Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(214,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 214.7 | ||
Character | \(\chi\) | \(=\) | 441.214 |
Dual form | 441.2.h.h.373.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0683740 | 0.0483477 | 0.0241739 | − | 0.999708i | \(-0.492304\pi\) | ||||
0.0241739 | + | 0.999708i | \(0.492304\pi\) | |||||||
\(3\) | −0.539550 | + | 1.64587i | −0.311509 | + | 0.950243i | ||||
\(4\) | −1.99532 | −0.997662 | ||||||||
\(5\) | 1.33190 | − | 2.30691i | 0.595642 | − | 1.03168i | −0.397814 | − | 0.917466i | \(-0.630231\pi\) |
0.993456 | − | 0.114216i | \(-0.0364355\pi\) | |||||||
\(6\) | −0.0368912 | + | 0.112535i | −0.0150608 | + | 0.0459421i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.273176 | −0.0965824 | ||||||||
\(9\) | −2.41777 | − | 1.77606i | −0.805924 | − | 0.592019i | ||||
\(10\) | 0.0910670 | − | 0.157733i | 0.0287979 | − | 0.0498794i | ||||
\(11\) | 0.799563 | + | 1.38488i | 0.241077 | + | 0.417558i | 0.961021 | − | 0.276474i | \(-0.0891659\pi\) |
−0.719944 | + | 0.694032i | \(0.755833\pi\) | |||||||
\(12\) | 1.07658 | − | 3.28404i | 0.310781 | − | 0.948022i | ||||
\(13\) | −2.62690 | − | 4.54992i | −0.728571 | − | 1.26192i | −0.957487 | − | 0.288476i | \(-0.906852\pi\) |
0.228916 | − | 0.973446i | \(-0.426482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.07825 | + | 3.43682i | 0.794801 | + | 0.887383i | ||||
\(16\) | 3.97197 | 0.992993 | ||||||||
\(17\) | 3.27360 | − | 5.67005i | 0.793966 | − | 1.37519i | −0.129528 | − | 0.991576i | \(-0.541346\pi\) |
0.923494 | − | 0.383613i | \(-0.125320\pi\) | |||||||
\(18\) | −0.165313 | − | 0.121436i | −0.0389646 | − | 0.0286228i | ||||
\(19\) | −0.950968 | − | 1.64713i | −0.218167 | − | 0.377877i | 0.736081 | − | 0.676894i | \(-0.236674\pi\) |
−0.954248 | + | 0.299017i | \(0.903341\pi\) | |||||||
\(20\) | −2.65756 | + | 4.60304i | −0.594249 | + | 1.02927i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0546693 | + | 0.0946900i | 0.0116555 | + | 0.0201880i | ||||
\(23\) | 1.53419 | − | 2.65729i | 0.319900 | − | 0.554083i | −0.660567 | − | 0.750767i | \(-0.729684\pi\) |
0.980467 | + | 0.196684i | \(0.0630173\pi\) | |||||||
\(24\) | 0.147392 | − | 0.449612i | 0.0300863 | − | 0.0917768i | ||||
\(25\) | −1.04789 | − | 1.81500i | −0.209578 | − | 0.363000i | ||||
\(26\) | −0.179612 | − | 0.311096i | −0.0352247 | − | 0.0610110i | ||||
\(27\) | 4.22767 | − | 3.02106i | 0.813615 | − | 0.581404i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.19452 | + | 5.53306i | −0.593207 | + | 1.02746i | 0.400591 | + | 0.916257i | \(0.368805\pi\) |
−0.993797 | + | 0.111207i | \(0.964528\pi\) | |||||||
\(30\) | 0.210472 | + | 0.234989i | 0.0384268 | + | 0.0429029i | ||||
\(31\) | 6.71923 | 1.20681 | 0.603405 | − | 0.797435i | \(-0.293810\pi\) | ||||
0.603405 | + | 0.797435i | \(0.293810\pi\) | |||||||
\(32\) | 0.817932 | 0.144591 | ||||||||
\(33\) | −2.71074 | + | 0.568763i | −0.471880 | + | 0.0990088i | ||||
\(34\) | 0.223829 | − | 0.387684i | 0.0383864 | − | 0.0664872i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.82424 | + | 3.54381i | 0.804040 | + | 0.590635i | ||||
\(37\) | −2.11477 | − | 3.66290i | −0.347667 | − | 0.602176i | 0.638168 | − | 0.769897i | \(-0.279693\pi\) |
−0.985835 | + | 0.167721i | \(0.946359\pi\) | |||||||
\(38\) | −0.0650215 | − | 0.112621i | −0.0105479 | − | 0.0182695i | ||||
\(39\) | 8.90592 | − | 1.86862i | 1.42609 | − | 0.299219i | ||||
\(40\) | −0.363842 | + | 0.630193i | −0.0575285 | + | 0.0996423i | ||||
\(41\) | −3.69648 | − | 6.40249i | −0.577293 | − | 0.999901i | −0.995788 | − | 0.0916820i | \(-0.970776\pi\) |
0.418495 | − | 0.908219i | \(-0.362558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.63176 | − | 9.75450i | 0.858836 | − | 1.48755i | −0.0142043 | − | 0.999899i | \(-0.504522\pi\) |
0.873040 | − | 0.487648i | \(-0.162145\pi\) | |||||||
\(44\) | −1.59539 | − | 2.76329i | −0.240514 | − | 0.416582i | ||||
\(45\) | −7.31743 | + | 3.21206i | −1.09082 | + | 0.478826i | ||||
\(46\) | 0.104898 | − | 0.181689i | 0.0154664 | − | 0.0267887i | ||||
\(47\) | 3.79918 | 0.554167 | 0.277083 | − | 0.960846i | \(-0.410632\pi\) | ||||
0.277083 | + | 0.960846i | \(0.410632\pi\) | |||||||
\(48\) | −2.14308 | + | 6.53735i | −0.309327 | + | 0.943585i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.0716485 | − | 0.124099i | −0.0101326 | − | 0.0175502i | ||||
\(51\) | 7.56589 | + | 8.44720i | 1.05944 | + | 1.18284i | ||||
\(52\) | 5.24152 | + | 9.07858i | 0.726868 | + | 1.25897i | ||||
\(53\) | −4.44931 | + | 7.70643i | −0.611160 | + | 1.05856i | 0.379885 | + | 0.925034i | \(0.375963\pi\) |
−0.991045 | + | 0.133527i | \(0.957370\pi\) | |||||||
\(54\) | 0.289062 | − | 0.206562i | 0.0393364 | − | 0.0281096i | ||||
\(55\) | 4.25974 | 0.574383 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.22405 | − | 0.676463i | 0.427036 | − | 0.0895997i | ||||
\(58\) | −0.218422 | + | 0.378317i | −0.0286802 | + | 0.0496755i | ||||
\(59\) | −10.8928 | −1.41812 | −0.709060 | − | 0.705148i | \(-0.750880\pi\) | ||||
−0.709060 | + | 0.705148i | \(0.750880\pi\) | |||||||
\(60\) | −6.14211 | − | 6.85757i | −0.792943 | − | 0.885309i | ||||
\(61\) | 2.71386 | 0.347475 | 0.173737 | − | 0.984792i | \(-0.444416\pi\) | ||||
0.173737 | + | 0.984792i | \(0.444416\pi\) | |||||||
\(62\) | 0.459420 | 0.0583465 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.88802 | −0.986002 | ||||||||
\(65\) | −13.9950 | −1.73587 | ||||||||
\(66\) | −0.185344 | + | 0.0388886i | −0.0228143 | + | 0.00478685i | ||||
\(67\) | −3.32533 | −0.406254 | −0.203127 | − | 0.979152i | \(-0.565110\pi\) | ||||
−0.203127 | + | 0.979152i | \(0.565110\pi\) | |||||||
\(68\) | −6.53190 | + | 11.3136i | −0.792110 | + | 1.37197i | ||||
\(69\) | 3.54578 | + | 3.95881i | 0.426862 | + | 0.476585i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3890 | −1.47031 | −0.735154 | − | 0.677900i | \(-0.762890\pi\) | ||||
−0.735154 | + | 0.677900i | \(0.762890\pi\) | |||||||
\(72\) | 0.660478 | + | 0.485177i | 0.0778381 | + | 0.0571786i | ||||
\(73\) | −1.09932 | + | 1.90407i | −0.128665 | + | 0.222855i | −0.923160 | − | 0.384417i | \(-0.874403\pi\) |
0.794494 | + | 0.607271i | \(0.207736\pi\) | |||||||
\(74\) | −0.144596 | − | 0.250447i | −0.0168089 | − | 0.0291138i | ||||
\(75\) | 3.55265 | − | 0.745409i | 0.410224 | − | 0.0860724i | ||||
\(76\) | 1.89749 | + | 3.28655i | 0.217657 | + | 0.376993i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.608933 | − | 0.127765i | 0.0689481 | − | 0.0144666i | ||||
\(79\) | 0.813556 | 0.0915322 | 0.0457661 | − | 0.998952i | \(-0.485427\pi\) | ||||
0.0457661 | + | 0.998952i | \(0.485427\pi\) | |||||||
\(80\) | 5.29025 | − | 9.16298i | 0.591468 | − | 1.02445i | ||||
\(81\) | 2.69124 | + | 8.58820i | 0.299027 | + | 0.954245i | ||||
\(82\) | −0.252743 | − | 0.437764i | −0.0279108 | − | 0.0483429i | ||||
\(83\) | −3.41842 | + | 5.92088i | −0.375220 | + | 0.649901i | −0.990360 | − | 0.138517i | \(-0.955766\pi\) |
0.615140 | + | 0.788418i | \(0.289100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.72020 | − | 15.1038i | −0.945838 | − | 1.63824i | ||||
\(86\) | 0.385066 | − | 0.666954i | 0.0415227 | − | 0.0719195i | ||||
\(87\) | −7.38310 | − | 8.24312i | −0.791551 | − | 0.883755i | ||||
\(88\) | −0.218422 | − | 0.378317i | −0.0232838 | − | 0.0403288i | ||||
\(89\) | −0.235286 | − | 0.407527i | −0.0249403 | − | 0.0431978i | 0.853286 | − | 0.521443i | \(-0.174606\pi\) |
−0.878226 | + | 0.478246i | \(0.841273\pi\) | |||||||
\(90\) | −0.500321 | + | 0.219621i | −0.0527385 | + | 0.0231501i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.06120 | + | 5.30216i | −0.319152 | + | 0.552788i | ||||
\(93\) | −3.62536 | + | 11.0590i | −0.375932 | + | 1.14676i | ||||
\(94\) | 0.259765 | 0.0267927 | ||||||||
\(95\) | −5.06636 | −0.519798 | ||||||||
\(96\) | −0.441315 | + | 1.34621i | −0.0450415 | + | 0.137397i | ||||
\(97\) | 2.57623 | − | 4.46216i | 0.261576 | − | 0.453064i | −0.705085 | − | 0.709123i | \(-0.749091\pi\) |
0.966661 | + | 0.256059i | \(0.0824243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.526472 | − | 4.76840i | 0.0529125 | − | 0.479243i | ||||
\(100\) | 2.09088 | + | 3.62152i | 0.209088 | + | 0.362152i | ||||
\(101\) | 0.922440 | + | 1.59771i | 0.0917862 | + | 0.158978i | 0.908263 | − | 0.418400i | \(-0.137409\pi\) |
−0.816477 | + | 0.577379i | \(0.804076\pi\) | |||||||
\(102\) | 0.517310 | + | 0.577569i | 0.0512213 | + | 0.0571878i | ||||
\(103\) | −2.58901 | + | 4.48430i | −0.255103 | + | 0.441851i | −0.964923 | − | 0.262531i | \(-0.915443\pi\) |
0.709821 | + | 0.704383i | \(0.248776\pi\) | |||||||
\(104\) | 0.717607 | + | 1.24293i | 0.0703671 | + | 0.121879i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.304217 | + | 0.526920i | −0.0295482 | + | 0.0511790i | ||||
\(107\) | 8.47445 | + | 14.6782i | 0.819256 | + | 1.41899i | 0.906231 | + | 0.422782i | \(0.138946\pi\) |
−0.0869755 | + | 0.996210i | \(0.527720\pi\) | |||||||
\(108\) | −8.43557 | + | 6.02801i | −0.811713 | + | 0.580045i | ||||
\(109\) | 4.24996 | − | 7.36115i | 0.407073 | − | 0.705070i | −0.587488 | − | 0.809233i | \(-0.699883\pi\) |
0.994560 | + | 0.104163i | \(0.0332163\pi\) | |||||||
\(110\) | 0.291255 | 0.0277701 | ||||||||
\(111\) | 7.16967 | − | 1.50433i | 0.680515 | − | 0.142784i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.95196 | − | 3.38089i | −0.183625 | − | 0.318048i | 0.759487 | − | 0.650522i | \(-0.225450\pi\) |
−0.943112 | + | 0.332474i | \(0.892116\pi\) | |||||||
\(114\) | 0.220441 | − | 0.0462525i | 0.0206462 | − | 0.00433194i | ||||
\(115\) | −4.08675 | − | 7.07847i | −0.381092 | − | 0.660070i | ||||
\(116\) | 6.37410 | − | 11.0403i | 0.591820 | − | 1.02506i | ||||
