Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(143,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([27, 34]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.bb (of order \(36\), degree \(12\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{36})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Character | \(\chi\) | \(=\) | 950.193 |
Dual form | 950.2.bb.b.507.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0871557 | − | 0.996195i | −0.0616284 | − | 0.704416i | ||||
\(3\) | 0.794263 | − | 1.70330i | 0.458568 | − | 0.983402i | −0.532047 | − | 0.846715i | \(-0.678577\pi\) |
0.990614 | − | 0.136687i | \(-0.0436453\pi\) | |||||||
\(4\) | −0.984808 | + | 0.173648i | −0.492404 | + | 0.0868241i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.76604 | − | 0.642788i | −0.720985 | − | 0.262417i | ||||
\(7\) | −3.76160 | − | 1.00792i | −1.42175 | − | 0.380957i | −0.535646 | − | 0.844443i | \(-0.679932\pi\) |
−0.886104 | + | 0.463486i | \(0.846598\pi\) | |||||||
\(8\) | 0.258819 | + | 0.965926i | 0.0915064 | + | 0.341506i | ||||
\(9\) | −0.342020 | − | 0.407604i | −0.114007 | − | 0.135868i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.56588 | + | 2.71219i | −0.472131 | + | 0.817755i | −0.999491 | − | 0.0318867i | \(-0.989848\pi\) |
0.527360 | + | 0.849642i | \(0.323182\pi\) | |||||||
\(12\) | −0.486421 | + | 1.81535i | −0.140418 | + | 0.524045i | ||||
\(13\) | −1.46798 | + | 0.684531i | −0.407145 | + | 0.189855i | −0.615392 | − | 0.788222i | \(-0.711002\pi\) |
0.208247 | + | 0.978076i | \(0.433224\pi\) | |||||||
\(14\) | −0.676236 | + | 3.83513i | −0.180732 | + | 1.02498i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.939693 | − | 0.342020i | 0.234923 | − | 0.0855050i | ||||
\(17\) | −6.30628 | + | 0.551728i | −1.52950 | + | 0.133814i | −0.820602 | − | 0.571500i | \(-0.806362\pi\) |
−0.708896 | + | 0.705313i | \(0.750806\pi\) | |||||||
\(18\) | −0.376244 | + | 0.376244i | −0.0886815 | + | 0.0886815i | ||||
\(19\) | 2.70709 | + | 3.41638i | 0.621050 | + | 0.783771i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.70448 | + | 5.60658i | −1.02660 | + | 1.22346i | ||||
\(22\) | 2.83834 | + | 1.32354i | 0.605136 | + | 0.282180i | ||||
\(23\) | −0.0168245 | + | 0.0240279i | −0.00350816 | + | 0.00501017i | −0.820902 | − | 0.571069i | \(-0.806529\pi\) |
0.817394 | + | 0.576079i | \(0.195418\pi\) | |||||||
\(24\) | 1.85083 | + | 0.326352i | 0.377800 | + | 0.0666163i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.809869 | + | 1.40273i | 0.158828 | + | 0.275099i | ||||
\(27\) | 4.48011 | − | 1.20044i | 0.862198 | − | 0.231025i | ||||
\(28\) | 3.87947 | + | 0.339410i | 0.733151 | + | 0.0641424i | ||||
\(29\) | 0.496737 | − | 0.416812i | 0.0922418 | − | 0.0774001i | −0.595501 | − | 0.803355i | \(-0.703046\pi\) |
0.687742 | + | 0.725955i | \(0.258602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.55008 | + | 3.78169i | −1.17643 | + | 0.679211i | −0.955186 | − | 0.296007i | \(-0.904345\pi\) |
−0.221243 | + | 0.975219i | \(0.571011\pi\) | |||||||
\(32\) | −0.422618 | − | 0.906308i | −0.0747091 | − | 0.160214i | ||||
\(33\) | 3.37595 | + | 4.82136i | 0.587677 | + | 0.839290i | ||||
\(34\) | 1.09926 | + | 6.23420i | 0.188521 | + | 1.06916i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.407604 | + | 0.342020i | 0.0679340 | + | 0.0570034i | ||||
\(37\) | −4.88201 | − | 4.88201i | −0.802598 | − | 0.802598i | 0.180903 | − | 0.983501i | \(-0.442098\pi\) |
−0.983501 | + | 0.180903i | \(0.942098\pi\) | |||||||
\(38\) | 3.16744 | − | 2.99455i | 0.513827 | − | 0.485780i | ||||
\(39\) | 3.04411i | 0.487448i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.29280 | − | 6.29940i | −0.358074 | − | 0.983801i | −0.979697 | − | 0.200484i | \(-0.935748\pi\) |
0.621622 | − | 0.783317i | \(-0.286474\pi\) | |||||||
\(42\) | 5.99527 | + | 4.19793i | 0.925090 | + | 0.647755i | ||||
\(43\) | 3.26829 | − | 2.28848i | 0.498409 | − | 0.348990i | −0.297185 | − | 0.954820i | \(-0.596048\pi\) |
0.795594 | + | 0.605830i | \(0.207159\pi\) | |||||||
\(44\) | 1.07113 | − | 2.94289i | 0.161478 | − | 0.443658i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0254029 | + | 0.0146663i | 0.00374545 | + | 0.00216244i | ||||
\(47\) | −1.16389 | + | 13.3033i | −0.169771 | + | 1.94049i | 0.141016 | + | 0.990007i | \(0.454963\pi\) |
−0.310787 | + | 0.950480i | \(0.600593\pi\) | |||||||
\(48\) | 0.163799 | − | 1.87223i | 0.0236424 | − | 0.270234i | ||||
\(49\) | 7.07153 | + | 4.08275i | 1.01022 | + | 0.583250i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.06908 | + | 11.1797i | −0.569786 | + | 1.56547i | ||||
\(52\) | 1.32681 | − | 0.929044i | 0.183996 | − | 0.128835i | ||||
\(53\) | 0.241049 | + | 0.168784i | 0.0331106 | + | 0.0231843i | 0.590015 | − | 0.807393i | \(-0.299122\pi\) |
−0.556904 | + | 0.830577i | \(0.688011\pi\) | |||||||
\(54\) | −1.58634 | − | 4.35844i | −0.215874 | − | 0.593109i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 3.89429i | − | 0.520396i | ||||||
\(57\) | 7.96927 | − | 1.89749i | 1.05556 | − | 0.251329i | ||||
\(58\) | −0.458520 | − | 0.458520i | −0.0602066 | − | 0.0602066i | ||||
\(59\) | −5.17755 | − | 4.34448i | −0.674060 | − | 0.565603i | 0.240204 | − | 0.970722i | \(-0.422786\pi\) |
−0.914264 | + | 0.405119i | \(0.867230\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0829556 | − | 0.470464i | −0.0106214 | − | 0.0602368i | 0.979036 | − | 0.203685i | \(-0.0652920\pi\) |
−0.989658 | + | 0.143449i | \(0.954181\pi\) | |||||||
\(62\) | 4.33818 | + | 6.19556i | 0.550949 | + | 0.786837i | ||||
\(63\) | 0.875711 | + | 1.87797i | 0.110329 | + | 0.236602i | ||||
\(64\) | −0.866025 | + | 0.500000i | −0.108253 | + | 0.0625000i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.50878 | − | 3.78331i | 0.554992 | − | 0.465694i | ||||
\(67\) | −7.83877 | − | 0.685803i | −0.957658 | − | 0.0837842i | −0.402401 | − | 0.915463i | \(-0.631824\pi\) |
−0.555256 | + | 0.831679i | \(0.687380\pi\) | |||||||
\(68\) | 6.11467 | − | 1.63842i | 0.741512 | − | 0.198688i | ||||
\(69\) | 0.0275637 | + | 0.0477418i | 0.00331828 | + | 0.00574743i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.21131 | − | 0.918895i | −0.618469 | − | 0.109053i | −0.144369 | − | 0.989524i | \(-0.546115\pi\) |
−0.474100 | + | 0.880471i | \(0.657226\pi\) | |||||||
\(72\) | 0.305194 | − | 0.435862i | 0.0359674 | − | 0.0513668i | ||||
\(73\) | 5.79337 | + | 2.70149i | 0.678063 | + | 0.316186i | 0.730966 | − | 0.682414i | \(-0.239070\pi\) |
−0.0529031 | + | 0.998600i | \(0.516847\pi\) | |||||||
\(74\) | −4.43794 | + | 5.28893i | −0.515900 | + | 0.614825i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.25921 | − | 2.89440i | −0.373857 | − | 0.332010i | ||||
\(77\) | 8.62387 | − | 8.62387i | 0.982781 | − | 0.982781i | ||||
\(78\) | 3.03253 | − | 0.265312i | 0.343366 | − | 0.0300407i | ||||
\(79\) | −11.2679 | + | 4.10117i | −1.26773 | + | 0.461417i | −0.886357 | − | 0.463003i | \(-0.846772\pi\) |
−0.381377 | + | 0.924420i | \(0.624550\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.79086 | − | 10.1565i | 0.198984 | − | 1.12850i | ||||
\(82\) | −6.07560 | + | 2.83310i | −0.670938 | + | 0.312864i | ||||
\(83\) | 3.42105 | − | 12.7675i | 0.375509 | − | 1.40142i | −0.477091 | − | 0.878854i | \(-0.658309\pi\) |
0.852600 | − | 0.522564i | \(-0.175025\pi\) | |||||||
\(84\) | 3.65944 | − | 6.33833i | 0.399277 | − | 0.691568i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.56462 | − | 3.05640i | −0.276550 | − | 0.329580i | ||||
\(87\) | −0.315417 | − | 1.17715i | −0.0338162 | − | 0.126204i | ||||
\(88\) | −3.02505 | − | 0.810560i | −0.322471 | − | 0.0864060i | ||||
\(89\) | −3.79474 | − | 1.38117i | −0.402241 | − | 0.146404i | 0.132974 | − | 0.991120i | \(-0.457547\pi\) |
−0.535215 | + | 0.844716i | \(0.679770\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.21190 | − | 1.09533i | 0.651185 | − | 0.114821i | ||||
\(92\) | 0.0123965 | − | 0.0265845i | 0.00129243 | − | 0.00277162i | ||||
\(93\) | 1.23888 | + | 14.1604i | 0.128465 | + | 1.46837i | ||||
\(94\) | 13.3541 | 1.37737 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.87939 | −0.191814 | ||||||||
\(97\) | −0.733447 | − | 8.38333i | −0.0744702 | − | 0.851199i | −0.937940 | − | 0.346798i | \(-0.887269\pi\) |
0.863470 | − | 0.504401i | \(-0.168287\pi\) | |||||||
\(98\) | 3.45089 | − | 7.40046i | 0.348592 | − | 0.747559i | ||||
\(99\) | 1.64106 | − | 0.289363i | 0.164933 | − | 0.0290821i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.30289 | + | 2.29407i | 0.627161 | + | 0.228268i | 0.635995 | − | 0.771693i | \(-0.280590\pi\) |
−0.00883393 | + | 0.999961i | \(0.502812\pi\) | |||||||
\(102\) | 11.4918 | + | 3.07922i | 1.13786 | + | 0.304888i | ||||
\(103\) | 3.56081 | + | 13.2891i | 0.350857 | + | 1.30941i | 0.885619 | + | 0.464412i | \(0.153734\pi\) |
−0.534763 | + | 0.845002i | \(0.679599\pi\) | |||||||
\(104\) | −1.04115 | − | 1.24079i | −0.102093 | − | 0.121670i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.147133 | − | 0.254842i | 0.0142909 | − | 0.0247525i | ||||
\(107\) | −0.423208 | + | 1.57944i | −0.0409131 | + | 0.152690i | −0.983361 | − | 0.181664i | \(-0.941852\pi\) |
0.942447 | + | 0.334354i | \(0.108518\pi\) | |||||||
\(108\) | −4.20360 | + | 1.96017i | −0.404491 | + | 0.188617i | ||||
\(109\) | 1.42174 | − | 8.06307i | 0.136178 | − | 0.772302i | −0.837855 | − | 0.545893i | \(-0.816190\pi\) |
0.974032 | − | 0.226409i | \(-0.0726985\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.1931 | + | 4.43794i | −1.15732 | + | 0.421230i | ||||
\(112\) | −3.87947 | + | 0.339410i | −0.366576 | + | 0.0320712i | ||||
\(113\) | −10.7410 | + | 10.7410i | −1.01043 | + | 1.01043i | −0.0104800 | + | 0.999945i | \(0.503336\pi\) |
