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 | 148.5 | ||
Character | \(\chi\) | \(=\) | 441.148 |
Dual form | 441.2.f.h.295.5 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.853685 | − | 0.520789i | \(-0.174362\pi\) |
−0.877859 | + | 0.478919i | \(0.841029\pi\) | |||||||
\(3\) | −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 | 0.397814 | + | 0.917466i | \(0.369769\pi\) |
−0.993456 | + | 0.114216i | \(0.963564\pi\) | |||||||
\(6\) | 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 | 0.961021 | − | 0.276474i | \(-0.0891659\pi\) |
−0.719944 | + | 0.694032i | \(0.755833\pi\) | |||||||
\(12\) | −2.30578 | + | 2.57437i | −0.665620 | + | 0.743155i | ||||
\(13\) | 2.62690 | − | 4.54992i | 0.728571 | − | 1.26192i | −0.228916 | − | 0.973446i | \(-0.573518\pi\) |
0.957487 | − | 0.288476i | \(-0.0931485\pi\) | |||||||
\(14\) | 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 | \(-0.208013\pi\) | ||||
0.793966 | + | 0.607963i | \(0.208013\pi\) | |||||||
\(18\) | −0.0225104 | − | 0.203883i | −0.00530576 | − | 0.0480557i | ||||
\(19\) | −1.90194 | −0.436334 | −0.218167 | − | 0.975911i | \(-0.570008\pi\) | ||||
−0.218167 | + | 0.975911i | \(0.570008\pi\) | |||||||
\(20\) | 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 | \(0.0630173\pi\) | |||||||
\(24\) | 0.463072 | + | 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 | −0.993797 | − | 0.111207i | \(-0.964528\pi\) |
0.400591 | − | 0.916257i | \(-0.368805\pi\) | |||||||
\(30\) | −0.308743 | − | 0.0647797i | −0.0563684 | − | 0.0118271i | ||||
\(31\) | 3.35961 | − | 5.81902i | 0.603405 | − | 1.04513i | −0.388897 | − | 0.921281i | \(-0.627144\pi\) |
0.992301 | − | 0.123846i | \(-0.0395229\pi\) | |||||||
\(32\) | −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 | −0.418495 | − | 0.908219i | \(-0.637442\pi\) |
0.995788 | − | 0.0916820i | \(-0.0292243\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.63176 | + | 9.75450i | 0.858836 | + | 1.48755i | 0.873040 | + | 0.487648i | \(0.162145\pi\) |
−0.0142043 | + | 0.999899i | \(0.504522\pi\) | |||||||
\(44\) | 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 | \(-0.0772989\pi\) |
−0.693575 | + | 0.720384i | \(0.743966\pi\) | |||||||
\(48\) | 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 | 0.256146 | + | 0.966638i | \(0.417547\pi\) |
−0.965206 | + | 0.261490i | \(0.915786\pi\) | |||||||
\(60\) | −2.86778 | − | 8.74801i | −0.370228 | − | 1.12936i | ||||
\(61\) | 1.35693 | + | 2.35027i | 0.173737 | + | 0.300922i | 0.939724 | − | 0.341935i | \(-0.111082\pi\) |
−0.765986 | + | 0.642857i | \(0.777749\pi\) | |||||||
\(62\) | −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 | −0.746407 | − | 0.665489i | \(-0.768223\pi\) |
0.949534 | + | 0.313663i | \(0.101556\pi\) | |||||||
\(68\) | 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 | \(-0.541069\pi\) | ||||
−0.128665 | + | 0.991688i | \(0.541069\pi\) | |||||||
\(74\) | −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 | 0.842235 | − | 0.539111i | \(-0.181240\pi\) |
−0.888001 | + | 0.459841i | \(0.847906\pi\) | |||||||
\(80\) | 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 | \(-0.0442337\pi\) |
−0.615140 | + | 0.788418i | \(0.710900\pi\) | |||||||
