Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(101,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bi (of order \(10\), degree \(4\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 101.10 | ||
Character | \(\chi\) | \(=\) | 825.101 |
Dual form | 825.2.bi.h.776.10 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0382790 | + | 0.117811i | −0.0270673 | + | 0.0833047i | −0.963678 | − | 0.267068i | \(-0.913945\pi\) |
0.936610 | + | 0.350373i | \(0.113945\pi\) | |||||||
\(3\) | −0.243783 | − | 1.71481i | −0.140748 | − | 0.990045i | ||||
\(4\) | 1.60562 | + | 1.16655i | 0.802810 | + | 0.583276i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.211354 | + | 0.0369209i | 0.0862851 | + | 0.0150729i | ||||
\(7\) | 1.86875 | − | 2.57211i | 0.706321 | − | 0.972167i | −0.293548 | − | 0.955944i | \(-0.594836\pi\) |
0.999868 | − | 0.0162228i | \(-0.00516411\pi\) | |||||||
\(8\) | −0.399325 | + | 0.290127i | −0.141183 | + | 0.102575i | ||||
\(9\) | −2.88114 | + | 0.836083i | −0.960380 | + | 0.278694i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.45933 | + | 2.22524i | 0.741516 | + | 0.670935i | ||||
\(12\) | 1.60899 | − | 3.03772i | 0.464475 | − | 0.876913i | ||||
\(13\) | 4.24445 | + | 1.37910i | 1.17720 | + | 0.382495i | 0.831325 | − | 0.555786i | \(-0.187583\pi\) |
0.345873 | + | 0.938281i | \(0.387583\pi\) | |||||||
\(14\) | 0.231488 | + | 0.318616i | 0.0618679 | + | 0.0851538i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.20769 | + | 3.71689i | 0.301923 | + | 0.929222i | ||||
\(17\) | 0.436543 | + | 1.34354i | 0.105877 | + | 0.325856i | 0.989935 | − | 0.141521i | \(-0.0451991\pi\) |
−0.884058 | + | 0.467377i | \(0.845199\pi\) | |||||||
\(18\) | 0.0117877 | − | 0.371433i | 0.00277839 | − | 0.0875476i | ||||
\(19\) | −2.96232 | − | 4.07728i | −0.679603 | − | 0.935393i | 0.320326 | − | 0.947307i | \(-0.396207\pi\) |
−0.999929 | + | 0.0119143i | \(0.996207\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.86625 | − | 2.57751i | −1.06190 | − | 0.562459i | ||||
\(22\) | −0.356298 | + | 0.204555i | −0.0759629 | + | 0.0436113i | ||||
\(23\) | − | 4.40944i | − | 0.919431i | −0.888066 | − | 0.459716i | \(-0.847951\pi\) | ||
0.888066 | − | 0.459716i | \(-0.152049\pi\) | |||||||
\(24\) | 0.594860 | + | 0.614038i | 0.121425 | + | 0.125340i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.324946 | + | 0.447250i | −0.0637272 | + | 0.0877130i | ||||
\(27\) | 2.13609 | + | 4.73678i | 0.411092 | + | 0.911594i | ||||
\(28\) | 6.00100 | − | 1.94984i | 1.13408 | − | 0.368486i | ||||
\(29\) | 4.72158 | + | 3.43043i | 0.876776 | + | 0.637015i | 0.932397 | − | 0.361437i | \(-0.117714\pi\) |
−0.0556204 | + | 0.998452i | \(0.517714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.721415 | − | 2.22029i | 0.129570 | − | 0.398775i | −0.865136 | − | 0.501537i | \(-0.832768\pi\) |
0.994706 | + | 0.102762i | \(0.0327680\pi\) | |||||||
\(32\) | −1.47130 | −0.260092 | ||||||||
\(33\) | 3.21632 | − | 4.75976i | 0.559889 | − | 0.828567i | ||||
\(34\) | −0.174994 | −0.0300112 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.60135 | − | 2.01857i | −0.933558 | − | 0.336428i | ||||
\(37\) | −3.86196 | − | 2.80588i | −0.634903 | − | 0.461284i | 0.223192 | − | 0.974774i | \(-0.428352\pi\) |
−0.858095 | + | 0.513490i | \(0.828352\pi\) | |||||||
\(38\) | 0.593742 | − | 0.192918i | 0.0963176 | − | 0.0312955i | ||||
\(39\) | 1.33018 | − | 7.61462i | 0.212999 | − | 1.21932i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.66980 | − | 1.93972i | 0.416953 | − | 0.302934i | −0.359458 | − | 0.933161i | \(-0.617038\pi\) |
0.776411 | + | 0.630227i | \(0.217038\pi\) | |||||||
\(42\) | 0.489933 | − | 0.474632i | 0.0755983 | − | 0.0732372i | ||||
\(43\) | 2.97470i | 0.453638i | 0.973937 | + | 0.226819i | \(0.0728326\pi\) | ||||
−0.973937 | + | 0.226819i | \(0.927167\pi\) | |||||||
\(44\) | 1.35289 | + | 6.44182i | 0.203956 | + | 0.971142i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.519478 | + | 0.168789i | 0.0765929 | + | 0.0248865i | ||||
\(47\) | −3.14996 | − | 4.33555i | −0.459469 | − | 0.632405i | 0.514929 | − | 0.857233i | \(-0.327818\pi\) |
−0.974399 | + | 0.224827i | \(0.927818\pi\) | |||||||
\(48\) | 6.07934 | − | 2.97707i | 0.877477 | − | 0.429703i | ||||
\(49\) | −0.960422 | − | 2.95587i | −0.137203 | − | 0.422268i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.19749 | − | 1.07612i | 0.307710 | − | 0.150687i | ||||
\(52\) | 5.20617 | + | 7.16568i | 0.721966 | + | 0.993702i | ||||
\(53\) | −0.249485 | − | 0.0810625i | −0.0342694 | − | 0.0111348i | 0.291832 | − | 0.956470i | \(-0.405735\pi\) |
−0.326102 | + | 0.945335i | \(0.605735\pi\) | |||||||
\(54\) | −0.639811 | + | 0.0703354i | −0.0870672 | + | 0.00957144i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.56928i | 0.209704i | ||||||||
\(57\) | −6.26960 | + | 6.07378i | −0.830429 | + | 0.804492i | ||||
\(58\) | −0.584879 | + | 0.424939i | −0.0767983 | + | 0.0557973i | ||||
\(59\) | 5.24873 | − | 7.22425i | 0.683326 | − | 0.940517i | −0.316642 | − | 0.948545i | \(-0.602555\pi\) |
0.999968 | + | 0.00802781i | \(0.00255536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.1273 | + | 4.59023i | −1.80881 | + | 0.587719i | −1.00000 | 0.000348407i | \(-0.999889\pi\) | |
−0.808812 | + | 0.588067i | \(0.799889\pi\) | |||||||
\(62\) | 0.233958 | + | 0.169981i | 0.0297127 | + | 0.0215876i | ||||
\(63\) | −3.23363 | + | 8.97305i | −0.407399 | + | 1.13050i | ||||
\(64\) | −2.35906 | + | 7.26044i | −0.294883 | + | 0.907555i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.437632 | + | 0.561115i | 0.0538688 | + | 0.0690685i | ||||
\(67\) | 1.33725 | 0.163371 | 0.0816854 | − | 0.996658i | \(-0.473970\pi\) | ||||
0.0816854 | + | 0.996658i | \(0.473970\pi\) | |||||||
\(68\) | −0.866386 | + | 2.66646i | −0.105065 | + | 0.323356i | ||||
\(69\) | −7.56134 | + | 1.07495i | −0.910279 | + | 0.129408i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.40085 | − | 1.75484i | 0.640964 | − | 0.208262i | 0.0295380 | − | 0.999564i | \(-0.490596\pi\) |
0.611426 | + | 0.791302i | \(0.290596\pi\) | |||||||
\(72\) | 0.907941 | − | 1.16976i | 0.107002 | − | 0.137858i | ||||
\(73\) | 3.84559 | − | 5.29300i | 0.450092 | − | 0.619499i | −0.522325 | − | 0.852746i | \(-0.674935\pi\) |
0.972417 | + | 0.233248i | \(0.0749353\pi\) | |||||||
\(74\) | 0.478395 | − | 0.347574i | 0.0556122 | − | 0.0404047i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 10.0023i | − | 1.14734i | ||||||
\(77\) | 10.3194 | − | 2.16726i | 1.17601 | − | 0.246982i | ||||
\(78\) | 0.846165 | + | 0.448189i | 0.0958093 | + | 0.0507474i | ||||
\(79\) | 4.98511 | + | 1.61976i | 0.560868 | + | 0.182237i | 0.575712 | − | 0.817653i | \(-0.304725\pi\) |
−0.0148435 | + | 0.999890i | \(0.504725\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.60193 | − | 4.81774i | 0.844659 | − | 0.535305i | ||||
\(82\) | 0.126323 | + | 0.388781i | 0.0139500 | + | 0.0429337i | ||||
\(83\) | −4.30625 | − | 13.2533i | −0.472672 | − | 1.45473i | −0.849072 | − | 0.528277i | \(-0.822838\pi\) |
0.376400 | − | 0.926457i | \(-0.377162\pi\) | |||||||
\(84\) | −4.80655 | − | 9.81523i | −0.524438 | − | 1.07093i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.350452 | − | 0.113869i | −0.0377902 | − | 0.0122788i | ||||
\(87\) | 4.73149 | − | 8.93290i | 0.507269 | − | 0.957707i | ||||
\(88\) | −1.62767 | − | 0.175077i | −0.173511 | − | 0.0186632i | ||||
\(89\) | 13.7521i | 1.45772i | 0.684663 | + | 0.728860i | \(0.259949\pi\) | ||||
−0.684663 | + | 0.728860i | \(0.740051\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.4790 | − | 8.34000i | 1.20333 | − | 0.874269i | ||||
\(92\) | 5.14383 | − | 7.07988i | 0.536282 | − | 0.738128i | ||||
\(93\) | −3.98324 | − | 0.695821i | −0.413043 | − | 0.0721533i | ||||
\(94\) | 0.631351 | − | 0.205139i | 0.0651189 | − | 0.0211584i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.358679 | + | 2.52300i | 0.0366075 | + | 0.257503i | ||||
\(97\) | 3.27721 | − | 10.0862i | 0.332750 | − | 1.02410i | −0.635070 | − | 0.772455i | \(-0.719029\pi\) |
0.967820 | − | 0.251645i | \(-0.0809714\pi\) | |||||||
\(98\) | 0.384997 | 0.0388906 | ||||||||
\(99\) | −8.94616 | − | 4.35502i | −0.899123 | − | 0.437696i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.366757 | + | 1.12876i | −0.0364937 | + | 0.112316i | −0.967644 | − | 0.252320i | \(-0.918807\pi\) |
0.931150 | + | 0.364636i | \(0.118807\pi\) | |||||||
\(102\) | 0.0426605 | + | 0.300081i | 0.00422402 | + | 0.0297124i | ||||
\(103\) | −3.79085 | − | 2.75421i | −0.373524 | − | 0.271381i | 0.385147 | − | 0.922855i | \(-0.374151\pi\) |
−0.758671 | + | 0.651474i | \(0.774151\pi\) | |||||||
\(104\) | −2.09503 | + | 0.680716i | −0.205434 | + | 0.0667497i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0191000 | − | 0.0262890i | 0.00185516 | − | 0.00255341i | ||||
\(107\) | −10.2420 | + | 7.44124i | −0.990130 | + | 0.719371i | −0.959950 | − | 0.280173i | \(-0.909608\pi\) |
−0.0301803 | + | 0.999544i | \(0.509608\pi\) | |||||||
\(108\) | −2.09594 | + | 10.0973i | −0.201682 | + | 0.971616i | ||||
\(109\) | 2.33097i | 0.223266i | 0.993749 | + | 0.111633i | \(0.0356081\pi\) | ||||
−0.993749 | + | 0.111633i | \(0.964392\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.87007 | + | 7.30656i | −0.367331 | + | 0.693508i | ||||
\(112\) | 11.8171 | + | 3.83962i | 1.11661 | + | 0.362810i | ||||
\(113\) | 9.53937 | + | 13.1298i | 0.897388 | + | 1.23515i | 0.971294 | + | 0.237884i | \(0.0764537\pi\) |
−0.0739054 | + | 0.997265i | \(0.523546\pi\) | |||||||
\(114\) | −0.475562 | − | 0.971123i | −0.0445405 | − | 0.0909540i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.57930 | + | 11.0159i | 0.332329 | + | 1.02280i | ||||