\(117\) | −1.72968 | + | 15.6662i | −0.159909 | + | 1.44834i | ||||
\(118\) | −0.744783 | −0.0685628 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.840905 | − | 0.938858i | −0.0767637 | − | 0.0857056i | ||||
\(121\) | 4.22140 | − | 7.31167i | 0.383763 | − | 0.664698i | ||||
\(122\) | 0.185558 | 0.0167996 | ||||||||
\(123\) | 12.5321 | − | 2.62946i | 1.12998 | − | 0.237090i | ||||
\(124\) | −13.4070 | −1.20399 | ||||||||
\(125\) | 7.73623 | 0.691949 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9533 | 0.971946 | 0.485973 | − | 0.873974i | \(-0.338465\pi\) | ||||
0.485973 | + | 0.873974i | \(0.338465\pi\) | |||||||
\(128\) | −2.17520 | −0.192262 | ||||||||
\(129\) | 13.0160 | + | 14.5322i | 1.14600 | + | 1.27949i | ||||
\(130\) | −0.956896 | −0.0839253 | ||||||||
\(131\) | 2.22671 | − | 3.85678i | 0.194549 | − | 0.336968i | −0.752204 | − | 0.658931i | \(-0.771009\pi\) |
0.946752 | + | 0.321962i | \(0.104342\pi\) | |||||||
\(132\) | 5.40881 | − | 1.13487i | 0.470777 | − | 0.0987774i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.227366 | −0.0196414 | ||||||||
\(135\) | −1.33852 | − | 13.7766i | −0.115201 | − | 1.18570i | ||||
\(136\) | −0.894271 | + | 1.54892i | −0.0766831 | + | 0.132819i | ||||
\(137\) | 9.76800 | + | 16.9187i | 0.834537 | + | 1.44546i | 0.894407 | + | 0.447254i | \(0.147598\pi\) |
−0.0598699 | + | 0.998206i | \(0.519069\pi\) | |||||||
\(138\) | 0.242439 | + | 0.270680i | 0.0206378 | + | 0.0230418i | ||||
\(139\) | −1.31540 | − | 2.27833i | −0.111570 | − | 0.193246i | 0.804833 | − | 0.593501i | \(-0.202255\pi\) |
−0.916404 | + | 0.400256i | \(0.868921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.04984 | + | 6.25295i | −0.172628 | + | 0.526593i | ||||
\(142\) | −0.847087 | −0.0710860 | ||||||||
\(143\) | 4.20075 | − | 7.27590i | 0.351284 | − | 0.608442i | ||||
\(144\) | −9.60332 | − | 7.05445i | −0.800277 | − | 0.587871i | ||||
\(145\) | 8.50952 | + | 14.7389i | 0.706677 | + | 1.22400i | ||||
\(146\) | −0.0751647 | + | 0.130189i | −0.00622067 | + | 0.0107745i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.21966 | + | 7.30867i | 0.346854 | + | 0.600769i | ||||
\(149\) | 4.40640 | − | 7.63212i | 0.360987 | − | 0.625247i | −0.627137 | − | 0.778909i | \(-0.715773\pi\) |
0.988124 | + | 0.153662i | \(0.0491066\pi\) | |||||||
\(150\) | 0.242908 | − | 0.0509666i | 0.0198334 | − | 0.00416140i | ||||
\(151\) | −2.33211 | − | 4.03933i | −0.189784 | − | 0.328716i | 0.755394 | − | 0.655271i | \(-0.227446\pi\) |
−0.945178 | + | 0.326555i | \(0.894112\pi\) | |||||||
\(152\) | 0.259782 | + | 0.449956i | 0.0210711 | + | 0.0364962i | ||||
\(153\) | −17.9852 | + | 7.89478i | −1.45401 | + | 0.638255i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.94931 | − | 15.5007i | 0.718826 | − | 1.24504i | ||||
\(156\) | −17.7702 | + | 3.72851i | −1.42276 | + | 0.298520i | ||||
\(157\) | −4.07294 | −0.325056 | −0.162528 | − | 0.986704i | \(-0.551965\pi\) | ||||
−0.162528 | + | 0.986704i | \(0.551965\pi\) | |||||||
\(158\) | 0.0556261 | 0.00442537 | ||||||||
\(159\) | −10.2832 | − | 11.4810i | −0.815507 | − | 0.910502i | ||||
\(160\) | 1.08940 | − | 1.88690i | 0.0861246 | − | 0.149172i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.184011 | + | 0.587210i | 0.0144573 | + | 0.0461355i | ||||
\(163\) | 6.06112 | + | 10.4982i | 0.474744 | + | 0.822280i | 0.999582 | − | 0.0289220i | \(-0.00920745\pi\) |
−0.524838 | + | 0.851202i | \(0.675874\pi\) | |||||||
\(164\) | 7.37568 | + | 12.7750i | 0.575944 | + | 0.997564i | ||||
\(165\) | −2.29834 | + | 7.01097i | −0.178926 | + | 0.545804i | ||||
\(166\) | −0.233731 | + | 0.404834i | −0.0181410 | + | 0.0314212i | ||||
\(167\) | 2.39951 | + | 4.15608i | 0.185680 | + | 0.321607i | 0.943805 | − | 0.330502i | \(-0.107218\pi\) |
−0.758126 | + | 0.652109i | \(0.773885\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.30121 | + | 12.6461i | −0.561631 | + | 0.972774i | ||||
\(170\) | −0.596235 | − | 1.03271i | −0.0457291 | − | 0.0792051i | ||||
\(171\) | −0.626165 | + | 5.67135i | −0.0478840 | + | 0.433699i | ||||
\(172\) | −11.2372 | + | 19.4634i | −0.856828 | + | 1.48407i | ||||
\(173\) | 5.03171 | 0.382554 | 0.191277 | − | 0.981536i | \(-0.438737\pi\) | ||||
0.191277 | + | 0.981536i | \(0.438737\pi\) | |||||||
\(174\) | −0.504812 | − | 0.563615i | −0.0382697 | − | 0.0427275i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.17584 | + | 5.50072i | 0.239388 | + | 0.414632i | ||||
\(177\) | 5.87720 | − | 17.9281i | 0.441758 | − | 1.34756i | ||||
\(178\) | −0.0160874 | − | 0.0278642i | −0.00120580 | − | 0.00208851i | ||||
\(179\) | 8.19896 | − | 14.2010i | 0.612819 | − | 1.06143i | −0.377944 | − | 0.925828i | \(-0.623369\pi\) |
0.990763 | − | 0.135605i | \(-0.0432977\pi\) | |||||||
\(180\) | 14.6006 | − | 6.40911i | 1.08827 | − | 0.477707i | ||||
\(181\) | −14.4345 | −1.07291 | −0.536454 | − | 0.843930i | \(-0.680237\pi\) | ||||
−0.536454 | + | 0.843930i | \(0.680237\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.46426 | + | 4.46666i | −0.108242 | + | 0.330185i | ||||
\(184\) | −0.419103 | + | 0.725908i | −0.0308967 | + | 0.0535147i | ||||
\(185\) | −11.2666 | −0.828339 | ||||||||
\(186\) | −0.247880 | + | 0.756146i | −0.0181755 | + | 0.0554433i | ||||
\(187\) | 10.4698 | 0.765629 | ||||||||
\(188\) | −7.58059 | −0.552871 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.346407 | −0.0251310 | ||||||||
\(191\) | 2.84131 | 0.205590 | 0.102795 | − | 0.994703i | \(-0.467221\pi\) | ||||
0.102795 | + | 0.994703i | \(0.467221\pi\) | |||||||
\(192\) | 4.25598 | − | 12.9826i | 0.307149 | − | 0.936942i | ||||
\(193\) | 8.82886 | 0.635515 | 0.317758 | − | 0.948172i | \(-0.397070\pi\) | ||||
0.317758 | + | 0.948172i | \(0.397070\pi\) | |||||||
\(194\) | 0.176147 | − | 0.305096i | 0.0126466 | − | 0.0219046i | ||||
\(195\) | 7.55102 | − | 23.0340i | 0.540739 | − | 1.64950i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.72354 | 0.407785 | 0.203893 | − | 0.978993i | \(-0.434641\pi\) | ||||
0.203893 | + | 0.978993i | \(0.434641\pi\) | |||||||
\(198\) | 0.0359970 | − | 0.326035i | 0.00255820 | − | 0.0231703i | ||||
\(199\) | 5.70752 | − | 9.88572i | 0.404596 | − | 0.700780i | −0.589679 | − | 0.807638i | \(-0.700746\pi\) |
0.994274 | + | 0.106858i | \(0.0340789\pi\) | |||||||
\(200\) | 0.286259 | + | 0.495815i | 0.0202416 | + | 0.0350594i | ||||
\(201\) | 1.79418 | − | 5.47306i | 0.126552 | − | 0.386040i | ||||
\(202\) | 0.0630709 | + | 0.109242i | 0.00443765 | + | 0.00768624i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −15.0964 | − | 16.8549i | −1.05696 | − | 1.18008i | ||||
\(205\) | −19.6933 | −1.37544 | ||||||||
\(206\) | −0.177021 | + | 0.306609i | −0.0123336 | + | 0.0213625i | ||||
\(207\) | −8.42881 | + | 3.69992i | −0.585843 | + | 0.257162i | ||||
\(208\) | −10.4340 | − | 18.0722i | −0.723466 | − | 1.25308i | ||||
\(209\) | 1.52072 | − | 2.63396i | 0.105190 | − | 0.182195i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6919 | + | 18.5189i | 0.736059 | + | 1.27489i | 0.954257 | + | 0.298986i | \(0.0966486\pi\) |
−0.218199 | + | 0.975904i | \(0.570018\pi\) | |||||||
\(212\) | 8.87782 | − | 15.3768i | 0.609731 | − | 1.05609i | ||||
\(213\) | 6.68450 | − | 20.3907i | 0.458014 | − | 1.39715i | ||||
\(214\) | 0.579432 | + | 1.00361i | 0.0396091 | + | 0.0686050i | ||||
\(215\) | −15.0018 | − | 25.9840i | −1.02312 | − | 1.77209i | ||||
\(216\) | −1.15490 | + | 0.825283i | −0.0785809 | + | 0.0561534i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.290587 | − | 0.503311i | 0.0196810 | − | 0.0340885i | ||||
\(219\) | −2.54072 | − | 2.83668i | −0.171686 | − | 0.191685i | ||||
\(220\) | −8.49956 | −0.573041 | ||||||||
\(221\) | −34.3977 | −2.31384 | ||||||||
\(222\) | 0.490219 | − | 0.102857i | 0.0329014 | − | 0.00690330i | ||||
\(223\) | −3.58387 | + | 6.20744i | −0.239994 | + | 0.415681i | −0.960712 | − | 0.277547i | \(-0.910479\pi\) |
0.720719 | + | 0.693228i | \(0.243812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.689984 | + | 6.24938i | −0.0459989 | + | 0.416625i | ||||
\(226\) | −0.133463 | − | 0.231165i | −0.00887784 | − | 0.0153769i | ||||
\(227\) | 6.89434 | + | 11.9413i | 0.457593 | + | 0.792575i | 0.998833 | − | 0.0482933i | \(-0.0153782\pi\) |
−0.541240 | + | 0.840868i | \(0.682045\pi\) | |||||||
\(228\) | −6.43302 | + | 1.34976i | −0.426037 | + | 0.0893903i | ||||
\(229\) | 13.1972 | − | 22.8581i | 0.872092 | − | 1.51051i | 0.0122645 | − | 0.999925i | \(-0.496096\pi\) |
0.859828 | − | 0.510584i | \(-0.170571\pi\) | |||||||
\(230\) | −0.279428 | − | 0.483983i | −0.0184249 | − | 0.0319129i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.872666 | − | 1.51150i | 0.0572933 | − | 0.0992349i | ||||
\(233\) | 6.32230 | + | 10.9505i | 0.414187 | + | 0.717394i | 0.995343 | − | 0.0963989i | \(-0.0307324\pi\) |
−0.581155 | + | 0.813793i | \(0.697399\pi\) | |||||||
\(234\) | −0.118265 | + | 1.07116i | −0.00773124 | + | 0.0700240i | ||||
\(235\) | 5.06010 | − | 8.76436i | 0.330085 | − | 0.571724i | ||||
\(236\) | 21.7346 | 1.41481 | ||||||||
\(237\) | −0.438954 | + | 1.33901i | −0.0285131 | + | 0.0869779i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.71640 | + | 13.3652i | 0.499133 | + | 0.864523i | 0.999999 | − | 0.00100121i | \(-0.000318696\pi\) |
−0.500867 | + | 0.865524i | \(0.666985\pi\) | |||||||
\(240\) | 12.2267 | + | 13.6510i | 0.789231 | + | 0.881165i | ||||
\(241\) | −0.589942 | − | 1.02181i | −0.0380015 | − | 0.0658205i | 0.846399 | − | 0.532549i | \(-0.178766\pi\) |
−0.884401 | + | 0.466729i | \(0.845432\pi\) | |||||||
\(242\) | 0.288634 | − | 0.499928i | 0.0185541 | − | 0.0321366i | ||||
\(243\) | −15.5871 | − | 0.204333i | −0.999914 | − | 0.0131080i | ||||
