Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(148,441)]
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([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.52140272914\) |
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 | 295.6 | ||
Character | \(\chi\) | \(=\) | 441.295 |
Dual form | 441.2.f.h.148.6 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0341870 | + | 0.0592136i | −0.0241739 | + | 0.0418703i | −0.877859 | − | 0.478919i | \(-0.841029\pi\) |
0.853685 | + | 0.520789i | \(0.174362\pi\) | |||||||
\(3\) | 1.69514 | − | 0.355671i | 0.978689 | − | 0.205347i | ||||
\(4\) | 0.997662 | + | 1.72800i | 0.498831 | + | 0.864001i | ||||
\(5\) | 1.33190 | + | 2.30691i | 0.595642 | + | 1.03168i | 0.993456 | + | 0.114216i | \(0.0364355\pi\) |
−0.397814 | + | 0.917466i | \(0.630231\pi\) | |||||||
\(6\) | −0.0368912 | + | 0.112535i | −0.0150608 | + | 0.0459421i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.273176 | −0.0965824 | ||||||||
\(9\) | 2.74700 | − | 1.20582i | 0.915666 | − | 0.401941i | ||||
\(10\) | −0.182134 | −0.0575958 | ||||||||
\(11\) | 0.799563 | − | 1.38488i | 0.241077 | − | 0.417558i | −0.719944 | − | 0.694032i | \(-0.755833\pi\) |
0.961021 | + | 0.276474i | \(0.0891659\pi\) | |||||||
\(12\) | 2.30578 | + | 2.57437i | 0.665620 | + | 0.743155i | ||||
\(13\) | −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 | ||||
\(16\) | −1.98599 | + | 3.43983i | −0.496496 | + | 0.859957i | ||||
\(17\) | −6.54721 | −1.58793 | −0.793966 | − | 0.607963i | \(-0.791987\pi\) | ||||
−0.793966 | + | 0.607963i | \(0.791987\pi\) | |||||||
\(18\) | −0.0225104 | + | 0.203883i | −0.00530576 | + | 0.0480557i | ||||
\(19\) | 1.90194 | 0.436334 | 0.218167 | − | 0.975911i | \(-0.429992\pi\) | ||||
0.218167 | + | 0.975911i | \(0.429992\pi\) | |||||||
\(20\) | −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 | 0.980467 | − | 0.196684i | \(-0.0630173\pi\) |
−0.660567 | + | 0.750767i | \(0.729684\pi\) | |||||||
\(24\) | −0.463072 | + | 0.0971608i | −0.0945242 | + | 0.0198329i | ||||
\(25\) | −1.04789 | + | 1.81500i | −0.209578 | + | 0.363000i | ||||
\(26\) | 0.359223 | 0.0704495 | ||||||||
\(27\) | 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 | \(0.964528\pi\) | |||||||
\(30\) | −0.308743 | + | 0.0647797i | −0.0563684 | + | 0.0118271i | ||||
\(31\) | −3.35961 | − | 5.81902i | −0.603405 | − | 1.04513i | −0.992301 | − | 0.123846i | \(-0.960477\pi\) |
0.388897 | − | 0.921281i | \(-0.372856\pi\) | |||||||
\(32\) | −0.408966 | − | 0.708350i | −0.0722957 | − | 0.125220i | ||||
\(33\) | 0.862809 | − | 2.63195i | 0.150196 | − | 0.458164i | ||||
\(34\) | 0.223829 | − | 0.387684i | 0.0383864 | − | 0.0664872i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.82424 | + | 3.54381i | 0.804040 | + | 0.590635i | ||||
\(37\) | 4.22955 | 0.695333 | 0.347667 | − | 0.937618i | \(-0.386974\pi\) | ||||
0.347667 | + | 0.937618i | \(0.386974\pi\) | |||||||
\(38\) | −0.0650215 | + | 0.112621i | −0.0105479 | + | 0.0182695i | ||||
\(39\) | −6.07124 | − | 6.77845i | −0.972176 | − | 1.08542i | ||||
\(40\) | −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 | \(-0.162145\pi\) | |||||||
\(44\) | 3.19078 | 0.481028 | ||||||||
\(45\) | 6.44044 | + | 4.73105i | 0.960084 | + | 0.705263i | ||||
\(46\) | −0.209797 | −0.0309329 | ||||||||
\(47\) | −1.89959 | + | 3.29018i | −0.277083 | + | 0.479922i | −0.970659 | − | 0.240462i | \(-0.922701\pi\) |
0.693575 | + | 0.720384i | \(0.256034\pi\) | |||||||
\(48\) | −2.14308 | + | 6.53735i | −0.309327 | + | 0.943585i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.0716485 | − | 0.124099i | −0.0101326 | − | 0.0175502i | ||||
\(51\) | −11.0984 | + | 2.32865i | −1.55409 | + | 0.326076i | ||||
\(52\) | 5.24152 | − | 9.07858i | 0.726868 | − | 1.25897i | ||||
\(53\) | 8.89862 | 1.22232 | 0.611160 | − | 0.791507i | \(-0.290703\pi\) | ||||
0.611160 | + | 0.791507i | \(0.290703\pi\) | |||||||
\(54\) | 0.0343569 | + | 0.353616i | 0.00467539 | + | 0.0481211i | ||||
\(55\) | 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 | ||||
\(59\) | 5.44639 | + | 9.43343i | 0.709060 | + | 1.22813i | 0.965206 | + | 0.261490i | \(0.0842138\pi\) |
−0.256146 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(60\) | −2.86778 | + | 8.74801i | −0.370228 | + | 1.12936i | ||||
\(61\) | −1.35693 | + | 2.35027i | −0.173737 | + | 0.300922i | −0.939724 | − | 0.341935i | \(-0.888918\pi\) |
0.765986 | + | 0.642857i | \(0.222251\pi\) | |||||||
\(62\) | 0.459420 | 0.0583465 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.88802 | −0.986002 | ||||||||
\(65\) | 6.99751 | − | 12.1200i | 0.867935 | − | 1.50331i | ||||
\(66\) | 0.126351 | + | 0.141069i | 0.0155527 | + | 0.0173643i | ||||
\(67\) | 1.66267 | + | 2.87982i | 0.203127 | + | 0.351826i | 0.949534 | − | 0.313663i | \(-0.101556\pi\) |
−0.746407 | + | 0.665489i | \(0.768223\pi\) | |||||||
\(68\) | −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 | \(0.762890\pi\) | |||||||
\(72\) | −0.750414 | + | 0.329402i | −0.0884372 | + | 0.0388204i | ||||
\(73\) | 2.19863 | 0.257331 | 0.128665 | − | 0.991688i | \(-0.458931\pi\) | ||||
0.128665 | + | 0.991688i | \(0.458931\pi\) | |||||||
\(74\) | −0.144596 | + | 0.250447i | −0.0168089 | + | 0.0291138i | ||||
\(75\) | −1.13078 | + | 3.44939i | −0.130571 | + | 0.398301i | ||||
\(76\) | 1.89749 | + | 3.28655i | 0.217657 | + | 0.376993i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.608933 | − | 0.127765i | 0.0689481 | − | 0.0144666i | ||||
\(79\) | −0.406778 | + | 0.704560i | −0.0457661 | + | 0.0792692i | −0.888001 | − | 0.459841i | \(-0.847906\pi\) |
0.842235 | + | 0.539111i | \(0.181240\pi\) | |||||||
\(80\) | −10.5805 | −1.18294 | ||||||||
\(81\) | 6.09198 | − | 6.62478i | 0.676887 | − | 0.736087i | ||||
\(82\) | 0.505486 | 0.0558216 | ||||||||
\(83\) | −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 | ||||
\(87\) | −3.44720 | + | 10.5155i | −0.369579 | + | 1.12738i | ||||
\(88\) | −0.218422 | + | 0.378317i | −0.0232838 | + | 0.0403288i | ||||
\(89\) | 0.470572 | 0.0498805 | 0.0249403 | − | 0.999689i | \(-0.492060\pi\) | ||||
0.0249403 | + | 0.999689i | \(0.492060\pi\) | |||||||
\(90\) | −0.500321 | + | 0.219621i | −0.0527385 | + | 0.0231501i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.06120 | + | 5.30216i | −0.319152 | + | 0.552788i | ||||
\(93\) | −7.76467 | − | 8.66914i | −0.805159 | − | 0.898948i | ||||
\(94\) | −0.129882 | − | 0.224963i | −0.0133963 | − | 0.0232031i | ||||
\(95\) | 2.53318 | + | 4.38760i | 0.259899 | + | 0.450158i | ||||
\(96\) | −0.945194 | − | 1.05529i | −0.0964684 | − | 0.107706i | ||||
\(97\) | 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 | ||||
\(100\) | −4.18177 | −0.418177 | ||||||||
\(101\) | 0.922440 | − | 1.59771i | 0.0917862 | − | 0.158978i | −0.816477 | − | 0.577379i | \(-0.804076\pi\) |
0.908263 | + | 0.418400i | \(0.137409\pi\) | |||||||
\(102\) | 0.241534 | − | 0.736788i | 0.0239155 | − | 0.0729529i | ||||
\(103\) | −2.58901 | − | 4.48430i | −0.255103 | − | 0.441851i | 0.709821 | − | 0.704383i | \(-0.248776\pi\) |
−0.964923 | + | 0.262531i | \(0.915443\pi\) | |||||||
\(104\) | 0.717607 | + | 1.24293i | 0.0703671 | + | 0.121879i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.304217 | + | 0.526920i | −0.0295482 | + | 0.0511790i | ||||
\(107\) | −16.9489 | −1.63851 | −0.819256 | − | 0.573428i | \(-0.805613\pi\) | ||||
−0.819256 | + | 0.573428i | \(0.805613\pi\) | |||||||
\(108\) | 9.43819 | + | 4.29141i | 0.908190 | + | 0.412942i | ||||
\(109\) | −8.49992 | −0.814145 | −0.407073 | − | 0.913396i | \(-0.633450\pi\) | ||||
−0.407073 | + | 0.913396i | \(0.633450\pi\) | |||||||
\(110\) | −0.145628 | + | 0.252235i | −0.0138851 | + | 0.0240496i | ||||
\(111\) | 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 | \(0.892116\pi\) | |||||||
\(114\) | −0.0701647 | + | 0.214034i | −0.00657152 | + | 0.0200461i | ||||
\(115\) | −4.08675 | + | 7.07847i | −0.381092 | + | 0.660070i | ||||