\(117\) | −13.3819 | − | 0.424685i | −1.23716 | − | 0.0392621i | ||||
\(118\) | 0.650177 | + | 0.894892i | 0.0598537 | + | 0.0823815i | ||||
\(119\) | 4.27152 | + | 1.38790i | 0.391570 | + | 0.127229i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.09661 | + | 10.9452i | 0.0996921 | + | 0.995018i | ||||
\(122\) | − | 1.84005i | − | 0.166590i | ||||||
\(123\) | −3.97711 | − | 4.10533i | −0.358604 | − | 0.370165i | ||||
\(124\) | 3.74840 | − | 2.72337i | 0.336616 | − | 0.244566i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.933340 | − | 0.724435i | −0.0831485 | − | 0.0645378i | ||||
\(127\) | −16.8339 | + | 5.46968i | −1.49377 | + | 0.485355i | −0.938194 | − | 0.346110i | \(-0.887502\pi\) |
−0.555576 | + | 0.831466i | \(0.687502\pi\) | |||||||
\(128\) | −3.14567 | − | 2.28547i | −0.278041 | − | 0.202009i | ||||
\(129\) | 5.10105 | − | 0.725182i | 0.449122 | − | 0.0638487i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.7072 | −1.28498 | −0.642488 | − | 0.766296i | \(-0.722098\pi\) | ||||
−0.642488 | + | 0.766296i | \(0.722098\pi\) | |||||||
\(132\) | 10.7167 | − | 3.89036i | 0.932768 | − | 0.338613i | ||||
\(133\) | −16.0231 | −1.38938 | ||||||||
\(134\) | −0.0511885 | + | 0.157542i | −0.00442201 | + | 0.0136096i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.564119 | − | 0.409856i | −0.0483728 | − | 0.0351449i | ||||
\(137\) | −7.48516 | + | 2.43208i | −0.639500 | + | 0.207786i | −0.610779 | − | 0.791801i | \(-0.709144\pi\) |
−0.0287215 | + | 0.999587i | \(0.509144\pi\) | |||||||
\(138\) | 0.162800 | − | 0.931954i | 0.0138585 | − | 0.0793332i | ||||
\(139\) | 0.816636 | − | 1.12400i | 0.0692661 | − | 0.0953367i | −0.772978 | − | 0.634432i | \(-0.781234\pi\) |
0.842245 | + | 0.539096i | \(0.181234\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.66674 | + | 6.45852i | −0.561441 | + | 0.543906i | ||||
\(142\) | 0.703452i | 0.0590323i | ||||||||
\(143\) | 7.36966 | + | 12.8366i | 0.616282 | + | 1.07345i | ||||
\(144\) | −6.58715 | − | 9.69915i | −0.548929 | − | 0.808262i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.476366 | + | 0.655662i | 0.0394243 | + | 0.0542630i | ||||
\(147\) | −4.83462 | + | 2.36753i | −0.398753 | + | 0.195271i | ||||
\(148\) | −2.92764 | − | 9.01036i | −0.240651 | − | 0.740647i | ||||
\(149\) | 3.59655 | + | 11.0690i | 0.294641 | + | 0.906811i | 0.983342 | + | 0.181766i | \(0.0581813\pi\) |
−0.688701 | + | 0.725045i | \(0.741819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.11546 | + | 2.91168i | 0.172154 | + | 0.236949i | 0.886372 | − | 0.462974i | \(-0.153218\pi\) |
−0.714218 | + | 0.699923i | \(0.753218\pi\) | |||||||
\(152\) | 2.36586 | + | 0.768713i | 0.191896 | + | 0.0623509i | ||||
\(153\) | −2.38105 | − | 3.50594i | −0.192496 | − | 0.283438i | ||||
\(154\) | −0.139692 | + | 1.29870i | −0.0112567 | + | 0.104652i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.0186 | − | 10.6745i | 0.882194 | − | 0.854641i | ||||
\(157\) | −5.49000 | + | 3.98872i | −0.438150 | + | 0.318335i | −0.784899 | − | 0.619623i | \(-0.787285\pi\) |
0.346749 | + | 0.937958i | \(0.387285\pi\) | |||||||
\(158\) | −0.381650 | + | 0.525296i | −0.0303624 | + | 0.0417903i | ||||
\(159\) | −0.0781866 | + | 0.447580i | −0.00620060 | + | 0.0354954i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.3416 | − | 8.24013i | −0.893841 | − | 0.649413i | ||||
\(162\) | 0.276587 | + | 1.08001i | 0.0217307 | + | 0.0848533i | ||||
\(163\) | −0.774742 | + | 2.38441i | −0.0606825 | + | 0.186761i | −0.976802 | − | 0.214143i | \(-0.931304\pi\) |
0.916120 | + | 0.400905i | \(0.131304\pi\) | |||||||
\(164\) | 6.54947 | 0.511428 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.72621 | 0.133980 | ||||||||
\(167\) | −4.07027 | + | 12.5270i | −0.314967 | + | 0.969368i | 0.660801 | + | 0.750561i | \(0.270217\pi\) |
−0.975768 | + | 0.218807i | \(0.929783\pi\) | |||||||
\(168\) | 2.69102 | − | 0.382564i | 0.207617 | − | 0.0295155i | ||||
\(169\) | 5.59619 | + | 4.06587i | 0.430476 | + | 0.312759i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.9438 | + | 9.27048i | 0.913365 | + | 0.708931i | ||||
\(172\) | −3.47014 | + | 4.77624i | −0.264596 | + | 0.364185i | ||||
\(173\) | −18.3410 | + | 13.3255i | −1.39444 | + | 1.01312i | −0.399077 | + | 0.916917i | \(0.630670\pi\) |
−0.995362 | + | 0.0962022i | \(0.969330\pi\) | |||||||
\(174\) | 0.871273 | + | 0.899362i | 0.0660510 | + | 0.0681805i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.30086 | + | 11.8285i | −0.399567 | + | 0.891604i | ||||
\(177\) | −13.6678 | − | 7.23941i | −1.02733 | − | 0.544148i | ||||
\(178\) | −1.62014 | − | 0.526416i | −0.121435 | − | 0.0394566i | ||||
\(179\) | 1.22646 | + | 1.68808i | 0.0916701 | + | 0.126173i | 0.852389 | − | 0.522909i | \(-0.175153\pi\) |
−0.760718 | + | 0.649082i | \(0.775153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.57897 | + | 7.93725i | 0.191693 | + | 0.589971i | 0.999999 | + | 0.00120838i | \(0.000384638\pi\) |
−0.808306 | + | 0.588762i | \(0.799615\pi\) | |||||||
\(182\) | 0.543135 | + | 1.67160i | 0.0402598 | + | 0.123907i | ||||
\(183\) | 11.3154 | + | 23.1066i | 0.836455 | + | 1.70809i | ||||
\(184\) | 1.27929 | + | 1.76080i | 0.0943109 | + | 0.129808i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.234449 | − | 0.442632i | 0.0171907 | − | 0.0324554i | ||||
\(187\) | −1.91610 | + | 4.27562i | −0.140119 | + | 0.312664i | ||||
\(188\) | − | 10.6358i | − | 0.775699i | ||||||
\(189\) | 16.1754 | + | 3.35758i | 1.17658 | + | 0.244228i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.85805 | − | 9.43930i | 0.496231 | − | 0.683004i | −0.485291 | − | 0.874353i | \(-0.661286\pi\) |
0.981522 | + | 0.191349i | \(0.0612862\pi\) | |||||||
\(192\) | 13.0254 | + | 2.27537i | 0.940025 | + | 0.164210i | ||||
\(193\) | −25.5534 | + | 8.30282i | −1.83938 | + | 0.597650i | −0.840979 | + | 0.541067i | \(0.818020\pi\) |
−0.998398 | + | 0.0565827i | \(0.981980\pi\) | |||||||
\(194\) | 1.06281 | + | 0.772180i | 0.0763056 | + | 0.0554393i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.90611 | − | 5.86639i | 0.136150 | − | 0.419028i | ||||
\(197\) | 2.87880 | 0.205106 | 0.102553 | − | 0.994728i | \(-0.467299\pi\) | ||||
0.102553 | + | 0.994728i | \(0.467299\pi\) | |||||||
\(198\) | 0.855518 | − | 0.887246i | 0.0607990 | − | 0.0630539i | ||||
\(199\) | −4.95263 | −0.351083 | −0.175541 | − | 0.984472i | \(-0.556168\pi\) | ||||
−0.175541 | + | 0.984472i | \(0.556168\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.325998 | − | 2.29312i | −0.0229941 | − | 0.161745i | ||||
\(202\) | −0.118941 | − | 0.0864157i | −0.00836866 | − | 0.00608019i | ||||
\(203\) | 17.6469 | − | 5.73383i | 1.23857 | − | 0.402436i | ||||
\(204\) | 4.78369 | + | 0.835649i | 0.334925 | + | 0.0585071i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.469586 | − | 0.341174i | 0.0327176 | − | 0.0237707i | ||||
\(207\) | 3.68665 | + | 12.7042i | 0.256240 | + | 0.883003i | ||||
\(208\) | 17.4417i | 1.20936i | ||||||||
\(209\) | 1.78761 | − | 16.6193i | 0.123652 | − | 1.14958i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.7924 | − | 3.50665i | −0.742976 | − | 0.241408i | −0.0870200 | − | 0.996207i | \(-0.527734\pi\) |
−0.655956 | + | 0.754799i | \(0.727734\pi\) | |||||||
\(212\) | −0.306014 | − | 0.421192i | −0.0210171 | − | 0.0289276i | ||||
\(213\) | −4.32586 | − | 8.83363i | −0.296403 | − | 0.605271i | ||||
\(214\) | −0.484604 | − | 1.49146i | −0.0331268 | − | 0.101954i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.22726 | − | 1.27178i | −0.151546 | − | 0.0865335i | ||||
\(217\) | −4.36269 | − | 6.00472i | −0.296158 | − | 0.407627i | ||||
\(218\) | −0.274613 | − | 0.0892271i | −0.0185991 | − | 0.00604322i | ||||
\(219\) | −10.0140 | − | 5.30411i | −0.676681 | − | 0.358418i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.30462i | 0.424095i | ||||||||
\(222\) | −0.712648 | − | 0.735623i | −0.0478298 | − | 0.0493718i | ||||
\(223\) | 2.06370 | − | 1.49937i | 0.138196 | − | 0.100405i | −0.516540 | − | 0.856263i | \(-0.672780\pi\) |
0.654735 | + | 0.755858i | \(0.272780\pi\) | |||||||
\(224\) | −2.74950 | + | 3.78436i | −0.183709 | + | 0.252853i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.91199 | + | 0.621243i | −0.127184 | + | 0.0413244i | ||||
\(227\) | 15.8798 | + | 11.5373i | 1.05398 | + | 0.765759i | 0.972965 | − | 0.230954i | \(-0.0741848\pi\) |
0.0810119 | + | 0.996713i | \(0.474185\pi\) | |||||||
\(228\) | −17.1520 | + | 2.43838i | −1.13592 | + | 0.161486i | ||||
\(229\) | 2.48950 | − | 7.66188i | 0.164511 | − | 0.506312i | −0.834489 | − | 0.551024i | \(-0.814237\pi\) |
0.999000 | + | 0.0447126i | \(0.0142372\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.23214 | − | 17.1675i | −0.410045 | − | 1.12954i | ||||
\(232\) | −2.88071 | −0.189128 | ||||||||
\(233\) | −3.92966 | + | 12.0942i | −0.257440 | + | 0.792320i | 0.735899 | + | 0.677092i | \(0.236760\pi\) |
−0.993339 | + | 0.115228i | \(0.963240\pi\) | |||||||
\(234\) | 0.562278 | − | 1.56027i | 0.0367572 | − | 0.101998i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16.8549 | − | 5.47649i | 1.09716 | − | 0.356489i | ||||
\(237\) | 1.56229 | − | 8.94338i | 0.101482 | − | 0.580935i | ||||
\(238\) | −0.327019 | + | 0.450103i | −0.0211975 | + | 0.0291759i | ||||
\(239\) | −11.6028 | + | 8.42996i | −0.750526 | + | 0.545289i | −0.895990 | − | 0.444075i | \(-0.853532\pi\) |
0.145464 | + | 0.989364i | \(0.453532\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.56980i | − | 0.358782i | −0.983778 | − | 0.179391i | \(-0.942587\pi\) | ||