\(84\) | 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 | \(-0.507940\pi\) | ||||
−0.0249403 | + | 0.999689i | \(0.507940\pi\) | |||||||
\(90\) | 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 | \(-0.250909\pi\) |
−0.966661 | + | 0.256059i | \(0.917576\pi\) | |||||||
\(98\) | 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 | \(-0.195924\pi\) |
−0.908263 | + | 0.418400i | \(0.862591\pi\) | |||||||
\(102\) | 0.241534 | + | 0.736788i | 0.0239155 | + | 0.0729529i | ||||
\(103\) | 2.58901 | − | 4.48430i | 0.255103 | − | 0.441851i | −0.709821 | − | 0.704383i | \(-0.751224\pi\) |
0.964923 | + | 0.262531i | \(0.0845573\pi\) | |||||||
\(104\) | −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 | −0.943112 | − | 0.332474i | \(-0.892116\pi\) |
0.759487 | + | 0.650522i | \(0.225450\pi\) | |||||||
\(114\) | −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 | \(-0.895658\pi\) |
0.752204 | + | 0.658931i | \(0.228991\pi\) | |||||||
\(132\) | −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 | 0.894407 | + | 0.447254i | \(0.147598\pi\) |
−0.0598699 | + | 0.998206i | \(0.519069\pi\) | |||||||
\(138\) | 0.355635 | + | 0.0746186i | 0.0302737 | + | 0.00635196i | ||||
\(139\) | 1.31540 | − | 2.27833i | 0.111570 | − | 0.193246i | −0.804833 | − | 0.593501i | \(-0.797745\pi\) |
0.916404 | + | 0.400256i | \(0.131079\pi\) | |||||||
\(140\) | 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 | −0.627137 | − | 0.778909i | \(-0.715773\pi\) |
0.988124 | + | 0.153662i | \(0.0491066\pi\) | |||||||
\(150\) | 0.165593 | − | 0.184882i | 0.0135206 | − | 0.0150955i | ||||
\(151\) | −2.33211 | − | 4.03933i | −0.189784 | − | 0.328716i | 0.755394 | − | 0.655271i | \(-0.227446\pi\) |
−0.945178 | + | 0.326555i | \(0.894112\pi\) | |||||||
\(152\) | 0.519564 | 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 | \(-0.885298\pi\) |
0.773247 | + | 0.634105i | \(0.218631\pi\) | |||||||
\(158\) | −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 | \(-0.892782\pi\) |
0.758126 | + | 0.652109i | \(0.226115\pi\) | |||||||
\(168\) | 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 | \(-0.105404\pi\) |
−0.754397 | + | 0.656419i | \(0.772071\pi\) | |||||||
\(174\) | 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 | \(-0.319763\pi\) | ||||
0.536454 | + | 0.843930i | \(0.319763\pi\) | |||||||
\(182\) | 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 | 0.810040 | − | 0.586374i | \(-0.199445\pi\) |
−0.912835 | + | 0.408328i | \(0.866112\pi\) | |||||||
\(192\) | 13.3713 | + | 2.80554i | 0.964990 | + | 0.202472i | ||||
\(193\) | −4.41443 | + | 7.64601i | −0.317758 | + | 0.550372i | −0.980020 | − | 0.198900i | \(-0.936263\pi\) |
0.662262 | + | 0.749272i | \(0.269596\pi\) | |||||||
\(194\) | −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 | \(-0.367412\pi\) | ||||
0.404596 | + | 0.914496i | \(0.367412\pi\) | |||||||
\(200\) | 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 | −0.218199 | − | 0.975904i | \(-0.570018\pi\) |
0.954257 | − | 0.298986i | \(-0.0966486\pi\) | |||||||
\(212\) | 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 | \(-0.0895213\pi\) |
−0.720719 | + | 0.693228i | \(0.756188\pi\) | |||||||
\(224\) | 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 | \(-0.317955\pi\) |