−0.999945 | + | 0.0104800i | \(0.996664\pi\) | |||||||
\(114\) | −2.58484 | − | 7.77356i | −0.242092 | − | 0.728061i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.416812 | + | 0.496737i | −0.0387000 | + | 0.0461209i | ||||
\(117\) | 0.781097 | + | 0.364231i | 0.0722124 | + | 0.0336732i | ||||
\(118\) | −3.87670 | + | 5.53649i | −0.356879 | + | 0.509676i | ||||
\(119\) | 24.2778 | + | 4.28083i | 2.22554 | + | 0.392423i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.596031 | + | 1.03236i | 0.0541846 | + | 0.0938505i | ||||
\(122\) | −0.461444 | + | 0.123644i | −0.0417772 | + | 0.0111942i | ||||
\(123\) | −12.5509 | − | 1.09806i | −1.13167 | − | 0.0990086i | ||||
\(124\) | 5.79388 | − | 4.86165i | 0.520306 | − | 0.436589i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.79450 | − | 1.03605i | 0.159867 | − | 0.0922991i | ||||
\(127\) | −2.53661 | − | 5.43978i | −0.225088 | − | 0.482702i | 0.761037 | − | 0.648709i | \(-0.224691\pi\) |
−0.986125 | + | 0.166006i | \(0.946913\pi\) | |||||||
\(128\) | 0.573576 | + | 0.819152i | 0.0506975 | + | 0.0724035i | ||||
\(129\) | −1.30209 | − | 7.38453i | −0.114643 | − | 0.650172i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2177 | + | 12.7692i | 1.32958 | + | 1.11565i | 0.984176 | + | 0.177194i | \(0.0567020\pi\) |
0.345402 | + | 0.938455i | \(0.387742\pi\) | |||||||
\(132\) | −4.16188 | − | 4.16188i | −0.362245 | − | 0.362245i | ||||
\(133\) | −6.73956 | − | 15.5796i | −0.584394 | − | 1.35092i | ||||
\(134\) | 7.86871i | 0.679753i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.16511 | − | 5.94860i | −0.185657 | − | 0.510088i | ||||
\(137\) | 6.78826 | + | 4.75319i | 0.579960 | + | 0.406093i | 0.826415 | − | 0.563062i | \(-0.190377\pi\) |
−0.246454 | + | 0.969154i | \(0.579266\pi\) | |||||||
\(138\) | 0.0451578 | − | 0.0316198i | 0.00384408 | − | 0.00269166i | ||||
\(139\) | −0.759848 | + | 2.08767i | −0.0644495 | + | 0.177074i | −0.967737 | − | 0.251962i | \(-0.918924\pi\) |
0.903288 | + | 0.429035i | \(0.141146\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.7351 | + | 12.5488i | 1.83043 | + | 1.05680i | ||||
\(142\) | −0.461202 | + | 5.27157i | −0.0387032 | + | 0.442380i | ||||
\(143\) | 0.442109 | − | 5.05333i | 0.0369711 | − | 0.422581i | ||||
\(144\) | −0.460802 | − | 0.266044i | −0.0384002 | − | 0.0221704i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.18629 | − | 6.00678i | 0.180939 | − | 0.497125i | ||||
\(147\) | 12.5708 | − | 8.80217i | 1.03682 | − | 0.725991i | ||||
\(148\) | 5.65559 | + | 3.96009i | 0.464887 | + | 0.325517i | ||||
\(149\) | −7.06188 | − | 19.4024i | −0.578532 | − | 1.58950i | −0.790656 | − | 0.612261i | \(-0.790260\pi\) |
0.212124 | − | 0.977243i | \(-0.431962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.61268i | 0.700890i | 0.936583 | + | 0.350445i | \(0.113970\pi\) | ||||
−0.936583 | + | 0.350445i | \(0.886030\pi\) | |||||||
\(152\) | −2.59932 | + | 3.49907i | −0.210833 | + | 0.283812i | ||||
\(153\) | 2.38176 | + | 2.38176i | 0.192554 | + | 0.192554i | ||||
\(154\) | −9.34267 | − | 7.83943i | −0.752854 | − | 0.631720i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.528605 | − | 2.99787i | −0.0423222 | − | 0.240021i | ||||
\(157\) | −11.5574 | − | 16.5057i | −0.922380 | − | 1.31729i | −0.948215 | − | 0.317629i | \(-0.897113\pi\) |
0.0258354 | − | 0.999666i | \(-0.491775\pi\) | |||||||
\(158\) | 5.06762 | + | 10.8675i | 0.403158 | + | 0.864575i | ||||
\(159\) | 0.478947 | − | 0.276520i | 0.0379830 | − | 0.0219295i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0875053 | − | 0.0734257i | 0.00689638 | − | 0.00578675i | ||||
\(162\) | −10.2739 | − | 0.898850i | −0.807194 | − | 0.0706203i | ||||
\(163\) | −15.8338 | + | 4.24265i | −1.24020 | + | 0.332310i | −0.818542 | − | 0.574446i | \(-0.805218\pi\) |
−0.421656 | + | 0.906756i | \(0.638551\pi\) | |||||||
\(164\) | 3.35184 | + | 5.80556i | 0.261735 | + | 0.453338i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.0171 | − | 2.29527i | −1.01032 | − | 0.178147i | ||||
\(167\) | −11.4611 | + | 16.3681i | −0.886885 | + | 1.26660i | 0.0761147 | + | 0.997099i | \(0.475748\pi\) |
−0.962999 | + | 0.269504i | \(0.913140\pi\) | |||||||
\(168\) | −6.63315 | − | 3.09309i | −0.511759 | − | 0.238637i | ||||
\(169\) | −6.66985 | + | 7.94882i | −0.513065 | + | 0.611448i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.466649 | − | 2.27189i | 0.0356855 | − | 0.173736i | ||||
\(172\) | −2.82124 | + | 2.82124i | −0.215118 | + | 0.215118i | ||||
\(173\) | 0.401314 | − | 0.0351104i | 0.0305113 | − | 0.00266939i | −0.0718899 | − | 0.997413i | \(-0.522903\pi\) |
0.102401 | + | 0.994743i | \(0.467347\pi\) | |||||||
\(174\) | −1.14518 | + | 0.416812i | −0.0868160 | + | 0.0315985i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.543825 | + | 3.08418i | −0.0409923 | + | 0.232479i | ||||
\(177\) | −11.5123 | + | 5.36827i | −0.865317 | + | 0.403504i | ||||
\(178\) | −1.04518 | + | 3.90067i | −0.0783397 | + | 0.292368i | ||||
\(179\) | −8.88327 | + | 15.3863i | −0.663966 | + | 1.15002i | 0.315598 | + | 0.948893i | \(0.397795\pi\) |
−0.979564 | + | 0.201131i | \(0.935538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.61930 | − | 10.2721i | −0.640668 | − | 0.763518i | 0.343808 | − | 0.939040i | \(-0.388283\pi\) |
−0.984475 | + | 0.175522i | \(0.943839\pi\) | |||||||
\(182\) | −1.63256 | − | 6.09280i | −0.121014 | − | 0.451629i | ||||
\(183\) | −0.867231 | − | 0.232374i | −0.0641076 | − | 0.0171776i | ||||
\(184\) | −0.0275637 | − | 0.0100324i | −0.00203202 | − | 0.000739596i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.9986 | − | 2.46832i | 1.02642 | − | 0.180986i | ||||
\(187\) | 8.37850 | − | 17.9677i | 0.612697 | − | 1.31393i | ||||
\(188\) | −1.16389 | − | 13.3033i | −0.0848853 | − | 0.970243i | ||||
\(189\) | −18.0623 | −1.31384 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.73888 | 0.632323 | 0.316162 | − | 0.948705i | \(-0.397606\pi\) | ||||
0.316162 | + | 0.948705i | \(0.397606\pi\) | |||||||
\(192\) | 0.163799 | + | 1.87223i | 0.0118212 | + | 0.135117i | ||||
\(193\) | 7.12362 | − | 15.2767i | 0.512769 | − | 1.09964i | −0.464097 | − | 0.885785i | \(-0.653621\pi\) |
0.976866 | − | 0.213853i | \(-0.0686013\pi\) | |||||||
\(194\) | −8.28751 | + | 1.46131i | −0.595008 | + | 0.104916i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.67306 | − | 2.79277i | −0.548076 | − | 0.199483i | ||||
\(197\) | −11.2338 | − | 3.01010i | −0.800378 | − | 0.214461i | −0.164628 | − | 0.986356i | \(-0.552642\pi\) |
−0.635750 | + | 0.771895i | \(0.719309\pi\) | |||||||
\(198\) | −0.431290 | − | 1.60960i | −0.0306504 | − | 0.114389i | ||||
\(199\) | 4.98476 | + | 5.94060i | 0.353360 | + | 0.421118i | 0.913219 | − | 0.407470i | \(-0.133589\pi\) |
−0.559858 | + | 0.828588i | \(0.689144\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.39417 | + | 12.8071i | −0.521544 | + | 0.903341i | ||||
\(202\) | 1.73600 | − | 6.47885i | 0.122145 | − | 0.455850i | ||||
\(203\) | −2.28864 | + | 1.06721i | −0.160631 | + | 0.0749034i | ||||
\(204\) | 2.06593 | − | 11.7165i | 0.144644 | − | 0.820316i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.9282 | − | 4.70548i | 0.900750 | − | 0.327846i | ||||
\(207\) | 0.0155482 | − | 0.00136029i | 0.00108068 | − | 9.45468e-5i | ||||
\(208\) | −1.14533 | + | 1.14533i | −0.0794142 | + | 0.0794142i | ||||
\(209\) | −13.5048 | + | 1.99249i | −0.934150 | + | 0.137824i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5506 | − | 19.7242i | 1.13939 | − | 1.35787i | 0.214914 | − | 0.976633i | \(-0.431053\pi\) |
0.924476 | − | 0.381240i | \(-0.124503\pi\) | |||||||
\(212\) | −0.266696 | − | 0.124362i | −0.0183168 | − | 0.00854125i | ||||
\(213\) | −5.70430 | + | 8.14659i | −0.390852 | + | 0.558195i | ||||
\(214\) | 1.61031 | + | 0.283941i | 0.110079 | + | 0.0194098i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.31908 | + | 4.01676i | 0.157793 | + | 0.273306i | ||||
\(217\) | 28.4504 | − | 7.62326i | 1.93134 | − | 0.517500i | ||||
\(218\) | −8.15630 | − | 0.713584i | −0.552414 | − | 0.0483300i | ||||
\(219\) | 9.20292 | − | 7.72217i | 0.621876 | − | 0.521816i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.87983 | − | 5.12677i | 0.597322 | − | 0.344864i | ||||
\(222\) | 5.48375 | + | 11.7599i | 0.368045 | + | 0.789276i | ||||
\(223\) | −16.0871 | − | 22.9748i | −1.07727 | − | 1.53851i | −0.820169 | − | 0.572122i | \(-0.806120\pi\) |
−0.257105 | − | 0.966384i | \(-0.582768\pi\) | |||||||
\(224\) | 0.676236 | + | 3.83513i | 0.0451830 | + | 0.256245i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.6362 | + | 9.76396i | 0.774031 | + | 0.649489i | ||||
\(227\) | −9.28705 | − | 9.28705i | −0.616403 | − | 0.616403i | 0.328204 | − | 0.944607i | \(-0.393557\pi\) |
−0.944607 | + | 0.328204i | \(0.893557\pi\) | |||||||
\(228\) | −7.51870 | + | 3.25251i | −0.497938 | + | 0.215403i | ||||
\(229\) | − | 6.90731i | − | 0.456448i | −0.973609 | − | 0.228224i | \(-0.926708\pi\) | ||
0.973609 | − | 0.228224i | \(-0.0732919\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.83943 | − | 21.5387i | −0.515797 | − | 1.41714i | ||||
\(232\) | 0.531175 | + | 0.371933i | 0.0348733 | + | 0.0244186i | ||||
\(233\) | −19.9672 | + | 13.9812i | −1.30810 | + | 0.915940i | −0.999380 | − | 0.0352142i | \(-0.988789\pi\) |
−0.308718 | + | 0.951154i | \(0.599900\pi\) | |||||||
\(234\) | 0.294768 | − | 0.809869i | 0.0192696 | − | 0.0529428i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.85330 | + | 3.37941i | 0.381018 | + | 0.219981i | ||||
\(237\) | −1.96412 | + | 22.4500i | −0.127583 | + | 1.45828i | ||||
\(238\) | 2.14859 | − | 24.5585i | 0.139272 | − | 1.59189i | ||||