\(244\) | −5.41504 | −0.346662 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.856869 | − | 0.179787i | 0.0546320 | − | 0.0114628i | ||||
\(247\) | −4.99620 | + | 8.65367i | −0.317900 | + | 0.550620i | ||||
\(248\) | −1.83553 | −0.116557 | ||||||||
\(249\) | −7.90059 | − | 8.82089i | −0.500679 | − | 0.559001i | ||||
\(250\) | 0.528957 | 0.0334542 | ||||||||
\(251\) | 5.54970 | 0.350294 | 0.175147 | − | 0.984542i | \(-0.443960\pi\) | ||||
0.175147 | + | 0.984542i | \(0.443960\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.90672 | 0.308483 | ||||||||
\(254\) | 0.748919 | 0.0469913 | ||||||||
\(255\) | 29.5639 | − | 6.20304i | 1.85136 | − | 0.388449i | ||||
\(256\) | 15.6273 | 0.976707 | ||||||||
\(257\) | −4.91538 | + | 8.51369i | −0.306613 | + | 0.531069i | −0.977619 | − | 0.210382i | \(-0.932529\pi\) |
0.671006 | + | 0.741452i | \(0.265862\pi\) | |||||||
\(258\) | 0.889957 | + | 0.993623i | 0.0554063 | + | 0.0618603i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 27.9246 | 1.73181 | ||||||||
\(261\) | 17.5506 | − | 7.70404i | 1.08636 | − | 0.476868i | ||||
\(262\) | 0.152249 | − | 0.263703i | 0.00940598 | − | 0.0162916i | ||||
\(263\) | −5.96612 | − | 10.3336i | −0.367887 | − | 0.637199i | 0.621348 | − | 0.783535i | \(-0.286585\pi\) |
−0.989235 | + | 0.146336i | \(0.953252\pi\) | |||||||
\(264\) | 0.740511 | − | 0.155372i | 0.0455753 | − | 0.00956251i | ||||
\(265\) | 11.8520 | + | 20.5283i | 0.728065 | + | 1.26105i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.797685 | − | 0.167369i | 0.0488175 | − | 0.0102428i | ||||
\(268\) | 6.63512 | 0.405304 | ||||||||
\(269\) | −14.9824 | + | 25.9503i | −0.913494 | + | 1.58222i | −0.104401 | + | 0.994535i | \(0.533293\pi\) |
−0.809092 | + | 0.587682i | \(0.800041\pi\) | |||||||
\(270\) | −0.0915197 | − | 0.941960i | −0.00556971 | − | 0.0573259i | ||||
\(271\) | 3.54825 | + | 6.14575i | 0.215541 | + | 0.373328i | 0.953440 | − | 0.301584i | \(-0.0975152\pi\) |
−0.737899 | + | 0.674911i | \(0.764182\pi\) | |||||||
\(272\) | 13.0027 | − | 22.5213i | 0.788402 | − | 1.36555i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.667877 | + | 1.15680i | 0.0403479 | + | 0.0698847i | ||||
\(275\) | 1.67571 | − | 2.90242i | 0.101049 | − | 0.175022i | ||||
\(276\) | −7.07499 | − | 7.89912i | −0.425864 | − | 0.475471i | ||||
\(277\) | 4.91175 | + | 8.50741i | 0.295119 | + | 0.511161i | 0.975013 | − | 0.222150i | \(-0.0713075\pi\) |
−0.679894 | + | 0.733311i | \(0.737974\pi\) | |||||||
\(278\) | −0.0899388 | − | 0.155779i | −0.00539417 | − | 0.00934298i | ||||
\(279\) | −16.2456 | − | 11.9337i | −0.972596 | − | 0.714454i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.9389 | − | 20.6787i | 0.712213 | − | 1.23359i | −0.251812 | − | 0.967776i | \(-0.581026\pi\) |
0.964025 | − | 0.265813i | \(-0.0856403\pi\) | |||||||
\(282\) | −0.140156 | + | 0.427539i | −0.00834617 | + | 0.0254596i | ||||
\(283\) | −3.01595 | −0.179280 | −0.0896399 | − | 0.995974i | \(-0.528572\pi\) | ||||
−0.0896399 | + | 0.995974i | \(0.528572\pi\) | |||||||
\(284\) | 24.7201 | 1.46687 | ||||||||
\(285\) | 2.73356 | − | 8.33857i | 0.161922 | − | 0.493934i | ||||
\(286\) | 0.287222 | − | 0.497483i | 0.0169838 | − | 0.0294168i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.97757 | − | 1.45269i | −0.116530 | − | 0.0856008i | ||||
\(289\) | −12.9330 | − | 22.4006i | −0.760763 | − | 1.31768i | ||||
\(290\) | 0.581830 | + | 1.00776i | 0.0341662 | + | 0.0591776i | ||||
\(291\) | 5.95413 | + | 6.64770i | 0.349037 | + | 0.389695i | ||||
\(292\) | 2.19350 | − | 3.79925i | 0.128365 | − | 0.222334i | ||||
\(293\) | −8.52913 | − | 14.7729i | −0.498277 | − | 0.863041i | 0.501721 | − | 0.865030i | \(-0.332700\pi\) |
−0.999998 | + | 0.00198814i | \(0.999367\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.5081 | + | 25.1287i | −0.844692 | + | 1.46305i | ||||
\(296\) | 0.577706 | + | 1.00062i | 0.0335785 | + | 0.0581596i | ||||
\(297\) | 7.56411 | + | 3.43930i | 0.438914 | + | 0.199568i | ||||
\(298\) | 0.301283 | − | 0.521838i | 0.0174529 | − | 0.0302293i | ||||
\(299\) | −16.1206 | −0.932280 | ||||||||
\(300\) | −7.08868 | + | 1.48733i | −0.409265 | + | 0.0858712i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.159456 | − | 0.276185i | −0.00917564 | − | 0.0158927i | ||||
\(303\) | −3.12733 | + | 0.656170i | −0.179660 | + | 0.0376960i | ||||
\(304\) | −3.77722 | − | 6.54234i | −0.216638 | − | 0.375229i | ||||
\(305\) | 3.61458 | − | 6.26064i | 0.206970 | − | 0.358483i | ||||
\(306\) | −1.22972 | + | 0.539797i | −0.0702982 | + | 0.0308582i | ||||
\(307\) | 23.2178 | 1.32511 | 0.662554 | − | 0.749014i | \(-0.269473\pi\) | ||||
0.662554 | + | 0.749014i | \(0.269473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.98367 | − | 6.68068i | −0.340399 | − | 0.380050i | ||||
\(310\) | 0.611900 | − | 1.05984i | 0.0347536 | − | 0.0601950i | ||||
\(311\) | 1.79093 | 0.101555 | 0.0507773 | − | 0.998710i | \(-0.483830\pi\) | ||||
0.0507773 | + | 0.998710i | \(0.483830\pi\) | |||||||
\(312\) | −2.43289 | + | 0.510463i | −0.137735 | + | 0.0288993i | ||||
\(313\) | 4.60917 | 0.260526 | 0.130263 | − | 0.991480i | \(-0.458418\pi\) | ||||
0.130263 | + | 0.991480i | \(0.458418\pi\) | |||||||
\(314\) | −0.278483 | −0.0157157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.62331 | −0.0913183 | ||||||||
\(317\) | −25.8841 | −1.45380 | −0.726898 | − | 0.686745i | \(-0.759039\pi\) | ||||
−0.726898 | + | 0.686745i | \(0.759039\pi\) | |||||||
\(318\) | −0.703100 | − | 0.785001i | −0.0394279 | − | 0.0440207i | ||||
\(319\) | −10.2169 | −0.572035 | ||||||||
\(320\) | −10.5060 | + | 18.1970i | −0.587304 | + | 1.01724i | ||||
\(321\) | −28.7307 | + | 6.02823i | −1.60359 | + | 0.336463i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.4524 | −0.692869 | ||||||||
\(324\) | −5.36990 | − | 17.1363i | −0.298328 | − | 0.952014i | ||||
\(325\) | −5.50541 | + | 9.53566i | −0.305385 | + | 0.528943i | ||||
\(326\) | 0.414423 | + | 0.717802i | 0.0229528 | + | 0.0397554i | ||||
\(327\) | 9.82242 | + | 10.9666i | 0.543181 | + | 0.606454i | ||||
\(328\) | 1.00979 | + | 1.74901i | 0.0557563 | + | 0.0965728i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.157147 | + | 0.479368i | −0.00865065 | + | 0.0263884i | ||||
\(331\) | 0.161323 | 0.00886714 | 0.00443357 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443357 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(332\) | 6.82086 | − | 11.8141i | 0.374343 | − | 0.648382i | ||||
\(333\) | −1.39247 | + | 12.6120i | −0.0763070 | + | 0.691134i | ||||
\(334\) | 0.164064 | + | 0.284168i | 0.00897719 | + | 0.0155490i | ||||
\(335\) | −4.42899 | + | 7.67124i | −0.241982 | + | 0.419125i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.52675 | + | 7.84057i | 0.246588 | + | 0.427103i | 0.962577 | − | 0.271009i | \(-0.0873572\pi\) |
−0.715989 | + | 0.698112i | \(0.754024\pi\) | |||||||
\(338\) | −0.499213 | + | 0.864662i | −0.0271536 | + | 0.0470314i | ||||
\(339\) | 6.61769 | − | 1.38851i | 0.359423 | − | 0.0754135i | ||||
\(340\) | 17.3996 | + | 30.1370i | 0.943627 | + | 1.63441i | ||||
\(341\) | 5.37245 | + | 9.30535i | 0.290934 | + | 0.503913i | ||||
\(342\) | −0.0428134 | + | 0.387773i | −0.00231508 | + | 0.0209683i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.53846 | + | 2.66470i | −0.0829484 | + | 0.143671i | ||||
\(345\) | 13.8552 | − | 2.90708i | 0.745941 | − | 0.156512i | ||||
\(346\) | 0.344038 | 0.0184956 | ||||||||
\(347\) | −5.81968 | −0.312417 | −0.156208 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156208 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(348\) | 14.7317 | + | 16.4477i | 0.789701 | + | 0.881689i | ||||
\(349\) | −13.6310 | + | 23.6095i | −0.729648 | + | 1.26379i | 0.227384 | + | 0.973805i | \(0.426983\pi\) |
−0.957032 | + | 0.289983i | \(0.906350\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.8513 | − | 11.2995i | −1.32646 | − | 0.603124i | ||||
\(352\) | 0.653988 | + | 1.13274i | 0.0348577 | + | 0.0603753i | ||||
\(353\) | 12.0948 | + | 20.9488i | 0.643741 | + | 1.11499i | 0.984591 | + | 0.174874i | \(0.0559517\pi\) |
−0.340850 | + | 0.940118i | \(0.610715\pi\) | |||||||
\(354\) | 0.401848 | − | 1.22582i | 0.0213580 | − | 0.0651514i | ||||
\(355\) | −16.5009 | + | 28.5804i | −0.875777 | + | 1.51689i | ||||
\(356\) | 0.469472 | + | 0.813149i | 0.0248820 | + | 0.0430968i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.560595 | − | 0.970979i | 0.0296284 | − | 0.0513179i | ||||
\(359\) | 10.5188 | + | 18.2191i | 0.555161 | + | 0.961567i | 0.997891 | + | 0.0649124i | \(0.0206768\pi\) |
−0.442730 | + | 0.896655i | \(0.645990\pi\) | |||||||
\(360\) | 1.99895 | − | 0.877459i | 0.105354 | − | 0.0462461i | ||||
\(361\) | 7.69132 | − | 13.3218i | 0.404806 | − | 0.701145i | ||||
\(362\) | −0.986944 | −0.0518726 | ||||||||
\(363\) | 9.75641 | + | 10.8929i | 0.512079 | + | 0.571728i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.92835 | + | 5.07205i | 0.153277 | + | 0.265483i | ||||
\(366\) | −0.100118 | + | 0.305404i | −0.00523323 | + | 0.0159637i | ||||
\(367\) | −17.5190 | − | 30.3438i | −0.914485 | − | 1.58393i | −0.807654 | − | 0.589657i | \(-0.799263\pi\) |
−0.106831 | − | 0.994277i | \(-0.534070\pi\) | |||||||
\(368\) | 6.09375 | − | 10.5547i | 0.317659 | − | 0.550201i | ||||
\(369\) | −2.43395 | + | 22.0449i | −0.126706 | + | 1.14761i | ||||
\(370\) | −0.770345 | −0.0400483 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.23377 | − | 22.0662i | 0.375054 | − | 1.14408i | ||||
\(373\) | −0.564310 | + | 0.977414i | −0.0292189 | + | 0.0506086i | −0.880265 | − | 0.474482i | \(-0.842635\pi\) |
0.851046 | + | 0.525091i | \(0.175969\pi\) | |||||||