−0.998833 | + | 0.0482933i | \(0.984622\pi\) | |||||||
\(228\) | 4.38544 | − | 4.89628i | 0.290433 | − | 0.324264i | ||||
\(229\) | −13.1972 | + | 22.8581i | −0.872092 | + | 1.51051i | −0.0122645 | + | 0.999925i | \(0.503904\pi\) |
−0.859828 | + | 0.510584i | \(0.829429\pi\) | |||||||
\(230\) | 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 | −0.500867 | − | 0.865524i | \(-0.666985\pi\) |
0.999999 | + | 0.00100121i | \(0.000318696\pi\) | |||||||
\(240\) | −17.9354 | − | 3.76318i | −1.15773 | − | 0.242912i | ||||
\(241\) | 0.589942 | + | 1.02181i | 0.0380015 | + | 0.0658205i | 0.884401 | − | 0.466729i | \(-0.154568\pi\) |
−0.846399 | + | 0.532549i | \(0.821234\pi\) | |||||||
\(242\) | −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 | \(-0.556040\pi\) | ||||
−0.175147 | + | 0.984542i | \(0.556040\pi\) | |||||||
\(252\) | 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 | \(-0.734138\pi\) |
0.977619 | + | 0.210382i | \(0.0674709\pi\) | |||||||
\(258\) | −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 | 0.621348 | − | 0.783535i | \(-0.286585\pi\) |
−0.989235 | + | 0.146336i | \(0.953252\pi\) | |||||||
\(264\) | 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 | \(-0.866626\pi\) | ||||
−0.913494 | + | 0.406853i | \(0.866626\pi\) | |||||||
\(270\) | −0.770002 | − | 0.550239i | −0.0468608 | − | 0.0334865i | ||||
\(271\) | 7.09650 | 0.431082 | 0.215541 | − | 0.976495i | \(-0.430849\pi\) | ||||
0.215541 | + | 0.976495i | \(0.430849\pi\) | |||||||
\(272\) | −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 | 0.975013 | − | 0.222150i | \(-0.0713075\pi\) |
−0.679894 | + | 0.733311i | \(0.737974\pi\) | |||||||
\(278\) | −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 | 0.964025 | + | 0.265813i | \(0.0856403\pi\) |
−0.251812 | + | 0.967776i | \(0.581026\pi\) | |||||||
\(282\) | −0.300181 | + | 0.335148i | −0.0178755 | + | 0.0199578i | ||||
\(283\) | −1.50798 | + | 2.61189i | −0.0896399 | + | 0.155261i | −0.907359 | − | 0.420357i | \(-0.861905\pi\) |
0.817719 | + | 0.575618i | \(0.195238\pi\) | |||||||
\(284\) | −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 | \(-0.667300\pi\) |
0.999998 | + | 0.00198814i | \(0.000632845\pi\) | |||||||
\(294\) | 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 | \(-0.730527\pi\) | ||||
−0.662554 | + | 0.749014i | \(0.730527\pi\) | |||||||
\(308\) | 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 | \(-0.817163\pi\) |
0.890297 | + | 0.455381i | \(0.150497\pi\) | |||||||
\(312\) | 1.65852 | − | 1.85171i | 0.0938951 | − | 0.104832i | ||||
\(313\) | 2.30458 | + | 3.99166i | 0.130263 | + | 0.225622i | 0.923778 | − | 0.382929i | \(-0.125085\pi\) |
−0.793515 | + | 0.608551i | \(0.791751\pi\) | |||||||
\(314\) | 0.278483 | 0.0157157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.62331 | −0.0913183 | ||||||||
\(317\) | 12.9421 | + | 22.4163i | 0.726898 | + | 1.25902i | 0.958188 | + | 0.286140i | \(0.0923721\pi\) |
−0.231290 | + | 0.972885i | \(0.574295\pi\) | |||||||
\(318\) | 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 | 0.863800 | − | 0.503835i | \(-0.168078\pi\) |
−0.868234 | + | 0.496156i | \(0.834745\pi\) | |||||||