\(239\) | −9.82220 | − | 5.67085i | −0.635345 | − | 0.366817i | 0.147474 | − | 0.989066i | \(-0.452886\pi\) |
−0.782819 | + | 0.622249i | \(0.786219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.18078 | − | 25.2240i | 0.591386 | − | 1.62482i | −0.176548 | − | 0.984292i | \(-0.556493\pi\) |
0.767935 | − | 0.640528i | \(-0.221285\pi\) | |||||||
\(242\) | 0.976480 | − | 0.683738i | 0.0627705 | − | 0.0439524i | ||||
\(243\) | −4.47905 | − | 3.13626i | −0.287331 | − | 0.201191i | ||||
\(244\) | 0.163391 | + | 0.448912i | 0.0104600 | + | 0.0287386i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.5988i | 0.803271i | ||||||||
\(247\) | −6.31258 | − | 3.16209i | −0.401660 | − | 0.201199i | ||||
\(248\) | −5.34812 | − | 5.34812i | −0.339606 | − | 0.339606i | ||||
\(249\) | −19.0297 | − | 15.9678i | −1.20596 | − | 1.01192i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.95636 | + | 22.4376i | 0.249723 | + | 1.41625i | 0.809263 | + | 0.587447i | \(0.199867\pi\) |
−0.559540 | + | 0.828803i | \(0.689022\pi\) | |||||||
\(252\) | −1.18851 | − | 1.69737i | −0.0748693 | − | 0.106924i | ||||
\(253\) | −0.0388230 | − | 0.0832562i | −0.00244078 | − | 0.00523427i | ||||
\(254\) | −5.19800 | + | 3.00107i | −0.326151 | + | 0.188304i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | − | 0.642788i | 0.0478778 | − | 0.0401742i | ||||
\(257\) | 6.29536 | + | 0.550772i | 0.392694 | + | 0.0343562i | 0.281793 | − | 0.959475i | \(-0.409071\pi\) |
0.110901 | + | 0.993831i | \(0.464626\pi\) | |||||||
\(258\) | −7.24295 | + | 1.94074i | −0.450926 | + | 0.120825i | ||||
\(259\) | 13.4435 | + | 23.2848i | 0.835338 | + | 1.44685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.339788 | − | 0.0599139i | −0.0210324 | − | 0.00370858i | ||||
\(262\) | 11.3943 | − | 16.2727i | 0.703941 | − | 1.00533i | ||||
\(263\) | 11.0948 | + | 5.17359i | 0.684135 | + | 0.319017i | 0.733428 | − | 0.679767i | \(-0.237919\pi\) |
−0.0492932 | + | 0.998784i | \(0.515697\pi\) | |||||||
\(264\) | −3.78331 | + | 4.50878i | −0.232847 | + | 0.277496i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.9329 | + | 8.07177i | −0.915594 | + | 0.494912i | ||||
\(267\) | −5.36657 | + | 5.36657i | −0.328429 | + | 0.328429i | ||||
\(268\) | 7.83877 | − | 0.685803i | 0.478829 | − | 0.0418921i | ||||
\(269\) | −14.0112 | + | 5.09967i | −0.854279 | + | 0.310932i | −0.731784 | − | 0.681537i | \(-0.761312\pi\) |
−0.122495 | + | 0.992469i | \(0.539090\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.85349 | − | 27.5255i | 0.294829 | − | 1.67206i | −0.373070 | − | 0.927803i | \(-0.621695\pi\) |
0.667898 | − | 0.744253i | \(-0.267194\pi\) | |||||||
\(272\) | −5.73726 | + | 2.67533i | −0.347873 | + | 0.162216i | ||||
\(273\) | 3.06821 | − | 11.4507i | 0.185697 | − | 0.693029i | ||||
\(274\) | 4.14347 | − | 7.17670i | 0.250316 | − | 0.433560i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.0354352 | − | 0.0422301i | −0.00213295 | − | 0.00254195i | ||||
\(277\) | 5.82108 | + | 21.7246i | 0.349755 | + | 1.30530i | 0.886958 | + | 0.461850i | \(0.152814\pi\) |
−0.537203 | + | 0.843453i | \(0.680519\pi\) | |||||||
\(278\) | 2.14595 | + | 0.575005i | 0.128705 | + | 0.0344865i | ||||
\(279\) | 3.78169 | + | 1.37642i | 0.226404 | + | 0.0824043i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.60956 | − | 0.812789i | 0.274983 | − | 0.0484869i | −0.0344560 | − | 0.999406i | \(-0.510970\pi\) |
0.309439 | + | 0.950919i | \(0.399859\pi\) | |||||||
\(282\) | 10.6067 | − | 22.7461i | 0.631619 | − | 1.35451i | ||||
\(283\) | −1.59322 | − | 18.2106i | −0.0947071 | − | 1.08251i | −0.883684 | − | 0.468084i | \(-0.844944\pi\) |
0.788977 | − | 0.614423i | \(-0.210611\pi\) | |||||||
\(284\) | 5.29170 | 0.314005 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.07264 | −0.299951 | ||||||||
\(287\) | 2.27530 | + | 26.0068i | 0.134306 | + | 1.53513i | ||||
\(288\) | −0.224870 | + | 0.482236i | −0.0132506 | + | 0.0284160i | ||||
\(289\) | 22.7230 | − | 4.00669i | 1.33665 | − | 0.235687i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8619 | − | 5.40929i | −0.871220 | − | 0.317098i | ||||
\(292\) | −6.17447 | − | 1.65444i | −0.361333 | − | 0.0968190i | ||||
\(293\) | 6.79240 | + | 25.3496i | 0.396816 | + | 1.48094i | 0.818665 | + | 0.574272i | \(0.194715\pi\) |
−0.421848 | + | 0.906666i | \(0.638619\pi\) | |||||||
\(294\) | −9.86430 | − | 11.7558i | −0.575297 | − | 0.685613i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.45210 | − | 5.97922i | 0.200649 | − | 0.347535i | ||||
\(297\) | −3.75950 | + | 14.0307i | −0.218148 | + | 0.814141i | ||||
\(298\) | −18.7130 | + | 8.72604i | −1.08402 | + | 0.505486i | ||||
\(299\) | 0.00825025 | − | 0.0467895i | 0.000477124 | − | 0.00270591i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.6006 | + | 5.31417i | −0.841563 | + | 0.306304i | ||||
\(302\) | 8.57991 | − | 0.750645i | 0.493718 | − | 0.0431947i | ||||
\(303\) | 8.91364 | − | 8.91364i | 0.512075 | − | 0.512075i | ||||
\(304\) | 3.71231 | + | 2.28447i | 0.212915 | + | 0.131023i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.16511 | − | 2.58028i | 0.123771 | − | 0.147505i | ||||
\(307\) | 3.14518 | + | 1.46662i | 0.179505 | + | 0.0837046i | 0.510293 | − | 0.860000i | \(-0.329537\pi\) |
−0.330788 | + | 0.943705i | \(0.607315\pi\) | |||||||
\(308\) | −6.99534 | + | 9.99037i | −0.398596 | + | 0.569254i | ||||
\(309\) | 25.4636 | + | 4.48991i | 1.44857 | + | 0.255422i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.15102 | − | 12.3859i | −0.405497 | − | 0.702341i | 0.588882 | − | 0.808219i | \(-0.299568\pi\) |
−0.994379 | + | 0.105878i | \(0.966235\pi\) | |||||||
\(312\) | −2.94039 | + | 0.787874i | −0.166467 | + | 0.0446046i | ||||
\(313\) | 6.50834 | + | 0.569406i | 0.367873 | + | 0.0321847i | 0.269594 | − | 0.962974i | \(-0.413111\pi\) |
0.0982792 | + | 0.995159i | \(0.468666\pi\) | |||||||
\(314\) | −15.4356 | + | 12.9520i | −0.871079 | + | 0.730922i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.3845 | − | 5.99550i | 0.584175 | − | 0.337273i | ||||
\(317\) | 3.66012 | + | 7.84916i | 0.205573 | + | 0.440853i | 0.981880 | − | 0.189502i | \(-0.0606873\pi\) |
−0.776307 | + | 0.630355i | \(0.782910\pi\) | |||||||
\(318\) | −0.317211 | − | 0.453024i | −0.0177883 | − | 0.0254043i | ||||
\(319\) | 0.352640 | + | 1.99992i | 0.0197441 | + | 0.111974i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.35412 | + | 1.97534i | 0.131394 | + | 0.110253i | ||||
\(322\) | −0.0807728 | − | 0.0807728i | −0.00450129 | − | 0.00450129i | ||||
\(323\) | −18.9566 | − | 20.0511i | −1.05477 | − | 1.11567i | ||||
\(324\) | 10.3131i | 0.572953i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.60651 | + | 15.4038i | 0.310516 | + | 0.853136i | ||||
\(327\) | −12.6046 | − | 8.82584i | −0.697036 | − | 0.488070i | ||||
\(328\) | 5.49134 | − | 3.84508i | 0.303208 | − | 0.212309i | ||||
\(329\) | 17.7867 | − | 48.8686i | 0.980613 | − | 2.69421i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.12265 | − | 4.68961i | −0.446461 | − | 0.257764i | 0.259873 | − | 0.965643i | \(-0.416319\pi\) |
−0.706334 | + | 0.707878i | \(0.749653\pi\) | |||||||
\(332\) | −1.15202 | + | 13.1676i | −0.0632252 | + | 0.722667i | ||||
\(333\) | −0.320180 | + | 3.65967i | −0.0175457 | + | 0.200549i | ||||
\(334\) | 17.3047 | + | 9.99089i | 0.946873 | + | 0.546677i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.50320 | + | 6.87749i | −0.136561 | + | 0.375198i | ||||
\(337\) | 11.2911 | − | 7.90612i | 0.615066 | − | 0.430674i | −0.224087 | − | 0.974569i | \(-0.571940\pi\) |
0.839153 | + | 0.543896i | \(0.183051\pi\) | |||||||
\(338\) | 8.49989 | + | 5.95169i | 0.462333 | + | 0.323729i | ||||
\(339\) | 9.76396 | + | 26.8263i | 0.530305 | + | 1.45700i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 23.6867i | − | 1.28271i | ||||||
\(342\) | −2.30392 | − | 0.266865i | −0.124582 | − | 0.0144304i | ||||
\(343\) | −3.20941 | − | 3.20941i | −0.173292 | − | 0.173292i | ||||
\(344\) | 3.05640 | + | 2.56462i | 0.164790 | + | 0.138275i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0699536 | − | 0.396726i | −0.00376073 | − | 0.0213281i | ||||
\(347\) | 10.8612 | + | 15.5115i | 0.583062 | + | 0.832698i | 0.996983 | − | 0.0776140i | \(-0.0247302\pi\) |
−0.413922 | + | 0.910312i | \(0.635841\pi\) | |||||||
\(348\) | 0.515035 | + | 1.10450i | 0.0276088 | + | 0.0592072i | ||||
\(349\) | 4.72687 | − | 2.72906i | 0.253024 | − | 0.146083i | −0.368124 | − | 0.929777i | \(-0.620000\pi\) |
0.621148 | + | 0.783693i | \(0.286667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.75499 | + | 4.82901i | −0.307178 | + | 0.257753i | ||||
\(352\) | 3.11985 | + | 0.272951i | 0.166288 | + | 0.0145483i | ||||
\(353\) | 16.5192 | − | 4.42630i | 0.879226 | − | 0.235588i | 0.209153 | − | 0.977883i | \(-0.432929\pi\) |
0.670073 | + | 0.742295i | \(0.266263\pi\) | |||||||
\(354\) | 6.35121 | + | 11.0006i | 0.337563 | + | 0.584676i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.97692 | + | 0.701239i | 0.210776 | + | 0.0371656i | ||||
\(357\) | 26.5745 | − | 37.9523i | 1.40647 | − | 2.00865i | ||||
\(358\) | 16.1019 | + | 7.50846i | 0.851014 | + | 0.396834i | ||||
\(359\) | 2.08887 | − | 2.48942i | 0.110247 | − | 0.131387i | −0.708099 | − | 0.706113i | \(-0.750447\pi\) |
0.818346 | + | 0.574726i | \(0.194891\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.34330 | + | 18.4969i | −0.228595 | + | 0.973522i | ||||
\(362\) | −9.48177 | + | 9.48177i | −0.498351 | + | 0.498351i | ||||
\(363\) | 2.23182 | − | 0.195259i | 0.117140 | − | 0.0102484i | ||||
\(364\) | −5.92733 | + | 2.15737i | −0.310677 | + | 0.113077i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.155905 | + | 0.884184i | −0.00814931 | + | 0.0462170i | ||||