\(116\) | −12.7482 | −1.18364 | ||||||||
\(117\) | −12.7025 | − | 9.33105i | −1.17435 | − | 0.862656i | ||||
\(118\) | −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 | ||||
\(122\) | −0.0927788 | − | 0.160698i | −0.00839980 | − | 0.0145489i | ||||
\(123\) | −8.54323 | − | 9.53838i | −0.770317 | − | 0.860047i | ||||
\(124\) | 6.70352 | − | 11.6108i | 0.601994 | − | 1.04268i | ||||
\(125\) | 7.73623 | 0.691949 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9533 | 0.971946 | 0.485973 | − | 0.873974i | \(-0.338465\pi\) | ||||
0.485973 | + | 0.873974i | \(0.338465\pi\) | |||||||
\(128\) | 1.08760 | − | 1.88378i | 0.0961311 | − | 0.166504i | ||||
\(129\) | 6.07724 | − | 18.5383i | 0.535071 | − | 1.63221i | ||||
\(130\) | 0.478448 | + | 0.828696i | 0.0419626 | + | 0.0726814i | ||||
\(131\) | 2.22671 | + | 3.85678i | 0.194549 | + | 0.336968i | 0.946752 | − | 0.321962i | \(-0.104342\pi\) |
−0.752204 | + | 0.658931i | \(0.771009\pi\) | |||||||
\(132\) | 5.40881 | − | 1.13487i | 0.470777 | − | 0.0987774i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.227366 | −0.0196414 | ||||||||
\(135\) | 12.6001 | + | 5.72911i | 1.08445 | + | 0.493083i | ||||
\(136\) | 1.78854 | 0.153366 | ||||||||
\(137\) | 9.76800 | − | 16.9187i | 0.834537 | − | 1.44546i | −0.0598699 | − | 0.998206i | \(-0.519069\pi\) |
0.894407 | − | 0.447254i | \(-0.147598\pi\) | |||||||
\(138\) | −0.355635 | + | 0.0746186i | −0.0302737 | + | 0.00635196i | ||||
\(139\) | −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 | ||||
\(142\) | 0.423544 | − | 0.733599i | 0.0355430 | − | 0.0615623i | ||||
\(143\) | −8.40149 | −0.702568 | ||||||||
\(144\) | −1.30767 | + | 11.8439i | −0.108973 | + | 0.986995i | ||||
\(145\) | −17.0190 | −1.41335 | ||||||||
\(146\) | −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 | 0.988124 | − | 0.153662i | \(-0.0491066\pi\) |
−0.627137 | + | 0.778909i | \(0.715773\pi\) | |||||||
\(150\) | −0.165593 | − | 0.184882i | −0.0135206 | − | 0.0150955i | ||||
\(151\) | −2.33211 | + | 4.03933i | −0.189784 | + | 0.328716i | −0.945178 | − | 0.326555i | \(-0.894112\pi\) |
0.755394 | + | 0.655271i | \(0.227446\pi\) | |||||||
\(152\) | −0.519564 | −0.0421422 | ||||||||
\(153\) | −17.9852 | + | 7.89478i | −1.45401 | + | 0.638255i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.94931 | − | 15.5007i | 0.718826 | − | 1.24504i | ||||
\(156\) | 5.65612 | − | 17.2537i | 0.452852 | − | 1.38140i | ||||
\(157\) | 2.03647 | + | 3.52727i | 0.162528 | + | 0.281506i | 0.935775 | − | 0.352599i | \(-0.114702\pi\) |
−0.773247 | + | 0.634105i | \(0.781369\pi\) | |||||||
\(158\) | −0.0278130 | − | 0.0481736i | −0.00221269 | − | 0.00383249i | ||||
\(159\) | 15.0844 | − | 3.16498i | 1.19627 | − | 0.250999i | ||||
\(160\) | 1.08940 | − | 1.88690i | 0.0861246 | − | 0.149172i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.184011 | + | 0.587210i | 0.0144573 | + | 0.0461355i | ||||
\(163\) | −12.1222 | −0.949487 | −0.474744 | − | 0.880124i | \(-0.657459\pi\) | ||||
−0.474744 | + | 0.880124i | \(0.657459\pi\) | |||||||
\(164\) | 7.37568 | − | 12.7750i | 0.575944 | − | 0.997564i | ||||
\(165\) | 7.22085 | − | 1.51506i | 0.562143 | − | 0.117948i | ||||
\(166\) | −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 | ||||
\(170\) | 1.19247 | 0.0914582 | ||||||||
\(171\) | 5.22461 | − | 2.29340i | 0.399536 | − | 0.175381i | ||||
\(172\) | 22.4744 | 1.71366 | ||||||||
\(173\) | −2.51585 | + | 4.35759i | −0.191277 | + | 0.331301i | −0.945674 | − | 0.325118i | \(-0.894596\pi\) |
0.754397 | + | 0.656419i | \(0.227929\pi\) | |||||||
\(174\) | −0.504812 | − | 0.563615i | −0.0382697 | − | 0.0427275i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.17584 | + | 5.50072i | 0.239388 | + | 0.414632i | ||||
\(177\) | 12.5876 | + | 14.0539i | 0.946141 | + | 1.05635i | ||||
\(178\) | −0.0160874 | + | 0.0278642i | −0.00120580 | + | 0.00208851i | ||||
\(179\) | −16.3979 | −1.22564 | −0.612819 | − | 0.790224i | \(-0.709964\pi\) | ||||
−0.612819 | + | 0.790224i | \(0.709964\pi\) | |||||||
\(180\) | −1.74987 | + | 15.8491i | −0.130428 | + | 1.18132i | ||||
\(181\) | −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 | ||||
\(185\) | 5.63332 | + | 9.75719i | 0.414170 | + | 0.717363i | ||||
\(186\) | 0.778782 | − | 0.163402i | 0.0571031 | − | 0.0119812i | ||||
\(187\) | −5.23491 | + | 9.06713i | −0.382814 | + | 0.663054i | ||||
\(188\) | −7.58059 | −0.552871 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.346407 | −0.0251310 | ||||||||
\(191\) | −1.42066 | + | 2.46065i | −0.102795 | + | 0.178046i | −0.912835 | − | 0.408328i | \(-0.866112\pi\) |
0.810040 | + | 0.586374i | \(0.199445\pi\) | |||||||
\(192\) | −13.3713 | + | 2.80554i | −0.964990 | + | 0.202472i | ||||
\(193\) | −4.41443 | − | 7.64601i | −0.317758 | − | 0.550372i | 0.662262 | − | 0.749272i | \(-0.269596\pi\) |
−0.980020 | + | 0.198900i | \(0.936263\pi\) | |||||||
\(194\) | 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 | \(0.434641\pi\) | |||||||
\(198\) | 0.264356 | + | 0.194192i | 0.0187870 | + | 0.0138006i | ||||
\(199\) | −11.4150 | −0.809191 | −0.404596 | − | 0.914496i | \(-0.632588\pi\) | ||||
−0.404596 | + | 0.914496i | \(0.632588\pi\) | |||||||
\(200\) | 0.286259 | − | 0.495815i | 0.0202416 | − | 0.0350594i | ||||
\(201\) | 3.84272 | + | 4.29034i | 0.271044 | + | 0.302617i | ||||
\(202\) | 0.0630709 | + | 0.109242i | 0.00443765 | + | 0.00768624i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −15.0964 | − | 16.8549i | −1.05696 | − | 1.18008i | ||||
\(205\) | 9.84665 | − | 17.0549i | 0.687720 | − | 1.19117i | ||||
\(206\) | 0.354042 | 0.0246673 | ||||||||
\(207\) | 7.41863 | + | 5.44961i | 0.515630 | + | 0.378774i | ||||
\(208\) | 20.8679 | 1.44693 | ||||||||
\(209\) | 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 | ||||
\(213\) | −21.0011 | + | 4.40642i | −1.43897 | + | 0.301923i | ||||
\(214\) | 0.579432 | − | 1.00361i | 0.0396091 | − | 0.0686050i | ||||
\(215\) | 30.0037 | 2.04623 | ||||||||
\(216\) | −1.15490 | + | 0.825283i | −0.0785809 | + | 0.0561534i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.290587 | − | 0.503311i | 0.0196810 | − | 0.0340885i | ||||
\(219\) | 3.72699 | − | 0.781990i | 0.251847 | − | 0.0528420i | ||||
\(220\) | 4.24978 | + | 7.36084i | 0.286520 | + | 0.496268i | ||||
\(221\) | 17.1989 | + | 29.7893i | 1.15692 | + | 2.00385i | ||||
\(222\) | −0.156033 | + | 0.475971i | −0.0104722 | + | 0.0319451i | ||||
\(223\) | −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 | ||||
\(226\) | 0.266926 | 0.0177557 | ||||||||
\(227\) | 6.89434 | − | 11.9413i | 0.457593 | − | 0.792575i | −0.541240 | − | 0.840868i | \(-0.682045\pi\) |
0.998833 | + | 0.0482933i | \(0.0153782\pi\) | |||||||
\(228\) | 4.38544 | + | 4.89628i | 0.290433 | + | 0.324264i | ||||
\(229\) | 13.1972 | + | 22.8581i | 0.872092 | + | 1.51051i | 0.859828 | + | 0.510584i | \(0.170571\pi\) |
0.0122645 | + | 0.999925i | \(0.496096\pi\) | |||||||
\(230\) | −0.279428 | − | 0.483983i | −0.0184249 | − | 0.0319129i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.872666 | − | 1.51150i | 0.0572933 | − | 0.0992349i | ||||
\(233\) | −12.6446 | −0.828375 | −0.414187 | − | 0.910192i | \(-0.635934\pi\) | ||||
−0.414187 | + | 0.910192i | \(0.635934\pi\) | |||||||
\(234\) | 0.986785 | − | 0.433160i | 0.0645081 | − | 0.0283165i | ||||
\(235\) | −10.1202 | −0.660170 | ||||||||
\(236\) | −10.8673 | + | 18.8228i | −0.707403 | + | 1.22526i | ||||
\(237\) | −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 | \(0.666985\pi\) | |||||||
\(240\) | −17.9354 | + | 3.76318i | −1.15773 | + | 0.242912i | ||||
\(241\) | −0.589942 | + | 1.02181i | −0.0380015 | + | 0.0658205i | −0.884401 | − | 0.466729i | \(-0.845432\pi\) |
0.846399 | + | 0.532549i | \(0.178766\pi\) | |||||||
\(242\) | −0.577267 | −0.0371082 | ||||||||
\(243\) | 7.97052 | − | 13.3967i | 0.511309 | − | 0.859397i | ||||
\(244\) | −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 | ||||
