − | 5.16329i | 0.741833 | − | 0.200526i | ||||
\(664\) | − | 0.505923i | − | 0.0196336i | ||||||
\(665\) | 24.5124 | + | 12.8761i | 0.950552 | + | 0.499316i | ||||
\(666\) | −6.15567 | + | 3.59022i | −0.238528 | + | 0.139118i | ||||
\(667\) | 6.74342 | + | 6.74342i | 0.261106 | + | 0.261106i | ||||
\(668\) | −2.96090 | − | 2.96090i | −0.114561 | − | 0.114561i | ||||
\(669\) | 36.2769 | + | 20.8381i | 1.40255 | + | 0.805648i | ||||
\(670\) | 6.20853 | + | 19.9487i | 0.239857 | + | 0.770684i | ||||
\(671\) | − | 13.9565i | − | 0.538784i | ||||||
\(672\) | 1.49657 | + | 5.53650i | 0.0577316 | + | 0.213575i | ||||
\(673\) | 20.3975 | − | 20.3975i | 0.786267 | − | 0.786267i | −0.194613 | − | 0.980880i | \(-0.562345\pi\) |
0.980880 | + | 0.194613i | \(0.0623451\pi\) | |||||||
\(674\) | −17.2686 | −0.665163 | ||||||||
\(675\) | 25.5824 | + | 4.53228i | 0.984666 | + | 0.174447i | ||||
\(676\) | −2.51194 | −0.0966129 | ||||||||
\(677\) | 30.0984 | − | 30.0984i | 1.15678 | − | 1.15678i | 0.171610 | − | 0.985165i | \(-0.445103\pi\) |
0.985165 | − | 0.171610i | \(-0.0548970\pi\) | |||||||
\(678\) | 4.19558 | + | 15.5213i | 0.161130 | + | 0.596093i | ||||
\(679\) | 25.8646i | 0.992592i | ||||||||
\(680\) | 1.92738 | + | 6.19287i | 0.0739117 | + | 0.237486i | ||||
\(681\) | −8.81667 | − | 5.06445i | −0.337855 | − | 0.194070i | ||||
\(682\) | 7.50692 | + | 7.50692i | 0.287455 | + | 0.287455i | ||||
\(683\) | −0.904638 | − | 0.904638i | −0.0346150 | − | 0.0346150i | 0.689587 | − | 0.724202i | \(-0.257792\pi\) |
−0.724202 | + | 0.689587i | \(0.757792\pi\) | |||||||
\(684\) | 9.69101 | − | 5.65216i | 0.370545 | − | 0.216116i | ||||
\(685\) | 15.7515 | + | 8.27411i | 0.601834 | + | 0.316137i | ||||
\(686\) | 10.0523i | 0.383798i | ||||||||
\(687\) | −6.99945 | + | 1.89203i | −0.267046 | + | 0.0721854i | ||||
\(688\) | −2.73681 | + | 2.73681i | −0.104340 | + | 0.104340i | ||||
\(689\) | −49.6889 | −1.89300 | ||||||||
\(690\) | 3.26957 | − | 2.07603i | 0.124471 | − | 0.0790330i | ||||
\(691\) | −8.98103 | −0.341654 | −0.170827 | − | 0.985301i | \(-0.554644\pi\) | ||||
−0.170827 | + | 0.985301i | \(0.554644\pi\) | |||||||
\(692\) | −16.0409 | + | 16.0409i | −0.609784 | + | 0.609784i | ||||
\(693\) | 12.4567 | − | 47.3219i | 0.473193 | − | 1.79761i | ||||
\(694\) | − | 28.4455i | − | 1.07978i | ||||||
\(695\) | −23.6917 | + | 7.37347i | −0.898678 | + | 0.279692i | ||||
\(696\) | −8.22745 | + | 14.3231i | −0.311861 | + | 0.542916i | ||||
\(697\) | −10.6337 | − | 10.6337i | −0.402780 | − | 0.402780i | ||||
\(698\) | 2.86317 | + | 2.86317i | 0.108373 | + | 0.108373i | ||||
\(699\) | 20.9459 | − | 36.4646i | 0.792247 | − | 1.37922i | ||||
\(700\) | −2.99580 | + | 16.2828i | −0.113231 | + | 0.615432i | ||||
\(701\) | 2.17193i | 0.0820325i | 0.999158 | + | 0.0410162i | \(0.0130595\pi\) | ||||
−0.999158 | + | 0.0410162i | \(0.986940\pi\) | |||||||
\(702\) | 14.3751 | − | 14.5663i | 0.542554 | − | 0.549771i | ||||
\(703\) | −6.28124 | + | 6.28124i | −0.236902 | + | 0.236902i | ||||
\(704\) | −4.92608 | −0.185659 | ||||||||
\(705\) | 10.3508 | − | 46.3587i | 0.389834 | − | 1.74597i | ||||
\(706\) | −37.0222 | −1.39335 | ||||||||
\(707\) | −42.8255 | + | 42.8255i | −1.61062 | + | 1.61062i | ||||