\(374\) | 0.715863 | 0.0370164 | ||||||||
\(375\) | −4.17408 | + | 12.7328i | −0.215549 | + | 0.657520i | ||||
\(376\) | −1.03784 | −0.0535227 | ||||||||
\(377\) | 33.5667 | 1.72877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9619 | −1.12811 | −0.564054 | − | 0.825738i | \(-0.690759\pi\) | ||||
−0.564054 | + | 0.825738i | \(0.690759\pi\) | |||||||
\(380\) | 10.1090 | 0.518583 | ||||||||
\(381\) | −5.90984 | + | 18.0277i | −0.302770 | + | 0.923585i | ||||
\(382\) | 0.194272 | 0.00993981 | ||||||||
\(383\) | 11.5200 | − | 19.9533i | 0.588647 | − | 1.01957i | −0.405763 | − | 0.913978i | \(-0.632994\pi\) |
0.994410 | − | 0.105588i | \(-0.0336724\pi\) | |||||||
\(384\) | 1.17363 | − | 3.58009i | 0.0598915 | − | 0.182696i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.603664 | 0.0307257 | ||||||||
\(387\) | −30.9409 | + | 13.5818i | −1.57281 | + | 0.690403i | ||||
\(388\) | −5.14042 | + | 8.90346i | −0.260965 | + | 0.452005i | ||||
\(389\) | −7.88753 | − | 13.6616i | −0.399914 | − | 0.692671i | 0.593801 | − | 0.804612i | \(-0.297627\pi\) |
−0.993715 | + | 0.111941i | \(0.964293\pi\) | |||||||
\(390\) | 0.516293 | − | 1.57493i | 0.0261435 | − | 0.0797494i | ||||
\(391\) | −10.0446 | − | 17.3978i | −0.507979 | − | 0.879846i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.14633 | + | 5.74580i | 0.259598 | + | 0.289837i | ||||
\(394\) | 0.391341 | 0.0197155 | ||||||||
\(395\) | 1.08357 | − | 1.87680i | 0.0545204 | − | 0.0944321i | ||||
\(396\) | −1.05048 | + | 9.51452i | −0.0527888 | + | 0.478122i | ||||
\(397\) | −8.25277 | − | 14.2942i | −0.414195 | − | 0.717406i | 0.581149 | − | 0.813797i | \(-0.302603\pi\) |
−0.995344 | + | 0.0963911i | \(0.969270\pi\) | |||||||
\(398\) | 0.390246 | − | 0.675926i | 0.0195613 | − | 0.0338811i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.16220 | − | 7.20914i | −0.208110 | − | 0.360457i | ||||
\(401\) | −10.8300 | + | 18.7581i | −0.540823 | + | 0.936733i | 0.458034 | + | 0.888935i | \(0.348554\pi\) |
−0.998857 | + | 0.0477986i | \(0.984779\pi\) | |||||||
\(402\) | 0.122675 | − | 0.374215i | 0.00611849 | − | 0.0186641i | ||||
\(403\) | −17.6507 | − | 30.5720i | −0.879246 | − | 1.52290i | ||||
\(404\) | −1.84057 | − | 3.18796i | −0.0915716 | − | 0.158607i | ||||
\(405\) | 23.3967 | + | 5.23014i | 1.16259 | + | 0.259888i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.38179 | − | 5.85743i | 0.167629 | − | 0.290342i | ||||
\(408\) | −2.06682 | − | 2.30757i | −0.102323 | − | 0.114242i | ||||
\(409\) | −30.5721 | −1.51169 | −0.755846 | − | 0.654750i | \(-0.772774\pi\) | ||||
−0.755846 | + | 0.654750i | \(0.772774\pi\) | |||||||
\(410\) | −1.34651 | −0.0664993 | ||||||||
\(411\) | −33.1163 | + | 6.94839i | −1.63350 | + | 0.342739i | ||||
\(412\) | 5.16592 | − | 8.94763i | 0.254507 | − | 0.440818i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.576311 | + | 0.252978i | −0.0283242 | + | 0.0124332i | ||||
\(415\) | 9.10596 | + | 15.7720i | 0.446994 | + | 0.774216i | ||||
\(416\) | −2.14863 | − | 3.72153i | −0.105345 | − | 0.182463i | ||||
\(417\) | 4.45956 | − | 0.935695i | 0.218385 | − | 0.0458212i | ||||
\(418\) | 0.103978 | − | 0.180094i | 0.00508571 | − | 0.00880871i | ||||
\(419\) | 10.8081 | + | 18.7202i | 0.528011 | + | 0.914542i | 0.999467 | + | 0.0326524i | \(0.0103954\pi\) |
−0.471456 | + | 0.881890i | \(0.656271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6217 | − | 23.5935i | 0.663881 | − | 1.14988i | −0.315706 | − | 0.948857i | \(-0.602241\pi\) |
0.979587 | − | 0.201019i | \(-0.0644252\pi\) | |||||||
\(422\) | 0.731046 | + | 1.26621i | 0.0355867 | + | 0.0616380i | ||||
\(423\) | −9.18554 | − | 6.74755i | −0.446616 | − | 0.328077i | ||||
\(424\) | 1.21545 | − | 2.10521i | 0.0590273 | − | 0.102238i | ||||
\(425\) | −13.7215 | −0.665592 | ||||||||
\(426\) | 0.457046 | − | 1.39419i | 0.0221439 | − | 0.0675490i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.9093 | − | 29.2877i | −0.817341 | − | 1.41568i | ||||
\(429\) | 9.70868 | + | 10.8396i | 0.468739 | + | 0.523340i | ||||
\(430\) | −1.02574 | − | 1.77663i | −0.0494654 | − | 0.0856765i | ||||
\(431\) | −4.09843 | + | 7.09869i | −0.197415 | + | 0.341932i | −0.947689 | − | 0.319194i | \(-0.896588\pi\) |
0.750275 | + | 0.661126i | \(0.229921\pi\) | |||||||
\(432\) | 16.7922 | − | 11.9996i | 0.807914 | − | 0.577330i | ||||
\(433\) | 3.41468 | 0.164099 | 0.0820494 | − | 0.996628i | \(-0.473853\pi\) | ||||
0.0820494 | + | 0.996628i | \(0.473853\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −28.8497 | + | 6.05318i | −1.38324 | + | 0.290228i | ||||
\(436\) | −8.48005 | + | 14.6879i | −0.406121 | + | 0.703422i | ||||
\(437\) | −5.83585 | −0.279167 | ||||||||
\(438\) | −0.173719 | − | 0.193955i | −0.00830062 | − | 0.00926752i | ||||
\(439\) | 6.58831 | 0.314443 | 0.157221 | − | 0.987563i | \(-0.449746\pi\) | ||||
0.157221 | + | 0.987563i | \(0.449746\pi\) | |||||||
\(440\) | −1.16366 | −0.0554753 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.35191 | −0.111869 | ||||||||
\(443\) | 28.6912 | 1.36316 | 0.681581 | − | 0.731743i | \(-0.261293\pi\) | ||||
0.681581 | + | 0.731743i | \(0.261293\pi\) | |||||||
\(444\) | −14.3058 | + | 3.00162i | −0.678925 | + | 0.142451i | ||||
\(445\) | −1.25350 | −0.0594218 | ||||||||
\(446\) | −0.245043 | + | 0.424428i | −0.0116031 | + | 0.0200972i | ||||
\(447\) | 10.1840 | + | 11.3703i | 0.481686 | + | 0.537796i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.457724 | 0.0216013 | 0.0108007 | − | 0.999942i | \(-0.496562\pi\) | ||||
0.0108007 | + | 0.999942i | \(0.496562\pi\) | |||||||
\(450\) | −0.0471770 | + | 0.427295i | −0.00222394 | + | 0.0201429i | ||||
\(451\) | 5.91114 | − | 10.2384i | 0.278345 | − | 0.482107i | ||||
\(452\) | 3.89479 | + | 6.74598i | 0.183196 | + | 0.317304i | ||||
\(453\) | 7.90650 | − | 1.65893i | 0.371480 | − | 0.0779431i | ||||
\(454\) | 0.471393 | + | 0.816477i | 0.0221236 | + | 0.0383192i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.880733 | + | 0.184794i | −0.0412441 | + | 0.00865376i | ||||
\(457\) | 20.2210 | 0.945900 | 0.472950 | − | 0.881089i | \(-0.343189\pi\) | ||||
0.472950 | + | 0.881089i | \(0.343189\pi\) | |||||||
\(458\) | 0.902342 | − | 1.56290i | 0.0421637 | − | 0.0730296i | ||||
\(459\) | −3.28988 | − | 33.8608i | −0.153558 | − | 1.58049i | ||||
\(460\) | 8.15440 | + | 14.1238i | 0.380201 | + | 0.658527i | ||||
\(461\) | −12.1036 | + | 20.9640i | −0.563719 | + | 0.976390i | 0.433449 | + | 0.901178i | \(0.357297\pi\) |
−0.997168 | + | 0.0752117i | \(0.976037\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.40242 | + | 4.16111i | 0.111650 | + | 0.193383i | 0.916436 | − | 0.400182i | \(-0.131053\pi\) |
−0.804786 | + | 0.593565i | \(0.797720\pi\) | |||||||
\(464\) | −12.6885 | + | 21.9772i | −0.589050 | + | 1.02026i | ||||
\(465\) | 20.6835 | + | 23.0928i | 0.959173 | + | 1.07090i | ||||
\(466\) | 0.432281 | + | 0.748732i | 0.0200250 | + | 0.0346843i | ||||
\(467\) | 13.6228 | + | 23.5954i | 0.630389 | + | 1.09187i | 0.987472 | + | 0.157793i | \(0.0504379\pi\) |
−0.357083 | + | 0.934073i | \(0.616229\pi\) | |||||||
\(468\) | 3.45128 | − | 31.2592i | 0.159535 | − | 1.44496i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.345979 | − | 0.599254i | 0.0159588 | − | 0.0276415i | ||||
\(471\) | 2.19755 | − | 6.70352i | 0.101258 | − | 0.308882i | ||||
\(472\) | 2.97565 | 0.136965 | ||||||||
\(473\) | 18.0118 | 0.828184 | ||||||||
\(474\) | −0.0300130 | + | 0.0915532i | −0.00137854 | + | 0.00420518i | ||||
\(475\) | −1.99302 | + | 3.45202i | −0.0914462 | + | 0.158389i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.4445 | − | 10.7302i | 1.11924 | − | 0.491301i | ||||
\(478\) | 0.527601 | + | 0.913832i | 0.0241319 | + | 0.0417977i | ||||
\(479\) | −10.2628 | − | 17.7756i | −0.468917 | − | 0.812188i | 0.530452 | − | 0.847715i | \(-0.322022\pi\) |
−0.999369 | + | 0.0355269i | \(0.988689\pi\) | |||||||
\(480\) | 2.51780 | + | 2.81108i | 0.114921 | + | 0.128308i | ||||
\(481\) | −11.1106 | + | 19.2441i | −0.506600 | + | 0.877457i | ||||
\(482\) | −0.0403366 | − | 0.0698651i | −0.00183728 | − | 0.00318227i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.42306 | + | 14.5892i | −0.382866 | + | 0.663144i | ||||
\(485\) | −6.86254 | − | 11.8863i | −0.311612 | − | 0.539727i | ||||
\(486\) | −1.06575 | − | 0.0139711i | −0.0483435 | − | 0.000633742i | ||||
\(487\) | −12.9224 | + | 22.3823i | −0.585571 | + | 1.01424i | 0.409233 | + | 0.912430i | \(0.365796\pi\) |
−0.994804 | + | 0.101809i | \(0.967537\pi\) | |||||||
\(488\) | −0.741363 | −0.0335599 | ||||||||
\(489\) | −20.5489 | + | 4.31153i | −0.929253 | + | 0.194974i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.80775 | − | 13.5234i | −0.352359 | − | 0.610303i | 0.634303 | − | 0.773084i | \(-0.281287\pi\) |
−0.986662 | + | 0.162781i | \(0.947954\pi\) | |||||||
\(492\) | −25.0056 | + | 5.24663i | −1.12734 | + | 0.236536i | ||||
\(493\) | 20.9152 | + | 36.2261i | 0.941971 | + | 1.63154i | ||||
\(494\) | −0.341610 | + | 0.591686i | −0.0153698 | + | 0.0266212i | ||||
\(495\) | −10.2991 | − | 7.56554i | −0.462909 | − | 0.340046i | ||||
\(496\) | 26.6886 | 1.19835 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.540194 | − | 0.603119i | −0.0242067 | − | 0.0270264i | ||||
\(499\) | −10.6345 | + | 18.4195i | −0.476066 | + | 0.824571i | −0.999624 | − | 0.0274192i | \(-0.991271\pi\) |
0.523558 | + | 0.851990i | \(0.324604\pi\) | |||||||
\(500\) | −15.4363 | −0.690332 | ||||||||
\(501\) | −8.13502 | + | 1.70687i | −0.363446 | + | 0.0762574i | ||||
\(502\) | 0.379455 | 0.0169359 | ||||||||
\(503\) | −16.3298 | −0.728110 | −0.364055 | − | 0.931377i | \(-0.618608\pi\) | ||||