\(367\) | −27.6591 | + | 12.8977i | −1.44379 | + | 0.673252i | −0.977414 | − | 0.211333i | \(-0.932220\pi\) |
−0.466380 | + | 0.884585i | \(0.654442\pi\) | |||||||
\(368\) | −0.00759186 | + | 0.0283332i | −0.000395753 | + | 0.00147697i | ||||
\(369\) | −1.78348 | + | 3.08907i | −0.0928442 | + | 0.160811i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.736609 | − | 0.877856i | −0.0382428 | − | 0.0455760i | ||||
\(372\) | −3.67898 | − | 13.7302i | −0.190746 | − | 0.711875i | ||||
\(373\) | 23.9199 | + | 6.40932i | 1.23853 | + | 0.331862i | 0.817893 | − | 0.575370i | \(-0.195142\pi\) |
0.420632 | + | 0.907231i | \(0.361808\pi\) | |||||||
\(374\) | −18.6296 | − | 6.78062i | −0.963314 | − | 0.350618i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.1512 | + | 2.31892i | −0.678224 | + | 0.119589i | ||||
\(377\) | −0.443881 | + | 0.951905i | −0.0228610 | + | 0.0490256i | ||||
\(378\) | 1.57424 | + | 17.9936i | 0.0809699 | + | 0.925491i | ||||
\(379\) | −2.41856 | −0.124233 | −0.0621165 | − | 0.998069i | \(-0.519785\pi\) | ||||
−0.0621165 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.2803 | −0.577908 | ||||||||
\(382\) | −0.761644 | − | 8.70563i | −0.0389691 | − | 0.445419i | ||||
\(383\) | 2.73038 | − | 5.85531i | 0.139516 | − | 0.299192i | −0.824118 | − | 0.566418i | \(-0.808329\pi\) |
0.963634 | + | 0.267225i | \(0.0861067\pi\) | |||||||
\(384\) | 1.85083 | − | 0.326352i | 0.0944499 | − | 0.0166541i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.8394 | − | 5.76506i | −0.806203 | − | 0.293434i | ||||
\(387\) | −2.05061 | − | 0.549460i | −0.104239 | − | 0.0279306i | ||||
\(388\) | 2.17805 | + | 8.12861i | 0.110574 | + | 0.412668i | ||||
\(389\) | 1.44246 | + | 1.71905i | 0.0731354 | + | 0.0871594i | 0.801372 | − | 0.598167i | \(-0.204104\pi\) |
−0.728236 | + | 0.685326i | \(0.759660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0928434 | − | 0.160810i | 0.00469529 | − | 0.00813249i | ||||
\(392\) | −2.11339 | + | 7.88727i | −0.106742 | + | 0.398367i | ||||
\(393\) | 33.8366 | − | 15.7783i | 1.70683 | − | 0.795909i | ||||
\(394\) | −2.01955 | + | 11.4534i | −0.101743 | + | 0.577016i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.56588 | + | 0.569934i | −0.0786885 | + | 0.0286403i | ||||
\(397\) | −14.4429 | + | 1.26359i | −0.724869 | + | 0.0634178i | −0.443617 | − | 0.896216i | \(-0.646305\pi\) |
−0.281251 | + | 0.959634i | \(0.590749\pi\) | |||||||
\(398\) | 5.48355 | − | 5.48355i | 0.274865 | − | 0.274865i | ||||
\(399\) | −31.8897 | − | 0.894756i | −1.59648 | − | 0.0447938i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.34649 | + | 1.60468i | −0.0672405 | + | 0.0801340i | −0.798616 | − | 0.601841i | \(-0.794434\pi\) |
0.731376 | + | 0.681975i | \(0.238879\pi\) | |||||||
\(402\) | 13.4028 | + | 6.24982i | 0.668470 | + | 0.311713i | ||||
\(403\) | 7.02671 | − | 10.0352i | 0.350025 | − | 0.499888i | ||||
\(404\) | −6.60550 | − | 1.16473i | −0.328636 | − | 0.0579474i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.26262 | + | 2.18692i | 0.0626626 | + | 0.108535i | ||||
\(407\) | 20.8856 | − | 5.59627i | 1.03526 | − | 0.277397i | ||||
\(408\) | −11.8519 | − | 1.03691i | −0.586758 | − | 0.0513347i | ||||
\(409\) | 27.6318 | − | 23.1858i | 1.36630 | − | 1.14646i | 0.392325 | − | 0.919827i | \(-0.371671\pi\) |
0.973979 | − | 0.226638i | \(-0.0727734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4878 | − | 7.78718i | 0.665303 | − | 0.384113i | ||||
\(412\) | −5.81434 | − | 12.4689i | −0.286452 | − | 0.614298i | ||||
\(413\) | 15.0970 | + | 21.5607i | 0.742874 | + | 1.06093i | ||||
\(414\) | −0.00271023 | − | 0.0153705i | −0.000133201 | − | 0.000755418i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.24079 | + | 1.04115i | 0.0608348 | + | 0.0510465i | ||||
\(417\) | 2.95241 | + | 2.95241i | 0.144580 | + | 0.144580i | ||||
\(418\) | 3.16194 | + | 13.2798i | 0.154655 | + | 0.649536i | ||||
\(419\) | 7.30395i | 0.356821i | 0.983956 | + | 0.178411i | \(0.0570956\pi\) | ||||
−0.983956 | + | 0.178411i | \(0.942904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.01347 | + | 13.7744i | 0.244342 | + | 0.671323i | 0.999869 | + | 0.0162059i | \(0.00515871\pi\) |
−0.755527 | + | 0.655118i | \(0.772619\pi\) | |||||||
\(422\) | −21.0917 | − | 14.7685i | −1.02673 | − | 0.718921i | ||||
\(423\) | 5.82055 | − | 4.07559i | 0.283005 | − | 0.198162i | ||||
\(424\) | −0.100645 | + | 0.276520i | −0.00488776 | + | 0.0134290i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.61275 | + | 4.97258i | 0.417289 | + | 0.240922i | ||||
\(427\) | −0.162144 | + | 1.85331i | −0.00784668 | + | 0.0896879i | ||||
\(428\) | 0.142513 | − | 1.62893i | 0.00688862 | − | 0.0787373i | ||||
\(429\) | −8.25620 | − | 4.76672i | −0.398613 | − | 0.230139i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.75827 | + | 26.8106i | −0.470039 | + | 1.29142i | 0.447681 | + | 0.894193i | \(0.352250\pi\) |
−0.917720 | + | 0.397228i | \(0.869972\pi\) | |||||||
\(432\) | 3.79935 | − | 2.66034i | 0.182797 | − | 0.127996i | ||||
\(433\) | −14.9022 | − | 10.4346i | −0.716155 | − | 0.501457i | 0.157796 | − | 0.987472i | \(-0.449561\pi\) |
−0.873951 | + | 0.486015i | \(0.838450\pi\) | |||||||
\(434\) | −10.0739 | − | 27.6777i | −0.483561 | − | 1.32857i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.18746i | 0.392108i | ||||||||
\(437\) | −0.127634 | + | 0.00756683i | −0.00610557 | + | 0.000361970i | ||||
\(438\) | −8.49487 | − | 8.49487i | −0.405900 | − | 0.405900i | ||||
\(439\) | −28.4376 | − | 23.8620i | −1.35725 | − | 1.13887i | −0.976820 | − | 0.214062i | \(-0.931331\pi\) |
−0.380432 | − | 0.924809i | \(-0.624225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.754462 | − | 4.27877i | −0.0359267 | − | 0.203751i | ||||
\(442\) | −5.88119 | − | 8.39921i | −0.279740 | − | 0.399510i | ||||
\(443\) | 8.05911 | + | 17.2828i | 0.382900 | + | 0.821132i | 0.999429 | + | 0.0337992i | \(0.0107607\pi\) |
−0.616529 | + | 0.787332i | \(0.711462\pi\) | |||||||
\(444\) | 11.2373 | − | 6.48783i | 0.533296 | − | 0.307899i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −21.4853 | + | 18.0283i | −1.01736 | + | 0.853664i | ||||
\(447\) | −38.6571 | − | 3.38205i | −1.82842 | − | 0.159966i | ||||
\(448\) | 3.76160 | − | 1.00792i | 0.177719 | − | 0.0476196i | ||||
\(449\) | 5.70099 | + | 9.87440i | 0.269046 | + | 0.466002i | 0.968616 | − | 0.248563i | \(-0.0799582\pi\) |
−0.699570 | + | 0.714564i | \(0.746625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6754 | + | 3.64563i | 0.973567 | + | 0.171666i | ||||
\(452\) | 8.71264 | − | 12.4429i | 0.409808 | − | 0.585266i | ||||
\(453\) | 14.6700 | + | 6.84073i | 0.689256 | + | 0.321405i | ||||
\(454\) | −8.44229 | + | 10.0611i | −0.396216 | + | 0.472192i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.89544 | + | 7.20661i | 0.182420 | + | 0.337481i | ||||
\(457\) | 15.7889 | − | 15.7889i | 0.738571 | − | 0.738571i | −0.233730 | − | 0.972302i | \(-0.575093\pi\) |
0.972302 | + | 0.233730i | \(0.0750932\pi\) | |||||||
\(458\) | −6.88103 | + | 0.602012i | −0.321529 | + | 0.0281302i | ||||
\(459\) | −27.5905 | + | 10.0421i | −1.28782 | + | 0.468727i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.44668 | − | 8.20452i | 0.0673785 | − | 0.382122i | −0.932407 | − | 0.361410i | \(-0.882295\pi\) |
0.999785 | − | 0.0207124i | \(-0.00659344\pi\) | |||||||
\(462\) | −20.7735 | + | 9.68682i | −0.966469 | + | 0.450672i | ||||
\(463\) | −6.01367 | + | 22.4433i | −0.279479 | + | 1.04303i | 0.673301 | + | 0.739368i | \(0.264876\pi\) |
−0.952780 | + | 0.303661i | \(0.901791\pi\) | |||||||
\(464\) | 0.324222 | − | 0.561570i | 0.0150516 | − | 0.0260702i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.6683 | + | 18.6727i | 0.725819 | + | 0.864997i | ||||
\(467\) | 9.41628 | + | 35.1421i | 0.435734 | + | 1.62618i | 0.739304 | + | 0.673371i | \(0.235154\pi\) |
−0.303571 | + | 0.952809i | \(0.598179\pi\) | |||||||
\(468\) | −0.832478 | − | 0.223062i | −0.0384813 | − | 0.0103110i | ||||
\(469\) | 28.7950 | + | 10.4805i | 1.32963 | + | 0.483946i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −37.2937 | + | 6.57589i | −1.71840 | + | 0.303001i | ||||
\(472\) | 2.85640 | − | 6.12556i | 0.131476 | − | 0.281952i | ||||
\(473\) | 1.08903 | + | 12.4477i | 0.0500737 | + | 0.572345i | ||||
\(474\) | 22.5357 | 1.03510 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −24.6523 | −1.12994 | ||||||||
\(477\) | −0.0136465 | − | 0.155980i | −0.000624830 | − | 0.00714184i | ||||
\(478\) | −4.79321 | + | 10.2791i | −0.219236 | + | 0.470154i | ||||
\(479\) | 37.1809 | − | 6.55600i | 1.69884 | − | 0.299551i | 0.761551 | − | 0.648105i | \(-0.224438\pi\) |
0.937289 | + | 0.348553i | \(0.113327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5086 | + | 3.82481i | 0.479151 | + | 0.174397i | ||||
\(482\) | −25.9282 | − | 6.94743i | −1.18100 | − | 0.316447i | ||||
\(483\) | −0.0555639 | − | 0.207367i | −0.00252824 | − | 0.00943553i | ||||
\(484\) | −0.766242 | − | 0.913172i | −0.0348292 | − | 0.0415078i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.73396 | + | 4.73535i | −0.124015 | + | 0.214800i | ||||
\(487\) | −3.02241 | + | 11.2798i | −0.136959 | + | 0.511137i | 0.863024 | + | 0.505164i | \(0.168568\pi\) |
−0.999982 | + | 0.00597286i | \(0.998099\pi\) | |||||||
\(488\) | 0.432963 | − | 0.201894i | 0.0195993 | − | 0.00913931i | ||||
\(489\) | −5.34967 | + | 30.3395i | −0.241921 | + | 1.37200i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.8360 | − | 6.85576i | 0.850059 | − | 0.309396i | 0.119995 | − | 0.992775i | \(-0.461712\pi\) |
0.730064 | + | 0.683378i | \(0.239490\pi\) | |||||||