\(332\) | 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 | −0.715989 | − | 0.698112i | \(-0.754024\pi\) |
0.962577 | + | 0.271009i | \(0.0873572\pi\) | |||||||
\(338\) | −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 | −0.777290 | − | 0.629142i | \(-0.783406\pi\) |
0.933498 | + | 0.358582i | \(0.116740\pi\) | |||||||
\(348\) | 21.6100 | + | 4.53416i | 1.15842 | + | 0.243056i | ||||
\(349\) | 13.6310 | + | 23.6095i | 0.729648 | + | 1.26379i | 0.957032 | + | 0.289983i | \(0.0936496\pi\) |
−0.227384 | + | 0.973805i | \(0.573017\pi\) | |||||||
\(350\) | 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 | −0.984591 | − | 0.174874i | \(-0.944048\pi\) |
0.340850 | − | 0.940118i | \(-0.389285\pi\) | |||||||
\(354\) | −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 | 0.807654 | + | 0.589657i | \(0.200737\pi\) |
0.106831 | + | 0.994277i | \(0.465930\pi\) | |||||||
\(368\) | −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 | −0.880265 | − | 0.474482i | \(-0.842635\pi\) |
0.851046 | + | 0.525091i | \(0.175969\pi\) | |||||||
\(374\) | 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 | 0.405763 | + | 0.913978i | \(0.367006\pi\) |
−0.994410 | + | 0.105588i | \(0.966328\pi\) | |||||||
\(384\) | −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 | 0.593801 | − | 0.804612i | \(-0.297627\pi\) |
−0.993715 | + | 0.111941i | \(0.964293\pi\) | |||||||
\(390\) | −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 | \(-0.635937\pi\) | ||||
−0.414195 | + | 0.910188i | \(0.635937\pi\) | |||||||
\(398\) | −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 | \(0.984779\pi\) | |||||||
\(402\) | 0.385417 | + | 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 | 0.189107 | + | 0.981956i | \(0.439441\pi\) |
−0.944953 | + | 0.327207i | \(0.893893\pi\) | |||||||
\(410\) | 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 | 0.471456 | + | 0.881890i | \(0.343729\pi\) |
−0.999467 | + | 0.0326524i | \(0.989605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6217 | + | 23.5935i | 0.663881 | + | 1.14988i | 0.979587 | + | 0.201019i | \(0.0644252\pi\) |
−0.315706 | + | 0.948857i | \(0.602241\pi\) | |||||||
\(422\) | −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 | \(-0.526147\pi\) | ||||
−0.0820494 | + | 0.996628i | \(0.526147\pi\) | |||||||
\(434\) | 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 | \(-0.116413\pi\) |
−0.776644 | + | 0.629939i | \(0.783080\pi\) | |||||||
\(440\) | 1.16366 | 0.0554753 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.35191 | −0.111869 | ||||||||
\(443\) | −14.3456 | − | 24.8473i | −0.681581 | − | 1.18053i | −0.974498 | − | 0.224395i | \(-0.927959\pi\) |
0.292917 | − | 0.956138i | \(-0.405374\pi\) | |||||||
\(444\) | −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 | 0.526571 | − | 0.850131i | \(-0.323477\pi\) |
−0.999521 | + | 0.0309581i | \(0.990144\pi\) | |||||||
\(458\) | 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 | 0.997168 | + | 0.0752117i | \(0.0239633\pi\) |
−0.433449 | + | 0.901178i | \(0.642703\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.40242 | − | 4.16111i | 0.111650 | − | 0.193383i | −0.804786 | − | 0.593565i | \(-0.797720\pi\) |
0.916436 | + | 0.400182i | \(0.131053\pi\) | |||||||