−0.364055 | + | 0.931377i | \(0.618608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.91437 | 0.218687 | ||||||||
\(506\) | 0.335492 | 0.0149144 | ||||||||
\(507\) | −16.8744 | − | 18.8400i | −0.749418 | − | 0.836714i | ||||
\(508\) | −21.8553 | −0.969674 | ||||||||
\(509\) | 6.73089 | − | 11.6582i | 0.298342 | − | 0.516743i | −0.677415 | − | 0.735601i | \(-0.736900\pi\) |
0.975757 | + | 0.218858i | \(0.0702332\pi\) | |||||||
\(510\) | 2.02140 | − | 0.424126i | 0.0895092 | − | 0.0187806i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.41890 | 0.239484 | ||||||||
\(513\) | −8.99645 | − | 4.09056i | −0.397203 | − | 0.180603i | ||||
\(514\) | −0.336084 | + | 0.582115i | −0.0148240 | + | 0.0256760i | ||||
\(515\) | 6.89659 | + | 11.9452i | 0.303900 | + | 0.526370i | ||||
\(516\) | −25.9712 | − | 28.9964i | −1.14332 | − | 1.27650i | ||||
\(517\) | 3.03768 | + | 5.26142i | 0.133597 | + | 0.231397i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.71486 | + | 8.28153i | −0.119169 | + | 0.363519i | ||||
\(520\) | 3.82311 | 0.167654 | ||||||||
\(521\) | 0.713095 | − | 1.23512i | 0.0312413 | − | 0.0541115i | −0.849982 | − | 0.526812i | \(-0.823387\pi\) |
0.881223 | + | 0.472700i | \(0.156721\pi\) | |||||||
\(522\) | 1.20001 | − | 0.526756i | 0.0525229 | − | 0.0230555i | ||||
\(523\) | 3.85530 | + | 6.67758i | 0.168581 | + | 0.291990i | 0.937921 | − | 0.346849i | \(-0.112748\pi\) |
−0.769340 | + | 0.638839i | \(0.779415\pi\) | |||||||
\(524\) | −4.44301 | + | 7.69553i | −0.194094 | + | 0.336181i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.407928 | − | 0.706551i | −0.0177865 | − | 0.0308071i | ||||
\(527\) | 21.9961 | − | 38.0984i | 0.958165 | − | 1.65959i | ||||
\(528\) | −10.7670 | + | 2.25911i | −0.468573 | + | 0.0983151i | ||||
\(529\) | 6.79254 | + | 11.7650i | 0.295328 | + | 0.511523i | ||||
\(530\) | 0.810371 | + | 1.40360i | 0.0352003 | + | 0.0609686i | ||||
\(531\) | 26.3363 | + | 19.3462i | 1.14290 | + | 0.839554i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.4206 | + | 33.6374i | −0.841198 | + | 1.45700i | ||||
\(534\) | 0.0545409 | − | 0.0114437i | 0.00236021 | − | 0.000495215i | ||||
\(535\) | 45.1483 | 1.95193 | ||||||||
\(536\) | 0.908402 | 0.0392370 | ||||||||
\(537\) | 18.9493 | + | 21.1566i | 0.817721 | + | 0.912973i | ||||
\(538\) | −1.02441 | + | 1.77432i | −0.0441653 | + | 0.0764966i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.67078 | + | 27.4888i | 0.114932 | + | 1.18293i | ||||
\(541\) | −14.0228 | − | 24.2882i | −0.602886 | − | 1.04423i | −0.992382 | − | 0.123201i | \(-0.960684\pi\) |
0.389495 | − | 0.921028i | \(-0.372649\pi\) | |||||||
\(542\) | 0.242608 | + | 0.420209i | 0.0104209 | + | 0.0180495i | ||||
\(543\) | 7.78813 | − | 23.7573i | 0.334221 | − | 1.01952i | ||||
\(544\) | 2.67759 | − | 4.63771i | 0.114801 | − | 0.198840i | ||||
\(545\) | −11.3210 | − | 19.6086i | −0.484939 | − | 0.839939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.7305 | − | 30.7101i | 0.758101 | − | 1.31307i | −0.185717 | − | 0.982603i | \(-0.559461\pi\) |
0.943818 | − | 0.330466i | \(-0.107206\pi\) | |||||||
\(548\) | −19.4903 | − | 33.7583i | −0.832586 | − | 1.44208i | ||||
\(549\) | −6.56150 | − | 4.81998i | −0.280038 | − | 0.205712i | ||||
\(550\) | 0.114575 | − | 0.198450i | 0.00488550 | − | 0.00846193i | ||||
\(551\) | 12.1515 | 0.517673 | ||||||||
\(552\) | −0.968623 | − | 1.08145i | −0.0412273 | − | 0.0460297i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.335836 | + | 0.581685i | 0.0142683 | + | 0.0247134i | ||||
\(555\) | 6.07891 | − | 18.5434i | 0.258035 | − | 0.787124i | ||||
\(556\) | 2.62464 | + | 4.54601i | 0.111310 | + | 0.192794i | ||||
\(557\) | −17.5209 | + | 30.3472i | −0.742386 | + | 1.28585i | 0.209019 | + | 0.977911i | \(0.432973\pi\) |
−0.951406 | + | 0.307940i | \(0.900361\pi\) | |||||||
\(558\) | −1.11077 | − | 0.815957i | −0.0470228 | − | 0.0345422i | ||||
\(559\) | −59.1763 | −2.50289 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.64899 | + | 17.2319i | −0.238500 | + | 0.727533i | ||||
\(562\) | 0.816308 | − | 1.41389i | 0.0344339 | − | 0.0596412i | ||||
\(563\) | 16.0262 | 0.675425 | 0.337712 | − | 0.941249i | \(-0.390347\pi\) | ||||
0.337712 | + | 0.941249i | \(0.390347\pi\) | |||||||
\(564\) | 4.09011 | − | 12.4767i | 0.172225 | − | 0.525362i | ||||
\(565\) | −10.3992 | −0.437499 | ||||||||
\(566\) | −0.206213 | −0.00866776 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.38439 | 0.142006 | ||||||||
\(569\) | 0.371302 | 0.0155658 | 0.00778290 | − | 0.999970i | \(-0.497523\pi\) | ||||
0.00778290 | + | 0.999970i | \(0.497523\pi\) | |||||||
\(570\) | 0.186904 | − | 0.570141i | 0.00782855 | − | 0.0238806i | ||||
\(571\) | 29.2304 | 1.22325 | 0.611626 | − | 0.791147i | \(-0.290516\pi\) | ||||
0.611626 | + | 0.791147i | \(0.290516\pi\) | |||||||
\(572\) | −8.38185 | + | 14.5178i | −0.350463 | + | 0.607019i | ||||
\(573\) | −1.53303 | + | 4.67643i | −0.0640432 | + | 0.195361i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.43065 | −0.268177 | ||||||||
\(576\) | 19.0714 | + | 14.0096i | 0.794643 | + | 0.583732i | ||||
\(577\) | 7.52852 | − | 13.0398i | 0.313417 | − | 0.542853i | −0.665683 | − | 0.746235i | \(-0.731860\pi\) |
0.979100 | + | 0.203381i | \(0.0651930\pi\) | |||||||
\(578\) | −0.884279 | − | 1.53162i | −0.0367811 | − | 0.0637068i | ||||
\(579\) | −4.76361 | + | 14.5311i | −0.197969 | + | 0.603894i | ||||
\(580\) | −16.9793 | − | 29.4089i | −0.705025 | − | 1.22114i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.407107 | + | 0.454529i | 0.0168751 | + | 0.0188408i | ||||
\(583\) | −14.2300 | −0.589347 | ||||||||
\(584\) | 0.300307 | − | 0.520148i | 0.0124268 | − | 0.0215239i | ||||
\(585\) | 33.8368 | + | 24.8560i | 1.39898 | + | 1.02767i | ||||
\(586\) | −0.583171 | − | 1.01008i | −0.0240906 | − | 0.0417261i | ||||
\(587\) | −0.835901 | + | 1.44782i | −0.0345013 | + | 0.0597580i | −0.882760 | − | 0.469823i | \(-0.844318\pi\) |
0.848259 | + | 0.529581i | \(0.177651\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.38977 | − | 11.0674i | −0.263286 | − | 0.456025i | ||||
\(590\) | −0.991973 | + | 1.71815i | −0.0408389 | + | 0.0707350i | ||||
\(591\) | −3.08814 | + | 9.42020i | −0.127029 | + | 0.387495i | ||||
\(592\) | −8.39982 | − | 14.5489i | −0.345231 | − | 0.597957i | ||||
\(593\) | 5.40871 | + | 9.36816i | 0.222109 | + | 0.384704i | 0.955448 | − | 0.295159i | \(-0.0953726\pi\) |
−0.733339 | + | 0.679863i | \(0.762039\pi\) | |||||||
\(594\) | 0.517188 | + | 0.235158i | 0.0212205 | + | 0.00964867i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.79221 | + | 15.2286i | −0.360143 | + | 0.623786i | ||||
\(597\) | 13.1911 | + | 14.7277i | 0.539876 | + | 0.602764i | ||||
\(598\) | −1.10223 | −0.0450736 | ||||||||
\(599\) | 16.6401 | 0.679898 | 0.339949 | − | 0.940444i | \(-0.389590\pi\) | ||||
0.339949 | + | 0.940444i | \(0.389590\pi\) | |||||||
\(600\) | −0.970498 | + | 0.203628i | −0.0396204 | + | 0.00831308i | ||||
\(601\) | 12.9011 | − | 22.3453i | 0.526246 | − | 0.911485i | −0.473286 | − | 0.880909i | \(-0.656932\pi\) |
0.999532 | − | 0.0305765i | \(-0.00973432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.03989 | + | 5.90598i | 0.327410 | + | 0.240510i | ||||
\(604\) | 4.65332 | + | 8.05978i | 0.189341 | + | 0.327948i | ||||
\(605\) | −11.2449 | − | 19.4768i | −0.457171 | − | 0.791843i | ||||
\(606\) | −0.213828 | + | 0.0448649i | −0.00868616 | + | 0.00182251i | ||||
\(607\) | 18.9025 | − | 32.7400i | 0.767227 | − | 1.32888i | −0.171834 | − | 0.985126i | \(-0.554969\pi\) |
0.939061 | − | 0.343750i | \(-0.111697\pi\) | |||||||
\(608\) | −0.777828 | − | 1.34724i | −0.0315451 | − | 0.0546377i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.247143 | − | 0.428065i | 0.0100065 | − | 0.0173318i | ||||
\(611\) | −9.98005 | − | 17.2860i | −0.403750 | − | 0.699315i | ||||
\(612\) | 35.8862 | − | 15.7526i | 1.45062 | − | 0.636763i | ||||
\(613\) | 6.47719 | − | 11.2188i | 0.261611 | − | 0.453124i | −0.705059 | − | 0.709149i | \(-0.749080\pi\) |
0.966670 | + | 0.256025i | \(0.0824129\pi\) | |||||||
\(614\) | 1.58749 | 0.0640659 | ||||||||
\(615\) | 10.6255 | − | 32.4126i | 0.428462 | − | 1.30700i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.2202 | + | 28.0941i | 0.652999 | + | 1.13103i | 0.982391 | + | 0.186834i | \(0.0598227\pi\) |
−0.329393 | + | 0.944193i | \(0.606844\pi\) | |||||||
\(618\) | −0.409127 | − | 0.456784i | −0.0164575 | − | 0.0183746i | ||||
\(619\) | 16.5987 | + | 28.7498i | 0.667157 | + | 1.15555i | 0.978696 | + | 0.205317i | \(0.0658224\pi\) |
−0.311538 | + | 0.950234i | \(0.600844\pi\) | |||||||
\(620\) | −17.8568 | + | 30.9289i | −0.717146 | + | 1.24213i | ||||
\(621\) | −1.54181 | − | 15.8690i | −0.0618708 | − | 0.636802i | ||||
\(622\) | 0.122453 | 0.00490993 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 35.3741 | − | 7.42212i | 1.41610 | − | 0.297122i | ||||
\(625\) | 15.5433 | − | 26.9218i | 0.621732 | − | 1.07687i | ||||
\(626\) | 0.315147 | 0.0125958 | ||||||||
\(627\) | 3.51465 | + | 3.92406i | 0.140362 | + | 0.156712i | ||||
\(628\) | 8.12683 | 0.324296 | ||||||||
\(629\) | −27.6917 | −1.10414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2773 | 1.28494 | 0.642470 | − | 0.766311i | \(-0.277910\pi\) | ||||
0.642470 | + | 0.766311i | \(0.277910\pi\) | |||||||
\(632\) | −0.222244 | −0.00884040 | ||||||||
\(633\) | −36.2484 | + | 7.60557i | −1.44075 | + | 0.302294i | ||||
\(634\) | −1.76980 | −0.0702877 | ||||||||
\(635\) | 14.5886 | − | 25.2682i | 0.578931 | − | 1.00274i | ||||
\(636\) | 20.5182 | + | 22.9083i | 0.813601 | + | 0.908374i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.698568 | −0.0276566 | ||||||||
\(639\) | 29.9538 | + | 22.0036i | 1.18496 | + | 0.870450i | ||||