0.983778 | − | 0.179391i | \(-0.0574128\pi\) | |||||||
\(242\) | −1.33144 | − | 0.289779i | −0.0855881 | − | 0.0186277i | ||||
\(243\) | −10.1147 | − | 11.8614i | −0.648860 | − | 0.760908i | ||||
\(244\) | −28.0378 | − | 9.11002i | −1.79493 | − | 0.583210i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.635891 | − | 0.311398i | 0.0405429 | − | 0.0198540i | ||||
\(247\) | −6.95041 | − | 21.3912i | −0.442244 | − | 1.36109i | ||||
\(248\) | 0.356085 | + | 1.09592i | 0.0226114 | + | 0.0695909i | ||||
\(249\) | −21.6770 | + | 10.6153i | −1.37373 | + | 0.672718i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.4384 | + | 7.29068i | 1.41630 | + | 0.460184i | 0.914425 | − | 0.404756i | \(-0.132644\pi\) |
0.501875 | + | 0.864940i | \(0.332644\pi\) | |||||||
\(252\) | −15.6595 | + | 10.6351i | −0.986456 | + | 0.669949i | ||||
\(253\) | 9.81205 | − | 10.8443i | 0.616879 | − | 0.681773i | ||||
\(254\) | − | 2.19259i | − | 0.137575i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.9625 | + | 8.69129i | −0.747658 | + | 0.543206i | ||||
\(257\) | 2.60990 | − | 3.59223i | 0.162801 | − | 0.224077i | −0.719821 | − | 0.694160i | \(-0.755776\pi\) |
0.882622 | + | 0.470083i | \(0.155776\pi\) | |||||||
\(258\) | −0.109829 | + | 0.628717i | −0.00683764 | + | 0.0391422i | ||||
\(259\) | −14.4341 | + | 4.68992i | −0.896891 | + | 0.291417i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.4717 | − | 5.93592i | −1.01957 | − | 0.367424i | ||||
\(262\) | 0.562978 | − | 1.73267i | 0.0347809 | − | 0.107045i | ||||
\(263\) | −16.3005 | −1.00513 | −0.502565 | − | 0.864540i | \(-0.667610\pi\) | ||||
−0.502565 | + | 0.864540i | \(0.667610\pi\) | |||||||
\(264\) | 0.0965758 | + | 2.83383i | 0.00594383 | + | 0.174410i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.613347 | − | 1.88769i | 0.0376067 | − | 0.115742i | ||||
\(267\) | 23.5822 | − | 3.35253i | 1.44321 | − | 0.205171i | ||||
\(268\) | 2.14711 | + | 1.55997i | 0.131156 | + | 0.0952902i | ||||
\(269\) | −1.84648 | + | 0.599958i | −0.112582 | + | 0.0365801i | −0.364766 | − | 0.931099i | \(-0.618851\pi\) |
0.252184 | + | 0.967679i | \(0.418851\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.23294 | − | 9.95529i | 0.439370 | − | 0.604741i | −0.530702 | − | 0.847559i | \(-0.678072\pi\) |
0.970072 | + | 0.242818i | \(0.0780716\pi\) | |||||||
\(272\) | −4.46658 | + | 3.24516i | −0.270826 | + | 0.196767i | ||||
\(273\) | −17.0999 | − | 17.6512i | −1.03493 | − | 1.06830i | ||||
\(274\) | − | 0.974929i | − | 0.0588976i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.3946 | − | 7.09474i | −0.806261 | − | 0.427053i | ||||
\(277\) | −3.47993 | − | 1.13070i | −0.209089 | − | 0.0679370i | 0.202600 | − | 0.979262i | \(-0.435061\pi\) |
−0.411689 | + | 0.911325i | \(0.635061\pi\) | |||||||
\(278\) | 0.101159 | + | 0.139234i | 0.00606714 | + | 0.00835070i | ||||
\(279\) | −0.222154 | + | 7.00012i | −0.0133000 | + | 0.419086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.71578 | − | 17.5914i | −0.340975 | − | 1.04941i | −0.963703 | − | 0.266975i | \(-0.913976\pi\) |
0.622729 | − | 0.782438i | \(-0.286024\pi\) | |||||||
\(282\) | −0.505686 | − | 1.03264i | −0.0301132 | − | 0.0614927i | ||||
\(283\) | 14.8456 | + | 20.4332i | 0.882480 | + | 1.21463i | 0.975728 | + | 0.218986i | \(0.0702749\pi\) |
−0.0932485 | + | 0.995643i | \(0.529725\pi\) | |||||||
\(284\) | 10.7188 | + | 3.48276i | 0.636046 | + | 0.206664i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.79439 | + | 0.376853i | −0.106104 | + | 0.0222838i | ||||
\(287\) | − | 10.4919i | − | 0.619317i | ||||||
\(288\) | 4.23903 | − | 1.23013i | 0.249787 | − | 0.0724862i | ||||
\(289\) | 12.1388 | − | 8.81932i | 0.714045 | − | 0.518784i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.0949 | − | 3.16094i | −1.06074 | − | 0.185298i | ||||
\(292\) | 12.3491 | − | 4.01247i | 0.722677 | − | 0.234812i | ||||
\(293\) | −0.689709 | − | 0.501103i | −0.0402932 | − | 0.0292747i | 0.567456 | − | 0.823403i | \(-0.307928\pi\) |
−0.607750 | + | 0.794129i | \(0.707928\pi\) | |||||||
\(294\) | −0.0938558 | − | 0.660197i | −0.00547378 | − | 0.0385035i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.35624 | 0.136954 | ||||||||
\(297\) | −5.28711 | + | 16.4026i | −0.306789 | + | 0.951777i | ||||
\(298\) | −1.44172 | −0.0835168 | ||||||||
\(299\) | 6.08107 | − | 18.7156i | 0.351678 | − | 1.08235i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.65128 | + | 5.55898i | 0.441012 | + | 0.320414i | ||||
\(302\) | −0.424005 | + | 0.137767i | −0.0243987 | + | 0.00792763i | ||||
\(303\) | 2.02502 | + | 0.353745i | 0.116334 | + | 0.0203221i | ||||
\(304\) | 11.5772 | − | 15.9347i | 0.664000 | − | 0.913918i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.504181 | − | 0.146309i | 0.0288221 | − | 0.00836393i | ||||
\(307\) | 13.3356i | 0.761105i | 0.924759 | + | 0.380553i | \(0.124266\pi\) | ||||
−0.924759 | + | 0.380553i | \(0.875734\pi\) | |||||||
\(308\) | 19.0973 | + | 8.55836i | 1.08817 | + | 0.487658i | ||||
\(309\) | −3.79881 | + | 7.17202i | −0.216107 | + | 0.408002i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.449547 | − | 0.618749i | −0.0254915 | − | 0.0350860i | 0.796081 | − | 0.605190i | \(-0.206903\pi\) |
−0.821573 | + | 0.570104i | \(0.806903\pi\) | |||||||
\(312\) | 1.67803 | + | 3.42663i | 0.0949998 | + | 0.193995i | ||||
\(313\) | −1.30074 | − | 4.00328i | −0.0735224 | − | 0.226279i | 0.907542 | − | 0.419962i | \(-0.137957\pi\) |
−0.981064 | + | 0.193683i | \(0.937957\pi\) | |||||||
\(314\) | −0.259762 | − | 0.799465i | −0.0146592 | − | 0.0451164i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.11466 | + | 8.41610i | 0.343976 | + | 0.473443i | ||||
\(317\) | −21.4920 | − | 6.98318i | −1.20711 | − | 0.392215i | −0.364739 | − | 0.931110i | \(-0.618842\pi\) |
−0.842373 | + | 0.538895i | \(0.818842\pi\) | |||||||
\(318\) | −0.0497368 | − | 0.0263441i | −0.00278910 | − | 0.00147731i | ||||
\(319\) | 3.97840 | + | 18.9432i | 0.222748 | + | 1.06062i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2571 | + | 15.7490i | 0.851569 | + | 0.879023i | ||||
\(322\) | 1.40492 | − | 1.02073i | 0.0782931 | − | 0.0568832i | ||||
\(323\) | 4.18481 | − | 5.75990i | 0.232849 | − | 0.320489i | ||||
\(324\) | 17.8260 | + | 1.13258i | 0.990331 | + | 0.0629212i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.251252 | − | 0.182546i | −0.0139156 | − | 0.0101103i | ||||
\(327\) | 3.99716 | − | 0.568250i | 0.221044 | − | 0.0314243i | ||||
\(328\) | −0.503353 | + | 1.54916i | −0.0277930 | + | 0.0855381i | ||||
\(329\) | −17.0380 | −0.939337 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.29336 | −0.235984 | −0.117992 | − | 0.993015i | \(-0.537646\pi\) | ||||
−0.117992 | + | 0.993015i | \(0.537646\pi\) | |||||||
\(332\) | 8.54641 | − | 26.3032i | 0.469045 | − | 1.44357i | ||||
\(333\) | 13.4728 | + | 4.85522i | 0.738305 | + | 0.266064i | ||||
\(334\) | −1.32001 | − | 0.959041i | −0.0722276 | − | 0.0524764i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.70340 | − | 21.2001i | 0.202037 | − | 1.15656i | ||||
\(337\) | 8.56709 | − | 11.7916i | 0.466679 | − | 0.642329i | −0.509198 | − | 0.860650i | \(-0.670058\pi\) |
0.975877 | + | 0.218320i | \(0.0700578\pi\) | |||||||
\(338\) | −0.693219 | + | 0.503653i | −0.0377061 | + | 0.0273951i | ||||
\(339\) | 20.1896 | − | 19.5590i | 1.09655 | − | 1.06230i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.71487 | − | 3.85510i | 0.363631 | − | 0.208765i | ||||
\(342\) | −1.54936 | + | 1.05224i | −0.0837796 | + | 0.0568987i | ||||
\(343\) | 11.7683 | + | 3.82374i | 0.635427 | + | 0.206463i | ||||
\(344\) | −0.863041 | − | 1.18787i | −0.0465320 | − | 0.0640459i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.867811 | − | 2.67085i | −0.0466538 | − | 0.143586i | ||||
\(347\) | −4.24886 | − | 13.0766i | −0.228091 | − | 0.701991i | −0.997963 | − | 0.0637934i | \(-0.979680\pi\) |
0.769872 | − | 0.638198i | \(-0.220320\pi\) | |||||||
\(348\) | 18.0177 | − | 8.82331i | 0.965848 | − | 0.472979i | ||||
\(349\) | 4.60029 | + | 6.33176i | 0.246248 | + | 0.338931i | 0.914193 | − | 0.405279i | \(-0.132826\pi\) |
−0.667945 | + | 0.744211i | \(0.732826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.53403 | + | 23.0509i | 0.135256 | + | 1.23037i | ||||
\(352\) | −3.61842 | − | 3.27400i | −0.192863 | − | 0.174505i | ||||
\(353\) | − | 32.8789i | − | 1.74997i | −0.484153 | − | 0.874983i | \(-0.660872\pi\) | ||
0.484153 | − | 0.874983i | \(-0.339128\pi\) | |||||||
\(354\) | 1.37607 | − | 1.33309i | 0.0731372 | − | 0.0708529i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16.0425 | + | 22.0806i | −0.850252 | + | 1.17027i | ||||
\(357\) | 1.33866 | − | 7.66320i | 0.0708495 | − | 0.405579i | ||||
\(358\) | −0.245822 | + | 0.0798723i | −0.0129921 | + | 0.00422138i | ||||
\(359\) | 13.9789 | + | 10.1563i | 0.737778 | + | 0.536027i | 0.892014 | − | 0.452007i | \(-0.149292\pi\) |
−0.154237 | + | 0.988034i | \(0.549292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.97758 | + | 6.08636i | −0.104083 | + | 0.320335i | ||||
\(362\) | −1.03381 | −0.0543359 | ||||||||
\(363\) | 18.5016 | − | 4.54874i | 0.971082 | − | 0.238747i | ||||
\(364\) | 28.1600 | 1.47598 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.15534 | + | 0.448573i | −0.164932 | + | 0.0234473i | ||||
\(367\) | 18.9024 | + | 13.7334i | 0.986696 | + | 0.716876i | 0.959195 | − | 0.282745i | \(-0.0912451\pi\) |
0.0275007 | + | 0.999622i | \(0.491245\pi\) | |||||||
\(368\) | 16.3894 | − | 5.32523i | 0.854356 | − | 0.277597i | ||||
\(369\) | −6.07030 | + | 7.82079i | −0.316007 | + | 0.407134i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.674726 | + | 0.490217i | −0.0350301 | + | 0.0254508i | ||||