\(464\) | −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 | \(-0.282895\pi\) | ||||
0.630389 | + | 0.776279i | \(0.282895\pi\) | |||||||
\(468\) | −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 | \(-0.0113109\pi\) |
−0.530452 | + | 0.847715i | \(0.677978\pi\) | |||||||
\(480\) | 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 | −0.986662 | − | 0.162781i | \(-0.947954\pi\) |
0.634303 | + | 0.773084i | \(0.281287\pi\) | |||||||
\(492\) | 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 | −0.999624 | − | 0.0274192i | \(-0.991271\pi\) |
0.523558 | + | 0.851990i | \(0.324604\pi\) | |||||||
\(500\) | −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 | \(-0.381392\pi\) | ||||
0.364055 | + | 0.931377i | \(0.381392\pi\) | |||||||
\(504\) | 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 | \(-0.929767\pi\) |
0.677415 | + | 0.735601i | \(0.263100\pi\) | |||||||
\(510\) | −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 | \(-0.490054\pi\) | ||||
0.0312413 | + | 0.999512i | \(0.490054\pi\) | |||||||
\(522\) | −1.05619 | + | 0.775859i | −0.0462281 | + | 0.0339584i | ||||
\(523\) | 7.71060 | 0.337161 | 0.168581 | − | 0.985688i | \(-0.446082\pi\) | ||||
0.168581 | + | 0.985688i | \(0.446082\pi\) | |||||||
\(524\) | 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 | 0.943818 | + | 0.330466i | \(0.107206\pi\) |
−0.185717 | + | 0.982603i | \(0.559461\pi\) | |||||||
\(548\) | 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 | \(-0.723680\pi\) |
0.984002 | + | 0.178157i | \(0.0570135\pi\) | |||||||
\(564\) | −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 | 0.862108 | − | 0.506725i | \(-0.169144\pi\) |
−0.869891 | + | 0.493245i | \(0.835811\pi\) | |||||||
\(570\) | 0.587209 | + | 0.123207i | 0.0245955 | + | 0.00516057i | ||||
\(571\) | −14.6152 | + | 25.3142i | −0.611626 | + | 1.05937i | 0.379340 | + | 0.925257i | \(0.376151\pi\) |
−0.990966 | + | 0.134110i | \(0.957182\pi\) | |||||||
\(572\) | 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 | \(-0.398526\pi\) | ||||
0.313417 | + | 0.949616i | \(0.398526\pi\) | |||||||
\(578\) | −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 | \(-0.155682\pi\) |
−0.848259 | + | 0.529581i | \(0.822349\pi\) | |||||||
\(588\) | 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 | \(-0.428706\pi\) | ||||
0.222109 | + | 0.975022i | \(0.428706\pi\) | |||||||
\(594\) | −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 | −0.984423 | − | 0.175817i | \(-0.943743\pi\) |
0.644474 | + | 0.764626i | \(0.277076\pi\) | |||||||
\(600\) | −0.308902 | − | 0.942290i | −0.0126109 | − | 0.0384688i | ||||
\(601\) | −12.9011 | − | 22.3453i | −0.526246 | − | 0.911485i | −0.999532 | − | 0.0305765i | \(-0.990266\pi\) |
0.473286 | − | 0.880909i | \(-0.343068\pi\) | |||||||
\(602\) | 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 | 0.171834 | + | 0.985126i | \(0.445031\pi\) |
−0.939061 | + | 0.343750i | \(0.888303\pi\) | |||||||
\(608\) | 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 | −0.329393 | − | 0.944193i | \(-0.606844\pi\) |
0.982391 | − | 0.186834i | \(-0.0598227\pi\) | |||||||
\(618\) | 0.600151 | + | 0.125922i | 0.0241416 | + | 0.00506534i | ||||