\(640\) | −2.89714 | + | 5.01799i | −0.114519 | + | 0.198353i | ||||
\(641\) | −21.5407 | − | 37.3096i | −0.850806 | − | 1.47364i | −0.880482 | − | 0.474079i | \(-0.842781\pi\) |
0.0296762 | − | 0.999560i | \(-0.490552\pi\) | |||||||
\(642\) | −1.96444 | + | 0.412174i | −0.0775301 | + | 0.0162672i | ||||
\(643\) | 3.20088 | + | 5.54409i | 0.126230 | + | 0.218638i | 0.922213 | − | 0.386682i | \(-0.126379\pi\) |
−0.795983 | + | 0.605319i | \(0.793045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 50.8604 | − | 10.6714i | 2.00263 | − | 0.420187i | ||||
\(646\) | −0.851419 | −0.0334986 | ||||||||
\(647\) | 1.94403 | − | 3.36716i | 0.0764278 | − | 0.132377i | −0.825278 | − | 0.564726i | \(-0.808982\pi\) |
0.901706 | + | 0.432349i | \(0.142315\pi\) | |||||||
\(648\) | −0.735183 | − | 2.34609i | −0.0288807 | − | 0.0921632i | ||||
\(649\) | −8.70947 | − | 15.0852i | −0.341877 | − | 0.592148i | ||||
\(650\) | −0.376427 | + | 0.651991i | −0.0147647 | + | 0.0255732i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0939 | − | 20.9473i | −0.473634 | − | 0.820358i | ||||
\(653\) | −7.55174 | + | 13.0800i | −0.295522 | + | 0.511860i | −0.975106 | − | 0.221738i | \(-0.928827\pi\) |
0.679584 | + | 0.733598i | \(0.262160\pi\) | |||||||
\(654\) | 0.671598 | + | 0.749829i | 0.0262616 | + | 0.0293206i | ||||
\(655\) | −5.93150 | − | 10.2737i | −0.231763 | − | 0.401425i | ||||
\(656\) | −14.6823 | − | 25.4305i | −0.573248 | − | 0.992895i | ||||
\(657\) | 6.03964 | − | 2.65116i | 0.235629 | − | 0.103432i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.13002 | + | 12.3496i | −0.277746 | + | 0.481070i | −0.970824 | − | 0.239792i | \(-0.922921\pi\) |
0.693078 | + | 0.720862i | \(0.256254\pi\) | |||||||
\(660\) | 4.58594 | − | 13.9892i | 0.178507 | − | 0.544528i | ||||
\(661\) | 19.4193 | 0.755323 | 0.377662 | − | 0.925944i | \(-0.376728\pi\) | ||||
0.377662 | + | 0.925944i | \(0.376728\pi\) | |||||||
\(662\) | 0.0110303 | 0.000428706 | ||||||||
\(663\) | 18.5593 | − | 56.6142i | 0.720783 | − | 2.19871i | ||||
\(664\) | 0.933832 | − | 1.61744i | 0.0362397 | − | 0.0627690i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0952089 | + | 0.862333i | −0.00368927 | + | 0.0334147i | ||||
\(667\) | 9.80197 | + | 16.9775i | 0.379534 | + | 0.657372i | ||||
\(668\) | −4.78781 | − | 8.29273i | −0.185246 | − | 0.320855i | ||||
\(669\) | −8.28297 | − | 9.24781i | −0.320238 | − | 0.357541i | ||||
\(670\) | −0.302828 | + | 0.524513i | −0.0116993 | + | 0.0202637i | ||||
\(671\) | 2.16991 | + | 3.75839i | 0.0837683 | + | 0.145091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.96563 | + | 5.13663i | −0.114317 | + | 0.198002i | −0.917506 | − | 0.397721i | \(-0.869801\pi\) |
0.803190 | + | 0.595723i | \(0.203135\pi\) | |||||||
\(674\) | 0.309512 | + | 0.536091i | 0.0119220 | + | 0.0206494i | ||||
\(675\) | −9.91337 | − | 4.50747i | −0.381566 | − | 0.173493i | ||||
\(676\) | 14.5683 | − | 25.2330i | 0.560318 | − | 0.970500i | ||||
\(677\) | −36.9826 | −1.42136 | −0.710678 | − | 0.703518i | \(-0.751612\pi\) | ||||
−0.710678 | + | 0.703518i | \(0.751612\pi\) | |||||||
\(678\) | 0.452477 | − | 0.0949379i | 0.0173773 | − | 0.00364607i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.38215 | + | 4.12601i | 0.0913513 | + | 0.158225i | ||||
\(681\) | −23.3737 | + | 4.90423i | −0.895683 | + | 0.187930i | ||||
\(682\) | 0.367336 | + | 0.636244i | 0.0140660 | + | 0.0243630i | ||||
\(683\) | −6.56800 | + | 11.3761i | −0.251317 | + | 0.435294i | −0.963889 | − | 0.266305i | \(-0.914197\pi\) |
0.712571 | + | 0.701600i | \(0.247530\pi\) | |||||||
\(684\) | 1.24940 | − | 11.3162i | 0.0477721 | − | 0.432685i | ||||
\(685\) | 52.0398 | 1.98834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.5010 | + | 34.0539i | 1.16369 | + | 1.29924i | ||||
\(688\) | 22.3692 | − | 38.7446i | 0.852818 | − | 1.47712i | ||||
\(689\) | 46.7516 | 1.78109 | ||||||||
\(690\) | 0.947338 | − | 0.198768i | 0.0360645 | − | 0.00756699i | ||||
\(691\) | −14.7658 | −0.561719 | −0.280860 | − | 0.959749i | \(-0.590620\pi\) | ||||
−0.280860 | + | 0.959749i | \(0.590620\pi\) | |||||||
\(692\) | −10.0399 | −0.381659 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.397915 | −0.0151046 | ||||||||
\(695\) | −7.00788 | −0.265824 | ||||||||
\(696\) | 2.01689 | + | 2.25182i | 0.0764499 | + | 0.0853552i | ||||
\(697\) | −48.4032 | −1.83340 | ||||||||
\(698\) | −0.932003 | + | 1.61428i | −0.0352768 | + | 0.0611012i | ||||
\(699\) | −21.4344 | + | 4.49731i | −0.810722 | + | 0.170104i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.4627 | −1.15056 | −0.575281 | − | 0.817956i | \(-0.695107\pi\) | ||||
−0.575281 | + | 0.817956i | \(0.695107\pi\) | |||||||
\(702\) | −1.69918 | − | 0.772594i | −0.0641314 | − | 0.0291597i | ||||
\(703\) | −4.02217 | + | 6.96660i | −0.151699 | + | 0.262750i | ||||
\(704\) | −6.30697 | − | 10.9240i | −0.237703 | − | 0.411713i | ||||
\(705\) | 11.6948 | + | 13.0571i | 0.440452 | + | 0.491758i | ||||
\(706\) | 0.826969 | + | 1.43235i | 0.0311234 | + | 0.0539073i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.7269 | + | 35.7724i | −0.440725 | + | 1.34441i | ||||
\(709\) | 14.1030 | 0.529650 | 0.264825 | − | 0.964296i | \(-0.414686\pi\) | ||||
0.264825 | + | 0.964296i | \(0.414686\pi\) | |||||||
\(710\) | −1.12823 | + | 1.95415i | −0.0423418 | + | 0.0733381i | ||||
\(711\) | −1.96699 | − | 1.44492i | −0.0737680 | − | 0.0541888i | ||||
\(712\) | 0.0642745 | + | 0.111327i | 0.00240879 | + | 0.00417215i | ||||
\(713\) | 10.3086 | − | 17.8549i | 0.386058 | − | 0.668673i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.1899 | − | 19.3815i | −0.418479 | − | 0.724827i | ||||
\(716\) | −16.3596 | + | 28.3356i | −0.611386 | + | 1.05895i | ||||
\(717\) | −26.1608 | + | 5.48900i | −0.976992 | + | 0.204990i | ||||
\(718\) | 0.719212 | + | 1.24571i | 0.0268408 | + | 0.0464896i | ||||
\(719\) | 7.49790 | + | 12.9867i | 0.279624 | + | 0.484324i | 0.971291 | − | 0.237893i | \(-0.0764567\pi\) |
−0.691667 | + | 0.722217i | \(0.743123\pi\) | |||||||
\(720\) | −29.0646 | + | 12.7582i | −1.08317 | + | 0.475471i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.525886 | − | 0.910861i | 0.0195715 | − | 0.0338987i | ||||
\(723\) | 2.00007 | − | 0.419650i | 0.0743833 | − | 0.0156069i | ||||
\(724\) | 28.8015 | 1.07040 | ||||||||
\(725\) | 13.3900 | 0.497293 | ||||||||
\(726\) | 0.667084 | + | 0.744790i | 0.0247578 | + | 0.0276417i | ||||
\(727\) | 13.0527 | − | 22.6080i | 0.484099 | − | 0.838485i | −0.515734 | − | 0.856749i | \(-0.672481\pi\) |
0.999833 | + | 0.0182642i | \(0.00581399\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.74633 | − | 25.5441i | 0.323938 | − | 0.946078i | ||||
\(730\) | 0.200223 | + | 0.346796i | 0.00741059 | + | 0.0128355i | ||||
\(731\) | −36.8723 | − | 63.8648i | −1.36377 | − | 2.36212i | ||||
\(732\) | 2.92168 | − | 8.91245i | 0.107989 | − | 0.329414i | ||||
\(733\) | 14.1911 | − | 24.5796i | 0.524159 | − | 0.907869i | −0.475446 | − | 0.879745i | \(-0.657713\pi\) |
0.999604 | − | 0.0281244i | \(-0.00895345\pi\) | |||||||
\(734\) | −1.19784 | − | 2.07473i | −0.0442132 | − | 0.0765796i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.25486 | − | 2.17348i | 0.0462548 | − | 0.0801156i | ||||
\(737\) | −2.65881 | − | 4.60520i | −0.0979386 | − | 0.169635i | ||||
\(738\) | −0.166419 | + | 1.50730i | −0.00612595 | + | 0.0554844i | ||||
\(739\) | −23.2933 | + | 40.3451i | −0.856857 | + | 1.48412i | 0.0180552 | + | 0.999837i | \(0.494253\pi\) |
−0.874912 | + | 0.484282i | \(0.839081\pi\) | |||||||
\(740\) | 22.4806 | 0.826403 | ||||||||
\(741\) | −11.5471 | − | 12.8922i | −0.424194 | − | 0.473606i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.169513 | − | 0.293606i | −0.00621884 | − | 0.0107713i | 0.862899 | − | 0.505376i | \(-0.168646\pi\) |
−0.869118 | + | 0.494605i | \(0.835313\pi\) | |||||||
\(744\) | 0.990362 | − | 3.02105i | 0.0363084 | − | 0.110757i | ||||
\(745\) | −11.7377 | − | 20.3304i | −0.430038 | − | 0.744847i | ||||
\(746\) | −0.0385841 | + | 0.0668297i | −0.00141267 | + | 0.00244681i | ||||
\(747\) | 18.7808 | − | 8.24402i | 0.687153 | − | 0.301633i | ||||
\(748\) | −20.8907 | −0.763839 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.285398 | + | 0.870593i | −0.0104213 | + | 0.0317896i | ||||
\(751\) | 18.1831 | − | 31.4940i | 0.663510 | − | 1.14923i | −0.316177 | − | 0.948700i | \(-0.602399\pi\) |
0.979687 | − | 0.200533i | \(-0.0642673\pi\) | |||||||
\(752\) | 15.0902 | 0.550284 | ||||||||
\(753\) | −2.99434 | + | 9.13408i | −0.109120 | + | 0.332864i | ||||
\(754\) | 2.29509 | 0.0835822 | ||||||||
\(755\) | −12.4245 | −0.452174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4703 | −0.998424 | −0.499212 | − | 0.866480i | \(-0.666377\pi\) | ||||
−0.499212 | + | 0.866480i | \(0.666377\pi\) | |||||||
\(758\) | −1.50162 | −0.0545415 | ||||||||
\(759\) | −2.64742 | + | 8.07582i | −0.0960952 | + | 0.293134i | ||||
\(760\) | 1.38401 | 0.0502033 | ||||||||
\(761\) | 16.5178 | − | 28.6097i | 0.598771 | − | 1.03710i | −0.394232 | − | 0.919011i | \(-0.628989\pi\) |
0.993003 | − | 0.118091i | \(-0.0376774\pi\) | |||||||
\(762\) | −0.404079 | + | 1.23262i | −0.0146382 | + | 0.0446532i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.66934 | −0.205110 | ||||||||
\(765\) | −5.74181 | + | 52.0052i | −0.207596 | + | 1.88025i | ||||
\(766\) | 0.787671 | − | 1.36429i | 0.0284597 | − | 0.0492937i | ||||
\(767\) | 28.6143 | + | 49.5614i | 1.03320 | + | 1.78956i | ||||
\(768\) | −8.43171 | + | 25.7205i | −0.304253 | + | 0.928109i | ||||
\(769\) | 1.28876 | + | 2.23219i | 0.0464738 | + | 0.0804949i | 0.888327 | − | 0.459212i | \(-0.151868\pi\) |