\(708\) | 7.42649 | − | 2.00746i | 0.279105 | − | 0.0754450i | ||||
\(709\) | 40.6428i | 1.52637i | 0.646179 | + | 0.763185i | \(0.276366\pi\) | ||||
−0.646179 | + | 0.763185i | \(0.723634\pi\) | |||||||
\(710\) | 1.44636 | − | 2.75345i | 0.0542809 | − | 0.103335i | ||||
\(711\) | 2.45538 | + | 4.20991i | 0.0920840 | + | 0.157884i | ||||
\(712\) | −5.60421 | − | 5.60421i | −0.210027 | − | 0.210027i | ||||
\(713\) | −1.52391 | − | 1.52391i | −0.0570710 | − | 0.0570710i | ||||
\(714\) | −14.4249 | − | 8.28592i | −0.539838 | − | 0.310093i | ||||
\(715\) | −20.1746 | + | 38.4066i | −0.754488 | + | 1.43633i | ||||
\(716\) | − | 1.42969i | − | 0.0534301i | ||||||
\(717\) | 1.54737 | + | 5.72440i | 0.0577874 | + | 0.213781i | ||||
\(718\) | −12.7840 | + | 12.7840i | −0.477096 | + | 0.477096i | ||||
\(719\) | −7.85539 | −0.292957 | −0.146478 | − | 0.989214i | \(-0.546794\pi\) | ||||
−0.146478 | + | 0.989214i | \(0.546794\pi\) | |||||||
\(720\) | 4.94896 | + | 4.52856i | 0.184437 | + | 0.168769i | ||||
\(721\) | 38.1213 | 1.41971 | ||||||||
\(722\) | −3.54633 | + | 3.54633i | −0.131981 | + | 0.131981i | ||||
\(723\) | −9.98969 | − | 36.9563i | −0.371521 | − | 1.37442i | ||||
\(724\) | − | 2.71065i | − | 0.100740i | ||||||
\(725\) | −39.2616 | + | 27.0595i | −1.45814 | + | 1.00496i | ||||
\(726\) | 19.9246 | + | 11.4451i | 0.739472 | + | 0.424766i | ||||
\(727\) | −29.7420 | − | 29.7420i | −1.10307 | − | 1.10307i | −0.994039 | − | 0.109029i | \(-0.965226\pi\) |
−0.109029 | − | 0.994039i | \(-0.534774\pi\) | |||||||
\(728\) | 9.22159 | + | 9.22159i | 0.341775 | + | 0.341775i | ||||
\(729\) | 0.356738 | + | 26.9976i | 0.0132125 | + | 0.999913i | ||||
\(730\) | −23.1234 | + | 7.19660i | −0.855836 | + | 0.266358i | ||||
\(731\) | − | 11.2264i | − | 0.415225i | ||||||
\(732\) | −4.73720 | + | 1.28052i | −0.175092 | + | 0.0473292i | ||||
\(733\) | 18.7628 | − | 18.7628i | 0.693019 | − | 0.693019i | −0.269876 | − | 0.962895i | \(-0.586983\pi\) |
0.962895 | + | 0.269876i | \(0.0869828\pi\) | |||||||
\(734\) | 11.9599 | 0.441448 | ||||||||
\(735\) | −8.22973 | − | 12.9611i | −0.303558 | − | 0.478079i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 32.5455 | − | 32.5455i | 1.19883 | − | 1.19883i | ||||
\(738\) | −15.0414 | − | 3.95942i | −0.553683 | − | 0.145748i | ||||
\(739\) | − | 4.14954i | − | 0.152643i | −0.997083 | − | 0.0763217i | \(-0.975682\pi\) | ||
0.997083 | − | 0.0763217i | \(-0.0243176\pi\) | |||||||
\(740\) | −4.70225 | − | 2.47004i | −0.172858 | − | 0.0908006i | ||||
\(741\) | 12.7066 | − | 22.1209i | 0.466789 | − | 0.812630i | ||||
\(742\) | 29.5392 | + | 29.5392i | 1.08442 | + | 1.08442i | ||||
\(743\) | 28.0568 | + | 28.0568i | 1.02930 | + | 1.02930i | 0.999558 | + | 0.0297448i | \(0.00946946\pi\) |
0.0297448 | + | 0.999558i | \(0.490531\pi\) | |||||||
\(744\) | 1.85928 | − | 3.23681i | 0.0681646 | − | 0.118667i | ||||
\(745\) | 8.47246 | + | 27.2229i | 0.310407 | + | 0.997369i | ||||
\(746\) | − | 35.6523i | − | 1.30532i | ||||||
\(747\) | 1.46777 | + | 0.386367i | 0.0537029 | + | 0.0141364i | ||||
\(748\) | 10.1034 | − | 10.1034i | 0.369418 | − | 0.369418i | ||||
\(749\) | 10.6493 | 0.389115 | ||||||||
\(750\) | 7.25066 | + | 17.9563i | 0.264757 | + | 0.655671i | ||||