\(619\) | −16.5987 | − | 28.7498i | −0.667157 | − | 1.15555i | −0.978696 | − | 0.205317i | \(-0.934178\pi\) |
0.311538 | − | 0.950234i | \(-0.399156\pi\) | |||||||
\(620\) | 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 | −0.880482 | − | 0.474079i | \(-0.842781\pi\) |
0.0296762 | − | 0.999560i | \(-0.490552\pi\) | |||||||
\(642\) | −0.625265 | − | 1.90734i | −0.0246772 | − | 0.0752766i | ||||
\(643\) | −3.20088 | + | 5.54409i | −0.126230 | + | 0.218638i | −0.922213 | − | 0.386682i | \(-0.873621\pi\) |
0.795983 | + | 0.605319i | \(0.206955\pi\) | |||||||
\(644\) | 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 | \(-0.475649\pi\) | ||||
0.0764278 | + | 0.997075i | \(0.475649\pi\) | |||||||
\(648\) | −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 | −0.975106 | − | 0.221738i | \(-0.928827\pi\) |
0.679584 | + | 0.733598i | \(0.262160\pi\) | |||||||
\(654\) | −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 | 0.693078 | − | 0.720862i | \(-0.256254\pi\) |
−0.970824 | + | 0.239792i | \(0.922921\pi\) | |||||||
\(660\) | 9.82201 | − | 10.9661i | 0.382321 | − | 0.426856i | ||||
\(661\) | 9.70965 | − | 16.8176i | 0.377662 | − | 0.654129i | −0.613060 | − | 0.790036i | \(-0.710062\pi\) |
0.990722 | + | 0.135907i | \(0.0433949\pi\) | |||||||
\(662\) | −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 | 0.803190 | − | 0.595723i | \(-0.203135\pi\) |
−0.917506 | + | 0.397721i | \(0.869801\pi\) | |||||||
\(674\) | −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 | −0.964603 | − | 0.263706i | \(-0.915055\pi\) |
0.253925 | − | 0.967224i | \(-0.418278\pi\) | |||||||
\(678\) | −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 | \(-0.257286\pi\) |
−0.971597 | + | 0.236643i | \(0.923953\pi\) | |||||||
\(692\) | 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 | 0.702693 | − | 0.711494i | \(-0.251981\pi\) |
−0.967518 | + | 0.252803i | \(0.918648\pi\) | |||||||
\(710\) | −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 | \(-0.409790\pi\) | ||||
0.279624 | + | 0.960109i | \(0.409790\pi\) | |||||||
\(720\) | 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 | \(-0.327519\pi\) |
−0.999833 | + | 0.0182642i | \(0.994186\pi\) | |||||||
\(728\) | 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 | 0.475446 | + | 0.879745i | \(0.342287\pi\) |
−0.999604 | + | 0.0281244i | \(0.991047\pi\) | |||||||
\(734\) | 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 | −0.869118 | − | 0.494605i | \(-0.835313\pi\) |
0.862899 | + | 0.505376i | \(0.168646\pi\) | |||||||
\(744\) | 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 | −0.316177 | − | 0.948700i | \(-0.602399\pi\) |
0.979687 | − | 0.200533i | \(-0.0642673\pi\) | |||||||
\(752\) | 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 | 0.394232 | + | 0.919011i | \(0.371011\pi\) |
−0.993003 | + | 0.118091i | \(0.962323\pi\) | |||||||
\(762\) | 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 | \(-0.848132\pi\) |
0.841853 | + | 0.539707i | \(0.181465\pi\) | |||||||
\(770\) | 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 | \(-0.461382\pi\) | ||||
0.121026 | + | 0.992649i | \(0.461382\pi\) | |||||||
\(774\) | 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 | 0.488963 | + | 0.872305i | \(0.337375\pi\) |