\(248\) | 0.917767 | + | 1.58962i | 0.0582783 | + | 0.100941i | ||||
\(249\) | −3.68882 | + | 11.2525i | −0.233769 | + | 0.713101i | ||||
\(250\) | −0.264478 | + | 0.458090i | −0.0167271 | + | 0.0289721i | ||||
\(251\) | 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 | ||||||||
\(254\) | −0.374459 | + | 0.648583i | −0.0234957 | + | 0.0406957i | ||||
\(255\) | −20.1539 | − | 22.5016i | −1.26209 | − | 1.40910i | ||||
\(256\) | −7.81365 | − | 13.5336i | −0.488353 | − | 0.845853i | ||||
\(257\) | −4.91538 | − | 8.51369i | −0.306613 | − | 0.531069i | 0.671006 | − | 0.741452i | \(-0.265862\pi\) |
−0.977619 | + | 0.210382i | \(0.932529\pi\) | |||||||
\(258\) | 0.889957 | + | 0.993623i | 0.0554063 | + | 0.0618603i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 27.9246 | 1.73181 | ||||||||
\(261\) | −2.10343 | + | 19.0513i | −0.130199 | + | 1.17925i | ||||
\(262\) | −0.304498 | −0.0188120 | ||||||||
\(263\) | −5.96612 | + | 10.3336i | −0.367887 | + | 0.637199i | −0.989235 | − | 0.146336i | \(-0.953252\pi\) |
0.621348 | + | 0.783535i | \(0.286585\pi\) | |||||||
\(264\) | −0.235699 | + | 0.718987i | −0.0145063 | + | 0.0442506i | ||||
\(265\) | 11.8520 | + | 20.5283i | 0.728065 | + | 1.26105i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.797685 | − | 0.167369i | 0.0488175 | − | 0.0102428i | ||||
\(268\) | −3.31756 | + | 5.74618i | −0.202652 | + | 0.351004i | ||||
\(269\) | 29.9648 | 1.82699 | 0.913494 | − | 0.406853i | \(-0.133374\pi\) | ||||
0.913494 | + | 0.406853i | \(0.133374\pi\) | |||||||
\(270\) | −0.770002 | + | 0.550239i | −0.0468608 | + | 0.0334865i | ||||
\(271\) | −7.09650 | −0.431082 | −0.215541 | − | 0.976495i | \(-0.569151\pi\) | ||||
−0.215541 | + | 0.976495i | \(0.569151\pi\) | |||||||
\(272\) | 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 | ||||
\(276\) | −3.30334 | + | 10.0767i | −0.198838 | + | 0.606545i | ||||
\(277\) | 4.91175 | − | 8.50741i | 0.295119 | − | 0.511161i | −0.679894 | − | 0.733311i | \(-0.737974\pi\) |
0.975013 | + | 0.222150i | \(0.0713075\pi\) | |||||||
\(278\) | 0.179878 | 0.0107883 | ||||||||
\(279\) | −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 | \(-0.0856403\pi\) | |||||||
\(282\) | −0.300181 | − | 0.335148i | −0.0178755 | − | 0.0199578i | ||||
\(283\) | 1.50798 | + | 2.61189i | 0.0896399 | + | 0.155261i | 0.907359 | − | 0.420357i | \(-0.138095\pi\) |
−0.817719 | + | 0.575618i | \(0.804762\pi\) | |||||||
\(284\) | −12.3601 | − | 21.4083i | −0.733435 | − | 1.27035i | ||||
\(285\) | 5.85464 | + | 6.53661i | 0.346799 | + | 0.387196i | ||||
\(286\) | 0.287222 | − | 0.497483i | 0.0169838 | − | 0.0294168i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.97757 | − | 1.45269i | −0.116530 | − | 0.0856008i | ||||
\(289\) | 25.8659 | 1.52153 | ||||||||
\(290\) | 0.581830 | − | 1.00776i | 0.0341662 | − | 0.0591776i | ||||
\(291\) | 2.78001 | − | 8.48027i | 0.162967 | − | 0.497123i | ||||
\(292\) | 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 | ||||
\(296\) | −1.15541 | −0.0671570 | ||||||||
\(297\) | −0.803538 | − | 8.27036i | −0.0466260 | − | 0.479895i | ||||
\(298\) | −0.602567 | −0.0349058 | ||||||||
\(299\) | 8.06031 | − | 13.9609i | 0.466140 | − | 0.807378i | ||||
\(300\) | −7.08868 | + | 1.48733i | −0.409265 | + | 0.0858712i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.159456 | − | 0.276185i | −0.00917564 | − | 0.0158927i | ||||
\(303\) | 0.995404 | − | 3.03643i | 0.0571845 | − | 0.174438i | ||||
\(304\) | −3.77722 | + | 6.54234i | −0.216638 | + | 0.375229i | ||||
\(305\) | −7.22917 | −0.413941 | ||||||||
\(306\) | 0.147380 | − | 1.33486i | 0.00842518 | − | 0.0763091i | ||||
\(307\) | 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 | ||||
\(311\) | −0.895467 | − | 1.55100i | −0.0507773 | − | 0.0879489i | 0.839520 | − | 0.543329i | \(-0.182837\pi\) |
−0.890297 | + | 0.455381i | \(0.849503\pi\) | |||||||
\(312\) | 1.65852 | + | 1.85171i | 0.0938951 | + | 0.104832i | ||||
\(313\) | −2.30458 | + | 3.99166i | −0.130263 | + | 0.225622i | −0.923778 | − | 0.382929i | \(-0.874915\pi\) |
0.793515 | + | 0.608551i | \(0.208249\pi\) | |||||||
\(314\) | −0.278483 | −0.0157157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.62331 | −0.0913183 | ||||||||
\(317\) | 12.9421 | − | 22.4163i | 0.726898 | − | 1.25902i | −0.231290 | − | 0.972885i | \(-0.574295\pi\) |
0.958188 | − | 0.286140i | \(-0.0923721\pi\) | |||||||
\(318\) | −0.328281 | + | 1.00140i | −0.0184091 | + | 0.0561559i | ||||
\(319\) | 5.10843 | + | 8.84807i | 0.286017 | + | 0.495397i | ||||
\(320\) | −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 | ||||||||
\(324\) | 17.5254 | + | 3.91766i | 0.973632 | + | 0.217648i | ||||
\(325\) | 11.0108 | 0.610771 | ||||||||
\(326\) | 0.414423 | − | 0.717802i | 0.0229528 | − | 0.0397554i | ||||
\(327\) | −14.4086 | + | 3.02317i | −0.796795 | + | 0.167182i | ||||
\(328\) | 1.00979 | + | 1.74901i | 0.0557563 | + | 0.0965728i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.157147 | + | 0.479368i | −0.00865065 | + | 0.0263884i | ||||
\(331\) | −0.0806617 | + | 0.139710i | −0.00443357 | + | 0.00767917i | −0.868234 | − | 0.496156i | \(-0.834745\pi\) |
0.863800 | + | 0.503835i | \(0.168078\pi\) | |||||||
\(332\) | −13.6417 | −0.748687 | ||||||||
\(333\) | 11.6186 | − | 5.10009i | 0.636693 | − | 0.279483i | ||||
\(334\) | −0.328128 | −0.0179544 | ||||||||
\(335\) | −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 | ||||
\(339\) | −4.51133 | − | 5.03683i | −0.245022 | − | 0.273563i | ||||
\(340\) | 17.3996 | − | 30.1370i | 0.943627 | − | 1.63441i | ||||
\(341\) | −10.7449 | −0.581869 | ||||||||
\(342\) | −0.0428134 | + | 0.387773i | −0.00231508 | + | 0.0209683i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.53846 | + | 2.66470i | −0.0829484 | + | 0.143671i | ||||
\(345\) | −4.41002 | + | 13.4525i | −0.237427 | + | 0.724260i | ||||
\(346\) | −0.172019 | − | 0.297945i | −0.00924779 | − | 0.0160176i | ||||
\(347\) | 2.90984 | + | 5.03999i | 0.156208 | + | 0.270561i | 0.933498 | − | 0.358582i | \(-0.116740\pi\) |
−0.777290 | + | 0.629142i | \(0.783406\pi\) | |||||||
\(348\) | −21.6100 | + | 4.53416i | −1.15842 | + | 0.243056i | ||||
\(349\) | −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 | ||||
\(352\) | −1.30798 | −0.0697154 | ||||||||
\(353\) | 12.0948 | − | 20.9488i | 0.643741 | − | 1.11499i | −0.340850 | − | 0.940118i | \(-0.610715\pi\) |
0.984591 | − | 0.174874i | \(-0.0559517\pi\) | |||||||
\(354\) | −1.26251 | + | 0.264898i | −0.0671017 | + | 0.0140791i | ||||
\(355\) | −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 | ||||
\(359\) | −21.0376 | −1.11032 | −0.555161 | − | 0.831743i | \(-0.687343\pi\) | ||||
−0.555161 | + | 0.831743i | \(0.687343\pi\) | |||||||
\(360\) | −1.75938 | − | 1.29241i | −0.0927272 | − | 0.0681160i | ||||
\(361\) | −15.3826 | −0.809612 | ||||||||
\(362\) | 0.493472 | − | 0.854719i | 0.0259363 | − | 0.0449230i | ||||
\(363\) | 9.75641 | + | 10.8929i | 0.512079 | + | 0.571728i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.92835 | + | 5.07205i | 0.153277 | + | 0.265483i | ||||
\(366\) | −0.214428 | − | 0.239406i | −0.0112084 | − | 0.0125140i | ||||
\(367\) | −17.5190 | + | 30.3438i | −0.914485 | + | 1.58393i | −0.106831 | + | 0.994277i | \(0.534070\pi\) |
−0.807654 | + | 0.589657i | \(0.799263\pi\) | |||||||
\(368\) | −12.1875 | −0.635317 | ||||||||
\(369\) | −17.8745 | − | 13.1303i | −0.930509 | − | 0.683537i | ||||
\(370\) | −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 | 0.851046 | − | 0.525091i | \(-0.175969\pi\) |
−0.880265 | + | 0.474482i | \(0.842635\pi\) | |||||||
\(374\) | −0.357931 | − | 0.619955i | −0.0185082 | − | 0.0320571i | ||||
\(375\) | 13.1140 | − | 2.75155i | 0.677203 | − | 0.142089i | ||||
\(376\) | 0.518922 | − | 0.898800i | 0.0267614 | − | 0.0463521i | ||||
\(377\) | 33.5667 | 1.72877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9619 | −1.12811 | −0.564054 | − | 0.825738i | \(-0.690759\pi\) | ||||