\(372\) | −5.58386 | − | 5.76387i | −0.289509 | − | 0.298843i | ||||
\(373\) | − | 26.3240i | − | 1.36301i | −0.731815 | − | 0.681503i | \(-0.761326\pi\) | ||
0.731815 | − | 0.681503i | \(-0.238674\pi\) | |||||||
\(374\) | −0.430367 | − | 0.389403i | −0.0222538 | − | 0.0201355i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.51572 | + | 0.817406i | 0.129738 | + | 0.0421545i | ||||
\(377\) | 15.3096 | + | 21.0718i | 0.788484 | + | 1.08526i | ||||
\(378\) | −1.01474 | + | 1.77710i | −0.0521923 | + | 0.0914044i | ||||
\(379\) | 5.20491 | + | 16.0191i | 0.267358 | + | 0.822843i | 0.991141 | + | 0.132815i | \(0.0424018\pi\) |
−0.723783 | + | 0.690028i | \(0.757598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4833 | + | 27.5336i | 0.690769 | + | 1.41059i | ||||
\(382\) | 0.849530 | + | 1.16928i | 0.0434658 | + | 0.0598255i | ||||
\(383\) | −16.9960 | − | 5.52233i | −0.868454 | − | 0.282178i | −0.159299 | − | 0.987230i | \(-0.550923\pi\) |
−0.709155 | + | 0.705053i | \(0.750923\pi\) | |||||||
\(384\) | −3.15228 | + | 5.95139i | −0.160864 | + | 0.303705i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3.32829i | − | 0.169406i | ||||||
\(387\) | −2.48710 | − | 8.57054i | −0.126426 | − | 0.435665i | ||||
\(388\) | 17.0280 | − | 12.3716i | 0.864467 | − | 0.628072i | ||||
\(389\) | −1.15007 | + | 1.58293i | −0.0583106 | + | 0.0802577i | −0.837176 | − | 0.546933i | \(-0.815795\pi\) |
0.778866 | + | 0.627191i | \(0.215795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.92425 | − | 1.92491i | 0.299602 | − | 0.0973467i | ||||
\(392\) | 1.24110 | + | 0.901710i | 0.0626849 | + | 0.0455432i | ||||
\(393\) | 3.58537 | + | 25.2201i | 0.180858 | + | 1.27218i | ||||
\(394\) | −0.110198 | + | 0.339154i | −0.00555168 | + | 0.0170863i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.28377 | − | 17.4287i | −0.466527 | − | 0.875823i | ||||
\(397\) | 5.31786 | 0.266896 | 0.133448 | − | 0.991056i | \(-0.457395\pi\) | ||||
0.133448 | + | 0.991056i | \(0.457395\pi\) | |||||||
\(398\) | 0.189582 | − | 0.583472i | 0.00950287 | − | 0.0292468i | ||||
\(399\) | 3.90615 | + | 27.4765i | 0.195552 | + | 1.37555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.8578 | + | 7.75185i | −1.19140 | + | 0.387109i | −0.836590 | − | 0.547830i | \(-0.815454\pi\) |
−0.354809 | + | 0.934939i | \(0.615454\pi\) | |||||||
\(402\) | 0.282633 | + | 0.0493724i | 0.0140965 | + | 0.00246247i | ||||
\(403\) | 6.12402 | − | 8.42899i | 0.305059 | − | 0.419878i | ||||
\(404\) | −1.90563 | + | 1.38452i | −0.0948087 | + | 0.0688825i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.29848i | 0.114072i | ||||||||
\(407\) | −3.25409 | − | 15.4944i | −0.161299 | − | 0.768028i | ||||
\(408\) | −0.565303 | + | 1.06727i | −0.0279867 | + | 0.0528378i | ||||
\(409\) | −24.4821 | − | 7.95473i | −1.21056 | − | 0.393336i | −0.366927 | − | 0.930250i | \(-0.619590\pi\) |
−0.843637 | + | 0.536914i | \(0.819590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.99530 | + | 12.2427i | 0.295726 | + | 0.603889i | ||||
\(412\) | −2.87373 | − | 8.84444i | −0.141579 | − | 0.435734i | ||||
\(413\) | −8.77304 | − | 27.0006i | −0.431693 | − | 1.32861i | ||||
\(414\) | −1.63781 | − | 0.0519772i | −0.0804940 | − | 0.00255454i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.24487 | − | 2.02908i | −0.306180 | − | 0.0994839i | ||||
\(417\) | −2.12653 | − | 1.12636i | −0.104137 | − | 0.0551582i | ||||
\(418\) | 1.88950 | + | 0.846768i | 0.0924183 | + | 0.0414168i | ||||
\(419\) | − | 33.0369i | − | 1.61396i | −0.590580 | − | 0.806979i | \(-0.701101\pi\) | ||
0.590580 | − | 0.806979i | \(-0.298899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.07346 | − | 5.86571i | 0.393476 | − | 0.285877i | −0.373402 | − | 0.927670i | \(-0.621809\pi\) |
0.766879 | + | 0.641792i | \(0.221809\pi\) | |||||||
\(422\) | 0.826241 | − | 1.13722i | 0.0402208 | − | 0.0553591i | ||||
\(423\) | 12.7004 | + | 9.85770i | 0.617513 | + | 0.479298i | ||||
\(424\) | 0.123144 | − | 0.0400119i | 0.00598040 | − | 0.00194315i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.20629 | − | 0.171490i | 0.0584447 | − | 0.00830869i | ||||
\(427\) | −14.5937 | + | 44.9149i | −0.706241 | + | 2.17359i | ||||
\(428\) | −25.1253 | −1.21448 | ||||||||
\(429\) | 20.2157 | − | 15.7669i | 0.976023 | − | 0.761233i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.63918 | − | 11.2002i | 0.175293 | − | 0.539496i | −0.824354 | − | 0.566075i | \(-0.808461\pi\) |
0.999647 | + | 0.0265786i | \(0.00846124\pi\) | |||||||
\(432\) | −15.0263 | + | 13.6602i | −0.722955 | + | 0.657226i | ||||
\(433\) | −8.82447 | − | 6.41135i | −0.424077 | − | 0.308110i | 0.355199 | − | 0.934791i | \(-0.384413\pi\) |
−0.779276 | + | 0.626681i | \(0.784413\pi\) | |||||||
\(434\) | 0.874419 | − | 0.284116i | 0.0419735 | − | 0.0136380i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.71919 | + | 3.74265i | −0.130226 | + | 0.179240i | ||||
\(437\) | −17.9785 | + | 13.0622i | −0.860029 | + | 0.624848i | ||||
\(438\) | 1.00820 | − | 0.976716i | 0.0481739 | − | 0.0466693i | ||||
\(439\) | − | 4.24090i | − | 0.202407i | −0.994866 | − | 0.101203i | \(-0.967731\pi\) | ||
0.994866 | − | 0.101203i | \(-0.0322693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.23846 | + | 7.71329i | 0.249451 | + | 0.367300i | ||||
\(442\) | −0.742751 | − | 0.241335i | −0.0353291 | − | 0.0114791i | ||||
\(443\) | 21.2625 | + | 29.2653i | 1.01021 | + | 1.39044i | 0.918845 | + | 0.394618i | \(0.129123\pi\) |
0.0913656 | + | 0.995817i | \(0.470877\pi\) | |||||||
\(444\) | −14.7373 | + | 7.21692i | −0.699403 | + | 0.342500i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0976450 | + | 0.300520i | 0.00462362 | + | 0.0142301i | ||||
\(447\) | 18.1045 | − | 8.86584i | 0.856314 | − | 0.419340i | ||||
\(448\) | 14.2662 | + | 19.6357i | 0.674014 | + | 0.927700i | ||||
\(449\) | −39.3387 | − | 12.7819i | −1.85651 | − | 0.603216i | −0.995515 | − | 0.0946009i | \(-0.969843\pi\) |
−0.860994 | − | 0.508615i | \(-0.830157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8823 | + | 1.17053i | 0.512426 | + | 0.0551179i | ||||
\(452\) | 32.2097i | 1.51501i | ||||||||
\(453\) | 4.47727 | − | 4.33743i | 0.210360 | − | 0.203790i | ||||
\(454\) | −1.96708 | + | 1.42917i | −0.0923196 | + | 0.0670741i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.741441 | − | 4.24439i | 0.0347212 | − | 0.198762i | ||||
\(457\) | 7.82596 | − | 2.54281i | 0.366083 | − | 0.118948i | −0.120198 | − | 0.992750i | \(-0.538353\pi\) |
0.486281 | + | 0.873802i | \(0.338353\pi\) | |||||||
\(458\) | 0.807356 | + | 0.586578i | 0.0377253 | + | 0.0274090i | ||||
\(459\) | −5.43156 | + | 4.93773i | −0.253523 | + | 0.230474i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0965 | 0.935989 | 0.467995 | − | 0.883731i | \(-0.344977\pi\) | ||||
0.467995 | + | 0.883731i | \(0.344977\pi\) | |||||||
\(462\) | 2.26108 | − | 0.0770566i | 0.105195 | − | 0.00358500i | ||||
\(463\) | 36.9595 | 1.71765 | 0.858827 | − | 0.512266i | \(-0.171194\pi\) | ||||
0.858827 | + | 0.512266i | \(0.171194\pi\) | |||||||
\(464\) | −7.04832 | + | 21.6925i | −0.327210 | + | 1.00705i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.27441 | − | 0.925910i | −0.0590357 | − | 0.0428920i | ||||
\(467\) | 13.3870 | − | 4.34970i | 0.619476 | − | 0.201280i | 0.0175683 | − | 0.999846i | \(-0.494408\pi\) |
0.601908 | + | 0.798566i | \(0.294408\pi\) | |||||||
\(468\) | −20.9908 | − | 16.2925i | −0.970301 | − | 0.753123i | ||||
\(469\) | 2.49898 | − | 3.43955i | 0.115392 | − | 0.158824i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.17826 | + | 8.44192i | 0.376834 | + | 0.388983i | ||||
\(472\) | 4.40762i | 0.202877i | ||||||||
\(473\) | −6.61943 | + | 7.31578i | −0.304362 | + | 0.336380i | ||||
\(474\) | 0.993822 | + | 0.526398i | 0.0456477 | + | 0.0241783i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.23939 | + | 7.21140i | 0.240147 | + | 0.330534i | ||||
\(477\) | 0.786575 | + | 0.0249626i | 0.0360148 | + | 0.00114296i | ||||
\(478\) | −0.548994 | − | 1.68963i | −0.0251104 | − | 0.0772818i | ||||
\(479\) | 0.417639 | + | 1.28536i | 0.0190824 | + | 0.0587297i | 0.960144 | − | 0.279505i | \(-0.0901703\pi\) |
−0.941062 | + | 0.338235i | \(0.890170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5223 | − | 17.2355i | −0.570968 | − | 0.785870i | ||||
\(482\) | 0.656181 | + | 0.213206i | 0.0298882 | + | 0.00971128i | ||||
\(483\) | −11.3654 | + | 21.4574i | −0.517142 | + | 0.976347i | ||||
\(484\) | −11.0074 | + | 18.8531i | −0.500336 | + | 0.856959i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.78458 | − | 0.737581i | 0.0809501 | − | 0.0334573i | ||||
\(487\) | 18.1884 | − | 13.2147i | 0.824196 | − | 0.598814i | −0.0937152 | − | 0.995599i | \(-0.529874\pi\) |
0.917911 | + | 0.396785i | \(0.129874\pi\) | |||||||
\(488\) | 4.30963 | − | 5.93169i | 0.195088 | − | 0.268515i | ||||
\(489\) | 4.27768 | + | 0.747256i | 0.193443 | + | 0.0337921i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.20950 | − | 6.69109i | −0.415619 | − | 0.301965i | 0.360254 | − | 0.932854i | \(-0.382690\pi\) |
−0.775873 | + | 0.630889i | \(0.782690\pi\) | |||||||
\(492\) | −1.59665 | − | 11.2311i | −0.0719825 | − | 0.506337i | ||||
\(493\) | −2.54775 | + | 7.84117i | −0.114745 | + | 0.353148i | ||||
\(494\) | 2.78616 | 0.125355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.12381 | 0.409671 | ||||||||
\(497\) | 5.57919 | − | 17.1710i | 0.250261 | − | 0.770223i | ||||
\(498\) | −0.420821 | − | 2.96013i | −0.0188575 | − | 0.132646i | ||||