\(751\) | −26.4718 | −0.965969 | −0.482984 | − | 0.875629i | \(-0.660447\pi\) | ||||
−0.482984 | + | 0.875629i | \(0.660447\pi\) | |||||||
\(752\) | 8.67231 | − | 8.67231i | 0.316247 | − | 0.316247i | ||||
\(753\) | −23.7108 | + | 6.40927i | −0.864068 | + | 0.233567i | ||||
\(754\) | 37.5602i | 1.36786i | ||||||||
\(755\) | 11.6148 | + | 37.3197i | 0.422708 | + | 1.35820i | ||||
\(756\) | −17.2052 | + | 0.113667i | −0.625748 | + | 0.00413404i | ||||
\(757\) | −20.0922 | − | 20.0922i | −0.730265 | − | 0.730265i | 0.240407 | − | 0.970672i | \(-0.422719\pi\) |
−0.970672 | + | 0.240407i | \(0.922719\pi\) | |||||||
\(758\) | −9.00754 | − | 9.00754i | −0.327168 | − | 0.327168i | ||||
\(759\) | −7.39849 | − | 4.24983i | −0.268548 | − | 0.154259i | ||||
\(760\) | 7.40284 | + | 3.88864i | 0.268529 | + | 0.141056i | ||||
\(761\) | 26.8485i | 0.973256i | 0.873609 | + | 0.486628i | \(0.161773\pi\) | ||||
−0.873609 | + | 0.486628i | \(0.838227\pi\) | |||||||
\(762\) | −5.65604 | − | 20.9242i | −0.204897 | − | 0.758004i | ||||
\(763\) | −7.49575 | + | 7.49575i | −0.271364 | + | 0.271364i | ||||
\(764\) | 2.70353 | 0.0978104 | ||||||||
\(765\) | −19.4385 | + | 0.862243i | −0.702800 | + | 0.0311745i | ||||
\(766\) | 26.7057 | 0.964917 | ||||||||
\(767\) | 12.3696 | − | 12.3696i | 0.446639 | − | 0.446639i | ||||
\(768\) | 0.451971 | + | 1.67204i | 0.0163091 | + | 0.0603346i | ||||
\(769\) | 7.25381i | 0.261579i | 0.991410 | + | 0.130790i | \(0.0417512\pi\) | ||||
−0.991410 | + | 0.130790i | \(0.958249\pi\) | |||||||
\(770\) | 34.8256 | − | 10.8386i | 1.25503 | − | 0.390597i | ||||
\(771\) | −36.6735 | − | 21.0659i | −1.32076 | − | 0.758670i | ||||
\(772\) | −9.56062 | − | 9.56062i | −0.344094 | − | 0.344094i | ||||
\(773\) | 15.1600 | + | 15.1600i | 0.545267 | + | 0.545267i | 0.925068 | − | 0.379801i | \(-0.124008\pi\) |
−0.379801 | + | 0.925068i | \(0.624008\pi\) | |||||||
\(774\) | −5.84988 | − | 10.0300i | −0.210269 | − | 0.360521i | ||||
\(775\) | 8.87254 | − | 6.11504i | 0.318711 | − | 0.219659i | ||||
\(776\) | 7.81120i | 0.280406i | ||||||||
\(777\) | 13.1513 | − | 3.55494i | 0.471800 | − | 0.127533i | ||||
\(778\) | 23.3645 | − | 23.3645i | 0.837659 | − | 0.837659i | ||||
\(779\) | −19.3885 | −0.694663 | ||||||||
\(780\) | 14.8873 | + | 3.32397i | 0.533049 | + | 0.119017i | ||||
\(781\) | −6.85183 | −0.245178 | ||||||||
\(782\) | −2.05101 | + | 2.05101i | −0.0733440 | + | 0.0733440i | ||||
\(783\) | −35.2706 | − | 34.8076i | −1.26047 | − | 1.24392i | ||||
\(784\) | − | 3.96417i | − | 0.141578i | ||||||
\(785\) | −13.9600 | + | 26.5758i | −0.498254 | + | 0.948531i | ||||
\(786\) | 0.770247 | − | 1.34092i | 0.0274738 | − | 0.0478290i | ||||
\(787\) | −18.6856 | − | 18.6856i | −0.666070 | − | 0.666070i | 0.290734 | − | 0.956804i | \(-0.406101\pi\) |
−0.956804 | + | 0.290734i | \(0.906101\pi\) | |||||||
\(788\) | −15.6486 | − | 15.6486i | −0.557458 | − | 0.557458i | ||||
\(789\) | −17.9852 | + | 31.3104i | −0.640291 | + | 1.11468i | ||||
\(790\) | −1.68928 | + | 3.21590i | −0.0601020 | + | 0.114417i | ||||
\(791\) | − | 30.7376i | − | 1.09290i | ||||||
\(792\) | 3.76198 | − | 14.2914i | 0.133676 | − | 0.507822i | ||||
\(793\) | −7.89028 | + | 7.89028i | −0.280192 | + | 0.280192i | ||||