−0.564054 | + | 0.825738i | \(0.690759\pi\) | |||||||
\(380\) | −5.05452 | + | 8.75468i | −0.259291 | + | 0.449106i | ||||
\(381\) | 18.5673 | − | 3.89576i | 0.951233 | − | 0.199586i | ||||
\(382\) | −0.0971359 | − | 0.168244i | −0.00496991 | − | 0.00860813i | ||||
\(383\) | 11.5200 | + | 19.9533i | 0.588647 | + | 1.01957i | 0.994410 | + | 0.105588i | \(0.0336724\pi\) |
−0.405763 | + | 0.913978i | \(0.632994\pi\) | |||||||
\(384\) | 1.17363 | − | 3.58009i | 0.0598915 | − | 0.182696i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.603664 | 0.0307257 | ||||||||
\(387\) | 3.70823 | − | 33.5865i | 0.188500 | − | 1.70730i | ||||
\(388\) | 10.2808 | 0.521930 | ||||||||
\(389\) | −7.88753 | + | 13.6616i | −0.399914 | + | 0.692671i | −0.993715 | − | 0.111941i | \(-0.964293\pi\) |
0.593801 | + | 0.804612i | \(0.297627\pi\) | |||||||
\(390\) | 1.10578 | + | 1.23459i | 0.0559933 | + | 0.0625157i | ||||
\(391\) | −10.0446 | − | 17.3978i | −0.507979 | − | 0.879846i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.14633 | + | 5.74580i | 0.259598 | + | 0.289837i | ||||
\(394\) | −0.195671 | + | 0.338912i | −0.00985774 | + | 0.0170741i | ||||
\(395\) | −2.16714 | −0.109041 | ||||||||
\(396\) | 8.76505 | − | 3.84751i | 0.440461 | − | 0.193345i | ||||
\(397\) | 16.5055 | 0.828389 | 0.414195 | − | 0.910188i | \(-0.364063\pi\) | ||||
0.414195 | + | 0.910188i | \(0.364063\pi\) | |||||||
\(398\) | 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 | −0.998857 | − | 0.0477986i | \(-0.984779\pi\) |
0.458034 | − | 0.888935i | \(-0.348554\pi\) | |||||||
\(402\) | −0.385417 | + | 0.0808675i | −0.0192229 | + | 0.00403330i | ||||
\(403\) | −17.6507 | + | 30.5720i | −0.879246 | + | 1.52290i | ||||
\(404\) | 3.68113 | 0.183143 | ||||||||
\(405\) | 23.3967 | + | 5.23014i | 1.16259 | + | 0.259888i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.38179 | − | 5.85743i | 0.167629 | − | 0.290342i | ||||
\(408\) | 3.03183 | − | 0.636132i | 0.150098 | − | 0.0314932i | ||||
\(409\) | 15.2860 | + | 26.4762i | 0.755846 | + | 1.30916i | 0.944953 | + | 0.327207i | \(0.106107\pi\) |
−0.189107 | + | 0.981956i | \(0.560559\pi\) | |||||||
\(410\) | 0.673255 | + | 1.16611i | 0.0332497 | + | 0.0575901i | ||||
\(411\) | 10.5407 | − | 32.1537i | 0.519932 | − | 1.58603i | ||||
\(412\) | 5.16592 | − | 8.94763i | 0.254507 | − | 0.440818i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.576311 | + | 0.252978i | −0.0283242 | + | 0.0124332i | ||||
\(415\) | −18.2119 | −0.893988 | ||||||||
\(416\) | −2.14863 | + | 3.72153i | −0.105345 | + | 0.182463i | ||||
\(417\) | −3.04011 | − | 3.39424i | −0.148875 | − | 0.166217i | ||||
\(418\) | 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 | \(-0.0644252\pi\) | |||||||
\(422\) | −1.46209 | −0.0711735 | ||||||||
\(423\) | −1.25078 | + | 11.3287i | −0.0608152 | + | 0.550820i | ||||
\(424\) | −2.43089 | −0.118055 | ||||||||
\(425\) | 6.86077 | − | 11.8832i | 0.332796 | − | 0.576420i | ||||
\(426\) | 0.457046 | − | 1.39419i | 0.0221439 | − | 0.0675490i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.9093 | − | 29.2877i | −0.817341 | − | 1.41568i | ||||
\(429\) | −14.2417 | + | 2.98816i | −0.687596 | + | 0.144270i | ||||
\(430\) | −1.02574 | + | 1.77663i | −0.0494654 | + | 0.0856765i | ||||
\(431\) | 8.19687 | 0.394829 | 0.197415 | − | 0.980320i | \(-0.436745\pi\) | ||||
0.197415 | + | 0.980320i | \(0.436745\pi\) | |||||||
\(432\) | 1.99586 | + | 20.5422i | 0.0960258 | + | 0.988339i | ||||
\(433\) | 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 | ||||
\(437\) | 2.91793 | + | 5.05400i | 0.139583 | + | 0.241765i | ||||
\(438\) | −0.0811102 | + | 0.247423i | −0.00387560 | + | 0.0118223i | ||||
\(439\) | −3.29416 | + | 5.70564i | −0.157221 | + | 0.272316i | −0.933866 | − | 0.357624i | \(-0.883587\pi\) |
0.776644 | + | 0.629939i | \(0.216920\pi\) | |||||||
\(440\) | −1.16366 | −0.0554753 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.35191 | −0.111869 | ||||||||
\(443\) | −14.3456 | + | 24.8473i | −0.681581 | + | 1.18053i | 0.292917 | + | 0.956138i | \(0.405374\pi\) |
−0.974498 | + | 0.224395i | \(0.927959\pi\) | |||||||
\(444\) | 9.75240 | + | 10.8884i | 0.462828 | + | 0.516741i | ||||
\(445\) | 0.626752 | + | 1.08557i | 0.0297109 | + | 0.0514608i | ||||
\(446\) | −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 | \(0.496562\pi\) | |||||||
\(450\) | −0.346460 | − | 0.254504i | −0.0163323 | − | 0.0119974i | ||||
\(451\) | −11.8223 | −0.556689 | ||||||||
\(452\) | 3.89479 | − | 6.74598i | 0.183196 | − | 0.317304i | ||||
\(453\) | −2.51658 | + | 7.67669i | −0.118239 | + | 0.360683i | ||||
\(454\) | 0.471393 | + | 0.816477i | 0.0221236 | + | 0.0383192i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.880733 | + | 0.184794i | −0.0412441 | + | 0.00865376i | ||||
\(457\) | −10.1105 | + | 17.5119i | −0.472950 | + | 0.819173i | −0.999521 | − | 0.0309581i | \(-0.990144\pi\) |
0.526571 | + | 0.850131i | \(0.323477\pi\) | |||||||
\(458\) | −1.80468 | −0.0843273 | ||||||||
\(459\) | −27.6794 | + | 19.7795i | −1.29196 | + | 0.923230i | ||||
\(460\) | −16.3088 | −0.760402 | ||||||||
\(461\) | −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 | ||||
\(465\) | 9.65720 | − | 29.4588i | 0.447842 | − | 1.36612i | ||||
\(466\) | 0.432281 | − | 0.748732i | 0.0200250 | − | 0.0346843i | ||||
\(467\) | −27.2456 | −1.26078 | −0.630389 | − | 0.776279i | \(-0.717105\pi\) | ||||
−0.630389 | + | 0.776279i | \(0.717105\pi\) | |||||||
\(468\) | 3.45128 | − | 31.2592i | 0.159535 | − | 1.44496i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.345979 | − | 0.599254i | 0.0159588 | − | 0.0276415i | ||||
\(471\) | 4.70664 | + | 5.25490i | 0.216871 | + | 0.242133i | ||||
\(472\) | −1.48783 | − | 2.57699i | −0.0684827 | − | 0.118616i | ||||
\(473\) | −9.00590 | − | 15.5987i | −0.414092 | − | 0.717228i | ||||
\(474\) | −0.0642809 | − | 0.0717687i | −0.00295252 | − | 0.00329644i | ||||
\(475\) | −1.99302 | + | 3.45202i | −0.0914462 | + | 0.158389i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.4445 | − | 10.7302i | 1.11924 | − | 0.491301i | ||||
\(478\) | −1.05520 | −0.0482638 | ||||||||
\(479\) | −10.2628 | + | 17.7756i | −0.468917 | + | 0.812188i | −0.999369 | − | 0.0355269i | \(-0.988689\pi\) |
0.530452 | + | 0.847715i | \(0.322022\pi\) | |||||||
\(480\) | 1.17557 | − | 3.58602i | 0.0536572 | − | 0.163679i | ||||
\(481\) | −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 | ||||
\(485\) | 13.7251 | 0.623224 | ||||||||
\(486\) | 0.520777 | + | 0.929955i | 0.0236229 | + | 0.0421836i | ||||
\(487\) | 25.8449 | 1.17114 | 0.585571 | − | 0.810621i | \(-0.300870\pi\) | ||||
0.585571 | + | 0.810621i | \(0.300870\pi\) | |||||||
\(488\) | 0.370682 | − | 0.642039i | 0.0167800 | − | 0.0290638i | ||||
\(489\) | −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 | \(0.947954\pi\) | |||||||
\(492\) | 7.95909 | − | 24.2788i | 0.358824 | − | 1.09457i | ||||
\(493\) | 20.9152 | − | 36.2261i | 0.941971 | − | 1.63154i | ||||
\(494\) | 0.683220 | 0.0307395 | ||||||||
\(495\) | 11.7015 | − | 5.13649i | 0.525943 | − | 0.230868i | ||||
\(496\) | 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 | 0.523558 | − | 0.851990i | \(-0.324604\pi\) |
−0.999624 | + | 0.0274192i | \(0.991271\pi\) | |||||||
\(500\) | 7.71814 | + | 13.3682i | 0.345166 | + | 0.597845i | ||||
\(501\) | 5.54570 | + | 6.19170i | 0.247764 | + | 0.276625i | ||||
\(502\) | −0.189728 | + | 0.328618i | −0.00846795 | + | 0.0146669i | ||||
\(503\) | −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 | ||||||||
\(506\) | −0.167746 | + | 0.290544i | −0.00745722 | + | 0.0129163i | ||||
\(507\) | −7.87873 | + | 24.0337i | −0.349907 | + | 1.06737i | ||||
\(508\) | 10.9277 | + | 18.9273i | 0.484837 | + | 0.839762i | ||||
\(509\) | 6.73089 | + | 11.6582i | 0.298342 | + | 0.516743i | 0.975757 | − | 0.218858i | \(-0.0702332\pi\) |
−0.677415 | + | 0.735601i | \(0.736900\pi\) | |||||||