\(499\) | −3.16117 | − | 2.29673i | −0.141513 | − | 0.102816i | 0.514776 | − | 0.857325i | \(-0.327875\pi\) |
−0.656290 | + | 0.754509i | \(0.727875\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.4737 | + | 3.92586i | 1.00405 | + | 0.175395i | ||||
\(502\) | −1.71784 | + | 2.36440i | −0.0766709 | + | 0.105528i | ||||
\(503\) | −19.7496 | + | 14.3489i | −0.880593 | + | 0.639788i | −0.933408 | − | 0.358816i | \(-0.883180\pi\) |
0.0528157 | + | 0.998604i | \(0.483180\pi\) | |||||||
\(504\) | −1.31205 | − | 4.52132i | −0.0584433 | − | 0.201396i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.901973 | + | 1.57107i | 0.0400976 | + | 0.0698426i | ||||
\(507\) | 5.60793 | − | 10.5876i | 0.249057 | − | 0.470211i | ||||
\(508\) | −33.4096 | − | 10.8554i | −1.48231 | − | 0.481631i | ||||
\(509\) | −13.5377 | − | 18.6330i | −0.600047 | − | 0.825894i | 0.395665 | − | 0.918395i | \(-0.370514\pi\) |
−0.995713 | + | 0.0925006i | \(0.970514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.42775 | − | 19.7826i | −0.284347 | − | 0.875130i | ||||
\(512\) | −2.96909 | − | 9.13793i | −0.131217 | − | 0.403843i | ||||
\(513\) | 12.9854 | − | 22.7413i | 0.573320 | − | 1.00405i | ||||
\(514\) | 0.323298 | + | 0.444981i | 0.0142601 | + | 0.0196273i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.03631 | + | 4.78627i | 0.397801 | + | 0.210704i | ||||
\(517\) | 1.90084 | − | 17.6720i | 0.0835991 | − | 0.777213i | ||||
\(518\) | − | 1.88001i | − | 0.0826031i | ||||||
\(519\) | 27.3219 | + | 28.2028i | 1.19930 | + | 1.23796i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.97322 | − | 6.84505i | 0.217881 | − | 0.299887i | −0.686060 | − | 0.727545i | \(-0.740661\pi\) |
0.903941 | + | 0.427658i | \(0.140661\pi\) | |||||||
\(522\) | 1.32983 | − | 1.71332i | 0.0582052 | − | 0.0749898i | ||||
\(523\) | −0.333579 | + | 0.108386i | −0.0145864 | + | 0.00473941i | −0.316301 | − | 0.948659i | \(-0.602441\pi\) |
0.301715 | + | 0.953398i | \(0.402441\pi\) | |||||||
\(524\) | −23.6142 | − | 17.1567i | −1.03159 | − | 0.749495i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.623965 | − | 1.92037i | 0.0272062 | − | 0.0837320i | ||||
\(527\) | 3.29797 | 0.143662 | ||||||||
\(528\) | 21.5758 | + | 6.20638i | 0.938966 | + | 0.270098i | ||||
\(529\) | 3.55687 | 0.154646 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.08224 | + | 25.2024i | −0.394136 | + | 1.09369i | ||||
\(532\) | −25.7270 | − | 18.6917i | −1.11540 | − | 0.810389i | ||||
\(533\) | 14.0069 | − | 4.55112i | 0.606707 | − | 0.197131i | ||||
\(534\) | −0.507740 | + | 2.90657i | −0.0219721 | + | 0.125779i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.533996 | + | 0.387971i | −0.0230651 | + | 0.0167578i | ||||
\(537\) | 2.59575 | − | 2.51467i | 0.112015 | − | 0.108516i | ||||
\(538\) | − | 0.240501i | − | 0.0103687i | ||||||
\(539\) | 4.21553 | − | 9.40664i | 0.181576 | − | 0.405173i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0739 | − | 10.4214i | −1.37896 | − | 0.448053i | −0.476635 | − | 0.879101i | \(-0.658144\pi\) |
−0.902329 | + | 0.431048i | \(0.858144\pi\) | |||||||
\(542\) | 0.895969 | + | 1.23320i | 0.0384852 | + | 0.0529703i | ||||
\(543\) | 12.9822 | − | 6.35740i | 0.557117 | − | 0.272822i | ||||
\(544\) | −0.642287 | − | 1.97675i | −0.0275378 | − | 0.0847527i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.73406 | − | 1.33888i | 0.117007 | − | 0.0572988i | ||||
\(547\) | 16.6409 | + | 22.9043i | 0.711515 | + | 0.979316i | 0.999763 | + | 0.0217602i | \(0.00692704\pi\) |
−0.288249 | + | 0.957556i | \(0.593073\pi\) | |||||||
\(548\) | −14.8555 | − | 4.82683i | −0.634594 | − | 0.206192i | ||||
\(549\) | 36.8648 | − | 25.0367i | 1.57335 | − | 1.06854i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 29.4133i | − | 1.25305i | ||||||
\(552\) | 2.70756 | − | 2.62300i | 0.115241 | − | 0.111642i | ||||
\(553\) | 13.4821 | − | 9.79533i | 0.573318 | − | 0.416540i | ||||
\(554\) | 0.266416 | − | 0.366690i | 0.0113189 | − | 0.0155792i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.62241 | − | 0.852074i | 0.111215 | − | 0.0361360i | ||||
\(557\) | 13.9281 | + | 10.1194i | 0.590153 | + | 0.428771i | 0.842370 | − | 0.538899i | \(-0.181160\pi\) |
−0.252217 | + | 0.967671i | \(0.581160\pi\) | |||||||
\(558\) | −0.816185 | − | 0.294130i | −0.0345519 | − | 0.0124515i | ||||
\(559\) | −4.10243 | + | 12.6260i | −0.173514 | + | 0.534022i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.79898 | + | 2.24342i | 0.329273 | + | 0.0947171i | ||||
\(562\) | 2.29124 | 0.0966503 | ||||||||
\(563\) | 9.76130 | − | 30.0422i | 0.411390 | − | 1.26613i | −0.504051 | − | 0.863674i | \(-0.668158\pi\) |
0.915441 | − | 0.402453i | \(-0.131842\pi\) | |||||||
\(564\) | −18.2384 | + | 2.59284i | −0.767977 | + | 0.109178i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.97552 | + | 0.966807i | −0.125071 | + | 0.0406379i | ||||
\(567\) | 1.81433 | − | 28.5562i | 0.0761948 | − | 1.19925i | ||||
\(568\) | −1.64757 | + | 2.26768i | −0.0691305 | + | 0.0951499i | ||||
\(569\) | 17.4236 | − | 12.6590i | 0.730435 | − | 0.530692i | −0.159266 | − | 0.987236i | \(-0.550913\pi\) |
0.889701 | + | 0.456543i | \(0.150913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.4210i | 1.31493i | 0.753485 | + | 0.657465i | \(0.228371\pi\) | ||||
−0.753485 | + | 0.657465i | \(0.771629\pi\) | |||||||
\(572\) | −3.14166 | + | 29.2078i | −0.131360 | + | 1.22124i | ||||
\(573\) | −17.8585 | − | 9.45911i | −0.746049 | − | 0.395160i | ||||
\(574\) | 1.23606 | + | 0.401619i | 0.0515920 | + | 0.0167632i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.726454 | − | 22.8907i | 0.0302689 | − | 0.953780i | ||||
\(577\) | 9.38846 | + | 28.8947i | 0.390847 | + | 1.20290i | 0.932149 | + | 0.362075i | \(0.117931\pi\) |
−0.541302 | + | 0.840828i | \(0.682069\pi\) | |||||||
\(578\) | 0.574351 | + | 1.76767i | 0.0238898 | + | 0.0735253i | ||||
\(579\) | 20.4672 | + | 41.7952i | 0.850590 | + | 1.73695i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.1362 | − | 13.6909i | −1.74810 | − | 0.567993i | ||||
\(582\) | 1.06504 | − | 2.01077i | 0.0441475 | − | 0.0833490i | ||||
\(583\) | −0.433182 | − | 0.754523i | −0.0179406 | − | 0.0312492i | ||||
\(584\) | 3.22933i | 0.133631i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0854366 | − | 0.0620733i | 0.00352935 | − | 0.00256422i | ||||
\(587\) | −5.46190 | + | 7.51766i | −0.225437 | + | 0.310287i | −0.906720 | − | 0.421733i | \(-0.861422\pi\) |
0.681283 | + | 0.732020i | \(0.261422\pi\) | |||||||
\(588\) | −10.5244 | − | 1.83848i | −0.434020 | − | 0.0758177i | ||||
\(589\) | −11.1898 | + | 3.63579i | −0.461068 | + | 0.149810i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.701804 | − | 4.93660i | −0.0288683 | − | 0.203065i | ||||
\(592\) | 5.76509 | − | 17.7431i | 0.236944 | − | 0.729238i | ||||
\(593\) | 17.5361 | 0.720120 | 0.360060 | − | 0.932929i | \(-0.382756\pi\) | ||||
0.360060 | + | 0.932929i | \(0.382756\pi\) | |||||||
\(594\) | −1.73002 | − | 1.25075i | −0.0709835 | − | 0.0513191i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.13791 | + | 21.9682i | −0.292380 | + | 0.899854i | ||||
\(597\) | 1.20737 | + | 8.49282i | 0.0494142 | + | 0.347588i | ||||
\(598\) | 1.97212 | + | 1.43283i | 0.0806460 | + | 0.0585928i | ||||
\(599\) | −25.5218 | + | 8.29252i | −1.04279 | + | 0.338823i | −0.779835 | − | 0.625985i | \(-0.784697\pi\) |
−0.262955 | + | 0.964808i | \(0.584697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0311549 | + | 0.0428810i | −0.00127083 | + | 0.00174915i | −0.809652 | − | 0.586910i | \(-0.800344\pi\) |
0.808381 | + | 0.588659i | \(0.200344\pi\) | |||||||
\(602\) | −0.947789 | + | 0.688609i | −0.0386290 | + | 0.0280656i | ||||
\(603\) | −3.85280 | + | 1.11805i | −0.156898 | + | 0.0455305i | ||||
\(604\) | 7.14285i | 0.290638i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.119191 | + | 0.225028i | −0.00484179 | + | 0.00914113i | ||||
\(607\) | −8.80594 | − | 2.86122i | −0.357422 | − | 0.116134i | 0.124801 | − | 0.992182i | \(-0.460171\pi\) |
−0.482223 | + | 0.876048i | \(0.660171\pi\) | |||||||
\(608\) | 4.35847 | + | 5.99892i | 0.176759 | + | 0.243288i | ||||
\(609\) | −14.1344 | − | 28.8633i | −0.572757 | − | 1.16960i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.39068 | − | 22.7462i | −0.298995 | − | 0.920211i | ||||
\(612\) | 0.266797 | − | 8.40682i | 0.0107846 | − | 0.339826i | ||||
\(613\) | −9.46428 | − | 13.0265i | −0.382259 | − | 0.526134i | 0.573922 | − | 0.818910i | \(-0.305421\pi\) |
−0.956181 | + | 0.292776i | \(0.905421\pi\) | |||||||
\(614\) | −1.57108 | − | 0.510475i | −0.0634036 | − | 0.0206011i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.49203 | + | 3.85938i | −0.140698 | + | 0.155499i | ||||
\(617\) | − | 32.5133i | − | 1.30894i | −0.756089 | − | 0.654469i | \(-0.772892\pi\) | ||
0.756089 | − | 0.654469i | \(-0.227108\pi\) | |||||||
\(618\) | −0.699525 | − | 0.722077i | −0.0281390 | − | 0.0290462i | ||||
\(619\) | 21.0066 | − | 15.2622i | 0.844325 | − | 0.613438i | −0.0792507 | − | 0.996855i | \(-0.525253\pi\) |
0.923575 | + | 0.383417i | \(0.125253\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.8865 | − | 9.41897i | 0.838148 | − | 0.377970i | ||||
\(622\) | 0.0901034 | − | 0.0292764i | 0.00361282 | − | 0.00117388i | ||||
\(623\) | 35.3720 | + | 25.6992i | 1.41715 | + | 1.02962i | ||||
\(624\) | 29.9091 | − | 4.25198i | 1.19732 | − | 0.170216i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.521419 | 0.0208401 | ||||||||
\(627\) | −28.9346 | + | 0.986082i | −1.15554 | + | 0.0393803i | ||||
\(628\) | −13.4679 | −0.537428 | ||||||||