\(794\) | −13.8905 | −0.492955 | ||||||||
\(795\) | 47.6879 | + | 10.6476i | 1.69131 | + | 0.377630i | ||||
\(796\) | −2.30260 | −0.0816135 | ||||||||
\(797\) | 20.4837 | − | 20.4837i | 0.725571 | − | 0.725571i | −0.244163 | − | 0.969734i | \(-0.578513\pi\) |
0.969734 | + | 0.244163i | \(0.0785133\pi\) | |||||||
\(798\) | −20.7044 | + | 5.59661i | −0.732927 | + | 0.198118i | ||||
\(799\) | 35.5740i | 1.25852i | ||||||||
\(800\) | −0.904744 | + | 4.91746i | −0.0319875 | + | 0.173859i | ||||
\(801\) | 20.5386 | − | 11.9789i | 0.725696 | − | 0.423253i | ||||
\(802\) | −11.1057 | − | 11.1057i | −0.392157 | − | 0.392157i | ||||
\(803\) | 37.7250 | + | 37.7250i | 1.33129 | + | 1.33129i | ||||
\(804\) | −14.0329 | − | 8.06073i | −0.494901 | − | 0.284280i | ||||
\(805\) | −7.06964 | + | 2.20025i | −0.249172 | + | 0.0775487i | ||||
\(806\) | − | 8.48806i | − | 0.298979i | ||||||
\(807\) | −11.6423 | − | 43.0699i | −0.409827 | − | 1.51613i | ||||
\(808\) | −12.9335 | + | 12.9335i | −0.454998 | + | 0.454998i | ||||
\(809\) | −24.7946 | −0.871733 | −0.435867 | − | 0.900011i | \(-0.643558\pi\) | ||||
−0.435867 | + | 0.900011i | \(0.643558\pi\) | |||||||
\(810\) | −16.9176 | + | 10.8994i | −0.594423 | + | 0.382964i | ||||
\(811\) | −43.1981 | −1.51689 | −0.758445 | − | 0.651737i | \(-0.774041\pi\) | ||||
−0.758445 | + | 0.651737i | \(0.774041\pi\) | |||||||
\(812\) | 22.3290 | − | 22.3290i | 0.783593 | − | 0.783593i | ||||
\(813\) | −0.155856 | − | 0.576581i | −0.00546612 | − | 0.0202216i | ||||
\(814\) | 11.7013i | 0.410131i | ||||||||
\(815\) | −32.4922 | − | 17.0678i | −1.13815 | − | 0.597859i | ||||
\(816\) | −4.35637 | − | 2.50238i | −0.152504 | − | 0.0876007i | ||||
\(817\) | −10.2346 | − | 10.2346i | −0.358064 | − | 0.358064i | ||||
\(818\) | 24.4179 | + | 24.4179i | 0.853750 | + | 0.853750i | ||||
\(819\) | −33.7958 | + | 19.7110i | −1.18092 | + | 0.688758i | ||||
\(820\) | −3.44509 | − | 11.0694i | −0.120308 | − | 0.386561i | ||||
\(821\) | − | 16.6133i | − | 0.579807i | −0.957056 | − | 0.289904i | \(-0.906377\pi\) | ||
0.957056 | − | 0.289904i | \(-0.0936233\pi\) | |||||||
\(822\) | −13.3045 | + | 3.59634i | −0.464046 | + | 0.125437i | ||||
\(823\) | −2.06898 | + | 2.06898i | −0.0721202 | + | 0.0721202i | −0.742247 | − | 0.670127i | \(-0.766240\pi\) |
0.670127 | + | 0.742247i | \(0.266240\pi\) | |||||||
\(824\) | 11.5128 | 0.401066 | ||||||||
\(825\) | 27.5921 | − | 32.5368i | 0.960634 | − | 1.13279i | ||||
\(826\) | −14.7070 | −0.511723 | ||||||||
\(827\) | −0.168649 | + | 0.168649i | −0.00586449 | + | 0.00586449i | −0.710033 | − | 0.704168i | \(-0.751320\pi\) |
0.704168 | + | 0.710033i | \(0.251320\pi\) | |||||||
\(828\) | −0.763687 | + | 2.90117i | −0.0265400 | + | 0.100823i | ||||
\(829\) | 5.57233i | 0.193535i | 0.995307 | + | 0.0967675i | \(0.0308503\pi\) | ||||
−0.995307 | + | 0.0967675i | \(0.969150\pi\) | |||||||
\(830\) | 0.336178 | + | 1.08017i | 0.0116689 | + | 0.0374934i | ||||
\(831\) | 26.6075 | − | 46.3208i | 0.923003 | − | 1.60685i | ||||
\(832\) | 2.78495 | + | 2.78495i | 0.0965509 | + | 0.0965509i | ||||
\(833\) | 8.13056 | + | 8.13056i | 0.281707 | + | 0.281707i | ||||
\(834\) | 9.57321 | − | 16.6659i | 0.331493 | − | 0.577094i | ||||