\(510\) | 2.02140 | − | 0.424126i | 0.0895092 | − | 0.0187806i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.41890 | 0.239484 | ||||||||
\(513\) | 8.04076 | − | 5.74587i | 0.355008 | − | 0.253687i | ||||
\(514\) | 0.672168 | 0.0296481 | ||||||||
\(515\) | 6.89659 | − | 11.9452i | 0.303900 | − | 0.526370i | ||||
\(516\) | 38.0972 | − | 7.99349i | 1.67714 | − | 0.351894i | ||||
\(517\) | 3.03768 | + | 5.26142i | 0.133597 | + | 0.231397i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.71486 | + | 8.28153i | −0.119169 | + | 0.363519i | ||||
\(520\) | −1.91155 | + | 3.31091i | −0.0838272 | + | 0.145193i | ||||
\(521\) | −1.42619 | −0.0624826 | −0.0312413 | − | 0.999512i | \(-0.509946\pi\) | ||||
−0.0312413 | + | 0.999512i | \(0.509946\pi\) | |||||||
\(522\) | −1.05619 | − | 0.775859i | −0.0462281 | − | 0.0339584i | ||||
\(523\) | −7.71060 | −0.337161 | −0.168581 | − | 0.985688i | \(-0.553918\pi\) | ||||
−0.168581 | + | 0.985688i | \(0.553918\pi\) | |||||||
\(524\) | −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 | ||||
\(528\) | 7.33994 | + | 8.19494i | 0.319430 | + | 0.356639i | ||||
\(529\) | 6.79254 | − | 11.7650i | 0.295328 | − | 0.511523i | ||||
\(530\) | −1.62074 | −0.0704005 | ||||||||
\(531\) | 26.3363 | + | 19.3462i | 1.14290 | + | 0.839554i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.4206 | + | 33.6374i | −0.841198 | + | 1.45700i | ||||
\(534\) | −0.0173599 | + | 0.0529556i | −0.000751238 | + | 0.00229161i | ||||
\(535\) | −22.5742 | − | 39.0996i | −0.975966 | − | 1.69042i | ||||
\(536\) | −0.454201 | − | 0.786699i | −0.0196185 | − | 0.0339802i | ||||
\(537\) | −27.7967 | + | 5.83226i | −1.19952 | + | 0.251680i | ||||
\(538\) | −1.02441 | + | 1.77432i | −0.0441653 | + | 0.0764966i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.67078 | + | 27.4888i | 0.114932 | + | 1.18293i | ||||
\(541\) | 28.0456 | 1.20577 | 0.602886 | − | 0.797827i | \(-0.294017\pi\) | ||||
0.602886 | + | 0.797827i | \(0.294017\pi\) | |||||||
\(542\) | 0.242608 | − | 0.420209i | 0.0104209 | − | 0.0180495i | ||||
\(543\) | −24.4685 | + | 5.13393i | −1.05004 | + | 0.220318i | ||||
\(544\) | 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 | \(-0.107206\pi\) | |||||||
\(548\) | 38.9807 | 1.66517 | ||||||||
\(549\) | −0.893471 | + | 8.09242i | −0.0381324 | + | 0.345376i | ||||
\(550\) | −0.229150 | −0.00977099 | ||||||||
\(551\) | −6.07577 | + | 10.5235i | −0.258836 | + | 0.448318i | ||||
\(552\) | −0.968623 | − | 1.08145i | −0.0412273 | − | 0.0460297i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.335836 | + | 0.581685i | 0.0142683 | + | 0.0247134i | ||||
\(555\) | 13.0196 | + | 14.5362i | 0.552651 | + | 0.617027i | ||||
\(556\) | 2.62464 | − | 4.54601i | 0.111310 | − | 0.192794i | ||||
\(557\) | 35.0419 | 1.48477 | 0.742386 | − | 0.669972i | \(-0.233694\pi\) | ||||
0.742386 | + | 0.669972i | \(0.233694\pi\) | |||||||
\(558\) | 1.26203 | − | 0.553980i | 0.0534258 | − | 0.0234518i | ||||
\(559\) | −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 | ||||
\(563\) | −8.01311 | − | 13.8791i | −0.337712 | − | 0.584935i | 0.646290 | − | 0.763092i | \(-0.276320\pi\) |
−0.984002 | + | 0.178157i | \(0.942986\pi\) | |||||||
\(564\) | −12.8502 | + | 2.69619i | −0.541089 | + | 0.113530i | ||||
\(565\) | 5.19961 | − | 9.00599i | 0.218749 | − | 0.378885i | ||||
\(566\) | −0.206213 | −0.00866776 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.38439 | 0.142006 | ||||||||
\(569\) | −0.185651 | + | 0.321557i | −0.00778290 | + | 0.0134804i | −0.869891 | − | 0.493245i | \(-0.835811\pi\) |
0.862108 | + | 0.506725i | \(0.169144\pi\) | |||||||
\(570\) | −0.587209 | + | 0.123207i | −0.0245955 | + | 0.00516057i | ||||
\(571\) | −14.6152 | − | 25.3142i | −0.611626 | − | 1.05937i | −0.990966 | − | 0.134110i | \(-0.957182\pi\) |
0.379340 | − | 0.925257i | \(-0.376151\pi\) | |||||||
\(572\) | −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 | ||||||||
\(576\) | −21.6684 | + | 9.51155i | −0.902848 | + | 0.396315i | ||||
\(577\) | −15.0570 | −0.626833 | −0.313417 | − | 0.949616i | \(-0.601474\pi\) | ||||
−0.313417 | + | 0.949616i | \(0.601474\pi\) | |||||||
\(578\) | −0.884279 | + | 1.53162i | −0.0367811 | + | 0.0637068i | ||||
\(579\) | −10.2025 | − | 11.3910i | −0.424003 | − | 0.473393i | ||||
\(580\) | −16.9793 | − | 29.4089i | −0.705025 | − | 1.22114i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.407107 | + | 0.454529i | 0.0168751 | + | 0.0188408i | ||||
\(583\) | 7.11501 | − | 12.3236i | 0.294674 | − | 0.510390i | ||||
\(584\) | −0.600615 | −0.0248536 | ||||||||
\(585\) | 4.60751 | − | 41.7315i | 0.190497 | − | 1.72538i | ||||
\(586\) | 1.16634 | 0.0481811 | ||||||||
\(587\) | −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 | ||||
\(591\) | 9.70220 | − | 2.03570i | 0.399095 | − | 0.0837374i | ||||
\(592\) | −8.39982 | + | 14.5489i | −0.345231 | + | 0.597957i | ||||
\(593\) | −10.8174 | −0.444218 | −0.222109 | − | 0.975022i | \(-0.571294\pi\) | ||||
−0.222109 | + | 0.975022i | \(0.571294\pi\) | |||||||
\(594\) | 0.517188 | + | 0.235158i | 0.0212205 | + | 0.00964867i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.79221 | + | 15.2286i | −0.360143 | + | 0.623786i | ||||
\(597\) | −19.3501 | + | 4.06000i | −0.791947 | + | 0.166165i | ||||
\(598\) | 0.551116 | + | 0.954560i | 0.0225368 | + | 0.0390349i | ||||
\(599\) | −8.32007 | − | 14.4108i | −0.339949 | − | 0.588809i | 0.644474 | − | 0.764626i | \(-0.277076\pi\) |
−0.984423 | + | 0.175817i | \(0.943743\pi\) | |||||||
\(600\) | 0.308902 | − | 0.942290i | 0.0126109 | − | 0.0384688i | ||||
\(601\) | 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 | ||||
\(604\) | −9.30663 | −0.378681 | ||||||||
\(605\) | −11.2449 | + | 19.4768i | −0.457171 | + | 0.791843i | ||||
\(606\) | 0.145768 | + | 0.162748i | 0.00592142 | + | 0.00661118i | ||||
\(607\) | 18.9025 | + | 32.7400i | 0.767227 | + | 1.32888i | 0.939061 | + | 0.343750i | \(0.111697\pi\) |
−0.171834 | + | 0.985126i | \(0.554969\pi\) | |||||||
\(608\) | −0.777828 | − | 1.34724i | −0.0315451 | − | 0.0546377i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.247143 | − | 0.428065i | 0.0100065 | − | 0.0173318i | ||||
\(611\) | 19.9601 | 0.807499 | ||||||||
\(612\) | −31.5853 | − | 23.2021i | −1.27676 | − | 0.937888i | ||||
\(613\) | −12.9544 | −0.523222 | −0.261611 | − | 0.965173i | \(-0.584254\pi\) | ||||
−0.261611 | + | 0.965173i | \(0.584254\pi\) | |||||||
\(614\) | −0.793745 | + | 1.37481i | −0.0320330 | + | 0.0554827i | ||||
\(615\) | 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 | \(0.606844\pi\) | |||||||
\(618\) | 0.600151 | − | 0.125922i | 0.0241416 | − | 0.00506534i | ||||
\(619\) | 16.5987 | − | 28.7498i | 0.667157 | − | 1.15555i | −0.311538 | − | 0.950234i | \(-0.600844\pi\) |
0.978696 | − | 0.205317i | \(-0.0658224\pi\) | |||||||
\(620\) | 35.7136 | 1.43429 | ||||||||
\(621\) | 14.5139 | + | 6.59926i | 0.582422 | + | 0.264819i | ||||
\(622\) | 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 | ||||
\(626\) | −0.157574 | − | 0.272925i | −0.00629791 | − | 0.0109083i | ||||
\(627\) | 1.64101 | − | 5.00581i | 0.0655355 | − | 0.199913i | ||||
\(628\) | −4.06342 | + | 7.03804i | −0.162148 | + | 0.280848i | ||||
\(629\) | −27.6917 | −1.10414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2773 | 1.28494 | 0.642470 | − | 0.766311i | \(-0.277910\pi\) | ||||
0.642470 | + | 0.766311i | \(0.277910\pi\) | |||||||
\(632\) | 0.111122 | − | 0.192469i | 0.00442020 | − | 0.00765601i | ||||
\(633\) | 24.7108 | + | 27.5893i | 0.982167 | + | 1.09657i | ||||
\(634\) | 0.884900 | + | 1.53269i | 0.0351439 | + | 0.0608709i | ||||
\(635\) | 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 | ||||||||
\(639\) | −34.0326 | + | 14.9390i | −1.34631 | + | 0.590977i | ||||
\(640\) | 5.79428 | 0.229039 | ||||||||
\(641\) | −21.5407 | + | 37.3096i | −0.850806 | + | 1.47364i | 0.0296762 | + | 0.999560i | \(0.490552\pi\) |