\(629\) | 2.08390 | − | 6.41359i | 0.0830906 | − | 0.255727i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5141 | − | 16.3575i | −0.896273 | − | 0.651181i | 0.0412329 | − | 0.999150i | \(-0.486871\pi\) |
−0.937506 | + | 0.347969i | \(0.886871\pi\) | |||||||
\(632\) | −2.46061 | + | 0.799502i | −0.0978779 | + | 0.0318025i | ||||
\(633\) | −3.38224 | + | 19.3617i | −0.134432 | + | 0.769558i | ||||
\(634\) | 1.64539 | − | 2.26468i | 0.0653466 | − | 0.0899419i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.647663 | + | 0.627435i | −0.0256815 | + | 0.0248794i | ||||
\(637\) | − | 13.8706i | − | 0.549572i | ||||||
\(638\) | −2.38400 | − | 0.256429i | −0.0943835 | − | 0.0101521i | ||||
\(639\) | −14.0934 | + | 9.57151i | −0.557527 | + | 0.378643i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.50741 | + | 3.45116i | 0.0990369 | + | 0.136313i | 0.855659 | − | 0.517539i | \(-0.173152\pi\) |
−0.756623 | + | 0.653852i | \(0.773152\pi\) | |||||||
\(642\) | −2.43943 | + | 1.19459i | −0.0962764 | + | 0.0471469i | ||||
\(643\) | 1.64010 | + | 5.04772i | 0.0646794 | + | 0.199063i | 0.978174 | − | 0.207789i | \(-0.0666267\pi\) |
−0.913494 | + | 0.406851i | \(0.866627\pi\) | |||||||
\(644\) | −8.59771 | − | 26.4610i | −0.338797 | − | 1.04271i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.518387 | + | 0.713499i | 0.0203957 | + | 0.0280722i | ||||
\(647\) | −19.9531 | − | 6.48314i | −0.784436 | − | 0.254879i | −0.110703 | − | 0.993854i | \(-0.535310\pi\) |
−0.673733 | + | 0.738975i | \(0.735310\pi\) | |||||||
\(648\) | −1.63789 | + | 4.12937i | −0.0643423 | + | 0.162217i | ||||
\(649\) | 28.9840 | − | 6.08715i | 1.13772 | − | 0.238941i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.23340 | + | 8.94502i | −0.361886 | + | 0.350583i | ||||
\(652\) | −4.02548 | + | 2.92468i | −0.157650 | + | 0.114539i | ||||
\(653\) | −13.2119 | + | 18.1846i | −0.517022 | + | 0.711620i | −0.985084 | − | 0.172076i | \(-0.944953\pi\) |
0.468061 | + | 0.883696i | \(0.344953\pi\) | |||||||
\(654\) | −0.0860615 | + | 0.492660i | −0.00336527 | + | 0.0192645i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.4340 | + | 7.58077i | 0.407380 | + | 0.295979i | ||||
\(657\) | −6.65429 | + | 18.4651i | −0.259609 | + | 0.720392i | ||||
\(658\) | 0.652198 | − | 2.00726i | 0.0254253 | − | 0.0782511i | ||||
\(659\) | 9.16132 | 0.356874 | 0.178437 | − | 0.983951i | \(-0.442896\pi\) | ||||
0.178437 | + | 0.983951i | \(0.442896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.3540 | 1.37511 | 0.687555 | − | 0.726132i | \(-0.258684\pi\) | ||||
0.687555 | + | 0.726132i | \(0.258684\pi\) | |||||||
\(662\) | 0.164345 | − | 0.505803i | 0.00638746 | − | 0.0196586i | ||||
\(663\) | 10.8112 | − | 1.53696i | 0.419873 | − | 0.0596906i | ||||
\(664\) | 5.56471 | + | 4.04300i | 0.215953 | + | 0.156899i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.08772 | + | 1.40139i | −0.0421483 | + | 0.0543026i | ||||
\(667\) | 15.1263 | − | 20.8195i | 0.585692 | − | 0.806135i | ||||
\(668\) | −21.1487 | + | 15.3654i | −0.818267 | + | 0.594506i | ||||
\(669\) | −3.07423 | − | 3.17334i | −0.118856 | − | 0.122688i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.9580 | − | 20.1477i | −1.73558 | − | 0.777793i | ||||
\(672\) | 7.15973 | + | 3.79230i | 0.276193 | + | 0.146291i | ||||
\(673\) | 3.60658 | + | 1.17185i | 0.139024 | + | 0.0451715i | 0.377702 | − | 0.925927i | \(-0.376714\pi\) |
−0.238679 | + | 0.971099i | \(0.576714\pi\) | |||||||
\(674\) | 1.06124 | + | 1.46066i | 0.0408772 | + | 0.0562627i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.24231 | + | 13.0565i | 0.163166 | + | 0.502172i | ||||
\(677\) | 3.41692 | + | 10.5162i | 0.131323 | + | 0.404171i | 0.995000 | − | 0.0998751i | \(-0.0318443\pi\) |
−0.863677 | + | 0.504046i | \(0.831844\pi\) | |||||||
\(678\) | 1.53142 | + | 3.12725i | 0.0588139 | + | 0.120101i | ||||
\(679\) | −19.8186 | − | 27.2780i | −0.760568 | − | 1.04683i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.9131 | − | 30.0434i | 0.609791 | − | 1.15126i | ||||
\(682\) | 0.197133 | + | 0.938652i | 0.00754862 | + | 0.0359429i | ||||
\(683\) | − | 1.80834i | − | 0.0691943i | −0.999401 | − | 0.0345971i | \(-0.988985\pi\) | ||
0.999401 | − | 0.0345971i | \(-0.0110148\pi\) | |||||||
\(684\) | 8.36272 | + | 28.8179i | 0.319757 | + | 1.10188i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.900955 | + | 1.24006i | −0.0343986 | + | 0.0473456i | ||||
\(687\) | −13.7456 | − | 2.40117i | −0.524426 | − | 0.0916105i | ||||
\(688\) | −11.0566 | + | 3.59252i | −0.421531 | + | 0.136964i | ||||
\(689\) | −0.947131 | − | 0.688131i | −0.0360828 | − | 0.0262157i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.32621 | + | 13.3147i | −0.164577 | + | 0.506516i | −0.999005 | − | 0.0446014i | \(-0.985798\pi\) |
0.834428 | + | 0.551117i | \(0.185798\pi\) | |||||||
\(692\) | −44.9935 | −1.71040 | ||||||||
\(693\) | −27.9197 | + | 14.8721i | −1.06058 | + | 0.564944i | ||||
\(694\) | 1.70321 | 0.0646530 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.702267 | + | 4.93986i | 0.0266194 | + | 0.187245i | ||||
\(697\) | 3.77158 | + | 2.74021i | 0.142859 | + | 0.103793i | ||||
\(698\) | −0.922043 | + | 0.299590i | −0.0348998 | + | 0.0113396i | ||||
\(699\) | 21.6973 | + | 3.79024i | 0.820667 | + | 0.143360i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.3467 | − | 7.51734i | 0.390791 | − | 0.283926i | −0.374989 | − | 0.927029i | \(-0.622353\pi\) |
0.765779 | + | 0.643103i | \(0.222353\pi\) | |||||||
\(702\) | −2.81264 | − | 0.583831i | −0.106156 | − | 0.0220353i | ||||
\(703\) | 24.0582i | 0.907374i | ||||||||
\(704\) | −21.9579 | + | 12.6063i | −0.827571 | + | 0.475120i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.87348 | + | 1.25857i | 0.145780 | + | 0.0473669i | ||||
\(707\) | 2.21793 | + | 3.05271i | 0.0834137 | + | 0.114809i | ||||
\(708\) | −13.5001 | − | 27.5679i | −0.507364 | − | 1.03606i | ||||
\(709\) | −14.2539 | − | 43.8689i | −0.535315 | − | 1.64753i | −0.742967 | − | 0.669328i | \(-0.766582\pi\) |
0.207651 | − | 0.978203i | \(-0.433418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.7170 | − | 0.498792i | −0.589435 | − | 0.0187062i | ||||
\(712\) | −3.98985 | − | 5.49156i | −0.149526 | − | 0.205805i | ||||
\(713\) | −9.79022 | − | 3.18103i | −0.366647 | − | 0.119131i | ||||
\(714\) | 0.851563 | + | 0.451048i | 0.0318689 | + | 0.0168800i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.14115i | 0.154762i | ||||||||
\(717\) | 17.2843 | + | 17.8416i | 0.645496 | + | 0.666306i | ||||
\(718\) | −1.73161 | + | 1.25809i | −0.0646232 | + | 0.0469515i | ||||
\(719\) | 13.3476 | − | 18.3713i | 0.497780 | − | 0.685135i | −0.484019 | − | 0.875057i | \(-0.660824\pi\) |
0.981799 | + | 0.189922i | \(0.0608236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1683 | + | 4.60356i | −0.527655 | + | 0.171446i | ||||
\(722\) | −0.641338 | − | 0.465959i | −0.0238681 | − | 0.0173412i | ||||
\(723\) | −9.55114 | + | 1.35782i | −0.355211 | + | 0.0504980i | ||||
\(724\) | −5.11836 | + | 15.7527i | −0.190222 | + | 0.585444i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.172333 | + | 2.35380i | −0.00639587 | + | 0.0873579i | ||||
\(727\) | −38.1765 | −1.41589 | −0.707944 | − | 0.706268i | \(-0.750377\pi\) | ||||
−0.707944 | + | 0.706268i | \(0.750377\pi\) | |||||||
\(728\) | −2.16421 | + | 6.66074i | −0.0802108 | + | 0.246863i | ||||
\(729\) | −17.8742 | + | 20.2364i | −0.662007 | + | 0.749497i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.99663 | + | 1.29858i | −0.147821 | + | 0.0480299i | ||||
\(732\) | −8.78682 | + | 50.3003i | −0.324770 | + | 1.85915i | ||||
\(733\) | −12.7538 | + | 17.5541i | −0.471072 | + | 0.648375i | −0.976759 | − | 0.214343i | \(-0.931239\pi\) |
0.505687 | + | 0.862717i | \(0.331239\pi\) | |||||||
\(734\) | −2.34150 | + | 1.70120i | −0.0864264 | + | 0.0627924i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.48762i | 0.239137i | ||||||||
\(737\) | 3.28873 | + | 2.97570i | 0.121142 | + | 0.109611i | ||||
\(738\) | −0.689007 | − | 1.01452i | −0.0253627 | − | 0.0373449i | ||||
\(739\) | −27.4778 | − | 8.92807i | −1.01079 | − | 0.328425i | −0.243619 | − | 0.969871i | \(-0.578335\pi\) |
−0.767168 | + | 0.641447i | \(0.778335\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34.9874 | + | 17.1334i | −1.28529 | + | 0.629412i | ||||
\(742\) | −0.0319250 | − | 0.0982550i | −0.00117200 | − | 0.00360705i | ||||
\(743\) | −5.10650 | − | 15.7162i | −0.187339 | − | 0.576571i | 0.812641 | − | 0.582764i | \(-0.198029\pi\) |
−0.999981 | + | 0.00619273i | \(0.998029\pi\) | |||||||
\(744\) | 1.79248 | − | 0.877784i | 0.0657156 | − | 0.0321811i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.10125 | + | 1.00766i | 0.113545 | + | 0.0368929i | ||||
\(747\) | 23.4877 | + | 34.5841i | 0.859371 | + | 1.26537i | ||||
\(748\) | −8.06425 | + | 4.62980i | −0.294858 | + | 0.169282i | ||||
\(749\) | 40.2493i | 1.47068i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6456 | − | 13.5468i | 0.680386 | − | 0.494330i | −0.193099 | − | 0.981179i | \(-0.561854\pi\) |
0.873486 | + | 0.486850i | \(0.161854\pi\) | |||||||
\(752\) | 12.3106 | − | 16.9441i | 0.448921 | − | 0.617887i | ||||
\(753\) | 7.03202 | − | 40.2549i | 0.256261 | − | 1.46697i | ||||
\(754\) | −3.06852 | + | 0.997024i | −0.111749 | + | 0.0363095i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 22.0547 | + | 24.2604i | 0.802122 | + | 0.882342i | ||||
\(757\) | −0.547305 | + | 1.68443i | −0.0198921 | + | 0.0612217i | −0.960510 | − | 0.278246i | \(-0.910247\pi\) |
0.940618 | + | 0.339468i | \(0.110247\pi\) | |||||||
\(758\) | −2.08645 | −0.0757834 | ||||||||