\(492\) | 12.5509 | − | 1.09806i | 0.565837 | − | 0.0495043i | ||||
\(493\) | −2.90260 | + | 2.90260i | −0.130726 | + | 0.130726i | ||||
\(494\) | −2.59988 | + | 6.56415i | −0.116974 | + | 0.295335i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.86165 | + | 5.79388i | −0.218294 | + | 0.260153i | ||||
\(497\) | 18.6767 | + | 8.70908i | 0.837763 | + | 0.390656i | ||||
\(498\) | −14.2485 | + | 20.3490i | −0.638492 | + | 0.911861i | ||||
\(499\) | 33.7600 | + | 5.95279i | 1.51130 | + | 0.266484i | 0.867008 | − | 0.498294i | \(-0.166040\pi\) |
0.644295 | + | 0.764777i | \(0.277151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.7767 | + | 32.5222i | 0.838882 | + | 1.45299i | ||||
\(502\) | 22.0074 | − | 5.89687i | 0.982239 | − | 0.263190i | ||||
\(503\) | −38.0979 | − | 3.33314i | −1.69870 | − | 0.148617i | −0.803806 | − | 0.594892i | \(-0.797195\pi\) |
−0.894896 | + | 0.446274i | \(0.852751\pi\) | |||||||
\(504\) | −1.58733 | + | 1.33193i | −0.0707052 | + | 0.0593287i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.0795557 | + | 0.0459315i | −0.00353668 | + | 0.00204191i | ||||
\(507\) | 8.24162 | + | 17.6742i | 0.366023 | + | 0.784940i | ||||
\(508\) | 3.44268 | + | 4.91666i | 0.152744 | + | 0.218141i | ||||
\(509\) | 2.71535 | + | 15.3995i | 0.120356 | + | 0.682570i | 0.983958 | + | 0.178398i | \(0.0570914\pi\) |
−0.863603 | + | 0.504173i | \(0.831798\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.0694 | − | 16.0012i | −0.843583 | − | 0.707850i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 16.2293 | + | 12.0561i | 0.716539 | + | 0.532288i | ||||
\(514\) | − | 6.31941i | − | 0.278737i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.56462 | + | 7.04624i | 0.112901 | + | 0.310193i | ||||
\(517\) | −34.2585 | − | 23.9881i | −1.50669 | − | 1.05499i | ||||
\(518\) | 22.0245 | − | 15.4217i | 0.967702 | − | 0.677592i | ||||
\(519\) | 0.258945 | − | 0.711445i | 0.0113664 | − | 0.0312290i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.45662 | − | 1.99568i | −0.151437 | − | 0.0874324i | 0.422367 | − | 0.906425i | \(-0.361200\pi\) |
−0.573804 | + | 0.818993i | \(0.694533\pi\) | |||||||
\(522\) | −0.0300714 | + | 0.343717i | −0.00131619 | + | 0.0150441i | ||||
\(523\) | −2.90529 | + | 33.2076i | −0.127039 | + | 1.45207i | 0.618595 | + | 0.785710i | \(0.287702\pi\) |
−0.745634 | + | 0.666356i | \(0.767853\pi\) | |||||||
\(524\) | −17.2039 | − | 9.93266i | −0.751555 | − | 0.433910i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.18693 | − | 11.5035i | 0.182559 | − | 0.501576i | ||||
\(527\) | 39.2202 | − | 27.4623i | 1.70846 | − | 1.19627i | ||||
\(528\) | 4.82136 | + | 3.37595i | 0.209823 | + | 0.146919i | ||||
\(529\) | 7.86617 | + | 21.6121i | 0.342007 | + | 0.939657i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.59629i | 0.156066i | ||||||||
\(532\) | 9.34254 | + | 14.1726i | 0.405050 | + | 0.614458i | ||||
\(533\) | 7.67792 | + | 7.67792i | 0.332568 | + | 0.332568i | ||||
\(534\) | 5.81387 | + | 4.87842i | 0.251591 | + | 0.211110i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.36639 | − | 7.74917i | −0.0590189 | − | 0.334713i | ||||
\(537\) | 19.1518 | + | 27.3516i | 0.826461 | + | 1.18031i | ||||
\(538\) | 6.30142 | + | 13.5134i | 0.271673 | + | 0.582606i | ||||
\(539\) | −22.1464 | + | 12.7862i | −0.953911 | + | 0.550741i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4057 | + | 19.6397i | −1.00629 | + | 0.844378i | −0.987843 | − | 0.155452i | \(-0.950317\pi\) |
−0.0184466 | + | 0.999830i | \(0.505872\pi\) | |||||||
\(542\) | −27.8438 | − | 2.43602i | −1.19599 | − | 0.104636i | ||||
\(543\) | −24.3424 | + | 6.52254i | −1.04463 | + | 0.279909i | ||||
\(544\) | 3.16518 | + | 5.48226i | 0.135706 | + | 0.235050i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.6746 | − | 2.05854i | −0.499625 | − | 0.0880974i | ||||
\(547\) | 15.4533 | − | 22.0696i | 0.660735 | − | 0.943628i | −0.339260 | − | 0.940693i | \(-0.610177\pi\) |
0.999996 | − | 0.00293537i | \(-0.000934358\pi\) | |||||||
\(548\) | −7.51052 | − | 3.50221i | −0.320833 | − | 0.149607i | ||||
\(549\) | −0.163391 | + | 0.194721i | −0.00697334 | + | 0.00831050i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.76870 | + | 0.568694i | 0.117951 | + | 0.0242272i | ||||
\(552\) | −0.0389810 | + | 0.0389810i | −0.00165914 | + | 0.00165914i | ||||
\(553\) | 46.5188 | − | 4.06987i | 1.97818 | − | 0.173068i | ||||
\(554\) | 21.1346 | − | 7.69236i | 0.897922 | − | 0.326817i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.385785 | − | 2.18790i | 0.0163609 | − | 0.0927875i | ||||
\(557\) | 2.31325 | − | 1.07869i | 0.0980156 | − | 0.0457054i | −0.372992 | − | 0.927835i | \(-0.621668\pi\) |
0.471008 | + | 0.882129i | \(0.343890\pi\) | |||||||
\(558\) | 1.04159 | − | 3.88726i | 0.0440940 | − | 0.164561i | ||||
\(559\) | −3.23125 | + | 5.59669i | −0.136667 | + | 0.236715i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.9498 | − | 28.5422i | −1.01116 | − | 1.20505i | ||||
\(562\) | −1.21145 | − | 4.52118i | −0.0511017 | − | 0.190714i | ||||
\(563\) | 33.5735 | + | 8.99598i | 1.41495 | + | 0.379136i | 0.883690 | − | 0.468072i | \(-0.155051\pi\) |
0.531263 | + | 0.847207i | \(0.321718\pi\) | |||||||
\(564\) | −23.5840 | − | 8.58387i | −0.993065 | − | 0.361446i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.0024 | + | 3.17432i | −0.756699 | + | 0.133426i | ||||
\(567\) | −16.9734 | + | 36.3995i | −0.712814 | + | 1.52864i | ||||
\(568\) | −0.461202 | − | 5.27157i | −0.0193516 | − | 0.221190i | ||||
\(569\) | −8.01662 | −0.336074 | −0.168037 | − | 0.985781i | \(-0.553743\pi\) | ||||
−0.168037 | + | 0.985781i | \(0.553743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.98332 | −0.166697 | −0.0833484 | − | 0.996520i | \(-0.526561\pi\) | ||||
−0.0833484 | + | 0.996520i | \(0.526561\pi\) | |||||||
\(572\) | 0.442109 | + | 5.05333i | 0.0184855 | + | 0.211291i | ||||
\(573\) | 6.94097 | − | 14.8849i | 0.289963 | − | 0.621828i | ||||
\(574\) | 25.7095 | − | 4.53328i | 1.07309 | − | 0.189215i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.181985i | 0.0208333 | + | 0.00758271i | ||||
\(577\) | −42.9708 | − | 11.5140i | −1.78890 | − | 0.479334i | −0.796741 | − | 0.604320i | \(-0.793445\pi\) |
−0.992158 | + | 0.124986i | \(0.960111\pi\) | |||||||
\(578\) | −5.97188 | − | 22.2874i | −0.248398 | − | 0.927032i | ||||
\(579\) | −20.3627 | − | 24.2673i | −0.846246 | − | 1.00852i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.7372 | + | 44.5782i | −1.06776 | + | 1.84941i | ||||
\(582\) | −4.09340 | + | 15.2768i | −0.169677 | + | 0.633243i | ||||
\(583\) | −0.835229 | + | 0.389474i | −0.0345917 | + | 0.0161304i | ||||
\(584\) | −1.11001 | + | 6.29517i | −0.0459325 | + | 0.260496i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.6611 | − | 8.97591i | 1.01874 | − | 0.370792i | ||||
\(587\) | 34.4649 | − | 3.01529i | 1.42252 | − | 0.124454i | 0.650237 | − | 0.759732i | \(-0.274670\pi\) |
0.772284 | + | 0.635277i | \(0.219114\pi\) | |||||||
\(588\) | −10.8513 | + | 10.8513i | −0.447502 | + | 0.447502i | ||||
\(589\) | −30.6514 | − | 12.1402i | −1.26297 | − | 0.500227i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.0497 | + | 16.7438i | −0.577928 | + | 0.688748i | ||||
\(592\) | −6.25734 | − | 2.91784i | −0.257175 | − | 0.119923i | ||||
\(593\) | 5.19308 | − | 7.41648i | 0.213254 | − | 0.304559i | −0.698246 | − | 0.715858i | \(-0.746036\pi\) |
0.911500 | + | 0.411299i | \(0.134925\pi\) | |||||||
\(594\) | 14.3049 | + | 2.52234i | 0.586938 | + | 0.103493i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.3238 | + | 17.8813i | 0.422879 | + | 0.732447i | ||||
\(597\) | 14.0778 | − | 3.77215i | 0.576168 | − | 0.154384i | ||||
\(598\) | −0.0473305 | − | 0.00414088i | −0.00193549 | − | 0.000169333i | ||||
\(599\) | 4.22725 | − | 3.54709i | 0.172721 | − | 0.144930i | −0.552329 | − | 0.833626i | \(-0.686261\pi\) |
0.725050 | + | 0.688696i | \(0.241816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.0345 | − | 16.1857i | 1.14355 | − | 0.660229i | 0.196243 | − | 0.980555i | \(-0.437126\pi\) |
0.947307 | + | 0.320326i | \(0.103792\pi\) | |||||||
\(602\) | 6.56648 | + | 14.0819i | 0.267630 | + | 0.573933i | ||||
\(603\) | 2.40148 | + | 3.42967i | 0.0977958 | + | 0.139667i | ||||
\(604\) | −1.49558 | − | 8.48183i | −0.0608541 | − | 0.345121i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.65659 | − | 8.10284i | −0.392272 | − | 0.329156i | ||||
\(607\) | 10.3802 | + | 10.3802i | 0.421318 | + | 0.421318i | 0.885657 | − | 0.464340i | \(-0.153708\pi\) |
−0.464340 | + | 0.885657i | \(0.653708\pi\) | |||||||
\(608\) | 1.95222 | − | 3.89728i | 0.0791732 | − | 0.158056i | ||||
\(609\) | 4.74588i | 0.192313i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.39796 | − | 20.3257i | −0.299289 | − | 0.822291i | ||||
\(612\) | −2.75917 | − | 1.93199i | −0.111533 | − | 0.0780960i | ||||
\(613\) | 19.7129 | − | 13.8031i | 0.796195 | − | 0.557502i | −0.103189 | − | 0.994662i | \(-0.532905\pi\) |
0.899384 | + | 0.437160i | \(0.144016\pi\) | |||||||
\(614\) | 1.18692 | − | 3.26104i | 0.0479003 | − | 0.131605i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.5620 | + | 6.09800i | 0.425557 | + | 0.245695i | ||||
\(617\) | −1.64823 | + | 18.8394i | −0.0663553 | + | 0.758445i | 0.888014 | + | 0.459816i | \(0.152085\pi\) |
−0.954369 | + | 0.298629i | \(0.903471\pi\) | |||||||
\(618\) | 2.25353 | − | 25.7580i | 0.0906504 | − | 1.03614i | ||||
\(619\) | 14.9536 | + | 8.63346i | 0.601035 | + | 0.347008i | 0.769449 | − | 0.638709i | \(-0.220531\pi\) |
−0.168413 | + | 0.985716i | \(0.553864\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0465317 | + | 0.127845i | −0.00186725 | + | 0.00513024i | ||||