−0.880482 | + | 0.474079i | \(0.842781\pi\) | |||||||
\(642\) | 0.625265 | − | 1.90734i | 0.0246772 | − | 0.0752766i | ||||
\(643\) | 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 | ||||
\(646\) | 0.425709 | − | 0.737350i | 0.0167493 | − | 0.0290107i | ||||
\(647\) | −3.88807 | −0.152856 | −0.0764278 | − | 0.997075i | \(-0.524351\pi\) | ||||
−0.0764278 | + | 0.997075i | \(0.524351\pi\) | |||||||
\(648\) | −1.66418 | + | 1.80973i | −0.0653753 | + | 0.0710931i | ||||
\(649\) | 17.4189 | 0.683753 | ||||||||
\(650\) | −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 | 0.679584 | − | 0.733598i | \(-0.262160\pi\) |
−0.975106 | + | 0.221738i | \(0.928827\pi\) | |||||||
\(654\) | 0.313572 | − | 0.956536i | 0.0122616 | − | 0.0374035i | ||||
\(655\) | −5.93150 | + | 10.2737i | −0.231763 | + | 0.401425i | ||||
\(656\) | 29.3646 | 1.14650 | ||||||||
\(657\) | 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 | \(0.256254\pi\) | |||||||
\(660\) | 9.82201 | + | 10.9661i | 0.382321 | + | 0.426856i | ||||
\(661\) | −9.70965 | − | 16.8176i | −0.377662 | − | 0.654129i | 0.613060 | − | 0.790036i | \(-0.289938\pi\) |
−0.990722 | + | 0.135907i | \(0.956605\pi\) | |||||||
\(662\) | −0.00551516 | − | 0.00955254i | −0.000214353 | − | 0.000371270i | ||||
\(663\) | 39.7497 | + | 44.3799i | 1.54375 | + | 1.72357i | ||||
\(664\) | 0.933832 | − | 1.61744i | 0.0362397 | − | 0.0627690i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0952089 | + | 0.862333i | −0.00368927 | + | 0.0334147i | ||||
\(667\) | −19.6039 | −0.759067 | ||||||||
\(668\) | −4.78781 | + | 8.29273i | −0.185246 | + | 0.320855i | ||||
\(669\) | −3.86735 | + | 11.7972i | −0.149521 | + | 0.456105i | ||||
\(670\) | −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 | \(0.203135\pi\) | |||||||
\(674\) | −0.619024 | −0.0238439 | ||||||||
\(675\) | 1.05310 | + | 10.8390i | 0.0405339 | + | 0.417192i | ||||
\(676\) | −29.1366 | −1.12064 | ||||||||
\(677\) | 18.4913 | − | 32.0278i | 0.710678 | − | 1.23093i | −0.253925 | − | 0.967224i | \(-0.581722\pi\) |
0.964603 | − | 0.263706i | \(-0.0849449\pi\) | |||||||
\(678\) | 0.452477 | − | 0.0949379i | 0.0173773 | − | 0.00364607i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.38215 | + | 4.12601i | 0.0913513 | + | 0.158225i | ||||
\(681\) | 7.43968 | − | 22.6944i | 0.285089 | − | 0.869650i | ||||
\(682\) | 0.367336 | − | 0.636244i | 0.0140660 | − | 0.0243630i | ||||
\(683\) | 13.1360 | 0.502635 | 0.251317 | − | 0.967905i | \(-0.419136\pi\) | ||||
0.251317 | + | 0.967905i | \(0.419136\pi\) | |||||||
\(684\) | 9.17540 | + | 6.74011i | 0.350830 | + | 0.257714i | ||||
\(685\) | 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 | ||||
\(689\) | −23.3758 | − | 40.4881i | −0.890547 | − | 1.54247i | ||||
\(690\) | −0.645807 | − | 0.721034i | −0.0245855 | − | 0.0274493i | ||||
\(691\) | 7.38292 | − | 12.7876i | 0.280860 | − | 0.486463i | −0.690737 | − | 0.723106i | \(-0.742714\pi\) |
0.971597 | + | 0.236643i | \(0.0760472\pi\) | |||||||
\(692\) | −10.0399 | −0.381659 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.397915 | −0.0151046 | ||||||||
\(695\) | 3.50394 | − | 6.06900i | 0.132912 | − | 0.230210i | ||||
\(696\) | 0.941693 | − | 2.87259i | 0.0356948 | − | 0.108885i | ||||
\(697\) | 24.2016 | + | 41.9184i | 0.916702 | + | 1.58777i | ||||
\(698\) | −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 | \(0.695107\pi\) | |||||||
\(702\) | 1.51868 | − | 1.08524i | 0.0573187 | − | 0.0409596i | ||||
\(703\) | 8.04433 | 0.303398 | ||||||||
\(704\) | −6.30697 | + | 10.9240i | −0.237703 | + | 0.411713i | ||||
\(705\) | −17.1552 | + | 3.59946i | −0.646101 | + | 0.135564i | ||||
\(706\) | 0.826969 | + | 1.43235i | 0.0311234 | + | 0.0539073i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.7269 | + | 35.7724i | −0.440725 | + | 1.34441i | ||||
\(709\) | −7.05152 | + | 12.2136i | −0.264825 | + | 0.458691i | −0.967518 | − | 0.252803i | \(-0.918648\pi\) |
0.702693 | + | 0.711494i | \(0.251981\pi\) | |||||||
\(710\) | 2.25646 | 0.0846836 | ||||||||
\(711\) | −0.267843 | + | 2.42593i | −0.0100449 | + | 0.0909794i | ||||
\(712\) | −0.128549 | −0.00481758 | ||||||||
\(713\) | 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 | ||||
\(717\) | 17.8340 | + | 19.9114i | 0.666023 | + | 0.743604i | ||||
\(718\) | 0.719212 | − | 1.24571i | 0.0268408 | − | 0.0464896i | ||||
\(719\) | −14.9958 | −0.559249 | −0.279624 | − | 0.960109i | \(-0.590210\pi\) | ||||
−0.279624 | + | 0.960109i | \(0.590210\pi\) | |||||||
\(720\) | −29.0646 | + | 12.7582i | −1.08317 | + | 0.475471i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.525886 | − | 0.910861i | 0.0195715 | − | 0.0338987i | ||||
\(723\) | −0.636606 | + | 1.94193i | −0.0236756 | + | 0.0722213i | ||||
\(724\) | −14.4008 | − | 24.9429i | −0.535200 | − | 0.926994i | ||||
\(725\) | −6.69501 | − | 11.5961i | −0.248646 | − | 0.430668i | ||||
\(726\) | −0.978549 | + | 0.205317i | −0.0363174 | + | 0.00762003i | ||||
\(727\) | 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 | ||||
\(730\) | −0.400446 | −0.0148212 | ||||||||
\(731\) | −36.8723 | + | 63.8648i | −1.36377 | + | 2.36212i | ||||
\(732\) | −9.17925 | + | 1.92597i | −0.339275 | + | 0.0711859i | ||||
\(733\) | 14.1911 | + | 24.5796i | 0.524159 | + | 0.907869i | 0.999604 | + | 0.0281244i | \(0.00895345\pi\) |
−0.475446 | + | 0.879745i | \(0.657713\pi\) | |||||||
\(734\) | −1.19784 | − | 2.07473i | −0.0442132 | − | 0.0765796i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.25486 | − | 2.17348i | 0.0462548 | − | 0.0801156i | ||||
\(737\) | 5.31763 | 0.195877 | ||||||||
\(738\) | 1.38857 | − | 0.609527i | 0.0511139 | − | 0.0224370i | ||||
\(739\) | 46.5865 | 1.71371 | 0.856857 | − | 0.515555i | \(-0.172414\pi\) | ||||
0.856857 | + | 0.515555i | \(0.172414\pi\) | |||||||
\(740\) | −11.2403 | + | 19.4688i | −0.413202 | + | 0.715686i | ||||
\(741\) | −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 | \(0.835313\pi\) | |||||||
\(744\) | 2.12112 | + | 2.36820i | 0.0777642 | + | 0.0868225i | ||||
\(745\) | −11.7377 | + | 20.3304i | −0.430038 | + | 0.744847i | ||||
\(746\) | 0.0771683 | 0.00282533 | ||||||||
\(747\) | −2.25086 | + | 20.3866i | −0.0823546 | + | 0.745908i | ||||
\(748\) | −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 | 0.979687 | + | 0.200533i | \(0.0642673\pi\) |
−0.316177 | + | 0.948700i | \(0.602399\pi\) | |||||||
\(752\) | −7.54511 | − | 13.0685i | −0.275142 | − | 0.476560i | ||||
\(753\) | 9.40752 | − | 1.97387i | 0.342829 | − | 0.0719317i | ||||
\(754\) | −1.14754 | + | 1.98760i | −0.0417911 | + | 0.0723843i | ||||
\(755\) | −12.4245 | −0.452174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4703 | −0.998424 | −0.499212 | − | 0.866480i | \(-0.666377\pi\) | ||||
−0.499212 | + | 0.866480i | \(0.666377\pi\) | |||||||
\(758\) | 0.750812 | − | 1.30044i | 0.0272707 | − | 0.0472343i | ||||
\(759\) | 8.31757 | − | 1.74518i | 0.301909 | − | 0.0633459i | ||||
\(760\) | −0.692005 | − | 1.19859i | −0.0251017 | − | 0.0434773i | ||||
\(761\) | 16.5178 | + | 28.6097i | 0.598771 | + | 1.03710i | 0.993003 | + | 0.118091i | \(0.0376774\pi\) |
−0.394232 | + | 0.919011i | \(0.628989\pi\) | |||||||
\(762\) | −0.404079 | + | 1.23262i | −0.0146382 | + | 0.0446532i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.66934 | −0.205110 | ||||||||
\(765\) | −42.1669 | − | 30.9751i | −1.52455 | − | 1.11991i | ||||
\(766\) | −1.57534 | −0.0569194 | ||||||||
\(767\) | 28.6143 | − | 49.5614i | 1.03320 | − | 1.78956i | ||||
\(768\) | −18.0588 | − | 20.1623i | −0.651639 | − | 0.727546i | ||||
\(769\) | 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 | ||||
\(772\) | 8.80822 | − | 15.2563i | 0.317015 | − | 0.549086i | ||||
\(773\) | −6.72973 | −0.242051 | −0.121026 | − | 0.992649i | \(-0.538618\pi\) | ||||
−0.121026 | + | 0.992649i | \(0.538618\pi\) | |||||||
\(774\) | 1.86200 | + | 1.36780i | 0.0669283 | + | 0.0491645i | ||||
\(775\) | 14.0820 | 0.505842 | ||||||||