\(759\) | −20.9878 | − | 14.1822i | −0.761811 | − | 0.514780i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.11640 | + | 28.0574i | −0.330469 | + | 1.01708i | 0.638441 | + | 0.769670i | \(0.279579\pi\) |
−0.968911 | + | 0.247410i | \(0.920421\pi\) | |||||||
\(762\) | −3.75987 | + | 0.534516i | −0.136206 | + | 0.0193635i | ||||
\(763\) | 5.99551 | + | 4.35600i | 0.217052 | + | 0.157698i | ||||
\(764\) | 22.0229 | − | 7.15566i | 0.796759 | − | 0.258883i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.30118 | − | 1.79092i | 0.0470134 | − | 0.0647085i | ||||
\(767\) | 32.2409 | − | 23.4244i | 1.16415 | − | 0.845807i | ||||
\(768\) | 17.8202 | + | 18.3947i | 0.643030 | + | 0.663761i | ||||
\(769\) | 49.6159i | 1.78919i | 0.446873 | + | 0.894597i | \(0.352538\pi\) | ||||
−0.446873 | + | 0.894597i | \(0.647462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.79623 | − | 3.59976i | −0.244760 | − | 0.129642i | ||||
\(772\) | −50.7148 | − | 16.4782i | −1.82526 | − | 0.593065i | ||||
\(773\) | −2.78805 | − | 3.83742i | −0.100279 | − | 0.138023i | 0.755929 | − | 0.654654i | \(-0.227186\pi\) |
−0.856208 | + | 0.516632i | \(0.827186\pi\) | |||||||
\(774\) | 1.10490 | + | 0.0350650i | 0.0397150 | + | 0.00126038i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.61761 | + | 4.97848i | 0.0580687 | + | 0.178717i | ||||
\(777\) | 11.5611 | + | 23.6084i | 0.414752 | + | 0.846946i | ||||
\(778\) | −0.142462 | − | 0.196083i | −0.00510753 | − | 0.00702991i | ||||
\(779\) | −15.8176 | − | 5.13945i | −0.566725 | − | 0.184140i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.1874 | + | 7.70246i | 0.615015 | + | 0.275616i | ||||
\(782\) | 0.771623i | 0.0275932i | ||||||||
\(783\) | −6.16345 | + | 29.6928i | −0.220264 | + | 1.06114i | ||||
\(784\) | 9.82676 | − | 7.13956i | 0.350956 | − | 0.254984i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.10844 | − | 0.543004i | −0.110874 | − | 0.0193683i | ||||
\(787\) | −15.8758 | + | 5.15836i | −0.565911 | + | 0.183876i | −0.577979 | − | 0.816051i | \(-0.696159\pi\) |
0.0120680 | + | 0.999927i | \(0.496159\pi\) | |||||||
\(788\) | 4.62227 | + | 3.35827i | 0.164661 | + | 0.119634i | ||||
\(789\) | 3.97378 | + | 27.9522i | 0.141470 | + | 0.995124i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.5981 | 1.83462 | ||||||||
\(792\) | 4.83593 | − | 0.856449i | 0.171837 | − | 0.0304326i | ||||
\(793\) | −66.2929 | −2.35413 | ||||||||
\(794\) | −0.203562 | + | 0.626500i | −0.00722415 | + | 0.0222337i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.95204 | − | 5.77750i | −0.281853 | − | 0.204778i | ||||
\(797\) | 23.7656 | − | 7.72191i | 0.841821 | − | 0.273524i | 0.143804 | − | 0.989606i | \(-0.454066\pi\) |
0.698016 | + | 0.716082i | \(0.254066\pi\) | |||||||
\(798\) | −3.38655 | − | 0.591586i | −0.119882 | − | 0.0209419i | ||||
\(799\) | 4.44989 | − | 6.12475i | 0.157426 | − | 0.216678i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.4979 | − | 39.6217i | −0.406258 | − | 1.39996i | ||||
\(802\) | − | 3.10743i | − | 0.109727i | ||||||
\(803\) | 21.2358 | − | 4.45988i | 0.749394 | − | 0.157386i | ||||
\(804\) | 2.15162 | − | 4.06218i | 0.0758817 | − | 0.143262i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.758603 | + | 1.04413i | 0.0267206 | + | 0.0367778i | ||||
\(807\) | 1.47895 | + | 3.02010i | 0.0520617 | + | 0.106313i | ||||
\(808\) | −0.181029 | − | 0.557149i | −0.00636856 | − | 0.0196004i | ||||
\(809\) | −3.70400 | − | 11.3997i | −0.130226 | − | 0.400794i | 0.864591 | − | 0.502476i | \(-0.167577\pi\) |
−0.994817 | + | 0.101682i | \(0.967577\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3957 | + | 23.9431i | 0.610845 | + | 0.840757i | 0.996647 | − | 0.0818253i | \(-0.0260750\pi\) |
−0.385801 | + | 0.922582i | \(0.626075\pi\) | |||||||
\(812\) | 35.0230 | + | 11.3797i | 1.22907 | + | 0.399348i | ||||
\(813\) | −18.8347 | − | 9.97619i | −0.660562 | − | 0.349880i | ||||
\(814\) | 1.94997 | + | 0.209743i | 0.0683463 | + | 0.00735150i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.65370 | + | 6.86821i | 0.232926 | + | 0.240436i | ||||
\(817\) | 12.1287 | − | 8.81203i | 0.424330 | − | 0.308294i | ||||
\(818\) | 1.87430 | − | 2.57976i | 0.0655335 | − | 0.0901991i | ||||
\(819\) | −26.0997 | + | 33.6261i | −0.911999 | + | 1.17499i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.9352 | + | 22.4757i | 1.07964 | + | 0.784408i | 0.977621 | − | 0.210374i | \(-0.0674683\pi\) |
0.102024 | + | 0.994782i | \(0.467468\pi\) | |||||||
\(822\) | −1.67182 | + | 0.237671i | −0.0583113 | + | 0.00828973i | ||||
\(823\) | −13.6460 | + | 41.9982i | −0.475671 | + | 1.46396i | 0.369380 | + | 0.929278i | \(0.379570\pi\) |
−0.845051 | + | 0.534686i | \(0.820430\pi\) | |||||||
\(824\) | 2.31285 | 0.0805720 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.51678 | 0.122365 | ||||||||
\(827\) | −7.12866 | + | 21.9398i | −0.247888 | + | 0.762920i | 0.747260 | + | 0.664532i | \(0.231369\pi\) |
−0.995148 | + | 0.0983889i | \(0.968631\pi\) | |||||||
\(828\) | −8.90074 | + | 24.6988i | −0.309322 | + | 0.858342i | ||||
\(829\) | 10.7964 | + | 7.84404i | 0.374974 | + | 0.272435i | 0.759271 | − | 0.650775i | \(-0.225556\pi\) |
−0.384296 | + | 0.923210i | \(0.625556\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.09058 | + | 6.24306i | −0.0378319 | + | 0.216569i | ||||
\(832\) | −20.0258 | + | 27.5632i | −0.694270 | + | 0.955581i | ||||
\(833\) | 3.55207 | − | 2.58073i | 0.123072 | − | 0.0894170i | ||||
\(834\) | 0.214099 | − | 0.207412i | 0.00741364 | − | 0.00718209i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 22.2574 | − | 24.5989i | 0.769790 | − | 0.850770i | ||||
\(837\) | 12.0580 | − | 1.32556i | 0.416786 | − | 0.0458180i | ||||
\(838\) | 3.89210 | + | 1.26462i | 0.134450 | + | 0.0436855i | ||||
\(839\) | −9.03502 | − | 12.4356i | −0.311923 | − | 0.429326i | 0.624056 | − | 0.781379i | \(-0.285484\pi\) |
−0.935980 | + | 0.352053i | \(0.885484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.56400 | + | 4.81351i | 0.0539312 | + | 0.165983i | ||||
\(842\) | 0.381999 | + | 1.17567i | 0.0131646 | + | 0.0405164i | ||||
\(843\) | −28.7724 | + | 14.0899i | −0.990975 | + | 0.485284i | ||||
\(844\) | −13.2377 | − | 18.2202i | −0.455662 | − | 0.627164i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.64750 | + | 1.11889i | −0.0566422 | + | 0.0384684i | ||||
\(847\) | 30.2016 | + | 17.6332i | 1.03774 | + | 0.605885i | ||||
\(848\) | − | 1.02521i | − | 0.0352057i | ||||||
\(849\) | 31.4200 | − | 30.4386i | 1.07833 | − | 1.04465i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.3724 | + | 17.0291i | −0.424119 | + | 0.583750i | ||||
\(852\) | 3.35920 | − | 19.2298i | 0.115084 | − | 0.658802i | ||||
\(853\) | 22.2057 | − | 7.21506i | 0.760307 | − | 0.247039i | 0.0968968 | − | 0.995294i | \(-0.469108\pi\) |
0.663411 | + | 0.748256i | \(0.269108\pi\) | |||||||
\(854\) | −4.73282 | − | 3.43860i | −0.161954 | − | 0.117666i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.93098 | − | 5.94294i | 0.0659995 | − | 0.203126i | ||||
\(857\) | 16.1869 | 0.552933 | 0.276467 | − | 0.961023i | \(-0.410836\pi\) | ||||
0.276467 | + | 0.961023i | \(0.410836\pi\) | |||||||
\(858\) | 1.08367 | + | 2.98516i | 0.0369959 | + | 0.101912i | ||||
\(859\) | 10.3515 | 0.353187 | 0.176594 | − | 0.984284i | \(-0.443492\pi\) | ||||
0.176594 | + | 0.984284i | \(0.443492\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.9916 | + | 2.55774i | −0.613151 | + | 0.0871677i | ||||
\(862\) | 1.18020 | + | 0.857467i | 0.0401979 | + | 0.0292055i | ||||
\(863\) | −33.3949 | + | 10.8507i | −1.13678 | + | 0.369361i | −0.816147 | − | 0.577844i | \(-0.803894\pi\) |
−0.320628 | + | 0.947205i | \(0.603894\pi\) | |||||||
\(864\) | −3.14284 | − | 6.96924i | −0.106922 | − | 0.237098i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.09312 | − | 0.794196i | 0.0371456 | − | 0.0269879i | ||||
\(867\) | −18.0827 | − | 18.6657i | −0.614120 | − | 0.633919i | ||||
\(868\) | − | 14.7306i | − | 0.499989i | ||||||
\(869\) | 8.65567 | + | 15.0766i | 0.293624 | + | 0.511438i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.67588 | + | 1.84421i | 0.192320 | + | 0.0624885i | ||||
\(872\) | −0.676276 | − | 0.930814i | −0.0229016 | − | 0.0315213i | ||||
\(873\) | −1.00919 | + | 31.7998i | −0.0341559 | + | 1.07626i | ||||
\(874\) | −0.850661 | − | 2.61807i | −0.0287741 | − | 0.0885574i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.89112 | − | 20.1982i | −0.334190 | − | 0.682434i | ||||
\(877\) | −23.6165 | − | 32.5053i | −0.797472 | − | 1.09763i | −0.993137 | − | 0.116956i | \(-0.962686\pi\) |
0.195665 | − | 0.980671i | \(-0.437314\pi\) | |||||||
\(878\) | 0.499622 | + | 0.162337i | 0.0168614 | + | 0.00547861i | ||||
\(879\) | −0.691156 | + | 1.30488i | −0.0233121 | + | 0.0440125i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 12.1990i | − | 0.410996i | −0.978658 | − | 0.205498i | \(-0.934119\pi\) | ||
0.978658 | − | 0.205498i | \(-0.0658813\pi\) | |||||||
\(882\) | −1.10923 | + | 0.321889i | −0.0373497 | + | 0.0108386i | ||||
\(883\) | −38.3546 | + | 27.8662i | −1.29073 | + | 0.937773i | −0.999820 | − | 0.0189757i | \(-0.993959\pi\) |
−0.290914 | + | 0.956749i | \(0.593959\pi\) | |||||||
\(884\) | −7.35466 | + | 10.1228i | −0.247364 | + | 0.340468i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.26167 | + | 1.38470i | −0.143173 | + | 0.0465199i | ||||
\(887\) | −22.7959 | − | 16.5622i | −0.765410 | − | 0.556103i | 0.135155 | − | 0.990824i | \(-0.456847\pi\) |
−0.900565 | + | 0.434721i | \(0.856847\pi\) | |||||||
\(888\) | −0.574411 | − | 4.04050i | −0.0192760 | − | 0.135590i | ||||