−0.841853 | + | 0.539707i | \(0.818535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.3603 | − | 12.6836i | −0.409132 | − | 0.456790i | ||||
\(772\) | −17.6164 | −0.634030 | ||||||||
\(773\) | 3.36486 | − | 5.82811i | 0.121026 | − | 0.209623i | −0.799147 | − | 0.601136i | \(-0.794715\pi\) |
0.920172 | + | 0.391513i | \(0.128048\pi\) | |||||||
\(774\) | −2.11555 | + | 0.928643i | −0.0760419 | + | 0.0333794i | ||||
\(775\) | −7.04102 | − | 12.1954i | −0.252921 | − | 0.438072i | ||||
\(776\) | −0.703765 | + | 1.21896i | −0.0252637 | + | 0.0437580i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.539302 | − | 0.934099i | −0.0193349 | − | 0.0334891i | ||||
\(779\) | −7.03047 | + | 12.1771i | −0.251893 | + | 0.436291i | ||||
\(780\) | −15.0667 | + | 45.9603i | −0.539475 | + | 1.64564i | ||||
\(781\) | −9.90581 | − | 17.1574i | −0.354458 | − | 0.613939i | ||||
\(782\) | −0.686792 | − | 1.18956i | −0.0245596 | − | 0.0425385i | ||||
\(783\) | 3.21039 | + | 33.0428i | 0.114730 | + | 1.18085i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.42473 | + | 9.39590i | −0.193617 | + | 0.335354i | ||||
\(786\) | 0.351875 | + | 0.392863i | 0.0125510 | + | 0.0140130i | ||||
\(787\) | −28.6683 | −1.02191 | −0.510956 | − | 0.859607i | \(-0.670709\pi\) | ||||
−0.510956 | + | 0.859607i | \(0.670709\pi\) | |||||||
\(788\) | −11.4203 | −0.406832 | ||||||||
\(789\) | 20.2268 | − | 4.24395i | 0.720094 | − | 0.151089i | ||||
\(790\) | 0.0740881 | − | 0.128324i | 0.00263594 | − | 0.00456558i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.143820 | + | 1.30261i | −0.00511041 | + | 0.0462864i | ||||
\(793\) | −7.12905 | − | 12.3479i | −0.253160 | − | 0.438486i | ||||
\(794\) | −0.564275 | − | 0.977352i | −0.0200254 | − | 0.0346849i | ||||
\(795\) | −40.1817 | + | 8.43085i | −1.42510 | + | 0.299011i | ||||
\(796\) | −11.3884 | + | 19.7252i | −0.403650 | + | 0.699142i | ||||
\(797\) | −11.4913 | − | 19.9035i | −0.407042 | − | 0.705017i | 0.587515 | − | 0.809213i | \(-0.300106\pi\) |
−0.994557 | + | 0.104196i | \(0.966773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.4370 | − | 21.5415i | 0.439989 | − | 0.762084i | ||||
\(800\) | −0.857104 | − | 1.48455i | −0.0303032 | − | 0.0524867i | ||||
\(801\) | −0.154924 | + | 1.40319i | −0.00547397 | + | 0.0495792i | ||||
\(802\) | −0.740489 | + | 1.28256i | −0.0261476 | + | 0.0452889i | ||||
\(803\) | −3.51589 | −0.124073 | ||||||||
\(804\) | −3.57998 | + | 10.9205i | −0.126256 | + | 0.385138i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.20685 | − | 2.09033i | −0.0425095 | − | 0.0736287i | ||||
\(807\) | −34.6270 | − | 38.6606i | −1.21893 | − | 1.36092i | ||||
\(808\) | −0.251989 | − | 0.436457i | −0.00886493 | − | 0.0153545i | ||||
\(809\) | 8.23894 | − | 14.2703i | 0.289666 | − | 0.501716i | −0.684064 | − | 0.729422i | \(-0.739789\pi\) |
0.973730 | + | 0.227706i | \(0.0731225\pi\) | |||||||
\(810\) | 1.59972 | + | 0.357605i | 0.0562085 | + | 0.0125650i | ||||
\(811\) | −40.4318 | −1.41975 | −0.709876 | − | 0.704326i | \(-0.751249\pi\) | ||||
−0.709876 | + | 0.704326i | \(0.751249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0296 | + | 2.52402i | −0.421895 | + | 0.0885212i | ||||
\(814\) | 0.231227 | − | 0.400496i | 0.00810449 | − | 0.0140374i | ||||
\(815\) | 32.2911 | 1.13111 | ||||||||
\(816\) | 30.0515 | + | 33.5520i | 1.05201 | + | 1.17456i | ||||
\(817\) | −21.4225 | −0.749479 | ||||||||
\(818\) | −2.09033 | −0.0730868 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 39.2945 | 1.37222 | ||||||||
\(821\) | −28.1086 | −0.980998 | −0.490499 | − | 0.871442i | \(-0.663186\pi\) | ||||
−0.490499 | + | 0.871442i | \(0.663186\pi\) | |||||||
\(822\) | −2.26429 | + | 0.475089i | −0.0789762 | + | 0.0165706i | ||||
\(823\) | 25.9058 | 0.903019 | 0.451510 | − | 0.892266i | \(-0.350886\pi\) | ||||
0.451510 | + | 0.892266i | \(0.350886\pi\) | |||||||
\(824\) | 0.707256 | − | 1.22500i | 0.0246384 | − | 0.0426750i | ||||
\(825\) | 3.87287 | + | 4.32400i | 0.134836 | + | 0.150542i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.7998 | −0.618961 | −0.309480 | − | 0.950906i | \(-0.600155\pi\) | ||||
−0.309480 | + | 0.950906i | \(0.600155\pi\) | |||||||
\(828\) | 16.8182 | − | 7.38254i | 0.584474 | − | 0.256561i | ||||
\(829\) | −7.85344 | + | 13.6026i | −0.272761 | + | 0.472436i | −0.969568 | − | 0.244823i | \(-0.921270\pi\) |
0.696807 | + | 0.717259i | \(0.254604\pi\) | |||||||
\(830\) | 0.622611 | + | 1.07839i | 0.0216111 | + | 0.0374316i | ||||
\(831\) | −16.6522 | + | 3.49393i | −0.577659 | + | 0.121203i | ||||
\(832\) | 20.7210 | + | 35.8899i | 0.718373 | + | 1.24426i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.304918 | − | 0.0639772i | 0.0105584 | − | 0.00221535i | ||||
\(835\) | 12.7836 | 0.442395 | ||||||||
\(836\) | −3.03433 | + | 5.25561i | −0.104944 | + | 0.181769i | ||||
\(837\) | 28.4067 | − | 20.2992i | 0.981878 | − | 0.701644i | ||||
\(838\) | 0.738994 | + | 1.27998i | 0.0255281 | + | 0.0442160i | ||||
\(839\) | 3.69822 | − | 6.40550i | 0.127677 | − | 0.221142i | −0.795099 | − | 0.606479i | \(-0.792581\pi\) |
0.922776 | + | 0.385337i | \(0.125915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.90986 | − | 10.2362i | −0.203788 | − | 0.352971i | ||||
\(842\) | 0.931370 | − | 1.61318i | 0.0320971 | − | 0.0555938i | ||||
\(843\) | 27.5929 | + | 30.8070i | 0.950349 | + | 1.06105i | ||||
\(844\) | −21.3338 | − | 36.9511i | −0.734338 | − | 1.27191i | ||||
\(845\) | 19.4489 | + | 33.6865i | 0.669062 | + | 1.15885i | ||||
\(846\) | −0.628052 | − | 0.461357i | −0.0215929 | − | 0.0158618i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −17.6725 | + | 30.6097i | −0.606878 | + | 1.05114i | ||||
\(849\) | 1.62726 | − | 4.96386i | 0.0558473 | − | 0.170359i | ||||
\(850\) | −0.938196 | −0.0321798 | ||||||||
\(851\) | −12.9778 | −0.444874 | ||||||||
\(852\) | −13.3378 | + | 40.6861i | −0.456944 | + | 1.39388i | ||||
\(853\) | 26.5631 | − | 46.0086i | 0.909503 | − | 1.57530i | 0.0947464 | − | 0.995501i | \(-0.469796\pi\) |
0.814756 | − | 0.579804i | \(-0.196871\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.2493 | + | 8.99815i | 0.418917 | + | 0.307730i | ||||
\(856\) | −2.31502 | − | 4.00973i | −0.0791257 | − | 0.137050i | ||||
\(857\) | 1.90765 | + | 3.30414i | 0.0651640 | + | 0.112867i | 0.896767 | − | 0.442504i | \(-0.145910\pi\) |
−0.831603 | + | 0.555371i | \(0.812576\pi\) | |||||||
\(858\) | 0.663821 | + | 0.741146i | 0.0226625 | + | 0.0253023i | ||||
\(859\) | −19.4884 | + | 33.7549i | −0.664936 | + | 1.15170i | 0.314367 | + | 0.949301i | \(0.398208\pi\) |
−0.979303 | + | 0.202401i | \(0.935126\pi\) | |||||||
\(860\) | 29.9336 | + | 51.8464i | 1.02073 | + | 1.76795i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.280226 | + | 0.485366i | −0.00954454 | + | 0.0165316i | ||||
\(863\) | −13.3368 | − | 23.1000i | −0.453989 | − | 0.786332i | 0.544640 | − | 0.838670i | \(-0.316666\pi\) |
−0.998629 | + | 0.0523375i | \(0.983333\pi\) | |||||||
\(864\) | 3.45794 | − | 2.47103i | 0.117642 | − | 0.0840660i | ||||
\(865\) | 6.70171 | − | 11.6077i | 0.227865 | − | 0.394674i | ||||
\(866\) | 0.233475 | 0.00793380 | ||||||||
\(867\) | 43.8464 | − | 9.19976i | 1.48910 | − | 0.312440i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.650490 | + | 1.12668i | 0.0220664 | + | 0.0382200i | ||||
\(870\) | −1.97257 | + | 0.413880i | −0.0668762 | + | 0.0140318i | ||||
\(871\) | 8.73531 | + | 15.1300i | 0.295985 | + | 0.512661i | ||||
\(872\) | −1.16099 | + | 2.01089i | −0.0393160 | + | 0.0680974i | ||||
\(873\) | −14.1538 | + | 6.21295i | −0.479033 | + | 0.210277i | ||||
\(874\) | −0.399020 | −0.0134971 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.06956 | + | 5.66009i | 0.171285 | + | 0.191237i | ||||
\(877\) | −12.0068 | + | 20.7963i | −0.405440 | + | 0.702242i | −0.994373 | − | 0.105940i | \(-0.966215\pi\) |
0.588933 | + | 0.808182i | \(0.299548\pi\) | |||||||
\(878\) | 0.450469 | 0.0152026 | ||||||||
\(879\) | 28.9161 | − | 6.06713i | 0.975317 | − | 0.204639i | ||||
\(880\) | 16.9196 | 0.570358 | ||||||||
\(881\) | −4.67326 | −0.157446 | −0.0787231 | − | 0.996897i | \(-0.525084\pi\) | ||||
−0.0787231 | + | 0.996897i | \(0.525084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6948 | −1.20122 | −0.600612 | − | 0.799541i | \(-0.705076\pi\) | ||||
−0.600612 | + | 0.799541i | \(0.705076\pi\) | |||||||
\(884\) | 68.6346 | 2.30843 | ||||||||
\(885\) | −33.5307 | − | 37.4365i | −1.12712 | − | 1.25842i | ||||
\(886\) | 1.96173 | 0.0659058 | ||||||||
\(887\) | −14.5516 | + | 25.2041i | −0.488596 | + | 0.846272i | −0.999914 | − | 0.0131191i | \(-0.995824\pi\) |
0.511318 | + | 0.859391i | \(0.329157\pi\) | |||||||
\(888\) | −1.95858 | + | 0.410946i | −0.0657258 | + | 0.0137905i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.0857071 | −0.00287291 | ||||||||
\(891\) | −9.74185 | + | 10.5939i | −0.326364 | + | 0.354908i | ||||
\(892\) | 7.15098 | − | 12.3859i | 0.239433 | − | 0.414710i | ||||
\(893\) | −3.61290 | − | 6.25772i | −0.120901 | − | 0.209407i | ||||
\(894\) | 0.696320 | + | 0.777431i | 0.0232884 | + | 0.0260012i | ||||
\(895\) | −21.8403 | − | 37.8285i | −0.730041 | − | 1.26447i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.69788 | − | 26.5324i | 0.290414 | − | 0.885892i | ||||
\(898\) | 0.0312964 | 0.00104437 | ||||||||
\(899\) | −21.4647 | + | 37.1779i | −0.715887 | + | 1.23995i | ||||
\(900\) | 1.37674 | − | 12.4695i | 0.0458914 | − | 0.415651i | ||||
\(901\) | 29.1306 | + | 50.4556i | 0.970480 | + | 1.68092i | ||||
\(902\) | 0.404168 | − | 0.700040i | 0.0134573 | − | 0.0233088i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.533229 | + | 0.923579i | 0.0177349 | + | 0.0307178i | ||||