−0.999919 | + | 0.0126980i | \(0.995958\pi\) | |||||||
\(788\) | 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 | \(-0.699894\pi\) |
0.994557 | + | 0.104196i | \(0.0332270\pi\) | |||||||
\(798\) | 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 | \(-0.248751\pi\) | ||||
0.709876 | + | 0.704326i | \(0.248751\pi\) | |||||||
\(812\) | 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 | 0.999940 | − | 0.0109361i | \(-0.00348114\pi\) |
−0.509441 | + | 0.860506i | \(0.670148\pi\) | |||||||
\(822\) | −1.54358 | + | 1.72339i | −0.0538387 | + | 0.0601101i | ||||
\(823\) | −12.9529 | + | 22.4351i | −0.451510 | + | 0.782038i | −0.998480 | − | 0.0551142i | \(-0.982448\pi\) |
0.546970 | + | 0.837152i | \(0.315781\pi\) | |||||||
\(824\) | −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 | \(-0.587937\pi\) | ||||
−0.272761 | + | 0.962082i | \(0.587937\pi\) | |||||||
\(830\) | 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 | \(-0.207419\pi\) |
−0.922776 | + | 0.385337i | \(0.874085\pi\) | |||||||
\(840\) | 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 | −0.814756 | − | 0.579804i | \(-0.803129\pi\) |
−0.0947464 | − | 0.995501i | \(-0.530204\pi\) | |||||||
\(854\) | 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 | \(-0.187424\pi\) |
−0.896767 | + | 0.442504i | \(0.854090\pi\) | |||||||
\(858\) | 0.309941 | + | 0.945459i | 0.0105812 | + | 0.0322774i | ||||
\(859\) | 19.4884 | − | 33.7549i | 0.664936 | − | 1.15170i | −0.314367 | − | 0.949301i | \(-0.601792\pi\) |
0.979303 | − | 0.202401i | \(-0.0648744\pi\) | |||||||
\(860\) | −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 | −0.994373 | − | 0.105940i | \(-0.966215\pi\) |
0.588933 | + | 0.808182i | \(0.299548\pi\) | |||||||
\(878\) | 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 | \(-0.474916\pi\) | ||||
0.0787231 | + | 0.996897i | \(0.474916\pi\) | |||||||
\(882\) | 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 | \(-0.670843\pi\) |
0.999914 | + | 0.0131191i | \(0.00417605\pi\) | |||||||
\(888\) | 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 | 0.973673 | + | 0.227950i | \(0.0732024\pi\) |
−0.289426 | + | 0.957201i | \(0.593464\pi\) | |||||||
\(908\) | −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 | 0.731508 | + | 0.681833i | \(0.238817\pi\) |
0.224731 | + | 0.974421i | \(0.427850\pi\) | |||||||
\(912\) | −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 | −0.902029 | − | 0.431675i | \(-0.857923\pi\) |
0.0771732 | − | 0.997018i | \(-0.475411\pi\) | |||||||
\(930\) | −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 | \(-0.595754\pi\) | ||||
−0.296303 | + | 0.955094i | \(0.595754\pi\) | |||||||
\(938\) | 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 | \(-0.922883\pi\) |
0.693163 | + | 0.720781i | \(0.256217\pi\) | |||||||
\(942\) | −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 | −0.999905 | − | 0.0137988i | \(-0.995608\pi\) |
0.488002 | − | 0.872842i | \(-0.337726\pi\) | |||||||
\(948\) | 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 | −0.568826 | − | 0.822458i | \(-0.692602\pi\) |
0.996682 | + | 0.0813886i | \(0.0259355\pi\) | |||||||
\(968\) | −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 | \(-0.137856\pi\) | ||||