\(889\) | −17.3898 | + | 53.5202i | −0.583234 | + | 1.79501i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.4163 | + | 5.06771i | 0.985483 | + | 0.169775i | ||||
\(892\) | 5.06261 | 0.169509 | ||||||||
\(893\) | −8.34608 | + | 25.6866i | −0.279291 | + | 0.859569i | ||||
\(894\) | 0.351467 | + | 2.47228i | 0.0117548 | + | 0.0826854i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.7570 | + | 3.82007i | −0.392772 | + | 0.127619i | ||||
\(897\) | −33.5762 | − | 5.86533i | −1.12108 | − | 0.195838i | ||||
\(898\) | 3.01169 | − | 4.14524i | 0.100501 | − | 0.138328i | ||||
\(899\) | 11.0228 | − | 8.00851i | 0.367630 | − | 0.267099i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.370580i | − | 0.0123458i | ||||||
\(902\) | −0.554463 | + | 1.23724i | −0.0184616 | + | 0.0411956i | ||||
\(903\) | 7.66733 | − | 14.4757i | 0.255153 | − | 0.481720i | ||||
\(904\) | −7.61861 | − | 2.47544i | −0.253391 | − | 0.0823318i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.339610 | + | 0.693502i | 0.0112828 | + | 0.0230400i | ||||
\(907\) | 7.61902 | + | 23.4489i | 0.252986 | + | 0.778610i | 0.994220 | + | 0.107363i | \(0.0342407\pi\) |
−0.741234 | + | 0.671246i | \(0.765759\pi\) | |||||||
\(908\) | 12.0380 | + | 37.0491i | 0.399494 | + | 1.22952i | ||||
\(909\) | 0.112940 | − | 3.55876i | 0.00374598 | − | 0.118037i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.6875 | + | 3.47258i | 0.354092 | + | 0.115052i | 0.480662 | − | 0.876906i | \(-0.340397\pi\) |
−0.126569 | + | 0.991958i | \(0.540397\pi\) | |||||||
\(912\) | −30.1473 | − | 15.9681i | −0.998277 | − | 0.528758i | ||||
\(913\) | 18.9012 | − | 42.1766i | 0.625539 | − | 1.39584i | ||||
\(914\) | 1.01932i | 0.0337160i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.9352 | − | 9.39795i | 0.427390 | − | 0.310517i | ||||
\(917\) | −27.4841 | + | 37.8286i | −0.907605 | + | 1.24921i | ||||
\(918\) | −0.373803 | − | 0.828907i | −0.0123373 | − | 0.0273580i | ||||
\(919\) | 47.3177 | − | 15.3745i | 1.56087 | − | 0.507157i | 0.603828 | − | 0.797115i | \(-0.293641\pi\) |
0.957039 | + | 0.289958i | \(0.0936413\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.8681 | − | 3.25100i | 0.753529 | − | 0.107124i | ||||
\(922\) | −0.769275 | + | 2.36759i | −0.0253347 | + | 0.0779723i | ||||
\(923\) | 25.3438 | 0.834200 | ||||||||
\(924\) | 10.0204 | − | 34.8346i | 0.329645 | − | 1.14598i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.41477 | + | 4.35422i | −0.0464923 | + | 0.143089i | ||||
\(927\) | 13.2247 | + | 4.76581i | 0.434357 | + | 0.156530i | ||||
\(928\) | −6.94688 | − | 5.04721i | −0.228043 | − | 0.165683i | ||||
\(929\) | 7.97273 | − | 2.59050i | 0.261577 | − | 0.0849915i | −0.175293 | − | 0.984516i | \(-0.556087\pi\) |
0.436869 | + | 0.899525i | \(0.356087\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.20686 | + | 12.6722i | −0.301743 | + | 0.415313i | ||||
\(932\) | −20.4181 | + | 14.8346i | −0.668816 | + | 0.485924i | ||||
\(933\) | −0.951444 | + | 0.921729i | −0.0311489 | + | 0.0301760i | ||||
\(934\) | 1.74363i | 0.0570534i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.46694 | − | 3.71286i | 0.178692 | − | 0.121358i | ||||
\(937\) | 35.4510 | + | 11.5187i | 1.15813 | + | 0.376300i | 0.824201 | − | 0.566297i | \(-0.191625\pi\) |
0.333931 | + | 0.942597i | \(0.391625\pi\) | |||||||
\(938\) | 0.309557 | + | 0.426069i | 0.0101074 | + | 0.0139116i | ||||
\(939\) | −6.54775 | + | 3.20646i | −0.213678 | + | 0.104639i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.62434 | + | 29.6207i | 0.313744 | + | 0.965606i | 0.976268 | + | 0.216565i | \(0.0694854\pi\) |
−0.662524 | + | 0.749041i | \(0.730515\pi\) | |||||||
\(942\) | −1.30760 | + | 0.640338i | −0.0426040 | + | 0.0208633i | ||||
\(943\) | −8.55309 | − | 11.7723i | −0.278527 | − | 0.383359i | ||||
\(944\) | 33.1906 | + | 10.7843i | 1.08026 | + | 0.350998i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.608491 | − | 1.05988i | −0.0197838 | − | 0.0344597i | ||||
\(947\) | 4.34152i | 0.141080i | 0.997509 | + | 0.0705402i | \(0.0224723\pi\) | ||||
−0.997509 | + | 0.0705402i | \(0.977528\pi\) | |||||||
\(948\) | 12.9414 | − | 12.5372i | 0.420316 | − | 0.407188i | ||||
\(949\) | 23.6220 | − | 17.1624i | 0.766803 | − | 0.557115i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.73543 | + | 38.5571i | −0.218411 | + | 1.25030i | ||||
\(952\) | −2.10839 | + | 0.685059i | −0.0683334 | + | 0.0222029i | ||||
\(953\) | −12.6364 | − | 9.18085i | −0.409332 | − | 0.297397i | 0.363999 | − | 0.931399i | \(-0.381411\pi\) |
−0.773331 | + | 0.634002i | \(0.781411\pi\) | |||||||
\(954\) | −0.0330502 | + | 0.0917114i | −0.00107004 | + | 0.00296927i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28.4637 | −0.920583 | ||||||||
\(957\) | 31.5141 | − | 11.4402i | 1.01871 | − | 0.369810i | ||||
\(958\) | −0.167416 | −0.00540897 | ||||||||
\(959\) | −7.73231 | + | 23.7976i | −0.249689 | + | 0.768465i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.6703 | + | 15.0178i | 0.666784 | + | 0.484447i | ||||
\(962\) | 2.50986 | − | 0.815504i | 0.0809212 | − | 0.0262929i | ||||
\(963\) | 23.2871 | − | 30.0024i | 0.750416 | − | 0.966813i | ||||
\(964\) | 6.49746 | − | 8.94298i | 0.209269 | − | 0.288034i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.09286 | − | 2.16033i | −0.0673366 | − | 0.0695075i | ||||
\(967\) | − | 40.2132i | − | 1.29317i | −0.762843 | − | 0.646584i | \(-0.776197\pi\) | ||
0.762843 | − | 0.646584i | \(-0.223803\pi\) | |||||||
\(968\) | −3.61340 | − | 4.05254i | −0.116139 | − | 0.130253i | ||||
\(969\) | −10.8973 | − | 5.77199i | −0.350072 | − | 0.185423i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.4169 | − | 28.1014i | −0.655209 | − | 0.901818i | 0.344102 | − | 0.938932i | \(-0.388183\pi\) |
−0.999311 | + | 0.0371145i | \(0.988183\pi\) | |||||||
\(972\) | −2.40350 | − | 30.8442i | −0.0770924 | − | 0.989329i | ||||
\(973\) | −1.36497 | − | 4.20096i | −0.0437591 | − | 0.134677i | ||||
\(974\) | 0.860593 | + | 2.64863i | 0.0275752 | + | 0.0848677i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.1227 | − | 46.9659i | −1.09224 | − | 1.50334i | ||||
\(977\) | −8.56456 | − | 2.78279i | −0.274004 | − | 0.0890294i | 0.168792 | − | 0.985652i | \(-0.446013\pi\) |
−0.442796 | + | 0.896622i | \(0.646013\pi\) | |||||||
\(978\) | −0.251780 | + | 0.475351i | −0.00805103 | + | 0.0152001i | ||||
\(979\) | −30.6017 | + | 33.8210i | −0.978035 | + | 1.08092i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.94888 | − | 6.71584i | −0.0622230 | − | 0.214420i | ||||
\(982\) | 1.14081 | − | 0.828849i | 0.0364048 | − | 0.0264496i | ||||
\(983\) | 22.2883 | − | 30.6772i | 0.710885 | − | 0.978450i | −0.288892 | − | 0.957362i | \(-0.593287\pi\) |
0.999778 | − | 0.0210882i | \(-0.00671308\pi\) | |||||||
\(984\) | 2.77922 | + | 0.485495i | 0.0885984 | + | 0.0154770i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.826247 | − | 0.600304i | −0.0263131 | − | 0.0191176i | ||||
\(987\) | 4.15358 | + | 29.2170i | 0.132210 | + | 0.929986i | ||||
\(988\) | 13.7942 | − | 42.4541i | 0.438851 | − | 1.35064i | ||||
\(989\) | 13.1168 | 0.417089 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.7931 | −1.10524 | −0.552620 | − | 0.833433i | \(-0.686372\pi\) | ||||
−0.552620 | + | 0.833433i | \(0.686372\pi\) | |||||||
\(992\) | −1.06142 | + | 3.26672i | −0.0337001 | + | 0.103718i | ||||
\(993\) | 1.04665 | + | 7.36229i | 0.0332144 | + | 0.233635i | ||||
\(994\) | 1.80936 | + | 1.31457i | 0.0573893 | + | 0.0416958i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −47.1884 | − | 8.24321i | −1.49522 | − | 0.261196i | ||||
\(997\) | −26.1445 | + | 35.9848i | −0.828004 | + | 1.13965i | 0.160288 | + | 0.987070i | \(0.448758\pi\) |
−0.988291 | + | 0.152579i | \(0.951242\pi\) | |||||||
\(998\) | 0.391585 | − | 0.284503i | 0.0123954 | − | 0.00900579i | ||||
\(999\) | 5.04133 | − | 24.2869i | 0.159500 | − | 0.768404i |
(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 | 825.2.bi.h.101.10 | 80 | ||
3.2 | odd | 2 | inner | 825.2.bi.h.101.12 | 80 | ||
5.2 | odd | 4 | 165.2.r.a.134.9 | ✓ | 80 | ||
5.3 | odd | 4 | 165.2.r.a.134.12 | yes | 80 | ||
5.4 | even | 2 | inner | 825.2.bi.h.101.11 | 80 | ||
11.6 | odd | 10 | inner | 825.2.bi.h.776.12 | 80 | ||
15.2 | even | 4 | 165.2.r.a.134.11 | yes | 80 | ||
15.8 | even | 4 | 165.2.r.a.134.10 | yes | 80 | ||
15.14 | odd | 2 | inner | 825.2.bi.h.101.9 | 80 | ||
33.17 | even | 10 | inner | 825.2.bi.h.776.10 | 80 | ||
55.17 | even | 20 | 165.2.r.a.149.10 | yes | 80 | ||
55.28 | even | 20 | 165.2.r.a.149.11 | yes | 80 | ||
55.39 | odd | 10 | inner | 825.2.bi.h.776.9 | 80 | ||
165.17 | odd | 20 | 165.2.r.a.149.12 | yes | 80 | ||
165.83 | odd | 20 | 165.2.r.a.149.9 | yes | 80 | ||
165.149 | even | 10 | inner | 825.2.bi.h.776.11 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.r.a.134.9 | ✓ | 80 | 5.2 | odd | 4 | ||
165.2.r.a.134.10 | yes | 80 | 15.8 | even | 4 | ||
165.2.r.a.134.11 | yes | 80 | 15.2 | even | 4 | ||
165.2.r.a.134.12 | yes | 80 | 5.3 | odd | 4 | ||
165.2.r.a.149.9 | yes | 80 | 165.83 | odd | 20 | ||
165.2.r.a.149.10 | yes | 80 | 55.17 | even | 20 | ||
165.2.r.a.149.11 | yes | 80 | 55.28 | even | 20 | ||
165.2.r.a.149.12 | yes | 80 | 165.17 | odd | 20 | ||
825.2.bi.h.101.9 | 80 | 15.14 | odd | 2 | inner | ||
825.2.bi.h.101.10 | 80 | 1.1 | even | 1 | trivial | ||
825.2.bi.h.101.11 | 80 | 5.4 | even | 2 | inner | ||
825.2.bi.h.101.12 | 80 | 3.2 | odd | 2 | inner | ||
825.2.bi.h.776.9 | 80 | 55.39 | odd | 10 | inner | ||
825.2.bi.h.776.10 | 80 | 33.17 | even | 10 | inner | ||
825.2.bi.h.776.11 | 80 | 165.149 | even | 10 | inner | ||
825.2.bi.h.776.12 | 80 | 11.6 | odd | 10 | inner |