\(905\) | −19.2252 | + | 33.2991i | −0.639069 | + | 1.10690i | ||||
\(906\) | 0.540599 | − | 0.113427i | 0.0179602 | − | 0.00376837i | ||||
\(907\) | 20.6071 | + | 35.6925i | 0.684247 | + | 1.18515i | 0.973673 | + | 0.227950i | \(0.0732024\pi\) |
−0.289426 | + | 0.957201i | \(0.593464\pi\) | |||||||
\(908\) | −13.7564 | − | 23.8269i | −0.456524 | − | 0.790722i | ||||
\(909\) | 0.607380 | − | 5.50121i | 0.0201455 | − | 0.182464i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.8619 | − | 49.9903i | 0.956239 | − | 1.65625i | 0.224731 | − | 0.974421i | \(-0.427850\pi\) |
0.731508 | − | 0.681833i | \(-0.238817\pi\) | |||||||
\(912\) | 12.8058 | − | 2.68689i | 0.424043 | − | 0.0889719i | ||||
\(913\) | −10.9330 | −0.361829 | ||||||||
\(914\) | 1.38259 | 0.0457321 | ||||||||
\(915\) | 8.35395 | + | 9.32706i | 0.276173 | + | 0.308343i | ||||
\(916\) | −26.3326 | + | 45.6094i | −0.870054 | + | 1.50698i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.224942 | − | 2.31520i | −0.00742419 | − | 0.0764130i | ||||
\(919\) | 25.7799 | + | 44.6521i | 0.850400 | + | 1.47294i | 0.880848 | + | 0.473400i | \(0.156973\pi\) |
−0.0304476 | + | 0.999536i | \(0.509693\pi\) | |||||||
\(920\) | 1.11640 | + | 1.93367i | 0.0368068 | + | 0.0637512i | ||||
\(921\) | −12.5271 | + | 38.2134i | −0.412783 | + | 1.25917i | ||||
\(922\) | −0.827569 | + | 1.43339i | −0.0272545 | + | 0.0472062i | ||||
\(923\) | 32.5447 | + | 56.3691i | 1.07122 | + | 1.85541i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.43211 | + | 7.67664i | −0.145727 | + | 0.252406i | ||||
\(926\) | 0.164263 | + | 0.284511i | 0.00539801 | + | 0.00934962i | ||||
\(927\) | 14.2240 | − | 6.24378i | 0.467178 | − | 0.205073i | ||||
\(928\) | −2.61290 | + | 4.52567i | −0.0857725 | + | 0.148562i | ||||
\(929\) | −50.2824 | −1.64971 | −0.824856 | − | 0.565343i | \(-0.808744\pi\) | ||||
−0.824856 | + | 0.565343i | \(0.808744\pi\) | |||||||
\(930\) | 1.41421 | + | 1.57895i | 0.0463738 | + | 0.0517757i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.6150 | − | 21.8499i | −0.413219 | − | 0.715717i | ||||
\(933\) | −0.966299 | + | 2.94764i | −0.0316352 | + | 0.0965016i | ||||
\(934\) | 0.931446 | + | 1.61331i | 0.0304779 | + | 0.0527892i | ||||
\(935\) | 13.9447 | − | 24.1529i | 0.456040 | − | 0.789885i | ||||
\(936\) | 0.472508 | − | 4.27963i | 0.0154444 | − | 0.139884i | ||||
\(937\) | 18.1400 | 0.592607 | 0.296303 | − | 0.955094i | \(-0.404246\pi\) | ||||
0.296303 | + | 0.955094i | \(0.404246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.48688 | + | 7.58609i | −0.0811561 | + | 0.247563i | ||||
\(940\) | −10.0966 | + | 17.4877i | −0.329313 | + | 0.570387i | ||||
\(941\) | −17.0332 | −0.555267 | −0.277633 | − | 0.960687i | \(-0.589550\pi\) | ||||
−0.277633 | + | 0.960687i | \(0.589550\pi\) | |||||||
\(942\) | 0.150255 | − | 0.458346i | 0.00489559 | − | 0.0149337i | ||||
\(943\) | −22.6844 | −0.738704 | ||||||||
\(944\) | −43.2658 | −1.40818 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.23154 | 0.0400408 | ||||||||
\(947\) | 31.5059 | 1.02381 | 0.511903 | − | 0.859044i | \(-0.328941\pi\) | ||||
0.511903 | + | 0.859044i | \(0.328941\pi\) | |||||||
\(948\) | 0.875856 | − | 2.67175i | 0.0284465 | − | 0.0867746i | ||||
\(949\) | 11.5512 | 0.374967 | ||||||||
\(950\) | −0.136271 | + | 0.236028i | −0.00442121 | + | 0.00765777i | ||||
\(951\) | 13.9658 | − | 42.6019i | 0.452871 | − | 1.38146i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.0677 | 0.520485 | 0.260242 | − | 0.965543i | \(-0.416197\pi\) | ||||
0.260242 | + | 0.965543i | \(0.416197\pi\) | |||||||
\(954\) | 1.67137 | − | 0.733664i | 0.0541125 | − | 0.0237533i | ||||
\(955\) | 3.78433 | − | 6.55465i | 0.122458 | − | 0.212104i | ||||
\(956\) | −15.3967 | − | 26.6679i | −0.497966 | − | 0.862502i | ||||
\(957\) | 5.51251 | − | 16.8156i | 0.178194 | − | 0.543572i | ||||
\(958\) | −0.701705 | − | 1.21539i | −0.0226711 | − | 0.0392674i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −24.2813 | − | 27.1097i | −0.783675 | − | 0.874962i | ||||
\(961\) | 14.1480 | 0.456388 | ||||||||
\(962\) | −0.759676 | + | 1.31580i | −0.0244929 | + | 0.0424230i | ||||
\(963\) | 5.58000 | − | 50.5396i | 0.179813 | − | 1.62862i | ||||
\(964\) | 1.17713 | + | 2.03884i | 0.0379126 | + | 0.0656666i | ||||
\(965\) | 11.7591 | − | 20.3674i | 0.378539 | − | 0.655649i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.3049 | + | 23.0448i | 0.427857 | + | 0.741069i | 0.996682 | − | 0.0813886i | \(-0.0259355\pi\) |
−0.568826 | + | 0.822458i | \(0.692602\pi\) | |||||||
\(968\) | −1.15319 | + | 1.99738i | −0.0370648 | + | 0.0641981i | ||||
\(969\) | 6.71868 | − | 20.4950i | 0.215835 | − | 0.658394i | ||||
\(970\) | −0.469219 | − | 0.812711i | −0.0150657 | − | 0.0260946i | ||||
\(971\) | 28.2839 | + | 48.9892i | 0.907674 | + | 1.57214i | 0.817287 | + | 0.576231i | \(0.195477\pi\) |
0.0903867 | + | 0.995907i | \(0.471190\pi\) | |||||||
\(972\) | 31.1014 | + | 0.407712i | 0.997577 | + | 0.0130774i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.883558 | + | 1.53037i | −0.0283110 | + | 0.0490361i | ||||
\(975\) | −12.7240 | − | 14.2062i | −0.407494 | − | 0.454961i | ||||
\(976\) | 10.7794 | 0.345040 | ||||||||
\(977\) | 53.7560 | 1.71981 | 0.859904 | − | 0.510456i | \(-0.170523\pi\) | ||||
0.859904 | + | 0.510456i | \(0.170523\pi\) | |||||||
\(978\) | −1.40501 | + | 0.294796i | −0.0449272 | + | 0.00942654i | ||||
\(979\) | 0.376252 | − | 0.651687i | 0.0120251 | − | 0.0208280i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.3493 | + | 10.2494i | −0.745485 | + | 0.327238i | ||||
\(982\) | −0.533847 | − | 0.924650i | −0.0170357 | − | 0.0295068i | ||||
\(983\) | −13.7051 | − | 23.7379i | −0.437125 | − | 0.757122i | 0.560342 | − | 0.828262i | \(-0.310670\pi\) |
−0.997466 | + | 0.0711394i | \(0.977336\pi\) | |||||||
\(984\) | −3.42347 | + | 0.718306i | −0.109136 | + | 0.0228988i | ||||
\(985\) | 7.62316 | − | 13.2037i | 0.242894 | − | 0.420705i | ||||
\(986\) | 1.43005 | + | 2.47692i | 0.0455421 | + | 0.0788813i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.96904 | − | 17.2669i | 0.317157 | − | 0.549333i | ||||
\(989\) | −17.2804 | − | 29.9305i | −0.549483 | − | 0.951733i | ||||
\(990\) | −0.704189 | − | 0.517286i | −0.0223806 | − | 0.0164404i | ||||
\(991\) | 8.66869 | − | 15.0146i | 0.275370 | − | 0.476955i | −0.694858 | − | 0.719147i | \(-0.744533\pi\) |
0.970228 | + | 0.242192i | \(0.0778663\pi\) | |||||||
\(992\) | 5.49587 | 0.174494 | ||||||||
\(993\) | −0.0870420 | + | 0.265517i | −0.00276220 | + | 0.00842594i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.2037 | − | 26.3335i | −0.481988 | − | 0.834828i | ||||
\(996\) | 15.7642 | + | 17.6005i | 0.499509 | + | 0.557694i | ||||
\(997\) | 17.8319 | + | 30.8858i | 0.564742 | + | 0.978162i | 0.997074 | + | 0.0764472i | \(0.0243576\pi\) |
−0.432332 | + | 0.901715i | \(0.642309\pi\) | |||||||
\(998\) | −0.727124 | + | 1.25942i | −0.0230167 | + | 0.0398661i | ||||
\(999\) | −20.0064 | − | 9.09664i | −0.632975 | − | 0.287805i |
(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 | 441.2.h.h.214.7 | 24 | ||
3.2 | odd | 2 | 1323.2.h.h.802.6 | 24 | |||
7.2 | even | 3 | 441.2.g.h.79.5 | 24 | |||
7.3 | odd | 6 | 441.2.f.h.295.5 | yes | 24 | ||
7.4 | even | 3 | 441.2.f.h.295.6 | yes | 24 | ||
7.5 | odd | 6 | 441.2.g.h.79.6 | 24 | |||
7.6 | odd | 2 | inner | 441.2.h.h.214.8 | 24 | ||
9.4 | even | 3 | 441.2.g.h.67.5 | 24 | |||
9.5 | odd | 6 | 1323.2.g.h.361.8 | 24 | |||
21.2 | odd | 6 | 1323.2.g.h.667.8 | 24 | |||
21.5 | even | 6 | 1323.2.g.h.667.7 | 24 | |||
21.11 | odd | 6 | 1323.2.f.h.883.7 | 24 | |||
21.17 | even | 6 | 1323.2.f.h.883.8 | 24 | |||
21.20 | even | 2 | 1323.2.h.h.802.5 | 24 | |||
63.4 | even | 3 | 441.2.f.h.148.6 | yes | 24 | ||
63.5 | even | 6 | 1323.2.h.h.226.5 | 24 | |||
63.11 | odd | 6 | 3969.2.a.bi.1.6 | 12 | |||
63.13 | odd | 6 | 441.2.g.h.67.6 | 24 | |||
63.23 | odd | 6 | 1323.2.h.h.226.6 | 24 | |||
63.25 | even | 3 | 3969.2.a.bh.1.7 | 12 | |||
63.31 | odd | 6 | 441.2.f.h.148.5 | ✓ | 24 | ||
63.32 | odd | 6 | 1323.2.f.h.442.7 | 24 | |||
63.38 | even | 6 | 3969.2.a.bi.1.5 | 12 | |||
63.40 | odd | 6 | inner | 441.2.h.h.373.8 | 24 | ||
63.41 | even | 6 | 1323.2.g.h.361.7 | 24 | |||
63.52 | odd | 6 | 3969.2.a.bh.1.8 | 12 | |||
63.58 | even | 3 | inner | 441.2.h.h.373.7 | 24 | ||
63.59 | even | 6 | 1323.2.f.h.442.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.5 | ✓ | 24 | 63.31 | odd | 6 | ||
441.2.f.h.148.6 | yes | 24 | 63.4 | even | 3 | ||
441.2.f.h.295.5 | yes | 24 | 7.3 | odd | 6 | ||
441.2.f.h.295.6 | yes | 24 | 7.4 | even | 3 | ||
441.2.g.h.67.5 | 24 | 9.4 | even | 3 | |||
441.2.g.h.67.6 | 24 | 63.13 | odd | 6 | |||
441.2.g.h.79.5 | 24 | 7.2 | even | 3 | |||
441.2.g.h.79.6 | 24 | 7.5 | odd | 6 | |||
441.2.h.h.214.7 | 24 | 1.1 | even | 1 | trivial | ||
441.2.h.h.214.8 | 24 | 7.6 | odd | 2 | inner | ||
441.2.h.h.373.7 | 24 | 63.58 | even | 3 | inner | ||
441.2.h.h.373.8 | 24 | 63.40 | odd | 6 | inner | ||
1323.2.f.h.442.7 | 24 | 63.32 | odd | 6 | |||
1323.2.f.h.442.8 | 24 | 63.59 | even | 6 | |||
1323.2.f.h.883.7 | 24 | 21.11 | odd | 6 | |||
1323.2.f.h.883.8 | 24 | 21.17 | even | 6 | |||
1323.2.g.h.361.7 | 24 | 63.41 | even | 6 | |||
1323.2.g.h.361.8 | 24 | 9.5 | odd | 6 | |||
1323.2.g.h.667.7 | 24 | 21.5 | even | 6 | |||
1323.2.g.h.667.8 | 24 | 21.2 | odd | 6 | |||
1323.2.h.h.226.5 | 24 | 63.5 | even | 6 | |||
1323.2.h.h.226.6 | 24 | 63.23 | odd | 6 | |||
1323.2.h.h.802.5 | 24 | 21.20 | even | 2 | |||
1323.2.h.h.802.6 | 24 | 3.2 | odd | 2 | |||
3969.2.a.bh.1.7 | 12 | 63.25 | even | 3 | |||
3969.2.a.bh.1.8 | 12 | 63.52 | odd | 6 | |||
3969.2.a.bi.1.5 | 12 | 63.38 | even | 6 | |||
3969.2.a.bi.1.6 | 12 | 63.11 | odd | 6 |