\(622\) | −11.7155 | + | 8.20331i | −0.469750 | + | 0.328923i | ||||
\(623\) | 12.8822 | + | 9.02018i | 0.516113 | + | 0.361386i | ||||
\(624\) | 1.04115 | + | 2.86053i | 0.0416793 | + | 0.114513i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 6.53320i | − | 0.261119i | ||||||
\(627\) | −7.33257 | + | 24.5854i | −0.292835 | + | 0.981846i | ||||
\(628\) | 14.2480 | + | 14.2480i | 0.568556 | + | 0.568556i | ||||
\(629\) | 33.4809 | + | 28.0938i | 1.33497 | + | 1.12017i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.26764 | + | 12.8604i | 0.0902734 | + | 0.511966i | 0.996094 | + | 0.0883035i | \(0.0281445\pi\) |
−0.905820 | + | 0.423662i | \(0.860744\pi\) | |||||||
\(632\) | −6.87776 | − | 9.82246i | −0.273583 | − | 0.390716i | ||||
\(633\) | −20.4508 | − | 43.8569i | −0.812847 | − | 1.74316i | ||||
\(634\) | 7.50029 | − | 4.33030i | 0.297875 | − | 0.171978i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.423654 | + | 0.355488i | −0.0167990 | + | 0.0140960i | ||||
\(637\) | −13.1756 | − | 1.15272i | −0.522038 | − | 0.0456724i | ||||
\(638\) | 1.96158 | − | 0.525603i | 0.0776596 | − | 0.0208088i | ||||
\(639\) | 1.40783 | + | 2.43843i | 0.0556928 | + | 0.0964628i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.97365 | − | 1.40597i | −0.314940 | − | 0.0555325i | 0.0139437 | − | 0.999903i | \(-0.495561\pi\) |
−0.328884 | + | 0.944370i | \(0.606673\pi\) | |||||||
\(642\) | 1.76265 | − | 2.51732i | 0.0695661 | − | 0.0993507i | ||||
\(643\) | −0.360894 | − | 0.168288i | −0.0142323 | − | 0.00663662i | 0.415489 | − | 0.909598i | \(-0.363610\pi\) |
−0.429721 | + | 0.902962i | \(0.641388\pi\) | |||||||
\(644\) | −0.0734257 | + | 0.0875053i | −0.00289338 | + | 0.00344819i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.3226 | + | 20.6320i | −0.720893 | + | 0.811756i | ||||
\(647\) | 15.0528 | − | 15.0528i | 0.591787 | − | 0.591787i | −0.346327 | − | 0.938114i | \(-0.612571\pi\) |
0.938114 | + | 0.346327i | \(0.112571\pi\) | |||||||
\(648\) | 10.2739 | − | 0.898850i | 0.403597 | − | 0.0353102i | ||||
\(649\) | 19.8905 | − | 7.23954i | 0.780769 | − | 0.284177i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.61237 | − | 54.5144i | 0.376738 | − | 2.13659i | ||||
\(652\) | 14.8565 | − | 6.92770i | 0.581826 | − | 0.271310i | ||||
\(653\) | −2.05471 | + | 7.66830i | −0.0804072 | + | 0.300084i | −0.994405 | − | 0.105636i | \(-0.966312\pi\) |
0.913998 | + | 0.405719i | \(0.132979\pi\) | |||||||
\(654\) | −7.69369 | + | 13.3259i | −0.300847 | + | 0.521083i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.30905 | − | 5.13532i | −0.168240 | − | 0.200501i | ||||
\(657\) | −0.880311 | − | 3.28537i | −0.0343442 | − | 0.128174i | ||||
\(658\) | −50.2328 | − | 13.4598i | −1.95828 | − | 0.524719i | ||||
\(659\) | −17.9446 | − | 6.53131i | −0.699024 | − | 0.254424i | −0.0320298 | − | 0.999487i | \(-0.510197\pi\) |
−0.666994 | + | 0.745063i | \(0.732419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.8594 | − | 7.90992i | 1.74483 | − | 0.307660i | 0.791854 | − | 0.610711i | \(-0.209116\pi\) |
0.952975 | + | 0.303050i | \(0.0980050\pi\) | |||||||
\(662\) | −3.96383 | + | 8.50047i | −0.154059 | + | 0.330380i | ||||
\(663\) | −1.67952 | − | 19.1970i | −0.0652273 | − | 0.745551i | ||||
\(664\) | 13.2179 | 0.512955 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.67365 | 0.142351 | ||||||||
\(667\) | 0.00165776 | + | 0.0189483i | 6.41886e−5 | + | 0.000733679i | ||||
\(668\) | 8.44466 | − | 18.1096i | 0.326734 | − | 0.700683i | ||||
\(669\) | −51.9104 | + | 9.15320i | −2.00697 | + | 0.353883i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.40589 | + | 0.511701i | 0.0542736 | + | 0.0197540i | ||||
\(672\) | 7.06949 | + | 1.89426i | 0.272711 | + | 0.0730728i | ||||
\(673\) | 0.207675 | + | 0.775055i | 0.00800530 | + | 0.0298762i | 0.969813 | − | 0.243850i | \(-0.0784105\pi\) |
−0.961808 | + | 0.273726i | \(0.911744\pi\) | |||||||
\(674\) | −8.86011 | − | 10.5591i | −0.341279 | − | 0.406720i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.18822 | − | 8.98627i | 0.199547 | − | 0.345626i | ||||
\(677\) | 11.2153 | − | 41.8561i | 0.431040 | − | 1.60866i | −0.319330 | − | 0.947644i | \(-0.603458\pi\) |
0.750370 | − | 0.661019i | \(-0.229876\pi\) | |||||||
\(678\) | 25.8732 | − | 12.0649i | 0.993654 | − | 0.463348i | ||||
\(679\) | −5.69077 | + | 32.2740i | −0.218392 | + | 1.23856i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.1950 | + | 8.44229i | −0.888834 | + | 0.323509i | ||||
\(682\) | −23.5966 | + | 2.06443i | −0.903560 | + | 0.0790512i | ||||
\(683\) | 6.91468 | − | 6.91468i | 0.264583 | − | 0.264583i | −0.562330 | − | 0.826913i | \(-0.690095\pi\) |
0.826913 | + | 0.562330i | \(0.190095\pi\) | |||||||
\(684\) | −0.0650496 | + | 2.31841i | −0.00248723 | + | 0.0886466i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.91748 | + | 3.47692i | −0.111390 | + | 0.132749i | ||||
\(687\) | −11.7652 | − | 5.48622i | −0.448872 | − | 0.209312i | ||||
\(688\) | 2.28848 | − | 3.26829i | 0.0872475 | − | 0.124602i | ||||
\(689\) | −0.469394 | − | 0.0827668i | −0.0178825 | − | 0.00315316i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.61528 | − | 9.72594i | −0.213615 | − | 0.369992i | 0.739228 | − | 0.673455i | \(-0.235191\pi\) |
−0.952843 | + | 0.303463i | \(0.901857\pi\) | |||||||
\(692\) | −0.389120 | + | 0.104264i | −0.0147921 | + | 0.00396354i | ||||
\(693\) | −6.46466 | − | 0.565584i | −0.245572 | − | 0.0214848i | ||||
\(694\) | 14.5058 | − | 12.1718i | 0.550633 | − | 0.462036i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.05541 | − | 0.609339i | 0.0400050 | − | 0.0230969i | ||||
\(697\) | 17.9346 | + | 38.4608i | 0.679320 | + | 1.45681i | ||||
\(698\) | −3.13065 | − | 4.47103i | −0.118497 | − | 0.169231i | ||||
\(699\) | 7.95499 | + | 45.1150i | 0.300885 | + | 1.70641i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.09358 | + | 3.43492i | 0.154612 | + | 0.129735i | 0.716812 | − | 0.697266i | \(-0.245600\pi\) |
−0.562200 | + | 0.827001i | \(0.690045\pi\) | |||||||
\(702\) | 5.31221 | + | 5.31221i | 0.200496 | + | 0.200496i | ||||
\(703\) | 3.46275 | − | 29.8949i | 0.130600 | − | 1.12751i | ||||
\(704\) | − | 3.13176i | − | 0.118033i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.84919 | − | 16.0705i | −0.220137 | − | 0.604822i | ||||
\(707\) | −21.3967 | − | 14.9821i | −0.804706 | − | 0.563461i | ||||
\(708\) | 10.4052 | − | 7.28580i | 0.391052 | − | 0.273817i | ||||
\(709\) | 8.82228 | − | 24.2390i | 0.331328 | − | 0.910315i | −0.656439 | − | 0.754379i | \(-0.727938\pi\) |
0.987767 | − | 0.155937i | \(-0.0498395\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.52549 | + | 3.19014i | 0.207222 | + | 0.119640i | ||||
\(712\) | 0.351959 | − | 4.02291i | 0.0131902 | − | 0.150765i | ||||
\(713\) | 0.0193359 | − | 0.221010i | 0.000724134 | − | 0.00827689i | ||||
\(714\) | −40.1240 | − | 23.1656i | −1.50160 | − | 0.866950i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.07651 | − | 16.6951i | 0.227090 | − | 0.623924i | ||||
\(717\) | −17.4606 | + | 12.2260i | −0.652077 | + | 0.456589i | ||||
\(718\) | −2.66201 | − | 1.86396i | −0.0993452 | − | 0.0695623i | ||||
\(719\) | −1.77083 | − | 4.86532i | −0.0660408 | − | 0.181446i | 0.902283 | − | 0.431145i | \(-0.141890\pi\) |
−0.968323 | + | 0.249700i | \(0.919668\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 53.5772i | − | 1.99532i | ||||||
\(722\) | 18.8051 | + | 2.71466i | 0.699852 | + | 0.101029i | ||||
\(723\) | −35.6721 | − | 35.6721i | −1.32666 | − | 1.32666i | ||||
\(724\) | 10.2721 | + | 8.61930i | 0.381759 | + | 0.320334i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.389031 | − | 2.20631i | −0.0144383 | − | 0.0818837i | ||||
\(727\) | −25.7797 | − | 36.8172i | −0.956117 | − | 1.36548i | −0.930694 | − | 0.365799i | \(-0.880796\pi\) |
−0.0254229 | − | 0.999677i | \(-0.508093\pi\) | |||||||
\(728\) | 2.66576 | + | 5.71675i | 0.0987998 | + | 0.211877i | ||||
\(729\) | 17.8948 | − | 10.3316i | 0.662770 | − | 0.382651i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.3481 | + | 16.2350i | −0.715616 | + | 0.600473i | ||||
\(732\) | 0.894407 | + | 0.0782505i | 0.0330582 | + | 0.00289222i | ||||
\(733\) | −31.0462 | + | 8.31879i | −1.14672 | + | 0.307262i | −0.781648 | − | 0.623719i | \(-0.785621\pi\) |
−0.365068 | + | 0.930981i | \(0.618954\pi\) | |||||||
\(734\) | 15.2592 | + | 26.4298i | 0.563228 | + | 0.975540i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0288871 | + | 0.00509357i | 0.00106479 | + | 0.000187751i | ||||
\(737\) | 14.1346 | − | 20.1863i | 0.520655 | − | 0.743572i | ||||
\(738\) | 3.23276 | + | 1.50746i | 0.119000 | + | 0.0554904i | ||||
\(739\) | −32.1725 | + | 38.3417i | −1.18349 | + | 1.41042i | −0.292575 | + | 0.956243i | \(0.594512\pi\) |
−0.890910 | + | 0.454180i | \(0.849932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.3998 | + | 8.24070i | −0.382048 | + | 0.302730i | ||||
\(742\) | −0.810316 | + | 0.810316i | −0.0297476 | + | 0.0297476i | ||||
\(743\) | −39.7687 | + | 3.47931i | −1.45897 | + | 0.127643i | −0.788840 | − | 0.614599i | \(-0.789318\pi\) |
−0.670131 | + | 0.742242i | \(0.733762\pi\) | |||||||
\(744\) | −13.3573 | + | 4.86165i | −0.489701 | + | 0.178237i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.30017 | − | 24.3875i | 0.157440 | − | 0.892889i | ||||
\(747\) | −6.37416 | + | 2.97232i | −0.233218 | + | 0.108751i | ||||
\(748\) | −5.13114 | + | 19.1497i | −0.187613 | + | 0.700182i | ||||
\(749\) | 3.18388 | − | 5.51464i | 0.116336 | − | 0.201501i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.728959 | + | 0.868740i | 0.0266001 | + | 0.0317008i | 0.779180 | − | 0.626800i | \(-0.215636\pi\) |