\(835\) | 8.28915 | + | 4.35421i | 0.286858 | + | 0.150684i | ||||
\(836\) | − | 18.4216i | − | 0.637126i | ||||||
\(837\) | 7.97063 | + | 7.86600i | 0.275505 | + | 0.271889i | ||||
\(838\) | 19.3916 | − | 19.3916i | 0.669872 | − | 0.669872i | ||||
\(839\) | 17.2878 | 0.596842 | 0.298421 | − | 0.954434i | \(-0.403540\pi\) | ||||
0.298421 | + | 0.954434i | \(0.403540\pi\) | |||||||
\(840\) | −6.87418 | − | 10.8263i | −0.237182 | − | 0.373542i | ||||
\(841\) | 61.9475 | 2.13612 | ||||||||
\(842\) | 22.3653 | − | 22.3653i | 0.770758 | − | 0.770758i | ||||
\(843\) | −13.1346 | + | 3.55043i | −0.452380 | + | 0.122283i | ||||
\(844\) | − | 24.4727i | − | 0.842385i | ||||||
\(845\) | 5.36312 | − | 1.66914i | 0.184497 | − | 0.0574202i | ||||
\(846\) | 18.5369 | + | 31.7828i | 0.637312 | + | 1.09271i | ||||
\(847\) | −31.0614 | − | 31.0614i | −1.06728 | − | 1.06728i | ||||
\(848\) | 8.92096 | + | 8.92096i | 0.306347 | + | 0.306347i | ||||
\(849\) | −17.1118 | − | 9.82934i | −0.587276 | − | 0.337342i | ||||
\(850\) | −8.23013 | − | 11.9414i | −0.282291 | − | 0.409587i | ||||
\(851\) | − | 2.37538i | − | 0.0814271i | ||||||
\(852\) | 0.628660 | + | 2.32569i | 0.0215375 | + | 0.0796769i | ||||
\(853\) | 27.9589 | − | 27.9589i | 0.957294 | − | 0.957294i | −0.0418310 | − | 0.999125i | \(-0.513319\pi\) |
0.999125 | + | 0.0418310i | \(0.0133191\pi\) | |||||||
\(854\) | 9.38129 | 0.321021 | ||||||||
\(855\) | −16.9351 | + | 18.5072i | −0.579167 | + | 0.632933i | ||||
\(856\) | 3.21611 | 0.109924 | ||||||||
\(857\) | −14.1163 | + | 14.1163i | −0.482204 | + | 0.482204i | −0.905835 | − | 0.423631i | \(-0.860755\pi\) |
0.423631 | + | 0.905835i | \(0.360755\pi\) | |||||||
\(858\) | −8.76889 | − | 32.4400i | −0.299365 | − | 1.10748i | ||||
\(859\) | − | 8.91885i | − | 0.304307i | −0.988357 | − | 0.152154i | \(-0.951379\pi\) | ||
0.988357 | − | 0.152154i | \(-0.0486208\pi\) | |||||||
\(860\) | 4.02467 | − | 7.66180i | 0.137240 | − | 0.261265i | ||||
\(861\) | 25.7837 | + | 14.8106i | 0.878708 | + | 0.504745i | ||||
\(862\) | 10.0510 | + | 10.0510i | 0.342337 | + | 0.342337i | ||||
\(863\) | 29.9481 | + | 29.9481i | 1.01945 | + | 1.01945i | 0.999807 | + | 0.0196395i | \(0.00625186\pi\) |
0.0196395 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(864\) | −5.19604 | + | 0.0343279i | −0.176773 | + | 0.00116786i | ||||
\(865\) | 23.5893 | − | 44.9072i | 0.802061 | − | 1.52689i | ||||
\(866\) | 2.85867i | 0.0971415i | ||||||||
\(867\) | −14.3573 | + | 3.88094i | −0.487601 | + | 0.131804i | ||||
\(868\) | −5.04601 | + | 5.04601i | −0.171273 | + | 0.171273i | ||||
\(869\) | 8.00263 | 0.271471 | ||||||||
\(870\) | 8.04858 | − | 36.0476i | 0.272872 | − | 1.22213i | ||||
\(871\) | −36.7991 | −1.24689 | ||||||||
\(872\) | −2.26374 | + | 2.26374i | −0.0766600 | + | 0.0766600i | ||||
\(873\) | −22.6616 | − | 5.96531i | −0.766979 | − | 0.201895i | ||||
\(874\) | 3.73962i | 0.126494i | ||||||||
\(875\) | −4.42345 | − | 36.7553i | −0.149540 | − | 1.24256i | ||||
\(876\) | 9.34357 | − | 16.2662i | 0.315690 | − | 0.549582i | ||||
\(877\) | −20.9067 | − | 20.9067i | −0.705969 | − | 0.705969i | 0.259716 | − | 0.965685i | \(-0.416371\pi\) |
−0.965685 | + | 0.259716i | \(0.916371\pi\) | |||||||