0.907674 | + | 0.419676i | \(0.137856\pi\) | |||||||
\(972\) | −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 | 0.0121160 | + | 0.999927i | \(0.496143\pi\) |
−0.872020 | + | 0.489471i | \(0.837190\pi\) | |||||||
\(978\) | −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 | \(-0.0226635\pi\) |
−0.560342 | + | 0.828262i | \(0.689330\pi\) | |||||||
\(984\) | 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 | −0.997074 | − | 0.0764472i | \(-0.975642\pi\) |
0.432332 | − | 0.901715i | \(-0.357691\pi\) | |||||||
\(998\) | 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.148.5 | ✓ | 24 | |
3.2 | odd | 2 | 1323.2.f.h.442.8 | 24 | |||
7.2 | even | 3 | 441.2.g.h.67.6 | 24 | |||
7.3 | odd | 6 | 441.2.h.h.373.7 | 24 | |||
7.4 | even | 3 | 441.2.h.h.373.8 | 24 | |||
7.5 | odd | 6 | 441.2.g.h.67.5 | 24 | |||
7.6 | odd | 2 | inner | 441.2.f.h.148.6 | yes | 24 | |
9.2 | odd | 6 | 1323.2.f.h.883.8 | 24 | |||
9.4 | even | 3 | 3969.2.a.bh.1.8 | 12 | |||
9.5 | odd | 6 | 3969.2.a.bi.1.5 | 12 | |||
9.7 | even | 3 | inner | 441.2.f.h.295.5 | yes | 24 | |
21.2 | odd | 6 | 1323.2.g.h.361.7 | 24 | |||
21.5 | even | 6 | 1323.2.g.h.361.8 | 24 | |||
21.11 | odd | 6 | 1323.2.h.h.226.5 | 24 | |||
21.17 | even | 6 | 1323.2.h.h.226.6 | 24 | |||
21.20 | even | 2 | 1323.2.f.h.442.7 | 24 | |||
63.2 | odd | 6 | 1323.2.h.h.802.5 | 24 | |||
63.11 | odd | 6 | 1323.2.g.h.667.7 | 24 | |||
63.13 | odd | 6 | 3969.2.a.bh.1.7 | 12 | |||
63.16 | even | 3 | 441.2.h.h.214.8 | 24 | |||
63.20 | even | 6 | 1323.2.f.h.883.7 | 24 | |||
63.25 | even | 3 | 441.2.g.h.79.6 | 24 | |||
63.34 | odd | 6 | inner | 441.2.f.h.295.6 | yes | 24 | |
63.38 | even | 6 | 1323.2.g.h.667.8 | 24 | |||
63.41 | even | 6 | 3969.2.a.bi.1.6 | 12 | |||
63.47 | even | 6 | 1323.2.h.h.802.6 | 24 | |||
63.52 | odd | 6 | 441.2.g.h.79.5 | 24 | |||
63.61 | odd | 6 | 441.2.h.h.214.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
441.2.f.h.148.6 | yes | 24 | 7.6 | odd | 2 | inner | |
441.2.f.h.295.5 | yes | 24 | 9.7 | even | 3 | inner | |
441.2.f.h.295.6 | yes | 24 | 63.34 | odd | 6 | inner | |
441.2.g.h.67.5 | 24 | 7.5 | odd | 6 | |||
441.2.g.h.67.6 | 24 | 7.2 | even | 3 | |||
441.2.g.h.79.5 | 24 | 63.52 | odd | 6 | |||
441.2.g.h.79.6 | 24 | 63.25 | even | 3 | |||
441.2.h.h.214.7 | 24 | 63.61 | odd | 6 | |||
441.2.h.h.214.8 | 24 | 63.16 | even | 3 | |||
441.2.h.h.373.7 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.373.8 | 24 | 7.4 | even | 3 | |||
1323.2.f.h.442.7 | 24 | 21.20 | even | 2 | |||
1323.2.f.h.442.8 | 24 | 3.2 | odd | 2 | |||
1323.2.f.h.883.7 | 24 | 63.20 | even | 6 | |||
1323.2.f.h.883.8 | 24 | 9.2 | odd | 6 | |||
1323.2.g.h.361.7 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.361.8 | 24 | 21.5 | even | 6 | |||
1323.2.g.h.667.7 | 24 | 63.11 | odd | 6 | |||
1323.2.g.h.667.8 | 24 | 63.38 | even | 6 | |||
1323.2.h.h.226.5 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.226.6 | 24 | 21.17 | even | 6 | |||
1323.2.h.h.802.5 | 24 | 63.2 | odd | 6 | |||
1323.2.h.h.802.6 | 24 | 63.47 | even | 6 | |||
3969.2.a.bh.1.7 | 12 | 63.13 | odd | 6 | |||
3969.2.a.bh.1.8 | 12 | 9.4 | even | 3 | |||
3969.2.a.bi.1.5 | 12 | 9.5 | odd | 6 | |||
3969.2.a.bi.1.6 | 12 | 63.41 | even | 6 |