−0.752580 | + | 0.658500i | \(0.771191\pi\) | |||||||
\(752\) | 3.45630 | + | 12.8991i | 0.126038 | + | 0.470382i | ||||
\(753\) | 41.3604 | + | 11.0825i | 1.50726 | + | 0.403868i | ||||
\(754\) | 0.986970 | + | 0.359228i | 0.0359433 | + | 0.0130823i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 17.7879 | − | 3.13649i | 0.646940 | − | 0.114073i | ||||
\(757\) | 0.177388 | − | 0.380410i | 0.00644727 | − | 0.0138262i | −0.903058 | − | 0.429519i | \(-0.858683\pi\) |
0.909505 | + | 0.415693i | \(0.136461\pi\) | |||||||
\(758\) | 0.210791 | + | 2.40935i | 0.00765628 | + | 0.0875117i | ||||
\(759\) | −0.172646 | −0.00626666 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.39812 | −0.231932 | −0.115966 | − | 0.993253i | \(-0.536996\pi\) | ||||
−0.115966 | + | 0.993253i | \(0.536996\pi\) | |||||||
\(762\) | 0.983144 | + | 11.2374i | 0.0356156 | + | 0.407088i | ||||
\(763\) | −13.4749 | + | 28.8970i | −0.487824 | + | 1.04614i | ||||
\(764\) | −8.60612 | + | 1.51749i | −0.311358 | + | 0.0549009i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.07100 | − | 2.20966i | −0.219354 | − | 0.0798383i | ||||
\(767\) | 10.5745 | + | 2.83342i | 0.381822 | + | 0.102309i | ||||
\(768\) | −0.486421 | − | 1.81535i | −0.0175522 | − | 0.0655057i | ||||
\(769\) | −12.6226 | − | 15.0430i | −0.455183 | − | 0.542466i | 0.488828 | − | 0.872380i | \(-0.337425\pi\) |
−0.944011 | + | 0.329915i | \(0.892980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.93830 | − | 10.2854i | 0.213863 | − | 0.370421i | ||||
\(772\) | −4.36263 | + | 16.2816i | −0.157015 | + | 0.585986i | ||||
\(773\) | −13.2998 | + | 6.20181i | −0.478361 | + | 0.223063i | −0.646816 | − | 0.762646i | \(-0.723900\pi\) |
0.168455 | + | 0.985709i | \(0.446122\pi\) | |||||||
\(774\) | −0.368647 | + | 2.09070i | −0.0132507 | + | 0.0751486i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.90785 | − | 2.87822i | 0.283875 | − | 0.103322i | ||||
\(777\) | 50.3387 | − | 4.40407i | 1.80589 | − | 0.157995i | ||||
\(778\) | 1.58679 | − | 1.58679i | 0.0568892 | − | 0.0568892i | ||||
\(779\) | 15.3143 | − | 24.8861i | 0.548693 | − | 0.891638i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6525 | − | 12.6952i | 0.381177 | − | 0.454269i | ||||
\(782\) | −0.168289 | − | 0.0784746i | −0.00601802 | − | 0.00280625i | ||||
\(783\) | 1.72508 | − | 2.46367i | 0.0616494 | − | 0.0880444i | ||||
\(784\) | 8.04145 | + | 1.41792i | 0.287195 | + | 0.0506402i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.6673 | − | 32.3327i | −0.665840 | − | 1.15327i | ||||
\(787\) | −23.7713 | + | 6.36949i | −0.847354 | + | 0.227048i | −0.656270 | − | 0.754526i | \(-0.727867\pi\) |
−0.191084 | + | 0.981574i | \(0.561200\pi\) | |||||||
\(788\) | 11.5859 | + | 1.01363i | 0.412730 | + | 0.0361092i | ||||
\(789\) | 17.6244 | − | 14.7886i | 0.627444 | − | 0.526488i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.2292 | − | 29.5772i | 1.82150 | − | 1.05164i | ||||
\(792\) | 0.704241 | + | 1.51025i | 0.0250241 | + | 0.0536644i | ||||
\(793\) | 0.443825 | + | 0.633847i | 0.0157607 | + | 0.0225086i | ||||
\(794\) | 2.51756 | + | 14.2778i | 0.0893450 | + | 0.506701i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.94060 | − | 4.98476i | −0.210559 | − | 0.176680i | ||||
\(797\) | −23.7905 | − | 23.7905i | −0.842704 | − | 0.842704i | 0.146506 | − | 0.989210i | \(-0.453197\pi\) |
−0.989210 | + | 0.146506i | \(0.953197\pi\) | |||||||
\(798\) | 1.88802 | + | 31.8463i | 0.0668351 | + | 1.12735i | ||||
\(799\) | − | 84.5365i | − | 2.99069i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.734906 | + | 2.01914i | 0.0259666 | + | 0.0713427i | ||||
\(802\) | 1.71593 | + | 1.20151i | 0.0605916 | + | 0.0424267i | ||||
\(803\) | −16.3987 | + | 11.4825i | −0.578697 | + | 0.405208i | ||||
\(804\) | 5.05791 | − | 13.8965i | 0.178379 | − | 0.490091i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.6094 | − | 6.12535i | −0.373701 | − | 0.215756i | ||||
\(807\) | −2.44232 | + | 27.9158i | −0.0859736 | + | 0.982683i | ||||
\(808\) | −0.584588 | + | 6.68188i | −0.0205657 | + | 0.235068i | ||||
\(809\) | −4.89923 | − | 2.82857i | −0.172248 | − | 0.0994472i | 0.411398 | − | 0.911456i | \(-0.365041\pi\) |
−0.583645 | + | 0.812009i | \(0.698374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.7827 | + | 35.1202i | −0.448862 | + | 1.23324i | 0.484655 | + | 0.874705i | \(0.338945\pi\) |
−0.933517 | + | 0.358533i | \(0.883277\pi\) | |||||||
\(812\) | 2.06855 | − | 1.44841i | 0.0725918 | − | 0.0508294i | ||||
\(813\) | −43.0293 | − | 30.1294i | −1.50910 | − | 1.05669i | ||||
\(814\) | −7.39527 | − | 20.3183i | −0.259204 | − | 0.712158i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.8972i | 0.416485i | ||||||||
\(817\) | 16.6659 | + | 4.97058i | 0.583065 | + | 0.173899i | ||||
\(818\) | −25.5059 | − | 25.5059i | −0.891791 | − | 0.891791i | ||||
\(819\) | −2.57106 | − | 2.15737i | −0.0898400 | − | 0.0753847i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.69704 | + | 49.3234i | 0.303529 | + | 1.72140i | 0.630350 | + | 0.776311i | \(0.282911\pi\) |
−0.326822 | + | 0.945086i | \(0.605978\pi\) | |||||||
\(822\) | −8.93308 | − | 12.7578i | −0.311577 | − | 0.444978i | ||||
\(823\) | −20.3206 | − | 43.5776i | −0.708331 | − | 1.51902i | −0.848673 | − | 0.528918i | \(-0.822598\pi\) |
0.140342 | − | 0.990103i | \(-0.455180\pi\) | |||||||
\(824\) | −11.9147 | + | 6.87895i | −0.415068 | + | 0.239639i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.1629 | − | 16.9187i | 0.701557 | − | 0.588676i | ||||
\(827\) | −28.2356 | − | 2.47030i | −0.981849 | − | 0.0859007i | −0.415087 | − | 0.909782i | \(-0.636249\pi\) |
−0.566762 | + | 0.823881i | \(0.691804\pi\) | |||||||
\(828\) | −0.0150758 | + | 0.00403954i | −0.000523920 | + | 0.000140384i | ||||
\(829\) | 5.95974 | + | 10.3226i | 0.206990 | + | 0.358518i | 0.950765 | − | 0.309913i | \(-0.100300\pi\) |
−0.743775 | + | 0.668430i | \(0.766966\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.6270 | + | 7.33996i | 1.44402 | + | 0.254620i | ||||
\(832\) | 0.929044 | − | 1.32681i | 0.0322088 | − | 0.0459989i | ||||
\(833\) | −46.8476 | − | 21.8454i | −1.62317 | − | 0.756898i | ||||
\(834\) | 2.68385 | − | 3.19849i | 0.0929342 | − | 0.110755i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.9537 | − | 4.30731i | 0.448012 | − | 0.148972i | ||||
\(837\) | −24.8054 | + | 24.8054i | −0.857400 | + | 0.857400i | ||||
\(838\) | 7.27616 | − | 0.636581i | 0.251351 | − | 0.0219903i | ||||
\(839\) | 14.8033 | − | 5.38796i | 0.511066 | − | 0.186013i | −0.0735985 | − | 0.997288i | \(-0.523448\pi\) |
0.584665 | + | 0.811275i | \(0.301226\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.96278 | + | 28.1453i | −0.171130 | + | 0.970529i | ||||
\(842\) | 13.2850 | − | 6.19491i | 0.457833 | − | 0.213491i | ||||
\(843\) | 2.27677 | − | 8.49703i | 0.0784162 | − | 0.292653i | ||||
\(844\) | −12.8741 | + | 22.2986i | −0.443144 | + | 0.767548i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.56738 | − | 5.44319i | −0.157030 | − | 0.187141i | ||||
\(847\) | −1.20150 | − | 4.48405i | −0.0412840 | − | 0.154074i | ||||
\(848\) | 0.284240 | + | 0.0761618i | 0.00976083 | + | 0.00261541i | ||||
\(849\) | −32.2836 | − | 11.7503i | −1.10797 | − | 0.403268i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.199442 | − | 0.0351671i | 0.00683679 | − | 0.00120551i | ||||
\(852\) | 4.20300 | − | 9.01337i | 0.143992 | − | 0.308793i | ||||
\(853\) | 0.838394 | + | 9.58289i | 0.0287061 | + | 0.328112i | 0.996946 | + | 0.0780902i | \(0.0248822\pi\) |
−0.968240 | + | 0.250022i | \(0.919562\pi\) | |||||||
\(854\) | 1.86039 | 0.0636612 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.63515 | −0.0558883 | ||||||||
\(857\) | 2.37512 | + | 27.1477i | 0.0811324 | + | 0.927348i | 0.922275 | + | 0.386534i | \(0.126328\pi\) |
−0.841143 | + | 0.540813i | \(0.818117\pi\) | |||||||
\(858\) | −4.02901 | + | 8.64023i | −0.137548 | + | 0.294973i | ||||
\(859\) | −24.3714 | + | 4.29734i | −0.831542 | + | 0.146623i | −0.573185 | − | 0.819426i | \(-0.694292\pi\) |
−0.258357 | + | 0.966049i | \(0.583181\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 46.1045 | + | 16.7807i | 1.57124 | + | 0.571884i | ||||
\(862\) | 27.5591 | + | 7.38443i | 0.938666 | + | 0.251515i | ||||
\(863\) | 8.17628 | + | 30.5143i | 0.278324 | + | 1.03872i | 0.953581 | + | 0.301136i | \(0.0973659\pi\) |
−0.675257 | + | 0.737582i | \(0.735967\pi\) | |||||||
\(864\) | −2.98135 | − | 3.55303i | −0.101428 | − | 0.120877i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.09612 | + | 15.7549i | −0.309099 | + | 0.535375i | ||||
\(867\) | 11.2235 | − | 41.8866i | 0.381169 | − | 1.42254i | ||||
\(868\) | −26.6944 | + | 12.4478i | −0.906067 | + | 0.422506i | ||||
\(869\) | 6.52101 | − | 36.9825i | 0.221210 | − | 1.25454i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9766 | − | 4.35913i | 0.405812 | − | 0.147704i | ||||
\(872\) | 8.15630 | − | 0.713584i | 0.276207 | − | 0.0241650i | ||||
\(873\) | −3.16622 | + | 3.16622i | −0.107160 | + | 0.107160i | ||||
\(874\) | 0.0186621 | + | 0.126489i | 0.000631254 | + | 0.00427855i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.72217 | + | 9.20292i | −0.260908 | + | 0.310938i | ||||
\(877\) | −1.54862 | − | 0.722132i | −0.0522931 | − | 0.0243847i | 0.396296 | − | 0.918123i | \(-0.370295\pi\) |
−0.448589 | + | 0.893738i | \(0.648073\pi\) | |||||||
\(878\) | −21.2927 | + | 30.4091i | −0.718593 | + | 1.02626i | ||||
\(879\) | 48.5729 | + | 8.56472i | 1.63832 | + | 0.288881i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.4268 | − | 35.3803i | −0.688197 | − | 1.19199i | −0.972421 | − | 0.233234i | \(-0.925069\pi\) |
0.284224 | − | 0.958758i | \(-0.408264\pi\) | |||||||