\(878\) | 21.8125 | + | 21.8125i | 0.736137 | + | 0.736137i | ||||
\(879\) | 25.9839 | − | 45.2352i | 0.876416 | − | 1.52575i | ||||
\(880\) | 10.5174 | − | 3.27330i | 0.354543 | − | 0.110343i | ||||
\(881\) | − | 4.83307i | − | 0.162830i | −0.996680 | − | 0.0814151i | \(-0.974056\pi\) | ||
0.996680 | − | 0.0814151i | \(-0.0259439\pi\) | |||||||
\(882\) | 11.5007 | + | 3.02739i | 0.387250 | + | 0.101937i | ||||
\(883\) | −21.8195 | + | 21.8195i | −0.734285 | + | 0.734285i | −0.971466 | − | 0.237181i | \(-0.923777\pi\) |
0.237181 | + | 0.971466i | \(0.423777\pi\) | |||||||
\(884\) | −11.4239 | −0.384229 | ||||||||
\(885\) | −14.5220 | + | 9.22083i | −0.488153 | + | 0.309955i | ||||
\(886\) | 10.8829 | 0.365618 | ||||||||
\(887\) | −11.3111 | + | 11.3111i | −0.379788 | + | 0.379788i | −0.871026 | − | 0.491238i | \(-0.836545\pi\) |
0.491238 | + | 0.871026i | \(0.336545\pi\) | |||||||
\(888\) | 3.97174 | − | 1.07360i | 0.133283 | − | 0.0360278i | ||||
\(889\) | 41.4372i | 1.38976i | ||||||||
\(890\) | 15.6892 | + | 8.24139i | 0.525903 | + | 0.276252i | ||||
\(891\) | 38.5888 | + | 21.8283i | 1.29277 | + | 0.731275i | ||||
\(892\) | −17.0794 | − | 17.0794i | −0.571862 | − | 0.571862i | ||||
\(893\) | 32.4311 | + | 32.4311i | 1.08527 | + | 1.08527i | ||||
\(894\) | −19.1499 | − | 11.0001i | −0.640469 | − | 0.367897i | ||||
\(895\) | 0.950007 | + | 3.05247i | 0.0317552 | + | 0.102033i | ||||
\(896\) | − | 3.31122i | − | 0.110620i | ||||||
\(897\) | 1.78010 | + | 6.58537i | 0.0594357 | + | 0.219879i | ||||
\(898\) | −22.8305 | + | 22.8305i | −0.761863 | + | 0.761863i | ||||
\(899\) | −20.5528 | −0.685474 | ||||||||
\(900\) | −13.5754 | − | 6.38022i | −0.452515 | − | 0.212674i | ||||
\(901\) | −36.5940 | −1.21912 | ||||||||
\(902\) | −18.0594 | + | 18.0594i | −0.601311 | + | 0.601311i | ||||
\(903\) | 5.79239 | + | 21.4286i | 0.192759 | + | 0.713100i | ||||
\(904\) | − | 9.28286i | − | 0.308743i | ||||||
\(905\) | 1.80118 | + | 5.78738i | 0.0598733 | + | 0.192379i | ||||
\(906\) | −26.2525 | − | 15.0799i | −0.872181 | − | 0.500996i | ||||
\(907\) | 21.4479 | + | 21.4479i | 0.712167 | + | 0.712167i | 0.966988 | − | 0.254821i | \(-0.0820165\pi\) |
−0.254821 | + | 0.966988i | \(0.582017\pi\) | |||||||
\(908\) | 4.15095 | + | 4.15095i | 0.137754 | + | 0.137754i | ||||
\(909\) | −27.6450 | − | 47.3993i | −0.916928 | − | 1.57213i | ||||
\(910\) | −25.8162 | − | 13.5610i | −0.855799 | − | 0.449543i | ||||
\(911\) | − | 39.0686i | − | 1.29440i | −0.762320 | − | 0.647200i | \(-0.775940\pi\) | ||
0.762320 | − | 0.647200i | \(-0.224060\pi\) | |||||||
\(912\) | −6.25279 | + | 1.69020i | −0.207051 | + | 0.0559680i | ||||
\(913\) | 1.76226 | − | 1.76226i | 0.0583224 | − | 0.0583224i | ||||
\(914\) | −17.6102 | −0.582494 | ||||||||
\(915\) | 9.26330 | − | 5.88177i | 0.306235 | − | 0.194445i | ||||
\(916\) | 4.18617 | 0.138315 | ||||||||
\(917\) | −2.09042 | + | 2.09042i | −0.0690317 | + | 0.0690317i | ||||
\(918\) | 10.5867 | − | 10.7275i | 0.349414 | − | 0.354062i | ||||
\(919\) | 38.4774i | 1.26925i | 0.772820 | + | 0.634625i | \(0.218846\pi\) | ||||
−0.772820 | + | 0.634625i | \(0.781154\pi\) | |||||||
\(920\) | −2.13506 | + | 0.664484i | −0.0703907 | + | 0.0219074i | ||||