\(776\) | −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 | ||||
\(780\) | 47.3361 | − | 9.93197i | 1.69491 | − | 0.355622i | ||||
\(781\) | −9.90581 | + | 17.1574i | −0.354458 | + | 0.613939i | ||||
\(782\) | 1.37358 | 0.0491193 | ||||||||
\(783\) | 3.21039 | + | 33.0428i | 0.114730 | + | 1.18085i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.42473 | + | 9.39590i | −0.193617 | + | 0.335354i | ||||
\(786\) | −0.516167 | + | 0.108301i | −0.0184111 | + | 0.00386297i | ||||
\(787\) | 14.3341 | + | 24.8274i | 0.510956 | + | 0.885003i | 0.999919 | + | 0.0126980i | \(0.00404201\pi\) |
−0.488963 | + | 0.872305i | \(0.662625\pi\) | |||||||
\(788\) | 5.71016 | + | 9.89029i | 0.203416 | + | 0.352327i | ||||
\(789\) | −6.43804 | + | 19.6389i | −0.229200 | + | 0.699164i | ||||
\(790\) | 0.0740881 | − | 0.128324i | 0.00263594 | − | 0.00456558i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.143820 | + | 1.30261i | −0.00511041 | + | 0.0462864i | ||||
\(793\) | 14.2581 | 0.506320 | ||||||||
\(794\) | −0.564275 | + | 0.977352i | −0.0200254 | + | 0.0346849i | ||||
\(795\) | 27.3922 | + | 30.5830i | 0.971501 | + | 1.08467i | ||||
\(796\) | −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 | ||||
\(800\) | 1.71421 | 0.0606064 | ||||||||
\(801\) | 1.29266 | − | 0.567426i | 0.0456739 | − | 0.0200490i | ||||
\(802\) | 1.48098 | 0.0522951 | ||||||||
\(803\) | 1.75795 | − | 3.04485i | 0.0620366 | − | 0.107451i | ||||
\(804\) | −3.57998 | + | 10.9205i | −0.126256 | + | 0.385138i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.20685 | − | 2.09033i | −0.0425095 | − | 0.0736287i | ||||
\(807\) | 50.7945 | − | 10.6576i | 1.78805 | − | 0.375166i | ||||
\(808\) | −0.251989 | + | 0.436457i | −0.00886493 | + | 0.0153545i | ||||
\(809\) | −16.4779 | −0.579332 | −0.289666 | − | 0.957128i | \(-0.593544\pi\) | ||||
−0.289666 | + | 0.957128i | \(0.593544\pi\) | |||||||
\(810\) | −1.10956 | + | 1.20660i | −0.0389859 | + | 0.0423955i | ||||
\(811\) | −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 | ||||
\(815\) | −16.1456 | − | 27.9649i | −0.565554 | − | 0.979569i | ||||
\(816\) | 14.0312 | − | 42.8014i | 0.491189 | − | 1.49835i | ||||
\(817\) | 10.7113 | − | 18.5524i | 0.374739 | − | 0.649068i | ||||
\(818\) | −2.09033 | −0.0730868 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 39.2945 | 1.37222 | ||||||||
\(821\) | 14.0543 | − | 24.3428i | 0.490499 | − | 0.849569i | −0.509441 | − | 0.860506i | \(-0.670148\pi\) |
0.999940 | + | 0.0109361i | \(0.00348114\pi\) | |||||||
\(822\) | 1.54358 | + | 1.72339i | 0.0538387 | + | 0.0601101i | ||||
\(823\) | −12.9529 | − | 22.4351i | −0.451510 | − | 0.782038i | 0.546970 | − | 0.837152i | \(-0.315781\pi\) |
−0.998480 | + | 0.0551142i | \(0.982448\pi\) | |||||||
\(824\) | 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 | \(0.600155\pi\) | |||||||
\(828\) | −2.01565 | + | 18.2563i | −0.0700486 | + | 0.634449i | ||||
\(829\) | 15.7069 | 0.545523 | 0.272761 | − | 0.962082i | \(-0.412063\pi\) | ||||
0.272761 | + | 0.962082i | \(0.412063\pi\) | |||||||
\(830\) | 0.622611 | − | 1.07839i | 0.0216111 | − | 0.0374316i | ||||
\(831\) | 5.30027 | − | 16.1682i | 0.183864 | − | 0.560869i | ||||
\(832\) | 20.7210 | + | 35.8899i | 0.718373 | + | 1.24426i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.304918 | − | 0.0639772i | 0.0105584 | − | 0.00221535i | ||||
\(835\) | −6.39180 | + | 11.0709i | −0.221197 | + | 0.383125i | ||||
\(836\) | 6.06866 | 0.209889 | ||||||||
\(837\) | −31.7830 | − | 14.4513i | −1.09858 | − | 0.499509i | ||||
\(838\) | −1.47799 | −0.0510563 | ||||||||
\(839\) | 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 | ||||
\(843\) | 12.8832 | − | 39.2996i | 0.443722 | − | 1.35355i | ||||
\(844\) | −21.3338 | + | 36.9511i | −0.734338 | + | 1.27191i | ||||
\(845\) | −38.8978 | −1.33812 | ||||||||
\(846\) | −0.628052 | − | 0.461357i | −0.0215929 | − | 0.0158618i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −17.6725 | + | 30.6097i | −0.606878 | + | 1.05114i | ||||
\(849\) | 3.48520 | + | 3.89118i | 0.119612 | + | 0.133545i | ||||
\(850\) | 0.469098 | + | 0.812501i | 0.0160899 | + | 0.0278686i | ||||
\(851\) | 6.48892 | + | 11.2391i | 0.222437 | + | 0.385273i | ||||
\(852\) | −28.5663 | − | 31.8939i | −0.978667 | − | 1.09267i | ||||
\(853\) | 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 | ||||
\(856\) | 4.63004 | 0.158251 | ||||||||
\(857\) | 1.90765 | − | 3.30414i | 0.0651640 | − | 0.112867i | −0.831603 | − | 0.555371i | \(-0.812576\pi\) |
0.896767 | + | 0.442504i | \(0.145910\pi\) | |||||||
\(858\) | 0.309941 | − | 0.945459i | 0.0105812 | − | 0.0322774i | ||||
\(859\) | −19.4884 | − | 33.7549i | −0.664936 | − | 1.15170i | −0.979303 | − | 0.202401i | \(-0.935126\pi\) |
0.314367 | − | 0.949301i | \(-0.398208\pi\) | |||||||
\(860\) | 29.9336 | + | 51.8464i | 1.02073 | + | 1.76795i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.280226 | + | 0.485366i | −0.00954454 | + | 0.0165316i | ||||
\(863\) | 26.6736 | 0.907978 | 0.453989 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453989 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(864\) | −3.86894 | − | 1.75915i | −0.131624 | − | 0.0598477i | ||||
\(865\) | −13.4034 | −0.455730 | ||||||||
\(866\) | −0.116737 | + | 0.202195i | −0.00396690 | + | 0.00687087i | ||||
\(867\) | 43.8464 | − | 9.19976i | 1.48910 | − | 0.312440i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.650490 | + | 1.12668i | 0.0220664 | + | 0.0382200i | ||||
\(870\) | 0.627852 | − | 1.91523i | 0.0212862 | − | 0.0649324i | ||||
\(871\) | 8.73531 | − | 15.1300i | 0.295985 | − | 0.512661i | ||||
\(872\) | 2.32198 | 0.0786321 | ||||||||
\(873\) | 1.69632 | − | 15.3640i | 0.0574117 | − | 0.519993i | ||||
\(874\) | −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 | 0.588933 | − | 0.808182i | \(-0.299548\pi\) |
−0.994373 | + | 0.105940i | \(0.966215\pi\) | |||||||
\(878\) | −0.225235 | − | 0.390118i | −0.00760130 | − | 0.0131658i | ||||
\(879\) | −19.7124 | − | 22.0085i | −0.664881 | − | 0.742330i | ||||
\(880\) | −8.45978 | + | 14.6528i | −0.285179 | + | 0.493945i | ||||
\(881\) | −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 | \(0.705076\pi\) | |||||||
\(884\) | −34.3173 | + | 59.4393i | −1.15422 | + | 1.99916i | ||||
\(885\) | −15.6556 | + | 47.7567i | −0.526259 | + | 1.60532i | ||||
\(886\) | −0.980867 | − | 1.69891i | −0.0329529 | − | 0.0570761i | ||||
\(887\) | −14.5516 | − | 25.2041i | −0.488596 | − | 0.846272i | 0.511318 | − | 0.859391i | \(-0.329157\pi\) |
−0.999914 | + | 0.0131191i | \(0.995824\pi\) | |||||||
\(888\) | −1.95858 | + | 0.410946i | −0.0657258 | + | 0.0137905i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.0857071 | −0.00287291 | ||||||||
\(891\) | −4.30363 | − | 13.7336i | −0.144177 | − | 0.460094i | ||||
\(892\) | −14.3020 | −0.478865 | ||||||||
\(893\) | −3.61290 | + | 6.25772i | −0.120901 | + | 0.209407i | ||||
\(894\) | −1.02143 | + | 0.214315i | −0.0341619 | + | 0.00716778i | ||||
\(895\) | −21.8403 | − | 37.8285i | −0.730041 | − | 1.26447i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.69788 | − | 26.5324i | 0.290414 | − | 0.885892i | ||||
\(898\) | −0.0156482 | + | 0.0271035i | −0.000522187 | + | 0.000904455i | ||||
\(899\) | 42.9294 | 1.43177 | ||||||||
\(900\) | −11.4873 | + | 5.04247i | −0.382910 | + | 0.168082i | ||||
\(901\) | −58.2611 | −1.94096 | ||||||||
\(902\) | 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 | ||||
\(906\) | −0.368530 | − | 0.411459i | −0.0122436 | − | 0.0136698i | ||||
\(907\) | 20.6071 | − | 35.6925i | 0.684247 | − | 1.18515i | −0.289426 | − | 0.957201i | \(-0.593464\pi\) |
0.973673 | − | 0.227950i | \(-0.0732024\pi\) | |||||||
\(908\) | 27.5129 | 0.913047 | ||||||||
\(909\) | 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 | \(-0.238817\pi\) | |||||||
\(912\) | −4.07600 | + | 12.4336i | −0.134970 | + | 0.411718i | ||||