\(882\) | −4.19673 | + | 1.12451i | −0.141311 | + | 0.0378642i | ||||
\(883\) | 25.2720 | + | 2.21101i | 0.850469 | + | 0.0744064i | 0.504051 | − | 0.863674i | \(-0.331842\pi\) |
0.346418 | + | 0.938080i | \(0.387398\pi\) | |||||||
\(884\) | −7.85467 | + | 6.59085i | −0.264181 | + | 0.221674i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.5147 | − | 9.53474i | 0.554821 | − | 0.320326i | ||||
\(887\) | 3.99264 | + | 8.56224i | 0.134060 | + | 0.287492i | 0.961866 | − | 0.273523i | \(-0.0881889\pi\) |
−0.827806 | + | 0.561015i | \(0.810411\pi\) | |||||||
\(888\) | −7.44253 | − | 10.6290i | −0.249755 | − | 0.356687i | ||||
\(889\) | 4.05886 | + | 23.0189i | 0.136130 | + | 0.772030i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.7420 | + | 20.7610i | 0.828887 | + | 0.695519i | ||||
\(892\) | 19.8322 | + | 19.8322i | 0.664033 | + | 0.664033i | ||||
\(893\) | −48.5999 | + | 32.0370i | −1.62633 | + | 1.07208i | ||||
\(894\) | 38.8047i | 1.29782i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.33193 | − | 3.65944i | −0.0444965 | − | 0.122253i | ||||
\(897\) | −0.0731438 | − | 0.0512158i | −0.00244220 | − | 0.00171005i | ||||
\(898\) | 9.33995 | − | 6.53990i | 0.311678 | − | 0.218239i | ||||
\(899\) | −1.67741 | + | 4.60866i | −0.0559449 | + | 0.153707i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.61325 | − | 0.931408i | −0.0537450 | − | 0.0310297i | ||||
\(902\) | 1.82978 | − | 20.9145i | 0.0609250 | − | 0.696375i | ||||
\(903\) | −2.54505 | + | 29.0900i | −0.0846939 | + | 0.968056i | ||||
\(904\) | −13.1549 | − | 7.59501i | −0.437527 | − | 0.252606i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.53612 | − | 15.2104i | 0.183925 | − | 0.505331i | ||||
\(907\) | 27.6363 | − | 19.3512i | 0.917650 | − | 0.642545i | −0.0163318 | − | 0.999867i | \(-0.505199\pi\) |
0.933981 | + | 0.357321i | \(0.116310\pi\) | |||||||
\(908\) | 10.7586 | + | 7.53328i | 0.357038 | + | 0.250001i | ||||
\(909\) | −1.22065 | − | 3.35370i | −0.0404863 | − | 0.111235i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.55634i | − | 0.0515640i | −0.999668 | − | 0.0257820i | \(-0.991792\pi\) | ||
0.999668 | − | 0.0257820i | \(-0.00820757\pi\) | |||||||
\(912\) | 6.83968 | − | 4.50871i | 0.226484 | − | 0.149298i | ||||
\(913\) | 29.2710 | + | 29.2710i | 0.968727 | + | 0.968727i | ||||
\(914\) | −17.1049 | − | 14.3527i | −0.565779 | − | 0.474745i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.19944 | + | 6.80238i | 0.0396307 | + | 0.224757i | ||||
\(917\) | −44.3726 | − | 63.3707i | −1.46531 | − | 2.09268i | ||||
\(918\) | 12.4086 | + | 26.6103i | 0.409545 | + | 0.878271i | ||||
\(919\) | −1.73927 | + | 1.00417i | −0.0573732 | + | 0.0331245i | −0.528412 | − | 0.848988i | \(-0.677212\pi\) |
0.471039 | + | 0.882112i | \(0.343879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.99620 | − | 4.19231i | 0.164631 | − | 0.138141i | ||||
\(922\) | −8.29938 | − | 0.726102i | −0.273326 | − | 0.0239129i | ||||
\(923\) | 8.27912 | − | 2.21838i | 0.272511 | − | 0.0730190i | ||||
\(924\) | 11.4605 | + | 19.8501i | 0.377022 | + | 0.653022i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.8820 | + | 4.03472i | 0.751950 | + | 0.132589i | ||||
\(927\) | 4.19882 | − | 5.99654i | 0.137907 | − | 0.196952i | ||||
\(928\) | −0.587691 | − | 0.274045i | −0.0192919 | − | 0.00899595i | ||||
\(929\) | 2.12800 | − | 2.53605i | 0.0698173 | − | 0.0832050i | −0.730005 | − | 0.683441i | \(-0.760482\pi\) |
0.799823 | + | 0.600236i | \(0.204927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.19506 | + | 35.2114i | 0.170261 | + | 1.15401i | ||||
\(932\) | 17.2361 | − | 17.2361i | 0.564587 | − | 0.564587i | ||||
\(933\) | −26.7767 | + | 2.34266i | −0.876631 | + | 0.0766953i | ||||
\(934\) | 34.1876 | − | 12.4433i | 1.11865 | − | 0.407157i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.149658 | + | 0.848752i | −0.00489172 | + | 0.0277423i | ||||
\(937\) | −42.3794 | + | 19.7619i | −1.38448 | + | 0.645592i | −0.965018 | − | 0.262183i | \(-0.915558\pi\) |
−0.419458 | + | 0.907775i | \(0.637780\pi\) | |||||||
\(938\) | 7.93100 | − | 29.5989i | 0.258956 | − | 0.966438i | ||||
\(939\) | 6.13920 | − | 10.6334i | 0.200345 | − | 0.347008i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.57407 | − | 4.25941i | −0.116511 | − | 0.138853i | 0.704636 | − | 0.709569i | \(-0.251110\pi\) |
−0.821148 | + | 0.570716i | \(0.806666\pi\) | |||||||
\(942\) | 9.80122 | + | 36.5787i | 0.319341 | + | 1.19180i | ||||
\(943\) | 0.189937 | + | 0.0508934i | 0.00618520 | + | 0.00165732i | ||||
\(944\) | −6.35121 | − | 2.31165i | −0.206714 | − | 0.0752378i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.3054 | − | 2.16978i | 0.400083 | − | 0.0705455i | ||||
\(947\) | −3.35296 | + | 7.19045i | −0.108957 | + | 0.233658i | −0.953225 | − | 0.302263i | \(-0.902258\pi\) |
0.844268 | + | 0.535921i | \(0.180036\pi\) | |||||||
\(948\) | −1.96412 | − | 22.4500i | −0.0637916 | − | 0.729141i | ||||
\(949\) | −10.3538 | −0.336099 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.2766 | 0.527805 | ||||||||
\(952\) | 2.14859 | + | 24.5585i | 0.0696362 | + | 0.795945i | ||||
\(953\) | 1.96874 | − | 4.22198i | 0.0637738 | − | 0.136763i | −0.871837 | − | 0.489795i | \(-0.837072\pi\) |
0.935611 | + | 0.353032i | \(0.114849\pi\) | |||||||
\(954\) | −0.154197 | + | 0.0271891i | −0.00499232 | + | 0.000880281i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.6577 | + | 3.87909i | 0.344695 | + | 0.125459i | ||||
\(957\) | 3.68656 | + | 0.987811i | 0.119170 | + | 0.0319314i | ||||
\(958\) | −9.77159 | − | 36.4681i | −0.315706 | − | 1.17823i | ||||
\(959\) | −20.7439 | − | 24.7216i | −0.669855 | − | 0.798302i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.1024 | − | 22.6939i | 0.422656 | − | 0.732062i | ||||
\(962\) | 2.89438 | − | 10.8020i | 0.0933184 | − | 0.348269i | ||||
\(963\) | 0.788530 | − | 0.367697i | 0.0254100 | − | 0.0118489i | ||||
\(964\) | −4.66121 | + | 26.4350i | −0.150127 | + | 0.851414i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.201735 | + | 0.0734257i | −0.00649073 | + | 0.00236243i | ||||
\(967\) | −21.3318 | + | 1.86629i | −0.685983 | + | 0.0600158i | −0.424819 | − | 0.905278i | \(-0.639662\pi\) |
−0.261165 | + | 0.965294i | \(0.584107\pi\) | |||||||
\(968\) | −0.842915 | + | 0.842915i | −0.0270923 | + | 0.0270923i | ||||
\(969\) | −49.2095 | + | 16.3630i | −1.58084 | + | 0.525655i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.7178 | + | 23.4987i | −0.632774 | + | 0.754111i | −0.983210 | − | 0.182476i | \(-0.941589\pi\) |
0.350436 | + | 0.936587i | \(0.386033\pi\) | |||||||
\(972\) | 4.95561 | + | 2.31084i | 0.158951 | + | 0.0741202i | ||||
\(973\) | 4.96244 | − | 7.08709i | 0.159088 | − | 0.227202i | ||||
\(974\) | 11.5003 | + | 2.02781i | 0.368493 | + | 0.0649753i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.238861 | − | 0.413719i | −0.00764576 | − | 0.0132428i | ||||
\(977\) | 5.74010 | − | 1.53806i | 0.183642 | − | 0.0492068i | −0.165826 | − | 0.986155i | \(-0.553029\pi\) |
0.349468 | + | 0.936948i | \(0.386362\pi\) | |||||||
\(978\) | 30.6903 | + | 2.68505i | 0.981368 | + | 0.0858585i | ||||
\(979\) | 9.68810 | − | 8.12928i | 0.309633 | − | 0.259813i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.77280 | + | 2.17823i | −0.120456 | + | 0.0695454i | ||||
\(982\) | −8.47134 | − | 18.1669i | −0.270331 | − | 0.579728i | ||||
\(983\) | −20.6160 | − | 29.4427i | −0.657548 | − | 0.939076i | 0.342452 | − | 0.939535i | \(-0.388743\pi\) |
−1.00000 | 0.000459562i | \(0.999854\pi\) | ||||||||
\(984\) | −2.18776 | − | 12.4074i | −0.0697432 | − | 0.395534i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.14453 | + | 2.63858i | 0.100142 | + | 0.0840294i | ||||
\(987\) | −69.1106 | − | 69.1106i | −2.19981 | − | 2.19981i | ||||
\(988\) | 6.76577 | + | 2.01789i | 0.215248 | + | 0.0641975i | ||||
\(989\) | 0.117033i | 0.00372143i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.30438 | + | 14.5737i | 0.168499 | + | 0.462948i | 0.994987 | − | 0.100007i | \(-0.0318866\pi\) |
−0.826488 | + | 0.562955i | \(0.809664\pi\) | |||||||
\(992\) | 6.19556 | + | 4.33818i | 0.196709 | + | 0.137737i | ||||
\(993\) | −14.4393 | + | 10.1105i | −0.458219 | + | 0.320848i | ||||
\(994\) | 7.04816 | − | 19.3647i | 0.223554 | − | 0.614210i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 21.5134 | + | 12.4208i | 0.681679 | + | 0.393567i | ||||
\(997\) | −0.149019 | + | 1.70329i | −0.00471948 | + | 0.0539439i | −0.998189 | − | 0.0601519i | \(-0.980842\pi\) |
0.993470 | + | 0.114096i | \(0.0363971\pi\) | |||||||
\(998\) | 2.98776 | − | 34.1503i | 0.0945760 | − | 1.08101i | ||||
\(999\) | −27.7325 | − | 16.0114i | −0.877419 | − | 0.506578i |
(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 | 950.2.bb.b.193.1 | ✓ | 48 | |
5.2 | odd | 4 | inner | 950.2.bb.b.307.4 | yes | 48 | |
5.3 | odd | 4 | inner | 950.2.bb.b.307.1 | yes | 48 | |
5.4 | even | 2 | inner | 950.2.bb.b.193.4 | yes | 48 | |
19.13 | odd | 18 | inner | 950.2.bb.b.393.4 | yes | 48 | |
95.13 | even | 36 | inner | 950.2.bb.b.507.4 | yes | 48 | |
95.32 | even | 36 | inner | 950.2.bb.b.507.1 | yes | 48 | |
95.89 | odd | 18 | inner | 950.2.bb.b.393.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.bb.b.193.1 | ✓ | 48 | 1.1 | even | 1 | trivial | |
950.2.bb.b.193.4 | yes | 48 | 5.4 | even | 2 | inner | |
950.2.bb.b.307.1 | yes | 48 | 5.3 | odd | 4 | inner | |
950.2.bb.b.307.4 | yes | 48 | 5.2 | odd | 4 | inner | |
950.2.bb.b.393.1 | yes | 48 | 95.89 | odd | 18 | inner | |
950.2.bb.b.393.4 | yes | 48 | 19.13 | odd | 18 | inner | |
950.2.bb.b.507.1 | yes | 48 | 95.32 | even | 36 | inner | |
950.2.bb.b.507.4 | yes | 48 | 95.13 | even | 36 | inner |