\(921\) | 9.02457 | − | 15.7108i | 0.297370 | − | 0.517689i | ||||
\(922\) | 6.83725 | + | 6.83725i | 0.225173 | + | 0.225173i | ||||
\(923\) | 3.87367 | + | 3.87367i | 0.127504 | + | 0.127504i | ||||
\(924\) | −14.0721 | + | 24.4980i | −0.462938 | + | 0.805926i | ||||
\(925\) | 11.6809 | + | 2.14911i | 0.384064 | + | 0.0706624i | ||||
\(926\) | − | 13.2915i | − | 0.436787i | ||||||
\(927\) | −8.79214 | + | 33.4005i | −0.288772 | + | 1.09701i | ||||
\(928\) | 6.74342 | − | 6.74342i | 0.221364 | − | 0.221364i | ||||
\(929\) | 10.8588 | 0.356264 | 0.178132 | − | 0.984007i | \(-0.442995\pi\) | ||||
0.178132 | + | 0.984007i | \(0.442995\pi\) | |||||||
\(930\) | −1.81886 | + | 8.14623i | −0.0596427 | + | 0.267125i | ||||
\(931\) | 14.8245 | 0.485853 | ||||||||
\(932\) | −17.1678 | + | 17.1678i | −0.562350 | + | 0.562350i | ||||
\(933\) | −38.8275 | + | 10.4955i | −1.27115 | + | 0.343607i | ||||
\(934\) | 13.9925i | 0.457847i | ||||||||
\(935\) | −14.8578 | + | 28.2850i | −0.485903 | + | 0.925018i | ||||
\(936\) | −10.2065 | + | 5.95279i | −0.333608 | + | 0.194573i | ||||
\(937\) | 10.6749 | + | 10.6749i | 0.348734 | + | 0.348734i | 0.859638 | − | 0.510904i | \(-0.170689\pi\) |
−0.510904 | + | 0.859638i | \(0.670689\pi\) | |||||||
\(938\) | 21.8765 | + | 21.8765i | 0.714292 | + | 0.714292i | ||||
\(939\) | −11.4431 | − | 6.57310i | −0.373430 | − | 0.214505i | ||||
\(940\) | −12.7533 | + | 24.2785i | −0.415965 | + | 0.791877i | ||||
\(941\) | 10.9070i | 0.355559i | 0.984070 | + | 0.177779i | \(0.0568913\pi\) | ||||
−0.984070 | + | 0.177779i | \(0.943109\pi\) | |||||||
\(942\) | −6.06772 | − | 22.4472i | −0.197697 | − | 0.731369i | ||||
\(943\) | 3.66607 | − | 3.66607i | 0.119384 | − | 0.119384i | ||||
\(944\) | −4.44157 | −0.144561 | ||||||||
\(945\) | 36.6586 | − | 11.6753i | 1.19250 | − | 0.379797i | ||||
\(946\) | −19.0660 | −0.619890 | ||||||||
\(947\) | 10.0701 | − | 10.0701i | 0.327234 | − | 0.327234i | −0.524300 | − | 0.851534i | \(-0.675673\pi\) |
0.851534 | + | 0.524300i | \(0.175673\pi\) | |||||||
\(948\) | −0.734246 | − | 2.71630i | −0.0238472 | − | 0.0882214i | ||||
\(949\) | − | 42.6556i | − | 1.38466i | ||||||
\(950\) | −18.3894 | − | 3.38339i | −0.596632 | − | 0.109772i | ||||
\(951\) | 9.33173 | + | 5.36031i | 0.302602 | + | 0.173820i | ||||
\(952\) | 6.79135 | + | 6.79135i | 0.220109 | + | 0.220109i | ||||
\(953\) | −17.8904 | − | 17.8904i | −0.579526 | − | 0.579526i | 0.355247 | − | 0.934773i | \(-0.384397\pi\) |
−0.934773 | + | 0.355247i | \(0.884397\pi\) | |||||||
\(954\) | −32.6940 | + | 19.0684i | −1.05851 | + | 0.617362i | ||||
\(955\) | −5.77219 | + | 1.79646i | −0.186784 | + | 0.0581319i | ||||
\(956\) | − | 3.42360i | − | 0.110727i | ||||||
\(957\) | −78.5496 | + | 21.2328i | −2.53915 | + | 0.686359i | ||||
\(958\) | −12.7732 | + | 12.7732i | −0.412683 | + | 0.412683i | ||||
\(959\) | 26.3474 | 0.850802 | ||||||||
\(960\) | −2.07603 | − | 3.26957i | −0.0670035 | − | 0.105525i | ||||
\(961\) | −26.3554 | −0.850173 | ||||||||
\(962\) | 6.61533 | − | 6.61533i | 0.213287 | − | 0.213287i | ||||
\(963\) | −2.45610 | + | 9.33049i | −0.0791468 | + | 0.300671i | ||||
\(964\) | 22.1025i | 0.711874i | ||||||||
\(965\) | 26.7653 | + | 14.0596i | 0.861607 | + | 0.452594i | ||||