\(913\) | 5.46649 | + | 9.46824i | 0.180914 | + | 0.313353i | ||||
\(914\) | −0.691296 | − | 1.19736i | −0.0228660 | − | 0.0396051i | ||||
\(915\) | −12.2544 | + | 2.57120i | −0.405119 | + | 0.0850013i | ||||
\(916\) | −26.3326 | + | 45.6094i | −0.870054 | + | 1.50698i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.224942 | − | 2.31520i | −0.00742419 | − | 0.0764130i | ||||
\(919\) | −51.5598 | −1.70080 | −0.850400 | − | 0.526137i | \(-0.823640\pi\) | ||||
−0.850400 | + | 0.526137i | \(0.823640\pi\) | |||||||
\(920\) | 1.11640 | − | 1.93367i | 0.0368068 | − | 0.0637512i | ||||
\(921\) | 39.3573 | − | 8.25788i | 1.29687 | − | 0.272106i | ||||
\(922\) | −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 | ||||
\(926\) | −0.328525 | −0.0107960 | ||||||||
\(927\) | −12.5193 | − | 9.19646i | −0.411187 | − | 0.302052i | ||||
\(928\) | 5.22579 | 0.171545 | ||||||||
\(929\) | 25.1412 | − | 43.5458i | 0.824856 | − | 1.42869i | −0.0771732 | − | 0.997018i | \(-0.524589\pi\) |
0.902029 | − | 0.431675i | \(-0.142077\pi\) | |||||||
\(930\) | 1.41421 | + | 1.57895i | 0.0463738 | + | 0.0517757i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.6150 | − | 21.8499i | −0.413219 | − | 0.715717i | ||||
\(933\) | −2.06959 | − | 2.31066i | −0.0677552 | − | 0.0756477i | ||||
\(934\) | 0.931446 | − | 1.61331i | 0.0304779 | − | 0.0527892i | ||||
\(935\) | −27.8894 | −0.912081 | ||||||||
\(936\) | 3.47002 | + | 2.54902i | 0.113421 | + | 0.0833174i | ||||
\(937\) | 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 | ||||
\(941\) | 8.51660 | + | 14.7512i | 0.277633 | + | 0.480875i | 0.970796 | − | 0.239906i | \(-0.0771166\pi\) |
−0.693163 | + | 0.720781i | \(0.743783\pi\) | |||||||
\(942\) | −0.472067 | + | 0.0990482i | −0.0153808 | + | 0.00322716i | ||||
\(943\) | 11.3422 | − | 19.6452i | 0.369352 | − | 0.639737i | ||||
\(944\) | −43.2658 | −1.40818 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.23154 | 0.0400408 | ||||||||
\(947\) | −15.7530 | + | 27.2849i | −0.511903 | + | 0.886641i | 0.488002 | + | 0.872842i | \(0.337726\pi\) |
−0.999905 | + | 0.0137988i | \(0.995608\pi\) | |||||||
\(948\) | −2.75174 | + | 0.577364i | −0.0893722 | + | 0.0187519i | ||||
\(949\) | −5.77559 | − | 10.0036i | −0.187484 | − | 0.324731i | ||||
\(950\) | −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 | \(0.416197\pi\) | |||||||
\(954\) | −0.200312 | + | 1.81428i | −0.00648533 | + | 0.0587394i | ||||
\(955\) | −7.56866 | −0.244916 | ||||||||
\(956\) | −15.3967 | + | 26.6679i | −0.497966 | + | 0.862502i | ||||
\(957\) | 11.8065 | + | 13.1818i | 0.381650 | + | 0.426107i | ||||
\(958\) | −0.701705 | − | 1.21539i | −0.0226711 | − | 0.0392674i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −24.2813 | − | 27.1097i | −0.783675 | − | 0.874962i | ||||
\(961\) | −7.07402 | + | 12.2526i | −0.228194 | + | 0.395244i | ||||
\(962\) | 1.51935 | 0.0489859 | ||||||||
\(963\) | −46.5586 | + | 20.4374i | −1.50033 | + | 0.658585i | ||||
\(964\) | −2.35425 | −0.0758253 | ||||||||
\(965\) | 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 | ||||
\(969\) | −21.1085 | + | 4.42895i | −0.678103 | + | 0.142278i | ||||
\(970\) | −0.469219 | + | 0.812711i | −0.0150657 | + | 0.0260946i | ||||
\(971\) | −56.5678 | −1.81535 | −0.907674 | − | 0.419676i | \(-0.862144\pi\) | ||||
−0.907674 | + | 0.419676i | \(0.862144\pi\) | |||||||
\(972\) | 31.1014 | + | 0.407712i | 0.997577 | + | 0.0130774i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.883558 | + | 1.53037i | −0.0283110 | + | 0.0490361i | ||||
\(975\) | 18.6649 | − | 3.91623i | 0.597755 | − | 0.125420i | ||||
\(976\) | −5.38969 | − | 9.33522i | −0.172520 | − | 0.298813i | ||||
\(977\) | −26.8780 | − | 46.5541i | −0.859904 | − | 1.48940i | −0.872020 | − | 0.489471i | \(-0.837190\pi\) |
0.0121160 | − | 0.999927i | \(-0.496143\pi\) | |||||||
\(978\) | 0.447204 | − | 1.36417i | 0.0143000 | − | 0.0436214i | ||||
\(979\) | 0.376252 | − | 0.651687i | 0.0120251 | − | 0.0208280i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.3493 | + | 10.2494i | −0.745485 | + | 0.327238i | ||||
\(982\) | 1.06769 | 0.0340715 | ||||||||
\(983\) | −13.7051 | + | 23.7379i | −0.437125 | + | 0.757122i | −0.997466 | − | 0.0711394i | \(-0.977336\pi\) |
0.560342 | + | 0.828262i | \(0.310670\pi\) | |||||||
\(984\) | 2.33381 | + | 2.60566i | 0.0743990 | + | 0.0830654i | ||||
\(985\) | 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 | ||||
\(989\) | 34.5607 | 1.09897 | ||||||||
\(990\) | −0.0958885 | + | 0.868489i | −0.00304754 | + | 0.0276024i | ||||
\(991\) | −17.3374 | −0.550740 | −0.275370 | − | 0.961338i | \(-0.588800\pi\) | ||||
−0.275370 | + | 0.961338i | \(0.588800\pi\) | |||||||
\(992\) | −2.74794 | + | 4.75957i | −0.0872471 | + | 0.151116i | ||||
\(993\) | −0.0870420 | + | 0.265517i | −0.00276220 | + | 0.00842594i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.2037 | − | 26.3335i | −0.481988 | − | 0.834828i | ||||
\(996\) | −23.1246 | + | 4.85196i | −0.732732 | + | 0.153740i | ||||
\(997\) | 17.8319 | − | 30.8858i | 0.564742 | − | 0.978162i | −0.432332 | − | 0.901715i | \(-0.642309\pi\) |
0.997074 | − | 0.0764472i | \(-0.0243576\pi\) | |||||||
\(998\) | 1.45425 | 0.0460334 | ||||||||
\(999\) | 17.8811 | − | 12.7777i | 0.565734 | − | 0.404270i |
(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.f.h.295.6 | yes | 24 | |
3.2 | odd | 2 | 1323.2.f.h.883.7 | 24 | |||
7.2 | even | 3 | 441.2.h.h.214.7 | 24 | |||
7.3 | odd | 6 | 441.2.g.h.79.6 | 24 | |||
7.4 | even | 3 | 441.2.g.h.79.5 | 24 | |||
7.5 | odd | 6 | 441.2.h.h.214.8 | 24 | |||
7.6 | odd | 2 | inner | 441.2.f.h.295.5 | yes | 24 | |
9.2 | odd | 6 | 3969.2.a.bi.1.6 | 12 | |||
9.4 | even | 3 | inner | 441.2.f.h.148.6 | yes | 24 | |
9.5 | odd | 6 | 1323.2.f.h.442.7 | 24 | |||
9.7 | even | 3 | 3969.2.a.bh.1.7 | 12 | |||
21.2 | odd | 6 | 1323.2.h.h.802.6 | 24 | |||
21.5 | even | 6 | 1323.2.h.h.802.5 | 24 | |||
21.11 | odd | 6 | 1323.2.g.h.667.8 | 24 | |||
21.17 | even | 6 | 1323.2.g.h.667.7 | 24 | |||
21.20 | even | 2 | 1323.2.f.h.883.8 | 24 | |||
63.4 | even | 3 | 441.2.h.h.373.7 | 24 | |||
63.5 | even | 6 | 1323.2.g.h.361.7 | 24 | |||
63.13 | odd | 6 | inner | 441.2.f.h.148.5 | ✓ | 24 | |
63.20 | even | 6 | 3969.2.a.bi.1.5 | 12 | |||
63.23 | odd | 6 | 1323.2.g.h.361.8 | 24 | |||
63.31 | odd | 6 | 441.2.h.h.373.8 | 24 | |||
63.32 | odd | 6 | 1323.2.h.h.226.6 | 24 | |||
63.34 | odd | 6 | 3969.2.a.bh.1.8 | 12 | |||
63.40 | odd | 6 | 441.2.g.h.67.6 | 24 | |||
63.41 | even | 6 | 1323.2.f.h.442.8 | 24 | |||
63.58 | even | 3 | 441.2.g.h.67.5 | 24 | |||
63.59 | even | 6 | 1323.2.h.h.226.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.5 | ✓ | 24 | 63.13 | odd | 6 | inner | |
441.2.f.h.148.6 | yes | 24 | 9.4 | even | 3 | inner | |
441.2.f.h.295.5 | yes | 24 | 7.6 | odd | 2 | inner | |
441.2.f.h.295.6 | yes | 24 | 1.1 | even | 1 | trivial | |
441.2.g.h.67.5 | 24 | 63.58 | even | 3 | |||
441.2.g.h.67.6 | 24 | 63.40 | odd | 6 | |||
441.2.g.h.79.5 | 24 | 7.4 | even | 3 | |||
441.2.g.h.79.6 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.214.7 | 24 | 7.2 | even | 3 | |||
441.2.h.h.214.8 | 24 | 7.5 | odd | 6 | |||
441.2.h.h.373.7 | 24 | 63.4 | even | 3 | |||
441.2.h.h.373.8 | 24 | 63.31 | odd | 6 | |||
1323.2.f.h.442.7 | 24 | 9.5 | odd | 6 | |||
1323.2.f.h.442.8 | 24 | 63.41 | even | 6 | |||
1323.2.f.h.883.7 | 24 | 3.2 | odd | 2 | |||
1323.2.f.h.883.8 | 24 | 21.20 | even | 2 | |||
1323.2.g.h.361.7 | 24 | 63.5 | even | 6 | |||
1323.2.g.h.361.8 | 24 | 63.23 | odd | 6 | |||
1323.2.g.h.667.7 | 24 | 21.17 | even | 6 | |||
1323.2.g.h.667.8 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.226.5 | 24 | 63.59 | even | 6 | |||
1323.2.h.h.226.6 | 24 | 63.32 | odd | 6 | |||
1323.2.h.h.802.5 | 24 | 21.5 | even | 6 | |||
1323.2.h.h.802.6 | 24 | 21.2 | odd | 6 | |||
3969.2.a.bh.1.7 | 12 | 9.7 | even | 3 | |||
3969.2.a.bh.1.8 | 12 | 63.34 | odd | 6 | |||
3969.2.a.bi.1.5 | 12 | 63.20 | even | 6 | |||
3969.2.a.bi.1.6 | 12 | 9.2 | odd | 6 |