\(966\) | 2.85666 | − | 4.97313i | 0.0919114 | − | 0.160008i | ||||
\(967\) | −39.4613 | − | 39.4613i | −1.26899 | − | 1.26899i | −0.946611 | − | 0.322379i | \(-0.895518\pi\) |
−0.322379 | − | 0.946611i | \(-0.604482\pi\) | |||||||
\(968\) | −9.38066 | − | 9.38066i | −0.301506 | − | 0.301506i | ||||
\(969\) | 9.35793 | − | 16.2912i | 0.300620 | − | 0.523347i | ||||
\(970\) | −5.19042 | − | 16.6773i | −0.166654 | − | 0.535477i | ||||
\(971\) | − | 38.7406i | − | 1.24325i | −0.783316 | − | 0.621623i | \(-0.786474\pi\) | ||
0.783316 | − | 0.621623i | \(-0.213526\pi\) | |||||||
\(972\) | 3.86856 | − | 15.1008i | 0.124084 | − | 0.484359i | ||||
\(973\) | −25.9813 | + | 25.9813i | −0.832921 | + | 0.832921i | ||||
\(974\) | −3.19547 | −0.102389 | ||||||||
\(975\) | −33.9938 | + | 2.79549i | −1.08867 | + | 0.0895273i | ||||
\(976\) | 2.83318 | 0.0906880 | ||||||||
\(977\) | 7.16664 | − | 7.16664i | 0.229281 | − | 0.229281i | −0.583111 | − | 0.812392i | \(-0.698165\pi\) |
0.812392 | + | 0.583111i | \(0.198165\pi\) | |||||||
\(978\) | 27.4444 | − | 7.41852i | 0.877575 | − | 0.237218i | ||||
\(979\) | − | 39.0419i | − | 1.24778i | ||||||
\(980\) | 2.63413 | + | 8.46372i | 0.0841442 | + | 0.270364i | ||||
\(981\) | −4.83871 | − | 8.29629i | −0.154488 | − | 0.264880i | ||||
\(982\) | −3.18285 | − | 3.18285i | −0.101569 | − | 0.101569i | ||||
\(983\) | −10.7928 | − | 10.7928i | −0.344238 | − | 0.344238i | 0.513720 | − | 0.857958i | \(-0.328267\pi\) |
−0.857958 | + | 0.513720i | \(0.828267\pi\) | |||||||
\(984\) | 7.78678 | + | 4.47287i | 0.248234 | + | 0.142590i | ||||
\(985\) | 43.8089 | + | 23.0124i | 1.39587 | + | 0.733236i | ||||
\(986\) | 27.6617i | 0.880927i | ||||||||
\(987\) | −18.3547 | − | 67.9024i | −0.584238 | − | 2.16136i | ||||
\(988\) | −10.4147 | + | 10.4147i | −0.331334 | + | 0.331334i | ||||
\(989\) | 3.87043 | 0.123072 | ||||||||
\(990\) | 1.46436 | + | 33.0127i | 0.0465405 | + | 1.04921i | ||||
\(991\) | −5.24770 | −0.166699 | −0.0833493 | − | 0.996520i | \(-0.526562\pi\) | ||||
−0.0833493 | + | 0.996520i | \(0.526562\pi\) | |||||||
\(992\) | −1.52391 | + | 1.52391i | −0.0483843 | + | 0.0483843i | ||||
\(993\) | 2.48691 | + | 9.20018i | 0.0789197 | + | 0.291959i | ||||
\(994\) | − | 4.60567i | − | 0.146083i | ||||||
\(995\) | 4.91618 | − | 1.53004i | 0.155853 | − | 0.0485056i | ||||
\(996\) | −0.759848 | − | 0.436470i | −0.0240767 | − | 0.0138301i | ||||
\(997\) | −8.68788 | − | 8.68788i | −0.275148 | − | 0.275148i | 0.556021 | − | 0.831169i | \(-0.312328\pi\) |
−0.831169 | + | 0.556021i | \(0.812328\pi\) | |||||||
\(998\) | −5.22255 | − | 5.22255i | −0.165317 | − | 0.165317i | ||||
\(999\) | 0.0815419 | + | 12.3426i | 0.00257987 | + | 0.390502i |
(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 | 690.2.i.e.47.4 | ✓ | 32 | |
3.2 | odd | 2 | inner | 690.2.i.e.47.9 | yes | 32 | |
5.3 | odd | 4 | inner | 690.2.i.e.323.9 | yes | 32 | |
15.8 | even | 4 | inner | 690.2.i.e.323.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.e.47.4 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.2.i.e.47.9 | yes | 32 | 3.2 | odd | 2 | inner | |
690.2.i.e.323.4 | yes | 32 | 15.8 | even | 4 | inner | |
690.2.i.e.323.9 | yes | 32 | 5.3 | odd | 4 | inner |